Section pdh. Let false:=False. Let false_ind:=False_ind. Variable dom:Set. Variable goal:Prop. Variable i:dom->dom->Prop. Variable l:dom->dom->Prop. Variable p:dom->dom->Prop. Variable a1 a1b1 a1c1 a2 a2b2 a2c2 ab ac b1 b1c1 b2 b2c2 bc c1 c2 o oa ob oc:dom. Hypothesis goal_normal:forall A:dom,(l A A)/\(i bc A)/\(i ac A)/\(i ab A)->goal. Hypothesis hessenberg_gap1:(i a1 b2c2)->goal. Hypothesis hessenberg_gap2:(i b2 a1c1)->goal. Hypothesis ia1b1:(i a1 a1b1). Hypothesis ib1a1:(i b1 a1b1). Hypothesis ia2b2:(i a2 a2b2). Hypothesis ib2a2:(i b2 a2b2). Hypothesis ia1c1:(i a1 a1c1). Hypothesis ic1a1:(i c1 a1c1). Hypothesis ia2c2:(i a2 a2c2). Hypothesis ic2a2:(i c2 a2c2). Hypothesis ic1b1:(i c1 b1c1). Hypothesis ib1c1:(i b1 b1c1). Hypothesis ic2b2:(i c2 b2c2). Hypothesis ib2c2:(i b2 b2c2). Hypothesis iooa:(i o oa). Hypothesis ioob:(i o ob). Hypothesis iooc:(i o oc). Hypothesis ia1oa:(i a1 oa). Hypothesis ia2oa:(i a2 oa). Hypothesis ib1ob:(i b1 ob). Hypothesis ib2ob:(i b2 ob). Hypothesis ic1oc:(i c1 oc). Hypothesis ic2oc:(i c2 oc). Hypothesis ibc1:(i bc b1c1). Hypothesis ibc2:(i bc b2c2). Hypothesis iac1:(i ac a1c1). Hypothesis iac2:(i ac a2c2). Hypothesis iab1:(i ab a1b1). Hypothesis iab2:(i ab a2b2). Hypothesis triangle1:forall A:dom,(i a1 A)/\(i b1 A)/\(i c1 A)->false. Hypothesis triangle2:forall A:dom,(i a2 A)/\(i b2 A)/\(i c2 A)->false. Hypothesis notaa:(p a2 a1)->false. Hypothesis notbb:(p b2 b1)->false. Hypothesis notcc:(p c2 c1)->false. Hypothesis notbc:(l b1c1 b2c2)->false. Hypothesis notac:(l a1c1 a2c2)->false. Hypothesis notab:(l a1b1 a2b2)->false. Hypothesis pref:forall A B:dom,(i A B)->(p A A). Hypothesis psym:forall A B:dom,(p A B)->(p B A). Hypothesis ptra:forall A B C:dom,(p A B)/\(p B C)->(p A C). Hypothesis lref:forall A B:dom,(i A B)->(l B B). Hypothesis lsym:forall A B:dom,(l A B)->(l B A). Hypothesis ltra:forall A B C:dom,(l A B)/\(l B C)->(l A C). Hypothesis pcon:forall A B C:dom,(p A B)/\(i B C)->(i A C). Hypothesis lcon:forall A B C:dom,(i A B)/\(l B C)->(i A C). Hypothesis unique:forall A B C D:dom,(i A C)/\(i A D)/\(i B C)/\(i B D)->(p A B) \/ (l C D). Hypothesis line:forall A B:dom,(p A A)/\(p B B)->(exists C:dom,(i A C)/\(i B C)). Hypothesis point:forall A B:dom,(l A A)/\(l B B)->(exists C:dom,(i C A)/\(i C B)). Hypothesis papp:forall A B C D E F G H I J K L M N O P Q:dom,(i A J)/\(i B J)/\(i C J)/\(i D K)/\(i E K)/\(i F K)/\(i B L)/\(i F L)/\(i G L)/\(i C M)/\(i E M)/\(i G M)/\(i B N)/\(i D N)/\(i H N)/\(i A O)/\(i E O)/\(i H O)/\(i C P)/\(i D P)/\(i I P)/\(i A Q)/\(i F Q)/\(i I Q)->(l L M) \/ (l N O) \/ (l P Q) \/ (exists R:dom,(l R R)/\(i G R)/\(i H R)/\(i I R)). Lemma pdh1: (i a1 a1b1). Proof. exact (ia1b1). Qed. Lemma pdh2: (i b1 a1b1). Proof. exact (ib1a1). Qed. Lemma pdh3: (i a2 a2b2). Proof. exact (ia2b2). Qed. Lemma pdh4: (i b2 a2b2). Proof. exact (ib2a2). Qed. Lemma pdh5: (i a1 a1c1). Proof. exact (ia1c1). Qed. Lemma pdh6: (i c1 a1c1). Proof. exact (ic1a1). Qed. Lemma pdh7: (i a2 a2c2). Proof. exact (ia2c2). Qed. Lemma pdh8: (i c2 a2c2). Proof. exact (ic2a2). Qed. Lemma pdh9: (i c1 b1c1). Proof. exact (ic1b1). Qed. Lemma pdh10: (i b1 b1c1). Proof. exact (ib1c1). Qed. Lemma pdh11: (i c2 b2c2). Proof. exact (ic2b2). Qed. Lemma pdh12: (i b2 b2c2). Proof. exact (ib2c2). Qed. Lemma pdh13: (i o oa). Proof. exact (iooa). Qed. Lemma pdh14: (i o ob). Proof. exact (ioob). Qed. Lemma pdh15: (i o oc). Proof. exact (iooc). Qed. Lemma pdh16: (i a1 oa). Proof. exact (ia1oa). Qed. Lemma pdh17: (i a2 oa). Proof. exact (ia2oa). Qed. Lemma pdh18: (i b1 ob). Proof. exact (ib1ob). Qed. Lemma pdh19: (i b2 ob). Proof. exact (ib2ob). Qed. Lemma pdh20: (i c1 oc). Proof. exact (ic1oc). Qed. Lemma pdh21: (i c2 oc). Proof. exact (ic2oc). Qed. Lemma pdh22: (i bc b1c1). Proof. exact (ibc1). Qed. Lemma pdh23: (i bc b2c2). Proof. exact (ibc2). Qed. Lemma pdh24: (i ac a1c1). Proof. exact (iac1). Qed. Lemma pdh25: (i ac a2c2). Proof. exact (iac2). Qed. Lemma pdh26: (i ab a1b1). Proof. exact (iab1). Qed. Lemma pdh27: (i ab a2b2). Proof. exact (iab2). Qed. Lemma pdh28: (p a1 a1). Proof. exact (((pref a1 a1b1) pdh1)). Qed. Lemma pdh31: (p b2 b2). Proof. exact (((pref b2 a2b2) pdh4)). Qed. Lemma pdh34: (p o o). Proof. exact (((pref o oa) pdh13)). Qed. Lemma pdh36: (p ac ac). Proof. exact (((pref ac a1c1) pdh24)). Qed. Lemma pdh38: (l a1b1 a1b1). Proof. exact (((lref a1 a1b1) pdh1)). Qed. Lemma pdh39: (l a2b2 a2b2). Proof. exact (((lref a2 a2b2) pdh3)). Qed. Lemma pdh40: (l a1c1 a1c1). Proof. exact (((lref a1 a1c1) pdh5)). Qed. Lemma pdh42: (l b1c1 b1c1). Proof. exact (((lref c1 b1c1) pdh9)). Qed. Lemma pdh43: (l b2c2 b2c2). Proof. exact (((lref c2 b2c2) pdh11)). Qed. Lemma pdh46: (l oc oc). Proof. exact (((lref o oc) pdh15)). Qed. Lemma pdh47: (exists A:dom,(i a1 A)/\(i b2 A)). Proof. exact (((line a1 b2) (conj pdh28 pdh31))). Qed. Lemma pdh48: forall C0:dom,(i a1 C0)->(i b2 C0)->(l C0 C0). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))=>((lref a1 C0) Via1C0)). Qed. Lemma pdh49: forall C0:dom,(i a1 C0)->(i b2 C0)->(exists A:dom,(i A C0)/\(i A oc)). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))=>((point C0 oc) (conj (pdh48 C0 Via1C0 Vib2C0) pdh46))). Qed. Lemma pdh50: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->(p C1 C1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))=>((pref C1 C0) ViC1C0)). Qed. Lemma pdh51: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->(exists A:dom,(i C1 A)/\(i ac A)). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))=>((line C1 ac) (conj (pdh50 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc) pdh36))). Qed. Lemma pdh52: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->(l C2 C2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))=>((lref C1 C2) ViC1C2)). Qed. Lemma pdh53: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->(exists A:dom,(i A C2)/\(i A a2b2)). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))=>((point C2 a2b2) (conj (pdh52 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2) pdh39))). Qed. Lemma pdh54: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->(p C3 C3). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))=>((pref C3 C2) ViC3C2)). Qed. Lemma pdh55: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->(exists A:dom,(i C3 A)/\(i o A)). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))=>((line C3 o) (conj (pdh54 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2) pdh34))). Qed. Lemma pdh56: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->(l C4 C4). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))=>((lref C3 C4) ViC3C4)). Qed. Lemma pdh57: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->(exists A:dom,(i A C4)/\(i A a1c1)). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))=>((point C4 a1c1) (conj (pdh56 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4) pdh40))). Qed. Lemma pdh59: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0) \/ (l a2c2 oc) \/ (l a1c1 C4) \/ (exists A:dom,(l A A)/\(i b2 A)/\(i c2 A)/\(i C5 A)). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))=>((papp o a2 a1 ac C1 C3 b2 c2 C5 oa C2 a2b2 C0 a2c2 oc a1c1 C4) (conj pdh13 (conj pdh17 (conj pdh16 (conj ViacC2 (conj ViC1C2 (conj ViC3C2 (conj pdh3 (conj ViC3a2b2 (conj pdh4 (conj Via1C0 (conj ViC1C0 (conj Vib2C0 (conj pdh7 (conj pdh25 (conj pdh8 (conj pdh15 (conj ViC1oc (conj pdh21 (conj pdh5 (conj pdh24 (conj ViC5a1c1 (conj VioC4 (conj ViC3C4 ViC5C4))))))))))))))))))))))))). Qed. Lemma pdh60: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(l C0 a2b2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))=>((lsym a2b2 C0) Vla2b2C0)). Qed. Lemma pdh62: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(i ab C0). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))=>((lcon ab a2b2 C0) (conj pdh27 Vla2b2C0))). Qed. Lemma pdh64: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(i C1 a2b2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))=>((lcon C1 C0 a2b2) (conj ViC1C0 (pdh60 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0)))). Qed. Lemma pdh66: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab) \/ (l a1b1 C0). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))=>((unique a1 ab a1b1 C0) (conj pdh1 (conj Via1C0 (conj pdh26 (pdh62 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0)))))). Qed. Lemma pdh67: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(p ab a1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))=>((psym a1 ab) Vpa1ab)). Qed. Lemma pdh68: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(i ab a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))=>((pcon ab a1 a1c1) (conj (pdh67 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab) pdh5))). Qed. Lemma pdh69: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(i ab oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))=>((pcon ab a1 oa) (conj (pdh67 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab) pdh16))). Qed. Lemma pdh70: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(p a2 ab) \/ (l a2b2 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))=>((unique a2 ab a2b2 oa) (conj pdh3 (conj pdh17 (conj pdh27 (pdh69 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab)))))). Qed. Lemma pdh71: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(p a2 ab)->(p ab a2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vpa2ab:(p a2 ab))=>((psym a2 ab) Vpa2ab)). Qed. Lemma pdh72: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(p a2 ab)->(p a1 a2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vpa2ab:(p a2 ab))=>((ptra a1 ab a2) (conj Vpa1ab (pdh71 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vpa2ab)))). Qed. Lemma pdh73: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(p a2 ab)->(p a2 a1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vpa2ab:(p a2 ab))=>((psym a1 a2) (pdh72 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vpa2ab))). Qed. Lemma pdh74: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(p a2 ab)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vpa2ab:(p a2 ab))=>(notaa (pdh73 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vpa2ab))). Qed. Lemma pdh75: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(p a2 ab)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vpa2ab:(p a2 ab))=>((false_ind goal) (pdh74 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vpa2ab))). Qed. Lemma pdh76: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(l oa a2b2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))=>((lsym a2b2 oa) Vla2b2oa)). Qed. Lemma pdh80: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(i o a2b2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))=>((lcon o oa a2b2) (conj pdh13 (pdh76 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa)))). Qed. Lemma pdh84: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o) \/ (l a2b2 ob). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))=>((unique b2 o a2b2 ob) (conj pdh4 (conj pdh19 (conj (pdh80 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa) pdh14))))). Qed. Lemma pdh86: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(i b2 oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))=>((pcon b2 o oc) (conj Vpb2o pdh15))). Qed. Lemma pdh87: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(i b2 C4). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))=>((pcon b2 o C4) (conj Vpb2o VioC4))). Qed. Lemma pdh89: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1) \/ (l a2b2 oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))=>((unique b2 C1 a2b2 oc) (conj pdh4 (conj (pdh86 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o) (conj (pdh64 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0) ViC1oc))))). Qed. Lemma pdh93: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(i b2 C2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))=>((pcon b2 C1 C2) (conj Vpb2C1 ViC1C2))). Qed. Lemma pdh98: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(p b2 C3) \/ (l a2b2 C4). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))=>((unique b2 C3 a2b2 C4) (conj pdh4 (conj (pdh87 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o) (conj ViC3a2b2 ViC3C4))))). Qed. Lemma pdh107: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(p b2 C3)->(p c2 b2) \/ (l b2c2 oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vpb2C3:(p b2 C3))=>((unique c2 b2 b2c2 oc) (conj pdh11 (conj pdh21 (conj pdh12 (pdh86 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o)))))). Qed. Lemma pdh115: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(p b2 C3)->(p c2 b2)->(i c2 a2b2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vpb2C3:(p b2 C3))(Vpc2b2:(p c2 b2))=>((pcon c2 b2 a2b2) (conj Vpc2b2 pdh4))). Qed. Lemma pdh116: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(p b2 C3)->(p c2 b2)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vpb2C3:(p b2 C3))(Vpc2b2:(p c2 b2))=>((triangle2 a2b2) (conj pdh3 (conj pdh4 (pdh115 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vpb2C3 Vpc2b2))))). Qed. Lemma pdh117: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(p b2 C3)->(p c2 b2)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vpb2C3:(p b2 C3))(Vpc2b2:(p c2 b2))=>((false_ind goal) (pdh116 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vpb2C3 Vpc2b2))). Qed. Lemma pdh120: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(p b2 C3)->(l b2c2 oc)->(i bc oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vpb2C3:(p b2 C3))(Vlb2c2oc:(l b2c2 oc))=>((lcon bc b2c2 oc) (conj pdh23 Vlb2c2oc))). Qed. Lemma pdh121: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(p b2 C3)->(l b2c2 oc)->(p c1 bc) \/ (l b1c1 oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vpb2C3:(p b2 C3))(Vlb2c2oc:(l b2c2 oc))=>((unique c1 bc b1c1 oc) (conj pdh9 (conj pdh20 (conj pdh22 (pdh120 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vpb2C3 Vlb2c2oc)))))). Qed. Lemma pdh122: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(p b2 C3)->(l b2c2 oc)->(p c1 bc)->(p bc c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vpb2C3:(p b2 C3))(Vlb2c2oc:(l b2c2 oc))(Vpc1bc:(p c1 bc))=>((psym c1 bc) Vpc1bc)). Qed. Lemma pdh123: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(p b2 C3)->(l b2c2 oc)->(p c1 bc)->(i bc a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vpb2C3:(p b2 C3))(Vlb2c2oc:(l b2c2 oc))(Vpc1bc:(p c1 bc))=>((pcon bc c1 a1c1) (conj (pdh122 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vpb2C3 Vlb2c2oc Vpc1bc) pdh6))). Qed. Lemma pdh124: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(p b2 C3)->(l b2c2 oc)->(p c1 bc)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vpb2C3:(p b2 C3))(Vlb2c2oc:(l b2c2 oc))(Vpc1bc:(p c1 bc))=>((goal_normal a1c1) (conj pdh40 (conj (pdh123 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vpb2C3 Vlb2c2oc Vpc1bc) (conj pdh24 (pdh68 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab)))))). Qed. Lemma pdh125: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(p b2 C3)->(l b2c2 oc)->(l b1c1 oc)->(l oc b1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vpb2C3:(p b2 C3))(Vlb2c2oc:(l b2c2 oc))(Vlb1c1oc:(l b1c1 oc))=>((lsym b1c1 oc) Vlb1c1oc)). Qed. Lemma pdh126: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(p b2 C3)->(l b2c2 oc)->(l b1c1 oc)->(l b2c2 b1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vpb2C3:(p b2 C3))(Vlb2c2oc:(l b2c2 oc))(Vlb1c1oc:(l b1c1 oc))=>((ltra b2c2 oc b1c1) (conj Vlb2c2oc (pdh125 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vpb2C3 Vlb2c2oc Vlb1c1oc)))). Qed. Lemma pdh127: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(p b2 C3)->(l b2c2 oc)->(l b1c1 oc)->(l b1c1 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vpb2C3:(p b2 C3))(Vlb2c2oc:(l b2c2 oc))(Vlb1c1oc:(l b1c1 oc))=>((lsym b2c2 b1c1) (pdh126 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vpb2C3 Vlb2c2oc Vlb1c1oc))). Qed. Lemma pdh128: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(p b2 C3)->(l b2c2 oc)->(l b1c1 oc)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vpb2C3:(p b2 C3))(Vlb2c2oc:(l b2c2 oc))(Vlb1c1oc:(l b1c1 oc))=>(notbc (pdh127 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vpb2C3 Vlb2c2oc Vlb1c1oc))). Qed. Lemma pdh129: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(p b2 C3)->(l b2c2 oc)->(l b1c1 oc)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vpb2C3:(p b2 C3))(Vlb2c2oc:(l b2c2 oc))(Vlb1c1oc:(l b1c1 oc))=>((false_ind goal) (pdh128 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vpb2C3 Vlb2c2oc Vlb1c1oc))). Qed. Lemma pdh130: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(p b2 C3)->(l b2c2 oc)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vpb2C3:(p b2 C3))(Vlb2c2oc:(l b2c2 oc))=>((or_ind ((pdh124 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vpb2C3 Vlb2c2oc))((pdh129 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vpb2C3 Vlb2c2oc)))(pdh121 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vpb2C3 Vlb2c2oc))). Qed. Lemma pdh131: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(p b2 C3)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vpb2C3:(p b2 C3))=>((or_ind ((pdh117 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vpb2C3))((pdh130 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vpb2C3)))(pdh107 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vpb2C3))). Qed. Lemma pdh135: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(l oa C4). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))=>((ltra oa a2b2 C4) (conj (pdh76 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa) Vla2b2C4))). Qed. Lemma pdh136: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(l C4 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))=>((lsym oa C4) (pdh135 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4))). Qed. Lemma pdh142: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(i C5 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))=>((lcon C5 C4 oa) (conj ViC5C4 (pdh136 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4)))). Qed. Lemma pdh143: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(p b2 C3) \/ (l a2b2 C2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))=>((unique b2 C3 a2b2 C2) (conj pdh4 (conj (pdh93 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1) (conj ViC3a2b2 ViC3C2))))). Qed. Lemma pdh152: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(p b2 C3)->(p a1 C5) \/ (l a1c1 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vpb2C3:(p b2 C3))=>((unique a1 C5 a1c1 oa) (conj pdh5 (conj pdh16 (conj ViC5a1c1 (pdh142 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4)))))). Qed. Lemma pdh157: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(p b2 C3)->(p a1 C5)->(p c2 b2) \/ (l b2c2 oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vpb2C3:(p b2 C3))(Vpa1C5:(p a1 C5))=>((unique c2 b2 b2c2 oc) (conj pdh11 (conj pdh21 (conj pdh12 (pdh86 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o)))))). Qed. Lemma pdh165: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(p b2 C3)->(p a1 C5)->(p c2 b2)->(i c2 a2b2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vpb2C3:(p b2 C3))(Vpa1C5:(p a1 C5))(Vpc2b2:(p c2 b2))=>((pcon c2 b2 a2b2) (conj Vpc2b2 pdh4))). Qed. Lemma pdh166: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(p b2 C3)->(p a1 C5)->(p c2 b2)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vpb2C3:(p b2 C3))(Vpa1C5:(p a1 C5))(Vpc2b2:(p c2 b2))=>((triangle2 a2b2) (conj pdh3 (conj pdh4 (pdh165 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vpb2C3 Vpa1C5 Vpc2b2))))). Qed. Lemma pdh167: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(p b2 C3)->(p a1 C5)->(p c2 b2)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vpb2C3:(p b2 C3))(Vpa1C5:(p a1 C5))(Vpc2b2:(p c2 b2))=>((false_ind goal) (pdh166 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vpb2C3 Vpa1C5 Vpc2b2))). Qed. Lemma pdh170: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(p b2 C3)->(p a1 C5)->(l b2c2 oc)->(i bc oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vpb2C3:(p b2 C3))(Vpa1C5:(p a1 C5))(Vlb2c2oc:(l b2c2 oc))=>((lcon bc b2c2 oc) (conj pdh23 Vlb2c2oc))). Qed. Lemma pdh171: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(p b2 C3)->(p a1 C5)->(l b2c2 oc)->(p c1 bc) \/ (l b1c1 oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vpb2C3:(p b2 C3))(Vpa1C5:(p a1 C5))(Vlb2c2oc:(l b2c2 oc))=>((unique c1 bc b1c1 oc) (conj pdh9 (conj pdh20 (conj pdh22 (pdh170 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vpb2C3 Vpa1C5 Vlb2c2oc)))))). Qed. Lemma pdh172: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(p b2 C3)->(p a1 C5)->(l b2c2 oc)->(p c1 bc)->(p bc c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vpb2C3:(p b2 C3))(Vpa1C5:(p a1 C5))(Vlb2c2oc:(l b2c2 oc))(Vpc1bc:(p c1 bc))=>((psym c1 bc) Vpc1bc)). Qed. Lemma pdh173: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(p b2 C3)->(p a1 C5)->(l b2c2 oc)->(p c1 bc)->(i bc a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vpb2C3:(p b2 C3))(Vpa1C5:(p a1 C5))(Vlb2c2oc:(l b2c2 oc))(Vpc1bc:(p c1 bc))=>((pcon bc c1 a1c1) (conj (pdh172 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vpb2C3 Vpa1C5 Vlb2c2oc Vpc1bc) pdh6))). Qed. Lemma pdh174: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(p b2 C3)->(p a1 C5)->(l b2c2 oc)->(p c1 bc)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vpb2C3:(p b2 C3))(Vpa1C5:(p a1 C5))(Vlb2c2oc:(l b2c2 oc))(Vpc1bc:(p c1 bc))=>((goal_normal a1c1) (conj pdh40 (conj (pdh173 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vpb2C3 Vpa1C5 Vlb2c2oc Vpc1bc) (conj pdh24 (pdh68 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab)))))). Qed. Lemma pdh175: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(p b2 C3)->(p a1 C5)->(l b2c2 oc)->(l b1c1 oc)->(l oc b1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vpb2C3:(p b2 C3))(Vpa1C5:(p a1 C5))(Vlb2c2oc:(l b2c2 oc))(Vlb1c1oc:(l b1c1 oc))=>((lsym b1c1 oc) Vlb1c1oc)). Qed. Lemma pdh176: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(p b2 C3)->(p a1 C5)->(l b2c2 oc)->(l b1c1 oc)->(l b2c2 b1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vpb2C3:(p b2 C3))(Vpa1C5:(p a1 C5))(Vlb2c2oc:(l b2c2 oc))(Vlb1c1oc:(l b1c1 oc))=>((ltra b2c2 oc b1c1) (conj Vlb2c2oc (pdh175 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vpb2C3 Vpa1C5 Vlb2c2oc Vlb1c1oc)))). Qed. Lemma pdh177: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(p b2 C3)->(p a1 C5)->(l b2c2 oc)->(l b1c1 oc)->(l b1c1 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vpb2C3:(p b2 C3))(Vpa1C5:(p a1 C5))(Vlb2c2oc:(l b2c2 oc))(Vlb1c1oc:(l b1c1 oc))=>((lsym b2c2 b1c1) (pdh176 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vpb2C3 Vpa1C5 Vlb2c2oc Vlb1c1oc))). Qed. Lemma pdh178: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(p b2 C3)->(p a1 C5)->(l b2c2 oc)->(l b1c1 oc)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vpb2C3:(p b2 C3))(Vpa1C5:(p a1 C5))(Vlb2c2oc:(l b2c2 oc))(Vlb1c1oc:(l b1c1 oc))=>(notbc (pdh177 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vpb2C3 Vpa1C5 Vlb2c2oc Vlb1c1oc))). Qed. Lemma pdh179: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(p b2 C3)->(p a1 C5)->(l b2c2 oc)->(l b1c1 oc)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vpb2C3:(p b2 C3))(Vpa1C5:(p a1 C5))(Vlb2c2oc:(l b2c2 oc))(Vlb1c1oc:(l b1c1 oc))=>((false_ind goal) (pdh178 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vpb2C3 Vpa1C5 Vlb2c2oc Vlb1c1oc))). Qed. Lemma pdh180: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(p b2 C3)->(p a1 C5)->(l b2c2 oc)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vpb2C3:(p b2 C3))(Vpa1C5:(p a1 C5))(Vlb2c2oc:(l b2c2 oc))=>((or_ind ((pdh174 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vpb2C3 Vpa1C5 Vlb2c2oc))((pdh179 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vpb2C3 Vpa1C5 Vlb2c2oc)))(pdh171 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vpb2C3 Vpa1C5 Vlb2c2oc))). Qed. Lemma pdh181: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(p b2 C3)->(p a1 C5)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vpb2C3:(p b2 C3))(Vpa1C5:(p a1 C5))=>((or_ind ((pdh167 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vpb2C3 Vpa1C5))((pdh180 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vpb2C3 Vpa1C5)))(pdh157 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vpb2C3 Vpa1C5))). Qed. Lemma pdh182: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(p b2 C3)->(l a1c1 oa)->(l oa a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vpb2C3:(p b2 C3))(Vla1c1oa:(l a1c1 oa))=>((lsym a1c1 oa) Vla1c1oa)). Qed. Lemma pdh183: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(p b2 C3)->(l a1c1 oa)->(l a2b2 a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vpb2C3:(p b2 C3))(Vla1c1oa:(l a1c1 oa))=>((ltra a2b2 oa a1c1) (conj Vla2b2oa (pdh182 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vpb2C3 Vla1c1oa)))). Qed. Lemma pdh190: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(p b2 C3)->(l a1c1 oa)->(i b2 a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vpb2C3:(p b2 C3))(Vla1c1oa:(l a1c1 oa))=>((lcon b2 a2b2 a1c1) (conj pdh4 (pdh183 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vpb2C3 Vla1c1oa)))). Qed. Lemma pdh191: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(p b2 C3)->(l a1c1 oa)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vpb2C3:(p b2 C3))(Vla1c1oa:(l a1c1 oa))=>(hessenberg_gap2 (pdh190 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vpb2C3 Vla1c1oa))). Qed. Lemma pdh192: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(p b2 C3)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vpb2C3:(p b2 C3))=>((or_ind ((pdh181 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vpb2C3))((pdh191 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vpb2C3)))(pdh152 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vpb2C3))). Qed. Lemma pdh193: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(l a2b2 C2)->(l C2 a2b2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vla2b2C2:(l a2b2 C2))=>((lsym a2b2 C2) Vla2b2C2)). Qed. Lemma pdh203: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(l a2b2 C2)->(i ac a2b2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vla2b2C2:(l a2b2 C2))=>((lcon ac C2 a2b2) (conj ViacC2 (pdh193 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vla2b2C2)))). Qed. Lemma pdh208: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(l a2b2 C2)->(p a2 ac) \/ (l a2b2 a2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vla2b2C2:(l a2b2 C2))=>((unique a2 ac a2b2 a2c2) (conj pdh3 (conj pdh7 (conj (pdh203 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vla2b2C2) pdh25))))). Qed. Lemma pdh210: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(l a2b2 C2)->(p a2 ac)->(i a2 a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vla2b2C2:(l a2b2 C2))(Vpa2ac:(p a2 ac))=>((pcon a2 ac a1c1) (conj Vpa2ac pdh24))). Qed. Lemma pdh211: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(l a2b2 C2)->(p a2 ac)->(p a2 ab) \/ (l a2b2 a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vla2b2C2:(l a2b2 C2))(Vpa2ac:(p a2 ac))=>((unique a2 ab a2b2 a1c1) (conj pdh3 (conj (pdh210 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vla2b2C2 Vpa2ac) (conj pdh27 (pdh68 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab)))))). Qed. Lemma pdh212: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(l a2b2 C2)->(p a2 ac)->(p a2 ab)->(p ab a2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vla2b2C2:(l a2b2 C2))(Vpa2ac:(p a2 ac))(Vpa2ab:(p a2 ab))=>((psym a2 ab) Vpa2ab)). Qed. Lemma pdh213: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(l a2b2 C2)->(p a2 ac)->(p a2 ab)->(p a1 a2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vla2b2C2:(l a2b2 C2))(Vpa2ac:(p a2 ac))(Vpa2ab:(p a2 ab))=>((ptra a1 ab a2) (conj Vpa1ab (pdh212 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vla2b2C2 Vpa2ac Vpa2ab)))). Qed. Lemma pdh214: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(l a2b2 C2)->(p a2 ac)->(p a2 ab)->(p a2 a1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vla2b2C2:(l a2b2 C2))(Vpa2ac:(p a2 ac))(Vpa2ab:(p a2 ab))=>((psym a1 a2) (pdh213 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vla2b2C2 Vpa2ac Vpa2ab))). Qed. Lemma pdh215: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(l a2b2 C2)->(p a2 ac)->(p a2 ab)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vla2b2C2:(l a2b2 C2))(Vpa2ac:(p a2 ac))(Vpa2ab:(p a2 ab))=>(notaa (pdh214 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vla2b2C2 Vpa2ac Vpa2ab))). Qed. Lemma pdh216: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(l a2b2 C2)->(p a2 ac)->(p a2 ab)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vla2b2C2:(l a2b2 C2))(Vpa2ac:(p a2 ac))(Vpa2ab:(p a2 ab))=>((false_ind goal) (pdh215 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vla2b2C2 Vpa2ac Vpa2ab))). Qed. Lemma pdh226: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(l a2b2 C2)->(p a2 ac)->(l a2b2 a1c1)->(i b2 a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vla2b2C2:(l a2b2 C2))(Vpa2ac:(p a2 ac))(Vla2b2a1c1:(l a2b2 a1c1))=>((lcon b2 a2b2 a1c1) (conj pdh4 Vla2b2a1c1))). Qed. Lemma pdh227: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(l a2b2 C2)->(p a2 ac)->(l a2b2 a1c1)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vla2b2C2:(l a2b2 C2))(Vpa2ac:(p a2 ac))(Vla2b2a1c1:(l a2b2 a1c1))=>(hessenberg_gap2 (pdh226 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vla2b2C2 Vpa2ac Vla2b2a1c1))). Qed. Lemma pdh228: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(l a2b2 C2)->(p a2 ac)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vla2b2C2:(l a2b2 C2))(Vpa2ac:(p a2 ac))=>((or_ind ((pdh216 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vla2b2C2 Vpa2ac))((pdh227 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vla2b2C2 Vpa2ac)))(pdh211 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vla2b2C2 Vpa2ac))). Qed. Lemma pdh238: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(l a2b2 C2)->(l a2b2 a2c2)->(i b2 a2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vla2b2C2:(l a2b2 C2))(Vla2b2a2c2:(l a2b2 a2c2))=>((lcon b2 a2b2 a2c2) (conj pdh4 Vla2b2a2c2))). Qed. Lemma pdh239: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(l a2b2 C2)->(l a2b2 a2c2)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vla2b2C2:(l a2b2 C2))(Vla2b2a2c2:(l a2b2 a2c2))=>((triangle2 a2c2) (conj pdh7 (conj (pdh238 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vla2b2C2 Vla2b2a2c2) pdh8)))). Qed. Lemma pdh240: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(l a2b2 C2)->(l a2b2 a2c2)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vla2b2C2:(l a2b2 C2))(Vla2b2a2c2:(l a2b2 a2c2))=>((false_ind goal) (pdh239 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vla2b2C2 Vla2b2a2c2))). Qed. Lemma pdh241: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->(l a2b2 C2)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))(Vla2b2C2:(l a2b2 C2))=>((or_ind ((pdh228 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vla2b2C2))((pdh240 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vla2b2C2)))(pdh208 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4 Vla2b2C2))). Qed. Lemma pdh242: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->(l a2b2 C4)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))(Vla2b2C4:(l a2b2 C4))=>((or_ind ((pdh192 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4))((pdh241 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4)))(pdh143 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1 Vla2b2C4))). Qed. Lemma pdh243: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(p b2 C1)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2C1:(p b2 C1))=>((or_ind ((pdh131 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1))((pdh242 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1)))(pdh98 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vpb2C1))). Qed. Lemma pdh249: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(l a2b2 oc)->(i a2 oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vla2b2oc:(l a2b2 oc))=>((lcon a2 a2b2 oc) (conj pdh3 Vla2b2oc))). Qed. Lemma pdh250: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(l a2b2 oc)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vla2b2oc:(l a2b2 oc))=>((triangle2 oc) (conj (pdh249 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vla2b2oc) (conj (pdh86 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o) pdh21)))). Qed. Lemma pdh251: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->(l a2b2 oc)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vla2b2oc:(l a2b2 oc))=>((false_ind goal) (pdh250 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o Vla2b2oc))). Qed. Lemma pdh252: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(p b2 o)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))=>((or_ind ((pdh243 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o))((pdh251 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o)))(pdh89 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vpb2o))). Qed. Lemma pdh256: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(l a2b2 ob)->(l oa ob). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vla2b2ob:(l a2b2 ob))=>((ltra oa a2b2 ob) (conj (pdh76 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa) Vla2b2ob))). Qed. Lemma pdh257: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(l a2b2 ob)->(l ob oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vla2b2ob:(l a2b2 ob))=>((lsym oa ob) (pdh256 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vla2b2ob))). Qed. Lemma pdh263: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(l a2b2 ob)->(i b1 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vla2b2ob:(l a2b2 ob))=>((lcon b1 ob oa) (conj pdh18 (pdh257 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vla2b2ob)))). Qed. Lemma pdh266: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(l a2b2 ob)->(p a1 b1) \/ (l a1b1 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vla2b2ob:(l a2b2 ob))=>((unique a1 b1 a1b1 oa) (conj pdh1 (conj pdh16 (conj pdh2 (pdh263 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vla2b2ob)))))). Qed. Lemma pdh270: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(l a2b2 ob)->(p a1 b1)->(i a1 b1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vla2b2ob:(l a2b2 ob))(Vpa1b1:(p a1 b1))=>((pcon a1 b1 b1c1) (conj Vpa1b1 pdh10))). Qed. Lemma pdh271: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(l a2b2 ob)->(p a1 b1)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vla2b2ob:(l a2b2 ob))(Vpa1b1:(p a1 b1))=>((triangle1 b1c1) (conj (pdh270 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vla2b2ob Vpa1b1) (conj pdh10 pdh9)))). Qed. Lemma pdh272: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(l a2b2 ob)->(p a1 b1)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vla2b2ob:(l a2b2 ob))(Vpa1b1:(p a1 b1))=>((false_ind goal) (pdh271 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vla2b2ob Vpa1b1))). Qed. Lemma pdh273: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(l a2b2 ob)->(l a1b1 oa)->(l oa a1b1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vla2b2ob:(l a2b2 ob))(Vla1b1oa:(l a1b1 oa))=>((lsym a1b1 oa) Vla1b1oa)). Qed. Lemma pdh274: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(l a2b2 ob)->(l a1b1 oa)->(l a2b2 a1b1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vla2b2ob:(l a2b2 ob))(Vla1b1oa:(l a1b1 oa))=>((ltra a2b2 oa a1b1) (conj Vla2b2oa (pdh273 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vla2b2ob Vla1b1oa)))). Qed. Lemma pdh275: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(l a2b2 ob)->(l a1b1 oa)->(l a1b1 a2b2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vla2b2ob:(l a2b2 ob))(Vla1b1oa:(l a1b1 oa))=>((lsym a2b2 a1b1) (pdh274 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vla2b2ob Vla1b1oa))). Qed. Lemma pdh276: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(l a2b2 ob)->(l a1b1 oa)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vla2b2ob:(l a2b2 ob))(Vla1b1oa:(l a1b1 oa))=>(notab (pdh275 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vla2b2ob Vla1b1oa))). Qed. Lemma pdh277: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(l a2b2 ob)->(l a1b1 oa)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vla2b2ob:(l a2b2 ob))(Vla1b1oa:(l a1b1 oa))=>((false_ind goal) (pdh276 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vla2b2ob Vla1b1oa))). Qed. Lemma pdh278: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->(l a2b2 ob)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))(Vla2b2ob:(l a2b2 ob))=>((or_ind ((pdh272 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vla2b2ob))((pdh277 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vla2b2ob)))(pdh266 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa Vla2b2ob))). Qed. Lemma pdh279: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->(l a2b2 oa)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))(Vla2b2oa:(l a2b2 oa))=>((or_ind ((pdh252 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa))((pdh278 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa)))(pdh84 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab Vla2b2oa))). Qed. Lemma pdh280: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(p a1 ab)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vpa1ab:(p a1 ab))=>((or_ind ((pdh75 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab))((pdh279 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab)))(pdh70 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vpa1ab))). Qed. Lemma pdh281: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(l a1b1 C0)->(l C0 a1b1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vla1b1C0:(l a1b1 C0))=>((lsym a1b1 C0) Vla1b1C0)). Qed. Lemma pdh282: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(l a1b1 C0)->(l a2b2 a1b1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vla1b1C0:(l a1b1 C0))=>((ltra a2b2 C0 a1b1) (conj Vla2b2C0 (pdh281 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vla1b1C0)))). Qed. Lemma pdh283: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(l a1b1 C0)->(l a1b1 a2b2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vla1b1C0:(l a1b1 C0))=>((lsym a2b2 a1b1) (pdh282 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vla1b1C0))). Qed. Lemma pdh284: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(l a1b1 C0)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vla1b1C0:(l a1b1 C0))=>(notab (pdh283 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vla1b1C0))). Qed. Lemma pdh285: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->(l a1b1 C0)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))(Vla1b1C0:(l a1b1 C0))=>((false_ind goal) (pdh284 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0 Vla1b1C0))). Qed. Lemma pdh286: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2b2 C0)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2b2C0:(l a2b2 C0))=>((or_ind ((pdh280 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0))((pdh285 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0)))(pdh66 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2b2C0))). Qed. Lemma pdh287: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(l oc a2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))=>((lsym a2c2 oc) Vla2c2oc)). Qed. Lemma pdh289: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(i o a2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))=>((lcon o oc a2c2) (conj pdh15 (pdh287 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc)))). Qed. Lemma pdh291: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(i ac oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))=>((lcon ac a2c2 oc) (conj pdh25 Vla2c2oc))). Qed. Lemma pdh293: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac) \/ (l a1c1 oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))=>((unique c1 ac a1c1 oc) (conj pdh6 (conj pdh20 (conj pdh24 (pdh291 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc)))))). Qed. Lemma pdh294: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(p ac c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))=>((psym c1 ac) Vpc1ac)). Qed. Lemma pdh296: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(i ac b1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))=>((pcon ac c1 b1c1) (conj (pdh294 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac) pdh9))). Qed. Lemma pdh297: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(p a2 o) \/ (l a2c2 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))=>((unique a2 o a2c2 oa) (conj pdh7 (conj pdh17 (conj (pdh289 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc) pdh13))))). Qed. Lemma pdh299: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(p a2 o)->(i a2 ob). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))(Vpa2o:(p a2 o))=>((pcon a2 o ob) (conj Vpa2o pdh14))). Qed. Lemma pdh302: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(p a2 o)->(p a2 b2) \/ (l a2b2 ob). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))(Vpa2o:(p a2 o))=>((unique a2 b2 a2b2 ob) (conj pdh3 (conj (pdh299 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac Vpa2o) (conj pdh4 pdh19))))). Qed. Lemma pdh306: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(p a2 o)->(p a2 b2)->(i a2 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))(Vpa2o:(p a2 o))(Vpa2b2:(p a2 b2))=>((pcon a2 b2 b2c2) (conj Vpa2b2 pdh12))). Qed. Lemma pdh307: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(p a2 o)->(p a2 b2)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))(Vpa2o:(p a2 o))(Vpa2b2:(p a2 b2))=>((triangle2 b2c2) (conj (pdh306 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac Vpa2o Vpa2b2) (conj pdh12 pdh11)))). Qed. Lemma pdh308: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(p a2 o)->(p a2 b2)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))(Vpa2o:(p a2 o))(Vpa2b2:(p a2 b2))=>((false_ind goal) (pdh307 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac Vpa2o Vpa2b2))). Qed. Lemma pdh311: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(p a2 o)->(l a2b2 ob)->(i ab ob). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))(Vpa2o:(p a2 o))(Vla2b2ob:(l a2b2 ob))=>((lcon ab a2b2 ob) (conj pdh27 Vla2b2ob))). Qed. Lemma pdh313: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(p a2 o)->(l a2b2 ob)->(p b1 ab) \/ (l a1b1 ob). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))(Vpa2o:(p a2 o))(Vla2b2ob:(l a2b2 ob))=>((unique b1 ab a1b1 ob) (conj pdh2 (conj pdh18 (conj pdh26 (pdh311 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac Vpa2o Vla2b2ob)))))). Qed. Lemma pdh314: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(p a2 o)->(l a2b2 ob)->(p b1 ab)->(p ab b1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))(Vpa2o:(p a2 o))(Vla2b2ob:(l a2b2 ob))(Vpb1ab:(p b1 ab))=>((psym b1 ab) Vpb1ab)). Qed. Lemma pdh315: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(p a2 o)->(l a2b2 ob)->(p b1 ab)->(i ab b1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))(Vpa2o:(p a2 o))(Vla2b2ob:(l a2b2 ob))(Vpb1ab:(p b1 ab))=>((pcon ab b1 b1c1) (conj (pdh314 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac Vpa2o Vla2b2ob Vpb1ab) pdh10))). Qed. Lemma pdh316: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(p a2 o)->(l a2b2 ob)->(p b1 ab)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))(Vpa2o:(p a2 o))(Vla2b2ob:(l a2b2 ob))(Vpb1ab:(p b1 ab))=>((goal_normal b1c1) (conj pdh42 (conj pdh22 (conj (pdh296 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac) (pdh315 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac Vpa2o Vla2b2ob Vpb1ab)))))). Qed. Lemma pdh317: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(p a2 o)->(l a2b2 ob)->(l a1b1 ob)->(l ob a1b1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))(Vpa2o:(p a2 o))(Vla2b2ob:(l a2b2 ob))(Vla1b1ob:(l a1b1 ob))=>((lsym a1b1 ob) Vla1b1ob)). Qed. Lemma pdh318: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(p a2 o)->(l a2b2 ob)->(l a1b1 ob)->(l a2b2 a1b1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))(Vpa2o:(p a2 o))(Vla2b2ob:(l a2b2 ob))(Vla1b1ob:(l a1b1 ob))=>((ltra a2b2 ob a1b1) (conj Vla2b2ob (pdh317 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac Vpa2o Vla2b2ob Vla1b1ob)))). Qed. Lemma pdh319: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(p a2 o)->(l a2b2 ob)->(l a1b1 ob)->(l a1b1 a2b2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))(Vpa2o:(p a2 o))(Vla2b2ob:(l a2b2 ob))(Vla1b1ob:(l a1b1 ob))=>((lsym a2b2 a1b1) (pdh318 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac Vpa2o Vla2b2ob Vla1b1ob))). Qed. Lemma pdh320: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(p a2 o)->(l a2b2 ob)->(l a1b1 ob)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))(Vpa2o:(p a2 o))(Vla2b2ob:(l a2b2 ob))(Vla1b1ob:(l a1b1 ob))=>(notab (pdh319 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac Vpa2o Vla2b2ob Vla1b1ob))). Qed. Lemma pdh321: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(p a2 o)->(l a2b2 ob)->(l a1b1 ob)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))(Vpa2o:(p a2 o))(Vla2b2ob:(l a2b2 ob))(Vla1b1ob:(l a1b1 ob))=>((false_ind goal) (pdh320 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac Vpa2o Vla2b2ob Vla1b1ob))). Qed. Lemma pdh322: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(p a2 o)->(l a2b2 ob)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))(Vpa2o:(p a2 o))(Vla2b2ob:(l a2b2 ob))=>((or_ind ((pdh316 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac Vpa2o Vla2b2ob))((pdh321 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac Vpa2o Vla2b2ob)))(pdh313 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac Vpa2o Vla2b2ob))). Qed. Lemma pdh323: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(p a2 o)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))(Vpa2o:(p a2 o))=>((or_ind ((pdh308 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac Vpa2o))((pdh322 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac Vpa2o)))(pdh302 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac Vpa2o))). Qed. Lemma pdh325: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(l a2c2 oa)->(l oc oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))(Vla2c2oa:(l a2c2 oa))=>((ltra oc a2c2 oa) (conj (pdh287 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc) Vla2c2oa))). Qed. Lemma pdh330: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(l a2c2 oa)->(i c1 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))(Vla2c2oa:(l a2c2 oa))=>((lcon c1 oc oa) (conj pdh20 (pdh325 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac Vla2c2oa)))). Qed. Lemma pdh333: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(l a2c2 oa)->(p a1 c1) \/ (l a1c1 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))(Vla2c2oa:(l a2c2 oa))=>((unique a1 c1 a1c1 oa) (conj pdh5 (conj pdh16 (conj pdh6 (pdh330 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac Vla2c2oa)))))). Qed. Lemma pdh337: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(l a2c2 oa)->(p a1 c1)->(i a1 b1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))(Vla2c2oa:(l a2c2 oa))(Vpa1c1:(p a1 c1))=>((pcon a1 c1 b1c1) (conj Vpa1c1 pdh9))). Qed. Lemma pdh338: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(l a2c2 oa)->(p a1 c1)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))(Vla2c2oa:(l a2c2 oa))(Vpa1c1:(p a1 c1))=>((triangle1 b1c1) (conj (pdh337 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac Vla2c2oa Vpa1c1) (conj pdh10 pdh9)))). Qed. Lemma pdh339: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(l a2c2 oa)->(p a1 c1)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))(Vla2c2oa:(l a2c2 oa))(Vpa1c1:(p a1 c1))=>((false_ind goal) (pdh338 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac Vla2c2oa Vpa1c1))). Qed. Lemma pdh340: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(l a2c2 oa)->(l a1c1 oa)->(l oa a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))(Vla2c2oa:(l a2c2 oa))(Vla1c1oa:(l a1c1 oa))=>((lsym a1c1 oa) Vla1c1oa)). Qed. Lemma pdh341: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(l a2c2 oa)->(l a1c1 oa)->(l a2c2 a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))(Vla2c2oa:(l a2c2 oa))(Vla1c1oa:(l a1c1 oa))=>((ltra a2c2 oa a1c1) (conj Vla2c2oa (pdh340 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac Vla2c2oa Vla1c1oa)))). Qed. Lemma pdh342: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(l a2c2 oa)->(l a1c1 oa)->(l a1c1 a2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))(Vla2c2oa:(l a2c2 oa))(Vla1c1oa:(l a1c1 oa))=>((lsym a2c2 a1c1) (pdh341 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac Vla2c2oa Vla1c1oa))). Qed. Lemma pdh343: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(l a2c2 oa)->(l a1c1 oa)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))(Vla2c2oa:(l a2c2 oa))(Vla1c1oa:(l a1c1 oa))=>(notac (pdh342 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac Vla2c2oa Vla1c1oa))). Qed. Lemma pdh344: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(l a2c2 oa)->(l a1c1 oa)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))(Vla2c2oa:(l a2c2 oa))(Vla1c1oa:(l a1c1 oa))=>((false_ind goal) (pdh343 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac Vla2c2oa Vla1c1oa))). Qed. Lemma pdh345: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->(l a2c2 oa)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))(Vla2c2oa:(l a2c2 oa))=>((or_ind ((pdh339 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac Vla2c2oa))((pdh344 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac Vla2c2oa)))(pdh333 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac Vla2c2oa))). Qed. Lemma pdh346: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(p c1 ac)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vpc1ac:(p c1 ac))=>((or_ind ((pdh323 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac))((pdh345 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac)))(pdh297 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vpc1ac))). Qed. Lemma pdh347: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(l a1c1 oc)->(l oc a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vla1c1oc:(l a1c1 oc))=>((lsym a1c1 oc) Vla1c1oc)). Qed. Lemma pdh348: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(l a1c1 oc)->(l a2c2 a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vla1c1oc:(l a1c1 oc))=>((ltra a2c2 oc a1c1) (conj Vla2c2oc (pdh347 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vla1c1oc)))). Qed. Lemma pdh349: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(l a1c1 oc)->(l a1c1 a2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vla1c1oc:(l a1c1 oc))=>((lsym a2c2 a1c1) (pdh348 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vla1c1oc))). Qed. Lemma pdh350: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(l a1c1 oc)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vla1c1oc:(l a1c1 oc))=>(notac (pdh349 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vla1c1oc))). Qed. Lemma pdh351: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->(l a1c1 oc)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))(Vla1c1oc:(l a1c1 oc))=>((false_ind goal) (pdh350 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc Vla1c1oc))). Qed. Lemma pdh352: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a2c2 oc)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla2c2oc:(l a2c2 oc))=>((or_ind ((pdh346 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc))((pdh351 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc)))(pdh293 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla2c2oc))). Qed. Lemma pdh353: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l C4 a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))=>((lsym a1c1 C4) Vla1c1C4)). Qed. Lemma pdh357: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(i C3 a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))=>((lcon C3 C4 a1c1) (conj ViC3C4 (pdh353 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4)))). Qed. Lemma pdh358: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(i o a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))=>((lcon o C4 a1c1) (conj VioC4 (pdh353 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4)))). Qed. Lemma pdh359: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o) \/ (l a1c1 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))=>((unique a1 o a1c1 oa) (conj pdh5 (conj pdh16 (conj (pdh358 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4) pdh13))))). Qed. Lemma pdh361: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(i a1 ob). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))=>((pcon a1 o ob) (conj Vpa1o pdh14))). Qed. Lemma pdh362: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(i a1 oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))=>((pcon a1 o oc) (conj Vpa1o pdh15))). Qed. Lemma pdh365: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(p a1 b1) \/ (l a1b1 ob). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))=>((unique a1 b1 a1b1 ob) (conj pdh1 (conj (pdh361 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o) (conj pdh2 pdh18))))). Qed. Lemma pdh369: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(p a1 b1)->(i a1 b1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vpa1b1:(p a1 b1))=>((pcon a1 b1 b1c1) (conj Vpa1b1 pdh10))). Qed. Lemma pdh370: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(p a1 b1)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vpa1b1:(p a1 b1))=>((triangle1 b1c1) (conj (pdh369 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vpa1b1) (conj pdh10 pdh9)))). Qed. Lemma pdh371: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(p a1 b1)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vpa1b1:(p a1 b1))=>((false_ind goal) (pdh370 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vpa1b1))). Qed. Lemma pdh372: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l ob a1b1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))=>((lsym a1b1 ob) Vla1b1ob)). Qed. Lemma pdh373: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(i b2 a1b1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))=>((lcon b2 ob a1b1) (conj pdh19 (pdh372 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob)))). Qed. Lemma pdh374: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(i ab ob). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))=>((lcon ab a1b1 ob) (conj pdh26 Vla1b1ob))). Qed. Lemma pdh375: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(p a1 b2) \/ (l a1b1 C0). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))=>((unique a1 b2 a1b1 C0) (conj pdh1 (conj Via1C0 (conj (pdh373 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob) Vib2C0))))). Qed. Lemma pdh381: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(p a1 b2)->(i a1 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vpa1b2:(p a1 b2))=>((pcon a1 b2 b2c2) (conj Vpa1b2 pdh12))). Qed. Lemma pdh382: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(p a1 b2)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vpa1b2:(p a1 b2))=>(hessenberg_gap1 (pdh381 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vpa1b2))). Qed. Lemma pdh383: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(l C0 a1b1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))=>((lsym a1b1 C0) Vla1b1C0)). Qed. Lemma pdh388: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(i C1 a1b1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))=>((lcon C1 C0 a1b1) (conj ViC1C0 (pdh383 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0)))). Qed. Lemma pdh390: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1) \/ (l a1b1 oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))=>((unique a1 C1 a1b1 oc) (conj pdh1 (conj (pdh362 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o) (conj (pdh388 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0) ViC1oc))))). Qed. Lemma pdh394: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(i a1 C2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))=>((pcon a1 C1 C2) (conj Vpa1C1 ViC1C2))). Qed. Lemma pdh399: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab) \/ (l a2b2 ob). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))=>((unique b2 ab a2b2 ob) (conj pdh4 (conj pdh19 (conj pdh27 (pdh374 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob)))))). Qed. Lemma pdh400: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(p ab b2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))=>((psym b2 ab) Vpb2ab)). Qed. Lemma pdh401: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(i ab b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))=>((pcon ab b2 b2c2) (conj (pdh400 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab) pdh12))). Qed. Lemma pdh402: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(p a1 c1) \/ (l a1c1 oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))=>((unique a1 c1 a1c1 oc) (conj pdh5 (conj (pdh362 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o) (conj pdh6 pdh20))))). Qed. Lemma pdh408: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(p a1 c1)->(i a1 b1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vpa1c1:(p a1 c1))=>((pcon a1 c1 b1c1) (conj Vpa1c1 pdh9))). Qed. Lemma pdh409: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(p a1 c1)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vpa1c1:(p a1 c1))=>((triangle1 b1c1) (conj (pdh408 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab Vpa1c1) (conj pdh10 pdh9)))). Qed. Lemma pdh410: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(p a1 c1)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vpa1c1:(p a1 c1))=>((false_ind goal) (pdh409 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab Vpa1c1))). Qed. Lemma pdh411: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(l a1c1 oc)->(l oc a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))=>((lsym a1c1 oc) Vla1c1oc)). Qed. Lemma pdh414: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(l a1c1 oc)->(i c2 a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))=>((lcon c2 oc a1c1) (conj pdh21 (pdh411 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab Vla1c1oc)))). Qed. Lemma pdh416: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(l a1c1 oc)->(i ac oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))=>((lcon ac a1c1 oc) (conj pdh24 Vla1c1oc))). Qed. Lemma pdh419: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(l a1c1 oc)->(p a1 ac) \/ (l a1c1 C2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))=>((unique a1 ac a1c1 C2) (conj pdh5 (conj (pdh394 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1) (conj pdh24 ViacC2))))). Qed. Lemma pdh425: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(l a1c1 oc)->(p a1 ac)->(i a1 a2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vpa1ac:(p a1 ac))=>((pcon a1 ac a2c2) (conj Vpa1ac pdh25))). Qed. Lemma pdh432: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(l a1c1 oc)->(p a1 ac)->(p a1 C3) \/ (l a1c1 C2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vpa1ac:(p a1 ac))=>((unique a1 C3 a1c1 C2) (conj pdh5 (conj (pdh394 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1) (conj (pdh357 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4) ViC3C2))))). Qed. Lemma pdh440: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(l a1c1 oc)->(p a1 ac)->(p a1 C3)->(i a1 a2b2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vpa1ac:(p a1 ac))(Vpa1C3:(p a1 C3))=>((pcon a1 C3 a2b2) (conj Vpa1C3 ViC3a2b2))). Qed. Lemma pdh449: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(l a1c1 oc)->(p a1 ac)->(p a1 C3)->(p a1 ab) \/ (l a1b1 a2b2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vpa1ac:(p a1 ac))(Vpa1C3:(p a1 C3))=>((unique a1 ab a1b1 a2b2) (conj pdh1 (conj (pdh440 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab Vla1c1oc Vpa1ac Vpa1C3) (conj pdh26 pdh27))))). Qed. Lemma pdh469: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(l a1c1 oc)->(p a1 ac)->(p a1 C3)->(p a1 ab)->(i a1 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vpa1ac:(p a1 ac))(Vpa1C3:(p a1 C3))(Vpa1ab:(p a1 ab))=>((pcon a1 ab b2c2) (conj Vpa1ab (pdh401 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab)))). Qed. Lemma pdh470: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(l a1c1 oc)->(p a1 ac)->(p a1 C3)->(p a1 ab)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vpa1ac:(p a1 ac))(Vpa1C3:(p a1 C3))(Vpa1ab:(p a1 ab))=>(hessenberg_gap1 (pdh469 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab Vla1c1oc Vpa1ac Vpa1C3 Vpa1ab))). Qed. Lemma pdh471: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(l a1c1 oc)->(p a1 ac)->(p a1 C3)->(l a1b1 a2b2)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vpa1ac:(p a1 ac))(Vpa1C3:(p a1 C3))(Vla1b1a2b2:(l a1b1 a2b2))=>(notab Vla1b1a2b2)). Qed. Lemma pdh472: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(l a1c1 oc)->(p a1 ac)->(p a1 C3)->(l a1b1 a2b2)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vpa1ac:(p a1 ac))(Vpa1C3:(p a1 C3))(Vla1b1a2b2:(l a1b1 a2b2))=>((false_ind goal) (pdh471 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab Vla1c1oc Vpa1ac Vpa1C3 Vla1b1a2b2))). Qed. Lemma pdh473: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(l a1c1 oc)->(p a1 ac)->(p a1 C3)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vpa1ac:(p a1 ac))(Vpa1C3:(p a1 C3))=>((or_ind ((pdh470 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab Vla1c1oc Vpa1ac Vpa1C3))((pdh472 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab Vla1c1oc Vpa1ac Vpa1C3)))(pdh449 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab Vla1c1oc Vpa1ac Vpa1C3))). Qed. Lemma pdh482: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(l a1c1 oc)->(p a1 ac)->(l a1c1 C2)->(p a1 c2) \/ (l a1c1 a2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vpa1ac:(p a1 ac))(Vla1c1C2:(l a1c1 C2))=>((unique a1 c2 a1c1 a2c2) (conj pdh5 (conj (pdh425 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab Vla1c1oc Vpa1ac) (conj (pdh414 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab Vla1c1oc) pdh8))))). Qed. Lemma pdh490: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(l a1c1 oc)->(p a1 ac)->(l a1c1 C2)->(p a1 c2)->(i a1 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vpa1ac:(p a1 ac))(Vla1c1C2:(l a1c1 C2))(Vpa1c2:(p a1 c2))=>((pcon a1 c2 b2c2) (conj Vpa1c2 pdh11))). Qed. Lemma pdh491: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(l a1c1 oc)->(p a1 ac)->(l a1c1 C2)->(p a1 c2)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vpa1ac:(p a1 ac))(Vla1c1C2:(l a1c1 C2))(Vpa1c2:(p a1 c2))=>(hessenberg_gap1 (pdh490 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab Vla1c1oc Vpa1ac Vla1c1C2 Vpa1c2))). Qed. Lemma pdh492: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(l a1c1 oc)->(p a1 ac)->(l a1c1 C2)->(l a1c1 a2c2)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vpa1ac:(p a1 ac))(Vla1c1C2:(l a1c1 C2))(Vla1c1a2c2:(l a1c1 a2c2))=>(notac Vla1c1a2c2)). Qed. Lemma pdh493: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(l a1c1 oc)->(p a1 ac)->(l a1c1 C2)->(l a1c1 a2c2)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vpa1ac:(p a1 ac))(Vla1c1C2:(l a1c1 C2))(Vla1c1a2c2:(l a1c1 a2c2))=>((false_ind goal) (pdh492 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab Vla1c1oc Vpa1ac Vla1c1C2 Vla1c1a2c2))). Qed. Lemma pdh494: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(l a1c1 oc)->(p a1 ac)->(l a1c1 C2)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vpa1ac:(p a1 ac))(Vla1c1C2:(l a1c1 C2))=>((or_ind ((pdh491 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab Vla1c1oc Vpa1ac Vla1c1C2))((pdh493 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab Vla1c1oc Vpa1ac Vla1c1C2)))(pdh482 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab Vla1c1oc Vpa1ac Vla1c1C2))). Qed. Lemma pdh495: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(l a1c1 oc)->(p a1 ac)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vpa1ac:(p a1 ac))=>((or_ind ((pdh473 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab Vla1c1oc Vpa1ac))((pdh494 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab Vla1c1oc Vpa1ac)))(pdh432 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab Vla1c1oc Vpa1ac))). Qed. Lemma pdh504: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(l a1c1 oc)->(l a1c1 C2)->(p c2 ac) \/ (l a2c2 oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vla1c1C2:(l a1c1 C2))=>((unique c2 ac a2c2 oc) (conj pdh8 (conj pdh21 (conj pdh25 (pdh416 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab Vla1c1oc)))))). Qed. Lemma pdh505: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(l a1c1 oc)->(l a1c1 C2)->(p c2 ac)->(p ac c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vla1c1C2:(l a1c1 C2))(Vpc2ac:(p c2 ac))=>((psym c2 ac) Vpc2ac)). Qed. Lemma pdh506: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(l a1c1 oc)->(l a1c1 C2)->(p c2 ac)->(i ac b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vla1c1C2:(l a1c1 C2))(Vpc2ac:(p c2 ac))=>((pcon ac c2 b2c2) (conj (pdh505 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab Vla1c1oc Vla1c1C2 Vpc2ac) pdh11))). Qed. Lemma pdh507: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(l a1c1 oc)->(l a1c1 C2)->(p c2 ac)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vla1c1C2:(l a1c1 C2))(Vpc2ac:(p c2 ac))=>((goal_normal b2c2) (conj pdh43 (conj pdh23 (conj (pdh506 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab Vla1c1oc Vla1c1C2 Vpc2ac) (pdh401 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab)))))). Qed. Lemma pdh508: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(l a1c1 oc)->(l a1c1 C2)->(l a2c2 oc)->(l oc a2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vla1c1C2:(l a1c1 C2))(Vla2c2oc:(l a2c2 oc))=>((lsym a2c2 oc) Vla2c2oc)). Qed. Lemma pdh509: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(l a1c1 oc)->(l a1c1 C2)->(l a2c2 oc)->(l a1c1 a2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vla1c1C2:(l a1c1 C2))(Vla2c2oc:(l a2c2 oc))=>((ltra a1c1 oc a2c2) (conj Vla1c1oc (pdh508 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab Vla1c1oc Vla1c1C2 Vla2c2oc)))). Qed. Lemma pdh510: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(l a1c1 oc)->(l a1c1 C2)->(l a2c2 oc)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vla1c1C2:(l a1c1 C2))(Vla2c2oc:(l a2c2 oc))=>(notac (pdh509 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab Vla1c1oc Vla1c1C2 Vla2c2oc))). Qed. Lemma pdh511: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(l a1c1 oc)->(l a1c1 C2)->(l a2c2 oc)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vla1c1C2:(l a1c1 C2))(Vla2c2oc:(l a2c2 oc))=>((false_ind goal) (pdh510 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab Vla1c1oc Vla1c1C2 Vla2c2oc))). Qed. Lemma pdh512: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(l a1c1 oc)->(l a1c1 C2)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vla1c1C2:(l a1c1 C2))=>((or_ind ((pdh507 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab Vla1c1oc Vla1c1C2))((pdh511 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab Vla1c1oc Vla1c1C2)))(pdh504 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab Vla1c1oc Vla1c1C2))). Qed. Lemma pdh513: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->(l a1c1 oc)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))=>((or_ind ((pdh495 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab Vla1c1oc))((pdh512 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab Vla1c1oc)))(pdh419 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab Vla1c1oc))). Qed. Lemma pdh514: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(p b2 ab)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vpb2ab:(p b2 ab))=>((or_ind ((pdh410 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab))((pdh513 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab)))(pdh402 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vpb2ab))). Qed. Lemma pdh515: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(l a2b2 ob)->(l ob a2b2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vla2b2ob:(l a2b2 ob))=>((lsym a2b2 ob) Vla2b2ob)). Qed. Lemma pdh516: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(l a2b2 ob)->(l a1b1 a2b2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vla2b2ob:(l a2b2 ob))=>((ltra a1b1 ob a2b2) (conj Vla1b1ob (pdh515 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vla2b2ob)))). Qed. Lemma pdh517: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(l a2b2 ob)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vla2b2ob:(l a2b2 ob))=>(notab (pdh516 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vla2b2ob))). Qed. Lemma pdh518: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->(l a2b2 ob)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))(Vla2b2ob:(l a2b2 ob))=>((false_ind goal) (pdh517 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1 Vla2b2ob))). Qed. Lemma pdh519: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C1)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C1:(p a1 C1))=>((or_ind ((pdh514 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1))((pdh518 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1)))(pdh399 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vpa1C1))). Qed. Lemma pdh525: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(l a1b1 oc)->(i b1 oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vla1b1oc:(l a1b1 oc))=>((lcon b1 a1b1 oc) (conj pdh2 Vla1b1oc))). Qed. Lemma pdh526: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(l a1b1 oc)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vla1b1oc:(l a1b1 oc))=>((triangle1 oc) (conj (pdh362 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o) (conj (pdh525 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vla1b1oc) pdh20)))). Qed. Lemma pdh527: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(l a1b1 oc)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vla1b1oc:(l a1b1 oc))=>((false_ind goal) (pdh526 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0 Vla1b1oc))). Qed. Lemma pdh528: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))=>((or_ind ((pdh519 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0))((pdh527 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0)))(pdh390 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob Vla1b1C0))). Qed. Lemma pdh529: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->(l a1b1 ob)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))=>((or_ind ((pdh382 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob))((pdh528 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob)))(pdh375 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o Vla1b1ob))). Qed. Lemma pdh530: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(p a1 o)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vpa1o:(p a1 o))=>((or_ind ((pdh371 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o))((pdh529 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o)))(pdh365 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vpa1o))). Qed. Lemma pdh531: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(l oa a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))=>((lsym a1c1 oa) Vla1c1oa)). Qed. Lemma pdh532: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(l C4 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))=>((ltra C4 a1c1 oa) (conj (pdh353 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4) Vla1c1oa))). Qed. Lemma pdh537: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(i ac oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))=>((lcon ac a1c1 oa) (conj pdh24 Vla1c1oa))). Qed. Lemma pdh538: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(i C3 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))=>((lcon C3 C4 oa) (conj ViC3C4 (pdh532 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa)))). Qed. Lemma pdh540: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3) \/ (l a2b2 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))=>((unique a2 C3 a2b2 oa) (conj pdh3 (conj pdh17 (conj ViC3a2b2 (pdh538 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa)))))). Qed. Lemma pdh541: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(p C3 a2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))=>((psym a2 C3) Vpa2C3)). Qed. Lemma pdh543: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(i C3 a2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))=>((pcon C3 a2 a2c2) (conj (pdh541 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3) pdh7))). Qed. Lemma pdh544: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(p c1 o) \/ (l a1c1 oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))=>((unique c1 o a1c1 oc) (conj pdh6 (conj pdh20 (conj (pdh358 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4) pdh15))))). Qed. Lemma pdh546: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(p c1 o)->(i c1 ob). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vpc1o:(p c1 o))=>((pcon c1 o ob) (conj Vpc1o pdh14))). Qed. Lemma pdh548: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(p c1 o)->(p a2 ac) \/ (l a2c2 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vpc1o:(p c1 o))=>((unique a2 ac a2c2 oa) (conj pdh7 (conj pdh17 (conj pdh25 (pdh537 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa)))))). Qed. Lemma pdh549: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(p c1 o)->(p a2 ac)->(p ac a2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vpc1o:(p c1 o))(Vpa2ac:(p a2 ac))=>((psym a2 ac) Vpa2ac)). Qed. Lemma pdh552: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(p c1 o)->(p a2 ac)->(i ac a2b2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vpc1o:(p c1 o))(Vpa2ac:(p a2 ac))=>((pcon ac a2 a2b2) (conj (pdh549 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vpc1o Vpa2ac) pdh3))). Qed. Lemma pdh553: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(p c1 o)->(p a2 ac)->(p c1 b1) \/ (l b1c1 ob). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vpc1o:(p c1 o))(Vpa2ac:(p a2 ac))=>((unique c1 b1 b1c1 ob) (conj pdh9 (conj (pdh546 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vpc1o) (conj pdh10 pdh18))))). Qed. Lemma pdh557: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(p c1 o)->(p a2 ac)->(p c1 b1)->(i c1 a1b1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vpc1o:(p c1 o))(Vpa2ac:(p a2 ac))(Vpc1b1:(p c1 b1))=>((pcon c1 b1 a1b1) (conj Vpc1b1 pdh2))). Qed. Lemma pdh558: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(p c1 o)->(p a2 ac)->(p c1 b1)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vpc1o:(p c1 o))(Vpa2ac:(p a2 ac))(Vpc1b1:(p c1 b1))=>((triangle1 a1b1) (conj pdh1 (conj pdh2 (pdh557 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vpc1o Vpa2ac Vpc1b1))))). Qed. Lemma pdh559: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(p c1 o)->(p a2 ac)->(p c1 b1)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vpc1o:(p c1 o))(Vpa2ac:(p a2 ac))(Vpc1b1:(p c1 b1))=>((false_ind goal) (pdh558 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vpc1o Vpa2ac Vpc1b1))). Qed. Lemma pdh562: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(p c1 o)->(p a2 ac)->(l b1c1 ob)->(i bc ob). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vpc1o:(p c1 o))(Vpa2ac:(p a2 ac))(Vlb1c1ob:(l b1c1 ob))=>((lcon bc b1c1 ob) (conj pdh22 Vlb1c1ob))). Qed. Lemma pdh563: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(p c1 o)->(p a2 ac)->(l b1c1 ob)->(p b2 bc) \/ (l b2c2 ob). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vpc1o:(p c1 o))(Vpa2ac:(p a2 ac))(Vlb1c1ob:(l b1c1 ob))=>((unique b2 bc b2c2 ob) (conj pdh12 (conj pdh19 (conj pdh23 (pdh562 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vpc1o Vpa2ac Vlb1c1ob)))))). Qed. Lemma pdh564: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(p c1 o)->(p a2 ac)->(l b1c1 ob)->(p b2 bc)->(p bc b2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vpc1o:(p c1 o))(Vpa2ac:(p a2 ac))(Vlb1c1ob:(l b1c1 ob))(Vpb2bc:(p b2 bc))=>((psym b2 bc) Vpb2bc)). Qed. Lemma pdh565: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(p c1 o)->(p a2 ac)->(l b1c1 ob)->(p b2 bc)->(i bc a2b2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vpc1o:(p c1 o))(Vpa2ac:(p a2 ac))(Vlb1c1ob:(l b1c1 ob))(Vpb2bc:(p b2 bc))=>((pcon bc b2 a2b2) (conj (pdh564 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vpc1o Vpa2ac Vlb1c1ob Vpb2bc) pdh4))). Qed. Lemma pdh566: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(p c1 o)->(p a2 ac)->(l b1c1 ob)->(p b2 bc)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vpc1o:(p c1 o))(Vpa2ac:(p a2 ac))(Vlb1c1ob:(l b1c1 ob))(Vpb2bc:(p b2 bc))=>((goal_normal a2b2) (conj pdh39 (conj (pdh565 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vpc1o Vpa2ac Vlb1c1ob Vpb2bc) (conj (pdh552 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vpc1o Vpa2ac) pdh27))))). Qed. Lemma pdh567: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(p c1 o)->(p a2 ac)->(l b1c1 ob)->(l b2c2 ob)->(l ob b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vpc1o:(p c1 o))(Vpa2ac:(p a2 ac))(Vlb1c1ob:(l b1c1 ob))(Vlb2c2ob:(l b2c2 ob))=>((lsym b2c2 ob) Vlb2c2ob)). Qed. Lemma pdh568: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(p c1 o)->(p a2 ac)->(l b1c1 ob)->(l b2c2 ob)->(l b1c1 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vpc1o:(p c1 o))(Vpa2ac:(p a2 ac))(Vlb1c1ob:(l b1c1 ob))(Vlb2c2ob:(l b2c2 ob))=>((ltra b1c1 ob b2c2) (conj Vlb1c1ob (pdh567 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vpc1o Vpa2ac Vlb1c1ob Vlb2c2ob)))). Qed. Lemma pdh569: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(p c1 o)->(p a2 ac)->(l b1c1 ob)->(l b2c2 ob)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vpc1o:(p c1 o))(Vpa2ac:(p a2 ac))(Vlb1c1ob:(l b1c1 ob))(Vlb2c2ob:(l b2c2 ob))=>(notbc (pdh568 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vpc1o Vpa2ac Vlb1c1ob Vlb2c2ob))). Qed. Lemma pdh570: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(p c1 o)->(p a2 ac)->(l b1c1 ob)->(l b2c2 ob)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vpc1o:(p c1 o))(Vpa2ac:(p a2 ac))(Vlb1c1ob:(l b1c1 ob))(Vlb2c2ob:(l b2c2 ob))=>((false_ind goal) (pdh569 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vpc1o Vpa2ac Vlb1c1ob Vlb2c2ob))). Qed. Lemma pdh571: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(p c1 o)->(p a2 ac)->(l b1c1 ob)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vpc1o:(p c1 o))(Vpa2ac:(p a2 ac))(Vlb1c1ob:(l b1c1 ob))=>((or_ind ((pdh566 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vpc1o Vpa2ac Vlb1c1ob))((pdh570 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vpc1o Vpa2ac Vlb1c1ob)))(pdh563 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vpc1o Vpa2ac Vlb1c1ob))). Qed. Lemma pdh572: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(p c1 o)->(p a2 ac)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vpc1o:(p c1 o))(Vpa2ac:(p a2 ac))=>((or_ind ((pdh559 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vpc1o Vpa2ac))((pdh571 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vpc1o Vpa2ac)))(pdh553 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vpc1o Vpa2ac))). Qed. Lemma pdh573: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(p c1 o)->(l a2c2 oa)->(l oa a2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vpc1o:(p c1 o))(Vla2c2oa:(l a2c2 oa))=>((lsym a2c2 oa) Vla2c2oa)). Qed. Lemma pdh574: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(p c1 o)->(l a2c2 oa)->(l a1c1 a2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vpc1o:(p c1 o))(Vla2c2oa:(l a2c2 oa))=>((ltra a1c1 oa a2c2) (conj Vla1c1oa (pdh573 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vpc1o Vla2c2oa)))). Qed. Lemma pdh575: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(p c1 o)->(l a2c2 oa)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vpc1o:(p c1 o))(Vla2c2oa:(l a2c2 oa))=>(notac (pdh574 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vpc1o Vla2c2oa))). Qed. Lemma pdh576: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(p c1 o)->(l a2c2 oa)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vpc1o:(p c1 o))(Vla2c2oa:(l a2c2 oa))=>((false_ind goal) (pdh575 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vpc1o Vla2c2oa))). Qed. Lemma pdh577: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(p c1 o)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vpc1o:(p c1 o))=>((or_ind ((pdh572 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vpc1o))((pdh576 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vpc1o)))(pdh548 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vpc1o))). Qed. Lemma pdh578: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(l oc a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))=>((lsym a1c1 oc) Vla1c1oc)). Qed. Lemma pdh581: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(l oa oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))=>((ltra oa a1c1 oc) (conj (pdh531 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa) Vla1c1oc))). Qed. Lemma pdh582: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(l oc oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))=>((lsym oa oc) (pdh581 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc))). Qed. Lemma pdh588: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(i c2 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))=>((lcon c2 oc oa) (conj pdh21 (pdh582 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc)))). Qed. Lemma pdh590: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(i C1 a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))=>((lcon C1 oc a1c1) (conj ViC1oc (pdh578 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc)))). Qed. Lemma pdh594: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(p a1 C1) \/ (l a1c1 C0). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))=>((unique a1 C1 a1c1 C0) (conj pdh5 (conj Via1C0 (conj (pdh590 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc) ViC1C0))))). Qed. Lemma pdh596: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(p a1 C1)->(i a1 C2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vpa1C1:(p a1 C1))=>((pcon a1 C1 C2) (conj Vpa1C1 ViC1C2))). Qed. Lemma pdh598: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(p a1 C1)->(p a1 ac) \/ (l a1c1 C2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vpa1C1:(p a1 C1))=>((unique a1 ac a1c1 C2) (conj pdh5 (conj (pdh596 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vpa1C1) (conj pdh24 ViacC2))))). Qed. Lemma pdh602: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(p a1 C1)->(p a1 ac)->(i a1 a2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vpa1C1:(p a1 C1))(Vpa1ac:(p a1 ac))=>((pcon a1 ac a2c2) (conj Vpa1ac pdh25))). Qed. Lemma pdh606: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(p a1 C1)->(p a1 ac)->(p a1 C3) \/ (l a1c1 C2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vpa1C1:(p a1 C1))(Vpa1ac:(p a1 ac))=>((unique a1 C3 a1c1 C2) (conj pdh5 (conj (pdh596 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vpa1C1) (conj (pdh357 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4) ViC3C2))))). Qed. Lemma pdh607: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(p a1 C1)->(p a1 ac)->(p a1 C3)->(p C3 a1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vpa1C1:(p a1 C1))(Vpa1ac:(p a1 ac))(Vpa1C3:(p a1 C3))=>((psym a1 C3) Vpa1C3)). Qed. Lemma pdh608: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(p a1 C1)->(p a1 ac)->(p a1 C3)->(p a2 a1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vpa1C1:(p a1 C1))(Vpa1ac:(p a1 ac))(Vpa1C3:(p a1 C3))=>((ptra a2 C3 a1) (conj Vpa2C3 (pdh607 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vpa1C1 Vpa1ac Vpa1C3)))). Qed. Lemma pdh609: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(p a1 C1)->(p a1 ac)->(p a1 C3)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vpa1C1:(p a1 C1))(Vpa1ac:(p a1 ac))(Vpa1C3:(p a1 C3))=>(notaa (pdh608 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vpa1C1 Vpa1ac Vpa1C3))). Qed. Lemma pdh610: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(p a1 C1)->(p a1 ac)->(p a1 C3)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vpa1C1:(p a1 C1))(Vpa1ac:(p a1 ac))(Vpa1C3:(p a1 C3))=>((false_ind goal) (pdh609 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vpa1C1 Vpa1ac Vpa1C3))). Qed. Lemma pdh622: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(p a1 C1)->(p a1 ac)->(l a1c1 C2)->(p a1 C3) \/ (l a1c1 a2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vpa1C1:(p a1 C1))(Vpa1ac:(p a1 ac))(Vla1c1C2:(l a1c1 C2))=>((unique a1 C3 a1c1 a2c2) (conj pdh5 (conj (pdh602 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vpa1C1 Vpa1ac) (conj (pdh357 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4) (pdh543 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3)))))). Qed. Lemma pdh623: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(p a1 C1)->(p a1 ac)->(l a1c1 C2)->(p a1 C3)->(p C3 a1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vpa1C1:(p a1 C1))(Vpa1ac:(p a1 ac))(Vla1c1C2:(l a1c1 C2))(Vpa1C3:(p a1 C3))=>((psym a1 C3) Vpa1C3)). Qed. Lemma pdh624: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(p a1 C1)->(p a1 ac)->(l a1c1 C2)->(p a1 C3)->(p a2 a1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vpa1C1:(p a1 C1))(Vpa1ac:(p a1 ac))(Vla1c1C2:(l a1c1 C2))(Vpa1C3:(p a1 C3))=>((ptra a2 C3 a1) (conj Vpa2C3 (pdh623 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vpa1C1 Vpa1ac Vla1c1C2 Vpa1C3)))). Qed. Lemma pdh625: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(p a1 C1)->(p a1 ac)->(l a1c1 C2)->(p a1 C3)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vpa1C1:(p a1 C1))(Vpa1ac:(p a1 ac))(Vla1c1C2:(l a1c1 C2))(Vpa1C3:(p a1 C3))=>(notaa (pdh624 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vpa1C1 Vpa1ac Vla1c1C2 Vpa1C3))). Qed. Lemma pdh626: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(p a1 C1)->(p a1 ac)->(l a1c1 C2)->(p a1 C3)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vpa1C1:(p a1 C1))(Vpa1ac:(p a1 ac))(Vla1c1C2:(l a1c1 C2))(Vpa1C3:(p a1 C3))=>((false_ind goal) (pdh625 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vpa1C1 Vpa1ac Vla1c1C2 Vpa1C3))). Qed. Lemma pdh627: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(p a1 C1)->(p a1 ac)->(l a1c1 C2)->(l a1c1 a2c2)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vpa1C1:(p a1 C1))(Vpa1ac:(p a1 ac))(Vla1c1C2:(l a1c1 C2))(Vla1c1a2c2:(l a1c1 a2c2))=>(notac Vla1c1a2c2)). Qed. Lemma pdh628: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(p a1 C1)->(p a1 ac)->(l a1c1 C2)->(l a1c1 a2c2)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vpa1C1:(p a1 C1))(Vpa1ac:(p a1 ac))(Vla1c1C2:(l a1c1 C2))(Vla1c1a2c2:(l a1c1 a2c2))=>((false_ind goal) (pdh627 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vpa1C1 Vpa1ac Vla1c1C2 Vla1c1a2c2))). Qed. Lemma pdh629: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(p a1 C1)->(p a1 ac)->(l a1c1 C2)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vpa1C1:(p a1 C1))(Vpa1ac:(p a1 ac))(Vla1c1C2:(l a1c1 C2))=>((or_ind ((pdh626 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vpa1C1 Vpa1ac Vla1c1C2))((pdh628 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vpa1C1 Vpa1ac Vla1c1C2)))(pdh622 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vpa1C1 Vpa1ac Vla1c1C2))). Qed. Lemma pdh630: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(p a1 C1)->(p a1 ac)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vpa1C1:(p a1 C1))(Vpa1ac:(p a1 ac))=>((or_ind ((pdh610 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vpa1C1 Vpa1ac))((pdh629 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vpa1C1 Vpa1ac)))(pdh606 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vpa1C1 Vpa1ac))). Qed. Lemma pdh642: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(p a1 C1)->(l a1c1 C2)->(p a2 c2) \/ (l a2c2 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vpa1C1:(p a1 C1))(Vla1c1C2:(l a1c1 C2))=>((unique a2 c2 a2c2 oa) (conj pdh7 (conj pdh17 (conj pdh8 (pdh588 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc)))))). Qed. Lemma pdh646: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(p a1 C1)->(l a1c1 C2)->(p a2 c2)->(i a2 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vpa1C1:(p a1 C1))(Vla1c1C2:(l a1c1 C2))(Vpa2c2:(p a2 c2))=>((pcon a2 c2 b2c2) (conj Vpa2c2 pdh11))). Qed. Lemma pdh647: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(p a1 C1)->(l a1c1 C2)->(p a2 c2)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vpa1C1:(p a1 C1))(Vla1c1C2:(l a1c1 C2))(Vpa2c2:(p a2 c2))=>((triangle2 b2c2) (conj (pdh646 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vpa1C1 Vla1c1C2 Vpa2c2) (conj pdh12 pdh11)))). Qed. Lemma pdh648: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(p a1 C1)->(l a1c1 C2)->(p a2 c2)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vpa1C1:(p a1 C1))(Vla1c1C2:(l a1c1 C2))(Vpa2c2:(p a2 c2))=>((false_ind goal) (pdh647 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vpa1C1 Vla1c1C2 Vpa2c2))). Qed. Lemma pdh649: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(p a1 C1)->(l a1c1 C2)->(l a2c2 oa)->(l oa a2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vpa1C1:(p a1 C1))(Vla1c1C2:(l a1c1 C2))(Vla2c2oa:(l a2c2 oa))=>((lsym a2c2 oa) Vla2c2oa)). Qed. Lemma pdh650: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(p a1 C1)->(l a1c1 C2)->(l a2c2 oa)->(l a1c1 a2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vpa1C1:(p a1 C1))(Vla1c1C2:(l a1c1 C2))(Vla2c2oa:(l a2c2 oa))=>((ltra a1c1 oa a2c2) (conj Vla1c1oa (pdh649 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vpa1C1 Vla1c1C2 Vla2c2oa)))). Qed. Lemma pdh651: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(p a1 C1)->(l a1c1 C2)->(l a2c2 oa)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vpa1C1:(p a1 C1))(Vla1c1C2:(l a1c1 C2))(Vla2c2oa:(l a2c2 oa))=>(notac (pdh650 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vpa1C1 Vla1c1C2 Vla2c2oa))). Qed. Lemma pdh652: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(p a1 C1)->(l a1c1 C2)->(l a2c2 oa)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vpa1C1:(p a1 C1))(Vla1c1C2:(l a1c1 C2))(Vla2c2oa:(l a2c2 oa))=>((false_ind goal) (pdh651 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vpa1C1 Vla1c1C2 Vla2c2oa))). Qed. Lemma pdh653: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(p a1 C1)->(l a1c1 C2)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vpa1C1:(p a1 C1))(Vla1c1C2:(l a1c1 C2))=>((or_ind ((pdh648 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vpa1C1 Vla1c1C2))((pdh652 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vpa1C1 Vla1c1C2)))(pdh642 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vpa1C1 Vla1c1C2))). Qed. Lemma pdh654: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(p a1 C1)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vpa1C1:(p a1 C1))=>((or_ind ((pdh630 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vpa1C1))((pdh653 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vpa1C1)))(pdh598 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vpa1C1))). Qed. Lemma pdh658: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(l a1c1 C0)->(l oa C0). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vla1c1C0:(l a1c1 C0))=>((ltra oa a1c1 C0) (conj (pdh531 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa) Vla1c1C0))). Qed. Lemma pdh660: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(l a1c1 C0)->(l oc C0). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vla1c1C0:(l a1c1 C0))=>((ltra oc a1c1 C0) (conj (pdh578 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc) Vla1c1C0))). Qed. Lemma pdh664: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(l a1c1 C0)->(i a2 C0). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vla1c1C0:(l a1c1 C0))=>((lcon a2 oa C0) (conj pdh17 (pdh658 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vla1c1C0)))). Qed. Lemma pdh666: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(l a1c1 C0)->(i c2 C0). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vla1c1C0:(l a1c1 C0))=>((lcon c2 oc C0) (conj pdh21 (pdh660 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vla1c1C0)))). Qed. Lemma pdh667: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(l a1c1 C0)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vla1c1C0:(l a1c1 C0))=>((triangle2 C0) (conj (pdh664 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vla1c1C0) (conj Vib2C0 (pdh666 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vla1c1C0))))). Qed. Lemma pdh668: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->(l a1c1 C0)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))(Vla1c1C0:(l a1c1 C0))=>((false_ind goal) (pdh667 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc Vla1c1C0))). Qed. Lemma pdh669: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->(l a1c1 oc)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1oc:(l a1c1 oc))=>((or_ind ((pdh654 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc))((pdh668 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc)))(pdh594 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3 Vla1c1oc))). Qed. Lemma pdh670: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(p a2 C3)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))=>((or_ind ((pdh577 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3))((pdh669 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3)))(pdh544 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vpa2C3))). Qed. Lemma pdh671: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(l a2b2 oa)->(l oa a2b2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vla2b2oa:(l a2b2 oa))=>((lsym a2b2 oa) Vla2b2oa)). Qed. Lemma pdh672: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(l a2b2 oa)->(l a1c1 a2b2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vla2b2oa:(l a2b2 oa))=>((ltra a1c1 oa a2b2) (conj Vla1c1oa (pdh671 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vla2b2oa)))). Qed. Lemma pdh673: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(l a2b2 oa)->(l a2b2 a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vla2b2oa:(l a2b2 oa))=>((lsym a1c1 a2b2) (pdh672 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vla2b2oa))). Qed. Lemma pdh677: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(l a2b2 oa)->(i b2 a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vla2b2oa:(l a2b2 oa))=>((lcon b2 a2b2 a1c1) (conj pdh4 (pdh673 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vla2b2oa)))). Qed. Lemma pdh678: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->(l a2b2 oa)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))(Vla2b2oa:(l a2b2 oa))=>(hessenberg_gap2 (pdh677 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa Vla2b2oa))). Qed. Lemma pdh679: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->(l a1c1 oa)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))(Vla1c1oa:(l a1c1 oa))=>((or_ind ((pdh670 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa))((pdh678 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa)))(pdh540 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4 Vla1c1oa))). Qed. Lemma pdh680: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->(l a1c1 C4)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(Vla1c1C4:(l a1c1 C4))=>((or_ind ((pdh530 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4))((pdh679 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4)))(pdh359 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 Vla1c1C4))). Qed. Lemma pdh681: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(p c2 b2) \/ (l b2c2 C6). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))=>((unique c2 b2 b2c2 C6) (conj pdh11 (conj Vic2C6 (conj pdh12 Vib2C6))))). Qed. Lemma pdh683: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(p c2 b2)->(i c2 a2b2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vpc2b2:(p c2 b2))=>((pcon c2 b2 a2b2) (conj Vpc2b2 pdh4))). Qed. Lemma pdh684: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(p c2 b2)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vpc2b2:(p c2 b2))=>((triangle2 a2b2) (conj pdh3 (conj pdh4 (pdh683 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vpc2b2))))). Qed. Lemma pdh685: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(p c2 b2)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vpc2b2:(p c2 b2))=>((false_ind goal) (pdh684 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vpc2b2))). Qed. Lemma pdh686: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->(l C6 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))=>((lsym b2c2 C6) Vlb2c2C6)). Qed. Lemma pdh688: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->(i C5 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))=>((lcon C5 C6 b2c2) (conj ViC5C6 (pdh686 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6)))). Qed. Lemma pdh689: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->(exists A:dom,(i A C4)/\(i A a1b1)). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))=>((point C4 a1b1) (conj (pdh56 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4) pdh38))). Qed. Lemma pdh691: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->(l oc C0) \/ (l C4 a1b1) \/ (l b2c2 b1c1) \/ (exists A:dom,(l A A)/\(i C1 A)/\(i C7 A)/\(i bc A)). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))=>((papp b1 o b2 C5 a1 c1 C1 C7 bc ob a1c1 oc C0 C4 a1b1 b2c2 b1c1) (conj pdh18 (conj pdh14 (conj pdh19 (conj ViC5a1c1 (conj pdh5 (conj pdh6 (conj pdh15 (conj pdh20 (conj ViC1oc (conj Vib2C0 (conj Via1C0 (conj ViC1C0 (conj VioC4 (conj ViC5C4 (conj ViC7C4 (conj pdh2 (conj pdh1 (conj ViC7a1b1 (conj pdh12 (conj (pdh688 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6) (conj pdh23 (conj pdh10 (conj pdh9 pdh22))))))))))))))))))))))))). Qed. Lemma pdh694: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->(l oc C0)->(i c1 C0). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(VlocC0:(l oc C0))=>((lcon c1 oc C0) (conj pdh20 VlocC0))). Qed. Lemma pdh698: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->(l oc C0)->(p a1 c1) \/ (l a1c1 C0). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(VlocC0:(l oc C0))=>((unique a1 c1 a1c1 C0) (conj pdh5 (conj Via1C0 (conj pdh6 (pdh694 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 VlocC0)))))). Qed. Lemma pdh700: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->(l oc C0)->(p a1 c1)->(i a1 b1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(VlocC0:(l oc C0))(Vpa1c1:(p a1 c1))=>((pcon a1 c1 b1c1) (conj Vpa1c1 pdh9))). Qed. Lemma pdh701: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->(l oc C0)->(p a1 c1)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(VlocC0:(l oc C0))(Vpa1c1:(p a1 c1))=>((triangle1 b1c1) (conj (pdh700 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 VlocC0 Vpa1c1) (conj pdh10 pdh9)))). Qed. Lemma pdh702: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->(l oc C0)->(p a1 c1)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(VlocC0:(l oc C0))(Vpa1c1:(p a1 c1))=>((false_ind goal) (pdh701 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 VlocC0 Vpa1c1))). Qed. Lemma pdh703: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->(l oc C0)->(l a1c1 C0)->(l C0 a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(VlocC0:(l oc C0))(Vla1c1C0:(l a1c1 C0))=>((lsym a1c1 C0) Vla1c1C0)). Qed. Lemma pdh710: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->(l oc C0)->(l a1c1 C0)->(i b2 a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(VlocC0:(l oc C0))(Vla1c1C0:(l a1c1 C0))=>((lcon b2 C0 a1c1) (conj Vib2C0 (pdh703 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 VlocC0 Vla1c1C0)))). Qed. Lemma pdh711: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->(l oc C0)->(l a1c1 C0)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(VlocC0:(l oc C0))(Vla1c1C0:(l a1c1 C0))=>(hessenberg_gap2 (pdh710 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 VlocC0 Vla1c1C0))). Qed. Lemma pdh712: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->(l oc C0)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(VlocC0:(l oc C0))=>((or_ind ((pdh702 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 VlocC0))((pdh711 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 VlocC0)))(pdh698 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 VlocC0))). Qed. Lemma pdh719: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->(l C4 a1b1)->(i C5 a1b1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(VlC4a1b1:(l C4 a1b1))=>((lcon C5 C4 a1b1) (conj ViC5C4 VlC4a1b1))). Qed. Lemma pdh720: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->(l C4 a1b1)->(p a1 C5) \/ (l a1b1 a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(VlC4a1b1:(l C4 a1b1))=>((unique a1 C5 a1b1 a1c1) (conj pdh1 (conj pdh5 (conj (pdh719 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 VlC4a1b1) ViC5a1c1))))). Qed. Lemma pdh723: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->(l C4 a1b1)->(p a1 C5)->(i a1 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(VlC4a1b1:(l C4 a1b1))(Vpa1C5:(p a1 C5))=>((pcon a1 C5 b2c2) (conj Vpa1C5 (pdh688 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6)))). Qed. Lemma pdh724: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->(l C4 a1b1)->(p a1 C5)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(VlC4a1b1:(l C4 a1b1))(Vpa1C5:(p a1 C5))=>(hessenberg_gap1 (pdh723 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 VlC4a1b1 Vpa1C5))). Qed. Lemma pdh728: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->(l C4 a1b1)->(l a1b1 a1c1)->(i b1 a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(VlC4a1b1:(l C4 a1b1))(Vla1b1a1c1:(l a1b1 a1c1))=>((lcon b1 a1b1 a1c1) (conj pdh2 Vla1b1a1c1))). Qed. Lemma pdh729: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->(l C4 a1b1)->(l a1b1 a1c1)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(VlC4a1b1:(l C4 a1b1))(Vla1b1a1c1:(l a1b1 a1c1))=>((triangle1 a1c1) (conj pdh5 (conj (pdh728 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 VlC4a1b1 Vla1b1a1c1) pdh6)))). Qed. Lemma pdh730: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->(l C4 a1b1)->(l a1b1 a1c1)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(VlC4a1b1:(l C4 a1b1))(Vla1b1a1c1:(l a1b1 a1c1))=>((false_ind goal) (pdh729 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 VlC4a1b1 Vla1b1a1c1))). Qed. Lemma pdh731: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->(l C4 a1b1)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(VlC4a1b1:(l C4 a1b1))=>((or_ind ((pdh724 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 VlC4a1b1))((pdh730 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 VlC4a1b1)))(pdh720 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 VlC4a1b1))). Qed. Lemma pdh732: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->(l b2c2 b1c1)->(l b1c1 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(Vlb2c2b1c1:(l b2c2 b1c1))=>((lsym b2c2 b1c1) Vlb2c2b1c1)). Qed. Lemma pdh733: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->(l b2c2 b1c1)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(Vlb2c2b1c1:(l b2c2 b1c1))=>(notbc (pdh732 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 Vlb2c2b1c1))). Qed. Lemma pdh734: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->(l b2c2 b1c1)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(Vlb2c2b1c1:(l b2c2 b1c1))=>((false_ind goal) (pdh733 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 Vlb2c2b1c1))). Qed. Lemma pdh735: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a2b2 a1b1) \/ (l b2c2 C8) \/ (l a1c1 C2) \/ (exists A:dom,(l A A)/\(i ab A)/\(i bc A)/\(i ac A)). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))=>((papp C1 b2 a1 C5 C7 C3 ab bc ac C0 C4 a2b2 a1b1 b2c2 C8 a1c1 C2) (conj ViC1C0 (conj Vib2C0 (conj Via1C0 (conj ViC5C4 (conj ViC7C4 (conj ViC3C4 (conj pdh4 (conj ViC3a2b2 (conj pdh27 (conj pdh1 (conj ViC7a1b1 (conj pdh26 (conj pdh12 (conj (pdh688 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6) (conj pdh23 (conj ViC1C8 (conj ViC7C8 (conj VibcC8 (conj pdh5 (conj ViC5a1c1 (conj pdh24 (conj ViC1C2 (conj ViC3C2 ViacC2))))))))))))))))))))))))). Qed. Lemma pdh736: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a2b2 a1b1)->(l a1b1 a2b2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla2b2a1b1:(l a2b2 a1b1))=>((lsym a2b2 a1b1) Vla2b2a1b1)). Qed. Lemma pdh737: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a2b2 a1b1)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla2b2a1b1:(l a2b2 a1b1))=>(notab (pdh736 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla2b2a1b1))). Qed. Lemma pdh738: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a2b2 a1b1)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla2b2a1b1:(l a2b2 a1b1))=>((false_ind goal) (pdh737 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla2b2a1b1))). Qed. Lemma pdh739: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l C8 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))=>((lsym b2c2 C8) Vlb2c2C8)). Qed. Lemma pdh745: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(i C1 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))=>((lcon C1 C8 b2c2) (conj ViC1C8 (pdh739 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8)))). Qed. Lemma pdh749: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(p c2 C1) \/ (l b2c2 oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))=>((unique c2 C1 b2c2 oc) (conj pdh11 (conj pdh21 (conj (pdh745 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8) ViC1oc))))). Qed. Lemma pdh751: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(p c2 C1)->(i c2 C0). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vpc2C1:(p c2 C1))=>((pcon c2 C1 C0) (conj Vpc2C1 ViC1C0))). Qed. Lemma pdh752: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(p c2 C1)->(i c2 C2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vpc2C1:(p c2 C1))=>((pcon c2 C1 C2) (conj Vpc2C1 ViC1C2))). Qed. Lemma pdh754: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(p c2 C1)->(p c2 ac) \/ (l a2c2 C2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vpc2C1:(p c2 C1))=>((unique c2 ac a2c2 C2) (conj pdh8 (conj (pdh752 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vpc2C1) (conj pdh25 ViacC2))))). Qed. Lemma pdh755: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(p c2 C1)->(p c2 ac)->(p ac c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vpc2C1:(p c2 C1))(Vpc2ac:(p c2 ac))=>((psym c2 ac) Vpc2ac)). Qed. Lemma pdh760: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(p c2 C1)->(p c2 ac)->(i ac b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vpc2C1:(p c2 C1))(Vpc2ac:(p c2 ac))=>((pcon ac c2 b2c2) (conj (pdh755 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vpc2C1 Vpc2ac) pdh11))). Qed. Lemma pdh764: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(p c2 C1)->(p c2 ac)->(i ac C0). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vpc2C1:(p c2 C1))(Vpc2ac:(p c2 ac))=>((pcon ac c2 C0) (conj (pdh755 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vpc2C1 Vpc2ac) (pdh751 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vpc2C1)))). Qed. Lemma pdh765: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(p c2 C1)->(p c2 ac)->(p a1 ac) \/ (l a1c1 C0). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vpc2C1:(p c2 C1))(Vpc2ac:(p c2 ac))=>((unique a1 ac a1c1 C0) (conj pdh5 (conj Via1C0 (conj pdh24 (pdh764 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vpc2C1 Vpc2ac)))))). Qed. Lemma pdh773: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(p c2 C1)->(p c2 ac)->(p a1 ac)->(i a1 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vpc2C1:(p c2 C1))(Vpc2ac:(p c2 ac))(Vpa1ac:(p a1 ac))=>((pcon a1 ac b2c2) (conj Vpa1ac (pdh760 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vpc2C1 Vpc2ac)))). Qed. Lemma pdh774: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(p c2 C1)->(p c2 ac)->(p a1 ac)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vpc2C1:(p c2 C1))(Vpc2ac:(p c2 ac))(Vpa1ac:(p a1 ac))=>(hessenberg_gap1 (pdh773 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vpc2C1 Vpc2ac Vpa1ac))). Qed. Lemma pdh775: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(p c2 C1)->(p c2 ac)->(l a1c1 C0)->(l C0 a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vpc2C1:(p c2 C1))(Vpc2ac:(p c2 ac))(Vla1c1C0:(l a1c1 C0))=>((lsym a1c1 C0) Vla1c1C0)). Qed. Lemma pdh777: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(p c2 C1)->(p c2 ac)->(l a1c1 C0)->(i b2 a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vpc2C1:(p c2 C1))(Vpc2ac:(p c2 ac))(Vla1c1C0:(l a1c1 C0))=>((lcon b2 C0 a1c1) (conj Vib2C0 (pdh775 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vpc2C1 Vpc2ac Vla1c1C0)))). Qed. Lemma pdh778: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(p c2 C1)->(p c2 ac)->(l a1c1 C0)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vpc2C1:(p c2 C1))(Vpc2ac:(p c2 ac))(Vla1c1C0:(l a1c1 C0))=>(hessenberg_gap2 (pdh777 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vpc2C1 Vpc2ac Vla1c1C0))). Qed. Lemma pdh779: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(p c2 C1)->(p c2 ac)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vpc2C1:(p c2 C1))(Vpc2ac:(p c2 ac))=>((or_ind ((pdh774 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vpc2C1 Vpc2ac))((pdh778 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vpc2C1 Vpc2ac)))(pdh765 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vpc2C1 Vpc2ac))). Qed. Lemma pdh780: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(p c2 C1)->(l a2c2 C2)->(l C2 a2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vpc2C1:(p c2 C1))(Vla2c2C2:(l a2c2 C2))=>((lsym a2c2 C2) Vla2c2C2)). Qed. Lemma pdh782: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(p c2 C1)->(l a2c2 C2)->(i C3 a2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vpc2C1:(p c2 C1))(Vla2c2C2:(l a2c2 C2))=>((lcon C3 C2 a2c2) (conj ViC3C2 (pdh780 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vpc2C1 Vla2c2C2)))). Qed. Lemma pdh783: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(p c2 C1)->(l a2c2 C2)->(p a2 C3) \/ (l a2b2 a2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vpc2C1:(p c2 C1))(Vla2c2C2:(l a2c2 C2))=>((unique a2 C3 a2b2 a2c2) (conj pdh3 (conj pdh7 (conj ViC3a2b2 (pdh782 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vpc2C1 Vla2c2C2)))))). Qed. Lemma pdh787: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(p c2 C1)->(l a2c2 C2)->(p a2 C3)->(p c2 b2) \/ (l b2c2 C0). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vpc2C1:(p c2 C1))(Vla2c2C2:(l a2c2 C2))(Vpa2C3:(p a2 C3))=>((unique c2 b2 b2c2 C0) (conj pdh11 (conj (pdh751 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vpc2C1) (conj pdh12 Vib2C0))))). Qed. Lemma pdh791: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(p c2 C1)->(l a2c2 C2)->(p a2 C3)->(p c2 b2)->(i c2 a2b2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vpc2C1:(p c2 C1))(Vla2c2C2:(l a2c2 C2))(Vpa2C3:(p a2 C3))(Vpc2b2:(p c2 b2))=>((pcon c2 b2 a2b2) (conj Vpc2b2 pdh4))). Qed. Lemma pdh792: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(p c2 C1)->(l a2c2 C2)->(p a2 C3)->(p c2 b2)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vpc2C1:(p c2 C1))(Vla2c2C2:(l a2c2 C2))(Vpa2C3:(p a2 C3))(Vpc2b2:(p c2 b2))=>((triangle2 a2b2) (conj pdh3 (conj pdh4 (pdh791 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vpc2C1 Vla2c2C2 Vpa2C3 Vpc2b2))))). Qed. Lemma pdh793: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(p c2 C1)->(l a2c2 C2)->(p a2 C3)->(p c2 b2)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vpc2C1:(p c2 C1))(Vla2c2C2:(l a2c2 C2))(Vpa2C3:(p a2 C3))(Vpc2b2:(p c2 b2))=>((false_ind goal) (pdh792 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vpc2C1 Vla2c2C2 Vpa2C3 Vpc2b2))). Qed. Lemma pdh794: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(p c2 C1)->(l a2c2 C2)->(p a2 C3)->(l b2c2 C0)->(l C0 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vpc2C1:(p c2 C1))(Vla2c2C2:(l a2c2 C2))(Vpa2C3:(p a2 C3))(Vlb2c2C0:(l b2c2 C0))=>((lsym b2c2 C0) Vlb2c2C0)). Qed. Lemma pdh800: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(p c2 C1)->(l a2c2 C2)->(p a2 C3)->(l b2c2 C0)->(i a1 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vpc2C1:(p c2 C1))(Vla2c2C2:(l a2c2 C2))(Vpa2C3:(p a2 C3))(Vlb2c2C0:(l b2c2 C0))=>((lcon a1 C0 b2c2) (conj Via1C0 (pdh794 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vpc2C1 Vla2c2C2 Vpa2C3 Vlb2c2C0)))). Qed. Lemma pdh801: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(p c2 C1)->(l a2c2 C2)->(p a2 C3)->(l b2c2 C0)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vpc2C1:(p c2 C1))(Vla2c2C2:(l a2c2 C2))(Vpa2C3:(p a2 C3))(Vlb2c2C0:(l b2c2 C0))=>(hessenberg_gap1 (pdh800 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vpc2C1 Vla2c2C2 Vpa2C3 Vlb2c2C0))). Qed. Lemma pdh802: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(p c2 C1)->(l a2c2 C2)->(p a2 C3)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vpc2C1:(p c2 C1))(Vla2c2C2:(l a2c2 C2))(Vpa2C3:(p a2 C3))=>((or_ind ((pdh793 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vpc2C1 Vla2c2C2 Vpa2C3))((pdh801 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vpc2C1 Vla2c2C2 Vpa2C3)))(pdh787 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vpc2C1 Vla2c2C2 Vpa2C3))). Qed. Lemma pdh806: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(p c2 C1)->(l a2c2 C2)->(l a2b2 a2c2)->(i b2 a2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vpc2C1:(p c2 C1))(Vla2c2C2:(l a2c2 C2))(Vla2b2a2c2:(l a2b2 a2c2))=>((lcon b2 a2b2 a2c2) (conj pdh4 Vla2b2a2c2))). Qed. Lemma pdh807: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(p c2 C1)->(l a2c2 C2)->(l a2b2 a2c2)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vpc2C1:(p c2 C1))(Vla2c2C2:(l a2c2 C2))(Vla2b2a2c2:(l a2b2 a2c2))=>((triangle2 a2c2) (conj pdh7 (conj (pdh806 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vpc2C1 Vla2c2C2 Vla2b2a2c2) pdh8)))). Qed. Lemma pdh808: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(p c2 C1)->(l a2c2 C2)->(l a2b2 a2c2)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vpc2C1:(p c2 C1))(Vla2c2C2:(l a2c2 C2))(Vla2b2a2c2:(l a2b2 a2c2))=>((false_ind goal) (pdh807 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vpc2C1 Vla2c2C2 Vla2b2a2c2))). Qed. Lemma pdh809: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(p c2 C1)->(l a2c2 C2)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vpc2C1:(p c2 C1))(Vla2c2C2:(l a2c2 C2))=>((or_ind ((pdh802 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vpc2C1 Vla2c2C2))((pdh808 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vpc2C1 Vla2c2C2)))(pdh783 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vpc2C1 Vla2c2C2))). Qed. Lemma pdh810: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(p c2 C1)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vpc2C1:(p c2 C1))=>((or_ind ((pdh779 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vpc2C1))((pdh809 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vpc2C1)))(pdh754 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vpc2C1))). Qed. Lemma pdh811: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(l oc b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))=>((lsym b2c2 oc) Vlb2c2oc)). Qed. Lemma pdh812: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(l C6 oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))=>((ltra C6 b2c2 oc) (conj (pdh686 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6) Vlb2c2oc))). Qed. Lemma pdh817: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(i o b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))=>((lcon o oc b2c2) (conj pdh15 (pdh811 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc)))). Qed. Lemma pdh823: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(i bc oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))=>((lcon bc b2c2 oc) (conj pdh23 Vlb2c2oc))). Qed. Lemma pdh824: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(i C5 oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))=>((lcon C5 C6 oc) (conj ViC5C6 (pdh812 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc)))). Qed. Lemma pdh826: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5) \/ (l a1c1 oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))=>((unique c1 C5 a1c1 oc) (conj pdh6 (conj pdh20 (conj ViC5a1c1 (pdh824 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc)))))). Qed. Lemma pdh830: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc) \/ (l b1c1 oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))=>((unique c1 bc b1c1 oc) (conj pdh9 (conj pdh20 (conj pdh22 (pdh823 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc)))))). Qed. Lemma pdh831: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(p bc c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))=>((psym c1 bc) Vpc1bc)). Qed. Lemma pdh834: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(i bc a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))=>((pcon bc c1 a1c1) (conj (pdh831 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc) pdh6))). Qed. Lemma pdh836: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(p b2 o) \/ (l b2c2 ob). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))=>((unique b2 o b2c2 ob) (conj pdh12 (conj pdh19 (conj (pdh817 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc) pdh14))))). Qed. Lemma pdh838: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(p b2 o)->(i b2 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vpb2o:(p b2 o))=>((pcon b2 o oa) (conj Vpb2o pdh13))). Qed. Lemma pdh842: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(p b2 o)->(p a2 b2) \/ (l a2b2 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vpb2o:(p b2 o))=>((unique a2 b2 a2b2 oa) (conj pdh3 (conj pdh17 (conj pdh4 (pdh838 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vpb2o)))))). Qed. Lemma pdh846: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(p b2 o)->(p a2 b2)->(i a2 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vpb2o:(p b2 o))(Vpa2b2:(p a2 b2))=>((pcon a2 b2 b2c2) (conj Vpa2b2 pdh12))). Qed. Lemma pdh847: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(p b2 o)->(p a2 b2)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vpb2o:(p b2 o))(Vpa2b2:(p a2 b2))=>((triangle2 b2c2) (conj (pdh846 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vpb2o Vpa2b2) (conj pdh12 pdh11)))). Qed. Lemma pdh848: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(p b2 o)->(p a2 b2)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vpb2o:(p b2 o))(Vpa2b2:(p a2 b2))=>((false_ind goal) (pdh847 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vpb2o Vpa2b2))). Qed. Lemma pdh851: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(p b2 o)->(l a2b2 oa)->(i ab oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vpb2o:(p b2 o))(Vla2b2oa:(l a2b2 oa))=>((lcon ab a2b2 oa) (conj pdh27 Vla2b2oa))). Qed. Lemma pdh853: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(p b2 o)->(l a2b2 oa)->(p a1 ab) \/ (l a1b1 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vpb2o:(p b2 o))(Vla2b2oa:(l a2b2 oa))=>((unique a1 ab a1b1 oa) (conj pdh1 (conj pdh16 (conj pdh26 (pdh851 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vpb2o Vla2b2oa)))))). Qed. Lemma pdh854: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(p b2 o)->(l a2b2 oa)->(p a1 ab)->(p ab a1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vpb2o:(p b2 o))(Vla2b2oa:(l a2b2 oa))(Vpa1ab:(p a1 ab))=>((psym a1 ab) Vpa1ab)). Qed. Lemma pdh855: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(p b2 o)->(l a2b2 oa)->(p a1 ab)->(i ab a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vpb2o:(p b2 o))(Vla2b2oa:(l a2b2 oa))(Vpa1ab:(p a1 ab))=>((pcon ab a1 a1c1) (conj (pdh854 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vpb2o Vla2b2oa Vpa1ab) pdh5))). Qed. Lemma pdh856: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(p b2 o)->(l a2b2 oa)->(p a1 ab)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vpb2o:(p b2 o))(Vla2b2oa:(l a2b2 oa))(Vpa1ab:(p a1 ab))=>((goal_normal a1c1) (conj pdh40 (conj (pdh834 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc) (conj pdh24 (pdh855 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vpb2o Vla2b2oa Vpa1ab)))))). Qed. Lemma pdh857: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(p b2 o)->(l a2b2 oa)->(l a1b1 oa)->(l oa a1b1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vpb2o:(p b2 o))(Vla2b2oa:(l a2b2 oa))(Vla1b1oa:(l a1b1 oa))=>((lsym a1b1 oa) Vla1b1oa)). Qed. Lemma pdh858: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(p b2 o)->(l a2b2 oa)->(l a1b1 oa)->(l a2b2 a1b1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vpb2o:(p b2 o))(Vla2b2oa:(l a2b2 oa))(Vla1b1oa:(l a1b1 oa))=>((ltra a2b2 oa a1b1) (conj Vla2b2oa (pdh857 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vpb2o Vla2b2oa Vla1b1oa)))). Qed. Lemma pdh859: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(p b2 o)->(l a2b2 oa)->(l a1b1 oa)->(l a1b1 a2b2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vpb2o:(p b2 o))(Vla2b2oa:(l a2b2 oa))(Vla1b1oa:(l a1b1 oa))=>((lsym a2b2 a1b1) (pdh858 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vpb2o Vla2b2oa Vla1b1oa))). Qed. Lemma pdh860: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(p b2 o)->(l a2b2 oa)->(l a1b1 oa)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vpb2o:(p b2 o))(Vla2b2oa:(l a2b2 oa))(Vla1b1oa:(l a1b1 oa))=>(notab (pdh859 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vpb2o Vla2b2oa Vla1b1oa))). Qed. Lemma pdh861: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(p b2 o)->(l a2b2 oa)->(l a1b1 oa)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vpb2o:(p b2 o))(Vla2b2oa:(l a2b2 oa))(Vla1b1oa:(l a1b1 oa))=>((false_ind goal) (pdh860 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vpb2o Vla2b2oa Vla1b1oa))). Qed. Lemma pdh862: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(p b2 o)->(l a2b2 oa)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vpb2o:(p b2 o))(Vla2b2oa:(l a2b2 oa))=>((or_ind ((pdh856 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vpb2o Vla2b2oa))((pdh861 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vpb2o Vla2b2oa)))(pdh853 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vpb2o Vla2b2oa))). Qed. Lemma pdh863: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(p b2 o)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vpb2o:(p b2 o))=>((or_ind ((pdh848 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vpb2o))((pdh862 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vpb2o)))(pdh842 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vpb2o))). Qed. Lemma pdh867: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(l b2c2 ob)->(l C8 ob). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vlb2c2ob:(l b2c2 ob))=>((ltra C8 b2c2 ob) (conj (pdh739 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8) Vlb2c2ob))). Qed. Lemma pdh869: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(l b2c2 ob)->(l oc ob). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vlb2c2ob:(l b2c2 ob))=>((ltra oc b2c2 ob) (conj (pdh811 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc) Vlb2c2ob))). Qed. Lemma pdh870: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(l b2c2 ob)->(l ob oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vlb2c2ob:(l b2c2 ob))=>((lsym oc ob) (pdh869 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vlb2c2ob))). Qed. Lemma pdh875: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(l b2c2 ob)->(i b1 oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vlb2c2ob:(l b2c2 ob))=>((lcon b1 ob oc) (conj pdh18 (pdh870 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vlb2c2ob)))). Qed. Lemma pdh876: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(l b2c2 ob)->(i c1 ob). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vlb2c2ob:(l b2c2 ob))=>((lcon c1 oc ob) (conj pdh20 (pdh869 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vlb2c2ob)))). Qed. Lemma pdh880: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(l b2c2 ob)->(i C7 ob). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vlb2c2ob:(l b2c2 ob))=>((lcon C7 C8 ob) (conj ViC7C8 (pdh867 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vlb2c2ob)))). Qed. Lemma pdh881: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(l b2c2 ob)->(p b1 C7) \/ (l a1b1 ob). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vlb2c2ob:(l b2c2 ob))=>((unique b1 C7 a1b1 ob) (conj pdh2 (conj pdh18 (conj ViC7a1b1 (pdh880 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vlb2c2ob)))))). Qed. Lemma pdh885: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(l b2c2 ob)->(p b1 C7)->(p c1 b1) \/ (l b1c1 oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vlb2c2ob:(l b2c2 ob))(Vpb1C7:(p b1 C7))=>((unique c1 b1 b1c1 oc) (conj pdh9 (conj pdh20 (conj pdh10 (pdh875 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vlb2c2ob)))))). Qed. Lemma pdh897: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(l b2c2 ob)->(p b1 C7)->(p c1 b1)->(i c1 a1b1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vlb2c2ob:(l b2c2 ob))(Vpb1C7:(p b1 C7))(Vpc1b1:(p c1 b1))=>((pcon c1 b1 a1b1) (conj Vpc1b1 pdh2))). Qed. Lemma pdh898: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(l b2c2 ob)->(p b1 C7)->(p c1 b1)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vlb2c2ob:(l b2c2 ob))(Vpb1C7:(p b1 C7))(Vpc1b1:(p c1 b1))=>((triangle1 a1b1) (conj pdh1 (conj pdh2 (pdh897 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vlb2c2ob Vpb1C7 Vpc1b1))))). Qed. Lemma pdh899: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(l b2c2 ob)->(p b1 C7)->(p c1 b1)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vlb2c2ob:(l b2c2 ob))(Vpb1C7:(p b1 C7))(Vpc1b1:(p c1 b1))=>((false_ind goal) (pdh898 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vlb2c2ob Vpb1C7 Vpc1b1))). Qed. Lemma pdh900: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(l b2c2 ob)->(p b1 C7)->(l b1c1 oc)->(l oc b1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vlb2c2ob:(l b2c2 ob))(Vpb1C7:(p b1 C7))(Vlb1c1oc:(l b1c1 oc))=>((lsym b1c1 oc) Vlb1c1oc)). Qed. Lemma pdh901: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(l b2c2 ob)->(p b1 C7)->(l b1c1 oc)->(l b2c2 b1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vlb2c2ob:(l b2c2 ob))(Vpb1C7:(p b1 C7))(Vlb1c1oc:(l b1c1 oc))=>((ltra b2c2 oc b1c1) (conj Vlb2c2oc (pdh900 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vlb2c2ob Vpb1C7 Vlb1c1oc)))). Qed. Lemma pdh902: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(l b2c2 ob)->(p b1 C7)->(l b1c1 oc)->(l b1c1 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vlb2c2ob:(l b2c2 ob))(Vpb1C7:(p b1 C7))(Vlb1c1oc:(l b1c1 oc))=>((lsym b2c2 b1c1) (pdh901 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vlb2c2ob Vpb1C7 Vlb1c1oc))). Qed. Lemma pdh903: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(l b2c2 ob)->(p b1 C7)->(l b1c1 oc)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vlb2c2ob:(l b2c2 ob))(Vpb1C7:(p b1 C7))(Vlb1c1oc:(l b1c1 oc))=>(notbc (pdh902 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vlb2c2ob Vpb1C7 Vlb1c1oc))). Qed. Lemma pdh904: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(l b2c2 ob)->(p b1 C7)->(l b1c1 oc)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vlb2c2ob:(l b2c2 ob))(Vpb1C7:(p b1 C7))(Vlb1c1oc:(l b1c1 oc))=>((false_ind goal) (pdh903 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vlb2c2ob Vpb1C7 Vlb1c1oc))). Qed. Lemma pdh905: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(l b2c2 ob)->(p b1 C7)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vlb2c2ob:(l b2c2 ob))(Vpb1C7:(p b1 C7))=>((or_ind ((pdh899 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vlb2c2ob Vpb1C7))((pdh904 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vlb2c2ob Vpb1C7)))(pdh885 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vlb2c2ob Vpb1C7))). Qed. Lemma pdh915: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(l b2c2 ob)->(l a1b1 ob)->(i a1 ob). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vlb2c2ob:(l b2c2 ob))(Vla1b1ob:(l a1b1 ob))=>((lcon a1 a1b1 ob) (conj pdh1 Vla1b1ob))). Qed. Lemma pdh916: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(l b2c2 ob)->(l a1b1 ob)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vlb2c2ob:(l b2c2 ob))(Vla1b1ob:(l a1b1 ob))=>((triangle1 ob) (conj (pdh915 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vlb2c2ob Vla1b1ob) (conj pdh18 (pdh876 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vlb2c2ob))))). Qed. Lemma pdh917: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(l b2c2 ob)->(l a1b1 ob)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vlb2c2ob:(l b2c2 ob))(Vla1b1ob:(l a1b1 ob))=>((false_ind goal) (pdh916 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vlb2c2ob Vla1b1ob))). Qed. Lemma pdh918: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->(l b2c2 ob)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))(Vlb2c2ob:(l b2c2 ob))=>((or_ind ((pdh905 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vlb2c2ob))((pdh917 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vlb2c2ob)))(pdh881 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc Vlb2c2ob))). Qed. Lemma pdh919: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(p c1 bc)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vpc1bc:(p c1 bc))=>((or_ind ((pdh863 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc))((pdh918 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc)))(pdh836 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vpc1bc))). Qed. Lemma pdh920: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(l b1c1 oc)->(l oc b1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vlb1c1oc:(l b1c1 oc))=>((lsym b1c1 oc) Vlb1c1oc)). Qed. Lemma pdh921: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(l b1c1 oc)->(l b2c2 b1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vlb1c1oc:(l b1c1 oc))=>((ltra b2c2 oc b1c1) (conj Vlb2c2oc (pdh920 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vlb1c1oc)))). Qed. Lemma pdh922: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(l b1c1 oc)->(l b1c1 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vlb1c1oc:(l b1c1 oc))=>((lsym b2c2 b1c1) (pdh921 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vlb1c1oc))). Qed. Lemma pdh923: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(l b1c1 oc)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vlb1c1oc:(l b1c1 oc))=>(notbc (pdh922 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vlb1c1oc))). Qed. Lemma pdh924: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->(l b1c1 oc)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))(Vlb1c1oc:(l b1c1 oc))=>((false_ind goal) (pdh923 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5 Vlb1c1oc))). Qed. Lemma pdh925: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(p c1 C5)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vpc1C5:(p c1 C5))=>((or_ind ((pdh919 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5))((pdh924 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5)))(pdh830 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vpc1C5))). Qed. Lemma pdh926: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(l a1c1 oc)->(l oc a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vla1c1oc:(l a1c1 oc))=>((lsym a1c1 oc) Vla1c1oc)). Qed. Lemma pdh927: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(l a1c1 oc)->(l b2c2 a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vla1c1oc:(l a1c1 oc))=>((ltra b2c2 oc a1c1) (conj Vlb2c2oc (pdh926 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vla1c1oc)))). Qed. Lemma pdh928: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(l a1c1 oc)->(l a1c1 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vla1c1oc:(l a1c1 oc))=>((lsym b2c2 a1c1) (pdh927 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vla1c1oc))). Qed. Lemma pdh934: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(l a1c1 oc)->(i a1 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vla1c1oc:(l a1c1 oc))=>((lcon a1 a1c1 b2c2) (conj pdh5 (pdh928 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vla1c1oc)))). Qed. Lemma pdh935: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->(l a1c1 oc)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))(Vla1c1oc:(l a1c1 oc))=>(hessenberg_gap1 (pdh934 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc Vla1c1oc))). Qed. Lemma pdh936: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->(l b2c2 oc)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))(Vlb2c2oc:(l b2c2 oc))=>((or_ind ((pdh925 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc))((pdh935 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc)))(pdh826 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8 Vlb2c2oc))). Qed. Lemma pdh937: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l b2c2 C8)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vlb2c2C8:(l b2c2 C8))=>((or_ind ((pdh810 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8))((pdh936 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8)))(pdh749 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vlb2c2C8))). Qed. Lemma pdh938: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(l C2 a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))=>((lsym a1c1 C2) Vla1c1C2)). Qed. Lemma pdh941: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(i C1 a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))=>((lcon C1 C2 a1c1) (conj ViC1C2 (pdh938 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2)))). Qed. Lemma pdh942: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(i C3 a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))=>((lcon C3 C2 a1c1) (conj ViC3C2 (pdh938 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2)))). Qed. Lemma pdh944: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1) \/ (l a1c1 C0). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))=>((unique a1 C1 a1c1 C0) (conj pdh5 (conj Via1C0 (conj (pdh941 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2) ViC1C0))))). Qed. Lemma pdh946: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(i a1 oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))=>((pcon a1 C1 oc) (conj Vpa1C1 ViC1oc))). Qed. Lemma pdh947: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(i a1 C8). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))=>((pcon a1 C1 C8) (conj Vpa1C1 ViC1C8))). Qed. Lemma pdh950: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7) \/ (l a1b1 C8). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))=>((unique a1 C7 a1b1 C8) (conj pdh1 (conj (pdh947 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1) (conj ViC7a1b1 ViC7C8))))). Qed. Lemma pdh954: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(i a1 C4). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))=>((pcon a1 C7 C4) (conj Vpa1C7 ViC7C4))). Qed. Lemma pdh961: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(p a1 c1) \/ (l a1c1 oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))=>((unique a1 c1 a1c1 oc) (conj pdh5 (conj (pdh946 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1) (conj pdh6 pdh20))))). Qed. Lemma pdh967: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(p a1 c1)->(i a1 b1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vpa1c1:(p a1 c1))=>((pcon a1 c1 b1c1) (conj Vpa1c1 pdh9))). Qed. Lemma pdh968: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(p a1 c1)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vpa1c1:(p a1 c1))=>((triangle1 b1c1) (conj (pdh967 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vpa1c1) (conj pdh10 pdh9)))). Qed. Lemma pdh969: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(p a1 c1)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vpa1c1:(p a1 c1))=>((false_ind goal) (pdh968 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vpa1c1))). Qed. Lemma pdh970: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(l oc a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))=>((lsym a1c1 oc) Vla1c1oc)). Qed. Lemma pdh973: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(i o a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))=>((lcon o oc a1c1) (conj pdh15 (pdh970 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc)))). Qed. Lemma pdh977: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(i ac oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))=>((lcon ac a1c1 oc) (conj pdh24 Vla1c1oc))). Qed. Lemma pdh980: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o) \/ (l a1c1 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))=>((unique a1 o a1c1 oa) (conj pdh5 (conj pdh16 (conj (pdh973 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc) pdh13))))). Qed. Lemma pdh986: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(i a1 ob). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))=>((pcon a1 o ob) (conj Vpa1o pdh14))). Qed. Lemma pdh992: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(p a1 b1) \/ (l a1b1 ob). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))=>((unique a1 b1 a1b1 ob) (conj pdh1 (conj (pdh986 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o) (conj pdh2 pdh18))))). Qed. Lemma pdh1000: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(p a1 b1)->(i a1 b1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vpa1b1:(p a1 b1))=>((pcon a1 b1 b1c1) (conj Vpa1b1 pdh10))). Qed. Lemma pdh1001: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(p a1 b1)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vpa1b1:(p a1 b1))=>((triangle1 b1c1) (conj (pdh1000 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o Vpa1b1) (conj pdh10 pdh9)))). Qed. Lemma pdh1002: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(p a1 b1)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vpa1b1:(p a1 b1))=>((false_ind goal) (pdh1001 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o Vpa1b1))). Qed. Lemma pdh1003: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l ob a1b1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))=>((lsym a1b1 ob) Vla1b1ob)). Qed. Lemma pdh1004: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(i b2 a1b1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))=>((lcon b2 ob a1b1) (conj pdh19 (pdh1003 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o Vla1b1ob)))). Qed. Lemma pdh1005: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(i ab ob). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))=>((lcon ab a1b1 ob) (conj pdh26 Vla1b1ob))). Qed. Lemma pdh1006: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(p a1 b2) \/ (l a1b1 C0). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))=>((unique a1 b2 a1b1 C0) (conj pdh1 (conj Via1C0 (conj (pdh1004 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o Vla1b1ob) Vib2C0))))). Qed. Lemma pdh1018: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(p a1 b2)->(i a1 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vpa1b2:(p a1 b2))=>((pcon a1 b2 b2c2) (conj Vpa1b2 pdh12))). Qed. Lemma pdh1019: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(p a1 b2)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vpa1b2:(p a1 b2))=>(hessenberg_gap1 (pdh1018 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o Vla1b1ob Vpa1b2))). Qed. Lemma pdh1025: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p b2 ab) \/ (l a2b2 ob). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))=>((unique b2 ab a2b2 ob) (conj pdh4 (conj pdh19 (conj pdh27 (pdh1005 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o Vla1b1ob)))))). Qed. Lemma pdh1026: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p b2 ab)->(p ab b2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpb2ab:(p b2 ab))=>((psym b2 ab) Vpb2ab)). Qed. Lemma pdh1027: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p b2 ab)->(i ab b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpb2ab:(p b2 ab))=>((pcon ab b2 b2c2) (conj (pdh1026 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vpb2ab) pdh12))). Qed. Lemma pdh1029: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p b2 ab)->(p a1 C5) \/ (l a1c1 C4). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpb2ab:(p b2 ab))=>((unique a1 C5 a1c1 C4) (conj pdh5 (conj (pdh954 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7) (conj ViC5a1c1 ViC5C4))))). Qed. Lemma pdh1041: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p b2 ab)->(p a1 C5)->(i a1 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpb2ab:(p b2 ab))(Vpa1C5:(p a1 C5))=>((pcon a1 C5 b2c2) (conj Vpa1C5 (pdh688 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6)))). Qed. Lemma pdh1042: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p b2 ab)->(p a1 C5)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpb2ab:(p b2 ab))(Vpa1C5:(p a1 C5))=>(hessenberg_gap1 (pdh1041 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vpb2ab Vpa1C5))). Qed. Lemma pdh1051: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p b2 ab)->(l a1c1 C4)->(p c2 ac) \/ (l a2c2 oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpb2ab:(p b2 ab))(Vla1c1C4:(l a1c1 C4))=>((unique c2 ac a2c2 oc) (conj pdh8 (conj pdh21 (conj pdh25 (pdh977 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc)))))). Qed. Lemma pdh1052: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p b2 ab)->(l a1c1 C4)->(p c2 ac)->(p ac c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpb2ab:(p b2 ab))(Vla1c1C4:(l a1c1 C4))(Vpc2ac:(p c2 ac))=>((psym c2 ac) Vpc2ac)). Qed. Lemma pdh1053: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p b2 ab)->(l a1c1 C4)->(p c2 ac)->(i ac b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpb2ab:(p b2 ab))(Vla1c1C4:(l a1c1 C4))(Vpc2ac:(p c2 ac))=>((pcon ac c2 b2c2) (conj (pdh1052 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vpb2ab Vla1c1C4 Vpc2ac) pdh11))). Qed. Lemma pdh1054: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p b2 ab)->(l a1c1 C4)->(p c2 ac)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpb2ab:(p b2 ab))(Vla1c1C4:(l a1c1 C4))(Vpc2ac:(p c2 ac))=>((goal_normal b2c2) (conj pdh43 (conj pdh23 (conj (pdh1053 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vpb2ab Vla1c1C4 Vpc2ac) (pdh1027 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vpb2ab)))))). Qed. Lemma pdh1055: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p b2 ab)->(l a1c1 C4)->(l a2c2 oc)->(l oc a2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpb2ab:(p b2 ab))(Vla1c1C4:(l a1c1 C4))(Vla2c2oc:(l a2c2 oc))=>((lsym a2c2 oc) Vla2c2oc)). Qed. Lemma pdh1056: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p b2 ab)->(l a1c1 C4)->(l a2c2 oc)->(l a1c1 a2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpb2ab:(p b2 ab))(Vla1c1C4:(l a1c1 C4))(Vla2c2oc:(l a2c2 oc))=>((ltra a1c1 oc a2c2) (conj Vla1c1oc (pdh1055 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vpb2ab Vla1c1C4 Vla2c2oc)))). Qed. Lemma pdh1057: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p b2 ab)->(l a1c1 C4)->(l a2c2 oc)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpb2ab:(p b2 ab))(Vla1c1C4:(l a1c1 C4))(Vla2c2oc:(l a2c2 oc))=>(notac (pdh1056 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vpb2ab Vla1c1C4 Vla2c2oc))). Qed. Lemma pdh1058: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p b2 ab)->(l a1c1 C4)->(l a2c2 oc)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpb2ab:(p b2 ab))(Vla1c1C4:(l a1c1 C4))(Vla2c2oc:(l a2c2 oc))=>((false_ind goal) (pdh1057 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vpb2ab Vla1c1C4 Vla2c2oc))). Qed. Lemma pdh1059: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p b2 ab)->(l a1c1 C4)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpb2ab:(p b2 ab))(Vla1c1C4:(l a1c1 C4))=>((or_ind ((pdh1054 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vpb2ab Vla1c1C4))((pdh1058 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vpb2ab Vla1c1C4)))(pdh1051 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vpb2ab Vla1c1C4))). Qed. Lemma pdh1060: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p b2 ab)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpb2ab:(p b2 ab))=>((or_ind ((pdh1042 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vpb2ab))((pdh1059 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vpb2ab)))(pdh1029 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vpb2ab))). Qed. Lemma pdh1061: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(l a2b2 ob)->(l ob a2b2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vla2b2ob:(l a2b2 ob))=>((lsym a2b2 ob) Vla2b2ob)). Qed. Lemma pdh1062: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(l a2b2 ob)->(l a1b1 a2b2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vla2b2ob:(l a2b2 ob))=>((ltra a1b1 ob a2b2) (conj Vla1b1ob (pdh1061 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vla2b2ob)))). Qed. Lemma pdh1063: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(l a2b2 ob)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vla2b2ob:(l a2b2 ob))=>(notab (pdh1062 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vla2b2ob))). Qed. Lemma pdh1064: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(l a2b2 ob)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vla2b2ob:(l a2b2 ob))=>((false_ind goal) (pdh1063 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vla2b2ob))). Qed. Lemma pdh1065: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))=>((or_ind ((pdh1060 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0))((pdh1064 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0)))(pdh1025 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0))). Qed. Lemma pdh1066: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))=>((or_ind ((pdh1019 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o Vla1b1ob))((pdh1065 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o Vla1b1ob)))(pdh1006 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o Vla1b1ob))). Qed. Lemma pdh1067: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(p a1 o)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))=>((or_ind ((pdh1002 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o))((pdh1066 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o)))(pdh992 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vpa1o))). Qed. Lemma pdh1069: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(l a1c1 oa)->(l C2 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))=>((ltra C2 a1c1 oa) (conj (pdh938 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2) Vla1c1oa))). Qed. Lemma pdh1071: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(l a1c1 oa)->(l oc oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))=>((ltra oc a1c1 oa) (conj (pdh970 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc) Vla1c1oa))). Qed. Lemma pdh1077: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(l a1c1 oa)->(i c2 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))=>((lcon c2 oc oa) (conj pdh21 (pdh1071 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vla1c1oa)))). Qed. Lemma pdh1079: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(l a1c1 oa)->(i C3 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))=>((lcon C3 C2 oa) (conj ViC3C2 (pdh1069 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vla1c1oa)))). Qed. Lemma pdh1081: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(l a1c1 oa)->(p a2 C3) \/ (l a2b2 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))=>((unique a2 C3 a2b2 oa) (conj pdh3 (conj pdh17 (conj ViC3a2b2 (pdh1079 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vla1c1oa)))))). Qed. Lemma pdh1085: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(l a1c1 oa)->(p a2 C3)->(p a1 C5) \/ (l a1c1 C4). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))=>((unique a1 C5 a1c1 C4) (conj pdh5 (conj (pdh954 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7) (conj ViC5a1c1 ViC5C4))))). Qed. Lemma pdh1094: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(l a1c1 oa)->(p a2 C3)->(p a1 C5)->(i a1 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vpa1C5:(p a1 C5))=>((pcon a1 C5 b2c2) (conj Vpa1C5 (pdh688 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6)))). Qed. Lemma pdh1095: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(l a1c1 oa)->(p a2 C3)->(p a1 C5)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vpa1C5:(p a1 C5))=>(hessenberg_gap1 (pdh1094 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vla1c1oa Vpa2C3 Vpa1C5))). Qed. Lemma pdh1106: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(l a1c1 oa)->(p a2 C3)->(l a1c1 C4)->(p a2 c2) \/ (l a2c2 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1C4:(l a1c1 C4))=>((unique a2 c2 a2c2 oa) (conj pdh7 (conj pdh17 (conj pdh8 (pdh1077 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vla1c1oa)))))). Qed. Lemma pdh1110: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(l a1c1 oa)->(p a2 C3)->(l a1c1 C4)->(p a2 c2)->(i a2 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1C4:(l a1c1 C4))(Vpa2c2:(p a2 c2))=>((pcon a2 c2 b2c2) (conj Vpa2c2 pdh11))). Qed. Lemma pdh1111: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(l a1c1 oa)->(p a2 C3)->(l a1c1 C4)->(p a2 c2)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1C4:(l a1c1 C4))(Vpa2c2:(p a2 c2))=>((triangle2 b2c2) (conj (pdh1110 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vla1c1oa Vpa2C3 Vla1c1C4 Vpa2c2) (conj pdh12 pdh11)))). Qed. Lemma pdh1112: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(l a1c1 oa)->(p a2 C3)->(l a1c1 C4)->(p a2 c2)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1C4:(l a1c1 C4))(Vpa2c2:(p a2 c2))=>((false_ind goal) (pdh1111 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vla1c1oa Vpa2C3 Vla1c1C4 Vpa2c2))). Qed. Lemma pdh1113: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(l a1c1 oa)->(p a2 C3)->(l a1c1 C4)->(l a2c2 oa)->(l oa a2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1C4:(l a1c1 C4))(Vla2c2oa:(l a2c2 oa))=>((lsym a2c2 oa) Vla2c2oa)). Qed. Lemma pdh1114: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(l a1c1 oa)->(p a2 C3)->(l a1c1 C4)->(l a2c2 oa)->(l a1c1 a2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1C4:(l a1c1 C4))(Vla2c2oa:(l a2c2 oa))=>((ltra a1c1 oa a2c2) (conj Vla1c1oa (pdh1113 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vla1c1oa Vpa2C3 Vla1c1C4 Vla2c2oa)))). Qed. Lemma pdh1115: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(l a1c1 oa)->(p a2 C3)->(l a1c1 C4)->(l a2c2 oa)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1C4:(l a1c1 C4))(Vla2c2oa:(l a2c2 oa))=>(notac (pdh1114 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vla1c1oa Vpa2C3 Vla1c1C4 Vla2c2oa))). Qed. Lemma pdh1116: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(l a1c1 oa)->(p a2 C3)->(l a1c1 C4)->(l a2c2 oa)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1C4:(l a1c1 C4))(Vla2c2oa:(l a2c2 oa))=>((false_ind goal) (pdh1115 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vla1c1oa Vpa2C3 Vla1c1C4 Vla2c2oa))). Qed. Lemma pdh1117: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(l a1c1 oa)->(p a2 C3)->(l a1c1 C4)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla1c1C4:(l a1c1 C4))=>((or_ind ((pdh1112 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vla1c1oa Vpa2C3 Vla1c1C4))((pdh1116 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vla1c1oa Vpa2C3 Vla1c1C4)))(pdh1106 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vla1c1oa Vpa2C3 Vla1c1C4))). Qed. Lemma pdh1118: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(l a1c1 oa)->(p a2 C3)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))=>((or_ind ((pdh1095 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vla1c1oa Vpa2C3))((pdh1117 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vla1c1oa Vpa2C3)))(pdh1085 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vla1c1oa Vpa2C3))). Qed. Lemma pdh1126: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(l a1c1 oa)->(l a2b2 oa)->(i b2 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vla2b2oa:(l a2b2 oa))=>((lcon b2 a2b2 oa) (conj pdh4 Vla2b2oa))). Qed. Lemma pdh1127: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(l a1c1 oa)->(l a2b2 oa)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vla2b2oa:(l a2b2 oa))=>((triangle2 oa) (conj pdh17 (conj (pdh1126 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vla1c1oa Vla2b2oa) (pdh1077 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vla1c1oa))))). Qed. Lemma pdh1128: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(l a1c1 oa)->(l a2b2 oa)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vla2b2oa:(l a2b2 oa))=>((false_ind goal) (pdh1127 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vla1c1oa Vla2b2oa))). Qed. Lemma pdh1129: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->(l a1c1 oa)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))=>((or_ind ((pdh1118 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vla1c1oa))((pdh1128 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vla1c1oa)))(pdh1081 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc Vla1c1oa))). Qed. Lemma pdh1130: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->(l a1c1 oc)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))(Vla1c1oc:(l a1c1 oc))=>((or_ind ((pdh1067 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc))((pdh1129 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc)))(pdh980 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7 Vla1c1oc))). Qed. Lemma pdh1131: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(p a1 C7)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vpa1C7:(p a1 C7))=>((or_ind ((pdh969 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7))((pdh1130 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7)))(pdh961 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vpa1C7))). Qed. Lemma pdh1132: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(l C8 a1b1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))=>((lsym a1b1 C8) Vla1b1C8)). Qed. Lemma pdh1135: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(i bc a1b1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))=>((lcon bc C8 a1b1) (conj VibcC8 (pdh1132 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8)))). Qed. Lemma pdh1136: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc) \/ (l a1b1 b1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))=>((unique b1 bc a1b1 b1c1) (conj pdh2 (conj pdh10 (conj (pdh1135 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8) pdh22))))). Qed. Lemma pdh1138: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(i b1 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))=>((pcon b1 bc b2c2) (conj Vpb1bc pdh23))). Qed. Lemma pdh1141: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(p a1 c1) \/ (l a1c1 oc). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))=>((unique a1 c1 a1c1 oc) (conj pdh5 (conj (pdh946 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1) (conj pdh6 pdh20))))). Qed. Lemma pdh1145: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(p a1 c1)->(i a1 b1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vpa1c1:(p a1 c1))=>((pcon a1 c1 b1c1) (conj Vpa1c1 pdh9))). Qed. Lemma pdh1146: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(p a1 c1)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vpa1c1:(p a1 c1))=>((triangle1 b1c1) (conj (pdh1145 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vpa1c1) (conj pdh10 pdh9)))). Qed. Lemma pdh1147: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(p a1 c1)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vpa1c1:(p a1 c1))=>((false_ind goal) (pdh1146 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vpa1c1))). Qed. Lemma pdh1148: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(l oc a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))=>((lsym a1c1 oc) Vla1c1oc)). Qed. Lemma pdh1151: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(i o a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))=>((lcon o oc a1c1) (conj pdh15 (pdh1148 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc)))). Qed. Lemma pdh1158: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o) \/ (l a1c1 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))=>((unique a1 o a1c1 oa) (conj pdh5 (conj pdh16 (conj (pdh1151 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc) pdh13))))). Qed. Lemma pdh1162: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(i a1 ob). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))=>((pcon a1 o ob) (conj Vpa1o pdh14))). Qed. Lemma pdh1164: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(i a1 C4). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))=>((pcon a1 o C4) (conj Vpa1o VioC4))). Qed. Lemma pdh1169: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(p a1 b1) \/ (l a1b1 ob). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))=>((unique a1 b1 a1b1 ob) (conj pdh1 (conj (pdh1162 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o) (conj pdh2 pdh18))))). Qed. Lemma pdh1181: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(p a1 b1)->(i a1 b1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vpa1b1:(p a1 b1))=>((pcon a1 b1 b1c1) (conj Vpa1b1 pdh10))). Qed. Lemma pdh1182: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(p a1 b1)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vpa1b1:(p a1 b1))=>((triangle1 b1c1) (conj (pdh1181 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vpa1b1) (conj pdh10 pdh9)))). Qed. Lemma pdh1183: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(p a1 b1)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vpa1b1:(p a1 b1))=>((false_ind goal) (pdh1182 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vpa1b1))). Qed. Lemma pdh1184: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l ob a1b1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))=>((lsym a1b1 ob) Vla1b1ob)). Qed. Lemma pdh1187: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(i b2 a1b1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))=>((lcon b2 ob a1b1) (conj pdh19 (pdh1184 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vla1b1ob)))). Qed. Lemma pdh1191: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(p a1 b2) \/ (l a1b1 C0). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))=>((unique a1 b2 a1b1 C0) (conj pdh1 (conj Via1C0 (conj (pdh1187 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vla1b1ob) Vib2C0))))). Qed. Lemma pdh1200: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(p a1 b2)->(i a1 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vpa1b2:(p a1 b2))=>((pcon a1 b2 b2c2) (conj Vpa1b2 pdh12))). Qed. Lemma pdh1201: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(p a1 b2)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vpa1b2:(p a1 b2))=>(hessenberg_gap1 (pdh1200 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vla1b1ob Vpa1b2))). Qed. Lemma pdh1211: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C7) \/ (l a1b1 C4). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))=>((unique a1 C7 a1b1 C4) (conj pdh1 (conj (pdh1164 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o) (conj ViC7a1b1 ViC7C4))))). Qed. Lemma pdh1221: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C7)->(p b1 b2) \/ (l a1b1 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C7:(p a1 C7))=>((unique b1 b2 a1b1 b2c2) (conj pdh2 (conj (pdh1138 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc) (conj (pdh1187 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vla1b1ob) pdh12))))). Qed. Lemma pdh1222: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C7)->(p b1 b2)->(p b2 b1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C7:(p a1 C7))(Vpb1b2:(p b1 b2))=>((psym b1 b2) Vpb1b2)). Qed. Lemma pdh1223: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C7)->(p b1 b2)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C7:(p a1 C7))(Vpb1b2:(p b1 b2))=>(notbb (pdh1222 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vpa1C7 Vpb1b2))). Qed. Lemma pdh1224: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C7)->(p b1 b2)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C7:(p a1 C7))(Vpb1b2:(p b1 b2))=>((false_ind goal) (pdh1223 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vpa1C7 Vpb1b2))). Qed. Lemma pdh1240: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C7)->(l a1b1 b2c2)->(i a1 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C7:(p a1 C7))(Vla1b1b2c2:(l a1b1 b2c2))=>((lcon a1 a1b1 b2c2) (conj pdh1 Vla1b1b2c2))). Qed. Lemma pdh1241: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C7)->(l a1b1 b2c2)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C7:(p a1 C7))(Vla1b1b2c2:(l a1b1 b2c2))=>(hessenberg_gap1 (pdh1240 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vpa1C7 Vla1b1b2c2))). Qed. Lemma pdh1242: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(p a1 C7)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vpa1C7:(p a1 C7))=>((or_ind ((pdh1224 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vpa1C7))((pdh1241 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vpa1C7)))(pdh1221 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vpa1C7))). Qed. Lemma pdh1243: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(l a1b1 C4)->(l C4 a1b1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vla1b1C4:(l a1b1 C4))=>((lsym a1b1 C4) Vla1b1C4)). Qed. Lemma pdh1254: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(l a1b1 C4)->(i C3 a1b1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vla1b1C4:(l a1b1 C4))=>((lcon C3 C4 a1b1) (conj ViC3C4 (pdh1243 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vla1b1C4)))). Qed. Lemma pdh1258: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(l a1b1 C4)->(i C5 a1b1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vla1b1C4:(l a1b1 C4))=>((lcon C5 C4 a1b1) (conj ViC5C4 (pdh1243 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vla1b1C4)))). Qed. Lemma pdh1262: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(l a1b1 C4)->(p a1 C3) \/ (l a1b1 a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vla1b1C4:(l a1b1 C4))=>((unique a1 C3 a1b1 a1c1) (conj pdh1 (conj pdh5 (conj (pdh1254 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vla1b1C4) (pdh942 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2)))))). Qed. Lemma pdh1272: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(l a1b1 C4)->(p a1 C3)->(p a1 C5) \/ (l a1b1 a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vla1b1C4:(l a1b1 C4))(Vpa1C3:(p a1 C3))=>((unique a1 C5 a1b1 a1c1) (conj pdh1 (conj pdh5 (conj (pdh1258 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vla1b1C4) ViC5a1c1))))). Qed. Lemma pdh1284: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(l a1b1 C4)->(p a1 C3)->(p a1 C5)->(i a1 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vla1b1C4:(l a1b1 C4))(Vpa1C3:(p a1 C3))(Vpa1C5:(p a1 C5))=>((pcon a1 C5 b2c2) (conj Vpa1C5 (pdh688 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6)))). Qed. Lemma pdh1285: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(l a1b1 C4)->(p a1 C3)->(p a1 C5)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vla1b1C4:(l a1b1 C4))(Vpa1C3:(p a1 C3))(Vpa1C5:(p a1 C5))=>(hessenberg_gap1 (pdh1284 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vla1b1C4 Vpa1C3 Vpa1C5))). Qed. Lemma pdh1315: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(l a1b1 C4)->(p a1 C3)->(l a1b1 a1c1)->(i b1 a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vla1b1C4:(l a1b1 C4))(Vpa1C3:(p a1 C3))(Vla1b1a1c1:(l a1b1 a1c1))=>((lcon b1 a1b1 a1c1) (conj pdh2 Vla1b1a1c1))). Qed. Lemma pdh1316: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(l a1b1 C4)->(p a1 C3)->(l a1b1 a1c1)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vla1b1C4:(l a1b1 C4))(Vpa1C3:(p a1 C3))(Vla1b1a1c1:(l a1b1 a1c1))=>((triangle1 a1c1) (conj pdh5 (conj (pdh1315 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vla1b1C4 Vpa1C3 Vla1b1a1c1) pdh6)))). Qed. Lemma pdh1317: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(l a1b1 C4)->(p a1 C3)->(l a1b1 a1c1)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vla1b1C4:(l a1b1 C4))(Vpa1C3:(p a1 C3))(Vla1b1a1c1:(l a1b1 a1c1))=>((false_ind goal) (pdh1316 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vla1b1C4 Vpa1C3 Vla1b1a1c1))). Qed. Lemma pdh1318: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(l a1b1 C4)->(p a1 C3)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vla1b1C4:(l a1b1 C4))(Vpa1C3:(p a1 C3))=>((or_ind ((pdh1285 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vla1b1C4 Vpa1C3))((pdh1317 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vla1b1C4 Vpa1C3)))(pdh1272 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vla1b1C4 Vpa1C3))). Qed. Lemma pdh1348: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(l a1b1 C4)->(l a1b1 a1c1)->(i b1 a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vla1b1C4:(l a1b1 C4))(Vla1b1a1c1:(l a1b1 a1c1))=>((lcon b1 a1b1 a1c1) (conj pdh2 Vla1b1a1c1))). Qed. Lemma pdh1349: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(l a1b1 C4)->(l a1b1 a1c1)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vla1b1C4:(l a1b1 C4))(Vla1b1a1c1:(l a1b1 a1c1))=>((triangle1 a1c1) (conj pdh5 (conj (pdh1348 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vla1b1C4 Vla1b1a1c1) pdh6)))). Qed. Lemma pdh1350: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(l a1b1 C4)->(l a1b1 a1c1)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vla1b1C4:(l a1b1 C4))(Vla1b1a1c1:(l a1b1 a1c1))=>((false_ind goal) (pdh1349 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vla1b1C4 Vla1b1a1c1))). Qed. Lemma pdh1351: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->(l a1b1 C4)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))(Vla1b1C4:(l a1b1 C4))=>((or_ind ((pdh1318 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vla1b1C4))((pdh1350 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vla1b1C4)))(pdh1262 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0 Vla1b1C4))). Qed. Lemma pdh1352: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->(l a1b1 C0)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))(Vla1b1C0:(l a1b1 C0))=>((or_ind ((pdh1242 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0))((pdh1351 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0)))(pdh1211 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vla1b1ob Vla1b1C0))). Qed. Lemma pdh1353: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->(l a1b1 ob)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vla1b1ob:(l a1b1 ob))=>((or_ind ((pdh1201 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vla1b1ob))((pdh1352 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vla1b1ob)))(pdh1191 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o Vla1b1ob))). Qed. Lemma pdh1354: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(p a1 o)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))=>((or_ind ((pdh1183 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o))((pdh1353 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o)))(pdh1169 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vpa1o))). Qed. Lemma pdh1356: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(l a1c1 oa)->(l C2 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))=>((ltra C2 a1c1 oa) (conj (pdh938 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2) Vla1c1oa))). Qed. Lemma pdh1358: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(l a1c1 oa)->(l oc oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))=>((ltra oc a1c1 oa) (conj (pdh1148 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc) Vla1c1oa))). Qed. Lemma pdh1364: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(l a1c1 oa)->(i c2 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))=>((lcon c2 oc oa) (conj pdh21 (pdh1358 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vla1c1oa)))). Qed. Lemma pdh1366: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(l a1c1 oa)->(i C3 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))=>((lcon C3 C2 oa) (conj ViC3C2 (pdh1356 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vla1c1oa)))). Qed. Lemma pdh1368: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(l a1c1 oa)->(p a2 C3) \/ (l a2b2 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))=>((unique a2 C3 a2b2 oa) (conj pdh3 (conj pdh17 (conj ViC3a2b2 (pdh1366 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vla1c1oa)))))). Qed. Lemma pdh1372: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(l a1c1 oa)->(p a2 C3)->(p a2 c2) \/ (l a2c2 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))=>((unique a2 c2 a2c2 oa) (conj pdh7 (conj pdh17 (conj pdh8 (pdh1364 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vla1c1oa)))))). Qed. Lemma pdh1376: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(l a1c1 oa)->(p a2 C3)->(p a2 c2)->(i a2 b2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vpa2c2:(p a2 c2))=>((pcon a2 c2 b2c2) (conj Vpa2c2 pdh11))). Qed. Lemma pdh1377: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(l a1c1 oa)->(p a2 C3)->(p a2 c2)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vpa2c2:(p a2 c2))=>((triangle2 b2c2) (conj (pdh1376 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vla1c1oa Vpa2C3 Vpa2c2) (conj pdh12 pdh11)))). Qed. Lemma pdh1378: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(l a1c1 oa)->(p a2 C3)->(p a2 c2)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vpa2c2:(p a2 c2))=>((false_ind goal) (pdh1377 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vla1c1oa Vpa2C3 Vpa2c2))). Qed. Lemma pdh1379: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(l a1c1 oa)->(p a2 C3)->(l a2c2 oa)->(l oa a2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla2c2oa:(l a2c2 oa))=>((lsym a2c2 oa) Vla2c2oa)). Qed. Lemma pdh1380: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(l a1c1 oa)->(p a2 C3)->(l a2c2 oa)->(l a1c1 a2c2). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla2c2oa:(l a2c2 oa))=>((ltra a1c1 oa a2c2) (conj Vla1c1oa (pdh1379 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vla1c1oa Vpa2C3 Vla2c2oa)))). Qed. Lemma pdh1381: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(l a1c1 oa)->(p a2 C3)->(l a2c2 oa)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla2c2oa:(l a2c2 oa))=>(notac (pdh1380 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vla1c1oa Vpa2C3 Vla2c2oa))). Qed. Lemma pdh1382: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(l a1c1 oa)->(p a2 C3)->(l a2c2 oa)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))(Vla2c2oa:(l a2c2 oa))=>((false_ind goal) (pdh1381 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vla1c1oa Vpa2C3 Vla2c2oa))). Qed. Lemma pdh1383: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(l a1c1 oa)->(p a2 C3)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpa2C3:(p a2 C3))=>((or_ind ((pdh1378 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vla1c1oa Vpa2C3))((pdh1382 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vla1c1oa Vpa2C3)))(pdh1372 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vla1c1oa Vpa2C3))). Qed. Lemma pdh1391: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(l a1c1 oa)->(l a2b2 oa)->(i b2 oa). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vla2b2oa:(l a2b2 oa))=>((lcon b2 a2b2 oa) (conj pdh4 Vla2b2oa))). Qed. Lemma pdh1392: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(l a1c1 oa)->(l a2b2 oa)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vla2b2oa:(l a2b2 oa))=>((triangle2 oa) (conj pdh17 (conj (pdh1391 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vla1c1oa Vla2b2oa) (pdh1364 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vla1c1oa))))). Qed. Lemma pdh1393: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(l a1c1 oa)->(l a2b2 oa)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vla2b2oa:(l a2b2 oa))=>((false_ind goal) (pdh1392 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vla1c1oa Vla2b2oa))). Qed. Lemma pdh1394: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->(l a1c1 oa)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))=>((or_ind ((pdh1383 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vla1c1oa))((pdh1393 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vla1c1oa)))(pdh1368 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc Vla1c1oa))). Qed. Lemma pdh1395: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->(l a1c1 oc)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))(Vla1c1oc:(l a1c1 oc))=>((or_ind ((pdh1354 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc))((pdh1394 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc)))(pdh1158 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc Vla1c1oc))). Qed. Lemma pdh1396: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(p b1 bc)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vpb1bc:(p b1 bc))=>((or_ind ((pdh1147 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc))((pdh1395 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc)))(pdh1141 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vpb1bc))). Qed. Lemma pdh1400: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(l a1b1 b1c1)->(i a1 b1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vla1b1b1c1:(l a1b1 b1c1))=>((lcon a1 a1b1 b1c1) (conj pdh1 Vla1b1b1c1))). Qed. Lemma pdh1401: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(l a1b1 b1c1)->false. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vla1b1b1c1:(l a1b1 b1c1))=>((triangle1 b1c1) (conj (pdh1400 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vla1b1b1c1) (conj pdh10 pdh9)))). Qed. Lemma pdh1402: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->(l a1b1 b1c1)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))(Vla1b1b1c1:(l a1b1 b1c1))=>((false_ind goal) (pdh1401 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8 Vla1b1b1c1))). Qed. Lemma pdh1403: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->(l a1b1 C8)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))(Vla1b1C8:(l a1b1 C8))=>((or_ind ((pdh1396 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8))((pdh1402 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8)))(pdh1136 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1 Vla1b1C8))). Qed. Lemma pdh1404: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(p a1 C1)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vpa1C1:(p a1 C1))=>((or_ind ((pdh1131 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1))((pdh1403 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1)))(pdh950 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vpa1C1))). Qed. Lemma pdh1405: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(l a1c1 C0)->(l C0 a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vla1c1C0:(l a1c1 C0))=>((lsym a1c1 C0) Vla1c1C0)). Qed. Lemma pdh1410: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(l a1c1 C0)->(i b2 a1c1). Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vla1c1C0:(l a1c1 C0))=>((lcon b2 C0 a1c1) (conj Vib2C0 (pdh1405 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vla1c1C0)))). Qed. Lemma pdh1411: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->(l a1c1 C0)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))(Vla1c1C0:(l a1c1 C0))=>(hessenberg_gap2 (pdh1410 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2 Vla1c1C0))). Qed. Lemma pdh1412: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->(l a1c1 C2)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(Vla1c1C2:(l a1c1 C2))=>((or_ind ((pdh1404 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2))((pdh1411 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2)))(pdh944 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 Vla1c1C2))). Qed. Lemma pdh1413: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->forall C9:dom,(l C9 C9)->(i ab C9)->(i bc C9)->(i ac C9)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))(C9:dom)(VlC9C9:(l C9 C9))(ViabC9:(i ab C9))(VibcC9:(i bc C9))(ViacC9:(i ac C9))=>((goal_normal C9) (conj VlC9C9 (conj VibcC9 (conj ViacC9 ViabC9))))). Qed. Lemma pdh1414: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->forall C8:dom,(l C8 C8)->(i C1 C8)->(i C7 C8)->(i bc C8)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))(C8:dom)(VlC8C8:(l C8 C8))(ViC1C8:(i C1 C8))(ViC7C8:(i C7 C8))(VibcC8:(i bc C8))=>((or_ind ((pdh738 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8))(or_ind ((pdh937 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8))(or_ind ((pdh1412 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8))(ex_ind (P:=fun C9:dom=>(l C9 C9)/\(i ab C9)/\(i bc C9)/\(i ac C9))(fun C9:dom=>(and_ind (fun VlC9C9:(l C9 C9)=>(and_ind (fun ViabC9:(i ab C9)=>(and_ind (pdh1413 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8 C9 VlC9C9 ViabC9)))))))))))(pdh735 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8 ViC7C8 VibcC8))). Qed. Lemma pdh1415: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->forall C7:dom,(i C7 C4)->(i C7 a1b1)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))(C7:dom)(ViC7C4:(i C7 C4))(ViC7a1b1:(i C7 a1b1))=>((or_ind ((pdh712 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1))(or_ind ((pdh731 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1))(or_ind ((pdh734 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1))(ex_ind (P:=fun C8:dom=>(l C8 C8)/\(i C1 C8)/\(i C7 C8)/\(i bc C8))(fun C8:dom=>(and_ind (fun VlC8C8:(l C8 C8)=>(and_ind (fun ViC1C8:(i C1 C8)=>(and_ind (pdh1414 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1 C8 VlC8C8 ViC1C8)))))))))))(pdh691 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7 ViC7C4 ViC7a1b1))). Qed. Lemma pdh1416: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->(l b2c2 C6)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))(Vlb2c2C6:(l b2c2 C6))=>((ex_ind (P:=fun C7:dom=>(i C7 C4)/\(i C7 a1b1))(fun C7:dom=>(and_ind (pdh1415 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6 C7))))(pdh689 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6 Vlb2c2C6))). Qed. Lemma pdh1417: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->forall C6:dom,(l C6 C6)->(i b2 C6)->(i c2 C6)->(i C5 C6)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))(C6:dom)(VlC6C6:(l C6 C6))(Vib2C6:(i b2 C6))(Vic2C6:(i c2 C6))(ViC5C6:(i C5 C6))=>((or_ind ((pdh685 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6))((pdh1416 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6)))(pdh681 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6 Vic2C6 ViC5C6))). Qed. Lemma pdh1418: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->forall C5:dom,(i C5 C4)->(i C5 a1c1)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))(C5:dom)(ViC5C4:(i C5 C4))(ViC5a1c1:(i C5 a1c1))=>((or_ind ((pdh286 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1))(or_ind ((pdh352 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1))(or_ind ((pdh680 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1))(ex_ind (P:=fun C6:dom=>(l C6 C6)/\(i b2 C6)/\(i c2 C6)/\(i C5 C6))(fun C6:dom=>(and_ind (fun VlC6C6:(l C6 C6)=>(and_ind (fun Vib2C6:(i b2 C6)=>(and_ind (pdh1417 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1 C6 VlC6C6 Vib2C6)))))))))))(pdh59 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5 ViC5C4 ViC5a1c1))). Qed. Lemma pdh1419: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->forall C4:dom,(i C3 C4)->(i o C4)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))(C4:dom)(ViC3C4:(i C3 C4))(VioC4:(i o C4))=>((ex_ind (P:=fun C5:dom=>(i C5 C4)/\(i C5 a1c1))(fun C5:dom=>(and_ind (pdh1418 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4 C5))))(pdh57 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4 ViC3C4 VioC4))). Qed. Lemma pdh1420: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->forall C3:dom,(i C3 C2)->(i C3 a2b2)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))(C3:dom)(ViC3C2:(i C3 C2))(ViC3a2b2:(i C3 a2b2))=>((ex_ind (P:=fun C4:dom=>(i C3 C4)/\(i o C4))(fun C4:dom=>(and_ind (pdh1419 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2 C4))))(pdh55 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3 ViC3C2 ViC3a2b2))). Qed. Lemma pdh1421: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->forall C2:dom,(i C1 C2)->(i ac C2)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))(C2:dom)(ViC1C2:(i C1 C2))(ViacC2:(i ac C2))=>((ex_ind (P:=fun C3:dom=>(i C3 C2)/\(i C3 a2b2))(fun C3:dom=>(and_ind (pdh1420 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2 C3))))(pdh53 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2 ViC1C2 ViacC2))). Qed. Lemma pdh1422: forall C0:dom,(i a1 C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oc)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oc:(i C1 oc))=>((ex_ind (P:=fun C2:dom=>(i C1 C2)/\(i ac C2))(fun C2:dom=>(and_ind (pdh1421 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc C2))))(pdh51 C0 Via1C0 Vib2C0 C1 ViC1C0 ViC1oc))). Qed. Lemma pdh1423: forall C0:dom,(i a1 C0)->(i b2 C0)->goal. Proof. exact (fun (C0:dom)(Via1C0:(i a1 C0))(Vib2C0:(i b2 C0))=>((ex_ind (P:=fun C1:dom=>(i C1 C0)/\(i C1 oc))(fun C1:dom=>(and_ind (pdh1422 C0 Via1C0 Vib2C0 C1))))(pdh49 C0 Via1C0 Vib2C0))). Qed. Lemma pdh1424: goal. Proof. exact (((ex_ind (P:=fun C0:dom=>(i a1 C0)/\(i b2 C0))(fun C0:dom=>(and_ind (pdh1423 C0))))pdh47)). Qed. Check pdh1424. End pdh.