Section pdc. 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_ax:forall A:dom,(l A A)/\(i bc A)/\(i ac A)/\(i ab A)->goal. Hypothesis gap_t1in2:(i a1 b2c2)/\(i b1 a2c2)/\(i c1 a2b2). 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 pdc1: (i a1 b2c2)/\(i b1 a2c2)/\(i c1 a2b2). Proof. exact (gap_t1in2). Qed. Lemma pdc2: (i a1 a1b1). Proof. exact (ia1b1). Qed. Lemma pdc3: (i b1 a1b1). Proof. exact (ib1a1). Qed. Lemma pdc4: (i a2 a2b2). Proof. exact (ia2b2). Qed. Lemma pdc5: (i b2 a2b2). Proof. exact (ib2a2). Qed. Lemma pdc6: (i a1 a1c1). Proof. exact (ia1c1). Qed. Lemma pdc7: (i c1 a1c1). Proof. exact (ic1a1). Qed. Lemma pdc8: (i a2 a2c2). Proof. exact (ia2c2). Qed. Lemma pdc9: (i c2 a2c2). Proof. exact (ic2a2). Qed. Lemma pdc10: (i c1 b1c1). Proof. exact (ic1b1). Qed. Lemma pdc11: (i b1 b1c1). Proof. exact (ib1c1). Qed. Lemma pdc12: (i c2 b2c2). Proof. exact (ic2b2). Qed. Lemma pdc13: (i b2 b2c2). Proof. exact (ib2c2). Qed. Lemma pdc14: (i o oa). Proof. exact (iooa). Qed. Lemma pdc15: (i o ob). Proof. exact (ioob). Qed. Lemma pdc16: (i o oc). Proof. exact (iooc). Qed. Lemma pdc17: (i a1 oa). Proof. exact (ia1oa). Qed. Lemma pdc18: (i a2 oa). Proof. exact (ia2oa). Qed. Lemma pdc19: (i b1 ob). Proof. exact (ib1ob). Qed. Lemma pdc20: (i b2 ob). Proof. exact (ib2ob). Qed. Lemma pdc21: (i c1 oc). Proof. exact (ic1oc). Qed. Lemma pdc22: (i c2 oc). Proof. exact (ic2oc). Qed. Lemma pdc23: (i bc b1c1). Proof. exact (ibc1). Qed. Lemma pdc24: (i bc b2c2). Proof. exact (ibc2). Qed. Lemma pdc25: (i ac a1c1). Proof. exact (iac1). Qed. Lemma pdc26: (i ac a2c2). Proof. exact (iac2). Qed. Lemma pdc27: (i ab a1b1). Proof. exact (iab1). Qed. Lemma pdc28: (i ab a2b2). Proof. exact (iab2). Qed. Lemma pdc33: (p b2 b2). Proof. exact (((pref b2 a2b2) pdc5)). Qed. Lemma pdc37: (p ac ac). Proof. exact (((pref ac a1c1) pdc25)). Qed. Lemma pdc45: (l oa oa). Proof. exact (((lref o oa) pdc14)). Qed. Lemma pdc47: (l oc oc). Proof. exact (((lref o oc) pdc16)). Qed. Lemma pdc48: (exists A:dom,(i ac A)/\(i b2 A)). Proof. exact (((line ac b2) (conj pdc37 pdc33))). Qed. Lemma pdc49: forall C0:dom,(i ac C0)->(i b2 C0)->(l C0 C0). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))=>((lref ac C0) ViacC0)). Qed. Lemma pdc50: forall C0:dom,(i ac C0)->(i b2 C0)->(exists A:dom,(i A C0)/\(i A oa)). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))=>((point C0 oa) (conj (pdc49 C0 ViacC0 Vib2C0) pdc45))). Qed. Lemma pdc52: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->(exists A:dom,(i A C0)/\(i A oc)). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))=>((point C0 oc) (conj (pdc49 C0 ViacC0 Vib2C0) pdc47))). Qed. Lemma pdc54: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2) \/ (l a2b2 a1b1) \/ (l C0 oa) \/ (exists A:dom,(l A A)/\(i c2 A)/\(i ab A)/\(i C1 A)). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))=>((papp a1 c1 ac b2 b1 o c2 ab C1 a1c1 ob oc a2c2 a2b2 a1b1 C0 oa) (conj pdc6 (conj pdc7 (conj pdc25 (conj pdc20 (conj pdc19 (conj pdc15 (conj pdc21 (conj pdc16 (conj pdc22 (conj pdc26 (conj (proj1 (proj2 pdc1)) (conj pdc9 (conj (proj2 (proj2 pdc1)) (conj pdc5 (conj pdc28 (conj pdc2 (conj pdc3 (conj pdc27 (conj ViacC0 (conj Vib2C0 (conj ViC1C0 (conj pdc17 (conj pdc14 ViC1oa))))))))))))))))))))))))). Qed. Lemma pdc58: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2)->(i o a2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vloca2c2:(l oc a2c2))=>((lcon o oc a2c2) (conj pdc16 Vloca2c2))). Qed. Lemma pdc59: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2)->(i c1 a2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vloca2c2:(l oc a2c2))=>((lcon c1 oc a2c2) (conj pdc21 Vloca2c2))). Qed. Lemma pdc62: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2)->(p b1 c1) \/ (l a2c2 b1c1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vloca2c2:(l oc a2c2))=>((unique b1 c1 a2c2 b1c1) (conj (proj1 (proj2 pdc1)) (conj pdc11 (conj (pdc59 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2) pdc10))))). Qed. Lemma pdc65: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2)->(p b1 c1)->(i b1 a1c1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vloca2c2:(l oc a2c2))(Vpb1c1:(p b1 c1))=>((pcon b1 c1 a1c1) (conj Vpb1c1 pdc7))). Qed. Lemma pdc66: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2)->(p b1 c1)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vloca2c2:(l oc a2c2))(Vpb1c1:(p b1 c1))=>((triangle1 a1c1) (conj pdc6 (conj (pdc65 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2 Vpb1c1) pdc7)))). Qed. Lemma pdc67: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2)->(p b1 c1)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vloca2c2:(l oc a2c2))(Vpb1c1:(p b1 c1))=>((false_ind goal) (pdc66 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2 Vpb1c1))). Qed. Lemma pdc68: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2)->(l a2c2 b1c1)->(l b1c1 a2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vloca2c2:(l oc a2c2))(Vla2c2b1c1:(l a2c2 b1c1))=>((lsym a2c2 b1c1) Vla2c2b1c1)). Qed. Lemma pdc78: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2)->(l a2c2 b1c1)->(p b1 o) \/ (l a2c2 ob). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vloca2c2:(l oc a2c2))(Vla2c2b1c1:(l a2c2 b1c1))=>((unique b1 o a2c2 ob) (conj (proj1 (proj2 pdc1)) (conj pdc19 (conj (pdc58 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2) pdc15))))). Qed. Lemma pdc80: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2)->(l a2c2 b1c1)->(p b1 o)->(i b1 oa). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vloca2c2:(l oc a2c2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpb1o:(p b1 o))=>((pcon b1 o oa) (conj Vpb1o pdc14))). Qed. Lemma pdc82: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2)->(l a2c2 b1c1)->(p b1 o)->(p b1 a2) \/ (l a2c2 oa). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vloca2c2:(l oc a2c2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpb1o:(p b1 o))=>((unique b1 a2 a2c2 oa) (conj (proj1 (proj2 pdc1)) (conj (pdc80 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2 Vla2c2b1c1 Vpb1o) (conj pdc8 pdc18))))). Qed. Lemma pdc86: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2)->(l a2c2 b1c1)->(p b1 o)->(p b1 a2)->(i b1 a2b2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vloca2c2:(l oc a2c2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))=>((pcon b1 a2 a2b2) (conj Vpb1a2 pdc4))). Qed. Lemma pdc90: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2)->(l a2c2 b1c1)->(p b1 o)->(p b1 a2)->(p b1 c1) \/ (l a2c2 a2b2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vloca2c2:(l oc a2c2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))=>((unique b1 c1 a2c2 a2b2) (conj (proj1 (proj2 pdc1)) (conj (pdc86 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2 Vla2c2b1c1 Vpb1o Vpb1a2) (conj (pdc59 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2) (proj2 (proj2 pdc1))))))). Qed. Lemma pdc96: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2)->(l a2c2 b1c1)->(p b1 o)->(p b1 a2)->(p b1 c1)->(i b1 a1c1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vloca2c2:(l oc a2c2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))(Vpb1c1:(p b1 c1))=>((pcon b1 c1 a1c1) (conj Vpb1c1 pdc7))). Qed. Lemma pdc97: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2)->(l a2c2 b1c1)->(p b1 o)->(p b1 a2)->(p b1 c1)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vloca2c2:(l oc a2c2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))(Vpb1c1:(p b1 c1))=>((triangle1 a1c1) (conj pdc6 (conj (pdc96 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2 Vla2c2b1c1 Vpb1o Vpb1a2 Vpb1c1) pdc7)))). Qed. Lemma pdc98: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2)->(l a2c2 b1c1)->(p b1 o)->(p b1 a2)->(p b1 c1)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vloca2c2:(l oc a2c2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))(Vpb1c1:(p b1 c1))=>((false_ind goal) (pdc97 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2 Vla2c2b1c1 Vpb1o Vpb1a2 Vpb1c1))). Qed. Lemma pdc99: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2)->(l a2c2 b1c1)->(p b1 o)->(p b1 a2)->(l a2c2 a2b2)->(l a2b2 a2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vloca2c2:(l oc a2c2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))(Vla2c2a2b2:(l a2c2 a2b2))=>((lsym a2c2 a2b2) Vla2c2a2b2)). Qed. Lemma pdc104: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2)->(l a2c2 b1c1)->(p b1 o)->(p b1 a2)->(l a2c2 a2b2)->(i b2 a2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vloca2c2:(l oc a2c2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))(Vla2c2a2b2:(l a2c2 a2b2))=>((lcon b2 a2b2 a2c2) (conj pdc5 (pdc99 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2 Vla2c2b1c1 Vpb1o Vpb1a2 Vla2c2a2b2)))). Qed. Lemma pdc105: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2)->(l a2c2 b1c1)->(p b1 o)->(p b1 a2)->(l a2c2 a2b2)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vloca2c2:(l oc a2c2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))(Vla2c2a2b2:(l a2c2 a2b2))=>((triangle2 a2c2) (conj pdc8 (conj (pdc104 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2 Vla2c2b1c1 Vpb1o Vpb1a2 Vla2c2a2b2) pdc9)))). Qed. Lemma pdc106: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2)->(l a2c2 b1c1)->(p b1 o)->(p b1 a2)->(l a2c2 a2b2)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vloca2c2:(l oc a2c2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))(Vla2c2a2b2:(l a2c2 a2b2))=>((false_ind goal) (pdc105 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2 Vla2c2b1c1 Vpb1o Vpb1a2 Vla2c2a2b2))). Qed. Lemma pdc107: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2)->(l a2c2 b1c1)->(p b1 o)->(p b1 a2)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vloca2c2:(l oc a2c2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))=>((or_ind ((pdc98 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2 Vla2c2b1c1 Vpb1o Vpb1a2))((pdc106 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2 Vla2c2b1c1 Vpb1o Vpb1a2)))(pdc90 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2 Vla2c2b1c1 Vpb1o Vpb1a2))). Qed. Lemma pdc111: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2)->(l a2c2 b1c1)->(p b1 o)->(l a2c2 oa)->(l b1c1 oa). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vloca2c2:(l oc a2c2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpb1o:(p b1 o))(Vla2c2oa:(l a2c2 oa))=>((ltra b1c1 a2c2 oa) (conj (pdc68 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2 Vla2c2b1c1) Vla2c2oa))). Qed. Lemma pdc114: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2)->(l a2c2 b1c1)->(p b1 o)->(l a2c2 oa)->(i c1 oa). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vloca2c2:(l oc a2c2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpb1o:(p b1 o))(Vla2c2oa:(l a2c2 oa))=>((lcon c1 b1c1 oa) (conj pdc10 (pdc111 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2 Vla2c2b1c1 Vpb1o Vla2c2oa)))). Qed. Lemma pdc115: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2)->(l a2c2 b1c1)->(p b1 o)->(l a2c2 oa)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vloca2c2:(l oc a2c2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpb1o:(p b1 o))(Vla2c2oa:(l a2c2 oa))=>((triangle1 oa) (conj pdc17 (conj (pdc80 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2 Vla2c2b1c1 Vpb1o) (pdc114 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2 Vla2c2b1c1 Vpb1o Vla2c2oa))))). Qed. Lemma pdc116: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2)->(l a2c2 b1c1)->(p b1 o)->(l a2c2 oa)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vloca2c2:(l oc a2c2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpb1o:(p b1 o))(Vla2c2oa:(l a2c2 oa))=>((false_ind goal) (pdc115 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2 Vla2c2b1c1 Vpb1o Vla2c2oa))). Qed. Lemma pdc117: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2)->(l a2c2 b1c1)->(p b1 o)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vloca2c2:(l oc a2c2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpb1o:(p b1 o))=>((or_ind ((pdc107 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2 Vla2c2b1c1 Vpb1o))((pdc116 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2 Vla2c2b1c1 Vpb1o)))(pdc82 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2 Vla2c2b1c1 Vpb1o))). Qed. Lemma pdc123: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2)->(l a2c2 b1c1)->(l a2c2 ob)->(i a2 ob). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vloca2c2:(l oc a2c2))(Vla2c2b1c1:(l a2c2 b1c1))(Vla2c2ob:(l a2c2 ob))=>((lcon a2 a2c2 ob) (conj pdc8 Vla2c2ob))). Qed. Lemma pdc124: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2)->(l a2c2 b1c1)->(l a2c2 ob)->(i c2 ob). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vloca2c2:(l oc a2c2))(Vla2c2b1c1:(l a2c2 b1c1))(Vla2c2ob:(l a2c2 ob))=>((lcon c2 a2c2 ob) (conj pdc9 Vla2c2ob))). Qed. Lemma pdc125: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2)->(l a2c2 b1c1)->(l a2c2 ob)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vloca2c2:(l oc a2c2))(Vla2c2b1c1:(l a2c2 b1c1))(Vla2c2ob:(l a2c2 ob))=>((triangle2 ob) (conj (pdc123 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2 Vla2c2b1c1 Vla2c2ob) (conj pdc20 (pdc124 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2 Vla2c2b1c1 Vla2c2ob))))). Qed. Lemma pdc126: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2)->(l a2c2 b1c1)->(l a2c2 ob)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vloca2c2:(l oc a2c2))(Vla2c2b1c1:(l a2c2 b1c1))(Vla2c2ob:(l a2c2 ob))=>((false_ind goal) (pdc125 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2 Vla2c2b1c1 Vla2c2ob))). Qed. Lemma pdc127: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2)->(l a2c2 b1c1)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vloca2c2:(l oc a2c2))(Vla2c2b1c1:(l a2c2 b1c1))=>((or_ind ((pdc117 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2 Vla2c2b1c1))((pdc126 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2 Vla2c2b1c1)))(pdc78 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2 Vla2c2b1c1))). Qed. Lemma pdc128: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l oc a2c2)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vloca2c2:(l oc a2c2))=>((or_ind ((pdc67 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2))((pdc127 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2)))(pdc62 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vloca2c2))). Qed. Lemma pdc129: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l a2b2 a1b1)->(l a1b1 a2b2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vla2b2a1b1:(l a2b2 a1b1))=>((lsym a2b2 a1b1) Vla2b2a1b1)). Qed. Lemma pdc130: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l a2b2 a1b1)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vla2b2a1b1:(l a2b2 a1b1))=>(notab (pdc129 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vla2b2a1b1))). Qed. Lemma pdc131: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l a2b2 a1b1)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(Vla2b2a1b1:(l a2b2 a1b1))=>((false_ind goal) (pdc130 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc Vla2b2a1b1))). Qed. Lemma pdc137: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(i b2 oa). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))=>((lcon b2 C0 oa) (conj Vib2C0 VlC0oa))). Qed. Lemma pdc139: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2) \/ (l b2c2 oa). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))=>((unique a1 b2 b2c2 oa) (conj (proj1 pdc1) (conj pdc17 (conj pdc13 (pdc137 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa)))))). Qed. Lemma pdc140: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(p b2 a1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))=>((psym a1 b2) Vpa1b2)). Qed. Lemma pdc141: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(i a1 a2b2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))=>((pcon a1 b2 a2b2) (conj Vpa1b2 pdc5))). Qed. Lemma pdc142: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(i a1 ob). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))=>((pcon a1 b2 ob) (conj Vpa1b2 pdc20))). Qed. Lemma pdc144: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(i b2 a1c1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))=>((pcon b2 a1 a1c1) (conj (pdc140 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2) pdc6))). Qed. Lemma pdc145: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(p c1 b2) \/ (l a2b2 a1c1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))=>((unique c1 b2 a2b2 a1c1) (conj (proj2 (proj2 pdc1)) (conj pdc7 (conj pdc5 (pdc144 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2)))))). Qed. Lemma pdc150: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(p c1 b2)->(i c1 ob). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vpc1b2:(p c1 b2))=>((pcon c1 b2 ob) (conj Vpc1b2 pdc20))). Qed. Lemma pdc151: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(p c1 b2)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vpc1b2:(p c1 b2))=>((triangle1 ob) (conj (pdc142 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2) (conj pdc19 (pdc150 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vpc1b2))))). Qed. Lemma pdc152: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(p c1 b2)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vpc1b2:(p c1 b2))=>((false_ind goal) (pdc151 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vpc1b2))). Qed. Lemma pdc156: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(i ab a1c1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))=>((lcon ab a2b2 a1c1) (conj pdc28 Vla2b2a1c1))). Qed. Lemma pdc157: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab) \/ (l a1b1 a1c1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))=>((unique a1 ab a1b1 a1c1) (conj pdc2 (conj pdc6 (conj pdc27 (pdc156 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1)))))). Qed. Lemma pdc165: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(p a1 b1) \/ (l a1b1 ob). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))=>((unique a1 b1 a1b1 ob) (conj pdc2 (conj (pdc142 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2) (conj pdc3 pdc19))))). Qed. Lemma pdc167: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(p a1 b1)->(p b2 b1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vpa1b1:(p a1 b1))=>((ptra b2 a1 b1) (conj (pdc140 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2) Vpa1b1))). Qed. Lemma pdc168: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(p a1 b1)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vpa1b1:(p a1 b1))=>(notbb (pdc167 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vpa1b1))). Qed. Lemma pdc169: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(p a1 b1)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vpa1b1:(p a1 b1))=>((false_ind goal) (pdc168 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vpa1b1))). Qed. Lemma pdc170: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(l ob a1b1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))=>((lsym a1b1 ob) Vla1b1ob)). Qed. Lemma pdc171: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(i o a1b1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))=>((lcon o ob a1b1) (conj pdc15 (pdc170 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob)))). Qed. Lemma pdc172: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(p a1 o) \/ (l a1b1 oa). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))=>((unique a1 o a1b1 oa) (conj pdc2 (conj pdc17 (conj (pdc171 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob) pdc14))))). Qed. Lemma pdc178: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(p a1 o)->(i a1 oc). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))=>((pcon a1 o oc) (conj Vpa1o pdc16))). Qed. Lemma pdc184: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(p a1 o)->(p a1 c2) \/ (l b2c2 oc). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))=>((unique a1 c2 b2c2 oc) (conj (proj1 pdc1) (conj (pdc178 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob Vpa1o) (conj pdc12 pdc22))))). Qed. Lemma pdc192: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(i a1 a2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))=>((pcon a1 c2 a2c2) (conj Vpa1c2 pdc9))). Qed. Lemma pdc193: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(i b2 a2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))=>((pcon b2 a1 a2c2) (conj (pdc140 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2) (pdc192 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob Vpa1o Vpa1c2)))). Qed. Lemma pdc194: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))=>((triangle2 a2c2) (conj pdc8 (conj (pdc193 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob Vpa1o Vpa1c2) pdc9)))). Qed. Lemma pdc195: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))=>((false_ind goal) (pdc194 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob Vpa1o Vpa1c2))). Qed. Lemma pdc196: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(p a1 o)->(l b2c2 oc)->(l oc b2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vlb2c2oc:(l b2c2 oc))=>((lsym b2c2 oc) Vlb2c2oc)). Qed. Lemma pdc197: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(p a1 o)->(l b2c2 oc)->(i c1 b2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vlb2c2oc:(l b2c2 oc))=>((lcon c1 oc b2c2) (conj pdc21 (pdc196 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob Vpa1o Vlb2c2oc)))). Qed. Lemma pdc200: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(p a1 o)->(l b2c2 oc)->(p a1 c1) \/ (l b2c2 a1c1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vlb2c2oc:(l b2c2 oc))=>((unique a1 c1 b2c2 a1c1) (conj (proj1 pdc1) (conj pdc6 (conj (pdc197 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob Vpa1o Vlb2c2oc) pdc7))))). Qed. Lemma pdc208: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(p a1 o)->(l b2c2 oc)->(p a1 c1)->(i a1 b1c1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vlb2c2oc:(l b2c2 oc))(Vpa1c1:(p a1 c1))=>((pcon a1 c1 b1c1) (conj Vpa1c1 pdc10))). Qed. Lemma pdc209: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(p a1 o)->(l b2c2 oc)->(p a1 c1)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vlb2c2oc:(l b2c2 oc))(Vpa1c1:(p a1 c1))=>((triangle1 b1c1) (conj (pdc208 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob Vpa1o Vlb2c2oc Vpa1c1) (conj pdc11 pdc10)))). Qed. Lemma pdc210: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(p a1 o)->(l b2c2 oc)->(p a1 c1)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vlb2c2oc:(l b2c2 oc))(Vpa1c1:(p a1 c1))=>((false_ind goal) (pdc209 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob Vpa1o Vlb2c2oc Vpa1c1))). Qed. Lemma pdc211: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(p a1 o)->(l b2c2 oc)->(l b2c2 a1c1)->(l a1c1 b2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vlb2c2oc:(l b2c2 oc))(Vlb2c2a1c1:(l b2c2 a1c1))=>((lsym b2c2 a1c1) Vlb2c2a1c1)). Qed. Lemma pdc212: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(p a1 o)->(l b2c2 oc)->(l b2c2 a1c1)->(l a2b2 b2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vlb2c2oc:(l b2c2 oc))(Vlb2c2a1c1:(l b2c2 a1c1))=>((ltra a2b2 a1c1 b2c2) (conj Vla2b2a1c1 (pdc211 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob Vpa1o Vlb2c2oc Vlb2c2a1c1)))). Qed. Lemma pdc218: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(p a1 o)->(l b2c2 oc)->(l b2c2 a1c1)->(i a2 b2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vlb2c2oc:(l b2c2 oc))(Vlb2c2a1c1:(l b2c2 a1c1))=>((lcon a2 a2b2 b2c2) (conj pdc4 (pdc212 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob Vpa1o Vlb2c2oc Vlb2c2a1c1)))). Qed. Lemma pdc219: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(p a1 o)->(l b2c2 oc)->(l b2c2 a1c1)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vlb2c2oc:(l b2c2 oc))(Vlb2c2a1c1:(l b2c2 a1c1))=>((triangle2 b2c2) (conj (pdc218 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob Vpa1o Vlb2c2oc Vlb2c2a1c1) (conj pdc13 pdc12)))). Qed. Lemma pdc220: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(p a1 o)->(l b2c2 oc)->(l b2c2 a1c1)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vlb2c2oc:(l b2c2 oc))(Vlb2c2a1c1:(l b2c2 a1c1))=>((false_ind goal) (pdc219 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob Vpa1o Vlb2c2oc Vlb2c2a1c1))). Qed. Lemma pdc221: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(p a1 o)->(l b2c2 oc)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vlb2c2oc:(l b2c2 oc))=>((or_ind ((pdc210 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob Vpa1o Vlb2c2oc))((pdc220 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob Vpa1o Vlb2c2oc)))(pdc200 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob Vpa1o Vlb2c2oc))). Qed. Lemma pdc222: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(p a1 o)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))=>((or_ind ((pdc195 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob Vpa1o))((pdc221 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob Vpa1o)))(pdc184 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob Vpa1o))). Qed. Lemma pdc223: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(l a1b1 oa)->(l oa a1b1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))(Vla1b1oa:(l a1b1 oa))=>((lsym a1b1 oa) Vla1b1oa)). Qed. Lemma pdc232: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(l a1b1 oa)->(i a2 a1b1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))(Vla1b1oa:(l a1b1 oa))=>((lcon a2 oa a1b1) (conj pdc18 (pdc223 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob Vla1b1oa)))). Qed. Lemma pdc240: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(l a1b1 oa)->(p b1 a2) \/ (l a2c2 a1b1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))(Vla1b1oa:(l a1b1 oa))=>((unique b1 a2 a2c2 a1b1) (conj (proj1 (proj2 pdc1)) (conj pdc3 (conj pdc8 (pdc232 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob Vla1b1oa)))))). Qed. Lemma pdc242: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(l a1b1 oa)->(p b1 a2)->(i b1 a2b2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))(Vla1b1oa:(l a1b1 oa))(Vpb1a2:(p b1 a2))=>((pcon b1 a2 a2b2) (conj Vpb1a2 pdc4))). Qed. Lemma pdc243: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(l a1b1 oa)->(p b1 a2)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))(Vla1b1oa:(l a1b1 oa))(Vpb1a2:(p b1 a2))=>((triangle1 a2b2) (conj (pdc141 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2) (conj (pdc242 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob Vla1b1oa Vpb1a2) (proj2 (proj2 pdc1)))))). Qed. Lemma pdc244: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(l a1b1 oa)->(p b1 a2)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))(Vla1b1oa:(l a1b1 oa))(Vpb1a2:(p b1 a2))=>((false_ind goal) (pdc243 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob Vla1b1oa Vpb1a2))). Qed. Lemma pdc245: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(l a1b1 oa)->(l a2c2 a1b1)->(l a1b1 a2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))(Vla1b1oa:(l a1b1 oa))(Vla2c2a1b1:(l a2c2 a1b1))=>((lsym a2c2 a1b1) Vla2c2a1b1)). Qed. Lemma pdc252: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(l a1b1 oa)->(l a2c2 a1b1)->(i a1 a2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))(Vla1b1oa:(l a1b1 oa))(Vla2c2a1b1:(l a2c2 a1b1))=>((lcon a1 a1b1 a2c2) (conj pdc2 (pdc245 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob Vla1b1oa Vla2c2a1b1)))). Qed. Lemma pdc253: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(l a1b1 oa)->(l a2c2 a1b1)->(i b2 a2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))(Vla1b1oa:(l a1b1 oa))(Vla2c2a1b1:(l a2c2 a1b1))=>((pcon b2 a1 a2c2) (conj (pdc140 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2) (pdc252 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob Vla1b1oa Vla2c2a1b1)))). Qed. Lemma pdc254: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(l a1b1 oa)->(l a2c2 a1b1)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))(Vla1b1oa:(l a1b1 oa))(Vla2c2a1b1:(l a2c2 a1b1))=>((triangle2 a2c2) (conj pdc8 (conj (pdc253 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob Vla1b1oa Vla2c2a1b1) pdc9)))). Qed. Lemma pdc255: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(l a1b1 oa)->(l a2c2 a1b1)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))(Vla1b1oa:(l a1b1 oa))(Vla2c2a1b1:(l a2c2 a1b1))=>((false_ind goal) (pdc254 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob Vla1b1oa Vla2c2a1b1))). Qed. Lemma pdc256: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->(l a1b1 oa)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))(Vla1b1oa:(l a1b1 oa))=>((or_ind ((pdc244 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob Vla1b1oa))((pdc255 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob Vla1b1oa)))(pdc240 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob Vla1b1oa))). Qed. Lemma pdc257: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->(l a1b1 ob)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))(Vla1b1ob:(l a1b1 ob))=>((or_ind ((pdc222 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob))((pdc256 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob)))(pdc172 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab Vla1b1ob))). Qed. Lemma pdc258: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(p a1 ab)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpa1ab:(p a1 ab))=>((or_ind ((pdc169 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab))((pdc257 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab)))(pdc165 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vpa1ab))). Qed. Lemma pdc259: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(l a1b1 a1c1)->(l a1c1 a1b1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vla1b1a1c1:(l a1b1 a1c1))=>((lsym a1b1 a1c1) Vla1b1a1c1)). Qed. Lemma pdc260: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(l a1b1 a1c1)->(l a2b2 a1b1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vla1b1a1c1:(l a1b1 a1c1))=>((ltra a2b2 a1c1 a1b1) (conj Vla2b2a1c1 (pdc259 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vla1b1a1c1)))). Qed. Lemma pdc261: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(l a1b1 a1c1)->(l a1b1 a2b2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vla1b1a1c1:(l a1b1 a1c1))=>((lsym a2b2 a1b1) (pdc260 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vla1b1a1c1))). Qed. Lemma pdc262: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(l a1b1 a1c1)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vla1b1a1c1:(l a1b1 a1c1))=>(notab (pdc261 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vla1b1a1c1))). Qed. Lemma pdc263: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->(l a1b1 a1c1)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vla1b1a1c1:(l a1b1 a1c1))=>((false_ind goal) (pdc262 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1 Vla1b1a1c1))). Qed. Lemma pdc264: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->(l a2b2 a1c1)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))=>((or_ind ((pdc258 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1))((pdc263 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1)))(pdc157 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2 Vla2b2a1c1))). Qed. Lemma pdc265: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(p a1 b2)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vpa1b2:(p a1 b2))=>((or_ind ((pdc152 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2))((pdc264 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2)))(pdc145 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vpa1b2))). Qed. Lemma pdc269: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(l b2c2 oa)->(i c2 oa). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vlb2c2oa:(l b2c2 oa))=>((lcon c2 b2c2 oa) (conj pdc12 Vlb2c2oa))). Qed. Lemma pdc270: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(l b2c2 oa)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vlb2c2oa:(l b2c2 oa))=>((triangle2 oa) (conj pdc18 (conj (pdc137 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa) (pdc269 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vlb2c2oa))))). Qed. Lemma pdc271: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->(l b2c2 oa)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))(Vlb2c2oa:(l b2c2 oa))=>((false_ind goal) (pdc270 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa Vlb2c2oa))). Qed. Lemma pdc272: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->(l C0 oa)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(VlC0oa:(l C0 oa))=>((or_ind ((pdc265 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa))((pdc271 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa)))(pdc139 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc VlC0oa))). Qed. Lemma pdc273: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l oa a2c2) \/ (l b2c2 b1c1) \/ (l C0 oc) \/ (exists A:dom,(l A A)/\(i a2 A)/\(i bc A)/\(i C2 A)). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))=>((papp c1 a1 ac b2 b1 o a2 bc C2 a1c1 ob oa a2c2 b2c2 b1c1 C0 oc) (conj pdc7 (conj pdc6 (conj pdc25 (conj pdc20 (conj pdc19 (conj pdc15 (conj pdc17 (conj pdc14 (conj pdc18 (conj pdc26 (conj (proj1 (proj2 pdc1)) (conj pdc8 (conj (proj1 pdc1) (conj pdc13 (conj pdc24 (conj pdc10 (conj pdc11 (conj pdc23 (conj ViacC0 (conj Vib2C0 (conj ViC2C0 (conj pdc21 (conj pdc16 ViC2oc))))))))))))))))))))))))). Qed. Lemma pdc274: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l oa a2c2)->(l a2c2 oa). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vloaa2c2:(l oa a2c2))=>((lsym oa a2c2) Vloaa2c2)). Qed. Lemma pdc276: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l oa a2c2)->(i c2 oa). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vloaa2c2:(l oa a2c2))=>((lcon c2 a2c2 oa) (conj pdc9 (pdc274 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2)))). Qed. Lemma pdc277: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l oa a2c2)->(i o a2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vloaa2c2:(l oa a2c2))=>((lcon o oa a2c2) (conj pdc14 Vloaa2c2))). Qed. Lemma pdc281: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l oa a2c2)->(p a1 c2) \/ (l b2c2 oa). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vloaa2c2:(l oa a2c2))=>((unique a1 c2 b2c2 oa) (conj (proj1 pdc1) (conj pdc17 (conj pdc12 (pdc276 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2)))))). Qed. Lemma pdc282: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l oa a2c2)->(p a1 c2)->(p c2 a1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vloaa2c2:(l oa a2c2))(Vpa1c2:(p a1 c2))=>((psym a1 c2) Vpa1c2)). Qed. Lemma pdc283: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l oa a2c2)->(p a1 c2)->(i a1 oc). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vloaa2c2:(l oa a2c2))(Vpa1c2:(p a1 c2))=>((pcon a1 c2 oc) (conj Vpa1c2 pdc22))). Qed. Lemma pdc285: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l oa a2c2)->(p a1 c2)->(i c2 a1b1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vloaa2c2:(l oa a2c2))(Vpa1c2:(p a1 c2))=>((pcon c2 a1 a1b1) (conj (pdc282 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2 Vpa1c2) pdc2))). Qed. Lemma pdc287: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l oa a2c2)->(p a1 c2)->(p b1 c2) \/ (l a2c2 a1b1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vloaa2c2:(l oa a2c2))(Vpa1c2:(p a1 c2))=>((unique b1 c2 a2c2 a1b1) (conj (proj1 (proj2 pdc1)) (conj pdc3 (conj pdc9 (pdc285 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2 Vpa1c2)))))). Qed. Lemma pdc292: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l oa a2c2)->(p a1 c2)->(p b1 c2)->(i b1 oc). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vloaa2c2:(l oa a2c2))(Vpa1c2:(p a1 c2))(Vpb1c2:(p b1 c2))=>((pcon b1 c2 oc) (conj Vpb1c2 pdc22))). Qed. Lemma pdc293: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l oa a2c2)->(p a1 c2)->(p b1 c2)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vloaa2c2:(l oa a2c2))(Vpa1c2:(p a1 c2))(Vpb1c2:(p b1 c2))=>((triangle1 oc) (conj (pdc283 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2 Vpa1c2) (conj (pdc292 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2 Vpa1c2 Vpb1c2) pdc21)))). Qed. Lemma pdc294: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l oa a2c2)->(p a1 c2)->(p b1 c2)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vloaa2c2:(l oa a2c2))(Vpa1c2:(p a1 c2))(Vpb1c2:(p b1 c2))=>((false_ind goal) (pdc293 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2 Vpa1c2 Vpb1c2))). Qed. Lemma pdc295: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l oa a2c2)->(p a1 c2)->(l a2c2 a1b1)->(l a1b1 a2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vloaa2c2:(l oa a2c2))(Vpa1c2:(p a1 c2))(Vla2c2a1b1:(l a2c2 a1b1))=>((lsym a2c2 a1b1) Vla2c2a1b1)). Qed. Lemma pdc304: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l oa a2c2)->(p a1 c2)->(l a2c2 a1b1)->(p b1 o) \/ (l a2c2 ob). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vloaa2c2:(l oa a2c2))(Vpa1c2:(p a1 c2))(Vla2c2a1b1:(l a2c2 a1b1))=>((unique b1 o a2c2 ob) (conj (proj1 (proj2 pdc1)) (conj pdc19 (conj (pdc277 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2) pdc15))))). Qed. Lemma pdc306: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l oa a2c2)->(p a1 c2)->(l a2c2 a1b1)->(p b1 o)->(i b1 oc). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vloaa2c2:(l oa a2c2))(Vpa1c2:(p a1 c2))(Vla2c2a1b1:(l a2c2 a1b1))(Vpb1o:(p b1 o))=>((pcon b1 o oc) (conj Vpb1o pdc16))). Qed. Lemma pdc307: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l oa a2c2)->(p a1 c2)->(l a2c2 a1b1)->(p b1 o)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vloaa2c2:(l oa a2c2))(Vpa1c2:(p a1 c2))(Vla2c2a1b1:(l a2c2 a1b1))(Vpb1o:(p b1 o))=>((triangle1 oc) (conj (pdc283 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2 Vpa1c2) (conj (pdc306 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2 Vpa1c2 Vla2c2a1b1 Vpb1o) pdc21)))). Qed. Lemma pdc308: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l oa a2c2)->(p a1 c2)->(l a2c2 a1b1)->(p b1 o)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vloaa2c2:(l oa a2c2))(Vpa1c2:(p a1 c2))(Vla2c2a1b1:(l a2c2 a1b1))(Vpb1o:(p b1 o))=>((false_ind goal) (pdc307 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2 Vpa1c2 Vla2c2a1b1 Vpb1o))). Qed. Lemma pdc312: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l oa a2c2)->(p a1 c2)->(l a2c2 a1b1)->(l a2c2 ob)->(l a1b1 ob). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vloaa2c2:(l oa a2c2))(Vpa1c2:(p a1 c2))(Vla2c2a1b1:(l a2c2 a1b1))(Vla2c2ob:(l a2c2 ob))=>((ltra a1b1 a2c2 ob) (conj (pdc295 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2 Vpa1c2 Vla2c2a1b1) Vla2c2ob))). Qed. Lemma pdc314: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l oa a2c2)->(p a1 c2)->(l a2c2 a1b1)->(l a2c2 ob)->(i a1 ob). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vloaa2c2:(l oa a2c2))(Vpa1c2:(p a1 c2))(Vla2c2a1b1:(l a2c2 a1b1))(Vla2c2ob:(l a2c2 ob))=>((lcon a1 a1b1 ob) (conj pdc2 (pdc312 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2 Vpa1c2 Vla2c2a1b1 Vla2c2ob)))). Qed. Lemma pdc315: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l oa a2c2)->(p a1 c2)->(l a2c2 a1b1)->(l a2c2 ob)->(i c2 ob). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vloaa2c2:(l oa a2c2))(Vpa1c2:(p a1 c2))(Vla2c2a1b1:(l a2c2 a1b1))(Vla2c2ob:(l a2c2 ob))=>((pcon c2 a1 ob) (conj (pdc282 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2 Vpa1c2) (pdc314 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2 Vpa1c2 Vla2c2a1b1 Vla2c2ob)))). Qed. Lemma pdc316: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l oa a2c2)->(p a1 c2)->(l a2c2 a1b1)->(l a2c2 ob)->(i a2 ob). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vloaa2c2:(l oa a2c2))(Vpa1c2:(p a1 c2))(Vla2c2a1b1:(l a2c2 a1b1))(Vla2c2ob:(l a2c2 ob))=>((lcon a2 a2c2 ob) (conj pdc8 Vla2c2ob))). Qed. Lemma pdc317: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l oa a2c2)->(p a1 c2)->(l a2c2 a1b1)->(l a2c2 ob)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vloaa2c2:(l oa a2c2))(Vpa1c2:(p a1 c2))(Vla2c2a1b1:(l a2c2 a1b1))(Vla2c2ob:(l a2c2 ob))=>((triangle2 ob) (conj (pdc316 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2 Vpa1c2 Vla2c2a1b1 Vla2c2ob) (conj pdc20 (pdc315 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2 Vpa1c2 Vla2c2a1b1 Vla2c2ob))))). Qed. Lemma pdc318: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l oa a2c2)->(p a1 c2)->(l a2c2 a1b1)->(l a2c2 ob)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vloaa2c2:(l oa a2c2))(Vpa1c2:(p a1 c2))(Vla2c2a1b1:(l a2c2 a1b1))(Vla2c2ob:(l a2c2 ob))=>((false_ind goal) (pdc317 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2 Vpa1c2 Vla2c2a1b1 Vla2c2ob))). Qed. Lemma pdc319: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l oa a2c2)->(p a1 c2)->(l a2c2 a1b1)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vloaa2c2:(l oa a2c2))(Vpa1c2:(p a1 c2))(Vla2c2a1b1:(l a2c2 a1b1))=>((or_ind ((pdc308 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2 Vpa1c2 Vla2c2a1b1))((pdc318 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2 Vpa1c2 Vla2c2a1b1)))(pdc304 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2 Vpa1c2 Vla2c2a1b1))). Qed. Lemma pdc320: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l oa a2c2)->(p a1 c2)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vloaa2c2:(l oa a2c2))(Vpa1c2:(p a1 c2))=>((or_ind ((pdc294 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2 Vpa1c2))((pdc319 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2 Vpa1c2)))(pdc287 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2 Vpa1c2))). Qed. Lemma pdc321: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l oa a2c2)->(l b2c2 oa)->(l oa b2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vloaa2c2:(l oa a2c2))(Vlb2c2oa:(l b2c2 oa))=>((lsym b2c2 oa) Vlb2c2oa)). Qed. Lemma pdc322: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l oa a2c2)->(l b2c2 oa)->(l a2c2 b2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vloaa2c2:(l oa a2c2))(Vlb2c2oa:(l b2c2 oa))=>((ltra a2c2 oa b2c2) (conj (pdc274 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2) (pdc321 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2 Vlb2c2oa)))). Qed. Lemma pdc325: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l oa a2c2)->(l b2c2 oa)->(i a2 b2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vloaa2c2:(l oa a2c2))(Vlb2c2oa:(l b2c2 oa))=>((lcon a2 a2c2 b2c2) (conj pdc8 (pdc322 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2 Vlb2c2oa)))). Qed. Lemma pdc326: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l oa a2c2)->(l b2c2 oa)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vloaa2c2:(l oa a2c2))(Vlb2c2oa:(l b2c2 oa))=>((triangle2 b2c2) (conj (pdc325 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2 Vlb2c2oa) (conj pdc13 pdc12)))). Qed. Lemma pdc327: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l oa a2c2)->(l b2c2 oa)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vloaa2c2:(l oa a2c2))(Vlb2c2oa:(l b2c2 oa))=>((false_ind goal) (pdc326 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2 Vlb2c2oa))). Qed. Lemma pdc328: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l oa a2c2)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vloaa2c2:(l oa a2c2))=>((or_ind ((pdc320 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2))((pdc327 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2)))(pdc281 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vloaa2c2))). Qed. Lemma pdc329: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l b2c2 b1c1)->(l b1c1 b2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vlb2c2b1c1:(l b2c2 b1c1))=>((lsym b2c2 b1c1) Vlb2c2b1c1)). Qed. Lemma pdc330: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l b2c2 b1c1)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vlb2c2b1c1:(l b2c2 b1c1))=>(notbc (pdc329 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vlb2c2b1c1))). Qed. Lemma pdc331: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l b2c2 b1c1)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(Vlb2c2b1c1:(l b2c2 b1c1))=>((false_ind goal) (pdc330 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 Vlb2c2b1c1))). Qed. Lemma pdc336: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(i ac oc). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))=>((lcon ac C0 oc) (conj ViacC0 VlC0oc))). Qed. Lemma pdc337: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(i b2 oc). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))=>((lcon b2 C0 oc) (conj Vib2C0 VlC0oc))). Qed. Lemma pdc339: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2) \/ (l a2b2 oc). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))=>((unique c1 b2 a2b2 oc) (conj (proj2 (proj2 pdc1)) (conj pdc21 (conj pdc5 (pdc337 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc)))))). Qed. Lemma pdc340: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(p b2 c1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))=>((psym c1 b2) Vpc1b2)). Qed. Lemma pdc342: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(i c1 ob). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))=>((pcon c1 b2 ob) (conj Vpc1b2 pdc20))). Qed. Lemma pdc343: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(i b2 a1c1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))=>((pcon b2 c1 a1c1) (conj (pdc340 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2) pdc7))). Qed. Lemma pdc345: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(p a1 b2) \/ (l b2c2 a1c1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))=>((unique a1 b2 b2c2 a1c1) (conj (proj1 pdc1) (conj pdc6 (conj pdc13 (pdc343 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2)))))). Qed. Lemma pdc350: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(p a1 b2)->(i a1 ob). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))(Vpa1b2:(p a1 b2))=>((pcon a1 b2 ob) (conj Vpa1b2 pdc20))). Qed. Lemma pdc351: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(p a1 b2)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))(Vpa1b2:(p a1 b2))=>((triangle1 ob) (conj (pdc350 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2 Vpa1b2) (conj pdc19 (pdc342 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2))))). Qed. Lemma pdc352: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(p a1 b2)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))(Vpa1b2:(p a1 b2))=>((false_ind goal) (pdc351 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2 Vpa1b2))). Qed. Lemma pdc353: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(l b2c2 a1c1)->(l a1c1 b2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))(Vlb2c2a1c1:(l b2c2 a1c1))=>((lsym b2c2 a1c1) Vlb2c2a1c1)). Qed. Lemma pdc355: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(l b2c2 a1c1)->(i bc a1c1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))(Vlb2c2a1c1:(l b2c2 a1c1))=>((lcon bc b2c2 a1c1) (conj pdc24 Vlb2c2a1c1))). Qed. Lemma pdc357: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(l b2c2 a1c1)->(p c1 bc) \/ (l a1c1 b1c1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))(Vlb2c2a1c1:(l b2c2 a1c1))=>((unique c1 bc a1c1 b1c1) (conj pdc7 (conj pdc10 (conj (pdc355 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2 Vlb2c2a1c1) pdc23))))). Qed. Lemma pdc365: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(l b2c2 a1c1)->(p c1 bc)->(p c1 ac) \/ (l a1c1 oc). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpc1bc:(p c1 bc))=>((unique c1 ac a1c1 oc) (conj pdc7 (conj pdc21 (conj pdc25 (pdc336 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc)))))). Qed. Lemma pdc371: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(l b2c2 a1c1)->(p c1 bc)->(p c1 ac)->(i c1 a2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpc1bc:(p c1 bc))(Vpc1ac:(p c1 ac))=>((pcon c1 ac a2c2) (conj Vpc1ac pdc26))). Qed. Lemma pdc372: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(l b2c2 a1c1)->(p c1 bc)->(p c1 ac)->(i b2 a2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpc1bc:(p c1 bc))(Vpc1ac:(p c1 ac))=>((pcon b2 c1 a2c2) (conj (pdc340 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2) (pdc371 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2 Vlb2c2a1c1 Vpc1bc Vpc1ac)))). Qed. Lemma pdc373: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(l b2c2 a1c1)->(p c1 bc)->(p c1 ac)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpc1bc:(p c1 bc))(Vpc1ac:(p c1 ac))=>((triangle2 a2c2) (conj pdc8 (conj (pdc372 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2 Vlb2c2a1c1 Vpc1bc Vpc1ac) pdc9)))). Qed. Lemma pdc374: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(l b2c2 a1c1)->(p c1 bc)->(p c1 ac)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpc1bc:(p c1 bc))(Vpc1ac:(p c1 ac))=>((false_ind goal) (pdc373 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2 Vlb2c2a1c1 Vpc1bc Vpc1ac))). Qed. Lemma pdc378: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(l b2c2 a1c1)->(p c1 bc)->(l a1c1 oc)->(l b2c2 oc). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpc1bc:(p c1 bc))(Vla1c1oc:(l a1c1 oc))=>((ltra b2c2 a1c1 oc) (conj Vlb2c2a1c1 Vla1c1oc))). Qed. Lemma pdc379: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(l b2c2 a1c1)->(p c1 bc)->(l a1c1 oc)->(l oc b2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpc1bc:(p c1 bc))(Vla1c1oc:(l a1c1 oc))=>((lsym b2c2 oc) (pdc378 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2 Vlb2c2a1c1 Vpc1bc Vla1c1oc))). Qed. Lemma pdc385: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(l b2c2 a1c1)->(p c1 bc)->(l a1c1 oc)->(i o b2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpc1bc:(p c1 bc))(Vla1c1oc:(l a1c1 oc))=>((lcon o oc b2c2) (conj pdc16 (pdc379 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2 Vlb2c2a1c1 Vpc1bc Vla1c1oc)))). Qed. Lemma pdc390: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(l b2c2 a1c1)->(p c1 bc)->(l a1c1 oc)->(p a1 o) \/ (l b2c2 oa). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpc1bc:(p c1 bc))(Vla1c1oc:(l a1c1 oc))=>((unique a1 o b2c2 oa) (conj (proj1 pdc1) (conj pdc17 (conj (pdc385 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2 Vlb2c2a1c1 Vpc1bc Vla1c1oc) pdc14))))). Qed. Lemma pdc392: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(l b2c2 a1c1)->(p c1 bc)->(l a1c1 oc)->(p a1 o)->(i a1 ob). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpc1bc:(p c1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))=>((pcon a1 o ob) (conj Vpa1o pdc15))). Qed. Lemma pdc393: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(l b2c2 a1c1)->(p c1 bc)->(l a1c1 oc)->(p a1 o)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpc1bc:(p c1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))=>((triangle1 ob) (conj (pdc392 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2 Vlb2c2a1c1 Vpc1bc Vla1c1oc Vpa1o) (conj pdc19 (pdc342 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2))))). Qed. Lemma pdc394: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(l b2c2 a1c1)->(p c1 bc)->(l a1c1 oc)->(p a1 o)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpc1bc:(p c1 bc))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))=>((false_ind goal) (pdc393 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2 Vlb2c2a1c1 Vpc1bc Vla1c1oc Vpa1o))). Qed. Lemma pdc396: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(l b2c2 a1c1)->(p c1 bc)->(l a1c1 oc)->(l b2c2 oa)->(l a1c1 oa). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpc1bc:(p c1 bc))(Vla1c1oc:(l a1c1 oc))(Vlb2c2oa:(l b2c2 oa))=>((ltra a1c1 b2c2 oa) (conj (pdc353 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2 Vlb2c2a1c1) Vlb2c2oa))). Qed. Lemma pdc402: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(l b2c2 a1c1)->(p c1 bc)->(l a1c1 oc)->(l b2c2 oa)->(i c1 oa). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpc1bc:(p c1 bc))(Vla1c1oc:(l a1c1 oc))(Vlb2c2oa:(l b2c2 oa))=>((lcon c1 a1c1 oa) (conj pdc7 (pdc396 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2 Vlb2c2a1c1 Vpc1bc Vla1c1oc Vlb2c2oa)))). Qed. Lemma pdc403: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(l b2c2 a1c1)->(p c1 bc)->(l a1c1 oc)->(l b2c2 oa)->(i b2 oa). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpc1bc:(p c1 bc))(Vla1c1oc:(l a1c1 oc))(Vlb2c2oa:(l b2c2 oa))=>((pcon b2 c1 oa) (conj (pdc340 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2) (pdc402 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2 Vlb2c2a1c1 Vpc1bc Vla1c1oc Vlb2c2oa)))). Qed. Lemma pdc405: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(l b2c2 a1c1)->(p c1 bc)->(l a1c1 oc)->(l b2c2 oa)->(i c2 oa). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpc1bc:(p c1 bc))(Vla1c1oc:(l a1c1 oc))(Vlb2c2oa:(l b2c2 oa))=>((lcon c2 b2c2 oa) (conj pdc12 Vlb2c2oa))). Qed. Lemma pdc406: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(l b2c2 a1c1)->(p c1 bc)->(l a1c1 oc)->(l b2c2 oa)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpc1bc:(p c1 bc))(Vla1c1oc:(l a1c1 oc))(Vlb2c2oa:(l b2c2 oa))=>((triangle2 oa) (conj pdc18 (conj (pdc403 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2 Vlb2c2a1c1 Vpc1bc Vla1c1oc Vlb2c2oa) (pdc405 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2 Vlb2c2a1c1 Vpc1bc Vla1c1oc Vlb2c2oa))))). Qed. Lemma pdc407: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(l b2c2 a1c1)->(p c1 bc)->(l a1c1 oc)->(l b2c2 oa)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpc1bc:(p c1 bc))(Vla1c1oc:(l a1c1 oc))(Vlb2c2oa:(l b2c2 oa))=>((false_ind goal) (pdc406 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2 Vlb2c2a1c1 Vpc1bc Vla1c1oc Vlb2c2oa))). Qed. Lemma pdc408: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(l b2c2 a1c1)->(p c1 bc)->(l a1c1 oc)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpc1bc:(p c1 bc))(Vla1c1oc:(l a1c1 oc))=>((or_ind ((pdc394 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2 Vlb2c2a1c1 Vpc1bc Vla1c1oc))((pdc407 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2 Vlb2c2a1c1 Vpc1bc Vla1c1oc)))(pdc390 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2 Vlb2c2a1c1 Vpc1bc Vla1c1oc))). Qed. Lemma pdc409: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(l b2c2 a1c1)->(p c1 bc)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpc1bc:(p c1 bc))=>((or_ind ((pdc374 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2 Vlb2c2a1c1 Vpc1bc))((pdc408 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2 Vlb2c2a1c1 Vpc1bc)))(pdc365 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2 Vlb2c2a1c1 Vpc1bc))). Qed. Lemma pdc411: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(l b2c2 a1c1)->(l a1c1 b1c1)->(l b2c2 b1c1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))(Vlb2c2a1c1:(l b2c2 a1c1))(Vla1c1b1c1:(l a1c1 b1c1))=>((ltra b2c2 a1c1 b1c1) (conj Vlb2c2a1c1 Vla1c1b1c1))). Qed. Lemma pdc412: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(l b2c2 a1c1)->(l a1c1 b1c1)->(l b1c1 b2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))(Vlb2c2a1c1:(l b2c2 a1c1))(Vla1c1b1c1:(l a1c1 b1c1))=>((lsym b2c2 b1c1) (pdc411 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2 Vlb2c2a1c1 Vla1c1b1c1))). Qed. Lemma pdc413: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(l b2c2 a1c1)->(l a1c1 b1c1)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))(Vlb2c2a1c1:(l b2c2 a1c1))(Vla1c1b1c1:(l a1c1 b1c1))=>(notbc (pdc412 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2 Vlb2c2a1c1 Vla1c1b1c1))). Qed. Lemma pdc414: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(l b2c2 a1c1)->(l a1c1 b1c1)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))(Vlb2c2a1c1:(l b2c2 a1c1))(Vla1c1b1c1:(l a1c1 b1c1))=>((false_ind goal) (pdc413 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2 Vlb2c2a1c1 Vla1c1b1c1))). Qed. Lemma pdc415: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->(l b2c2 a1c1)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))(Vlb2c2a1c1:(l b2c2 a1c1))=>((or_ind ((pdc409 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2 Vlb2c2a1c1))((pdc414 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2 Vlb2c2a1c1)))(pdc357 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2 Vlb2c2a1c1))). Qed. Lemma pdc416: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(p c1 b2)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vpc1b2:(p c1 b2))=>((or_ind ((pdc352 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2))((pdc415 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2)))(pdc345 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vpc1b2))). Qed. Lemma pdc420: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(l a2b2 oc)->(i a2 oc). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vla2b2oc:(l a2b2 oc))=>((lcon a2 a2b2 oc) (conj pdc4 Vla2b2oc))). Qed. Lemma pdc421: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(l a2b2 oc)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vla2b2oc:(l a2b2 oc))=>((triangle2 oc) (conj (pdc420 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vla2b2oc) (conj (pdc337 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc) pdc22)))). Qed. Lemma pdc422: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->(l a2b2 oc)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))(Vla2b2oc:(l a2b2 oc))=>((false_ind goal) (pdc421 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc Vla2b2oc))). Qed. Lemma pdc423: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->(l C0 oc)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(VlC0oc:(l C0 oc))=>((or_ind ((pdc416 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc))((pdc422 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc)))(pdc339 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 VlC0oc))). Qed. Lemma pdc424: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l a2b2 C3) \/ (l C4 b2c2) \/ (l C0 a1c1) \/ (exists A:dom,(l A A)/\(i ab A)/\(i bc A)/\(i ac A)). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))=>((papp a1 a2 C1 C2 c2 c1 ab bc ac oa oc a2b2 C3 C4 b2c2 C0 a1c1) (conj pdc17 (conj pdc18 (conj ViC1oa (conj ViC2oc (conj pdc22 (conj pdc21 (conj pdc4 (conj (proj2 (proj2 pdc1)) (conj pdc28 (conj ViC1C3 (conj Vic2C3 (conj ViabC3 (conj Via2C4 (conj ViC2C4 (conj VibcC4 (conj (proj1 pdc1) (conj pdc12 (conj pdc24 (conj ViC1C0 (conj ViC2C0 (conj ViacC0 (conj pdc6 (conj pdc7 pdc25))))))))))))))))))))))))). Qed. Lemma pdc427: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l a2b2 C3)->(i a2 C3). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(Vla2b2C3:(l a2b2 C3))=>((lcon a2 a2b2 C3) (conj pdc4 Vla2b2C3))). Qed. Lemma pdc428: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l a2b2 C3)->(i b2 C3). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(Vla2b2C3:(l a2b2 C3))=>((lcon b2 a2b2 C3) (conj pdc5 Vla2b2C3))). Qed. Lemma pdc429: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l a2b2 C3)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(Vla2b2C3:(l a2b2 C3))=>((triangle2 C3) (conj (pdc427 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 Vla2b2C3) (conj (pdc428 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 Vla2b2C3) Vic2C3)))). Qed. Lemma pdc430: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l a2b2 C3)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(Vla2b2C3:(l a2b2 C3))=>((false_ind goal) (pdc429 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 Vla2b2C3))). Qed. Lemma pdc431: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C4 b2c2)->(l b2c2 C4). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC4b2c2:(l C4 b2c2))=>((lsym C4 b2c2) VlC4b2c2)). Qed. Lemma pdc433: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C4 b2c2)->(i c2 C4). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC4b2c2:(l C4 b2c2))=>((lcon c2 b2c2 C4) (conj pdc12 (pdc431 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC4b2c2)))). Qed. Lemma pdc434: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C4 b2c2)->(i b2 C4). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC4b2c2:(l C4 b2c2))=>((lcon b2 b2c2 C4) (conj pdc13 (pdc431 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC4b2c2)))). Qed. Lemma pdc435: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C4 b2c2)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC4b2c2:(l C4 b2c2))=>((triangle2 C4) (conj Via2C4 (conj (pdc434 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC4b2c2) (pdc433 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC4b2c2))))). Qed. Lemma pdc436: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C4 b2c2)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC4b2c2:(l C4 b2c2))=>((false_ind goal) (pdc435 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC4b2c2))). Qed. Lemma pdc440: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(i b2 a1c1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))=>((lcon b2 C0 a1c1) (conj Vib2C0 VlC0a1c1))). Qed. Lemma pdc443: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2) \/ (l b2c2 a1c1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))=>((unique a1 b2 b2c2 a1c1) (conj (proj1 pdc1) (conj pdc6 (conj pdc13 (pdc440 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1)))))). Qed. Lemma pdc444: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(p b2 a1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))=>((psym a1 b2) Vpa1b2)). Qed. Lemma pdc445: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(i a1 a2b2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))=>((pcon a1 b2 a2b2) (conj Vpa1b2 pdc5))). Qed. Lemma pdc446: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(i a1 ob). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))=>((pcon a1 b2 ob) (conj Vpa1b2 pdc20))). Qed. Lemma pdc448: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(i b2 oa). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))=>((pcon b2 a1 oa) (conj (pdc444 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2) pdc17))). Qed. Lemma pdc449: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(p c1 b2) \/ (l a2b2 a1c1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))=>((unique c1 b2 a2b2 a1c1) (conj (proj2 (proj2 pdc1)) (conj pdc7 (conj pdc5 (pdc440 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1)))))). Qed. Lemma pdc454: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(p c1 b2)->(i c1 ob). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vpc1b2:(p c1 b2))=>((pcon c1 b2 ob) (conj Vpc1b2 pdc20))). Qed. Lemma pdc455: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(p c1 b2)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vpc1b2:(p c1 b2))=>((triangle1 ob) (conj (pdc446 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2) (conj pdc19 (pdc454 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vpc1b2))))). Qed. Lemma pdc456: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(p c1 b2)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vpc1b2:(p c1 b2))=>((false_ind goal) (pdc455 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vpc1b2))). Qed. Lemma pdc457: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(l a1c1 a2b2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))=>((lsym a2b2 a1c1) Vla2b2a1c1)). Qed. Lemma pdc458: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(l C0 a2b2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))=>((ltra C0 a1c1 a2b2) (conj VlC0a1c1 (pdc457 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1)))). Qed. Lemma pdc462: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(i ac a2b2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))=>((lcon ac a1c1 a2b2) (conj pdc25 (pdc457 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1)))). Qed. Lemma pdc466: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(i C2 a2b2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))=>((lcon C2 C0 a2b2) (conj ViC2C0 (pdc458 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1)))). Qed. Lemma pdc467: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2) \/ (l a2b2 oc). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))=>((unique c1 C2 a2b2 oc) (conj (proj2 (proj2 pdc1)) (conj pdc21 (conj (pdc466 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1) ViC2oc))))). Qed. Lemma pdc469: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(i c1 C4). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))=>((pcon c1 C2 C4) (conj Vpc1C2 ViC2C4))). Qed. Lemma pdc471: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2) \/ (l a2b2 C4). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))=>((unique c1 a2 a2b2 C4) (conj (proj2 (proj2 pdc1)) (conj (pdc469 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2) (conj pdc4 Via2C4))))). Qed. Lemma pdc472: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(p a2 c1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))=>((psym c1 a2) Vpc1a2)). Qed. Lemma pdc477: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(i c1 oa). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))=>((pcon c1 a2 oa) (conj Vpc1a2 pdc18))). Qed. Lemma pdc479: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(i a2 b1c1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))=>((pcon a2 c1 b1c1) (conj (pdc472 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2) pdc10))). Qed. Lemma pdc480: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(i a2 oc). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))=>((pcon a2 c1 oc) (conj (pdc472 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2) pdc21))). Qed. Lemma pdc481: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(p b1 a2) \/ (l a2c2 b1c1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))=>((unique b1 a2 a2c2 b1c1) (conj (proj1 (proj2 pdc1)) (conj pdc11 (conj pdc8 (pdc479 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2)))))). Qed. Lemma pdc487: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(p b1 a2)->(i b1 a2b2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))(Vpb1a2:(p b1 a2))=>((pcon b1 a2 a2b2) (conj Vpb1a2 pdc4))). Qed. Lemma pdc488: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(p b1 a2)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))(Vpb1a2:(p b1 a2))=>((triangle1 a2b2) (conj (pdc445 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2) (conj (pdc487 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2 Vpb1a2) (proj2 (proj2 pdc1)))))). Qed. Lemma pdc489: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(p b1 a2)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))(Vpb1a2:(p b1 a2))=>((false_ind goal) (pdc488 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2 Vpb1a2))). Qed. Lemma pdc493: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(l a2c2 b1c1)->(i ac b1c1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))(Vla2c2b1c1:(l a2c2 b1c1))=>((lcon ac a2c2 b1c1) (conj pdc26 Vla2c2b1c1))). Qed. Lemma pdc494: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(l a2c2 b1c1)->(p c1 ac) \/ (l a2b2 b1c1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))(Vla2c2b1c1:(l a2c2 b1c1))=>((unique c1 ac a2b2 b1c1) (conj (proj2 (proj2 pdc1)) (conj pdc10 (conj (pdc462 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1) (pdc493 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2 Vla2c2b1c1)))))). Qed. Lemma pdc503: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(l a2c2 b1c1)->(p c1 ac)->(p c1 b2) \/ (l a2b2 oa). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))=>((unique c1 b2 a2b2 oa) (conj (proj2 (proj2 pdc1)) (conj (pdc477 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2) (conj pdc5 (pdc448 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2)))))). Qed. Lemma pdc511: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(l a2c2 b1c1)->(p c1 ac)->(p c1 b2)->(p a2 b2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc1b2:(p c1 b2))=>((ptra a2 c1 b2) (conj (pdc472 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2) Vpc1b2))). Qed. Lemma pdc512: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(l a2c2 b1c1)->(p c1 ac)->(p c1 b2)->(p b2 a2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc1b2:(p c1 b2))=>((psym a2 b2) (pdc511 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2 Vla2c2b1c1 Vpc1ac Vpc1b2))). Qed. Lemma pdc513: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(l a2c2 b1c1)->(p c1 ac)->(p c1 b2)->(p a1 a2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc1b2:(p c1 b2))=>((ptra a1 b2 a2) (conj Vpa1b2 (pdc512 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2 Vla2c2b1c1 Vpc1ac Vpc1b2)))). Qed. Lemma pdc514: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(l a2c2 b1c1)->(p c1 ac)->(p c1 b2)->(p a2 a1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc1b2:(p c1 b2))=>((psym a1 a2) (pdc513 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2 Vla2c2b1c1 Vpc1ac Vpc1b2))). Qed. Lemma pdc515: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(l a2c2 b1c1)->(p c1 ac)->(p c1 b2)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc1b2:(p c1 b2))=>(notaa (pdc514 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2 Vla2c2b1c1 Vpc1ac Vpc1b2))). Qed. Lemma pdc516: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(l a2c2 b1c1)->(p c1 ac)->(p c1 b2)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc1b2:(p c1 b2))=>((false_ind goal) (pdc515 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2 Vla2c2b1c1 Vpc1ac Vpc1b2))). Qed. Lemma pdc517: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(l a2c2 b1c1)->(p c1 ac)->(l a2b2 oa)->(l oa a2b2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vla2b2oa:(l a2b2 oa))=>((lsym a2b2 oa) Vla2b2oa)). Qed. Lemma pdc522: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(l a2c2 b1c1)->(p c1 ac)->(l a2b2 oa)->(i o a2b2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vla2b2oa:(l a2b2 oa))=>((lcon o oa a2b2) (conj pdc14 (pdc517 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2 Vla2c2b1c1 Vpc1ac Vla2b2oa)))). Qed. Lemma pdc526: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(l a2c2 b1c1)->(p c1 ac)->(l a2b2 oa)->(p c1 o) \/ (l a2b2 oc). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vla2b2oa:(l a2b2 oa))=>((unique c1 o a2b2 oc) (conj (proj2 (proj2 pdc1)) (conj pdc21 (conj (pdc522 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2 Vla2c2b1c1 Vpc1ac Vla2b2oa) pdc16))))). Qed. Lemma pdc534: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(l a2c2 b1c1)->(p c1 ac)->(l a2b2 oa)->(p c1 o)->(i c1 ob). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vla2b2oa:(l a2b2 oa))(Vpc1o:(p c1 o))=>((pcon c1 o ob) (conj Vpc1o pdc15))). Qed. Lemma pdc535: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(l a2c2 b1c1)->(p c1 ac)->(l a2b2 oa)->(p c1 o)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vla2b2oa:(l a2b2 oa))(Vpc1o:(p c1 o))=>((triangle1 ob) (conj (pdc446 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2) (conj pdc19 (pdc534 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2 Vla2c2b1c1 Vpc1ac Vla2b2oa Vpc1o))))). Qed. Lemma pdc536: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(l a2c2 b1c1)->(p c1 ac)->(l a2b2 oa)->(p c1 o)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vla2b2oa:(l a2b2 oa))(Vpc1o:(p c1 o))=>((false_ind goal) (pdc535 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2 Vla2c2b1c1 Vpc1ac Vla2b2oa Vpc1o))). Qed. Lemma pdc544: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(l a2c2 b1c1)->(p c1 ac)->(l a2b2 oa)->(l a2b2 oc)->(i b2 oc). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vla2b2oa:(l a2b2 oa))(Vla2b2oc:(l a2b2 oc))=>((lcon b2 a2b2 oc) (conj pdc5 Vla2b2oc))). Qed. Lemma pdc545: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(l a2c2 b1c1)->(p c1 ac)->(l a2b2 oa)->(l a2b2 oc)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vla2b2oa:(l a2b2 oa))(Vla2b2oc:(l a2b2 oc))=>((triangle2 oc) (conj (pdc480 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2) (conj (pdc544 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2 Vla2c2b1c1 Vpc1ac Vla2b2oa Vla2b2oc) pdc22)))). Qed. Lemma pdc546: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(l a2c2 b1c1)->(p c1 ac)->(l a2b2 oa)->(l a2b2 oc)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vla2b2oa:(l a2b2 oa))(Vla2b2oc:(l a2b2 oc))=>((false_ind goal) (pdc545 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2 Vla2c2b1c1 Vpc1ac Vla2b2oa Vla2b2oc))). Qed. Lemma pdc547: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(l a2c2 b1c1)->(p c1 ac)->(l a2b2 oa)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vla2b2oa:(l a2b2 oa))=>((or_ind ((pdc536 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2 Vla2c2b1c1 Vpc1ac Vla2b2oa))((pdc546 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2 Vla2c2b1c1 Vpc1ac Vla2b2oa)))(pdc526 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2 Vla2c2b1c1 Vpc1ac Vla2b2oa))). Qed. Lemma pdc548: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(l a2c2 b1c1)->(p c1 ac)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))=>((or_ind ((pdc516 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2 Vla2c2b1c1 Vpc1ac))((pdc547 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2 Vla2c2b1c1 Vpc1ac)))(pdc503 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2 Vla2c2b1c1 Vpc1ac))). Qed. Lemma pdc549: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(l a2c2 b1c1)->(l a2b2 b1c1)->(l b1c1 a2b2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))(Vla2c2b1c1:(l a2c2 b1c1))(Vla2b2b1c1:(l a2b2 b1c1))=>((lsym a2b2 b1c1) Vla2b2b1c1)). Qed. Lemma pdc554: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(l a2c2 b1c1)->(l a2b2 b1c1)->(l a2c2 a2b2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))(Vla2c2b1c1:(l a2c2 b1c1))(Vla2b2b1c1:(l a2b2 b1c1))=>((ltra a2c2 b1c1 a2b2) (conj Vla2c2b1c1 (pdc549 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2 Vla2c2b1c1 Vla2b2b1c1)))). Qed. Lemma pdc555: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(l a2c2 b1c1)->(l a2b2 b1c1)->(l a2b2 a2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))(Vla2c2b1c1:(l a2c2 b1c1))(Vla2b2b1c1:(l a2b2 b1c1))=>((lsym a2c2 a2b2) (pdc554 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2 Vla2c2b1c1 Vla2b2b1c1))). Qed. Lemma pdc556: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(l a2c2 b1c1)->(l a2b2 b1c1)->(l a1c1 a2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))(Vla2c2b1c1:(l a2c2 b1c1))(Vla2b2b1c1:(l a2b2 b1c1))=>((ltra a1c1 a2b2 a2c2) (conj (pdc457 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1) (pdc555 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2 Vla2c2b1c1 Vla2b2b1c1)))). Qed. Lemma pdc557: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(l a2c2 b1c1)->(l a2b2 b1c1)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))(Vla2c2b1c1:(l a2c2 b1c1))(Vla2b2b1c1:(l a2b2 b1c1))=>(notac (pdc556 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2 Vla2c2b1c1 Vla2b2b1c1))). Qed. Lemma pdc558: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(l a2c2 b1c1)->(l a2b2 b1c1)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))(Vla2c2b1c1:(l a2c2 b1c1))(Vla2b2b1c1:(l a2b2 b1c1))=>((false_ind goal) (pdc557 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2 Vla2c2b1c1 Vla2b2b1c1))). Qed. Lemma pdc559: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->(l a2c2 b1c1)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))(Vla2c2b1c1:(l a2c2 b1c1))=>((or_ind ((pdc548 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2 Vla2c2b1c1))((pdc558 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2 Vla2c2b1c1)))(pdc494 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2 Vla2c2b1c1))). Qed. Lemma pdc560: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(p c1 a2)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vpc1a2:(p c1 a2))=>((or_ind ((pdc489 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2))((pdc559 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2)))(pdc481 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vpc1a2))). Qed. Lemma pdc562: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(l a2b2 C4)->(l a1c1 C4). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vla2b2C4:(l a2b2 C4))=>((ltra a1c1 a2b2 C4) (conj (pdc457 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1) Vla2b2C4))). Qed. Lemma pdc568: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(l a2b2 C4)->(i ac C4). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vla2b2C4:(l a2b2 C4))=>((lcon ac a1c1 C4) (conj pdc25 (pdc562 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vla2b2C4)))). Qed. Lemma pdc569: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(l a2b2 C4)->(i ab C4). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vla2b2C4:(l a2b2 C4))=>((lcon ab a2b2 C4) (conj pdc28 Vla2b2C4))). Qed. Lemma pdc570: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->(l a2b2 C4)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))(Vla2b2C4:(l a2b2 C4))=>((goal_ax C4) (conj VlC4C4 (conj VibcC4 (conj (pdc568 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vla2b2C4) (pdc569 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2 Vla2b2C4)))))). Qed. Lemma pdc571: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(p c1 C2)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vpc1C2:(p c1 C2))=>((or_ind ((pdc560 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2))((pdc570 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2)))(pdc471 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vpc1C2))). Qed. Lemma pdc577: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(l a2b2 oc)->(i a2 oc). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vla2b2oc:(l a2b2 oc))=>((lcon a2 a2b2 oc) (conj pdc4 Vla2b2oc))). Qed. Lemma pdc578: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(l a2b2 oc)->(i b2 oc). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vla2b2oc:(l a2b2 oc))=>((lcon b2 a2b2 oc) (conj pdc5 Vla2b2oc))). Qed. Lemma pdc579: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(l a2b2 oc)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vla2b2oc:(l a2b2 oc))=>((triangle2 oc) (conj (pdc577 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vla2b2oc) (conj (pdc578 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vla2b2oc) pdc22)))). Qed. Lemma pdc580: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->(l a2b2 oc)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))(Vla2b2oc:(l a2b2 oc))=>((false_ind goal) (pdc579 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1 Vla2b2oc))). Qed. Lemma pdc581: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->(l a2b2 a1c1)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))(Vla2b2a1c1:(l a2b2 a1c1))=>((or_ind ((pdc571 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1))((pdc580 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1)))(pdc467 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2 Vla2b2a1c1))). Qed. Lemma pdc582: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(p a1 b2)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vpa1b2:(p a1 b2))=>((or_ind ((pdc456 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2))((pdc581 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2)))(pdc449 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vpa1b2))). Qed. Lemma pdc583: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(l a1c1 b2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))=>((lsym b2c2 a1c1) Vlb2c2a1c1)). Qed. Lemma pdc584: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(l C0 b2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))=>((ltra C0 a1c1 b2c2) (conj VlC0a1c1 (pdc583 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1)))). Qed. Lemma pdc586: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(i c1 b2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))=>((lcon c1 a1c1 b2c2) (conj pdc7 (pdc583 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1)))). Qed. Lemma pdc591: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(i ac b2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))=>((lcon ac a1c1 b2c2) (conj pdc25 (pdc583 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1)))). Qed. Lemma pdc592: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(i C1 b2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))=>((lcon C1 C0 b2c2) (conj ViC1C0 (pdc584 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1)))). Qed. Lemma pdc594: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1) \/ (l b2c2 oa). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))=>((unique a1 C1 b2c2 oa) (conj (proj1 pdc1) (conj pdc17 (conj (pdc592 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1) ViC1oa))))). Qed. Lemma pdc596: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(i a1 C3). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))=>((pcon a1 C1 C3) (conj Vpa1C1 ViC1C3))). Qed. Lemma pdc598: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2) \/ (l b2c2 C3). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))=>((unique a1 c2 b2c2 C3) (conj (proj1 pdc1) (conj (pdc596 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1) (conj pdc12 Vic2C3))))). Qed. Lemma pdc599: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->(p c2 a1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))=>((psym a1 c2) Vpa1c2)). Qed. Lemma pdc602: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->(i a1 a2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))=>((pcon a1 c2 a2c2) (conj Vpa1c2 pdc9))). Qed. Lemma pdc604: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->(i a1 oc). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))=>((pcon a1 c2 oc) (conj Vpa1c2 pdc22))). Qed. Lemma pdc607: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->(i c2 oa). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))=>((pcon c2 a1 oa) (conj (pdc599 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2) pdc17))). Qed. Lemma pdc608: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->(p a1 ac) \/ (l b2c2 a2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))=>((unique a1 ac b2c2 a2c2) (conj (proj1 pdc1) (conj (pdc602 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2) (conj (pdc591 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1) pdc26))))). Qed. Lemma pdc618: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->(p a1 ac)->(p a1 c1) \/ (l b2c2 oc). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))=>((unique a1 c1 b2c2 oc) (conj (proj1 pdc1) (conj (pdc604 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2) (conj (pdc586 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1) pdc21))))). Qed. Lemma pdc622: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->(p a1 ac)->(p a1 c1)->(p c2 c1). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vpa1c1:(p a1 c1))=>((ptra c2 a1 c1) (conj (pdc599 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2) Vpa1c1))). Qed. Lemma pdc623: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->(p a1 ac)->(p a1 c1)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vpa1c1:(p a1 c1))=>(notcc (pdc622 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2 Vpa1ac Vpa1c1))). Qed. Lemma pdc624: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->(p a1 ac)->(p a1 c1)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vpa1c1:(p a1 c1))=>((false_ind goal) (pdc623 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2 Vpa1ac Vpa1c1))). Qed. Lemma pdc625: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->(p a1 ac)->(l b2c2 oc)->(l oc b2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vlb2c2oc:(l b2c2 oc))=>((lsym b2c2 oc) Vlb2c2oc)). Qed. Lemma pdc631: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->(p a1 ac)->(l b2c2 oc)->(i o b2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vlb2c2oc:(l b2c2 oc))=>((lcon o oc b2c2) (conj pdc16 (pdc625 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2 Vpa1ac Vlb2c2oc)))). Qed. Lemma pdc635: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->(p a1 ac)->(l b2c2 oc)->(p a1 o) \/ (l b2c2 oa). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vlb2c2oc:(l b2c2 oc))=>((unique a1 o b2c2 oa) (conj (proj1 pdc1) (conj pdc17 (conj (pdc631 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2 Vpa1ac Vlb2c2oc) pdc14))))). Qed. Lemma pdc643: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->(p a1 ac)->(l b2c2 oc)->(p a1 o)->(i a1 ob). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vlb2c2oc:(l b2c2 oc))(Vpa1o:(p a1 o))=>((pcon a1 o ob) (conj Vpa1o pdc15))). Qed. Lemma pdc650: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->(p a1 ac)->(l b2c2 oc)->(p a1 o)->(p a1 b2) \/ (l b2c2 ob). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vlb2c2oc:(l b2c2 oc))(Vpa1o:(p a1 o))=>((unique a1 b2 b2c2 ob) (conj (proj1 pdc1) (conj (pdc643 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2 Vpa1ac Vlb2c2oc Vpa1o) (conj pdc13 pdc20))))). Qed. Lemma pdc660: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->(p a1 ac)->(l b2c2 oc)->(p a1 o)->(p a1 b2)->(i a1 a2b2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vlb2c2oc:(l b2c2 oc))(Vpa1o:(p a1 o))(Vpa1b2:(p a1 b2))=>((pcon a1 b2 a2b2) (conj Vpa1b2 pdc5))). Qed. Lemma pdc662: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->(p a1 ac)->(l b2c2 oc)->(p a1 o)->(p a1 b2)->(i c2 a2b2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vlb2c2oc:(l b2c2 oc))(Vpa1o:(p a1 o))(Vpa1b2:(p a1 b2))=>((pcon c2 a1 a2b2) (conj (pdc599 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2) (pdc660 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2 Vpa1ac Vlb2c2oc Vpa1o Vpa1b2)))). Qed. Lemma pdc663: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->(p a1 ac)->(l b2c2 oc)->(p a1 o)->(p a1 b2)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vlb2c2oc:(l b2c2 oc))(Vpa1o:(p a1 o))(Vpa1b2:(p a1 b2))=>((triangle2 a2b2) (conj pdc4 (conj pdc5 (pdc662 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2 Vpa1ac Vlb2c2oc Vpa1o Vpa1b2))))). Qed. Lemma pdc664: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->(p a1 ac)->(l b2c2 oc)->(p a1 o)->(p a1 b2)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vlb2c2oc:(l b2c2 oc))(Vpa1o:(p a1 o))(Vpa1b2:(p a1 b2))=>((false_ind goal) (pdc663 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2 Vpa1ac Vlb2c2oc Vpa1o Vpa1b2))). Qed. Lemma pdc666: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->(p a1 ac)->(l b2c2 oc)->(p a1 o)->(l b2c2 ob)->(l a1c1 ob). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vlb2c2oc:(l b2c2 oc))(Vpa1o:(p a1 o))(Vlb2c2ob:(l b2c2 ob))=>((ltra a1c1 b2c2 ob) (conj (pdc583 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1) Vlb2c2ob))). Qed. Lemma pdc672: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->(p a1 ac)->(l b2c2 oc)->(p a1 o)->(l b2c2 ob)->(i c1 ob). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vlb2c2oc:(l b2c2 oc))(Vpa1o:(p a1 o))(Vlb2c2ob:(l b2c2 ob))=>((lcon c1 a1c1 ob) (conj pdc7 (pdc666 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2 Vpa1ac Vlb2c2oc Vpa1o Vlb2c2ob)))). Qed. Lemma pdc673: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->(p a1 ac)->(l b2c2 oc)->(p a1 o)->(l b2c2 ob)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vlb2c2oc:(l b2c2 oc))(Vpa1o:(p a1 o))(Vlb2c2ob:(l b2c2 ob))=>((triangle1 ob) (conj (pdc643 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2 Vpa1ac Vlb2c2oc Vpa1o) (conj pdc19 (pdc672 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2 Vpa1ac Vlb2c2oc Vpa1o Vlb2c2ob))))). Qed. Lemma pdc674: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->(p a1 ac)->(l b2c2 oc)->(p a1 o)->(l b2c2 ob)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vlb2c2oc:(l b2c2 oc))(Vpa1o:(p a1 o))(Vlb2c2ob:(l b2c2 ob))=>((false_ind goal) (pdc673 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2 Vpa1ac Vlb2c2oc Vpa1o Vlb2c2ob))). Qed. Lemma pdc675: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->(p a1 ac)->(l b2c2 oc)->(p a1 o)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vlb2c2oc:(l b2c2 oc))(Vpa1o:(p a1 o))=>((or_ind ((pdc664 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2 Vpa1ac Vlb2c2oc Vpa1o))((pdc674 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2 Vpa1ac Vlb2c2oc Vpa1o)))(pdc650 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2 Vpa1ac Vlb2c2oc Vpa1o))). Qed. Lemma pdc684: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->(p a1 ac)->(l b2c2 oc)->(l b2c2 oa)->(i b2 oa). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vlb2c2oc:(l b2c2 oc))(Vlb2c2oa:(l b2c2 oa))=>((lcon b2 b2c2 oa) (conj pdc13 Vlb2c2oa))). Qed. Lemma pdc685: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->(p a1 ac)->(l b2c2 oc)->(l b2c2 oa)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vlb2c2oc:(l b2c2 oc))(Vlb2c2oa:(l b2c2 oa))=>((triangle2 oa) (conj pdc18 (conj (pdc684 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2 Vpa1ac Vlb2c2oc Vlb2c2oa) (pdc607 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2))))). Qed. Lemma pdc686: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->(p a1 ac)->(l b2c2 oc)->(l b2c2 oa)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vlb2c2oc:(l b2c2 oc))(Vlb2c2oa:(l b2c2 oa))=>((false_ind goal) (pdc685 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2 Vpa1ac Vlb2c2oc Vlb2c2oa))). Qed. Lemma pdc687: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->(p a1 ac)->(l b2c2 oc)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vlb2c2oc:(l b2c2 oc))=>((or_ind ((pdc675 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2 Vpa1ac Vlb2c2oc))((pdc686 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2 Vpa1ac Vlb2c2oc)))(pdc635 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2 Vpa1ac Vlb2c2oc))). Qed. Lemma pdc688: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->(p a1 ac)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))=>((or_ind ((pdc624 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2 Vpa1ac))((pdc687 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2 Vpa1ac)))(pdc618 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2 Vpa1ac))). Qed. Lemma pdc690: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->(l b2c2 a2c2)->(l a1c1 a2c2). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))(Vlb2c2a2c2:(l b2c2 a2c2))=>((ltra a1c1 b2c2 a2c2) (conj (pdc583 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1) Vlb2c2a2c2))). Qed. Lemma pdc691: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->(l b2c2 a2c2)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))(Vlb2c2a2c2:(l b2c2 a2c2))=>(notac (pdc690 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2 Vlb2c2a2c2))). Qed. Lemma pdc692: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->(l b2c2 a2c2)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))(Vlb2c2a2c2:(l b2c2 a2c2))=>((false_ind goal) (pdc691 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2 Vlb2c2a2c2))). Qed. Lemma pdc693: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(p a1 c2)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vpa1c2:(p a1 c2))=>((or_ind ((pdc688 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2))((pdc692 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2)))(pdc608 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vpa1c2))). Qed. Lemma pdc695: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(l b2c2 C3)->(l a1c1 C3). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vlb2c2C3:(l b2c2 C3))=>((ltra a1c1 b2c2 C3) (conj (pdc583 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1) Vlb2c2C3))). Qed. Lemma pdc701: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(l b2c2 C3)->(i bc C3). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vlb2c2C3:(l b2c2 C3))=>((lcon bc b2c2 C3) (conj pdc24 Vlb2c2C3))). Qed. Lemma pdc702: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(l b2c2 C3)->(i ac C3). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vlb2c2C3:(l b2c2 C3))=>((lcon ac a1c1 C3) (conj pdc25 (pdc695 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vlb2c2C3)))). Qed. Lemma pdc703: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->(l b2c2 C3)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))(Vlb2c2C3:(l b2c2 C3))=>((goal_ax C3) (conj VlC3C3 (conj (pdc701 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vlb2c2C3) (conj (pdc702 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1 Vlb2c2C3) ViabC3))))). Qed. Lemma pdc704: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(p a1 C1)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vpa1C1:(p a1 C1))=>((or_ind ((pdc693 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1))((pdc703 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1)))(pdc598 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vpa1C1))). Qed. Lemma pdc711: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(l b2c2 oa)->(i c2 oa). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vlb2c2oa:(l b2c2 oa))=>((lcon c2 b2c2 oa) (conj pdc12 Vlb2c2oa))). Qed. Lemma pdc712: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(l b2c2 oa)->(i b2 oa). Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vlb2c2oa:(l b2c2 oa))=>((lcon b2 b2c2 oa) (conj pdc13 Vlb2c2oa))). Qed. Lemma pdc713: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(l b2c2 oa)->false. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vlb2c2oa:(l b2c2 oa))=>((triangle2 oa) (conj pdc18 (conj (pdc712 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vlb2c2oa) (pdc711 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vlb2c2oa))))). Qed. Lemma pdc714: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->(l b2c2 oa)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))(Vlb2c2oa:(l b2c2 oa))=>((false_ind goal) (pdc713 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1 Vlb2c2oa))). Qed. Lemma pdc715: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->(l b2c2 a1c1)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))(Vlb2c2a1c1:(l b2c2 a1c1))=>((or_ind ((pdc704 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1))((pdc714 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1)))(pdc594 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1 Vlb2c2a1c1))). Qed. Lemma pdc716: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->(l C0 a1c1)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(VlC0a1c1:(l C0 a1c1))=>((or_ind ((pdc582 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1))((pdc715 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1)))(pdc443 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 VlC0a1c1))). Qed. Lemma pdc717: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->forall C5:dom,(l C5 C5)->(i ab C5)->(i bc C5)->(i ac C5)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))(C5:dom)(VlC5C5:(l C5 C5))(ViabC5:(i ab C5))(VibcC5:(i bc C5))(ViacC5:(i ac C5))=>((goal_ax C5) (conj VlC5C5 (conj VibcC5 (conj ViacC5 ViabC5))))). Qed. Lemma pdc718: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->forall C4:dom,(l C4 C4)->(i a2 C4)->(i bc C4)->(i C2 C4)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))(C4:dom)(VlC4C4:(l C4 C4))(Via2C4:(i a2 C4))(VibcC4:(i bc C4))(ViC2C4:(i C2 C4))=>((or_ind ((pdc430 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4))(or_ind ((pdc436 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4))(or_ind ((pdc716 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4))(ex_ind (P:=fun C5:dom=>(l C5 C5)/\(i ab C5)/\(i bc C5)/\(i ac C5))(fun C5:dom=>(and_ind (fun VlC5C5:(l C5 C5)=>(and_ind (fun ViabC5:(i ab C5)=>(and_ind (pdc717 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4 C5 VlC5C5 ViabC5)))))))))))(pdc424 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4 VibcC4 ViC2C4))). Qed. Lemma pdc719: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->forall C3:dom,(l C3 C3)->(i c2 C3)->(i ab C3)->(i C1 C3)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))(C3:dom)(VlC3C3:(l C3 C3))(Vic2C3:(i c2 C3))(ViabC3:(i ab C3))(ViC1C3:(i C1 C3))=>((or_ind ((pdc328 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3))(or_ind ((pdc331 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3))(or_ind ((pdc423 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3))(ex_ind (P:=fun C4:dom=>(l C4 C4)/\(i a2 C4)/\(i bc C4)/\(i C2 C4))(fun C4:dom=>(and_ind (fun VlC4C4:(l C4 C4)=>(and_ind (fun Via2C4:(i a2 C4)=>(and_ind (pdc718 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3 C4 VlC4C4 Via2C4)))))))))))(pdc273 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3 ViabC3 ViC1C3))). Qed. Lemma pdc720: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->forall C2:dom,(i C2 C0)->(i C2 oc)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))(C2:dom)(ViC2C0:(i C2 C0))(ViC2oc:(i C2 oc))=>((or_ind ((pdc128 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc))(or_ind ((pdc131 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc))(or_ind ((pdc272 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc))(ex_ind (P:=fun C3:dom=>(l C3 C3)/\(i c2 C3)/\(i ab C3)/\(i C1 C3))(fun C3:dom=>(and_ind (fun VlC3C3:(l C3 C3)=>(and_ind (fun Vic2C3:(i c2 C3)=>(and_ind (pdc719 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc C3 VlC3C3 Vic2C3)))))))))))(pdc54 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2 ViC2C0 ViC2oc))). Qed. Lemma pdc721: forall C0:dom,(i ac C0)->(i b2 C0)->forall C1:dom,(i C1 C0)->(i C1 oa)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))(C1:dom)(ViC1C0:(i C1 C0))(ViC1oa:(i C1 oa))=>((ex_ind (P:=fun C2:dom=>(i C2 C0)/\(i C2 oc))(fun C2:dom=>(and_ind (pdc720 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa C2))))(pdc52 C0 ViacC0 Vib2C0 C1 ViC1C0 ViC1oa))). Qed. Lemma pdc722: forall C0:dom,(i ac C0)->(i b2 C0)->goal. Proof. exact (fun (C0:dom)(ViacC0:(i ac C0))(Vib2C0:(i b2 C0))=>((ex_ind (P:=fun C1:dom=>(i C1 C0)/\(i C1 oa))(fun C1:dom=>(and_ind (pdc721 C0 ViacC0 Vib2C0 C1))))(pdc50 C0 ViacC0 Vib2C0))). Qed. Lemma pdc723: goal. Proof. exact (((ex_ind (P:=fun C0:dom=>(i ac C0)/\(i b2 C0))(fun C0:dom=>(and_ind (pdc722 C0))))pdc48)). Qed. Check pdc723. End pdc.