Section p1p2_. Let false:=False. Let false_ind:=False_ind. Variable dom:Set. Variable col:dom->dom->dom->dom->Prop. Variable el:dom->dom->Prop. Variable ep:dom->dom->Prop. Variable goal:Prop. Variable pl:dom->dom->Prop. Variable a b c d e f g h i l m n o p q r s:dom. Hypothesis assump1:(col a b c l)/\(col d e f m). Hypothesis assump2:(col b f g n)/\(col c e g o). Hypothesis assump3:(col b d h p)/\(col a e h q). Hypothesis assump4:(col c d i r)/\(col a f i s). Hypothesis goal1:(el n o)->goal. Hypothesis goal2:(el p q)->goal. Hypothesis goal3:(el s r)->goal. Hypothesis goal4:forall A:dom,(el A A)/\(pl g A)/\(pl h A)/\(pl i A)->goal. Hypothesis col_elim1:forall A B C D:dom,(col A B C D)->(pl A D). Hypothesis col_elim2:forall A B C D:dom,(col A B C D)->(pl B D). Hypothesis col_elim3:forall A B C D:dom,(col A B C D)->(pl C D). Hypothesis pref:forall A B:dom,(pl A B)->(ep A A). Hypothesis psym:forall A B:dom,(ep A B)->(ep B A). Hypothesis ptra:forall A B C:dom,(ep A B)/\(ep B C)->(ep A C). Hypothesis lref:forall A B:dom,(pl A B)->(el B B). Hypothesis lsym:forall A B:dom,(el A B)->(el B A). Hypothesis ltra:forall A B C:dom,(el A B)/\(el B C)->(el A C). Hypothesis pcon:forall A B C:dom,(ep A B)/\(pl B C)->(pl A C). Hypothesis lcon:forall A B C:dom,(pl A B)/\(el B C)->(pl A C). Hypothesis papp1:forall A B C D E F G H I J K L M N O P Q:dom,(col A B C J)/\(col D E F K)/\(col B F G L)/\(col C E G M)/\(col B D H N)/\(col A E H O)/\(col C D I P)/\(col A F I Q)->(exists R:dom,(col G H I R)) \/ (pl A K) \/ (pl B K) \/ (pl C K) \/ (pl D J) \/ (pl E J) \/ (pl F J). Hypothesis unique:forall A B C D:dom,(pl C A)/\(pl C B)/\(pl D A)/\(pl D B)->(ep C D) \/ (el A B). Hypothesis line:forall A B:dom,(ep A A)/\(ep B B)->(exists C:dom,(pl A C)/\(pl B C)). Hypothesis point:forall A B C:dom,(el C C)/\(el B B)->(exists A:dom,(pl A B)/\(pl A C)). Lemma p1p2_1: (col a b c l)/\(col d e f m). Proof. exact (assump1). Qed. Lemma p1p2_2: (col b f g n)/\(col c e g o). Proof. exact (assump2). Qed. Lemma p1p2_3: (col b d h p)/\(col a e h q). Proof. exact (assump3). Qed. Lemma p1p2_4: (col c d i r)/\(col a f i s). Proof. exact (assump4). Qed. Lemma p1p2_5: (pl a l). Proof. exact (((col_elim1 a b c l) (proj1 p1p2_1))). Qed. Lemma p1p2_6: (pl d m). Proof. exact (((col_elim1 d e f m) (proj2 p1p2_1))). Qed. Lemma p1p2_7: (pl b n). Proof. exact (((col_elim1 b f g n) (proj1 p1p2_2))). Qed. Lemma p1p2_8: (pl c o). Proof. exact (((col_elim1 c e g o) (proj2 p1p2_2))). Qed. Lemma p1p2_9: (pl b p). Proof. exact (((col_elim1 b d h p) (proj1 p1p2_3))). Qed. Lemma p1p2_10: (pl a q). Proof. exact (((col_elim1 a e h q) (proj2 p1p2_3))). Qed. Lemma p1p2_11: (pl c r). Proof. exact (((col_elim1 c d i r) (proj1 p1p2_4))). Qed. Lemma p1p2_12: (pl a s). Proof. exact (((col_elim1 a f i s) (proj2 p1p2_4))). Qed. Lemma p1p2_13: (pl b l). Proof. exact (((col_elim2 a b c l) (proj1 p1p2_1))). Qed. Lemma p1p2_14: (pl e m). Proof. exact (((col_elim2 d e f m) (proj2 p1p2_1))). Qed. Lemma p1p2_15: (pl f n). Proof. exact (((col_elim2 b f g n) (proj1 p1p2_2))). Qed. Lemma p1p2_16: (pl e o). Proof. exact (((col_elim2 c e g o) (proj2 p1p2_2))). Qed. Lemma p1p2_17: (pl d p). Proof. exact (((col_elim2 b d h p) (proj1 p1p2_3))). Qed. Lemma p1p2_18: (pl e q). Proof. exact (((col_elim2 a e h q) (proj2 p1p2_3))). Qed. Lemma p1p2_19: (pl d r). Proof. exact (((col_elim2 c d i r) (proj1 p1p2_4))). Qed. Lemma p1p2_20: (pl f s). Proof. exact (((col_elim2 a f i s) (proj2 p1p2_4))). Qed. Lemma p1p2_21: (pl c l). Proof. exact (((col_elim3 a b c l) (proj1 p1p2_1))). Qed. Lemma p1p2_22: (pl f m). Proof. exact (((col_elim3 d e f m) (proj2 p1p2_1))). Qed. Lemma p1p2_23: (pl g n). Proof. exact (((col_elim3 b f g n) (proj1 p1p2_2))). Qed. Lemma p1p2_24: (pl g o). Proof. exact (((col_elim3 c e g o) (proj2 p1p2_2))). Qed. Lemma p1p2_25: (pl h p). Proof. exact (((col_elim3 b d h p) (proj1 p1p2_3))). Qed. Lemma p1p2_26: (pl h q). Proof. exact (((col_elim3 a e h q) (proj2 p1p2_3))). Qed. Lemma p1p2_27: (pl i r). Proof. exact (((col_elim3 c d i r) (proj1 p1p2_4))). Qed. Lemma p1p2_28: (pl i s). Proof. exact (((col_elim3 a f i s) (proj2 p1p2_4))). Qed. Lemma p1p2_29: (ep a a). Proof. exact (((pref a l) p1p2_5)). Qed. Lemma p1p2_30: (ep d d). Proof. exact (((pref d m) p1p2_6)). Qed. Lemma p1p2_31: (ep b b). Proof. exact (((pref b n) p1p2_7)). Qed. Lemma p1p2_32: (ep c c). Proof. exact (((pref c o) p1p2_8)). Qed. Lemma p1p2_33: (ep e e). Proof. exact (((pref e m) p1p2_14)). Qed. Lemma p1p2_34: (ep f f). Proof. exact (((pref f n) p1p2_15)). Qed. Lemma p1p2_35: (ep g g). Proof. exact (((pref g n) p1p2_23)). Qed. Lemma p1p2_36: (ep h h). Proof. exact (((pref h p) p1p2_25)). Qed. Lemma p1p2_37: (ep i i). Proof. exact (((pref i r) p1p2_27)). Qed. Lemma p1p2_38: (el l l). Proof. exact (((lref a l) p1p2_5)). Qed. Lemma p1p2_40: (el n n). Proof. exact (((lref b n) p1p2_7)). Qed. Lemma p1p2_41: (el o o). Proof. exact (((lref c o) p1p2_8)). Qed. Lemma p1p2_42: (el p p). Proof. exact (((lref b p) p1p2_9)). Qed. Lemma p1p2_43: (el q q). Proof. exact (((lref a q) p1p2_10)). Qed. Lemma p1p2_44: (el r r). Proof. exact (((lref c r) p1p2_11)). Qed. Lemma p1p2_45: (el s s). Proof. exact (((lref a s) p1p2_12)). Qed. Lemma p1p2_46: (exists A:dom,(col g h i A)) \/ (pl a m) \/ (pl b m) \/ (pl c m) \/ (pl d l) \/ (pl e l) \/ (pl f l). Proof. exact (((papp1 a b c d e f g h i l m n o p q r s) (conj (proj1 p1p2_1) (conj (proj2 p1p2_1) (conj (proj1 p1p2_2) (conj (proj2 p1p2_2) (conj (proj1 p1p2_3) (conj (proj2 p1p2_3) (conj (proj1 p1p2_4) (proj2 p1p2_4)))))))))). Qed. Lemma p1p2_47: forall C0:dom,(col g h i C0)->(pl g C0). Proof. exact (fun (C0:dom)(VcolghiC0:(col g h i C0))=>((col_elim1 g h i C0) VcolghiC0)). Qed. Lemma p1p2_48: forall C0:dom,(col g h i C0)->(pl h C0). Proof. exact (fun (C0:dom)(VcolghiC0:(col g h i C0))=>((col_elim2 g h i C0) VcolghiC0)). Qed. Lemma p1p2_49: forall C0:dom,(col g h i C0)->(pl i C0). Proof. exact (fun (C0:dom)(VcolghiC0:(col g h i C0))=>((col_elim3 g h i C0) VcolghiC0)). Qed. Lemma p1p2_50: forall C0:dom,(col g h i C0)->(el C0 C0). Proof. exact (fun (C0:dom)(VcolghiC0:(col g h i C0))=>((lref g C0) (p1p2_47 C0 VcolghiC0))). Qed. Lemma p1p2_51: forall C0:dom,(col g h i C0)->goal. Proof. exact (fun (C0:dom)(VcolghiC0:(col g h i C0))=>((goal4 C0) (conj (p1p2_50 C0 VcolghiC0) (conj (p1p2_47 C0 VcolghiC0) (conj (p1p2_48 C0 VcolghiC0) (p1p2_49 C0 VcolghiC0)))))). Qed. Lemma p1p2_52: (pl a m)->(ep a e) \/ (el q m). Proof. exact (fun (Vplam:(pl a m))=>((unique q m a e) (conj p1p2_10 (conj Vplam (conj p1p2_18 p1p2_14))))). Qed. Lemma p1p2_53: (pl a m)->(ep a e)->(ep e a). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))=>((psym a e) Vepae)). Qed. Lemma p1p2_54: (pl a m)->(ep a e)->(pl a o). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))=>((pcon a e o) (conj Vepae p1p2_16))). Qed. Lemma p1p2_56: (pl a m)->(ep a e)->(pl e s). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))=>((pcon e a s) (conj (p1p2_53 Vplam Vepae) p1p2_12))). Qed. Lemma p1p2_57: (pl a m)->(ep a e)->(ep a c) \/ (el l o). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))=>((unique l o a c) (conj p1p2_5 (conj (p1p2_54 Vplam Vepae) (conj p1p2_21 p1p2_8))))). Qed. Lemma p1p2_58: (pl a m)->(ep a e)->(ep a c)->(ep c a). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))=>((psym a c) Vepac)). Qed. Lemma p1p2_61: (pl a m)->(ep a e)->(ep a c)->(pl a r). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))=>((pcon a c r) (conj Vepac p1p2_11))). Qed. Lemma p1p2_62: (pl a m)->(ep a e)->(ep a c)->(pl e r). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))=>((pcon e a r) (conj (p1p2_53 Vplam Vepae) (p1p2_61 Vplam Vepae Vepac)))). Qed. Lemma p1p2_63: (pl a m)->(ep a e)->(ep a c)->(pl c q). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))=>((pcon c a q) (conj (p1p2_58 Vplam Vepae Vepac) p1p2_10))). Qed. Lemma p1p2_64: (pl a m)->(ep a e)->(ep a c)->(pl c s). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))=>((pcon c a s) (conj (p1p2_58 Vplam Vepae Vepac) p1p2_12))). Qed. Lemma p1p2_66: (pl a m)->(ep a e)->(ep a c)->(ep d e) \/ (el m r). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))=>((unique m r d e) (conj p1p2_6 (conj p1p2_19 (conj p1p2_14 (p1p2_62 Vplam Vepae Vepac)))))). Qed. Lemma p1p2_67: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep e d). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))=>((psym d e) Vepde)). Qed. Lemma p1p2_72: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(pl d o). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))=>((pcon d e o) (conj Vepde p1p2_16))). Qed. Lemma p1p2_75: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(pl d s). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))=>((pcon d e s) (conj Vepde (p1p2_56 Vplam Vepae)))). Qed. Lemma p1p2_76: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(pl e p). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))=>((pcon e d p) (conj (p1p2_67 Vplam Vepae Vepac Vepde) p1p2_17))). Qed. Lemma p1p2_77: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(pl a p). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))=>((pcon a e p) (conj Vepae (p1p2_76 Vplam Vepae Vepac Vepde)))). Qed. Lemma p1p2_79: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b) \/ (el l p). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))=>((unique l p a b) (conj p1p2_5 (conj (p1p2_77 Vplam Vepae Vepac Vepde) (conj p1p2_13 p1p2_9))))). Qed. Lemma p1p2_80: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(ep b a). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))=>((psym a b) Vepab)). Qed. Lemma p1p2_87: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(pl a n). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))=>((pcon a b n) (conj Vepab p1p2_7))). Qed. Lemma p1p2_88: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(pl e n). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))=>((pcon e a n) (conj (p1p2_53 Vplam Vepae) (p1p2_87 Vplam Vepae Vepac Vepde Vepab)))). Qed. Lemma p1p2_90: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(pl d n). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))=>((pcon d e n) (conj Vepde (p1p2_88 Vplam Vepae Vepac Vepde Vepab)))). Qed. Lemma p1p2_91: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(pl b q). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))=>((pcon b a q) (conj (p1p2_80 Vplam Vepae Vepac Vepde Vepab) p1p2_10))). Qed. Lemma p1p2_92: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(pl b s). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))=>((pcon b a s) (conj (p1p2_80 Vplam Vepae Vepac Vepde Vepab) p1p2_12))). Qed. Lemma p1p2_94: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(pl b o). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))=>((pcon b a o) (conj (p1p2_80 Vplam Vepae Vepac Vepde Vepab) (p1p2_54 Vplam Vepae)))). Qed. Lemma p1p2_96: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(ep d f) \/ (el m s). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))=>((unique m s d f) (conj p1p2_6 (conj (p1p2_75 Vplam Vepae Vepac Vepde) (conj p1p2_22 p1p2_20))))). Qed. Lemma p1p2_111: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(ep d f)->(ep b g) \/ (el n o). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdf:(ep d f))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_94 Vplam Vepae Vepac Vepde Vepab) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_112: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(ep d f)->(ep b g)->(ep g b). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_126: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(ep d f)->(ep b g)->(pl g s). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepbg:(ep b g))=>((pcon g b s) (conj (p1p2_112 Vplam Vepae Vepac Vepde Vepab Vepdf Vepbg) (p1p2_92 Vplam Vepae Vepac Vepde Vepab)))). Qed. Lemma p1p2_129: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(ep d f)->(ep b g)->(ep b h) \/ (el p q). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepbg:(ep b g))=>((unique p q b h) (conj p1p2_9 (conj (p1p2_91 Vplam Vepae Vepac Vepde Vepab) (conj p1p2_25 p1p2_26))))). Qed. Lemma p1p2_130: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(ep d f)->(ep b g)->(ep b h)->(ep h b). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepbg:(ep b g))(Vepbh:(ep b h))=>((psym b h) Vepbh)). Qed. Lemma p1p2_145: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(ep d f)->(ep b g)->(ep b h)->(pl h s). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepbg:(ep b g))(Vepbh:(ep b h))=>((pcon h b s) (conj (p1p2_130 Vplam Vepae Vepac Vepde Vepab Vepdf Vepbg Vepbh) (p1p2_92 Vplam Vepae Vepac Vepde Vepab)))). Qed. Lemma p1p2_146: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(ep d f)->(ep b g)->(ep b h)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepbg:(ep b g))(Vepbh:(ep b h))=>((goal4 s) (conj p1p2_45 (conj (p1p2_126 Vplam Vepae Vepac Vepde Vepab Vepdf Vepbg) (conj (p1p2_145 Vplam Vepae Vepac Vepde Vepab Vepdf Vepbg Vepbh) p1p2_28))))). Qed. Lemma p1p2_147: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(ep d f)->(ep b g)->(el p q)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepbg:(ep b g))(Velpq:(el p q))=>(goal2 Velpq)). Qed. Lemma p1p2_148: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(ep d f)->(ep b g)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepbg:(ep b g))=>((or_ind ((p1p2_146 Vplam Vepae Vepac Vepde Vepab Vepdf Vepbg))((p1p2_147 Vplam Vepae Vepac Vepde Vepab Vepdf Vepbg)))(p1p2_129 Vplam Vepae Vepac Vepde Vepab Vepdf Vepbg))). Qed. Lemma p1p2_149: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(ep d f)->(el n o)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdf:(ep d f))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_150: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(ep d f)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdf:(ep d f))=>((or_ind ((p1p2_148 Vplam Vepae Vepac Vepde Vepab Vepdf))((p1p2_149 Vplam Vepae Vepac Vepde Vepab Vepdf)))(p1p2_111 Vplam Vepae Vepac Vepde Vepab Vepdf))). Qed. Lemma p1p2_151: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(el s m). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))=>((lsym m s) Velms)). Qed. Lemma p1p2_152: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(pl i m). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))=>((lcon i s m) (conj p1p2_28 (p1p2_151 Vplam Vepae Vepac Vepde Vepab Velms)))). Qed. Lemma p1p2_153: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i) \/ (el m r). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))=>((unique m r d i) (conj p1p2_6 (conj p1p2_19 (conj (p1p2_152 Vplam Vepae Vepac Vepde Vepab Velms) p1p2_27))))). Qed. Lemma p1p2_154: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(ep i d). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))=>((psym d i) Vepdi)). Qed. Lemma p1p2_163: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(pl i p). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))=>((pcon i d p) (conj (p1p2_154 Vplam Vepae Vepac Vepde Vepab Velms Vepdi) p1p2_17))). Qed. Lemma p1p2_168: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(ep d f) \/ (el m n). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))=>((unique m n d f) (conj p1p2_6 (conj (p1p2_90 Vplam Vepae Vepac Vepde Vepab) (conj p1p2_22 p1p2_15))))). Qed. Lemma p1p2_185: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(ep d f)->(ep b g) \/ (el n o). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Vepdf:(ep d f))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_94 Vplam Vepae Vepac Vepde Vepab) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_186: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(ep d f)->(ep b g)->(ep g b). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Vepdf:(ep d f))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_199: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(ep d f)->(ep b g)->(pl g p). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Vepdf:(ep d f))(Vepbg:(ep b g))=>((pcon g b p) (conj (p1p2_186 Vplam Vepae Vepac Vepde Vepab Velms Vepdi Vepdf Vepbg) p1p2_9))). Qed. Lemma p1p2_200: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(ep d f)->(ep b g)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Vepdf:(ep d f))(Vepbg:(ep b g))=>((goal4 p) (conj p1p2_42 (conj (p1p2_199 Vplam Vepae Vepac Vepde Vepab Velms Vepdi Vepdf Vepbg) (conj p1p2_25 (p1p2_163 Vplam Vepae Vepac Vepde Vepab Velms Vepdi)))))). Qed. Lemma p1p2_201: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(ep d f)->(el n o)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Vepdf:(ep d f))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_202: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(ep d f)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Vepdf:(ep d f))=>((or_ind ((p1p2_200 Vplam Vepae Vepac Vepde Vepab Velms Vepdi Vepdf))((p1p2_201 Vplam Vepae Vepac Vepde Vepab Velms Vepdi Vepdf)))(p1p2_185 Vplam Vepae Vepac Vepde Vepab Velms Vepdi Vepdf))). Qed. Lemma p1p2_203: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(el m n)->(el n m). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Velmn:(el m n))=>((lsym m n) Velmn)). Qed. Lemma p1p2_206: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(el m n)->(pl g m). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Velmn:(el m n))=>((lcon g n m) (conj p1p2_23 (p1p2_203 Vplam Vepae Vepac Vepde Vepab Velms Vepdi Velmn)))). Qed. Lemma p1p2_208: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(el m n)->(ep d g) \/ (el m o). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Velmn:(el m n))=>((unique m o d g) (conj p1p2_6 (conj (p1p2_72 Vplam Vepae Vepac Vepde) (conj (p1p2_206 Vplam Vepae Vepac Vepde Vepab Velms Vepdi Velmn) p1p2_24))))). Qed. Lemma p1p2_209: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(el m n)->(ep d g)->(ep g d). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Velmn:(el m n))(Vepdg:(ep d g))=>((psym d g) Vepdg)). Qed. Lemma p1p2_220: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(el m n)->(ep d g)->(pl g p). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Velmn:(el m n))(Vepdg:(ep d g))=>((pcon g d p) (conj (p1p2_209 Vplam Vepae Vepac Vepde Vepab Velms Vepdi Velmn Vepdg) p1p2_17))). Qed. Lemma p1p2_221: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(el m n)->(ep d g)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Velmn:(el m n))(Vepdg:(ep d g))=>((goal4 p) (conj p1p2_42 (conj (p1p2_220 Vplam Vepae Vepac Vepde Vepab Velms Vepdi Velmn Vepdg) (conj p1p2_25 (p1p2_163 Vplam Vepae Vepac Vepde Vepab Velms Vepdi)))))). Qed. Lemma p1p2_225: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(el m n)->(el m o)->(el n o). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Velmn:(el m n))(Velmo:(el m o))=>((ltra n m o) (conj (p1p2_203 Vplam Vepae Vepac Vepde Vepab Velms Vepdi Velmn) Velmo))). Qed. Lemma p1p2_226: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(el m n)->(el m o)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Velmn:(el m n))(Velmo:(el m o))=>(goal1 (p1p2_225 Vplam Vepae Vepac Vepde Vepab Velms Vepdi Velmn Velmo))). Qed. Lemma p1p2_227: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(el m n)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Velmn:(el m n))=>((or_ind ((p1p2_221 Vplam Vepae Vepac Vepde Vepab Velms Vepdi Velmn))((p1p2_226 Vplam Vepae Vepac Vepde Vepab Velms Vepdi Velmn)))(p1p2_208 Vplam Vepae Vepac Vepde Vepab Velms Vepdi Velmn))). Qed. Lemma p1p2_228: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))=>((or_ind ((p1p2_202 Vplam Vepae Vepac Vepde Vepab Velms Vepdi))((p1p2_227 Vplam Vepae Vepac Vepde Vepab Velms Vepdi)))(p1p2_168 Vplam Vepae Vepac Vepde Vepab Velms Vepdi))). Qed. Lemma p1p2_230: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(el m r)->(el s r). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Velmr:(el m r))=>((ltra s m r) (conj (p1p2_151 Vplam Vepae Vepac Vepde Vepab Velms) Velmr))). Qed. Lemma p1p2_231: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(el m r)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Velmr:(el m r))=>(goal3 (p1p2_230 Vplam Vepae Vepac Vepde Vepab Velms Velmr))). Qed. Lemma p1p2_232: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))=>((or_ind ((p1p2_228 Vplam Vepae Vepac Vepde Vepab Velms))((p1p2_231 Vplam Vepae Vepac Vepde Vepab Velms)))(p1p2_153 Vplam Vepae Vepac Vepde Vepab Velms))). Qed. Lemma p1p2_233: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))=>((or_ind ((p1p2_150 Vplam Vepae Vepac Vepde Vepab))((p1p2_232 Vplam Vepae Vepac Vepde Vepab)))(p1p2_96 Vplam Vepae Vepac Vepde Vepab))). Qed. Lemma p1p2_234: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(el p l). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))=>((lsym l p) Vellp)). Qed. Lemma p1p2_235: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(pl h l). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))=>((lcon h p l) (conj p1p2_25 (p1p2_234 Vplam Vepae Vepac Vepde Vellp)))). Qed. Lemma p1p2_236: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h) \/ (el l q). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))=>((unique l q a h) (conj p1p2_5 (conj p1p2_10 (conj (p1p2_235 Vplam Vepae Vepac Vepde Vellp) p1p2_26))))). Qed. Lemma p1p2_237: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep h a). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))=>((psym a h) Vepah)). Qed. Lemma p1p2_244: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(pl h s). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))=>((pcon h a s) (conj (p1p2_237 Vplam Vepae Vepac Vepde Vellp Vepah) p1p2_12))). Qed. Lemma p1p2_246: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(pl h o). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))=>((pcon h a o) (conj (p1p2_237 Vplam Vepae Vepac Vepde Vellp Vepah) (p1p2_54 Vplam Vepae)))). Qed. Lemma p1p2_248: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f) \/ (el m s). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))=>((unique m s d f) (conj p1p2_6 (conj (p1p2_75 Vplam Vepae Vepac Vepde) (conj p1p2_22 p1p2_20))))). Qed. Lemma p1p2_258: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(pl d n). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))=>((pcon d f n) (conj Vepdf p1p2_15))). Qed. Lemma p1p2_259: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(pl e n). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))=>((pcon e d n) (conj (p1p2_67 Vplam Vepae Vepac Vepde) (p1p2_258 Vplam Vepae Vepac Vepde Vellp Vepah Vepdf)))). Qed. Lemma p1p2_260: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(pl a n). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))=>((pcon a e n) (conj Vepae (p1p2_259 Vplam Vepae Vepac Vepde Vellp Vepah Vepdf)))). Qed. Lemma p1p2_268: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(ep a b) \/ (el l n). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))=>((unique l n a b) (conj p1p2_5 (conj (p1p2_260 Vplam Vepae Vepac Vepde Vellp Vepah Vepdf) (conj p1p2_13 p1p2_7))))). Qed. Lemma p1p2_269: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(ep a b)->(ep b a). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Vepab:(ep a b))=>((psym a b) Vepab)). Qed. Lemma p1p2_281: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(ep a b)->(pl b s). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Vepab:(ep a b))=>((pcon b a s) (conj (p1p2_269 Vplam Vepae Vepac Vepde Vellp Vepah Vepdf Vepab) p1p2_12))). Qed. Lemma p1p2_283: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(ep a b)->(pl b o). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Vepab:(ep a b))=>((pcon b a o) (conj (p1p2_269 Vplam Vepae Vepac Vepde Vellp Vepah Vepdf Vepab) (p1p2_54 Vplam Vepae)))). Qed. Lemma p1p2_285: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(ep a b)->(ep b g) \/ (el n o). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Vepab:(ep a b))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_283 Vplam Vepae Vepac Vepde Vellp Vepah Vepdf Vepab) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_286: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(ep a b)->(ep b g)->(ep g b). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_302: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(ep a b)->(ep b g)->(pl g s). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepbg:(ep b g))=>((pcon g b s) (conj (p1p2_286 Vplam Vepae Vepac Vepde Vellp Vepah Vepdf Vepab Vepbg) (p1p2_281 Vplam Vepae Vepac Vepde Vellp Vepah Vepdf Vepab)))). Qed. Lemma p1p2_303: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(ep a b)->(ep b g)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepbg:(ep b g))=>((goal4 s) (conj p1p2_45 (conj (p1p2_302 Vplam Vepae Vepac Vepde Vellp Vepah Vepdf Vepab Vepbg) (conj (p1p2_244 Vplam Vepae Vepac Vepde Vellp Vepah) p1p2_28))))). Qed. Lemma p1p2_304: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(ep a b)->(el n o)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Vepab:(ep a b))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_305: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(ep a b)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Vepab:(ep a b))=>((or_ind ((p1p2_303 Vplam Vepae Vepac Vepde Vellp Vepah Vepdf Vepab))((p1p2_304 Vplam Vepae Vepac Vepde Vellp Vepah Vepdf Vepab)))(p1p2_285 Vplam Vepae Vepac Vepde Vellp Vepah Vepdf Vepab))). Qed. Lemma p1p2_306: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(el l n)->(el n l). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Velln:(el l n))=>((lsym l n) Velln)). Qed. Lemma p1p2_309: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(el l n)->(pl g l). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Velln:(el l n))=>((lcon g n l) (conj p1p2_23 (p1p2_306 Vplam Vepae Vepac Vepde Vellp Vepah Vepdf Velln)))). Qed. Lemma p1p2_311: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(el l n)->(ep a g) \/ (el l o). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Velln:(el l n))=>((unique l o a g) (conj p1p2_5 (conj (p1p2_54 Vplam Vepae) (conj (p1p2_309 Vplam Vepae Vepac Vepde Vellp Vepah Vepdf Velln) p1p2_24))))). Qed. Lemma p1p2_312: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(el l n)->(ep a g)->(ep g a). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Velln:(el l n))(Vepag:(ep a g))=>((psym a g) Vepag)). Qed. Lemma p1p2_324: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(el l n)->(ep a g)->(pl g s). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Velln:(el l n))(Vepag:(ep a g))=>((pcon g a s) (conj (p1p2_312 Vplam Vepae Vepac Vepde Vellp Vepah Vepdf Velln Vepag) p1p2_12))). Qed. Lemma p1p2_325: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(el l n)->(ep a g)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Velln:(el l n))(Vepag:(ep a g))=>((goal4 s) (conj p1p2_45 (conj (p1p2_324 Vplam Vepae Vepac Vepde Vellp Vepah Vepdf Velln Vepag) (conj (p1p2_244 Vplam Vepae Vepac Vepde Vellp Vepah) p1p2_28))))). Qed. Lemma p1p2_329: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(el l n)->(el l o)->(el n o). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Velln:(el l n))(Vello:(el l o))=>((ltra n l o) (conj (p1p2_306 Vplam Vepae Vepac Vepde Vellp Vepah Vepdf Velln) Vello))). Qed. Lemma p1p2_330: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(el l n)->(el l o)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Velln:(el l n))(Vello:(el l o))=>(goal1 (p1p2_329 Vplam Vepae Vepac Vepde Vellp Vepah Vepdf Velln Vello))). Qed. Lemma p1p2_331: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(el l n)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Velln:(el l n))=>((or_ind ((p1p2_325 Vplam Vepae Vepac Vepde Vellp Vepah Vepdf Velln))((p1p2_330 Vplam Vepae Vepac Vepde Vellp Vepah Vepdf Velln)))(p1p2_311 Vplam Vepae Vepac Vepde Vellp Vepah Vepdf Velln))). Qed. Lemma p1p2_332: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))=>((or_ind ((p1p2_305 Vplam Vepae Vepac Vepde Vellp Vepah Vepdf))((p1p2_331 Vplam Vepae Vepac Vepde Vellp Vepah Vepdf)))(p1p2_268 Vplam Vepae Vepac Vepde Vellp Vepah Vepdf))). Qed. Lemma p1p2_333: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(el m s)->(el s m). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Velms:(el m s))=>((lsym m s) Velms)). Qed. Lemma p1p2_334: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(el m s)->(pl i m). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Velms:(el m s))=>((lcon i s m) (conj p1p2_28 (p1p2_333 Vplam Vepae Vepac Vepde Vellp Vepah Velms)))). Qed. Lemma p1p2_335: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(el m s)->(ep d i) \/ (el m r). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Velms:(el m s))=>((unique m r d i) (conj p1p2_6 (conj p1p2_19 (conj (p1p2_334 Vplam Vepae Vepac Vepde Vellp Vepah Velms) p1p2_27))))). Qed. Lemma p1p2_336: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(el m s)->(ep d i)->(ep i d). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Velms:(el m s))(Vepdi:(ep d i))=>((psym d i) Vepdi)). Qed. Lemma p1p2_346: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(el m s)->(ep d i)->(pl i o). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Velms:(el m s))(Vepdi:(ep d i))=>((pcon i d o) (conj (p1p2_336 Vplam Vepae Vepac Vepde Vellp Vepah Velms Vepdi) (p1p2_72 Vplam Vepae Vepac Vepde)))). Qed. Lemma p1p2_347: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(el m s)->(ep d i)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Velms:(el m s))(Vepdi:(ep d i))=>((goal4 o) (conj p1p2_41 (conj p1p2_24 (conj (p1p2_246 Vplam Vepae Vepac Vepde Vellp Vepah) (p1p2_346 Vplam Vepae Vepac Vepde Vellp Vepah Velms Vepdi)))))). Qed. Lemma p1p2_349: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(el m s)->(el m r)->(el s r). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Velms:(el m s))(Velmr:(el m r))=>((ltra s m r) (conj (p1p2_333 Vplam Vepae Vepac Vepde Vellp Vepah Velms) Velmr))). Qed. Lemma p1p2_350: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(el m s)->(el m r)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Velms:(el m s))(Velmr:(el m r))=>(goal3 (p1p2_349 Vplam Vepae Vepac Vepde Vellp Vepah Velms Velmr))). Qed. Lemma p1p2_351: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(el m s)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Velms:(el m s))=>((or_ind ((p1p2_347 Vplam Vepae Vepac Vepde Vellp Vepah Velms))((p1p2_350 Vplam Vepae Vepac Vepde Vellp Vepah Velms)))(p1p2_335 Vplam Vepae Vepac Vepde Vellp Vepah Velms))). Qed. Lemma p1p2_352: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))=>((or_ind ((p1p2_332 Vplam Vepae Vepac Vepde Vellp Vepah))((p1p2_351 Vplam Vepae Vepac Vepde Vellp Vepah)))(p1p2_248 Vplam Vepae Vepac Vepde Vellp Vepah))). Qed. Lemma p1p2_354: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(el l q)->(el p q). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vellq:(el l q))=>((ltra p l q) (conj (p1p2_234 Vplam Vepae Vepac Vepde Vellp) Vellq))). Qed. Lemma p1p2_355: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(el l q)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vellq:(el l q))=>(goal2 (p1p2_354 Vplam Vepae Vepac Vepde Vellp Vellq))). Qed. Lemma p1p2_356: (pl a m)->(ep a e)->(ep a c)->(ep d e)->(el l p)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))=>((or_ind ((p1p2_352 Vplam Vepae Vepac Vepde Vellp))((p1p2_355 Vplam Vepae Vepac Vepde Vellp)))(p1p2_236 Vplam Vepae Vepac Vepde Vellp))). Qed. Lemma p1p2_357: (pl a m)->(ep a e)->(ep a c)->(ep d e)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))=>((or_ind ((p1p2_233 Vplam Vepae Vepac Vepde))((p1p2_356 Vplam Vepae Vepac Vepde)))(p1p2_79 Vplam Vepae Vepac Vepde))). Qed. Lemma p1p2_359: (pl a m)->(ep a e)->(ep a c)->(el m r)->(pl f r). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))=>((lcon f m r) (conj p1p2_22 Velmr))). Qed. Lemma p1p2_361: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i) \/ (el r s). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))=>((unique r s c i) (conj p1p2_11 (conj (p1p2_64 Vplam Vepae Vepac) (conj p1p2_27 p1p2_28))))). Qed. Lemma p1p2_362: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep i c). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))=>((psym c i) Vepci)). Qed. Lemma p1p2_369: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(pl i q). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))=>((pcon i c q) (conj (p1p2_362 Vplam Vepae Vepac Velmr Vepci) (p1p2_63 Vplam Vepae Vepac)))). Qed. Lemma p1p2_370: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f) \/ (el r s). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))=>((unique r s c f) (conj p1p2_11 (conj (p1p2_64 Vplam Vepae Vepac) (conj (p1p2_359 Vplam Vepae Vepac Velmr) p1p2_20))))). Qed. Lemma p1p2_378: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(pl c n). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))=>((pcon c f n) (conj Vepcf p1p2_15))). Qed. Lemma p1p2_379: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(pl a n). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))=>((pcon a c n) (conj Vepac (p1p2_378 Vplam Vepae Vepac Velmr Vepci Vepcf)))). Qed. Lemma p1p2_385: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b) \/ (el l n). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))=>((unique l n a b) (conj p1p2_5 (conj (p1p2_379 Vplam Vepae Vepac Velmr Vepci Vepcf) (conj p1p2_13 p1p2_7))))). Qed. Lemma p1p2_386: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(ep b a). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))=>((psym a b) Vepab)). Qed. Lemma p1p2_395: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(pl a p). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))=>((pcon a b p) (conj Vepab p1p2_9))). Qed. Lemma p1p2_396: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(pl e p). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))=>((pcon e a p) (conj (p1p2_53 Vplam Vepae) (p1p2_395 Vplam Vepae Vepac Velmr Vepci Vepcf Vepab)))). Qed. Lemma p1p2_397: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(pl c p). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))=>((pcon c a p) (conj (p1p2_58 Vplam Vepae Vepac) (p1p2_395 Vplam Vepae Vepac Velmr Vepci Vepcf Vepab)))). Qed. Lemma p1p2_398: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(pl i p). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))=>((pcon i c p) (conj (p1p2_362 Vplam Vepae Vepac Velmr Vepci) (p1p2_397 Vplam Vepae Vepac Velmr Vepci Vepcf Vepab)))). Qed. Lemma p1p2_403: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(pl b o). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))=>((pcon b a o) (conj (p1p2_386 Vplam Vepae Vepac Velmr Vepci Vepcf Vepab) (p1p2_54 Vplam Vepae)))). Qed. Lemma p1p2_405: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(ep d e) \/ (el m p). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))=>((unique m p d e) (conj p1p2_6 (conj p1p2_17 (conj p1p2_14 (p1p2_396 Vplam Vepae Vepac Velmr Vepci Vepcf Vepab)))))). Qed. Lemma p1p2_422: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(ep d e)->(ep b g) \/ (el n o). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Vepde:(ep d e))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_403 Vplam Vepae Vepac Velmr Vepci Vepcf Vepab) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_423: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(ep d e)->(ep b g)->(ep g b). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Vepde:(ep d e))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_436: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(ep d e)->(ep b g)->(pl g p). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Vepde:(ep d e))(Vepbg:(ep b g))=>((pcon g b p) (conj (p1p2_423 Vplam Vepae Vepac Velmr Vepci Vepcf Vepab Vepde Vepbg) p1p2_9))). Qed. Lemma p1p2_437: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(ep d e)->(ep b g)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Vepde:(ep d e))(Vepbg:(ep b g))=>((goal4 p) (conj p1p2_42 (conj (p1p2_436 Vplam Vepae Vepac Velmr Vepci Vepcf Vepab Vepde Vepbg) (conj p1p2_25 (p1p2_398 Vplam Vepae Vepac Velmr Vepci Vepcf Vepab)))))). Qed. Lemma p1p2_438: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(ep d e)->(el n o)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Vepde:(ep d e))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_439: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(ep d e)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Vepde:(ep d e))=>((or_ind ((p1p2_437 Vplam Vepae Vepac Velmr Vepci Vepcf Vepab Vepde))((p1p2_438 Vplam Vepae Vepac Velmr Vepci Vepcf Vepab Vepde)))(p1p2_422 Vplam Vepae Vepac Velmr Vepci Vepcf Vepab Vepde))). Qed. Lemma p1p2_445: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(el m p)->(ep b g) \/ (el n o). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Velmp:(el m p))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_403 Vplam Vepae Vepac Velmr Vepci Vepcf Vepab) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_446: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(el m p)->(ep b g)->(ep g b). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_457: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(el m p)->(ep b g)->(pl g p). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbg:(ep b g))=>((pcon g b p) (conj (p1p2_446 Vplam Vepae Vepac Velmr Vepci Vepcf Vepab Velmp Vepbg) p1p2_9))). Qed. Lemma p1p2_458: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(el m p)->(ep b g)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbg:(ep b g))=>((goal4 p) (conj p1p2_42 (conj (p1p2_457 Vplam Vepae Vepac Velmr Vepci Vepcf Vepab Velmp Vepbg) (conj p1p2_25 (p1p2_398 Vplam Vepae Vepac Velmr Vepci Vepcf Vepab)))))). Qed. Lemma p1p2_459: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(el m p)->(el n o)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Velmp:(el m p))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_460: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(el m p)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Velmp:(el m p))=>((or_ind ((p1p2_458 Vplam Vepae Vepac Velmr Vepci Vepcf Vepab Velmp))((p1p2_459 Vplam Vepae Vepac Velmr Vepci Vepcf Vepab Velmp)))(p1p2_445 Vplam Vepae Vepac Velmr Vepci Vepcf Vepab Velmp))). Qed. Lemma p1p2_461: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))=>((or_ind ((p1p2_439 Vplam Vepae Vepac Velmr Vepci Vepcf Vepab))((p1p2_460 Vplam Vepae Vepac Velmr Vepci Vepcf Vepab)))(p1p2_405 Vplam Vepae Vepac Velmr Vepci Vepcf Vepab))). Qed. Lemma p1p2_462: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(el l n)->(el n l). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Velln:(el l n))=>((lsym l n) Velln)). Qed. Lemma p1p2_463: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(el l n)->(pl g l). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Velln:(el l n))=>((lcon g n l) (conj p1p2_23 (p1p2_462 Vplam Vepae Vepac Velmr Vepci Vepcf Velln)))). Qed. Lemma p1p2_464: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(el l n)->(ep a g) \/ (el l o). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Velln:(el l n))=>((unique l o a g) (conj p1p2_5 (conj (p1p2_54 Vplam Vepae) (conj (p1p2_463 Vplam Vepae Vepac Velmr Vepci Vepcf Velln) p1p2_24))))). Qed. Lemma p1p2_465: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(el l n)->(ep a g)->(ep g a). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Velln:(el l n))(Vepag:(ep a g))=>((psym a g) Vepag)). Qed. Lemma p1p2_474: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(el l n)->(ep a g)->(pl g q). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Velln:(el l n))(Vepag:(ep a g))=>((pcon g a q) (conj (p1p2_465 Vplam Vepae Vepac Velmr Vepci Vepcf Velln Vepag) p1p2_10))). Qed. Lemma p1p2_475: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(el l n)->(ep a g)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Velln:(el l n))(Vepag:(ep a g))=>((goal4 q) (conj p1p2_43 (conj (p1p2_474 Vplam Vepae Vepac Velmr Vepci Vepcf Velln Vepag) (conj p1p2_26 (p1p2_369 Vplam Vepae Vepac Velmr Vepci)))))). Qed. Lemma p1p2_477: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(el l n)->(el l o)->(el n o). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Velln:(el l n))(Vello:(el l o))=>((ltra n l o) (conj (p1p2_462 Vplam Vepae Vepac Velmr Vepci Vepcf Velln) Vello))). Qed. Lemma p1p2_478: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(el l n)->(el l o)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Velln:(el l n))(Vello:(el l o))=>(goal1 (p1p2_477 Vplam Vepae Vepac Velmr Vepci Vepcf Velln Vello))). Qed. Lemma p1p2_479: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(el l n)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Velln:(el l n))=>((or_ind ((p1p2_475 Vplam Vepae Vepac Velmr Vepci Vepcf Velln))((p1p2_478 Vplam Vepae Vepac Velmr Vepci Vepcf Velln)))(p1p2_464 Vplam Vepae Vepac Velmr Vepci Vepcf Velln))). Qed. Lemma p1p2_480: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))=>((or_ind ((p1p2_461 Vplam Vepae Vepac Velmr Vepci Vepcf))((p1p2_479 Vplam Vepae Vepac Velmr Vepci Vepcf)))(p1p2_385 Vplam Vepae Vepac Velmr Vepci Vepcf))). Qed. Lemma p1p2_481: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(el r s)->(el s r). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Velrs:(el r s))=>((lsym r s) Velrs)). Qed. Lemma p1p2_482: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(el r s)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Velrs:(el r s))=>(goal3 (p1p2_481 Vplam Vepae Vepac Velmr Vepci Velrs))). Qed. Lemma p1p2_483: (pl a m)->(ep a e)->(ep a c)->(el m r)->(ep c i)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))=>((or_ind ((p1p2_480 Vplam Vepae Vepac Velmr Vepci))((p1p2_482 Vplam Vepae Vepac Velmr Vepci)))(p1p2_370 Vplam Vepae Vepac Velmr Vepci))). Qed. Lemma p1p2_484: (pl a m)->(ep a e)->(ep a c)->(el m r)->(el r s)->(el s r). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Velrs:(el r s))=>((lsym r s) Velrs)). Qed. Lemma p1p2_485: (pl a m)->(ep a e)->(ep a c)->(el m r)->(el r s)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Velrs:(el r s))=>(goal3 (p1p2_484 Vplam Vepae Vepac Velmr Velrs))). Qed. Lemma p1p2_486: (pl a m)->(ep a e)->(ep a c)->(el m r)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))=>((or_ind ((p1p2_483 Vplam Vepae Vepac Velmr))((p1p2_485 Vplam Vepae Vepac Velmr)))(p1p2_361 Vplam Vepae Vepac Velmr))). Qed. Lemma p1p2_487: (pl a m)->(ep a e)->(ep a c)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vepac:(ep a c))=>((or_ind ((p1p2_357 Vplam Vepae Vepac))((p1p2_486 Vplam Vepae Vepac)))(p1p2_66 Vplam Vepae Vepac))). Qed. Lemma p1p2_488: (pl a m)->(ep a e)->(el l o)->(el o l). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))=>((lsym l o) Vello)). Qed. Lemma p1p2_490: (pl a m)->(ep a e)->(el l o)->(pl g l). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))=>((lcon g o l) (conj p1p2_24 (p1p2_488 Vplam Vepae Vello)))). Qed. Lemma p1p2_491: (pl a m)->(ep a e)->(el l o)->(ep b g) \/ (el n l). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))=>((unique n l b g) (conj p1p2_7 (conj p1p2_13 (conj p1p2_23 (p1p2_490 Vplam Vepae Vello)))))). Qed. Lemma p1p2_492: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep g b). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_493: (pl a m)->(ep a e)->(el l o)->(ep b g)->(pl g p). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))=>((pcon g b p) (conj (p1p2_492 Vplam Vepae Vello Vepbg) p1p2_9))). Qed. Lemma p1p2_494: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f) \/ (el s m). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))=>((unique s m a f) (conj p1p2_12 (conj Vplam (conj p1p2_20 p1p2_22))))). Qed. Lemma p1p2_498: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(pl a n). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))=>((pcon a f n) (conj Vepaf p1p2_15))). Qed. Lemma p1p2_503: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b) \/ (el l n). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))=>((unique l n a b) (conj p1p2_5 (conj (p1p2_498 Vplam Vepae Vello Vepbg Vepaf) (conj p1p2_13 p1p2_7))))). Qed. Lemma p1p2_504: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep b a). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))=>((psym a b) Vepab)). Qed. Lemma p1p2_515: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(pl a p). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))=>((pcon a b p) (conj Vepab p1p2_9))). Qed. Lemma p1p2_516: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(pl e p). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))=>((pcon e a p) (conj (p1p2_53 Vplam Vepae) (p1p2_515 Vplam Vepae Vello Vepbg Vepaf Vepab)))). Qed. Lemma p1p2_518: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(pl b q). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))=>((pcon b a q) (conj (p1p2_504 Vplam Vepae Vello Vepbg Vepaf Vepab) p1p2_10))). Qed. Lemma p1p2_519: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(pl g q). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))=>((pcon g b q) (conj (p1p2_492 Vplam Vepae Vello Vepbg) (p1p2_518 Vplam Vepae Vello Vepbg Vepaf Vepab)))). Qed. Lemma p1p2_520: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(pl b s). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))=>((pcon b a s) (conj (p1p2_504 Vplam Vepae Vello Vepbg Vepaf Vepab) p1p2_12))). Qed. Lemma p1p2_521: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(pl g s). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))=>((pcon g b s) (conj (p1p2_492 Vplam Vepae Vello Vepbg) (p1p2_520 Vplam Vepae Vello Vepbg Vepaf Vepab)))). Qed. Lemma p1p2_524: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e) \/ (el m p). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))=>((unique m p d e) (conj p1p2_6 (conj p1p2_17 (conj p1p2_14 (p1p2_516 Vplam Vepae Vello Vepbg Vepaf Vepab)))))). Qed. Lemma p1p2_525: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(ep e d). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))=>((psym d e) Vepde)). Qed. Lemma p1p2_539: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(pl e r). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))=>((pcon e d r) (conj (p1p2_525 Vplam Vepae Vello Vepbg Vepaf Vepab Vepde) p1p2_19))). Qed. Lemma p1p2_540: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(pl a r). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))=>((pcon a e r) (conj Vepae (p1p2_539 Vplam Vepae Vello Vepbg Vepaf Vepab Vepde)))). Qed. Lemma p1p2_544: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(ep a c) \/ (el l r). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))=>((unique l r a c) (conj p1p2_5 (conj (p1p2_540 Vplam Vepae Vello Vepbg Vepaf Vepab Vepde) (conj p1p2_21 p1p2_11))))). Qed. Lemma p1p2_561: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(ep a c)->(ep b h) \/ (el p q). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vepac:(ep a c))=>((unique p q b h) (conj p1p2_9 (conj (p1p2_518 Vplam Vepae Vello Vepbg Vepaf Vepab) (conj p1p2_25 p1p2_26))))). Qed. Lemma p1p2_562: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(ep a c)->(ep b h)->(ep h b). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vepac:(ep a c))(Vepbh:(ep b h))=>((psym b h) Vepbh)). Qed. Lemma p1p2_578: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(ep a c)->(ep b h)->(pl h s). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vepac:(ep a c))(Vepbh:(ep b h))=>((pcon h b s) (conj (p1p2_562 Vplam Vepae Vello Vepbg Vepaf Vepab Vepde Vepac Vepbh) (p1p2_520 Vplam Vepae Vello Vepbg Vepaf Vepab)))). Qed. Lemma p1p2_579: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(ep a c)->(ep b h)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vepac:(ep a c))(Vepbh:(ep b h))=>((goal4 s) (conj p1p2_45 (conj (p1p2_521 Vplam Vepae Vello Vepbg Vepaf Vepab) (conj (p1p2_578 Vplam Vepae Vello Vepbg Vepaf Vepab Vepde Vepac Vepbh) p1p2_28))))). Qed. Lemma p1p2_580: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(ep a c)->(el p q)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vepac:(ep a c))(Velpq:(el p q))=>(goal2 Velpq)). Qed. Lemma p1p2_581: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(ep a c)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vepac:(ep a c))=>((or_ind ((p1p2_579 Vplam Vepae Vello Vepbg Vepaf Vepab Vepde Vepac))((p1p2_580 Vplam Vepae Vello Vepbg Vepaf Vepab Vepde Vepac)))(p1p2_561 Vplam Vepae Vello Vepbg Vepaf Vepab Vepde Vepac))). Qed. Lemma p1p2_582: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(el l r)->(el r l). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vellr:(el l r))=>((lsym l r) Vellr)). Qed. Lemma p1p2_585: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(el l r)->(pl i l). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vellr:(el l r))=>((lcon i r l) (conj p1p2_27 (p1p2_582 Vplam Vepae Vello Vepbg Vepaf Vepab Vepde Vellr)))). Qed. Lemma p1p2_587: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(el l r)->(ep a i) \/ (el l s). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vellr:(el l r))=>((unique l s a i) (conj p1p2_5 (conj p1p2_12 (conj (p1p2_585 Vplam Vepae Vello Vepbg Vepaf Vepab Vepde Vellr) p1p2_28))))). Qed. Lemma p1p2_588: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(el l r)->(ep a i)->(ep i a). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vellr:(el l r))(Vepai:(ep a i))=>((psym a i) Vepai)). Qed. Lemma p1p2_599: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(el l r)->(ep a i)->(pl i q). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vellr:(el l r))(Vepai:(ep a i))=>((pcon i a q) (conj (p1p2_588 Vplam Vepae Vello Vepbg Vepaf Vepab Vepde Vellr Vepai) p1p2_10))). Qed. Lemma p1p2_600: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(el l r)->(ep a i)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vellr:(el l r))(Vepai:(ep a i))=>((goal4 q) (conj p1p2_43 (conj (p1p2_519 Vplam Vepae Vello Vepbg Vepaf Vepab) (conj p1p2_26 (p1p2_599 Vplam Vepae Vello Vepbg Vepaf Vepab Vepde Vellr Vepai)))))). Qed. Lemma p1p2_604: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(el l r)->(el l s)->(el r s). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vellr:(el l r))(Vells:(el l s))=>((ltra r l s) (conj (p1p2_582 Vplam Vepae Vello Vepbg Vepaf Vepab Vepde Vellr) Vells))). Qed. Lemma p1p2_605: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(el l r)->(el l s)->(el s r). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vellr:(el l r))(Vells:(el l s))=>((lsym r s) (p1p2_604 Vplam Vepae Vello Vepbg Vepaf Vepab Vepde Vellr Vells))). Qed. Lemma p1p2_606: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(el l r)->(el l s)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vellr:(el l r))(Vells:(el l s))=>(goal3 (p1p2_605 Vplam Vepae Vello Vepbg Vepaf Vepab Vepde Vellr Vells))). Qed. Lemma p1p2_607: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(el l r)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vellr:(el l r))=>((or_ind ((p1p2_600 Vplam Vepae Vello Vepbg Vepaf Vepab Vepde Vellr))((p1p2_606 Vplam Vepae Vello Vepbg Vepaf Vepab Vepde Vellr)))(p1p2_587 Vplam Vepae Vello Vepbg Vepaf Vepab Vepde Vellr))). Qed. Lemma p1p2_608: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))=>((or_ind ((p1p2_581 Vplam Vepae Vello Vepbg Vepaf Vepab Vepde))((p1p2_607 Vplam Vepae Vello Vepbg Vepaf Vepab Vepde)))(p1p2_544 Vplam Vepae Vello Vepbg Vepaf Vepab Vepde))). Qed. Lemma p1p2_611: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(el m p)->(ep b h) \/ (el p q). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))=>((unique p q b h) (conj p1p2_9 (conj (p1p2_518 Vplam Vepae Vello Vepbg Vepaf Vepab) (conj p1p2_25 p1p2_26))))). Qed. Lemma p1p2_612: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep h b). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))=>((psym b h) Vepbh)). Qed. Lemma p1p2_624: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(pl h s). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))=>((pcon h b s) (conj (p1p2_612 Vplam Vepae Vello Vepbg Vepaf Vepab Velmp Vepbh) (p1p2_520 Vplam Vepae Vello Vepbg Vepaf Vepab)))). Qed. Lemma p1p2_625: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(el m p)->(ep b h)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))=>((goal4 s) (conj p1p2_45 (conj (p1p2_521 Vplam Vepae Vello Vepbg Vepaf Vepab) (conj (p1p2_624 Vplam Vepae Vello Vepbg Vepaf Vepab Velmp Vepbh) p1p2_28))))). Qed. Lemma p1p2_626: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(el m p)->(el p q)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Velpq:(el p q))=>(goal2 Velpq)). Qed. Lemma p1p2_627: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(el m p)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))=>((or_ind ((p1p2_625 Vplam Vepae Vello Vepbg Vepaf Vepab Velmp))((p1p2_626 Vplam Vepae Vello Vepbg Vepaf Vepab Velmp)))(p1p2_611 Vplam Vepae Vello Vepbg Vepaf Vepab Velmp))). Qed. Lemma p1p2_628: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))=>((or_ind ((p1p2_608 Vplam Vepae Vello Vepbg Vepaf Vepab))((p1p2_627 Vplam Vepae Vello Vepbg Vepaf Vepab)))(p1p2_524 Vplam Vepae Vello Vepbg Vepaf Vepab))). Qed. Lemma p1p2_630: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(el l n)->(el o n). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Velln:(el l n))=>((ltra o l n) (conj (p1p2_488 Vplam Vepae Vello) Velln))). Qed. Lemma p1p2_631: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(el l n)->(el n o). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Velln:(el l n))=>((lsym o n) (p1p2_630 Vplam Vepae Vello Vepbg Vepaf Velln))). Qed. Lemma p1p2_632: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(el l n)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Velln:(el l n))=>(goal1 (p1p2_631 Vplam Vepae Vello Vepbg Vepaf Velln))). Qed. Lemma p1p2_633: (pl a m)->(ep a e)->(el l o)->(ep b g)->(ep a f)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))=>((or_ind ((p1p2_628 Vplam Vepae Vello Vepbg Vepaf))((p1p2_632 Vplam Vepae Vello Vepbg Vepaf)))(p1p2_503 Vplam Vepae Vello Vepbg Vepaf))). Qed. Lemma p1p2_636: (pl a m)->(ep a e)->(el l o)->(ep b g)->(el s m)->(pl i m). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Velsm:(el s m))=>((lcon i s m) (conj p1p2_28 Velsm))). Qed. Lemma p1p2_637: (pl a m)->(ep a e)->(el l o)->(ep b g)->(el s m)->(ep d i) \/ (el m r). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Velsm:(el s m))=>((unique m r d i) (conj p1p2_6 (conj p1p2_19 (conj (p1p2_636 Vplam Vepae Vello Vepbg Velsm) p1p2_27))))). Qed. Lemma p1p2_638: (pl a m)->(ep a e)->(el l o)->(ep b g)->(el s m)->(ep d i)->(ep i d). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Velsm:(el s m))(Vepdi:(ep d i))=>((psym d i) Vepdi)). Qed. Lemma p1p2_639: (pl a m)->(ep a e)->(el l o)->(ep b g)->(el s m)->(ep d i)->(pl i p). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Velsm:(el s m))(Vepdi:(ep d i))=>((pcon i d p) (conj (p1p2_638 Vplam Vepae Vello Vepbg Velsm Vepdi) p1p2_17))). Qed. Lemma p1p2_640: (pl a m)->(ep a e)->(el l o)->(ep b g)->(el s m)->(ep d i)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Velsm:(el s m))(Vepdi:(ep d i))=>((goal4 p) (conj p1p2_42 (conj (p1p2_493 Vplam Vepae Vello Vepbg) (conj p1p2_25 (p1p2_639 Vplam Vepae Vello Vepbg Velsm Vepdi)))))). Qed. Lemma p1p2_642: (pl a m)->(ep a e)->(el l o)->(ep b g)->(el s m)->(el m r)->(el s r). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Velsm:(el s m))(Velmr:(el m r))=>((ltra s m r) (conj Velsm Velmr))). Qed. Lemma p1p2_643: (pl a m)->(ep a e)->(el l o)->(ep b g)->(el s m)->(el m r)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Velsm:(el s m))(Velmr:(el m r))=>(goal3 (p1p2_642 Vplam Vepae Vello Vepbg Velsm Velmr))). Qed. Lemma p1p2_644: (pl a m)->(ep a e)->(el l o)->(ep b g)->(el s m)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Velsm:(el s m))=>((or_ind ((p1p2_640 Vplam Vepae Vello Vepbg Velsm))((p1p2_643 Vplam Vepae Vello Vepbg Velsm)))(p1p2_637 Vplam Vepae Vello Vepbg Velsm))). Qed. Lemma p1p2_645: (pl a m)->(ep a e)->(el l o)->(ep b g)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))=>((or_ind ((p1p2_633 Vplam Vepae Vello Vepbg))((p1p2_644 Vplam Vepae Vello Vepbg)))(p1p2_494 Vplam Vepae Vello Vepbg))). Qed. Lemma p1p2_646: (pl a m)->(ep a e)->(el l o)->(el n l)->(el l n). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Velnl:(el n l))=>((lsym n l) Velnl)). Qed. Lemma p1p2_647: (pl a m)->(ep a e)->(el l o)->(el n l)->(el o n). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Velnl:(el n l))=>((ltra o l n) (conj (p1p2_488 Vplam Vepae Vello) (p1p2_646 Vplam Vepae Vello Velnl)))). Qed. Lemma p1p2_648: (pl a m)->(ep a e)->(el l o)->(el n l)->(el n o). Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Velnl:(el n l))=>((lsym o n) (p1p2_647 Vplam Vepae Vello Velnl))). Qed. Lemma p1p2_649: (pl a m)->(ep a e)->(el l o)->(el n l)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))(Velnl:(el n l))=>(goal1 (p1p2_648 Vplam Vepae Vello Velnl))). Qed. Lemma p1p2_650: (pl a m)->(ep a e)->(el l o)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))(Vello:(el l o))=>((or_ind ((p1p2_645 Vplam Vepae Vello))((p1p2_649 Vplam Vepae Vello)))(p1p2_491 Vplam Vepae Vello))). Qed. Lemma p1p2_651: (pl a m)->(ep a e)->goal. Proof. exact (fun (Vplam:(pl a m))(Vepae:(ep a e))=>((or_ind ((p1p2_487 Vplam Vepae))((p1p2_650 Vplam Vepae)))(p1p2_57 Vplam Vepae))). Qed. Lemma p1p2_652: (pl a m)->(el q m)->(el m q). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))=>((lsym q m) Velqm)). Qed. Lemma p1p2_654: (pl a m)->(el q m)->(pl f q). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))=>((lcon f m q) (conj p1p2_22 (p1p2_652 Vplam Velqm)))). Qed. Lemma p1p2_655: (pl a m)->(el q m)->(pl h m). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))=>((lcon h q m) (conj p1p2_26 Velqm))). Qed. Lemma p1p2_656: (pl a m)->(el q m)->(ep d h) \/ (el m p). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))=>((unique m p d h) (conj p1p2_6 (conj p1p2_17 (conj (p1p2_655 Vplam Velqm) p1p2_25))))). Qed. Lemma p1p2_657: (pl a m)->(el q m)->(ep d h)->(ep h d). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))=>((psym d h) Vepdh)). Qed. Lemma p1p2_658: (pl a m)->(el q m)->(ep d h)->(pl h r). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))=>((pcon h d r) (conj (p1p2_657 Vplam Velqm Vepdh) p1p2_19))). Qed. Lemma p1p2_659: (pl a m)->(el q m)->(ep d h)->(ep a f) \/ (el q s). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))=>((unique q s a f) (conj p1p2_10 (conj p1p2_12 (conj (p1p2_654 Vplam Velqm) p1p2_20))))). Qed. Lemma p1p2_660: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep f a). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))=>((psym a f) Vepaf)). Qed. Lemma p1p2_661: (pl a m)->(el q m)->(ep d h)->(ep a f)->(pl a n). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))=>((pcon a f n) (conj Vepaf p1p2_15))). Qed. Lemma p1p2_663: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b) \/ (el l n). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))=>((unique l n a b) (conj p1p2_5 (conj (p1p2_661 Vplam Velqm Vepdh Vepaf) (conj p1p2_13 p1p2_7))))). Qed. Lemma p1p2_664: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep b a). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))=>((psym a b) Vepab)). Qed. Lemma p1p2_667: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(pl a p). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))=>((pcon a b p) (conj Vepab p1p2_9))). Qed. Lemma p1p2_668: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(pl f p). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))=>((pcon f a p) (conj (p1p2_660 Vplam Velqm Vepdh Vepaf) (p1p2_667 Vplam Velqm Vepdh Vepaf Vepab)))). Qed. Lemma p1p2_670: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(pl b s). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))=>((pcon b a s) (conj (p1p2_664 Vplam Velqm Vepdh Vepaf Vepab) p1p2_12))). Qed. Lemma p1p2_672: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f) \/ (el m p). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))=>((unique m p d f) (conj p1p2_6 (conj p1p2_17 (conj p1p2_22 (p1p2_668 Vplam Velqm Vepdh Vepaf Vepab)))))). Qed. Lemma p1p2_673: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(ep f d). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))=>((psym d f) Vepdf)). Qed. Lemma p1p2_684: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(pl d n). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))=>((pcon d f n) (conj Vepdf p1p2_15))). Qed. Lemma p1p2_685: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(pl h n). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))=>((pcon h d n) (conj (p1p2_657 Vplam Velqm Vepdh) (p1p2_684 Vplam Velqm Vepdh Vepaf Vepab Vepdf)))). Qed. Lemma p1p2_686: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(pl d s). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))=>((pcon d f s) (conj Vepdf p1p2_20))). Qed. Lemma p1p2_687: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(pl h s). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))=>((pcon h d s) (conj (p1p2_657 Vplam Velqm Vepdh) (p1p2_686 Vplam Velqm Vepdh Vepaf Vepab Vepdf)))). Qed. Lemma p1p2_690: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(pl f r). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))=>((pcon f d r) (conj (p1p2_673 Vplam Velqm Vepdh Vepaf Vepab Vepdf) p1p2_19))). Qed. Lemma p1p2_691: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(pl a r). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))=>((pcon a f r) (conj Vepaf (p1p2_690 Vplam Velqm Vepdh Vepaf Vepab Vepdf)))). Qed. Lemma p1p2_693: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(ep a c) \/ (el l r). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))=>((unique l r a c) (conj p1p2_5 (conj (p1p2_691 Vplam Velqm Vepdh Vepaf Vepab Vepdf) (conj p1p2_21 p1p2_11))))). Qed. Lemma p1p2_703: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(pl a o). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))=>((pcon a c o) (conj Vepac p1p2_8))). Qed. Lemma p1p2_704: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(pl f o). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))=>((pcon f a o) (conj (p1p2_660 Vplam Velqm Vepdh Vepaf) (p1p2_703 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vepac)))). Qed. Lemma p1p2_705: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(pl b o). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))=>((pcon b a o) (conj (p1p2_664 Vplam Velqm Vepdh Vepaf Vepab) (p1p2_703 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vepac)))). Qed. Lemma p1p2_706: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(pl d o). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))=>((pcon d f o) (conj Vepdf (p1p2_704 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vepac)))). Qed. Lemma p1p2_713: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(ep d e) \/ (el m o). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))=>((unique m o d e) (conj p1p2_6 (conj (p1p2_706 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vepac) (conj p1p2_14 p1p2_16))))). Qed. Lemma p1p2_730: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(ep d e)->(ep b g) \/ (el n o). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Vepde:(ep d e))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_705 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vepac) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_731: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(ep d e)->(ep b g)->(ep g b). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_747: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(ep d e)->(ep b g)->(pl g s). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))=>((pcon g b s) (conj (p1p2_731 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vepac Vepde Vepbg) (p1p2_670 Vplam Velqm Vepdh Vepaf Vepab)))). Qed. Lemma p1p2_748: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(ep d e)->(ep b g)->goal. Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))=>((goal4 s) (conj p1p2_45 (conj (p1p2_747 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vepac Vepde Vepbg) (conj (p1p2_687 Vplam Velqm Vepdh Vepaf Vepab Vepdf) p1p2_28))))). Qed. Lemma p1p2_749: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(ep d e)->(el n o)->goal. Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Vepde:(ep d e))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_750: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(ep d e)->goal. Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Vepde:(ep d e))=>((or_ind ((p1p2_748 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vepac Vepde))((p1p2_749 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vepac Vepde)))(p1p2_730 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vepac Vepde))). Qed. Lemma p1p2_751: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m o)->(el o m). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmo:(el m o))=>((lsym m o) Velmo)). Qed. Lemma p1p2_754: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m o)->(pl g m). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmo:(el m o))=>((lcon g o m) (conj p1p2_24 (p1p2_751 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vepac Velmo)))). Qed. Lemma p1p2_756: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m o)->(ep d g) \/ (el m n). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmo:(el m o))=>((unique m n d g) (conj p1p2_6 (conj (p1p2_684 Vplam Velqm Vepdh Vepaf Vepab Vepdf) (conj (p1p2_754 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vepac Velmo) p1p2_23))))). Qed. Lemma p1p2_757: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m o)->(ep d g)->(ep g d). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmo:(el m o))(Vepdg:(ep d g))=>((psym d g) Vepdg)). Qed. Lemma p1p2_769: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m o)->(ep d g)->(pl g r). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmo:(el m o))(Vepdg:(ep d g))=>((pcon g d r) (conj (p1p2_757 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vepac Velmo Vepdg) p1p2_19))). Qed. Lemma p1p2_770: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m o)->(ep d g)->goal. Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmo:(el m o))(Vepdg:(ep d g))=>((goal4 r) (conj p1p2_44 (conj (p1p2_769 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vepac Velmo Vepdg) (conj (p1p2_658 Vplam Velqm Vepdh) p1p2_27))))). Qed. Lemma p1p2_774: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m o)->(el m n)->(el o n). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmo:(el m o))(Velmn:(el m n))=>((ltra o m n) (conj (p1p2_751 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vepac Velmo) Velmn))). Qed. Lemma p1p2_775: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m o)->(el m n)->(el n o). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmo:(el m o))(Velmn:(el m n))=>((lsym o n) (p1p2_774 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vepac Velmo Velmn))). Qed. Lemma p1p2_776: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m o)->(el m n)->goal. Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmo:(el m o))(Velmn:(el m n))=>(goal1 (p1p2_775 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vepac Velmo Velmn))). Qed. Lemma p1p2_777: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m o)->goal. Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmo:(el m o))=>((or_ind ((p1p2_770 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vepac Velmo))((p1p2_776 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vepac Velmo)))(p1p2_756 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vepac Velmo))). Qed. Lemma p1p2_778: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->goal. Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))=>((or_ind ((p1p2_750 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vepac))((p1p2_777 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vepac)))(p1p2_713 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vepac))). Qed. Lemma p1p2_779: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(el r l). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))=>((lsym l r) Vellr)). Qed. Lemma p1p2_780: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(pl i l). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))=>((lcon i r l) (conj p1p2_27 (p1p2_779 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vellr)))). Qed. Lemma p1p2_781: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i) \/ (el l s). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))=>((unique l s a i) (conj p1p2_5 (conj p1p2_12 (conj (p1p2_780 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vellr) p1p2_28))))). Qed. Lemma p1p2_782: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(ep i a). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))=>((psym a i) Vepai)). Qed. Lemma p1p2_793: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(pl i n). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))=>((pcon i a n) (conj (p1p2_782 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vellr Vepai) (p1p2_661 Vplam Velqm Vepdh Vepaf)))). Qed. Lemma p1p2_794: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->goal. Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))=>((goal4 n) (conj p1p2_40 (conj p1p2_23 (conj (p1p2_685 Vplam Velqm Vepdh Vepaf Vepab Vepdf) (p1p2_793 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vellr Vepai)))))). Qed. Lemma p1p2_796: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(el l s)->(el r s). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vells:(el l s))=>((ltra r l s) (conj (p1p2_779 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vellr) Vells))). Qed. Lemma p1p2_797: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(el l s)->(el s r). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vells:(el l s))=>((lsym r s) (p1p2_796 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vellr Vells))). Qed. Lemma p1p2_798: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(el l s)->goal. Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vells:(el l s))=>(goal3 (p1p2_797 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vellr Vells))). Qed. Lemma p1p2_799: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->(el l r)->goal. Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))=>((or_ind ((p1p2_794 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vellr))((p1p2_798 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vellr)))(p1p2_781 Vplam Velqm Vepdh Vepaf Vepab Vepdf Vellr))). Qed. Lemma p1p2_800: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(ep d f)->goal. Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))=>((or_ind ((p1p2_778 Vplam Velqm Vepdh Vepaf Vepab Vepdf))((p1p2_799 Vplam Velqm Vepdh Vepaf Vepab Vepdf)))(p1p2_693 Vplam Velqm Vepdh Vepaf Vepab Vepdf))). Qed. Lemma p1p2_802: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(el m p)->(el q p). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))=>((ltra q m p) (conj Velqm Velmp))). Qed. Lemma p1p2_803: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(el m p)->(el p q). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))=>((lsym q p) (p1p2_802 Vplam Velqm Vepdh Vepaf Vepab Velmp))). Qed. Lemma p1p2_804: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->(el m p)->goal. Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))=>(goal2 (p1p2_803 Vplam Velqm Vepdh Vepaf Vepab Velmp))). Qed. Lemma p1p2_805: (pl a m)->(el q m)->(ep d h)->(ep a f)->(ep a b)->goal. Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Vepab:(ep a b))=>((or_ind ((p1p2_800 Vplam Velqm Vepdh Vepaf Vepab))((p1p2_804 Vplam Velqm Vepdh Vepaf Vepab)))(p1p2_672 Vplam Velqm Vepdh Vepaf Vepab))). Qed. Lemma p1p2_806: (pl a m)->(el q m)->(ep d h)->(ep a f)->(el l n)->(el n l). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Velln:(el l n))=>((lsym l n) Velln)). Qed. Lemma p1p2_808: (pl a m)->(el q m)->(ep d h)->(ep a f)->(el l n)->(pl g l). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Velln:(el l n))=>((lcon g n l) (conj p1p2_23 (p1p2_806 Vplam Velqm Vepdh Vepaf Velln)))). Qed. Lemma p1p2_809: (pl a m)->(el q m)->(ep d h)->(ep a f)->(el l n)->(ep c g) \/ (el o l). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Velln:(el l n))=>((unique o l c g) (conj p1p2_8 (conj p1p2_21 (conj p1p2_24 (p1p2_808 Vplam Velqm Vepdh Vepaf Velln)))))). Qed. Lemma p1p2_810: (pl a m)->(el q m)->(ep d h)->(ep a f)->(el l n)->(ep c g)->(ep g c). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))=>((psym c g) Vepcg)). Qed. Lemma p1p2_811: (pl a m)->(el q m)->(ep d h)->(ep a f)->(el l n)->(ep c g)->(pl g r). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))=>((pcon g c r) (conj (p1p2_810 Vplam Velqm Vepdh Vepaf Velln Vepcg) p1p2_11))). Qed. Lemma p1p2_812: (pl a m)->(el q m)->(ep d h)->(ep a f)->(el l n)->(ep c g)->goal. Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))=>((goal4 r) (conj p1p2_44 (conj (p1p2_811 Vplam Velqm Vepdh Vepaf Velln Vepcg) (conj (p1p2_658 Vplam Velqm Vepdh) p1p2_27))))). Qed. Lemma p1p2_813: (pl a m)->(el q m)->(ep d h)->(ep a f)->(el l n)->(el o l)->(el l o). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Velln:(el l n))(Velol:(el o l))=>((lsym o l) Velol)). Qed. Lemma p1p2_814: (pl a m)->(el q m)->(ep d h)->(ep a f)->(el l n)->(el o l)->(el n o). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Velln:(el l n))(Velol:(el o l))=>((ltra n l o) (conj (p1p2_806 Vplam Velqm Vepdh Vepaf Velln) (p1p2_813 Vplam Velqm Vepdh Vepaf Velln Velol)))). Qed. Lemma p1p2_815: (pl a m)->(el q m)->(ep d h)->(ep a f)->(el l n)->(el o l)->goal. Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Velln:(el l n))(Velol:(el o l))=>(goal1 (p1p2_814 Vplam Velqm Vepdh Vepaf Velln Velol))). Qed. Lemma p1p2_816: (pl a m)->(el q m)->(ep d h)->(ep a f)->(el l n)->goal. Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))(Velln:(el l n))=>((or_ind ((p1p2_812 Vplam Velqm Vepdh Vepaf Velln))((p1p2_815 Vplam Velqm Vepdh Vepaf Velln)))(p1p2_809 Vplam Velqm Vepdh Vepaf Velln))). Qed. Lemma p1p2_817: (pl a m)->(el q m)->(ep d h)->(ep a f)->goal. Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Vepaf:(ep a f))=>((or_ind ((p1p2_805 Vplam Velqm Vepdh Vepaf))((p1p2_816 Vplam Velqm Vepdh Vepaf)))(p1p2_663 Vplam Velqm Vepdh Vepaf))). Qed. Lemma p1p2_818: (pl a m)->(el q m)->(ep d h)->(el q s)->(el s q). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Velqs:(el q s))=>((lsym q s) Velqs)). Qed. Lemma p1p2_819: (pl a m)->(el q m)->(ep d h)->(el q s)->(el m s). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Velqs:(el q s))=>((ltra m q s) (conj (p1p2_652 Vplam Velqm) Velqs))). Qed. Lemma p1p2_820: (pl a m)->(el q m)->(ep d h)->(el q s)->(el s m). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Velqs:(el q s))=>((lsym m s) (p1p2_819 Vplam Velqm Vepdh Velqs))). Qed. Lemma p1p2_825: (pl a m)->(el q m)->(ep d h)->(el q s)->(pl i m). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Velqs:(el q s))=>((lcon i s m) (conj p1p2_28 (p1p2_820 Vplam Velqm Vepdh Velqs)))). Qed. Lemma p1p2_826: (pl a m)->(el q m)->(ep d h)->(el q s)->(ep d i) \/ (el m r). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Velqs:(el q s))=>((unique m r d i) (conj p1p2_6 (conj p1p2_19 (conj (p1p2_825 Vplam Velqm Vepdh Velqs) p1p2_27))))). Qed. Lemma p1p2_827: (pl a m)->(el q m)->(ep d h)->(el q s)->(ep d i)->(ep i d). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Velqs:(el q s))(Vepdi:(ep d i))=>((psym d i) Vepdi)). Qed. Lemma p1p2_831: (pl a m)->(el q m)->(ep d h)->(el q s)->(ep d i)->(exists A:dom,(pl a A)/\(pl g A)). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Velqs:(el q s))(Vepdi:(ep d i))=>((line a g) (conj p1p2_29 p1p2_35))). Qed. Lemma p1p2_833: (pl a m)->(el q m)->(ep d h)->(el q s)->(ep d i)->forall C0:dom,(pl a C0)->(pl g C0)->(exists A:dom,(pl d A)/\(pl g A)). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Velqs:(el q s))(Vepdi:(ep d i))(C0:dom)(VplaC0:(pl a C0))(VplgC0:(pl g C0))=>((line d g) (conj p1p2_30 p1p2_35))). Qed. Lemma p1p2_834: (pl a m)->(el q m)->(ep d h)->(el q s)->(ep d i)->forall C0:dom,(pl a C0)->(pl g C0)->forall C1:dom,(pl d C1)->(pl g C1)->(el C1 C1). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Velqs:(el q s))(Vepdi:(ep d i))(C0:dom)(VplaC0:(pl a C0))(VplgC0:(pl g C0))(C1:dom)(VpldC1:(pl d C1))(VplgC1:(pl g C1))=>((lref d C1) VpldC1)). Qed. Lemma p1p2_835: (pl a m)->(el q m)->(ep d h)->(el q s)->(ep d i)->forall C0:dom,(pl a C0)->(pl g C0)->forall C1:dom,(pl d C1)->(pl g C1)->(pl h C1). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Velqs:(el q s))(Vepdi:(ep d i))(C0:dom)(VplaC0:(pl a C0))(VplgC0:(pl g C0))(C1:dom)(VpldC1:(pl d C1))(VplgC1:(pl g C1))=>((pcon h d C1) (conj (p1p2_657 Vplam Velqm Vepdh) VpldC1))). Qed. Lemma p1p2_836: (pl a m)->(el q m)->(ep d h)->(el q s)->(ep d i)->forall C0:dom,(pl a C0)->(pl g C0)->forall C1:dom,(pl d C1)->(pl g C1)->(pl i C1). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Velqs:(el q s))(Vepdi:(ep d i))(C0:dom)(VplaC0:(pl a C0))(VplgC0:(pl g C0))(C1:dom)(VpldC1:(pl d C1))(VplgC1:(pl g C1))=>((pcon i d C1) (conj (p1p2_827 Vplam Velqm Vepdh Velqs Vepdi) VpldC1))). Qed. Lemma p1p2_837: (pl a m)->(el q m)->(ep d h)->(el q s)->(ep d i)->forall C0:dom,(pl a C0)->(pl g C0)->forall C1:dom,(pl d C1)->(pl g C1)->goal. Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Velqs:(el q s))(Vepdi:(ep d i))(C0:dom)(VplaC0:(pl a C0))(VplgC0:(pl g C0))(C1:dom)(VpldC1:(pl d C1))(VplgC1:(pl g C1))=>((goal4 C1) (conj (p1p2_834 Vplam Velqm Vepdh Velqs Vepdi C0 VplaC0 VplgC0 C1 VpldC1 VplgC1) (conj VplgC1 (conj (p1p2_835 Vplam Velqm Vepdh Velqs Vepdi C0 VplaC0 VplgC0 C1 VpldC1 VplgC1) (p1p2_836 Vplam Velqm Vepdh Velqs Vepdi C0 VplaC0 VplgC0 C1 VpldC1 VplgC1)))))). Qed. Lemma p1p2_838: (pl a m)->(el q m)->(ep d h)->(el q s)->(ep d i)->forall C0:dom,(pl a C0)->(pl g C0)->goal. Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Velqs:(el q s))(Vepdi:(ep d i))(C0:dom)(VplaC0:(pl a C0))(VplgC0:(pl g C0))=>((ex_ind (P:=fun C1:dom=>(pl d C1)/\(pl g C1))(fun C1:dom=>(and_ind (p1p2_837 Vplam Velqm Vepdh Velqs Vepdi C0 VplaC0 VplgC0 C1))))(p1p2_833 Vplam Velqm Vepdh Velqs Vepdi C0 VplaC0 VplgC0))). Qed. Lemma p1p2_839: (pl a m)->(el q m)->(ep d h)->(el q s)->(ep d i)->goal. Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Velqs:(el q s))(Vepdi:(ep d i))=>((ex_ind (P:=fun C0:dom=>(pl a C0)/\(pl g C0))(fun C0:dom=>(and_ind (p1p2_838 Vplam Velqm Vepdh Velqs Vepdi C0))))(p1p2_831 Vplam Velqm Vepdh Velqs Vepdi))). Qed. Lemma p1p2_841: (pl a m)->(el q m)->(ep d h)->(el q s)->(el m r)->(el q r). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Velqs:(el q s))(Velmr:(el m r))=>((ltra q m r) (conj Velqm Velmr))). Qed. Lemma p1p2_843: (pl a m)->(el q m)->(ep d h)->(el q s)->(el m r)->(el s r). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Velqs:(el q s))(Velmr:(el m r))=>((ltra s q r) (conj (p1p2_818 Vplam Velqm Vepdh Velqs) (p1p2_841 Vplam Velqm Vepdh Velqs Velmr)))). Qed. Lemma p1p2_844: (pl a m)->(el q m)->(ep d h)->(el q s)->(el m r)->goal. Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Velqs:(el q s))(Velmr:(el m r))=>(goal3 (p1p2_843 Vplam Velqm Vepdh Velqs Velmr))). Qed. Lemma p1p2_845: (pl a m)->(el q m)->(ep d h)->(el q s)->goal. Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))(Velqs:(el q s))=>((or_ind ((p1p2_839 Vplam Velqm Vepdh Velqs))((p1p2_844 Vplam Velqm Vepdh Velqs)))(p1p2_826 Vplam Velqm Vepdh Velqs))). Qed. Lemma p1p2_846: (pl a m)->(el q m)->(ep d h)->goal. Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Vepdh:(ep d h))=>((or_ind ((p1p2_817 Vplam Velqm Vepdh))((p1p2_845 Vplam Velqm Vepdh)))(p1p2_659 Vplam Velqm Vepdh))). Qed. Lemma p1p2_848: (pl a m)->(el q m)->(el m p)->(el q p). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Velmp:(el m p))=>((ltra q m p) (conj Velqm Velmp))). Qed. Lemma p1p2_849: (pl a m)->(el q m)->(el m p)->(el p q). Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Velmp:(el m p))=>((lsym q p) (p1p2_848 Vplam Velqm Velmp))). Qed. Lemma p1p2_850: (pl a m)->(el q m)->(el m p)->goal. Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))(Velmp:(el m p))=>(goal2 (p1p2_849 Vplam Velqm Velmp))). Qed. Lemma p1p2_851: (pl a m)->(el q m)->goal. Proof. exact (fun (Vplam:(pl a m))(Velqm:(el q m))=>((or_ind ((p1p2_846 Vplam Velqm))((p1p2_850 Vplam Velqm)))(p1p2_656 Vplam Velqm))). Qed. Lemma p1p2_852: (pl a m)->goal. Proof. exact (fun (Vplam:(pl a m))=>((or_ind ((p1p2_651 Vplam))((p1p2_851 Vplam)))(p1p2_52 Vplam))). Qed. Lemma p1p2_853: (pl b m)->(ep d b) \/ (el m p). Proof. exact (fun (Vplbm:(pl b m))=>((unique m p d b) (conj p1p2_6 (conj p1p2_17 (conj Vplbm p1p2_9))))). Qed. Lemma p1p2_854: (pl b m)->(ep d b)->(ep b d). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))=>((psym d b) Vepdb)). Qed. Lemma p1p2_855: (pl b m)->(ep d b)->(pl d n). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))=>((pcon d b n) (conj Vepdb p1p2_7))). Qed. Lemma p1p2_856: (pl b m)->(ep d b)->(pl d l). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))=>((pcon d b l) (conj Vepdb p1p2_13))). Qed. Lemma p1p2_857: (pl b m)->(ep d b)->(pl b r). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))=>((pcon b d r) (conj (p1p2_854 Vplbm Vepdb) p1p2_19))). Qed. Lemma p1p2_858: (pl b m)->(ep d b)->(ep d f) \/ (el m n). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))=>((unique m n d f) (conj p1p2_6 (conj (p1p2_855 Vplbm Vepdb) (conj p1p2_22 p1p2_15))))). Qed. Lemma p1p2_862: (pl b m)->(ep d b)->(ep d f)->(pl d s). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))=>((pcon d f s) (conj Vepdf p1p2_20))). Qed. Lemma p1p2_863: (pl b m)->(ep d b)->(ep d f)->(pl b s). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))=>((pcon b d s) (conj (p1p2_854 Vplbm Vepdb) (p1p2_862 Vplbm Vepdb Vepdf)))). Qed. Lemma p1p2_867: (pl b m)->(ep d b)->(ep d f)->(ep a b) \/ (el l s). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))=>((unique l s a b) (conj p1p2_5 (conj p1p2_12 (conj p1p2_13 (p1p2_863 Vplbm Vepdb Vepdf)))))). Qed. Lemma p1p2_868: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep b a). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))=>((psym a b) Vepab)). Qed. Lemma p1p2_873: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(pl a n). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))=>((pcon a b n) (conj Vepab p1p2_7))). Qed. Lemma p1p2_874: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(pl a p). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))=>((pcon a b p) (conj Vepab p1p2_9))). Qed. Lemma p1p2_876: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(pl a r). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))=>((pcon a b r) (conj Vepab (p1p2_857 Vplbm Vepdb)))). Qed. Lemma p1p2_877: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(pl b q). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))=>((pcon b a q) (conj (p1p2_868 Vplbm Vepdb Vepdf Vepab) p1p2_10))). Qed. Lemma p1p2_878: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(pl d q). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))=>((pcon d b q) (conj Vepdb (p1p2_877 Vplbm Vepdb Vepdf Vepab)))). Qed. Lemma p1p2_880: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c) \/ (el l r). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))=>((unique l r a c) (conj p1p2_5 (conj (p1p2_876 Vplbm Vepdb Vepdf Vepab) (conj p1p2_21 p1p2_11))))). Qed. Lemma p1p2_888: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(pl a o). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))=>((pcon a c o) (conj Vepac p1p2_8))). Qed. Lemma p1p2_889: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(pl b o). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))=>((pcon b a o) (conj (p1p2_868 Vplbm Vepdb Vepdf Vepab) (p1p2_888 Vplbm Vepdb Vepdf Vepab Vepac)))). Qed. Lemma p1p2_890: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(pl d o). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))=>((pcon d b o) (conj Vepdb (p1p2_889 Vplbm Vepdb Vepdf Vepab Vepac)))). Qed. Lemma p1p2_897: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(ep d e) \/ (el m q). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))=>((unique m q d e) (conj p1p2_6 (conj (p1p2_878 Vplbm Vepdb Vepdf Vepab) (conj p1p2_14 p1p2_18))))). Qed. Lemma p1p2_912: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(ep d e)->(ep b g) \/ (el n o). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Vepde:(ep d e))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_889 Vplbm Vepdb Vepdf Vepab Vepac) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_913: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(ep d e)->(ep b g)->(ep g b). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_927: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(ep d e)->(ep b g)->(pl g r). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))=>((pcon g b r) (conj (p1p2_913 Vplbm Vepdb Vepdf Vepab Vepac Vepde Vepbg) (p1p2_857 Vplbm Vepdb)))). Qed. Lemma p1p2_930: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(ep d e)->(ep b g)->(ep b h) \/ (el p q). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))=>((unique p q b h) (conj p1p2_9 (conj (p1p2_877 Vplbm Vepdb Vepdf Vepab) (conj p1p2_25 p1p2_26))))). Qed. Lemma p1p2_931: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(ep d e)->(ep b g)->(ep b h)->(ep h b). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))(Vepbh:(ep b h))=>((psym b h) Vepbh)). Qed. Lemma p1p2_947: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(ep d e)->(ep b g)->(ep b h)->(pl h r). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))(Vepbh:(ep b h))=>((pcon h b r) (conj (p1p2_931 Vplbm Vepdb Vepdf Vepab Vepac Vepde Vepbg Vepbh) (p1p2_857 Vplbm Vepdb)))). Qed. Lemma p1p2_948: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(ep d e)->(ep b g)->(ep b h)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))(Vepbh:(ep b h))=>((goal4 r) (conj p1p2_44 (conj (p1p2_927 Vplbm Vepdb Vepdf Vepab Vepac Vepde Vepbg) (conj (p1p2_947 Vplbm Vepdb Vepdf Vepab Vepac Vepde Vepbg Vepbh) p1p2_27))))). Qed. Lemma p1p2_949: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(ep d e)->(ep b g)->(el p q)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))(Velpq:(el p q))=>(goal2 Velpq)). Qed. Lemma p1p2_950: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(ep d e)->(ep b g)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))=>((or_ind ((p1p2_948 Vplbm Vepdb Vepdf Vepab Vepac Vepde Vepbg))((p1p2_949 Vplbm Vepdb Vepdf Vepab Vepac Vepde Vepbg)))(p1p2_930 Vplbm Vepdb Vepdf Vepab Vepac Vepde Vepbg))). Qed. Lemma p1p2_951: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(ep d e)->(el n o)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Vepde:(ep d e))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_952: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(ep d e)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Vepde:(ep d e))=>((or_ind ((p1p2_950 Vplbm Vepdb Vepdf Vepab Vepac Vepde))((p1p2_951 Vplbm Vepdb Vepdf Vepab Vepac Vepde)))(p1p2_912 Vplbm Vepdb Vepdf Vepab Vepac Vepde))). Qed. Lemma p1p2_953: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(el q m). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))=>((lsym m q) Velmq)). Qed. Lemma p1p2_954: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(pl h m). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))=>((lcon h q m) (conj p1p2_26 (p1p2_953 Vplbm Vepdb Vepdf Vepab Vepac Velmq)))). Qed. Lemma p1p2_955: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h) \/ (el m p). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))=>((unique m p d h) (conj p1p2_6 (conj p1p2_17 (conj (p1p2_954 Vplbm Vepdb Vepdf Vepab Vepac Velmq) p1p2_25))))). Qed. Lemma p1p2_956: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(ep h d). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))=>((psym d h) Vepdh)). Qed. Lemma p1p2_965: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(pl h r). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))=>((pcon h d r) (conj (p1p2_956 Vplbm Vepdb Vepdf Vepab Vepac Velmq Vepdh) p1p2_19))). Qed. Lemma p1p2_970: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(ep d e) \/ (el m o). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))=>((unique m o d e) (conj p1p2_6 (conj (p1p2_890 Vplbm Vepdb Vepdf Vepab Vepac) (conj p1p2_14 p1p2_16))))). Qed. Lemma p1p2_987: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(ep d e)->(ep b g) \/ (el n o). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Vepde:(ep d e))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_889 Vplbm Vepdb Vepdf Vepab Vepac) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_988: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(ep d e)->(ep b g)->(ep g b). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Vepde:(ep d e))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_1004: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(ep d e)->(ep b g)->(pl g r). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Vepde:(ep d e))(Vepbg:(ep b g))=>((pcon g b r) (conj (p1p2_988 Vplbm Vepdb Vepdf Vepab Vepac Velmq Vepdh Vepde Vepbg) (p1p2_857 Vplbm Vepdb)))). Qed. Lemma p1p2_1005: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(ep d e)->(ep b g)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Vepde:(ep d e))(Vepbg:(ep b g))=>((goal4 r) (conj p1p2_44 (conj (p1p2_1004 Vplbm Vepdb Vepdf Vepab Vepac Velmq Vepdh Vepde Vepbg) (conj (p1p2_965 Vplbm Vepdb Vepdf Vepab Vepac Velmq Vepdh) p1p2_27))))). Qed. Lemma p1p2_1006: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(ep d e)->(el n o)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Vepde:(ep d e))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_1007: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(ep d e)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Vepde:(ep d e))=>((or_ind ((p1p2_1005 Vplbm Vepdb Vepdf Vepab Vepac Velmq Vepdh Vepde))((p1p2_1006 Vplbm Vepdb Vepdf Vepab Vepac Velmq Vepdh Vepde)))(p1p2_987 Vplbm Vepdb Vepdf Vepab Vepac Velmq Vepdh Vepde))). Qed. Lemma p1p2_1008: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(el m o)->(el o m). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Velmo:(el m o))=>((lsym m o) Velmo)). Qed. Lemma p1p2_1011: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(el m o)->(pl g m). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Velmo:(el m o))=>((lcon g o m) (conj p1p2_24 (p1p2_1008 Vplbm Vepdb Vepdf Vepab Vepac Velmq Vepdh Velmo)))). Qed. Lemma p1p2_1013: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(el m o)->(ep d g) \/ (el m n). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Velmo:(el m o))=>((unique m n d g) (conj p1p2_6 (conj (p1p2_855 Vplbm Vepdb) (conj (p1p2_1011 Vplbm Vepdb Vepdf Vepab Vepac Velmq Vepdh Velmo) p1p2_23))))). Qed. Lemma p1p2_1014: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(el m o)->(ep d g)->(ep g d). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Velmo:(el m o))(Vepdg:(ep d g))=>((psym d g) Vepdg)). Qed. Lemma p1p2_1026: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(el m o)->(ep d g)->(pl g r). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Velmo:(el m o))(Vepdg:(ep d g))=>((pcon g d r) (conj (p1p2_1014 Vplbm Vepdb Vepdf Vepab Vepac Velmq Vepdh Velmo Vepdg) p1p2_19))). Qed. Lemma p1p2_1027: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(el m o)->(ep d g)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Velmo:(el m o))(Vepdg:(ep d g))=>((goal4 r) (conj p1p2_44 (conj (p1p2_1026 Vplbm Vepdb Vepdf Vepab Vepac Velmq Vepdh Velmo Vepdg) (conj (p1p2_965 Vplbm Vepdb Vepdf Vepab Vepac Velmq Vepdh) p1p2_27))))). Qed. Lemma p1p2_1031: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(el m o)->(el m n)->(el o n). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Velmo:(el m o))(Velmn:(el m n))=>((ltra o m n) (conj (p1p2_1008 Vplbm Vepdb Vepdf Vepab Vepac Velmq Vepdh Velmo) Velmn))). Qed. Lemma p1p2_1032: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(el m o)->(el m n)->(el n o). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Velmo:(el m o))(Velmn:(el m n))=>((lsym o n) (p1p2_1031 Vplbm Vepdb Vepdf Vepab Vepac Velmq Vepdh Velmo Velmn))). Qed. Lemma p1p2_1033: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(el m o)->(el m n)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Velmo:(el m o))(Velmn:(el m n))=>(goal1 (p1p2_1032 Vplbm Vepdb Vepdf Vepab Vepac Velmq Vepdh Velmo Velmn))). Qed. Lemma p1p2_1034: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(el m o)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Velmo:(el m o))=>((or_ind ((p1p2_1027 Vplbm Vepdb Vepdf Vepab Vepac Velmq Vepdh Velmo))((p1p2_1033 Vplbm Vepdb Vepdf Vepab Vepac Velmq Vepdh Velmo)))(p1p2_1013 Vplbm Vepdb Vepdf Vepab Vepac Velmq Vepdh Velmo))). Qed. Lemma p1p2_1035: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))=>((or_ind ((p1p2_1007 Vplbm Vepdb Vepdf Vepab Vepac Velmq Vepdh))((p1p2_1034 Vplbm Vepdb Vepdf Vepab Vepac Velmq Vepdh)))(p1p2_970 Vplbm Vepdb Vepdf Vepab Vepac Velmq Vepdh))). Qed. Lemma p1p2_1037: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(el m p)->(el q p). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Velmp:(el m p))=>((ltra q m p) (conj (p1p2_953 Vplbm Vepdb Vepdf Vepab Vepac Velmq) Velmp))). Qed. Lemma p1p2_1038: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(el m p)->(el p q). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Velmp:(el m p))=>((lsym q p) (p1p2_1037 Vplbm Vepdb Vepdf Vepab Vepac Velmq Velmp))). Qed. Lemma p1p2_1039: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(el m p)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Velmp:(el m p))=>(goal2 (p1p2_1038 Vplbm Vepdb Vepdf Vepab Vepac Velmq Velmp))). Qed. Lemma p1p2_1040: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->(el m q)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))=>((or_ind ((p1p2_1035 Vplbm Vepdb Vepdf Vepab Vepac Velmq))((p1p2_1039 Vplbm Vepdb Vepdf Vepab Vepac Velmq)))(p1p2_955 Vplbm Vepdb Vepdf Vepab Vepac Velmq))). Qed. Lemma p1p2_1041: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(ep a c)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))=>((or_ind ((p1p2_952 Vplbm Vepdb Vepdf Vepab Vepac))((p1p2_1040 Vplbm Vepdb Vepdf Vepab Vepac)))(p1p2_897 Vplbm Vepdb Vepdf Vepab Vepac))). Qed. Lemma p1p2_1042: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(el r l). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))=>((lsym l r) Vellr)). Qed. Lemma p1p2_1043: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(pl i l). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))=>((lcon i r l) (conj p1p2_27 (p1p2_1042 Vplbm Vepdb Vepdf Vepab Vellr)))). Qed. Lemma p1p2_1044: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i) \/ (el l s). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))=>((unique l s a i) (conj p1p2_5 (conj p1p2_12 (conj (p1p2_1043 Vplbm Vepdb Vepdf Vepab Vellr) p1p2_28))))). Qed. Lemma p1p2_1045: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep i a). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))=>((psym a i) Vepai)). Qed. Lemma p1p2_1052: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(pl i q). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))=>((pcon i a q) (conj (p1p2_1045 Vplbm Vepdb Vepdf Vepab Vellr Vepai) p1p2_10))). Qed. Lemma p1p2_1053: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(pl i n). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))=>((pcon i a n) (conj (p1p2_1045 Vplbm Vepdb Vepdf Vepab Vellr Vepai) (p1p2_873 Vplbm Vepdb Vepdf Vepab)))). Qed. Lemma p1p2_1054: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(pl i p). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))=>((pcon i a p) (conj (p1p2_1045 Vplbm Vepdb Vepdf Vepab Vellr Vepai) (p1p2_874 Vplbm Vepdb Vepdf Vepab)))). Qed. Lemma p1p2_1056: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e) \/ (el m q). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))=>((unique m q d e) (conj p1p2_6 (conj (p1p2_878 Vplbm Vepdb Vepdf Vepab) (conj p1p2_14 p1p2_18))))). Qed. Lemma p1p2_1066: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(pl d o). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))=>((pcon d e o) (conj Vepde p1p2_16))). Qed. Lemma p1p2_1067: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(pl b o). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))=>((pcon b d o) (conj (p1p2_854 Vplbm Vepdb) (p1p2_1066 Vplbm Vepdb Vepdf Vepab Vellr Vepai Vepde)))). Qed. Lemma p1p2_1069: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(pl a o). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))=>((pcon a b o) (conj Vepab (p1p2_1067 Vplbm Vepdb Vepdf Vepab Vellr Vepai Vepde)))). Qed. Lemma p1p2_1076: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(ep a c) \/ (el l o). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))=>((unique l o a c) (conj p1p2_5 (conj (p1p2_1069 Vplbm Vepdb Vepdf Vepab Vellr Vepai Vepde) (conj p1p2_21 p1p2_8))))). Qed. Lemma p1p2_1093: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(ep a c)->(ep b g) \/ (el n o). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vepac:(ep a c))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_1067 Vplbm Vepdb Vepdf Vepab Vellr Vepai Vepde) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_1094: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(ep a c)->(ep b g)->(ep g b). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vepac:(ep a c))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_1107: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(ep a c)->(ep b g)->(pl g p). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vepac:(ep a c))(Vepbg:(ep b g))=>((pcon g b p) (conj (p1p2_1094 Vplbm Vepdb Vepdf Vepab Vellr Vepai Vepde Vepac Vepbg) p1p2_9))). Qed. Lemma p1p2_1108: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(ep a c)->(ep b g)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vepac:(ep a c))(Vepbg:(ep b g))=>((goal4 p) (conj p1p2_42 (conj (p1p2_1107 Vplbm Vepdb Vepdf Vepab Vellr Vepai Vepde Vepac Vepbg) (conj p1p2_25 (p1p2_1054 Vplbm Vepdb Vepdf Vepab Vellr Vepai)))))). Qed. Lemma p1p2_1109: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(ep a c)->(el n o)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vepac:(ep a c))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_1110: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(ep a c)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vepac:(ep a c))=>((or_ind ((p1p2_1108 Vplbm Vepdb Vepdf Vepab Vellr Vepai Vepde Vepac))((p1p2_1109 Vplbm Vepdb Vepdf Vepab Vellr Vepai Vepde Vepac)))(p1p2_1093 Vplbm Vepdb Vepdf Vepab Vellr Vepai Vepde Vepac))). Qed. Lemma p1p2_1111: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(el l o)->(el o l). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vello:(el l o))=>((lsym l o) Vello)). Qed. Lemma p1p2_1114: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(el l o)->(pl g l). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vello:(el l o))=>((lcon g o l) (conj p1p2_24 (p1p2_1111 Vplbm Vepdb Vepdf Vepab Vellr Vepai Vepde Vello)))). Qed. Lemma p1p2_1116: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(el l o)->(ep a g) \/ (el l n). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vello:(el l o))=>((unique l n a g) (conj p1p2_5 (conj (p1p2_873 Vplbm Vepdb Vepdf Vepab) (conj (p1p2_1114 Vplbm Vepdb Vepdf Vepab Vellr Vepai Vepde Vello) p1p2_23))))). Qed. Lemma p1p2_1117: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(el l o)->(ep a g)->(ep g a). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vello:(el l o))(Vepag:(ep a g))=>((psym a g) Vepag)). Qed. Lemma p1p2_1128: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(el l o)->(ep a g)->(pl g q). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vello:(el l o))(Vepag:(ep a g))=>((pcon g a q) (conj (p1p2_1117 Vplbm Vepdb Vepdf Vepab Vellr Vepai Vepde Vello Vepag) p1p2_10))). Qed. Lemma p1p2_1129: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(el l o)->(ep a g)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vello:(el l o))(Vepag:(ep a g))=>((goal4 q) (conj p1p2_43 (conj (p1p2_1128 Vplbm Vepdb Vepdf Vepab Vellr Vepai Vepde Vello Vepag) (conj p1p2_26 (p1p2_1052 Vplbm Vepdb Vepdf Vepab Vellr Vepai)))))). Qed. Lemma p1p2_1133: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(el l o)->(el l n)->(el o n). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vello:(el l o))(Velln:(el l n))=>((ltra o l n) (conj (p1p2_1111 Vplbm Vepdb Vepdf Vepab Vellr Vepai Vepde Vello) Velln))). Qed. Lemma p1p2_1134: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(el l o)->(el l n)->(el n o). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vello:(el l o))(Velln:(el l n))=>((lsym o n) (p1p2_1133 Vplbm Vepdb Vepdf Vepab Vellr Vepai Vepde Vello Velln))). Qed. Lemma p1p2_1135: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(el l o)->(el l n)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vello:(el l o))(Velln:(el l n))=>(goal1 (p1p2_1134 Vplbm Vepdb Vepdf Vepab Vellr Vepai Vepde Vello Velln))). Qed. Lemma p1p2_1136: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(el l o)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vello:(el l o))=>((or_ind ((p1p2_1129 Vplbm Vepdb Vepdf Vepab Vellr Vepai Vepde Vello))((p1p2_1135 Vplbm Vepdb Vepdf Vepab Vellr Vepai Vepde Vello)))(p1p2_1116 Vplbm Vepdb Vepdf Vepab Vellr Vepai Vepde Vello))). Qed. Lemma p1p2_1137: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))=>((or_ind ((p1p2_1110 Vplbm Vepdb Vepdf Vepab Vellr Vepai Vepde))((p1p2_1136 Vplbm Vepdb Vepdf Vepab Vellr Vepai Vepde)))(p1p2_1076 Vplbm Vepdb Vepdf Vepab Vellr Vepai Vepde))). Qed. Lemma p1p2_1138: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(el m q)->(el q m). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Velmq:(el m q))=>((lsym m q) Velmq)). Qed. Lemma p1p2_1139: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(el m q)->(pl h m). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Velmq:(el m q))=>((lcon h q m) (conj p1p2_26 (p1p2_1138 Vplbm Vepdb Vepdf Vepab Vellr Vepai Velmq)))). Qed. Lemma p1p2_1140: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(el m q)->(ep d h) \/ (el m p). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Velmq:(el m q))=>((unique m p d h) (conj p1p2_6 (conj p1p2_17 (conj (p1p2_1139 Vplbm Vepdb Vepdf Vepab Vellr Vepai Velmq) p1p2_25))))). Qed. Lemma p1p2_1141: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(el m q)->(ep d h)->(ep h d). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Velmq:(el m q))(Vepdh:(ep d h))=>((psym d h) Vepdh)). Qed. Lemma p1p2_1151: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(el m q)->(ep d h)->(pl h n). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Velmq:(el m q))(Vepdh:(ep d h))=>((pcon h d n) (conj (p1p2_1141 Vplbm Vepdb Vepdf Vepab Vellr Vepai Velmq Vepdh) (p1p2_855 Vplbm Vepdb)))). Qed. Lemma p1p2_1152: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(el m q)->(ep d h)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Velmq:(el m q))(Vepdh:(ep d h))=>((goal4 n) (conj p1p2_40 (conj p1p2_23 (conj (p1p2_1151 Vplbm Vepdb Vepdf Vepab Vellr Vepai Velmq Vepdh) (p1p2_1053 Vplbm Vepdb Vepdf Vepab Vellr Vepai)))))). Qed. Lemma p1p2_1154: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(el m q)->(el m p)->(el q p). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Velmq:(el m q))(Velmp:(el m p))=>((ltra q m p) (conj (p1p2_1138 Vplbm Vepdb Vepdf Vepab Vellr Vepai Velmq) Velmp))). Qed. Lemma p1p2_1155: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(el m q)->(el m p)->(el p q). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Velmq:(el m q))(Velmp:(el m p))=>((lsym q p) (p1p2_1154 Vplbm Vepdb Vepdf Vepab Vellr Vepai Velmq Velmp))). Qed. Lemma p1p2_1156: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(el m q)->(el m p)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Velmq:(el m q))(Velmp:(el m p))=>(goal2 (p1p2_1155 Vplbm Vepdb Vepdf Vepab Vellr Vepai Velmq Velmp))). Qed. Lemma p1p2_1157: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(el m q)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Velmq:(el m q))=>((or_ind ((p1p2_1152 Vplbm Vepdb Vepdf Vepab Vellr Vepai Velmq))((p1p2_1156 Vplbm Vepdb Vepdf Vepab Vellr Vepai Velmq)))(p1p2_1140 Vplbm Vepdb Vepdf Vepab Vellr Vepai Velmq))). Qed. Lemma p1p2_1158: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(ep a i)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))=>((or_ind ((p1p2_1137 Vplbm Vepdb Vepdf Vepab Vellr Vepai))((p1p2_1157 Vplbm Vepdb Vepdf Vepab Vellr Vepai)))(p1p2_1056 Vplbm Vepdb Vepdf Vepab Vellr Vepai))). Qed. Lemma p1p2_1160: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(el l s)->(el r s). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vells:(el l s))=>((ltra r l s) (conj (p1p2_1042 Vplbm Vepdb Vepdf Vepab Vellr) Vells))). Qed. Lemma p1p2_1161: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(el l s)->(el s r). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vells:(el l s))=>((lsym r s) (p1p2_1160 Vplbm Vepdb Vepdf Vepab Vellr Vells))). Qed. Lemma p1p2_1162: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->(el l s)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vells:(el l s))=>(goal3 (p1p2_1161 Vplbm Vepdb Vepdf Vepab Vellr Vells))). Qed. Lemma p1p2_1163: (pl b m)->(ep d b)->(ep d f)->(ep a b)->(el l r)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))=>((or_ind ((p1p2_1158 Vplbm Vepdb Vepdf Vepab Vellr))((p1p2_1162 Vplbm Vepdb Vepdf Vepab Vellr)))(p1p2_1044 Vplbm Vepdb Vepdf Vepab Vellr))). Qed. Lemma p1p2_1164: (pl b m)->(ep d b)->(ep d f)->(ep a b)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vepab:(ep a b))=>((or_ind ((p1p2_1041 Vplbm Vepdb Vepdf Vepab))((p1p2_1163 Vplbm Vepdb Vepdf Vepab)))(p1p2_880 Vplbm Vepdb Vepdf Vepab))). Qed. Lemma p1p2_1165: (pl b m)->(ep d b)->(ep d f)->(el l s)->(el s l). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))=>((lsym l s) Vells)). Qed. Lemma p1p2_1167: (pl b m)->(ep d b)->(ep d f)->(el l s)->(pl i l). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))=>((lcon i s l) (conj p1p2_28 (p1p2_1165 Vplbm Vepdb Vepdf Vells)))). Qed. Lemma p1p2_1168: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d) \/ (el r l). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))=>((unique r l c d) (conj p1p2_11 (conj p1p2_21 (conj p1p2_19 (p1p2_856 Vplbm Vepdb)))))). Qed. Lemma p1p2_1169: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(ep d c). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))=>((psym c d) Vepcd)). Qed. Lemma p1p2_1175: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(pl c p). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))=>((pcon c d p) (conj Vepcd p1p2_17))). Qed. Lemma p1p2_1177: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(pl d o). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))=>((pcon d c o) (conj (p1p2_1169 Vplbm Vepdb Vepdf Vells Vepcd) p1p2_8))). Qed. Lemma p1p2_1178: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(pl b o). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))=>((pcon b d o) (conj (p1p2_854 Vplbm Vepdb) (p1p2_1177 Vplbm Vepdb Vepdf Vells Vepcd)))). Qed. Lemma p1p2_1180: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(ep d e) \/ (el m o). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))=>((unique m o d e) (conj p1p2_6 (conj (p1p2_1177 Vplbm Vepdb Vepdf Vells Vepcd) (conj p1p2_14 p1p2_16))))). Qed. Lemma p1p2_1188: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(pl d q). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))=>((pcon d e q) (conj Vepde p1p2_18))). Qed. Lemma p1p2_1189: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(pl b q). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))=>((pcon b d q) (conj (p1p2_854 Vplbm Vepdb) (p1p2_1188 Vplbm Vepdb Vepdf Vells Vepcd Vepde)))). Qed. Lemma p1p2_1197: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(ep a b) \/ (el l q). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))=>((unique l q a b) (conj p1p2_5 (conj p1p2_10 (conj p1p2_13 (p1p2_1189 Vplbm Vepdb Vepdf Vells Vepcd Vepde)))))). Qed. Lemma p1p2_1208: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(ep a b)->(pl a p). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))=>((pcon a b p) (conj Vepab p1p2_9))). Qed. Lemma p1p2_1210: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(ep a b)->(pl a r). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))=>((pcon a b r) (conj Vepab (p1p2_857 Vplbm Vepdb)))). Qed. Lemma p1p2_1212: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(ep a b)->(ep a i) \/ (el l r). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))=>((unique l r a i) (conj p1p2_5 (conj (p1p2_1210 Vplbm Vepdb Vepdf Vells Vepcd Vepde Vepab) (conj (p1p2_1167 Vplbm Vepdb Vepdf Vells) p1p2_27))))). Qed. Lemma p1p2_1213: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(ep a b)->(ep a i)->(ep i a). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepai:(ep a i))=>((psym a i) Vepai)). Qed. Lemma p1p2_1226: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(ep a b)->(ep a i)->(pl i p). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepai:(ep a i))=>((pcon i a p) (conj (p1p2_1213 Vplbm Vepdb Vepdf Vells Vepcd Vepde Vepab Vepai) (p1p2_1208 Vplbm Vepdb Vepdf Vells Vepcd Vepde Vepab)))). Qed. Lemma p1p2_1229: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(ep a b)->(ep a i)->(ep b g) \/ (el n o). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepai:(ep a i))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_1178 Vplbm Vepdb Vepdf Vells Vepcd) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_1230: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(ep a b)->(ep a i)->(ep b g)->(ep g b). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepai:(ep a i))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_1243: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(ep a b)->(ep a i)->(ep b g)->(pl g p). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepai:(ep a i))(Vepbg:(ep b g))=>((pcon g b p) (conj (p1p2_1230 Vplbm Vepdb Vepdf Vells Vepcd Vepde Vepab Vepai Vepbg) p1p2_9))). Qed. Lemma p1p2_1244: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(ep a b)->(ep a i)->(ep b g)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepai:(ep a i))(Vepbg:(ep b g))=>((goal4 p) (conj p1p2_42 (conj (p1p2_1243 Vplbm Vepdb Vepdf Vells Vepcd Vepde Vepab Vepai Vepbg) (conj p1p2_25 (p1p2_1226 Vplbm Vepdb Vepdf Vells Vepcd Vepde Vepab Vepai)))))). Qed. Lemma p1p2_1245: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(ep a b)->(ep a i)->(el n o)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepai:(ep a i))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_1246: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(ep a b)->(ep a i)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepai:(ep a i))=>((or_ind ((p1p2_1244 Vplbm Vepdb Vepdf Vells Vepcd Vepde Vepab Vepai))((p1p2_1245 Vplbm Vepdb Vepdf Vells Vepcd Vepde Vepab Vepai)))(p1p2_1229 Vplbm Vepdb Vepdf Vells Vepcd Vepde Vepab Vepai))). Qed. Lemma p1p2_1248: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(ep a b)->(el l r)->(el s r). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vellr:(el l r))=>((ltra s l r) (conj (p1p2_1165 Vplbm Vepdb Vepdf Vells) Vellr))). Qed. Lemma p1p2_1249: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(ep a b)->(el l r)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vellr:(el l r))=>(goal3 (p1p2_1248 Vplbm Vepdb Vepdf Vells Vepcd Vepde Vepab Vellr))). Qed. Lemma p1p2_1250: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(ep a b)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))=>((or_ind ((p1p2_1246 Vplbm Vepdb Vepdf Vells Vepcd Vepde Vepab))((p1p2_1249 Vplbm Vepdb Vepdf Vells Vepcd Vepde Vepab)))(p1p2_1212 Vplbm Vepdb Vepdf Vells Vepcd Vepde Vepab))). Qed. Lemma p1p2_1251: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(el l q)->(el q l). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))=>((lsym l q) Vellq)). Qed. Lemma p1p2_1254: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(el l q)->(pl h l). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))=>((lcon h q l) (conj p1p2_26 (p1p2_1251 Vplbm Vepdb Vepdf Vells Vepcd Vepde Vellq)))). Qed. Lemma p1p2_1257: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(el l q)->(ep b g) \/ (el n o). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_1178 Vplbm Vepdb Vepdf Vells Vepcd) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_1258: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(el l q)->(ep b g)->(ep g b). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_1268: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(el l q)->(ep b g)->(pl g l). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Vepbg:(ep b g))=>((pcon g b l) (conj (p1p2_1258 Vplbm Vepdb Vepdf Vells Vepcd Vepde Vellq Vepbg) p1p2_13))). Qed. Lemma p1p2_1269: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(el l q)->(ep b g)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Vepbg:(ep b g))=>((goal4 l) (conj p1p2_38 (conj (p1p2_1268 Vplbm Vepdb Vepdf Vells Vepcd Vepde Vellq Vepbg) (conj (p1p2_1254 Vplbm Vepdb Vepdf Vells Vepcd Vepde Vellq) (p1p2_1167 Vplbm Vepdb Vepdf Vells)))))). Qed. Lemma p1p2_1270: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(el l q)->(el n o)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_1271: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(el l q)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))=>((or_ind ((p1p2_1269 Vplbm Vepdb Vepdf Vells Vepcd Vepde Vellq))((p1p2_1270 Vplbm Vepdb Vepdf Vells Vepcd Vepde Vellq)))(p1p2_1257 Vplbm Vepdb Vepdf Vells Vepcd Vepde Vellq))). Qed. Lemma p1p2_1272: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(ep d e)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))=>((or_ind ((p1p2_1250 Vplbm Vepdb Vepdf Vells Vepcd Vepde))((p1p2_1271 Vplbm Vepdb Vepdf Vells Vepcd Vepde)))(p1p2_1197 Vplbm Vepdb Vepdf Vells Vepcd Vepde))). Qed. Lemma p1p2_1273: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(el m o)->(el o m). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))=>((lsym m o) Velmo)). Qed. Lemma p1p2_1274: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(el m o)->(pl g m). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))=>((lcon g o m) (conj p1p2_24 (p1p2_1273 Vplbm Vepdb Vepdf Vells Vepcd Velmo)))). Qed. Lemma p1p2_1275: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(el m o)->(ep d g) \/ (el m n). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))=>((unique m n d g) (conj p1p2_6 (conj (p1p2_855 Vplbm Vepdb) (conj (p1p2_1274 Vplbm Vepdb Vepdf Vells Vepcd Velmo) p1p2_23))))). Qed. Lemma p1p2_1276: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(el m o)->(ep d g)->(ep g d). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))(Vepdg:(ep d g))=>((psym d g) Vepdg)). Qed. Lemma p1p2_1283: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(el m o)->(ep d g)->(pl g p). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))(Vepdg:(ep d g))=>((pcon g d p) (conj (p1p2_1276 Vplbm Vepdb Vepdf Vells Vepcd Velmo Vepdg) p1p2_17))). Qed. Lemma p1p2_1287: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(el m o)->(ep d g)->(ep c i) \/ (el r l). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))(Vepdg:(ep d g))=>((unique r l c i) (conj p1p2_11 (conj p1p2_21 (conj p1p2_27 (p1p2_1167 Vplbm Vepdb Vepdf Vells)))))). Qed. Lemma p1p2_1288: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(el m o)->(ep d g)->(ep c i)->(ep i c). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))(Vepdg:(ep d g))(Vepci:(ep c i))=>((psym c i) Vepci)). Qed. Lemma p1p2_1299: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(el m o)->(ep d g)->(ep c i)->(pl i p). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))(Vepdg:(ep d g))(Vepci:(ep c i))=>((pcon i c p) (conj (p1p2_1288 Vplbm Vepdb Vepdf Vells Vepcd Velmo Vepdg Vepci) (p1p2_1175 Vplbm Vepdb Vepdf Vells Vepcd)))). Qed. Lemma p1p2_1300: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(el m o)->(ep d g)->(ep c i)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))(Vepdg:(ep d g))(Vepci:(ep c i))=>((goal4 p) (conj p1p2_42 (conj (p1p2_1283 Vplbm Vepdb Vepdf Vells Vepcd Velmo Vepdg) (conj p1p2_25 (p1p2_1299 Vplbm Vepdb Vepdf Vells Vepcd Velmo Vepdg Vepci)))))). Qed. Lemma p1p2_1301: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(el m o)->(ep d g)->(el r l)->(el l r). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))(Vepdg:(ep d g))(Velrl:(el r l))=>((lsym r l) Velrl)). Qed. Lemma p1p2_1302: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(el m o)->(ep d g)->(el r l)->(el s r). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))(Vepdg:(ep d g))(Velrl:(el r l))=>((ltra s l r) (conj (p1p2_1165 Vplbm Vepdb Vepdf Vells) (p1p2_1301 Vplbm Vepdb Vepdf Vells Vepcd Velmo Vepdg Velrl)))). Qed. Lemma p1p2_1303: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(el m o)->(ep d g)->(el r l)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))(Vepdg:(ep d g))(Velrl:(el r l))=>(goal3 (p1p2_1302 Vplbm Vepdb Vepdf Vells Vepcd Velmo Vepdg Velrl))). Qed. Lemma p1p2_1304: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(el m o)->(ep d g)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))(Vepdg:(ep d g))=>((or_ind ((p1p2_1300 Vplbm Vepdb Vepdf Vells Vepcd Velmo Vepdg))((p1p2_1303 Vplbm Vepdb Vepdf Vells Vepcd Velmo Vepdg)))(p1p2_1287 Vplbm Vepdb Vepdf Vells Vepcd Velmo Vepdg))). Qed. Lemma p1p2_1306: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(el m o)->(el m n)->(el o n). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))(Velmn:(el m n))=>((ltra o m n) (conj (p1p2_1273 Vplbm Vepdb Vepdf Vells Vepcd Velmo) Velmn))). Qed. Lemma p1p2_1307: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(el m o)->(el m n)->(el n o). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))(Velmn:(el m n))=>((lsym o n) (p1p2_1306 Vplbm Vepdb Vepdf Vells Vepcd Velmo Velmn))). Qed. Lemma p1p2_1308: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(el m o)->(el m n)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))(Velmn:(el m n))=>(goal1 (p1p2_1307 Vplbm Vepdb Vepdf Vells Vepcd Velmo Velmn))). Qed. Lemma p1p2_1309: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->(el m o)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))=>((or_ind ((p1p2_1304 Vplbm Vepdb Vepdf Vells Vepcd Velmo))((p1p2_1308 Vplbm Vepdb Vepdf Vells Vepcd Velmo)))(p1p2_1275 Vplbm Vepdb Vepdf Vells Vepcd Velmo))). Qed. Lemma p1p2_1310: (pl b m)->(ep d b)->(ep d f)->(el l s)->(ep c d)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))=>((or_ind ((p1p2_1272 Vplbm Vepdb Vepdf Vells Vepcd))((p1p2_1309 Vplbm Vepdb Vepdf Vells Vepcd)))(p1p2_1180 Vplbm Vepdb Vepdf Vells Vepcd))). Qed. Lemma p1p2_1311: (pl b m)->(ep d b)->(ep d f)->(el l s)->(el r l)->(el l r). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Velrl:(el r l))=>((lsym r l) Velrl)). Qed. Lemma p1p2_1312: (pl b m)->(ep d b)->(ep d f)->(el l s)->(el r l)->(el s r). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Velrl:(el r l))=>((ltra s l r) (conj (p1p2_1165 Vplbm Vepdb Vepdf Vells) (p1p2_1311 Vplbm Vepdb Vepdf Vells Velrl)))). Qed. Lemma p1p2_1313: (pl b m)->(ep d b)->(ep d f)->(el l s)->(el r l)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))(Velrl:(el r l))=>(goal3 (p1p2_1312 Vplbm Vepdb Vepdf Vells Velrl))). Qed. Lemma p1p2_1314: (pl b m)->(ep d b)->(ep d f)->(el l s)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))(Vells:(el l s))=>((or_ind ((p1p2_1310 Vplbm Vepdb Vepdf Vells))((p1p2_1313 Vplbm Vepdb Vepdf Vells)))(p1p2_1168 Vplbm Vepdb Vepdf Vells))). Qed. Lemma p1p2_1315: (pl b m)->(ep d b)->(ep d f)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Vepdf:(ep d f))=>((or_ind ((p1p2_1164 Vplbm Vepdb Vepdf))((p1p2_1314 Vplbm Vepdb Vepdf)))(p1p2_867 Vplbm Vepdb Vepdf))). Qed. Lemma p1p2_1316: (pl b m)->(ep d b)->(el m n)->(el n m). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))=>((lsym m n) Velmn)). Qed. Lemma p1p2_1318: (pl b m)->(ep d b)->(el m n)->(pl g m). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))=>((lcon g n m) (conj p1p2_23 (p1p2_1316 Vplbm Vepdb Velmn)))). Qed. Lemma p1p2_1319: (pl b m)->(ep d b)->(el m n)->(ep c d) \/ (el r l). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))=>((unique r l c d) (conj p1p2_11 (conj p1p2_21 (conj p1p2_19 (p1p2_856 Vplbm Vepdb)))))). Qed. Lemma p1p2_1320: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d c). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))=>((psym c d) Vepcd)). Qed. Lemma p1p2_1326: (pl b m)->(ep d b)->(el m n)->(ep c d)->(pl d o). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))=>((pcon d c o) (conj (p1p2_1320 Vplbm Vepdb Velmn Vepcd) p1p2_8))). Qed. Lemma p1p2_1328: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e) \/ (el m o). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))=>((unique m o d e) (conj p1p2_6 (conj (p1p2_1326 Vplbm Vepdb Velmn Vepcd) (conj p1p2_14 p1p2_16))))). Qed. Lemma p1p2_1334: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(pl d q). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))=>((pcon d e q) (conj Vepde p1p2_18))). Qed. Lemma p1p2_1335: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(pl b q). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))=>((pcon b d q) (conj (p1p2_854 Vplbm Vepdb) (p1p2_1334 Vplbm Vepdb Velmn Vepcd Vepde)))). Qed. Lemma p1p2_1340: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(ep a b) \/ (el l q). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))=>((unique l q a b) (conj p1p2_5 (conj p1p2_10 (conj p1p2_13 (p1p2_1335 Vplbm Vepdb Velmn Vepcd Vepde)))))). Qed. Lemma p1p2_1341: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep b a). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))=>((psym a b) Vepab)). Qed. Lemma p1p2_1353: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(pl b s). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))=>((pcon b a s) (conj (p1p2_1341 Vplbm Vepdb Velmn Vepcd Vepde Vepab) p1p2_12))). Qed. Lemma p1p2_1354: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(pl d s). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))=>((pcon d b s) (conj Vepdb (p1p2_1353 Vplbm Vepdb Velmn Vepcd Vepde Vepab)))). Qed. Lemma p1p2_1357: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g) \/ (el m o). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))=>((unique m o d g) (conj p1p2_6 (conj (p1p2_1326 Vplbm Vepdb Velmn Vepcd) (conj (p1p2_1318 Vplbm Vepdb Velmn) p1p2_24))))). Qed. Lemma p1p2_1358: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(ep g d). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))=>((psym d g) Vepdg)). Qed. Lemma p1p2_1367: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(pl g p). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))=>((pcon g d p) (conj (p1p2_1358 Vplbm Vepdb Velmn Vepcd Vepde Vepab Vepdg) p1p2_17))). Qed. Lemma p1p2_1368: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(pl g r). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))=>((pcon g d r) (conj (p1p2_1358 Vplbm Vepdb Velmn Vepcd Vepde Vepab Vepdg) p1p2_19))). Qed. Lemma p1p2_1372: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(ep d f) \/ (el m s). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))=>((unique m s d f) (conj p1p2_6 (conj (p1p2_1354 Vplbm Vepdb Velmn Vepcd Vepde Vepab) (conj p1p2_22 p1p2_20))))). Qed. Lemma p1p2_1389: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(ep d f)->(ep b h) \/ (el p q). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))(Vepdf:(ep d f))=>((unique p q b h) (conj p1p2_9 (conj (p1p2_1335 Vplbm Vepdb Velmn Vepcd Vepde) (conj p1p2_25 p1p2_26))))). Qed. Lemma p1p2_1390: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(ep d f)->(ep b h)->(ep h b). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))(Vepdf:(ep d f))(Vepbh:(ep b h))=>((psym b h) Vepbh)). Qed. Lemma p1p2_1406: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(ep d f)->(ep b h)->(pl h r). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))(Vepdf:(ep d f))(Vepbh:(ep b h))=>((pcon h b r) (conj (p1p2_1390 Vplbm Vepdb Velmn Vepcd Vepde Vepab Vepdg Vepdf Vepbh) (p1p2_857 Vplbm Vepdb)))). Qed. Lemma p1p2_1407: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(ep d f)->(ep b h)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))(Vepdf:(ep d f))(Vepbh:(ep b h))=>((goal4 r) (conj p1p2_44 (conj (p1p2_1368 Vplbm Vepdb Velmn Vepcd Vepde Vepab Vepdg) (conj (p1p2_1406 Vplbm Vepdb Velmn Vepcd Vepde Vepab Vepdg Vepdf Vepbh) p1p2_27))))). Qed. Lemma p1p2_1408: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(ep d f)->(el p q)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))(Vepdf:(ep d f))(Velpq:(el p q))=>(goal2 Velpq)). Qed. Lemma p1p2_1409: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(ep d f)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))(Vepdf:(ep d f))=>((or_ind ((p1p2_1407 Vplbm Vepdb Velmn Vepcd Vepde Vepab Vepdg Vepdf))((p1p2_1408 Vplbm Vepdb Velmn Vepcd Vepde Vepab Vepdg Vepdf)))(p1p2_1389 Vplbm Vepdb Velmn Vepcd Vepde Vepab Vepdg Vepdf))). Qed. Lemma p1p2_1410: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(el m s)->(el s m). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))(Velms:(el m s))=>((lsym m s) Velms)). Qed. Lemma p1p2_1413: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(el m s)->(pl i m). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))(Velms:(el m s))=>((lcon i s m) (conj p1p2_28 (p1p2_1410 Vplbm Vepdb Velmn Vepcd Vepde Vepab Vepdg Velms)))). Qed. Lemma p1p2_1415: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(el m s)->(ep d i) \/ (el m r). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))(Velms:(el m s))=>((unique m r d i) (conj p1p2_6 (conj p1p2_19 (conj (p1p2_1413 Vplbm Vepdb Velmn Vepcd Vepde Vepab Vepdg Velms) p1p2_27))))). Qed. Lemma p1p2_1416: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(el m s)->(ep d i)->(ep i d). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))(Velms:(el m s))(Vepdi:(ep d i))=>((psym d i) Vepdi)). Qed. Lemma p1p2_1427: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(el m s)->(ep d i)->(pl i p). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))(Velms:(el m s))(Vepdi:(ep d i))=>((pcon i d p) (conj (p1p2_1416 Vplbm Vepdb Velmn Vepcd Vepde Vepab Vepdg Velms Vepdi) p1p2_17))). Qed. Lemma p1p2_1428: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(el m s)->(ep d i)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))(Velms:(el m s))(Vepdi:(ep d i))=>((goal4 p) (conj p1p2_42 (conj (p1p2_1367 Vplbm Vepdb Velmn Vepcd Vepde Vepab Vepdg) (conj p1p2_25 (p1p2_1427 Vplbm Vepdb Velmn Vepcd Vepde Vepab Vepdg Velms Vepdi)))))). Qed. Lemma p1p2_1432: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(el m s)->(el m r)->(el s r). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))(Velms:(el m s))(Velmr:(el m r))=>((ltra s m r) (conj (p1p2_1410 Vplbm Vepdb Velmn Vepcd Vepde Vepab Vepdg Velms) Velmr))). Qed. Lemma p1p2_1433: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(el m s)->(el m r)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))(Velms:(el m s))(Velmr:(el m r))=>(goal3 (p1p2_1432 Vplbm Vepdb Velmn Vepcd Vepde Vepab Vepdg Velms Velmr))). Qed. Lemma p1p2_1434: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(el m s)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))(Velms:(el m s))=>((or_ind ((p1p2_1428 Vplbm Vepdb Velmn Vepcd Vepde Vepab Vepdg Velms))((p1p2_1433 Vplbm Vepdb Velmn Vepcd Vepde Vepab Vepdg Velms)))(p1p2_1415 Vplbm Vepdb Velmn Vepcd Vepde Vepab Vepdg Velms))). Qed. Lemma p1p2_1435: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))=>((or_ind ((p1p2_1409 Vplbm Vepdb Velmn Vepcd Vepde Vepab Vepdg))((p1p2_1434 Vplbm Vepdb Velmn Vepcd Vepde Vepab Vepdg)))(p1p2_1372 Vplbm Vepdb Velmn Vepcd Vepde Vepab Vepdg))). Qed. Lemma p1p2_1437: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(el m o)->(el n o). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Velmo:(el m o))=>((ltra n m o) (conj (p1p2_1316 Vplbm Vepdb Velmn) Velmo))). Qed. Lemma p1p2_1438: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(el m o)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Velmo:(el m o))=>(goal1 (p1p2_1437 Vplbm Vepdb Velmn Vepcd Vepde Vepab Velmo))). Qed. Lemma p1p2_1439: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(ep a b)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))=>((or_ind ((p1p2_1435 Vplbm Vepdb Velmn Vepcd Vepde Vepab))((p1p2_1438 Vplbm Vepdb Velmn Vepcd Vepde Vepab)))(p1p2_1357 Vplbm Vepdb Velmn Vepcd Vepde Vepab))). Qed. Lemma p1p2_1440: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(el l q)->(el q l). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))=>((lsym l q) Vellq)). Qed. Lemma p1p2_1441: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(el l q)->(pl h l). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))=>((lcon h q l) (conj p1p2_26 (p1p2_1440 Vplbm Vepdb Velmn Vepcd Vepde Vellq)))). Qed. Lemma p1p2_1442: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(el l q)->(ep d g) \/ (el m o). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))=>((unique m o d g) (conj p1p2_6 (conj (p1p2_1326 Vplbm Vepdb Velmn Vepcd) (conj (p1p2_1318 Vplbm Vepdb Velmn) p1p2_24))))). Qed. Lemma p1p2_1443: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(el l q)->(ep d g)->(ep g d). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Vepdg:(ep d g))=>((psym d g) Vepdg)). Qed. Lemma p1p2_1451: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(el l q)->(ep d g)->(pl g r). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Vepdg:(ep d g))=>((pcon g d r) (conj (p1p2_1443 Vplbm Vepdb Velmn Vepcd Vepde Vellq Vepdg) p1p2_19))). Qed. Lemma p1p2_1454: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(el l q)->(ep d g)->(ep b h) \/ (el p l). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Vepdg:(ep d g))=>((unique p l b h) (conj p1p2_9 (conj p1p2_13 (conj p1p2_25 (p1p2_1441 Vplbm Vepdb Velmn Vepcd Vepde Vellq)))))). Qed. Lemma p1p2_1455: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(el l q)->(ep d g)->(ep b h)->(ep h b). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Vepdg:(ep d g))(Vepbh:(ep b h))=>((psym b h) Vepbh)). Qed. Lemma p1p2_1466: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(el l q)->(ep d g)->(ep b h)->(pl h r). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Vepdg:(ep d g))(Vepbh:(ep b h))=>((pcon h b r) (conj (p1p2_1455 Vplbm Vepdb Velmn Vepcd Vepde Vellq Vepdg Vepbh) (p1p2_857 Vplbm Vepdb)))). Qed. Lemma p1p2_1467: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(el l q)->(ep d g)->(ep b h)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Vepdg:(ep d g))(Vepbh:(ep b h))=>((goal4 r) (conj p1p2_44 (conj (p1p2_1451 Vplbm Vepdb Velmn Vepcd Vepde Vellq Vepdg) (conj (p1p2_1466 Vplbm Vepdb Velmn Vepcd Vepde Vellq Vepdg Vepbh) p1p2_27))))). Qed. Lemma p1p2_1468: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(el l q)->(ep d g)->(el p l)->(el l p). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Vepdg:(ep d g))(Velpl:(el p l))=>((lsym p l) Velpl)). Qed. Lemma p1p2_1469: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(el l q)->(ep d g)->(el p l)->(el q p). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Vepdg:(ep d g))(Velpl:(el p l))=>((ltra q l p) (conj (p1p2_1440 Vplbm Vepdb Velmn Vepcd Vepde Vellq) (p1p2_1468 Vplbm Vepdb Velmn Vepcd Vepde Vellq Vepdg Velpl)))). Qed. Lemma p1p2_1470: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(el l q)->(ep d g)->(el p l)->(el p q). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Vepdg:(ep d g))(Velpl:(el p l))=>((lsym q p) (p1p2_1469 Vplbm Vepdb Velmn Vepcd Vepde Vellq Vepdg Velpl))). Qed. Lemma p1p2_1471: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(el l q)->(ep d g)->(el p l)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Vepdg:(ep d g))(Velpl:(el p l))=>(goal2 (p1p2_1470 Vplbm Vepdb Velmn Vepcd Vepde Vellq Vepdg Velpl))). Qed. Lemma p1p2_1472: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(el l q)->(ep d g)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Vepdg:(ep d g))=>((or_ind ((p1p2_1467 Vplbm Vepdb Velmn Vepcd Vepde Vellq Vepdg))((p1p2_1471 Vplbm Vepdb Velmn Vepcd Vepde Vellq Vepdg)))(p1p2_1454 Vplbm Vepdb Velmn Vepcd Vepde Vellq Vepdg))). Qed. Lemma p1p2_1474: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(el l q)->(el m o)->(el n o). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Velmo:(el m o))=>((ltra n m o) (conj (p1p2_1316 Vplbm Vepdb Velmn) Velmo))). Qed. Lemma p1p2_1475: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(el l q)->(el m o)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Velmo:(el m o))=>(goal1 (p1p2_1474 Vplbm Vepdb Velmn Vepcd Vepde Vellq Velmo))). Qed. Lemma p1p2_1476: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->(el l q)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))=>((or_ind ((p1p2_1472 Vplbm Vepdb Velmn Vepcd Vepde Vellq))((p1p2_1475 Vplbm Vepdb Velmn Vepcd Vepde Vellq)))(p1p2_1442 Vplbm Vepdb Velmn Vepcd Vepde Vellq))). Qed. Lemma p1p2_1477: (pl b m)->(ep d b)->(el m n)->(ep c d)->(ep d e)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))=>((or_ind ((p1p2_1439 Vplbm Vepdb Velmn Vepcd Vepde))((p1p2_1476 Vplbm Vepdb Velmn Vepcd Vepde)))(p1p2_1340 Vplbm Vepdb Velmn Vepcd Vepde))). Qed. Lemma p1p2_1479: (pl b m)->(ep d b)->(el m n)->(ep c d)->(el m o)->(el n o). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Velmo:(el m o))=>((ltra n m o) (conj (p1p2_1316 Vplbm Vepdb Velmn) Velmo))). Qed. Lemma p1p2_1480: (pl b m)->(ep d b)->(el m n)->(ep c d)->(el m o)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))(Velmo:(el m o))=>(goal1 (p1p2_1479 Vplbm Vepdb Velmn Vepcd Velmo))). Qed. Lemma p1p2_1481: (pl b m)->(ep d b)->(el m n)->(ep c d)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Vepcd:(ep c d))=>((or_ind ((p1p2_1477 Vplbm Vepdb Velmn Vepcd))((p1p2_1480 Vplbm Vepdb Velmn Vepcd)))(p1p2_1328 Vplbm Vepdb Velmn Vepcd))). Qed. Lemma p1p2_1484: (pl b m)->(ep d b)->(el m n)->(el r l)->(pl i l). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Velrl:(el r l))=>((lcon i r l) (conj p1p2_27 Velrl))). Qed. Lemma p1p2_1485: (pl b m)->(ep d b)->(el m n)->(el r l)->(ep a i) \/ (el l s). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Velrl:(el r l))=>((unique l s a i) (conj p1p2_5 (conj p1p2_12 (conj (p1p2_1484 Vplbm Vepdb Velmn Velrl) p1p2_28))))). Qed. Lemma p1p2_1486: (pl b m)->(ep d b)->(el m n)->(el r l)->(ep a i)->(ep i a). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Velrl:(el r l))(Vepai:(ep a i))=>((psym a i) Vepai)). Qed. Lemma p1p2_1487: (pl b m)->(ep d b)->(el m n)->(el r l)->(ep a i)->(pl i q). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Velrl:(el r l))(Vepai:(ep a i))=>((pcon i a q) (conj (p1p2_1486 Vplbm Vepdb Velmn Velrl Vepai) p1p2_10))). Qed. Lemma p1p2_1488: (pl b m)->(ep d b)->(el m n)->(el r l)->(ep a i)->(ep e g) \/ (el m o). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Velrl:(el r l))(Vepai:(ep a i))=>((unique m o e g) (conj p1p2_14 (conj p1p2_16 (conj (p1p2_1318 Vplbm Vepdb Velmn) p1p2_24))))). Qed. Lemma p1p2_1489: (pl b m)->(ep d b)->(el m n)->(el r l)->(ep a i)->(ep e g)->(ep g e). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Velrl:(el r l))(Vepai:(ep a i))(Vepeg:(ep e g))=>((psym e g) Vepeg)). Qed. Lemma p1p2_1490: (pl b m)->(ep d b)->(el m n)->(el r l)->(ep a i)->(ep e g)->(pl g q). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Velrl:(el r l))(Vepai:(ep a i))(Vepeg:(ep e g))=>((pcon g e q) (conj (p1p2_1489 Vplbm Vepdb Velmn Velrl Vepai Vepeg) p1p2_18))). Qed. Lemma p1p2_1491: (pl b m)->(ep d b)->(el m n)->(el r l)->(ep a i)->(ep e g)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Velrl:(el r l))(Vepai:(ep a i))(Vepeg:(ep e g))=>((goal4 q) (conj p1p2_43 (conj (p1p2_1490 Vplbm Vepdb Velmn Velrl Vepai Vepeg) (conj p1p2_26 (p1p2_1487 Vplbm Vepdb Velmn Velrl Vepai)))))). Qed. Lemma p1p2_1493: (pl b m)->(ep d b)->(el m n)->(el r l)->(ep a i)->(el m o)->(el n o). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Velrl:(el r l))(Vepai:(ep a i))(Velmo:(el m o))=>((ltra n m o) (conj (p1p2_1316 Vplbm Vepdb Velmn) Velmo))). Qed. Lemma p1p2_1494: (pl b m)->(ep d b)->(el m n)->(el r l)->(ep a i)->(el m o)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Velrl:(el r l))(Vepai:(ep a i))(Velmo:(el m o))=>(goal1 (p1p2_1493 Vplbm Vepdb Velmn Velrl Vepai Velmo))). Qed. Lemma p1p2_1495: (pl b m)->(ep d b)->(el m n)->(el r l)->(ep a i)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Velrl:(el r l))(Vepai:(ep a i))=>((or_ind ((p1p2_1491 Vplbm Vepdb Velmn Velrl Vepai))((p1p2_1494 Vplbm Vepdb Velmn Velrl Vepai)))(p1p2_1488 Vplbm Vepdb Velmn Velrl Vepai))). Qed. Lemma p1p2_1497: (pl b m)->(ep d b)->(el m n)->(el r l)->(el l s)->(el r s). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Velrl:(el r l))(Vells:(el l s))=>((ltra r l s) (conj Velrl Vells))). Qed. Lemma p1p2_1498: (pl b m)->(ep d b)->(el m n)->(el r l)->(el l s)->(el s r). Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Velrl:(el r l))(Vells:(el l s))=>((lsym r s) (p1p2_1497 Vplbm Vepdb Velmn Velrl Vells))). Qed. Lemma p1p2_1499: (pl b m)->(ep d b)->(el m n)->(el r l)->(el l s)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Velrl:(el r l))(Vells:(el l s))=>(goal3 (p1p2_1498 Vplbm Vepdb Velmn Velrl Vells))). Qed. Lemma p1p2_1500: (pl b m)->(ep d b)->(el m n)->(el r l)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))(Velrl:(el r l))=>((or_ind ((p1p2_1495 Vplbm Vepdb Velmn Velrl))((p1p2_1499 Vplbm Vepdb Velmn Velrl)))(p1p2_1485 Vplbm Vepdb Velmn Velrl))). Qed. Lemma p1p2_1501: (pl b m)->(ep d b)->(el m n)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))(Velmn:(el m n))=>((or_ind ((p1p2_1481 Vplbm Vepdb Velmn))((p1p2_1500 Vplbm Vepdb Velmn)))(p1p2_1319 Vplbm Vepdb Velmn))). Qed. Lemma p1p2_1502: (pl b m)->(ep d b)->goal. Proof. exact (fun (Vplbm:(pl b m))(Vepdb:(ep d b))=>((or_ind ((p1p2_1315 Vplbm Vepdb))((p1p2_1501 Vplbm Vepdb)))(p1p2_858 Vplbm Vepdb))). Qed. Lemma p1p2_1503: (pl b m)->(el m p)->(el p m). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))=>((lsym m p) Velmp)). Qed. Lemma p1p2_1504: (pl b m)->(el m p)->(pl e p). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))=>((lcon e m p) (conj p1p2_14 Velmp))). Qed. Lemma p1p2_1505: (pl b m)->(el m p)->(pl f p). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))=>((lcon f m p) (conj p1p2_22 Velmp))). Qed. Lemma p1p2_1506: (pl b m)->(el m p)->(pl h m). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))=>((lcon h p m) (conj p1p2_25 (p1p2_1503 Vplbm Velmp)))). Qed. Lemma p1p2_1507: (pl b m)->(el m p)->(ep b f) \/ (el n p). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))=>((unique n p b f) (conj p1p2_7 (conj p1p2_9 (conj p1p2_15 (p1p2_1505 Vplbm Velmp)))))). Qed. Lemma p1p2_1509: (pl b m)->(el m p)->(ep b f)->(pl b s). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))=>((pcon b f s) (conj Vepbf p1p2_20))). Qed. Lemma p1p2_1511: (pl b m)->(el m p)->(ep b f)->(ep a b) \/ (el l s). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))=>((unique l s a b) (conj p1p2_5 (conj p1p2_12 (conj p1p2_13 (p1p2_1509 Vplbm Velmp Vepbf)))))). Qed. Lemma p1p2_1512: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b a). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))=>((psym a b) Vepab)). Qed. Lemma p1p2_1515: (pl b m)->(el m p)->(ep b f)->(ep a b)->(pl a n). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))=>((pcon a b n) (conj Vepab p1p2_7))). Qed. Lemma p1p2_1518: (pl b m)->(el m p)->(ep b f)->(ep a b)->(pl b q). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))=>((pcon b a q) (conj (p1p2_1512 Vplbm Velmp Vepbf Vepab) p1p2_10))). Qed. Lemma p1p2_1520: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h) \/ (el p q). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))=>((unique p q b h) (conj p1p2_9 (conj (p1p2_1518 Vplbm Velmp Vepbf Vepab) (conj p1p2_25 p1p2_26))))). Qed. Lemma p1p2_1521: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep h b). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))=>((psym b h) Vepbh)). Qed. Lemma p1p2_1528: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(pl h s). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))=>((pcon h b s) (conj (p1p2_1521 Vplbm Velmp Vepbf Vepab Vepbh) (p1p2_1509 Vplbm Velmp Vepbf)))). Qed. Lemma p1p2_1529: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e) \/ (el p q). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))=>((unique p q b e) (conj p1p2_9 (conj (p1p2_1518 Vplbm Velmp Vepbf Vepab) (conj (p1p2_1504 Vplbm Velmp) p1p2_18))))). Qed. Lemma p1p2_1530: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(ep e b). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))=>((psym b e) Vepbe)). Qed. Lemma p1p2_1537: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(pl b o). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))=>((pcon b e o) (conj Vepbe p1p2_16))). Qed. Lemma p1p2_1539: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(pl a o). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))=>((pcon a b o) (conj Vepab (p1p2_1537 Vplbm Velmp Vepbf Vepab Vepbh Vepbe)))). Qed. Lemma p1p2_1544: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(ep a c) \/ (el l o). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))=>((unique l o a c) (conj p1p2_5 (conj (p1p2_1539 Vplbm Velmp Vepbf Vepab Vepbh Vepbe) (conj p1p2_21 p1p2_8))))). Qed. Lemma p1p2_1554: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(ep a c)->(pl a r). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))=>((pcon a c r) (conj Vepac p1p2_11))). Qed. Lemma p1p2_1555: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(ep a c)->(pl b r). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))=>((pcon b a r) (conj (p1p2_1512 Vplbm Velmp Vepbf Vepab) (p1p2_1554 Vplbm Velmp Vepbf Vepab Vepbh Vepbe Vepac)))). Qed. Lemma p1p2_1558: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(ep a c)->(pl e r). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))=>((pcon e b r) (conj (p1p2_1530 Vplbm Velmp Vepbf Vepab Vepbh Vepbe) (p1p2_1555 Vplbm Velmp Vepbf Vepab Vepbh Vepbe Vepac)))). Qed. Lemma p1p2_1564: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(ep a c)->(ep d e) \/ (el m r). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))=>((unique m r d e) (conj p1p2_6 (conj p1p2_19 (conj p1p2_14 (p1p2_1558 Vplbm Velmp Vepbf Vepab Vepbh Vepbe Vepac)))))). Qed. Lemma p1p2_1581: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(ep a c)->(ep d e)->(ep b g) \/ (el n o). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))(Vepde:(ep d e))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_1537 Vplbm Velmp Vepbf Vepab Vepbh Vepbe) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_1582: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(ep a c)->(ep d e)->(ep b g)->(ep g b). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_1598: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(ep a c)->(ep d e)->(ep b g)->(pl g s). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))=>((pcon g b s) (conj (p1p2_1582 Vplbm Velmp Vepbf Vepab Vepbh Vepbe Vepac Vepde Vepbg) (p1p2_1509 Vplbm Velmp Vepbf)))). Qed. Lemma p1p2_1599: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(ep a c)->(ep d e)->(ep b g)->goal. Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))=>((goal4 s) (conj p1p2_45 (conj (p1p2_1598 Vplbm Velmp Vepbf Vepab Vepbh Vepbe Vepac Vepde Vepbg) (conj (p1p2_1528 Vplbm Velmp Vepbf Vepab Vepbh) p1p2_28))))). Qed. Lemma p1p2_1600: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(ep a c)->(ep d e)->(el n o)->goal. Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))(Vepde:(ep d e))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_1601: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(ep a c)->(ep d e)->goal. Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))(Vepde:(ep d e))=>((or_ind ((p1p2_1599 Vplbm Velmp Vepbf Vepab Vepbh Vepbe Vepac Vepde))((p1p2_1600 Vplbm Velmp Vepbf Vepab Vepbh Vepbe Vepac Vepde)))(p1p2_1581 Vplbm Velmp Vepbf Vepab Vepbh Vepbe Vepac Vepde))). Qed. Lemma p1p2_1603: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(ep a c)->(el m r)->(el p r). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))(Velmr:(el m r))=>((ltra p m r) (conj (p1p2_1503 Vplbm Velmp) Velmr))). Qed. Lemma p1p2_1604: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(ep a c)->(el m r)->(el r p). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))(Velmr:(el m r))=>((lsym p r) (p1p2_1603 Vplbm Velmp Vepbf Vepab Vepbh Vepbe Vepac Velmr))). Qed. Lemma p1p2_1606: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(ep a c)->(el m r)->(pl i p). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))(Velmr:(el m r))=>((lcon i r p) (conj p1p2_27 (p1p2_1604 Vplbm Velmp Vepbf Vepab Vepbh Vepbe Vepac Velmr)))). Qed. Lemma p1p2_1607: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(ep a c)->(el m r)->(ep b g) \/ (el n o). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))(Velmr:(el m r))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_1537 Vplbm Velmp Vepbf Vepab Vepbh Vepbe) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_1608: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(ep a c)->(el m r)->(ep b g)->(ep g b). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))(Velmr:(el m r))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_1619: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(ep a c)->(el m r)->(ep b g)->(pl g p). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))(Velmr:(el m r))(Vepbg:(ep b g))=>((pcon g b p) (conj (p1p2_1608 Vplbm Velmp Vepbf Vepab Vepbh Vepbe Vepac Velmr Vepbg) p1p2_9))). Qed. Lemma p1p2_1620: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(ep a c)->(el m r)->(ep b g)->goal. Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))(Velmr:(el m r))(Vepbg:(ep b g))=>((goal4 p) (conj p1p2_42 (conj (p1p2_1619 Vplbm Velmp Vepbf Vepab Vepbh Vepbe Vepac Velmr Vepbg) (conj p1p2_25 (p1p2_1606 Vplbm Velmp Vepbf Vepab Vepbh Vepbe Vepac Velmr)))))). Qed. Lemma p1p2_1621: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(ep a c)->(el m r)->(el n o)->goal. Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))(Velmr:(el m r))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_1622: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(ep a c)->(el m r)->goal. Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))(Velmr:(el m r))=>((or_ind ((p1p2_1620 Vplbm Velmp Vepbf Vepab Vepbh Vepbe Vepac Velmr))((p1p2_1621 Vplbm Velmp Vepbf Vepab Vepbh Vepbe Vepac Velmr)))(p1p2_1607 Vplbm Velmp Vepbf Vepab Vepbh Vepbe Vepac Velmr))). Qed. Lemma p1p2_1623: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(ep a c)->goal. Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))=>((or_ind ((p1p2_1601 Vplbm Velmp Vepbf Vepab Vepbh Vepbe Vepac))((p1p2_1622 Vplbm Velmp Vepbf Vepab Vepbh Vepbe Vepac)))(p1p2_1564 Vplbm Velmp Vepbf Vepab Vepbh Vepbe Vepac))). Qed. Lemma p1p2_1624: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(el l o)->(el o l). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vello:(el l o))=>((lsym l o) Vello)). Qed. Lemma p1p2_1625: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(el l o)->(pl g l). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vello:(el l o))=>((lcon g o l) (conj p1p2_24 (p1p2_1624 Vplbm Velmp Vepbf Vepab Vepbh Vepbe Vello)))). Qed. Lemma p1p2_1626: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(el l o)->(ep a g) \/ (el l n). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vello:(el l o))=>((unique l n a g) (conj p1p2_5 (conj (p1p2_1515 Vplbm Velmp Vepbf Vepab) (conj (p1p2_1625 Vplbm Velmp Vepbf Vepab Vepbh Vepbe Vello) p1p2_23))))). Qed. Lemma p1p2_1627: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(el l o)->(ep a g)->(ep g a). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vello:(el l o))(Vepag:(ep a g))=>((psym a g) Vepag)). Qed. Lemma p1p2_1637: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(el l o)->(ep a g)->(pl g s). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vello:(el l o))(Vepag:(ep a g))=>((pcon g a s) (conj (p1p2_1627 Vplbm Velmp Vepbf Vepab Vepbh Vepbe Vello Vepag) p1p2_12))). Qed. Lemma p1p2_1638: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(el l o)->(ep a g)->goal. Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vello:(el l o))(Vepag:(ep a g))=>((goal4 s) (conj p1p2_45 (conj (p1p2_1637 Vplbm Velmp Vepbf Vepab Vepbh Vepbe Vello Vepag) (conj (p1p2_1528 Vplbm Velmp Vepbf Vepab Vepbh) p1p2_28))))). Qed. Lemma p1p2_1640: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(el l o)->(el l n)->(el o n). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vello:(el l o))(Velln:(el l n))=>((ltra o l n) (conj (p1p2_1624 Vplbm Velmp Vepbf Vepab Vepbh Vepbe Vello) Velln))). Qed. Lemma p1p2_1641: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(el l o)->(el l n)->(el n o). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vello:(el l o))(Velln:(el l n))=>((lsym o n) (p1p2_1640 Vplbm Velmp Vepbf Vepab Vepbh Vepbe Vello Velln))). Qed. Lemma p1p2_1642: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(el l o)->(el l n)->goal. Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vello:(el l o))(Velln:(el l n))=>(goal1 (p1p2_1641 Vplbm Velmp Vepbf Vepab Vepbh Vepbe Vello Velln))). Qed. Lemma p1p2_1643: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->(el l o)->goal. Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vello:(el l o))=>((or_ind ((p1p2_1638 Vplbm Velmp Vepbf Vepab Vepbh Vepbe Vello))((p1p2_1642 Vplbm Velmp Vepbf Vepab Vepbh Vepbe Vello)))(p1p2_1626 Vplbm Velmp Vepbf Vepab Vepbh Vepbe Vello))). Qed. Lemma p1p2_1644: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(ep b e)->goal. Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Vepbe:(ep b e))=>((or_ind ((p1p2_1623 Vplbm Velmp Vepbf Vepab Vepbh Vepbe))((p1p2_1643 Vplbm Velmp Vepbf Vepab Vepbh Vepbe)))(p1p2_1544 Vplbm Velmp Vepbf Vepab Vepbh Vepbe))). Qed. Lemma p1p2_1645: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->(el p q)->goal. Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))(Velpq:(el p q))=>(goal2 Velpq)). Qed. Lemma p1p2_1646: (pl b m)->(el m p)->(ep b f)->(ep a b)->(ep b h)->goal. Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Vepbh:(ep b h))=>((or_ind ((p1p2_1644 Vplbm Velmp Vepbf Vepab Vepbh))((p1p2_1645 Vplbm Velmp Vepbf Vepab Vepbh)))(p1p2_1529 Vplbm Velmp Vepbf Vepab Vepbh))). Qed. Lemma p1p2_1647: (pl b m)->(el m p)->(ep b f)->(ep a b)->(el p q)->goal. Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))(Velpq:(el p q))=>(goal2 Velpq)). Qed. Lemma p1p2_1648: (pl b m)->(el m p)->(ep b f)->(ep a b)->goal. Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vepab:(ep a b))=>((or_ind ((p1p2_1646 Vplbm Velmp Vepbf Vepab))((p1p2_1647 Vplbm Velmp Vepbf Vepab)))(p1p2_1520 Vplbm Velmp Vepbf Vepab))). Qed. Lemma p1p2_1649: (pl b m)->(el m p)->(ep b f)->(el l s)->(el s l). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vells:(el l s))=>((lsym l s) Vells)). Qed. Lemma p1p2_1651: (pl b m)->(el m p)->(ep b f)->(el l s)->(pl i l). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vells:(el l s))=>((lcon i s l) (conj p1p2_28 (p1p2_1649 Vplbm Velmp Vepbf Vells)))). Qed. Lemma p1p2_1652: (pl b m)->(el m p)->(ep b f)->(el l s)->(ep c i) \/ (el r l). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vells:(el l s))=>((unique r l c i) (conj p1p2_11 (conj p1p2_21 (conj p1p2_27 (p1p2_1651 Vplbm Velmp Vepbf Vells)))))). Qed. Lemma p1p2_1653: (pl b m)->(el m p)->(ep b f)->(el l s)->(ep c i)->(ep i c). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vells:(el l s))(Vepci:(ep c i))=>((psym c i) Vepci)). Qed. Lemma p1p2_1654: (pl b m)->(el m p)->(ep b f)->(el l s)->(ep c i)->(pl i o). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vells:(el l s))(Vepci:(ep c i))=>((pcon i c o) (conj (p1p2_1653 Vplbm Velmp Vepbf Vells Vepci) p1p2_8))). Qed. Lemma p1p2_1655: (pl b m)->(el m p)->(ep b f)->(el l s)->(ep c i)->(ep e h) \/ (el m q). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vells:(el l s))(Vepci:(ep c i))=>((unique m q e h) (conj p1p2_14 (conj p1p2_18 (conj (p1p2_1506 Vplbm Velmp) p1p2_26))))). Qed. Lemma p1p2_1656: (pl b m)->(el m p)->(ep b f)->(el l s)->(ep c i)->(ep e h)->(ep h e). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vells:(el l s))(Vepci:(ep c i))(Vepeh:(ep e h))=>((psym e h) Vepeh)). Qed. Lemma p1p2_1657: (pl b m)->(el m p)->(ep b f)->(el l s)->(ep c i)->(ep e h)->(pl h o). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vells:(el l s))(Vepci:(ep c i))(Vepeh:(ep e h))=>((pcon h e o) (conj (p1p2_1656 Vplbm Velmp Vepbf Vells Vepci Vepeh) p1p2_16))). Qed. Lemma p1p2_1658: (pl b m)->(el m p)->(ep b f)->(el l s)->(ep c i)->(ep e h)->goal. Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vells:(el l s))(Vepci:(ep c i))(Vepeh:(ep e h))=>((goal4 o) (conj p1p2_41 (conj p1p2_24 (conj (p1p2_1657 Vplbm Velmp Vepbf Vells Vepci Vepeh) (p1p2_1654 Vplbm Velmp Vepbf Vells Vepci)))))). Qed. Lemma p1p2_1660: (pl b m)->(el m p)->(ep b f)->(el l s)->(ep c i)->(el m q)->(el p q). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vells:(el l s))(Vepci:(ep c i))(Velmq:(el m q))=>((ltra p m q) (conj (p1p2_1503 Vplbm Velmp) Velmq))). Qed. Lemma p1p2_1661: (pl b m)->(el m p)->(ep b f)->(el l s)->(ep c i)->(el m q)->goal. Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vells:(el l s))(Vepci:(ep c i))(Velmq:(el m q))=>(goal2 (p1p2_1660 Vplbm Velmp Vepbf Vells Vepci Velmq))). Qed. Lemma p1p2_1662: (pl b m)->(el m p)->(ep b f)->(el l s)->(ep c i)->goal. Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vells:(el l s))(Vepci:(ep c i))=>((or_ind ((p1p2_1658 Vplbm Velmp Vepbf Vells Vepci))((p1p2_1661 Vplbm Velmp Vepbf Vells Vepci)))(p1p2_1655 Vplbm Velmp Vepbf Vells Vepci))). Qed. Lemma p1p2_1663: (pl b m)->(el m p)->(ep b f)->(el l s)->(el r l)->(el l r). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vells:(el l s))(Velrl:(el r l))=>((lsym r l) Velrl)). Qed. Lemma p1p2_1664: (pl b m)->(el m p)->(ep b f)->(el l s)->(el r l)->(el s r). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vells:(el l s))(Velrl:(el r l))=>((ltra s l r) (conj (p1p2_1649 Vplbm Velmp Vepbf Vells) (p1p2_1663 Vplbm Velmp Vepbf Vells Velrl)))). Qed. Lemma p1p2_1665: (pl b m)->(el m p)->(ep b f)->(el l s)->(el r l)->goal. Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vells:(el l s))(Velrl:(el r l))=>(goal3 (p1p2_1664 Vplbm Velmp Vepbf Vells Velrl))). Qed. Lemma p1p2_1666: (pl b m)->(el m p)->(ep b f)->(el l s)->goal. Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))(Vells:(el l s))=>((or_ind ((p1p2_1662 Vplbm Velmp Vepbf Vells))((p1p2_1665 Vplbm Velmp Vepbf Vells)))(p1p2_1652 Vplbm Velmp Vepbf Vells))). Qed. Lemma p1p2_1667: (pl b m)->(el m p)->(ep b f)->goal. Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Vepbf:(ep b f))=>((or_ind ((p1p2_1648 Vplbm Velmp Vepbf))((p1p2_1666 Vplbm Velmp Vepbf)))(p1p2_1511 Vplbm Velmp Vepbf))). Qed. Lemma p1p2_1668: (pl b m)->(el m p)->(el n p)->(el p n). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Velnp:(el n p))=>((lsym n p) Velnp)). Qed. Lemma p1p2_1669: (pl b m)->(el m p)->(el n p)->(el m n). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Velnp:(el n p))=>((ltra m p n) (conj Velmp (p1p2_1668 Vplbm Velmp Velnp)))). Qed. Lemma p1p2_1670: (pl b m)->(el m p)->(el n p)->(el n m). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Velnp:(el n p))=>((lsym m n) (p1p2_1669 Vplbm Velmp Velnp))). Qed. Lemma p1p2_1674: (pl b m)->(el m p)->(el n p)->(pl g m). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Velnp:(el n p))=>((lcon g n m) (conj p1p2_23 (p1p2_1670 Vplbm Velmp Velnp)))). Qed. Lemma p1p2_1676: (pl b m)->(el m p)->(el n p)->(ep e g) \/ (el m o). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Velnp:(el n p))=>((unique m o e g) (conj p1p2_14 (conj p1p2_16 (conj (p1p2_1674 Vplbm Velmp Velnp) p1p2_24))))). Qed. Lemma p1p2_1677: (pl b m)->(el m p)->(el n p)->(ep e g)->(ep g e). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Velnp:(el n p))(Vepeg:(ep e g))=>((psym e g) Vepeg)). Qed. Lemma p1p2_1679: (pl b m)->(el m p)->(el n p)->(ep e g)->(ep e h) \/ (el m q). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Velnp:(el n p))(Vepeg:(ep e g))=>((unique m q e h) (conj p1p2_14 (conj p1p2_18 (conj (p1p2_1506 Vplbm Velmp) p1p2_26))))). Qed. Lemma p1p2_1680: (pl b m)->(el m p)->(el n p)->(ep e g)->(ep e h)->(ep h e). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Velnp:(el n p))(Vepeg:(ep e g))(Vepeh:(ep e h))=>((psym e h) Vepeh)). Qed. Lemma p1p2_1684: (pl b m)->(el m p)->(el n p)->(ep e g)->(ep e h)->(exists A:dom,(pl a A)/\(pl d A)). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Velnp:(el n p))(Vepeg:(ep e g))(Vepeh:(ep e h))=>((line a d) (conj p1p2_29 p1p2_30))). Qed. Lemma p1p2_1686: (pl b m)->(el m p)->(el n p)->(ep e g)->(ep e h)->forall C0:dom,(pl a C0)->(pl d C0)->(exists A:dom,(pl b A)/\(pl i A)). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Velnp:(el n p))(Vepeg:(ep e g))(Vepeh:(ep e h))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))=>((line b i) (conj p1p2_31 p1p2_37))). Qed. Lemma p1p2_1688: (pl b m)->(el m p)->(el n p)->(ep e g)->(ep e h)->forall C0:dom,(pl a C0)->(pl d C0)->forall C1:dom,(pl b C1)->(pl i C1)->(exists A:dom,(pl c A)/\(pl f A)). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Velnp:(el n p))(Vepeg:(ep e g))(Vepeh:(ep e h))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))(C1:dom)(VplbC1:(pl b C1))(VpliC1:(pl i C1))=>((line c f) (conj p1p2_32 p1p2_34))). Qed. Lemma p1p2_1690: (pl b m)->(el m p)->(el n p)->(ep e g)->(ep e h)->forall C0:dom,(pl a C0)->(pl d C0)->forall C1:dom,(pl b C1)->(pl i C1)->forall C2:dom,(pl c C2)->(pl f C2)->(exists A:dom,(pl e A)/\(pl i A)). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Velnp:(el n p))(Vepeg:(ep e g))(Vepeh:(ep e h))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))(C1:dom)(VplbC1:(pl b C1))(VpliC1:(pl i C1))(C2:dom)(VplcC2:(pl c C2))(VplfC2:(pl f C2))=>((line e i) (conj p1p2_33 p1p2_37))). Qed. Lemma p1p2_1691: (pl b m)->(el m p)->(el n p)->(ep e g)->(ep e h)->forall C0:dom,(pl a C0)->(pl d C0)->forall C1:dom,(pl b C1)->(pl i C1)->forall C2:dom,(pl c C2)->(pl f C2)->forall C3:dom,(pl e C3)->(pl i C3)->(el C3 C3). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Velnp:(el n p))(Vepeg:(ep e g))(Vepeh:(ep e h))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))(C1:dom)(VplbC1:(pl b C1))(VpliC1:(pl i C1))(C2:dom)(VplcC2:(pl c C2))(VplfC2:(pl f C2))(C3:dom)(VpleC3:(pl e C3))(VpliC3:(pl i C3))=>((lref e C3) VpleC3)). Qed. Lemma p1p2_1692: (pl b m)->(el m p)->(el n p)->(ep e g)->(ep e h)->forall C0:dom,(pl a C0)->(pl d C0)->forall C1:dom,(pl b C1)->(pl i C1)->forall C2:dom,(pl c C2)->(pl f C2)->forall C3:dom,(pl e C3)->(pl i C3)->(pl g C3). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Velnp:(el n p))(Vepeg:(ep e g))(Vepeh:(ep e h))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))(C1:dom)(VplbC1:(pl b C1))(VpliC1:(pl i C1))(C2:dom)(VplcC2:(pl c C2))(VplfC2:(pl f C2))(C3:dom)(VpleC3:(pl e C3))(VpliC3:(pl i C3))=>((pcon g e C3) (conj (p1p2_1677 Vplbm Velmp Velnp Vepeg) VpleC3))). Qed. Lemma p1p2_1693: (pl b m)->(el m p)->(el n p)->(ep e g)->(ep e h)->forall C0:dom,(pl a C0)->(pl d C0)->forall C1:dom,(pl b C1)->(pl i C1)->forall C2:dom,(pl c C2)->(pl f C2)->forall C3:dom,(pl e C3)->(pl i C3)->(pl h C3). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Velnp:(el n p))(Vepeg:(ep e g))(Vepeh:(ep e h))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))(C1:dom)(VplbC1:(pl b C1))(VpliC1:(pl i C1))(C2:dom)(VplcC2:(pl c C2))(VplfC2:(pl f C2))(C3:dom)(VpleC3:(pl e C3))(VpliC3:(pl i C3))=>((pcon h e C3) (conj (p1p2_1680 Vplbm Velmp Velnp Vepeg Vepeh) VpleC3))). Qed. Lemma p1p2_1694: (pl b m)->(el m p)->(el n p)->(ep e g)->(ep e h)->forall C0:dom,(pl a C0)->(pl d C0)->forall C1:dom,(pl b C1)->(pl i C1)->forall C2:dom,(pl c C2)->(pl f C2)->forall C3:dom,(pl e C3)->(pl i C3)->goal. Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Velnp:(el n p))(Vepeg:(ep e g))(Vepeh:(ep e h))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))(C1:dom)(VplbC1:(pl b C1))(VpliC1:(pl i C1))(C2:dom)(VplcC2:(pl c C2))(VplfC2:(pl f C2))(C3:dom)(VpleC3:(pl e C3))(VpliC3:(pl i C3))=>((goal4 C3) (conj (p1p2_1691 Vplbm Velmp Velnp Vepeg Vepeh C0 VplaC0 VpldC0 C1 VplbC1 VpliC1 C2 VplcC2 VplfC2 C3 VpleC3 VpliC3) (conj (p1p2_1692 Vplbm Velmp Velnp Vepeg Vepeh C0 VplaC0 VpldC0 C1 VplbC1 VpliC1 C2 VplcC2 VplfC2 C3 VpleC3 VpliC3) (conj (p1p2_1693 Vplbm Velmp Velnp Vepeg Vepeh C0 VplaC0 VpldC0 C1 VplbC1 VpliC1 C2 VplcC2 VplfC2 C3 VpleC3 VpliC3) VpliC3))))). Qed. Lemma p1p2_1695: (pl b m)->(el m p)->(el n p)->(ep e g)->(ep e h)->forall C0:dom,(pl a C0)->(pl d C0)->forall C1:dom,(pl b C1)->(pl i C1)->forall C2:dom,(pl c C2)->(pl f C2)->goal. Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Velnp:(el n p))(Vepeg:(ep e g))(Vepeh:(ep e h))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))(C1:dom)(VplbC1:(pl b C1))(VpliC1:(pl i C1))(C2:dom)(VplcC2:(pl c C2))(VplfC2:(pl f C2))=>((ex_ind (P:=fun C3:dom=>(pl e C3)/\(pl i C3))(fun C3:dom=>(and_ind (p1p2_1694 Vplbm Velmp Velnp Vepeg Vepeh C0 VplaC0 VpldC0 C1 VplbC1 VpliC1 C2 VplcC2 VplfC2 C3))))(p1p2_1690 Vplbm Velmp Velnp Vepeg Vepeh C0 VplaC0 VpldC0 C1 VplbC1 VpliC1 C2 VplcC2 VplfC2))). Qed. Lemma p1p2_1696: (pl b m)->(el m p)->(el n p)->(ep e g)->(ep e h)->forall C0:dom,(pl a C0)->(pl d C0)->forall C1:dom,(pl b C1)->(pl i C1)->goal. Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Velnp:(el n p))(Vepeg:(ep e g))(Vepeh:(ep e h))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))(C1:dom)(VplbC1:(pl b C1))(VpliC1:(pl i C1))=>((ex_ind (P:=fun C2:dom=>(pl c C2)/\(pl f C2))(fun C2:dom=>(and_ind (p1p2_1695 Vplbm Velmp Velnp Vepeg Vepeh C0 VplaC0 VpldC0 C1 VplbC1 VpliC1 C2))))(p1p2_1688 Vplbm Velmp Velnp Vepeg Vepeh C0 VplaC0 VpldC0 C1 VplbC1 VpliC1))). Qed. Lemma p1p2_1697: (pl b m)->(el m p)->(el n p)->(ep e g)->(ep e h)->forall C0:dom,(pl a C0)->(pl d C0)->goal. Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Velnp:(el n p))(Vepeg:(ep e g))(Vepeh:(ep e h))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))=>((ex_ind (P:=fun C1:dom=>(pl b C1)/\(pl i C1))(fun C1:dom=>(and_ind (p1p2_1696 Vplbm Velmp Velnp Vepeg Vepeh C0 VplaC0 VpldC0 C1))))(p1p2_1686 Vplbm Velmp Velnp Vepeg Vepeh C0 VplaC0 VpldC0))). Qed. Lemma p1p2_1698: (pl b m)->(el m p)->(el n p)->(ep e g)->(ep e h)->goal. Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Velnp:(el n p))(Vepeg:(ep e g))(Vepeh:(ep e h))=>((ex_ind (P:=fun C0:dom=>(pl a C0)/\(pl d C0))(fun C0:dom=>(and_ind (p1p2_1697 Vplbm Velmp Velnp Vepeg Vepeh C0))))(p1p2_1684 Vplbm Velmp Velnp Vepeg Vepeh))). Qed. Lemma p1p2_1700: (pl b m)->(el m p)->(el n p)->(ep e g)->(el m q)->(el p q). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Velnp:(el n p))(Vepeg:(ep e g))(Velmq:(el m q))=>((ltra p m q) (conj (p1p2_1503 Vplbm Velmp) Velmq))). Qed. Lemma p1p2_1701: (pl b m)->(el m p)->(el n p)->(ep e g)->(el m q)->goal. Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Velnp:(el n p))(Vepeg:(ep e g))(Velmq:(el m q))=>(goal2 (p1p2_1700 Vplbm Velmp Velnp Vepeg Velmq))). Qed. Lemma p1p2_1702: (pl b m)->(el m p)->(el n p)->(ep e g)->goal. Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Velnp:(el n p))(Vepeg:(ep e g))=>((or_ind ((p1p2_1698 Vplbm Velmp Velnp Vepeg))((p1p2_1701 Vplbm Velmp Velnp Vepeg)))(p1p2_1679 Vplbm Velmp Velnp Vepeg))). Qed. Lemma p1p2_1704: (pl b m)->(el m p)->(el n p)->(el m o)->(el p o). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Velnp:(el n p))(Velmo:(el m o))=>((ltra p m o) (conj (p1p2_1503 Vplbm Velmp) Velmo))). Qed. Lemma p1p2_1706: (pl b m)->(el m p)->(el n p)->(el m o)->(el n o). Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Velnp:(el n p))(Velmo:(el m o))=>((ltra n p o) (conj Velnp (p1p2_1704 Vplbm Velmp Velnp Velmo)))). Qed. Lemma p1p2_1707: (pl b m)->(el m p)->(el n p)->(el m o)->goal. Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Velnp:(el n p))(Velmo:(el m o))=>(goal1 (p1p2_1706 Vplbm Velmp Velnp Velmo))). Qed. Lemma p1p2_1708: (pl b m)->(el m p)->(el n p)->goal. Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))(Velnp:(el n p))=>((or_ind ((p1p2_1702 Vplbm Velmp Velnp))((p1p2_1707 Vplbm Velmp Velnp)))(p1p2_1676 Vplbm Velmp Velnp))). Qed. Lemma p1p2_1709: (pl b m)->(el m p)->goal. Proof. exact (fun (Vplbm:(pl b m))(Velmp:(el m p))=>((or_ind ((p1p2_1667 Vplbm Velmp))((p1p2_1708 Vplbm Velmp)))(p1p2_1507 Vplbm Velmp))). Qed. Lemma p1p2_1710: (pl b m)->goal. Proof. exact (fun (Vplbm:(pl b m))=>((or_ind ((p1p2_1502 Vplbm))((p1p2_1709 Vplbm)))(p1p2_853 Vplbm))). Qed. Lemma p1p2_1711: (pl c m)->(ep d c) \/ (el m r). Proof. exact (fun (Vplcm:(pl c m))=>((unique m r d c) (conj p1p2_6 (conj p1p2_19 (conj Vplcm p1p2_11))))). Qed. Lemma p1p2_1712: (pl c m)->(ep d c)->(ep c d). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))=>((psym d c) Vepdc)). Qed. Lemma p1p2_1713: (pl c m)->(ep d c)->(pl d o). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))=>((pcon d c o) (conj Vepdc p1p2_8))). Qed. Lemma p1p2_1714: (pl c m)->(ep d c)->(pl d l). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))=>((pcon d c l) (conj Vepdc p1p2_21))). Qed. Lemma p1p2_1715: (pl c m)->(ep d c)->(pl c p). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))=>((pcon c d p) (conj (p1p2_1712 Vplcm Vepdc) p1p2_17))). Qed. Lemma p1p2_1716: (pl c m)->(ep d c)->(ep d e) \/ (el m o). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))=>((unique m o d e) (conj p1p2_6 (conj (p1p2_1713 Vplcm Vepdc) (conj p1p2_14 p1p2_16))))). Qed. Lemma p1p2_1720: (pl c m)->(ep d c)->(ep d e)->(pl d q). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))=>((pcon d e q) (conj Vepde p1p2_18))). Qed. Lemma p1p2_1721: (pl c m)->(ep d c)->(ep d e)->(pl c q). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))=>((pcon c d q) (conj (p1p2_1712 Vplcm Vepdc) (p1p2_1720 Vplcm Vepdc Vepde)))). Qed. Lemma p1p2_1725: (pl c m)->(ep d c)->(ep d e)->(ep a c) \/ (el l q). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))=>((unique l q a c) (conj p1p2_5 (conj p1p2_10 (conj p1p2_21 (p1p2_1721 Vplcm Vepdc Vepde)))))). Qed. Lemma p1p2_1726: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep c a). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))=>((psym a c) Vepac)). Qed. Lemma p1p2_1731: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(pl a o). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))=>((pcon a c o) (conj Vepac p1p2_8))). Qed. Lemma p1p2_1734: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(pl a p). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))=>((pcon a c p) (conj Vepac (p1p2_1715 Vplcm Vepdc)))). Qed. Lemma p1p2_1735: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(pl c s). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))=>((pcon c a s) (conj (p1p2_1726 Vplcm Vepdc Vepde Vepac) p1p2_12))). Qed. Lemma p1p2_1736: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(pl d s). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))=>((pcon d c s) (conj Vepdc (p1p2_1735 Vplcm Vepdc Vepde Vepac)))). Qed. Lemma p1p2_1738: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b) \/ (el l p). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))=>((unique l p a b) (conj p1p2_5 (conj (p1p2_1734 Vplcm Vepdc Vepde Vepac) (conj p1p2_13 p1p2_9))))). Qed. Lemma p1p2_1739: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(ep b a). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))=>((psym a b) Vepab)). Qed. Lemma p1p2_1746: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(pl a n). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))=>((pcon a b n) (conj Vepab p1p2_7))). Qed. Lemma p1p2_1747: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(pl c n). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))=>((pcon c a n) (conj (p1p2_1726 Vplcm Vepdc Vepde Vepac) (p1p2_1746 Vplcm Vepdc Vepde Vepac Vepab)))). Qed. Lemma p1p2_1748: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(pl d n). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))=>((pcon d c n) (conj Vepdc (p1p2_1747 Vplcm Vepdc Vepde Vepac Vepab)))). Qed. Lemma p1p2_1750: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(pl b q). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))=>((pcon b a q) (conj (p1p2_1739 Vplcm Vepdc Vepde Vepac Vepab) p1p2_10))). Qed. Lemma p1p2_1751: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(pl b s). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))=>((pcon b a s) (conj (p1p2_1739 Vplcm Vepdc Vepde Vepac Vepab) p1p2_12))). Qed. Lemma p1p2_1752: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(pl b o). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))=>((pcon b a o) (conj (p1p2_1739 Vplcm Vepdc Vepde Vepac Vepab) (p1p2_1731 Vplcm Vepdc Vepde Vepac)))). Qed. Lemma p1p2_1755: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(ep d f) \/ (el m s). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))=>((unique m s d f) (conj p1p2_6 (conj (p1p2_1736 Vplcm Vepdc Vepde Vepac) (conj p1p2_22 p1p2_20))))). Qed. Lemma p1p2_1770: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(ep d f)->(ep b g) \/ (el n o). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Vepdf:(ep d f))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_1752 Vplcm Vepdc Vepde Vepac Vepab) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_1771: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(ep d f)->(ep b g)->(ep g b). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_1785: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(ep d f)->(ep b g)->(pl g s). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepbg:(ep b g))=>((pcon g b s) (conj (p1p2_1771 Vplcm Vepdc Vepde Vepac Vepab Vepdf Vepbg) (p1p2_1751 Vplcm Vepdc Vepde Vepac Vepab)))). Qed. Lemma p1p2_1788: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(ep d f)->(ep b g)->(ep b h) \/ (el p q). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepbg:(ep b g))=>((unique p q b h) (conj p1p2_9 (conj (p1p2_1750 Vplcm Vepdc Vepde Vepac Vepab) (conj p1p2_25 p1p2_26))))). Qed. Lemma p1p2_1789: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(ep d f)->(ep b g)->(ep b h)->(ep h b). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepbg:(ep b g))(Vepbh:(ep b h))=>((psym b h) Vepbh)). Qed. Lemma p1p2_1804: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(ep d f)->(ep b g)->(ep b h)->(pl h s). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepbg:(ep b g))(Vepbh:(ep b h))=>((pcon h b s) (conj (p1p2_1789 Vplcm Vepdc Vepde Vepac Vepab Vepdf Vepbg Vepbh) (p1p2_1751 Vplcm Vepdc Vepde Vepac Vepab)))). Qed. Lemma p1p2_1805: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(ep d f)->(ep b g)->(ep b h)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepbg:(ep b g))(Vepbh:(ep b h))=>((goal4 s) (conj p1p2_45 (conj (p1p2_1785 Vplcm Vepdc Vepde Vepac Vepab Vepdf Vepbg) (conj (p1p2_1804 Vplcm Vepdc Vepde Vepac Vepab Vepdf Vepbg Vepbh) p1p2_28))))). Qed. Lemma p1p2_1806: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(ep d f)->(ep b g)->(el p q)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepbg:(ep b g))(Velpq:(el p q))=>(goal2 Velpq)). Qed. Lemma p1p2_1807: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(ep d f)->(ep b g)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepbg:(ep b g))=>((or_ind ((p1p2_1805 Vplcm Vepdc Vepde Vepac Vepab Vepdf Vepbg))((p1p2_1806 Vplcm Vepdc Vepde Vepac Vepab Vepdf Vepbg)))(p1p2_1788 Vplcm Vepdc Vepde Vepac Vepab Vepdf Vepbg))). Qed. Lemma p1p2_1808: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(ep d f)->(el n o)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Vepdf:(ep d f))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_1809: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(ep d f)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Vepdf:(ep d f))=>((or_ind ((p1p2_1807 Vplcm Vepdc Vepde Vepac Vepab Vepdf))((p1p2_1808 Vplcm Vepdc Vepde Vepac Vepab Vepdf)))(p1p2_1770 Vplcm Vepdc Vepde Vepac Vepab Vepdf))). Qed. Lemma p1p2_1810: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(el m s)->(el s m). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Velms:(el m s))=>((lsym m s) Velms)). Qed. Lemma p1p2_1811: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(el m s)->(pl i m). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Velms:(el m s))=>((lcon i s m) (conj p1p2_28 (p1p2_1810 Vplcm Vepdc Vepde Vepac Vepab Velms)))). Qed. Lemma p1p2_1812: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(el m s)->(ep d i) \/ (el m r). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Velms:(el m s))=>((unique m r d i) (conj p1p2_6 (conj p1p2_19 (conj (p1p2_1811 Vplcm Vepdc Vepde Vepac Vepab Velms) p1p2_27))))). Qed. Lemma p1p2_1813: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(el m s)->(ep d i)->(ep i d). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))=>((psym d i) Vepdi)). Qed. Lemma p1p2_1822: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(el m s)->(ep d i)->(pl i p). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))=>((pcon i d p) (conj (p1p2_1813 Vplcm Vepdc Vepde Vepac Vepab Velms Vepdi) p1p2_17))). Qed. Lemma p1p2_1827: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(el m s)->(ep d i)->(ep d f) \/ (el m n). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))=>((unique m n d f) (conj p1p2_6 (conj (p1p2_1748 Vplcm Vepdc Vepde Vepac Vepab) (conj p1p2_22 p1p2_15))))). Qed. Lemma p1p2_1844: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(el m s)->(ep d i)->(ep d f)->(ep b g) \/ (el n o). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Vepdf:(ep d f))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_1752 Vplcm Vepdc Vepde Vepac Vepab) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_1845: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(el m s)->(ep d i)->(ep d f)->(ep b g)->(ep g b). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Vepdf:(ep d f))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_1858: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(el m s)->(ep d i)->(ep d f)->(ep b g)->(pl g p). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Vepdf:(ep d f))(Vepbg:(ep b g))=>((pcon g b p) (conj (p1p2_1845 Vplcm Vepdc Vepde Vepac Vepab Velms Vepdi Vepdf Vepbg) p1p2_9))). Qed. Lemma p1p2_1859: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(el m s)->(ep d i)->(ep d f)->(ep b g)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Vepdf:(ep d f))(Vepbg:(ep b g))=>((goal4 p) (conj p1p2_42 (conj (p1p2_1858 Vplcm Vepdc Vepde Vepac Vepab Velms Vepdi Vepdf Vepbg) (conj p1p2_25 (p1p2_1822 Vplcm Vepdc Vepde Vepac Vepab Velms Vepdi)))))). Qed. Lemma p1p2_1860: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(el m s)->(ep d i)->(ep d f)->(el n o)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Vepdf:(ep d f))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_1861: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(el m s)->(ep d i)->(ep d f)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Vepdf:(ep d f))=>((or_ind ((p1p2_1859 Vplcm Vepdc Vepde Vepac Vepab Velms Vepdi Vepdf))((p1p2_1860 Vplcm Vepdc Vepde Vepac Vepab Velms Vepdi Vepdf)))(p1p2_1844 Vplcm Vepdc Vepde Vepac Vepab Velms Vepdi Vepdf))). Qed. Lemma p1p2_1862: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(el m s)->(ep d i)->(el m n)->(el n m). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Velmn:(el m n))=>((lsym m n) Velmn)). Qed. Lemma p1p2_1865: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(el m s)->(ep d i)->(el m n)->(pl g m). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Velmn:(el m n))=>((lcon g n m) (conj p1p2_23 (p1p2_1862 Vplcm Vepdc Vepde Vepac Vepab Velms Vepdi Velmn)))). Qed. Lemma p1p2_1867: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(el m s)->(ep d i)->(el m n)->(ep d g) \/ (el m o). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Velmn:(el m n))=>((unique m o d g) (conj p1p2_6 (conj (p1p2_1713 Vplcm Vepdc) (conj (p1p2_1865 Vplcm Vepdc Vepde Vepac Vepab Velms Vepdi Velmn) p1p2_24))))). Qed. Lemma p1p2_1868: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(el m s)->(ep d i)->(el m n)->(ep d g)->(ep g d). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Velmn:(el m n))(Vepdg:(ep d g))=>((psym d g) Vepdg)). Qed. Lemma p1p2_1879: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(el m s)->(ep d i)->(el m n)->(ep d g)->(pl g p). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Velmn:(el m n))(Vepdg:(ep d g))=>((pcon g d p) (conj (p1p2_1868 Vplcm Vepdc Vepde Vepac Vepab Velms Vepdi Velmn Vepdg) p1p2_17))). Qed. Lemma p1p2_1880: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(el m s)->(ep d i)->(el m n)->(ep d g)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Velmn:(el m n))(Vepdg:(ep d g))=>((goal4 p) (conj p1p2_42 (conj (p1p2_1879 Vplcm Vepdc Vepde Vepac Vepab Velms Vepdi Velmn Vepdg) (conj p1p2_25 (p1p2_1822 Vplcm Vepdc Vepde Vepac Vepab Velms Vepdi)))))). Qed. Lemma p1p2_1884: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(el m s)->(ep d i)->(el m n)->(el m o)->(el n o). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Velmn:(el m n))(Velmo:(el m o))=>((ltra n m o) (conj (p1p2_1862 Vplcm Vepdc Vepde Vepac Vepab Velms Vepdi Velmn) Velmo))). Qed. Lemma p1p2_1885: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(el m s)->(ep d i)->(el m n)->(el m o)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Velmn:(el m n))(Velmo:(el m o))=>(goal1 (p1p2_1884 Vplcm Vepdc Vepde Vepac Vepab Velms Vepdi Velmn Velmo))). Qed. Lemma p1p2_1886: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(el m s)->(ep d i)->(el m n)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Velmn:(el m n))=>((or_ind ((p1p2_1880 Vplcm Vepdc Vepde Vepac Vepab Velms Vepdi Velmn))((p1p2_1885 Vplcm Vepdc Vepde Vepac Vepab Velms Vepdi Velmn)))(p1p2_1867 Vplcm Vepdc Vepde Vepac Vepab Velms Vepdi Velmn))). Qed. Lemma p1p2_1887: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(el m s)->(ep d i)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))=>((or_ind ((p1p2_1861 Vplcm Vepdc Vepde Vepac Vepab Velms Vepdi))((p1p2_1886 Vplcm Vepdc Vepde Vepac Vepab Velms Vepdi)))(p1p2_1827 Vplcm Vepdc Vepde Vepac Vepab Velms Vepdi))). Qed. Lemma p1p2_1889: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(el m s)->(el m r)->(el s r). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Velms:(el m s))(Velmr:(el m r))=>((ltra s m r) (conj (p1p2_1810 Vplcm Vepdc Vepde Vepac Vepab Velms) Velmr))). Qed. Lemma p1p2_1890: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(el m s)->(el m r)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Velms:(el m s))(Velmr:(el m r))=>(goal3 (p1p2_1889 Vplcm Vepdc Vepde Vepac Vepab Velms Velmr))). Qed. Lemma p1p2_1891: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->(el m s)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))(Velms:(el m s))=>((or_ind ((p1p2_1887 Vplcm Vepdc Vepde Vepac Vepab Velms))((p1p2_1890 Vplcm Vepdc Vepde Vepac Vepab Velms)))(p1p2_1812 Vplcm Vepdc Vepde Vepac Vepab Velms))). Qed. Lemma p1p2_1892: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(ep a b)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vepab:(ep a b))=>((or_ind ((p1p2_1809 Vplcm Vepdc Vepde Vepac Vepab))((p1p2_1891 Vplcm Vepdc Vepde Vepac Vepab)))(p1p2_1755 Vplcm Vepdc Vepde Vepac Vepab))). Qed. Lemma p1p2_1893: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(el p l). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))=>((lsym l p) Vellp)). Qed. Lemma p1p2_1894: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(pl h l). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))=>((lcon h p l) (conj p1p2_25 (p1p2_1893 Vplcm Vepdc Vepde Vepac Vellp)))). Qed. Lemma p1p2_1895: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h) \/ (el l q). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))=>((unique l q a h) (conj p1p2_5 (conj p1p2_10 (conj (p1p2_1894 Vplcm Vepdc Vepde Vepac Vellp) p1p2_26))))). Qed. Lemma p1p2_1896: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(ep h a). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))=>((psym a h) Vepah)). Qed. Lemma p1p2_1903: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(pl h s). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))=>((pcon h a s) (conj (p1p2_1896 Vplcm Vepdc Vepde Vepac Vellp Vepah) p1p2_12))). Qed. Lemma p1p2_1904: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(pl h o). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))=>((pcon h a o) (conj (p1p2_1896 Vplcm Vepdc Vepde Vepac Vellp Vepah) (p1p2_1731 Vplcm Vepdc Vepde Vepac)))). Qed. Lemma p1p2_1907: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(ep d f) \/ (el m s). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))=>((unique m s d f) (conj p1p2_6 (conj (p1p2_1736 Vplcm Vepdc Vepde Vepac) (conj p1p2_22 p1p2_20))))). Qed. Lemma p1p2_1917: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(ep d f)->(pl d n). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))=>((pcon d f n) (conj Vepdf p1p2_15))). Qed. Lemma p1p2_1918: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(ep d f)->(pl c n). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))=>((pcon c d n) (conj (p1p2_1712 Vplcm Vepdc) (p1p2_1917 Vplcm Vepdc Vepde Vepac Vellp Vepah Vepdf)))). Qed. Lemma p1p2_1920: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(ep d f)->(pl a n). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))=>((pcon a c n) (conj Vepac (p1p2_1918 Vplcm Vepdc Vepde Vepac Vellp Vepah Vepdf)))). Qed. Lemma p1p2_1927: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(ep d f)->(ep a b) \/ (el l n). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))=>((unique l n a b) (conj p1p2_5 (conj (p1p2_1920 Vplcm Vepdc Vepde Vepac Vellp Vepah Vepdf) (conj p1p2_13 p1p2_7))))). Qed. Lemma p1p2_1928: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(ep d f)->(ep a b)->(ep b a). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Vepab:(ep a b))=>((psym a b) Vepab)). Qed. Lemma p1p2_1940: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(ep d f)->(ep a b)->(pl b s). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Vepab:(ep a b))=>((pcon b a s) (conj (p1p2_1928 Vplcm Vepdc Vepde Vepac Vellp Vepah Vepdf Vepab) p1p2_12))). Qed. Lemma p1p2_1941: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(ep d f)->(ep a b)->(pl b o). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Vepab:(ep a b))=>((pcon b a o) (conj (p1p2_1928 Vplcm Vepdc Vepde Vepac Vellp Vepah Vepdf Vepab) (p1p2_1731 Vplcm Vepdc Vepde Vepac)))). Qed. Lemma p1p2_1944: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(ep d f)->(ep a b)->(ep b g) \/ (el n o). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Vepab:(ep a b))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_1941 Vplcm Vepdc Vepde Vepac Vellp Vepah Vepdf Vepab) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_1945: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(ep d f)->(ep a b)->(ep b g)->(ep g b). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_1961: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(ep d f)->(ep a b)->(ep b g)->(pl g s). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepbg:(ep b g))=>((pcon g b s) (conj (p1p2_1945 Vplcm Vepdc Vepde Vepac Vellp Vepah Vepdf Vepab Vepbg) (p1p2_1940 Vplcm Vepdc Vepde Vepac Vellp Vepah Vepdf Vepab)))). Qed. Lemma p1p2_1962: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(ep d f)->(ep a b)->(ep b g)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepbg:(ep b g))=>((goal4 s) (conj p1p2_45 (conj (p1p2_1961 Vplcm Vepdc Vepde Vepac Vellp Vepah Vepdf Vepab Vepbg) (conj (p1p2_1903 Vplcm Vepdc Vepde Vepac Vellp Vepah) p1p2_28))))). Qed. Lemma p1p2_1963: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(ep d f)->(ep a b)->(el n o)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Vepab:(ep a b))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_1964: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(ep d f)->(ep a b)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Vepab:(ep a b))=>((or_ind ((p1p2_1962 Vplcm Vepdc Vepde Vepac Vellp Vepah Vepdf Vepab))((p1p2_1963 Vplcm Vepdc Vepde Vepac Vellp Vepah Vepdf Vepab)))(p1p2_1944 Vplcm Vepdc Vepde Vepac Vellp Vepah Vepdf Vepab))). Qed. Lemma p1p2_1965: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(ep d f)->(el l n)->(el n l). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Velln:(el l n))=>((lsym l n) Velln)). Qed. Lemma p1p2_1968: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(ep d f)->(el l n)->(pl g l). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Velln:(el l n))=>((lcon g n l) (conj p1p2_23 (p1p2_1965 Vplcm Vepdc Vepde Vepac Vellp Vepah Vepdf Velln)))). Qed. Lemma p1p2_1970: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(ep d f)->(el l n)->(ep a g) \/ (el l o). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Velln:(el l n))=>((unique l o a g) (conj p1p2_5 (conj (p1p2_1731 Vplcm Vepdc Vepde Vepac) (conj (p1p2_1968 Vplcm Vepdc Vepde Vepac Vellp Vepah Vepdf Velln) p1p2_24))))). Qed. Lemma p1p2_1971: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(ep d f)->(el l n)->(ep a g)->(ep g a). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Velln:(el l n))(Vepag:(ep a g))=>((psym a g) Vepag)). Qed. Lemma p1p2_1983: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(ep d f)->(el l n)->(ep a g)->(pl g s). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Velln:(el l n))(Vepag:(ep a g))=>((pcon g a s) (conj (p1p2_1971 Vplcm Vepdc Vepde Vepac Vellp Vepah Vepdf Velln Vepag) p1p2_12))). Qed. Lemma p1p2_1984: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(ep d f)->(el l n)->(ep a g)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Velln:(el l n))(Vepag:(ep a g))=>((goal4 s) (conj p1p2_45 (conj (p1p2_1983 Vplcm Vepdc Vepde Vepac Vellp Vepah Vepdf Velln Vepag) (conj (p1p2_1903 Vplcm Vepdc Vepde Vepac Vellp Vepah) p1p2_28))))). Qed. Lemma p1p2_1988: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(ep d f)->(el l n)->(el l o)->(el n o). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Velln:(el l n))(Vello:(el l o))=>((ltra n l o) (conj (p1p2_1965 Vplcm Vepdc Vepde Vepac Vellp Vepah Vepdf Velln) Vello))). Qed. Lemma p1p2_1989: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(ep d f)->(el l n)->(el l o)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Velln:(el l n))(Vello:(el l o))=>(goal1 (p1p2_1988 Vplcm Vepdc Vepde Vepac Vellp Vepah Vepdf Velln Vello))). Qed. Lemma p1p2_1990: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(ep d f)->(el l n)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Velln:(el l n))=>((or_ind ((p1p2_1984 Vplcm Vepdc Vepde Vepac Vellp Vepah Vepdf Velln))((p1p2_1989 Vplcm Vepdc Vepde Vepac Vellp Vepah Vepdf Velln)))(p1p2_1970 Vplcm Vepdc Vepde Vepac Vellp Vepah Vepdf Velln))). Qed. Lemma p1p2_1991: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(ep d f)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))=>((or_ind ((p1p2_1964 Vplcm Vepdc Vepde Vepac Vellp Vepah Vepdf))((p1p2_1990 Vplcm Vepdc Vepde Vepac Vellp Vepah Vepdf)))(p1p2_1927 Vplcm Vepdc Vepde Vepac Vellp Vepah Vepdf))). Qed. Lemma p1p2_1992: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(el m s)->(el s m). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Velms:(el m s))=>((lsym m s) Velms)). Qed. Lemma p1p2_1993: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(el m s)->(pl i m). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Velms:(el m s))=>((lcon i s m) (conj p1p2_28 (p1p2_1992 Vplcm Vepdc Vepde Vepac Vellp Vepah Velms)))). Qed. Lemma p1p2_1994: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(el m s)->(ep d i) \/ (el m r). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Velms:(el m s))=>((unique m r d i) (conj p1p2_6 (conj p1p2_19 (conj (p1p2_1993 Vplcm Vepdc Vepde Vepac Vellp Vepah Velms) p1p2_27))))). Qed. Lemma p1p2_1995: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(el m s)->(ep d i)->(ep i d). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Velms:(el m s))(Vepdi:(ep d i))=>((psym d i) Vepdi)). Qed. Lemma p1p2_2005: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(el m s)->(ep d i)->(pl i o). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Velms:(el m s))(Vepdi:(ep d i))=>((pcon i d o) (conj (p1p2_1995 Vplcm Vepdc Vepde Vepac Vellp Vepah Velms Vepdi) (p1p2_1713 Vplcm Vepdc)))). Qed. Lemma p1p2_2006: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(el m s)->(ep d i)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Velms:(el m s))(Vepdi:(ep d i))=>((goal4 o) (conj p1p2_41 (conj p1p2_24 (conj (p1p2_1904 Vplcm Vepdc Vepde Vepac Vellp Vepah) (p1p2_2005 Vplcm Vepdc Vepde Vepac Vellp Vepah Velms Vepdi)))))). Qed. Lemma p1p2_2008: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(el m s)->(el m r)->(el s r). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Velms:(el m s))(Velmr:(el m r))=>((ltra s m r) (conj (p1p2_1992 Vplcm Vepdc Vepde Vepac Vellp Vepah Velms) Velmr))). Qed. Lemma p1p2_2009: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(el m s)->(el m r)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Velms:(el m s))(Velmr:(el m r))=>(goal3 (p1p2_2008 Vplcm Vepdc Vepde Vepac Vellp Vepah Velms Velmr))). Qed. Lemma p1p2_2010: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->(el m s)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))(Velms:(el m s))=>((or_ind ((p1p2_2006 Vplcm Vepdc Vepde Vepac Vellp Vepah Velms))((p1p2_2009 Vplcm Vepdc Vepde Vepac Vellp Vepah Velms)))(p1p2_1994 Vplcm Vepdc Vepde Vepac Vellp Vepah Velms))). Qed. Lemma p1p2_2011: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(ep a h)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vepah:(ep a h))=>((or_ind ((p1p2_1991 Vplcm Vepdc Vepde Vepac Vellp Vepah))((p1p2_2010 Vplcm Vepdc Vepde Vepac Vellp Vepah)))(p1p2_1907 Vplcm Vepdc Vepde Vepac Vellp Vepah))). Qed. Lemma p1p2_2013: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(el l q)->(el p q). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vellq:(el l q))=>((ltra p l q) (conj (p1p2_1893 Vplcm Vepdc Vepde Vepac Vellp) Vellq))). Qed. Lemma p1p2_2014: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->(el l q)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))(Vellq:(el l q))=>(goal2 (p1p2_2013 Vplcm Vepdc Vepde Vepac Vellp Vellq))). Qed. Lemma p1p2_2015: (pl c m)->(ep d c)->(ep d e)->(ep a c)->(el l p)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))(Vellp:(el l p))=>((or_ind ((p1p2_2011 Vplcm Vepdc Vepde Vepac Vellp))((p1p2_2014 Vplcm Vepdc Vepde Vepac Vellp)))(p1p2_1895 Vplcm Vepdc Vepde Vepac Vellp))). Qed. Lemma p1p2_2016: (pl c m)->(ep d c)->(ep d e)->(ep a c)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vepac:(ep a c))=>((or_ind ((p1p2_1892 Vplcm Vepdc Vepde Vepac))((p1p2_2015 Vplcm Vepdc Vepde Vepac)))(p1p2_1738 Vplcm Vepdc Vepde Vepac))). Qed. Lemma p1p2_2017: (pl c m)->(ep d c)->(ep d e)->(el l q)->(el q l). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))=>((lsym l q) Vellq)). Qed. Lemma p1p2_2019: (pl c m)->(ep d c)->(ep d e)->(el l q)->(pl h l). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))=>((lcon h q l) (conj p1p2_26 (p1p2_2017 Vplcm Vepdc Vepde Vellq)))). Qed. Lemma p1p2_2020: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d) \/ (el p l). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))=>((unique p l b d) (conj p1p2_9 (conj p1p2_13 (conj p1p2_17 (p1p2_1714 Vplcm Vepdc)))))). Qed. Lemma p1p2_2021: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(ep d b). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))=>((psym b d) Vepbd)). Qed. Lemma p1p2_2027: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(pl b r). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))=>((pcon b d r) (conj Vepbd p1p2_19))). Qed. Lemma p1p2_2028: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(pl b o). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))=>((pcon b d o) (conj Vepbd (p1p2_1713 Vplcm Vepdc)))). Qed. Lemma p1p2_2029: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(pl d n). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))=>((pcon d b n) (conj (p1p2_2021 Vplcm Vepdc Vepde Vellq Vepbd) p1p2_7))). Qed. Lemma p1p2_2032: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(ep d f) \/ (el m n). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))=>((unique m n d f) (conj p1p2_6 (conj (p1p2_2029 Vplcm Vepdc Vepde Vellq Vepbd) (conj p1p2_22 p1p2_15))))). Qed. Lemma p1p2_2040: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(ep d f)->(pl d s). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Vepdf:(ep d f))=>((pcon d f s) (conj Vepdf p1p2_20))). Qed. Lemma p1p2_2043: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(ep d f)->(pl b s). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Vepdf:(ep d f))=>((pcon b d s) (conj Vepbd (p1p2_2040 Vplcm Vepdc Vepde Vellq Vepbd Vepdf)))). Qed. Lemma p1p2_2049: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(ep d f)->(ep a b) \/ (el l s). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Vepdf:(ep d f))=>((unique l s a b) (conj p1p2_5 (conj p1p2_12 (conj p1p2_13 (p1p2_2043 Vplcm Vepdc Vepde Vellq Vepbd Vepdf)))))). Qed. Lemma p1p2_2060: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(ep d f)->(ep a b)->(pl a p). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))=>((pcon a b p) (conj Vepab p1p2_9))). Qed. Lemma p1p2_2062: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(ep d f)->(ep a b)->(pl a r). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))=>((pcon a b r) (conj Vepab (p1p2_2027 Vplcm Vepdc Vepde Vellq Vepbd)))). Qed. Lemma p1p2_2064: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(ep d f)->(ep a b)->(ep a h) \/ (el l p). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))=>((unique l p a h) (conj p1p2_5 (conj (p1p2_2060 Vplcm Vepdc Vepde Vellq Vepbd Vepdf Vepab) (conj (p1p2_2019 Vplcm Vepdc Vepde Vellq) p1p2_25))))). Qed. Lemma p1p2_2065: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(ep d f)->(ep a b)->(ep a h)->(ep h a). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepah:(ep a h))=>((psym a h) Vepah)). Qed. Lemma p1p2_2079: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(ep d f)->(ep a b)->(ep a h)->(pl h r). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepah:(ep a h))=>((pcon h a r) (conj (p1p2_2065 Vplcm Vepdc Vepde Vellq Vepbd Vepdf Vepab Vepah) (p1p2_2062 Vplcm Vepdc Vepde Vellq Vepbd Vepdf Vepab)))). Qed. Lemma p1p2_2081: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(ep d f)->(ep a b)->(ep a h)->(ep b g) \/ (el n o). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepah:(ep a h))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_2028 Vplcm Vepdc Vepde Vellq Vepbd) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_2082: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(ep d f)->(ep a b)->(ep a h)->(ep b g)->(ep g b). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepah:(ep a h))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_2099: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(ep d f)->(ep a b)->(ep a h)->(ep b g)->(pl g r). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepah:(ep a h))(Vepbg:(ep b g))=>((pcon g b r) (conj (p1p2_2082 Vplcm Vepdc Vepde Vellq Vepbd Vepdf Vepab Vepah Vepbg) (p1p2_2027 Vplcm Vepdc Vepde Vellq Vepbd)))). Qed. Lemma p1p2_2100: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(ep d f)->(ep a b)->(ep a h)->(ep b g)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepah:(ep a h))(Vepbg:(ep b g))=>((goal4 r) (conj p1p2_44 (conj (p1p2_2099 Vplcm Vepdc Vepde Vellq Vepbd Vepdf Vepab Vepah Vepbg) (conj (p1p2_2079 Vplcm Vepdc Vepde Vellq Vepbd Vepdf Vepab Vepah) p1p2_27))))). Qed. Lemma p1p2_2101: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(ep d f)->(ep a b)->(ep a h)->(el n o)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepah:(ep a h))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_2102: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(ep d f)->(ep a b)->(ep a h)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepah:(ep a h))=>((or_ind ((p1p2_2100 Vplcm Vepdc Vepde Vellq Vepbd Vepdf Vepab Vepah))((p1p2_2101 Vplcm Vepdc Vepde Vellq Vepbd Vepdf Vepab Vepah)))(p1p2_2081 Vplcm Vepdc Vepde Vellq Vepbd Vepdf Vepab Vepah))). Qed. Lemma p1p2_2104: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(ep d f)->(ep a b)->(el l p)->(el q p). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellp:(el l p))=>((ltra q l p) (conj (p1p2_2017 Vplcm Vepdc Vepde Vellq) Vellp))). Qed. Lemma p1p2_2105: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(ep d f)->(ep a b)->(el l p)->(el p q). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellp:(el l p))=>((lsym q p) (p1p2_2104 Vplcm Vepdc Vepde Vellq Vepbd Vepdf Vepab Vellp))). Qed. Lemma p1p2_2106: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(ep d f)->(ep a b)->(el l p)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellp:(el l p))=>(goal2 (p1p2_2105 Vplcm Vepdc Vepde Vellq Vepbd Vepdf Vepab Vellp))). Qed. Lemma p1p2_2107: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(ep d f)->(ep a b)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))=>((or_ind ((p1p2_2102 Vplcm Vepdc Vepde Vellq Vepbd Vepdf Vepab))((p1p2_2106 Vplcm Vepdc Vepde Vellq Vepbd Vepdf Vepab)))(p1p2_2064 Vplcm Vepdc Vepde Vellq Vepbd Vepdf Vepab))). Qed. Lemma p1p2_2108: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(ep d f)->(el l s)->(el s l). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))=>((lsym l s) Vells)). Qed. Lemma p1p2_2112: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(ep d f)->(el l s)->(pl i l). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))=>((lcon i s l) (conj p1p2_28 (p1p2_2108 Vplcm Vepdc Vepde Vellq Vepbd Vepdf Vells)))). Qed. Lemma p1p2_2114: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(ep d f)->(el l s)->(ep b g) \/ (el n o). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_2028 Vplcm Vepdc Vepde Vellq Vepbd) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_2115: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(ep d f)->(el l s)->(ep b g)->(ep g b). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_2125: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(ep d f)->(el l s)->(ep b g)->(pl g l). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepbg:(ep b g))=>((pcon g b l) (conj (p1p2_2115 Vplcm Vepdc Vepde Vellq Vepbd Vepdf Vells Vepbg) p1p2_13))). Qed. Lemma p1p2_2126: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(ep d f)->(el l s)->(ep b g)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepbg:(ep b g))=>((goal4 l) (conj p1p2_38 (conj (p1p2_2125 Vplcm Vepdc Vepde Vellq Vepbd Vepdf Vells Vepbg) (conj (p1p2_2019 Vplcm Vepdc Vepde Vellq) (p1p2_2112 Vplcm Vepdc Vepde Vellq Vepbd Vepdf Vells)))))). Qed. Lemma p1p2_2127: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(ep d f)->(el l s)->(el n o)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_2128: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(ep d f)->(el l s)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))=>((or_ind ((p1p2_2126 Vplcm Vepdc Vepde Vellq Vepbd Vepdf Vells))((p1p2_2127 Vplcm Vepdc Vepde Vellq Vepbd Vepdf Vells)))(p1p2_2114 Vplcm Vepdc Vepde Vellq Vepbd Vepdf Vells))). Qed. Lemma p1p2_2129: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(ep d f)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Vepdf:(ep d f))=>((or_ind ((p1p2_2107 Vplcm Vepdc Vepde Vellq Vepbd Vepdf))((p1p2_2128 Vplcm Vepdc Vepde Vellq Vepbd Vepdf)))(p1p2_2049 Vplcm Vepdc Vepde Vellq Vepbd Vepdf))). Qed. Lemma p1p2_2130: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(el m n)->(el n m). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Velmn:(el m n))=>((lsym m n) Velmn)). Qed. Lemma p1p2_2131: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(el m n)->(pl g m). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Velmn:(el m n))=>((lcon g n m) (conj p1p2_23 (p1p2_2130 Vplcm Vepdc Vepde Vellq Vepbd Velmn)))). Qed. Lemma p1p2_2132: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(el m n)->(ep d g) \/ (el m o). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Velmn:(el m n))=>((unique m o d g) (conj p1p2_6 (conj (p1p2_1713 Vplcm Vepdc) (conj (p1p2_2131 Vplcm Vepdc Vepde Vellq Vepbd Velmn) p1p2_24))))). Qed. Lemma p1p2_2133: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(el m n)->(ep d g)->(ep g d). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Velmn:(el m n))(Vepdg:(ep d g))=>((psym d g) Vepdg)). Qed. Lemma p1p2_2141: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(el m n)->(ep d g)->(pl g r). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Velmn:(el m n))(Vepdg:(ep d g))=>((pcon g d r) (conj (p1p2_2133 Vplcm Vepdc Vepde Vellq Vepbd Velmn Vepdg) p1p2_19))). Qed. Lemma p1p2_2144: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(el m n)->(ep d g)->(ep b h) \/ (el p l). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Velmn:(el m n))(Vepdg:(ep d g))=>((unique p l b h) (conj p1p2_9 (conj p1p2_13 (conj p1p2_25 (p1p2_2019 Vplcm Vepdc Vepde Vellq)))))). Qed. Lemma p1p2_2145: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(el m n)->(ep d g)->(ep b h)->(ep h b). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Velmn:(el m n))(Vepdg:(ep d g))(Vepbh:(ep b h))=>((psym b h) Vepbh)). Qed. Lemma p1p2_2156: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(el m n)->(ep d g)->(ep b h)->(pl h r). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Velmn:(el m n))(Vepdg:(ep d g))(Vepbh:(ep b h))=>((pcon h b r) (conj (p1p2_2145 Vplcm Vepdc Vepde Vellq Vepbd Velmn Vepdg Vepbh) (p1p2_2027 Vplcm Vepdc Vepde Vellq Vepbd)))). Qed. Lemma p1p2_2157: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(el m n)->(ep d g)->(ep b h)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Velmn:(el m n))(Vepdg:(ep d g))(Vepbh:(ep b h))=>((goal4 r) (conj p1p2_44 (conj (p1p2_2141 Vplcm Vepdc Vepde Vellq Vepbd Velmn Vepdg) (conj (p1p2_2156 Vplcm Vepdc Vepde Vellq Vepbd Velmn Vepdg Vepbh) p1p2_27))))). Qed. Lemma p1p2_2158: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(el m n)->(ep d g)->(el p l)->(el l p). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Velmn:(el m n))(Vepdg:(ep d g))(Velpl:(el p l))=>((lsym p l) Velpl)). Qed. Lemma p1p2_2159: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(el m n)->(ep d g)->(el p l)->(el q p). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Velmn:(el m n))(Vepdg:(ep d g))(Velpl:(el p l))=>((ltra q l p) (conj (p1p2_2017 Vplcm Vepdc Vepde Vellq) (p1p2_2158 Vplcm Vepdc Vepde Vellq Vepbd Velmn Vepdg Velpl)))). Qed. Lemma p1p2_2160: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(el m n)->(ep d g)->(el p l)->(el p q). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Velmn:(el m n))(Vepdg:(ep d g))(Velpl:(el p l))=>((lsym q p) (p1p2_2159 Vplcm Vepdc Vepde Vellq Vepbd Velmn Vepdg Velpl))). Qed. Lemma p1p2_2161: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(el m n)->(ep d g)->(el p l)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Velmn:(el m n))(Vepdg:(ep d g))(Velpl:(el p l))=>(goal2 (p1p2_2160 Vplcm Vepdc Vepde Vellq Vepbd Velmn Vepdg Velpl))). Qed. Lemma p1p2_2162: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(el m n)->(ep d g)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Velmn:(el m n))(Vepdg:(ep d g))=>((or_ind ((p1p2_2157 Vplcm Vepdc Vepde Vellq Vepbd Velmn Vepdg))((p1p2_2161 Vplcm Vepdc Vepde Vellq Vepbd Velmn Vepdg)))(p1p2_2144 Vplcm Vepdc Vepde Vellq Vepbd Velmn Vepdg))). Qed. Lemma p1p2_2164: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(el m n)->(el m o)->(el n o). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Velmn:(el m n))(Velmo:(el m o))=>((ltra n m o) (conj (p1p2_2130 Vplcm Vepdc Vepde Vellq Vepbd Velmn) Velmo))). Qed. Lemma p1p2_2165: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(el m n)->(el m o)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Velmn:(el m n))(Velmo:(el m o))=>(goal1 (p1p2_2164 Vplcm Vepdc Vepde Vellq Vepbd Velmn Velmo))). Qed. Lemma p1p2_2166: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->(el m n)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))(Velmn:(el m n))=>((or_ind ((p1p2_2162 Vplcm Vepdc Vepde Vellq Vepbd Velmn))((p1p2_2165 Vplcm Vepdc Vepde Vellq Vepbd Velmn)))(p1p2_2132 Vplcm Vepdc Vepde Vellq Vepbd Velmn))). Qed. Lemma p1p2_2167: (pl c m)->(ep d c)->(ep d e)->(el l q)->(ep b d)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Vepbd:(ep b d))=>((or_ind ((p1p2_2129 Vplcm Vepdc Vepde Vellq Vepbd))((p1p2_2166 Vplcm Vepdc Vepde Vellq Vepbd)))(p1p2_2032 Vplcm Vepdc Vepde Vellq Vepbd))). Qed. Lemma p1p2_2168: (pl c m)->(ep d c)->(ep d e)->(el l q)->(el p l)->(el l p). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Velpl:(el p l))=>((lsym p l) Velpl)). Qed. Lemma p1p2_2169: (pl c m)->(ep d c)->(ep d e)->(el l q)->(el p l)->(el q p). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Velpl:(el p l))=>((ltra q l p) (conj (p1p2_2017 Vplcm Vepdc Vepde Vellq) (p1p2_2168 Vplcm Vepdc Vepde Vellq Velpl)))). Qed. Lemma p1p2_2170: (pl c m)->(ep d c)->(ep d e)->(el l q)->(el p l)->(el p q). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Velpl:(el p l))=>((lsym q p) (p1p2_2169 Vplcm Vepdc Vepde Vellq Velpl))). Qed. Lemma p1p2_2171: (pl c m)->(ep d c)->(ep d e)->(el l q)->(el p l)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))(Velpl:(el p l))=>(goal2 (p1p2_2170 Vplcm Vepdc Vepde Vellq Velpl))). Qed. Lemma p1p2_2172: (pl c m)->(ep d c)->(ep d e)->(el l q)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))(Vellq:(el l q))=>((or_ind ((p1p2_2167 Vplcm Vepdc Vepde Vellq))((p1p2_2171 Vplcm Vepdc Vepde Vellq)))(p1p2_2020 Vplcm Vepdc Vepde Vellq))). Qed. Lemma p1p2_2173: (pl c m)->(ep d c)->(ep d e)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Vepde:(ep d e))=>((or_ind ((p1p2_2016 Vplcm Vepdc Vepde))((p1p2_2172 Vplcm Vepdc Vepde)))(p1p2_1725 Vplcm Vepdc Vepde))). Qed. Lemma p1p2_2174: (pl c m)->(ep d c)->(el m o)->(el o m). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))=>((lsym m o) Velmo)). Qed. Lemma p1p2_2176: (pl c m)->(ep d c)->(el m o)->(pl g m). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))=>((lcon g o m) (conj p1p2_24 (p1p2_2174 Vplcm Vepdc Velmo)))). Qed. Lemma p1p2_2177: (pl c m)->(ep d c)->(el m o)->(ep b d) \/ (el p l). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))=>((unique p l b d) (conj p1p2_9 (conj p1p2_13 (conj p1p2_17 (p1p2_1714 Vplcm Vepdc)))))). Qed. Lemma p1p2_2178: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d b). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))=>((psym b d) Vepbd)). Qed. Lemma p1p2_2182: (pl c m)->(ep d c)->(el m o)->(ep b d)->(pl b r). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))=>((pcon b d r) (conj Vepbd p1p2_19))). Qed. Lemma p1p2_2184: (pl c m)->(ep d c)->(el m o)->(ep b d)->(pl d n). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))=>((pcon d b n) (conj (p1p2_2178 Vplcm Vepdc Velmo Vepbd) p1p2_7))). Qed. Lemma p1p2_2186: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f) \/ (el m n). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))=>((unique m n d f) (conj p1p2_6 (conj (p1p2_2184 Vplcm Vepdc Velmo Vepbd) (conj p1p2_22 p1p2_15))))). Qed. Lemma p1p2_2192: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(pl d s). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))=>((pcon d f s) (conj Vepdf p1p2_20))). Qed. Lemma p1p2_2194: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(pl b s). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))=>((pcon b d s) (conj Vepbd (p1p2_2192 Vplcm Vepdc Velmo Vepbd Vepdf)))). Qed. Lemma p1p2_2198: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(ep a b) \/ (el l s). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))=>((unique l s a b) (conj p1p2_5 (conj p1p2_12 (conj p1p2_13 (p1p2_2194 Vplcm Vepdc Velmo Vepbd Vepdf)))))). Qed. Lemma p1p2_2199: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(ep a b)->(ep b a). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))=>((psym a b) Vepab)). Qed. Lemma p1p2_2211: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(ep a b)->(pl b q). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))=>((pcon b a q) (conj (p1p2_2199 Vplcm Vepdc Velmo Vepbd Vepdf Vepab) p1p2_10))). Qed. Lemma p1p2_2212: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(ep a b)->(pl d q). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))=>((pcon d b q) (conj (p1p2_2178 Vplcm Vepdc Velmo Vepbd) (p1p2_2211 Vplcm Vepdc Velmo Vepbd Vepdf Vepab)))). Qed. Lemma p1p2_2215: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(ep a b)->(ep d g) \/ (el m n). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))=>((unique m n d g) (conj p1p2_6 (conj (p1p2_2184 Vplcm Vepdc Velmo Vepbd) (conj (p1p2_2176 Vplcm Vepdc Velmo) p1p2_23))))). Qed. Lemma p1p2_2216: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(ep a b)->(ep d g)->(ep g d). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepdg:(ep d g))=>((psym d g) Vepdg)). Qed. Lemma p1p2_2226: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(ep a b)->(ep d g)->(pl g r). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepdg:(ep d g))=>((pcon g d r) (conj (p1p2_2216 Vplcm Vepdc Velmo Vepbd Vepdf Vepab Vepdg) p1p2_19))). Qed. Lemma p1p2_2230: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(ep a b)->(ep d g)->(ep d e) \/ (el m q). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepdg:(ep d g))=>((unique m q d e) (conj p1p2_6 (conj (p1p2_2212 Vplcm Vepdc Velmo Vepbd Vepdf Vepab) (conj p1p2_14 p1p2_18))))). Qed. Lemma p1p2_2247: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(ep a b)->(ep d g)->(ep d e)->(ep b h) \/ (el p q). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepdg:(ep d g))(Vepde:(ep d e))=>((unique p q b h) (conj p1p2_9 (conj (p1p2_2211 Vplcm Vepdc Velmo Vepbd Vepdf Vepab) (conj p1p2_25 p1p2_26))))). Qed. Lemma p1p2_2248: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(ep a b)->(ep d g)->(ep d e)->(ep b h)->(ep h b). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepdg:(ep d g))(Vepde:(ep d e))(Vepbh:(ep b h))=>((psym b h) Vepbh)). Qed. Lemma p1p2_2264: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(ep a b)->(ep d g)->(ep d e)->(ep b h)->(pl h r). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepdg:(ep d g))(Vepde:(ep d e))(Vepbh:(ep b h))=>((pcon h b r) (conj (p1p2_2248 Vplcm Vepdc Velmo Vepbd Vepdf Vepab Vepdg Vepde Vepbh) (p1p2_2182 Vplcm Vepdc Velmo Vepbd)))). Qed. Lemma p1p2_2265: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(ep a b)->(ep d g)->(ep d e)->(ep b h)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepdg:(ep d g))(Vepde:(ep d e))(Vepbh:(ep b h))=>((goal4 r) (conj p1p2_44 (conj (p1p2_2226 Vplcm Vepdc Velmo Vepbd Vepdf Vepab Vepdg) (conj (p1p2_2264 Vplcm Vepdc Velmo Vepbd Vepdf Vepab Vepdg Vepde Vepbh) p1p2_27))))). Qed. Lemma p1p2_2266: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(ep a b)->(ep d g)->(ep d e)->(el p q)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepdg:(ep d g))(Vepde:(ep d e))(Velpq:(el p q))=>(goal2 Velpq)). Qed. Lemma p1p2_2267: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(ep a b)->(ep d g)->(ep d e)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepdg:(ep d g))(Vepde:(ep d e))=>((or_ind ((p1p2_2265 Vplcm Vepdc Velmo Vepbd Vepdf Vepab Vepdg Vepde))((p1p2_2266 Vplcm Vepdc Velmo Vepbd Vepdf Vepab Vepdg Vepde)))(p1p2_2247 Vplcm Vepdc Velmo Vepbd Vepdf Vepab Vepdg Vepde))). Qed. Lemma p1p2_2268: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(ep a b)->(ep d g)->(el m q)->(el q m). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepdg:(ep d g))(Velmq:(el m q))=>((lsym m q) Velmq)). Qed. Lemma p1p2_2271: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(ep a b)->(ep d g)->(el m q)->(pl h m). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepdg:(ep d g))(Velmq:(el m q))=>((lcon h q m) (conj p1p2_26 (p1p2_2268 Vplcm Vepdc Velmo Vepbd Vepdf Vepab Vepdg Velmq)))). Qed. Lemma p1p2_2273: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(ep a b)->(ep d g)->(el m q)->(ep d h) \/ (el m p). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepdg:(ep d g))(Velmq:(el m q))=>((unique m p d h) (conj p1p2_6 (conj p1p2_17 (conj (p1p2_2271 Vplcm Vepdc Velmo Vepbd Vepdf Vepab Vepdg Velmq) p1p2_25))))). Qed. Lemma p1p2_2274: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(ep a b)->(ep d g)->(el m q)->(ep d h)->(ep h d). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepdg:(ep d g))(Velmq:(el m q))(Vepdh:(ep d h))=>((psym d h) Vepdh)). Qed. Lemma p1p2_2285: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(ep a b)->(ep d g)->(el m q)->(ep d h)->(pl h r). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepdg:(ep d g))(Velmq:(el m q))(Vepdh:(ep d h))=>((pcon h d r) (conj (p1p2_2274 Vplcm Vepdc Velmo Vepbd Vepdf Vepab Vepdg Velmq Vepdh) p1p2_19))). Qed. Lemma p1p2_2286: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(ep a b)->(ep d g)->(el m q)->(ep d h)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepdg:(ep d g))(Velmq:(el m q))(Vepdh:(ep d h))=>((goal4 r) (conj p1p2_44 (conj (p1p2_2226 Vplcm Vepdc Velmo Vepbd Vepdf Vepab Vepdg) (conj (p1p2_2285 Vplcm Vepdc Velmo Vepbd Vepdf Vepab Vepdg Velmq Vepdh) p1p2_27))))). Qed. Lemma p1p2_2290: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(ep a b)->(ep d g)->(el m q)->(el m p)->(el q p). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepdg:(ep d g))(Velmq:(el m q))(Velmp:(el m p))=>((ltra q m p) (conj (p1p2_2268 Vplcm Vepdc Velmo Vepbd Vepdf Vepab Vepdg Velmq) Velmp))). Qed. Lemma p1p2_2291: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(ep a b)->(ep d g)->(el m q)->(el m p)->(el p q). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepdg:(ep d g))(Velmq:(el m q))(Velmp:(el m p))=>((lsym q p) (p1p2_2290 Vplcm Vepdc Velmo Vepbd Vepdf Vepab Vepdg Velmq Velmp))). Qed. Lemma p1p2_2292: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(ep a b)->(ep d g)->(el m q)->(el m p)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepdg:(ep d g))(Velmq:(el m q))(Velmp:(el m p))=>(goal2 (p1p2_2291 Vplcm Vepdc Velmo Vepbd Vepdf Vepab Vepdg Velmq Velmp))). Qed. Lemma p1p2_2293: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(ep a b)->(ep d g)->(el m q)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepdg:(ep d g))(Velmq:(el m q))=>((or_ind ((p1p2_2286 Vplcm Vepdc Velmo Vepbd Vepdf Vepab Vepdg Velmq))((p1p2_2292 Vplcm Vepdc Velmo Vepbd Vepdf Vepab Vepdg Velmq)))(p1p2_2273 Vplcm Vepdc Velmo Vepbd Vepdf Vepab Vepdg Velmq))). Qed. Lemma p1p2_2294: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(ep a b)->(ep d g)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepdg:(ep d g))=>((or_ind ((p1p2_2267 Vplcm Vepdc Velmo Vepbd Vepdf Vepab Vepdg))((p1p2_2293 Vplcm Vepdc Velmo Vepbd Vepdf Vepab Vepdg)))(p1p2_2230 Vplcm Vepdc Velmo Vepbd Vepdf Vepab Vepdg))). Qed. Lemma p1p2_2296: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(ep a b)->(el m n)->(el o n). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Velmn:(el m n))=>((ltra o m n) (conj (p1p2_2174 Vplcm Vepdc Velmo) Velmn))). Qed. Lemma p1p2_2297: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(ep a b)->(el m n)->(el n o). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Velmn:(el m n))=>((lsym o n) (p1p2_2296 Vplcm Vepdc Velmo Vepbd Vepdf Vepab Velmn))). Qed. Lemma p1p2_2298: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(ep a b)->(el m n)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Velmn:(el m n))=>(goal1 (p1p2_2297 Vplcm Vepdc Velmo Vepbd Vepdf Vepab Velmn))). Qed. Lemma p1p2_2299: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(ep a b)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))=>((or_ind ((p1p2_2294 Vplcm Vepdc Velmo Vepbd Vepdf Vepab))((p1p2_2298 Vplcm Vepdc Velmo Vepbd Vepdf Vepab)))(p1p2_2215 Vplcm Vepdc Velmo Vepbd Vepdf Vepab))). Qed. Lemma p1p2_2300: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(el l s)->(el s l). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))=>((lsym l s) Vells)). Qed. Lemma p1p2_2301: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(el l s)->(pl i l). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))=>((lcon i s l) (conj p1p2_28 (p1p2_2300 Vplcm Vepdc Velmo Vepbd Vepdf Vells)))). Qed. Lemma p1p2_2302: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(el l s)->(ep d g) \/ (el m n). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))=>((unique m n d g) (conj p1p2_6 (conj (p1p2_2184 Vplcm Vepdc Velmo Vepbd) (conj (p1p2_2176 Vplcm Vepdc Velmo) p1p2_23))))). Qed. Lemma p1p2_2303: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(el l s)->(ep d g)->(ep g d). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepdg:(ep d g))=>((psym d g) Vepdg)). Qed. Lemma p1p2_2310: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(el l s)->(ep d g)->(pl g p). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepdg:(ep d g))=>((pcon g d p) (conj (p1p2_2303 Vplcm Vepdc Velmo Vepbd Vepdf Vells Vepdg) p1p2_17))). Qed. Lemma p1p2_2314: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(el l s)->(ep d g)->(ep c i) \/ (el r l). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepdg:(ep d g))=>((unique r l c i) (conj p1p2_11 (conj p1p2_21 (conj p1p2_27 (p1p2_2301 Vplcm Vepdc Velmo Vepbd Vepdf Vells)))))). Qed. Lemma p1p2_2315: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(el l s)->(ep d g)->(ep c i)->(ep i c). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepdg:(ep d g))(Vepci:(ep c i))=>((psym c i) Vepci)). Qed. Lemma p1p2_2326: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(el l s)->(ep d g)->(ep c i)->(pl i p). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepdg:(ep d g))(Vepci:(ep c i))=>((pcon i c p) (conj (p1p2_2315 Vplcm Vepdc Velmo Vepbd Vepdf Vells Vepdg Vepci) (p1p2_1715 Vplcm Vepdc)))). Qed. Lemma p1p2_2327: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(el l s)->(ep d g)->(ep c i)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepdg:(ep d g))(Vepci:(ep c i))=>((goal4 p) (conj p1p2_42 (conj (p1p2_2310 Vplcm Vepdc Velmo Vepbd Vepdf Vells Vepdg) (conj p1p2_25 (p1p2_2326 Vplcm Vepdc Velmo Vepbd Vepdf Vells Vepdg Vepci)))))). Qed. Lemma p1p2_2328: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(el l s)->(ep d g)->(el r l)->(el l r). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepdg:(ep d g))(Velrl:(el r l))=>((lsym r l) Velrl)). Qed. Lemma p1p2_2329: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(el l s)->(ep d g)->(el r l)->(el s r). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepdg:(ep d g))(Velrl:(el r l))=>((ltra s l r) (conj (p1p2_2300 Vplcm Vepdc Velmo Vepbd Vepdf Vells) (p1p2_2328 Vplcm Vepdc Velmo Vepbd Vepdf Vells Vepdg Velrl)))). Qed. Lemma p1p2_2330: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(el l s)->(ep d g)->(el r l)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepdg:(ep d g))(Velrl:(el r l))=>(goal3 (p1p2_2329 Vplcm Vepdc Velmo Vepbd Vepdf Vells Vepdg Velrl))). Qed. Lemma p1p2_2331: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(el l s)->(ep d g)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepdg:(ep d g))=>((or_ind ((p1p2_2327 Vplcm Vepdc Velmo Vepbd Vepdf Vells Vepdg))((p1p2_2330 Vplcm Vepdc Velmo Vepbd Vepdf Vells Vepdg)))(p1p2_2314 Vplcm Vepdc Velmo Vepbd Vepdf Vells Vepdg))). Qed. Lemma p1p2_2333: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(el l s)->(el m n)->(el o n). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Velmn:(el m n))=>((ltra o m n) (conj (p1p2_2174 Vplcm Vepdc Velmo) Velmn))). Qed. Lemma p1p2_2334: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(el l s)->(el m n)->(el n o). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Velmn:(el m n))=>((lsym o n) (p1p2_2333 Vplcm Vepdc Velmo Vepbd Vepdf Vells Velmn))). Qed. Lemma p1p2_2335: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(el l s)->(el m n)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Velmn:(el m n))=>(goal1 (p1p2_2334 Vplcm Vepdc Velmo Vepbd Vepdf Vells Velmn))). Qed. Lemma p1p2_2336: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->(el l s)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))=>((or_ind ((p1p2_2331 Vplcm Vepdc Velmo Vepbd Vepdf Vells))((p1p2_2335 Vplcm Vepdc Velmo Vepbd Vepdf Vells)))(p1p2_2302 Vplcm Vepdc Velmo Vepbd Vepdf Vells))). Qed. Lemma p1p2_2337: (pl c m)->(ep d c)->(el m o)->(ep b d)->(ep d f)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Vepdf:(ep d f))=>((or_ind ((p1p2_2299 Vplcm Vepdc Velmo Vepbd Vepdf))((p1p2_2336 Vplcm Vepdc Velmo Vepbd Vepdf)))(p1p2_2198 Vplcm Vepdc Velmo Vepbd Vepdf))). Qed. Lemma p1p2_2339: (pl c m)->(ep d c)->(el m o)->(ep b d)->(el m n)->(el o n). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Velmn:(el m n))=>((ltra o m n) (conj (p1p2_2174 Vplcm Vepdc Velmo) Velmn))). Qed. Lemma p1p2_2340: (pl c m)->(ep d c)->(el m o)->(ep b d)->(el m n)->(el n o). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Velmn:(el m n))=>((lsym o n) (p1p2_2339 Vplcm Vepdc Velmo Vepbd Velmn))). Qed. Lemma p1p2_2341: (pl c m)->(ep d c)->(el m o)->(ep b d)->(el m n)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))(Velmn:(el m n))=>(goal1 (p1p2_2340 Vplcm Vepdc Velmo Vepbd Velmn))). Qed. Lemma p1p2_2342: (pl c m)->(ep d c)->(el m o)->(ep b d)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Vepbd:(ep b d))=>((or_ind ((p1p2_2337 Vplcm Vepdc Velmo Vepbd))((p1p2_2341 Vplcm Vepdc Velmo Vepbd)))(p1p2_2186 Vplcm Vepdc Velmo Vepbd))). Qed. Lemma p1p2_2345: (pl c m)->(ep d c)->(el m o)->(el p l)->(pl h l). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Velpl:(el p l))=>((lcon h p l) (conj p1p2_25 Velpl))). Qed. Lemma p1p2_2346: (pl c m)->(ep d c)->(el m o)->(el p l)->(ep a h) \/ (el l q). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Velpl:(el p l))=>((unique l q a h) (conj p1p2_5 (conj p1p2_10 (conj (p1p2_2345 Vplcm Vepdc Velmo Velpl) p1p2_26))))). Qed. Lemma p1p2_2347: (pl c m)->(ep d c)->(el m o)->(el p l)->(ep a h)->(ep h a). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Velpl:(el p l))(Vepah:(ep a h))=>((psym a h) Vepah)). Qed. Lemma p1p2_2348: (pl c m)->(ep d c)->(el m o)->(el p l)->(ep a h)->(pl h s). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Velpl:(el p l))(Vepah:(ep a h))=>((pcon h a s) (conj (p1p2_2347 Vplcm Vepdc Velmo Velpl Vepah) p1p2_12))). Qed. Lemma p1p2_2349: (pl c m)->(ep d c)->(el m o)->(el p l)->(ep a h)->(ep f g) \/ (el n m). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Velpl:(el p l))(Vepah:(ep a h))=>((unique n m f g) (conj p1p2_15 (conj p1p2_22 (conj p1p2_23 (p1p2_2176 Vplcm Vepdc Velmo)))))). Qed. Lemma p1p2_2350: (pl c m)->(ep d c)->(el m o)->(el p l)->(ep a h)->(ep f g)->(ep g f). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Velpl:(el p l))(Vepah:(ep a h))(Vepfg:(ep f g))=>((psym f g) Vepfg)). Qed. Lemma p1p2_2351: (pl c m)->(ep d c)->(el m o)->(el p l)->(ep a h)->(ep f g)->(pl g s). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Velpl:(el p l))(Vepah:(ep a h))(Vepfg:(ep f g))=>((pcon g f s) (conj (p1p2_2350 Vplcm Vepdc Velmo Velpl Vepah Vepfg) p1p2_20))). Qed. Lemma p1p2_2352: (pl c m)->(ep d c)->(el m o)->(el p l)->(ep a h)->(ep f g)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Velpl:(el p l))(Vepah:(ep a h))(Vepfg:(ep f g))=>((goal4 s) (conj p1p2_45 (conj (p1p2_2351 Vplcm Vepdc Velmo Velpl Vepah Vepfg) (conj (p1p2_2348 Vplcm Vepdc Velmo Velpl Vepah) p1p2_28))))). Qed. Lemma p1p2_2353: (pl c m)->(ep d c)->(el m o)->(el p l)->(ep a h)->(el n m)->(el m n). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Velpl:(el p l))(Vepah:(ep a h))(Velnm:(el n m))=>((lsym n m) Velnm)). Qed. Lemma p1p2_2354: (pl c m)->(ep d c)->(el m o)->(el p l)->(ep a h)->(el n m)->(el o n). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Velpl:(el p l))(Vepah:(ep a h))(Velnm:(el n m))=>((ltra o m n) (conj (p1p2_2174 Vplcm Vepdc Velmo) (p1p2_2353 Vplcm Vepdc Velmo Velpl Vepah Velnm)))). Qed. Lemma p1p2_2355: (pl c m)->(ep d c)->(el m o)->(el p l)->(ep a h)->(el n m)->(el n o). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Velpl:(el p l))(Vepah:(ep a h))(Velnm:(el n m))=>((lsym o n) (p1p2_2354 Vplcm Vepdc Velmo Velpl Vepah Velnm))). Qed. Lemma p1p2_2356: (pl c m)->(ep d c)->(el m o)->(el p l)->(ep a h)->(el n m)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Velpl:(el p l))(Vepah:(ep a h))(Velnm:(el n m))=>(goal1 (p1p2_2355 Vplcm Vepdc Velmo Velpl Vepah Velnm))). Qed. Lemma p1p2_2357: (pl c m)->(ep d c)->(el m o)->(el p l)->(ep a h)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Velpl:(el p l))(Vepah:(ep a h))=>((or_ind ((p1p2_2352 Vplcm Vepdc Velmo Velpl Vepah))((p1p2_2356 Vplcm Vepdc Velmo Velpl Vepah)))(p1p2_2349 Vplcm Vepdc Velmo Velpl Vepah))). Qed. Lemma p1p2_2359: (pl c m)->(ep d c)->(el m o)->(el p l)->(el l q)->(el p q). Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Velpl:(el p l))(Vellq:(el l q))=>((ltra p l q) (conj Velpl Vellq))). Qed. Lemma p1p2_2360: (pl c m)->(ep d c)->(el m o)->(el p l)->(el l q)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Velpl:(el p l))(Vellq:(el l q))=>(goal2 (p1p2_2359 Vplcm Vepdc Velmo Velpl Vellq))). Qed. Lemma p1p2_2361: (pl c m)->(ep d c)->(el m o)->(el p l)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))(Velpl:(el p l))=>((or_ind ((p1p2_2357 Vplcm Vepdc Velmo Velpl))((p1p2_2360 Vplcm Vepdc Velmo Velpl)))(p1p2_2346 Vplcm Vepdc Velmo Velpl))). Qed. Lemma p1p2_2362: (pl c m)->(ep d c)->(el m o)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))(Velmo:(el m o))=>((or_ind ((p1p2_2342 Vplcm Vepdc Velmo))((p1p2_2361 Vplcm Vepdc Velmo)))(p1p2_2177 Vplcm Vepdc Velmo))). Qed. Lemma p1p2_2363: (pl c m)->(ep d c)->goal. Proof. exact (fun (Vplcm:(pl c m))(Vepdc:(ep d c))=>((or_ind ((p1p2_2173 Vplcm Vepdc))((p1p2_2362 Vplcm Vepdc)))(p1p2_1716 Vplcm Vepdc))). Qed. Lemma p1p2_2364: (pl c m)->(el m r)->(el r m). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))=>((lsym m r) Velmr)). Qed. Lemma p1p2_2365: (pl c m)->(el m r)->(pl e r). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))=>((lcon e m r) (conj p1p2_14 Velmr))). Qed. Lemma p1p2_2366: (pl c m)->(el m r)->(pl f r). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))=>((lcon f m r) (conj p1p2_22 Velmr))). Qed. Lemma p1p2_2367: (pl c m)->(el m r)->(pl i m). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))=>((lcon i r m) (conj p1p2_27 (p1p2_2364 Vplcm Velmr)))). Qed. Lemma p1p2_2368: (pl c m)->(el m r)->(ep c e) \/ (el o r). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))=>((unique o r c e) (conj p1p2_8 (conj p1p2_11 (conj p1p2_16 (p1p2_2365 Vplcm Velmr)))))). Qed. Lemma p1p2_2369: (pl c m)->(el m r)->(ep c e)->(ep e c). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))=>((psym c e) Vepce)). Qed. Lemma p1p2_2370: (pl c m)->(el m r)->(ep c e)->(pl c q). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))=>((pcon c e q) (conj Vepce p1p2_18))). Qed. Lemma p1p2_2372: (pl c m)->(el m r)->(ep c e)->(ep a c) \/ (el l q). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))=>((unique l q a c) (conj p1p2_5 (conj p1p2_10 (conj p1p2_21 (p1p2_2370 Vplcm Velmr Vepce)))))). Qed. Lemma p1p2_2373: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c a). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))=>((psym a c) Vepac)). Qed. Lemma p1p2_2376: (pl c m)->(el m r)->(ep c e)->(ep a c)->(pl a o). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))=>((pcon a c o) (conj Vepac p1p2_8))). Qed. Lemma p1p2_2379: (pl c m)->(el m r)->(ep c e)->(ep a c)->(pl c s). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))=>((pcon c a s) (conj (p1p2_2373 Vplcm Velmr Vepce Vepac) p1p2_12))). Qed. Lemma p1p2_2381: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i) \/ (el r s). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))=>((unique r s c i) (conj p1p2_11 (conj (p1p2_2379 Vplcm Velmr Vepce Vepac) (conj p1p2_27 p1p2_28))))). Qed. Lemma p1p2_2382: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep i c). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))=>((psym c i) Vepci)). Qed. Lemma p1p2_2389: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(pl i q). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))=>((pcon i c q) (conj (p1p2_2382 Vplcm Velmr Vepce Vepac Vepci) (p1p2_2370 Vplcm Velmr Vepce)))). Qed. Lemma p1p2_2390: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f) \/ (el r s). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))=>((unique r s c f) (conj p1p2_11 (conj (p1p2_2379 Vplcm Velmr Vepce Vepac) (conj (p1p2_2366 Vplcm Velmr) p1p2_20))))). Qed. Lemma p1p2_2398: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(pl c n). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))=>((pcon c f n) (conj Vepcf p1p2_15))). Qed. Lemma p1p2_2400: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(pl a n). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))=>((pcon a c n) (conj Vepac (p1p2_2398 Vplcm Velmr Vepce Vepac Vepci Vepcf)))). Qed. Lemma p1p2_2405: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(ep a b) \/ (el l n). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))=>((unique l n a b) (conj p1p2_5 (conj (p1p2_2400 Vplcm Velmr Vepce Vepac Vepci Vepcf) (conj p1p2_13 p1p2_7))))). Qed. Lemma p1p2_2406: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(ep a b)->(ep b a). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))=>((psym a b) Vepab)). Qed. Lemma p1p2_2415: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(ep a b)->(pl a p). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))=>((pcon a b p) (conj Vepab p1p2_9))). Qed. Lemma p1p2_2416: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(ep a b)->(pl c p). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))=>((pcon c a p) (conj (p1p2_2373 Vplcm Velmr Vepce Vepac) (p1p2_2415 Vplcm Velmr Vepce Vepac Vepci Vepcf Vepab)))). Qed. Lemma p1p2_2417: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(ep a b)->(pl e p). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))=>((pcon e c p) (conj (p1p2_2369 Vplcm Velmr Vepce) (p1p2_2416 Vplcm Velmr Vepce Vepac Vepci Vepcf Vepab)))). Qed. Lemma p1p2_2418: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(ep a b)->(pl i p). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))=>((pcon i c p) (conj (p1p2_2382 Vplcm Velmr Vepce Vepac Vepci) (p1p2_2416 Vplcm Velmr Vepce Vepac Vepci Vepcf Vepab)))). Qed. Lemma p1p2_2422: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(ep a b)->(pl b o). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))=>((pcon b a o) (conj (p1p2_2406 Vplcm Velmr Vepce Vepac Vepci Vepcf Vepab) (p1p2_2376 Vplcm Velmr Vepce Vepac)))). Qed. Lemma p1p2_2425: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(ep a b)->(ep d e) \/ (el m p). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))=>((unique m p d e) (conj p1p2_6 (conj p1p2_17 (conj p1p2_14 (p1p2_2417 Vplcm Velmr Vepce Vepac Vepci Vepcf Vepab)))))). Qed. Lemma p1p2_2442: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(ep a b)->(ep d e)->(ep b g) \/ (el n o). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Vepde:(ep d e))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_2422 Vplcm Velmr Vepce Vepac Vepci Vepcf Vepab) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_2443: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(ep a b)->(ep d e)->(ep b g)->(ep g b). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Vepde:(ep d e))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_2456: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(ep a b)->(ep d e)->(ep b g)->(pl g p). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Vepde:(ep d e))(Vepbg:(ep b g))=>((pcon g b p) (conj (p1p2_2443 Vplcm Velmr Vepce Vepac Vepci Vepcf Vepab Vepde Vepbg) p1p2_9))). Qed. Lemma p1p2_2457: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(ep a b)->(ep d e)->(ep b g)->goal. Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Vepde:(ep d e))(Vepbg:(ep b g))=>((goal4 p) (conj p1p2_42 (conj (p1p2_2456 Vplcm Velmr Vepce Vepac Vepci Vepcf Vepab Vepde Vepbg) (conj p1p2_25 (p1p2_2418 Vplcm Velmr Vepce Vepac Vepci Vepcf Vepab)))))). Qed. Lemma p1p2_2458: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(ep a b)->(ep d e)->(el n o)->goal. Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Vepde:(ep d e))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_2459: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(ep a b)->(ep d e)->goal. Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Vepde:(ep d e))=>((or_ind ((p1p2_2457 Vplcm Velmr Vepce Vepac Vepci Vepcf Vepab Vepde))((p1p2_2458 Vplcm Velmr Vepce Vepac Vepci Vepcf Vepab Vepde)))(p1p2_2442 Vplcm Velmr Vepce Vepac Vepci Vepcf Vepab Vepde))). Qed. Lemma p1p2_2465: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(ep a b)->(el m p)->(ep b g) \/ (el n o). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Velmp:(el m p))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_2422 Vplcm Velmr Vepce Vepac Vepci Vepcf Vepab) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_2466: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(ep a b)->(el m p)->(ep b g)->(ep g b). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_2477: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(ep a b)->(el m p)->(ep b g)->(pl g p). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbg:(ep b g))=>((pcon g b p) (conj (p1p2_2466 Vplcm Velmr Vepce Vepac Vepci Vepcf Vepab Velmp Vepbg) p1p2_9))). Qed. Lemma p1p2_2478: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(ep a b)->(el m p)->(ep b g)->goal. Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbg:(ep b g))=>((goal4 p) (conj p1p2_42 (conj (p1p2_2477 Vplcm Velmr Vepce Vepac Vepci Vepcf Vepab Velmp Vepbg) (conj p1p2_25 (p1p2_2418 Vplcm Velmr Vepce Vepac Vepci Vepcf Vepab)))))). Qed. Lemma p1p2_2479: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(ep a b)->(el m p)->(el n o)->goal. Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Velmp:(el m p))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_2480: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(ep a b)->(el m p)->goal. Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Velmp:(el m p))=>((or_ind ((p1p2_2478 Vplcm Velmr Vepce Vepac Vepci Vepcf Vepab Velmp))((p1p2_2479 Vplcm Velmr Vepce Vepac Vepci Vepcf Vepab Velmp)))(p1p2_2465 Vplcm Velmr Vepce Vepac Vepci Vepcf Vepab Velmp))). Qed. Lemma p1p2_2481: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(ep a b)->goal. Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))=>((or_ind ((p1p2_2459 Vplcm Velmr Vepce Vepac Vepci Vepcf Vepab))((p1p2_2480 Vplcm Velmr Vepce Vepac Vepci Vepcf Vepab)))(p1p2_2425 Vplcm Velmr Vepce Vepac Vepci Vepcf Vepab))). Qed. Lemma p1p2_2482: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(el l n)->(el n l). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))(Velln:(el l n))=>((lsym l n) Velln)). Qed. Lemma p1p2_2483: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(el l n)->(pl g l). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))(Velln:(el l n))=>((lcon g n l) (conj p1p2_23 (p1p2_2482 Vplcm Velmr Vepce Vepac Vepci Vepcf Velln)))). Qed. Lemma p1p2_2484: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(el l n)->(ep a g) \/ (el l o). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))(Velln:(el l n))=>((unique l o a g) (conj p1p2_5 (conj (p1p2_2376 Vplcm Velmr Vepce Vepac) (conj (p1p2_2483 Vplcm Velmr Vepce Vepac Vepci Vepcf Velln) p1p2_24))))). Qed. Lemma p1p2_2485: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(el l n)->(ep a g)->(ep g a). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))(Velln:(el l n))(Vepag:(ep a g))=>((psym a g) Vepag)). Qed. Lemma p1p2_2494: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(el l n)->(ep a g)->(pl g q). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))(Velln:(el l n))(Vepag:(ep a g))=>((pcon g a q) (conj (p1p2_2485 Vplcm Velmr Vepce Vepac Vepci Vepcf Velln Vepag) p1p2_10))). Qed. Lemma p1p2_2495: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(el l n)->(ep a g)->goal. Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))(Velln:(el l n))(Vepag:(ep a g))=>((goal4 q) (conj p1p2_43 (conj (p1p2_2494 Vplcm Velmr Vepce Vepac Vepci Vepcf Velln Vepag) (conj p1p2_26 (p1p2_2389 Vplcm Velmr Vepce Vepac Vepci)))))). Qed. Lemma p1p2_2497: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(el l n)->(el l o)->(el n o). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))(Velln:(el l n))(Vello:(el l o))=>((ltra n l o) (conj (p1p2_2482 Vplcm Velmr Vepce Vepac Vepci Vepcf Velln) Vello))). Qed. Lemma p1p2_2498: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(el l n)->(el l o)->goal. Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))(Velln:(el l n))(Vello:(el l o))=>(goal1 (p1p2_2497 Vplcm Velmr Vepce Vepac Vepci Vepcf Velln Vello))). Qed. Lemma p1p2_2499: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->(el l n)->goal. Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))(Velln:(el l n))=>((or_ind ((p1p2_2495 Vplcm Velmr Vepce Vepac Vepci Vepcf Velln))((p1p2_2498 Vplcm Velmr Vepce Vepac Vepci Vepcf Velln)))(p1p2_2484 Vplcm Velmr Vepce Vepac Vepci Vepcf Velln))). Qed. Lemma p1p2_2500: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(ep c f)->goal. Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Vepcf:(ep c f))=>((or_ind ((p1p2_2481 Vplcm Velmr Vepce Vepac Vepci Vepcf))((p1p2_2499 Vplcm Velmr Vepce Vepac Vepci Vepcf)))(p1p2_2405 Vplcm Velmr Vepce Vepac Vepci Vepcf))). Qed. Lemma p1p2_2501: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(el r s)->(el s r). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Velrs:(el r s))=>((lsym r s) Velrs)). Qed. Lemma p1p2_2502: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->(el r s)->goal. Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))(Velrs:(el r s))=>(goal3 (p1p2_2501 Vplcm Velmr Vepce Vepac Vepci Velrs))). Qed. Lemma p1p2_2503: (pl c m)->(el m r)->(ep c e)->(ep a c)->(ep c i)->goal. Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Vepci:(ep c i))=>((or_ind ((p1p2_2500 Vplcm Velmr Vepce Vepac Vepci))((p1p2_2502 Vplcm Velmr Vepce Vepac Vepci)))(p1p2_2390 Vplcm Velmr Vepce Vepac Vepci))). Qed. Lemma p1p2_2504: (pl c m)->(el m r)->(ep c e)->(ep a c)->(el r s)->(el s r). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Velrs:(el r s))=>((lsym r s) Velrs)). Qed. Lemma p1p2_2505: (pl c m)->(el m r)->(ep c e)->(ep a c)->(el r s)->goal. Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))(Velrs:(el r s))=>(goal3 (p1p2_2504 Vplcm Velmr Vepce Vepac Velrs))). Qed. Lemma p1p2_2506: (pl c m)->(el m r)->(ep c e)->(ep a c)->goal. Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vepac:(ep a c))=>((or_ind ((p1p2_2503 Vplcm Velmr Vepce Vepac))((p1p2_2505 Vplcm Velmr Vepce Vepac)))(p1p2_2381 Vplcm Velmr Vepce Vepac))). Qed. Lemma p1p2_2507: (pl c m)->(el m r)->(ep c e)->(el l q)->(el q l). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vellq:(el l q))=>((lsym l q) Vellq)). Qed. Lemma p1p2_2509: (pl c m)->(el m r)->(ep c e)->(el l q)->(pl h l). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vellq:(el l q))=>((lcon h q l) (conj p1p2_26 (p1p2_2507 Vplcm Velmr Vepce Vellq)))). Qed. Lemma p1p2_2510: (pl c m)->(el m r)->(ep c e)->(el l q)->(ep b h) \/ (el p l). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vellq:(el l q))=>((unique p l b h) (conj p1p2_9 (conj p1p2_13 (conj p1p2_25 (p1p2_2509 Vplcm Velmr Vepce Vellq)))))). Qed. Lemma p1p2_2511: (pl c m)->(el m r)->(ep c e)->(el l q)->(ep b h)->(ep h b). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vellq:(el l q))(Vepbh:(ep b h))=>((psym b h) Vepbh)). Qed. Lemma p1p2_2512: (pl c m)->(el m r)->(ep c e)->(el l q)->(ep b h)->(pl h n). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vellq:(el l q))(Vepbh:(ep b h))=>((pcon h b n) (conj (p1p2_2511 Vplcm Velmr Vepce Vellq Vepbh) p1p2_7))). Qed. Lemma p1p2_2513: (pl c m)->(el m r)->(ep c e)->(el l q)->(ep b h)->(ep f i) \/ (el s m). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vellq:(el l q))(Vepbh:(ep b h))=>((unique s m f i) (conj p1p2_20 (conj p1p2_22 (conj p1p2_28 (p1p2_2367 Vplcm Velmr)))))). Qed. Lemma p1p2_2514: (pl c m)->(el m r)->(ep c e)->(el l q)->(ep b h)->(ep f i)->(ep i f). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vellq:(el l q))(Vepbh:(ep b h))(Vepfi:(ep f i))=>((psym f i) Vepfi)). Qed. Lemma p1p2_2515: (pl c m)->(el m r)->(ep c e)->(el l q)->(ep b h)->(ep f i)->(pl i n). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vellq:(el l q))(Vepbh:(ep b h))(Vepfi:(ep f i))=>((pcon i f n) (conj (p1p2_2514 Vplcm Velmr Vepce Vellq Vepbh Vepfi) p1p2_15))). Qed. Lemma p1p2_2516: (pl c m)->(el m r)->(ep c e)->(el l q)->(ep b h)->(ep f i)->goal. Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vellq:(el l q))(Vepbh:(ep b h))(Vepfi:(ep f i))=>((goal4 n) (conj p1p2_40 (conj p1p2_23 (conj (p1p2_2512 Vplcm Velmr Vepce Vellq Vepbh) (p1p2_2515 Vplcm Velmr Vepce Vellq Vepbh Vepfi)))))). Qed. Lemma p1p2_2517: (pl c m)->(el m r)->(ep c e)->(el l q)->(ep b h)->(el s m)->(el m s). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vellq:(el l q))(Vepbh:(ep b h))(Velsm:(el s m))=>((lsym s m) Velsm)). Qed. Lemma p1p2_2518: (pl c m)->(el m r)->(ep c e)->(el l q)->(ep b h)->(el s m)->(el r s). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vellq:(el l q))(Vepbh:(ep b h))(Velsm:(el s m))=>((ltra r m s) (conj (p1p2_2364 Vplcm Velmr) (p1p2_2517 Vplcm Velmr Vepce Vellq Vepbh Velsm)))). Qed. Lemma p1p2_2519: (pl c m)->(el m r)->(ep c e)->(el l q)->(ep b h)->(el s m)->(el s r). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vellq:(el l q))(Vepbh:(ep b h))(Velsm:(el s m))=>((lsym r s) (p1p2_2518 Vplcm Velmr Vepce Vellq Vepbh Velsm))). Qed. Lemma p1p2_2520: (pl c m)->(el m r)->(ep c e)->(el l q)->(ep b h)->(el s m)->goal. Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vellq:(el l q))(Vepbh:(ep b h))(Velsm:(el s m))=>(goal3 (p1p2_2519 Vplcm Velmr Vepce Vellq Vepbh Velsm))). Qed. Lemma p1p2_2521: (pl c m)->(el m r)->(ep c e)->(el l q)->(ep b h)->goal. Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vellq:(el l q))(Vepbh:(ep b h))=>((or_ind ((p1p2_2516 Vplcm Velmr Vepce Vellq Vepbh))((p1p2_2520 Vplcm Velmr Vepce Vellq Vepbh)))(p1p2_2513 Vplcm Velmr Vepce Vellq Vepbh))). Qed. Lemma p1p2_2522: (pl c m)->(el m r)->(ep c e)->(el l q)->(el p l)->(el l p). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vellq:(el l q))(Velpl:(el p l))=>((lsym p l) Velpl)). Qed. Lemma p1p2_2523: (pl c m)->(el m r)->(ep c e)->(el l q)->(el p l)->(el q p). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vellq:(el l q))(Velpl:(el p l))=>((ltra q l p) (conj (p1p2_2507 Vplcm Velmr Vepce Vellq) (p1p2_2522 Vplcm Velmr Vepce Vellq Velpl)))). Qed. Lemma p1p2_2524: (pl c m)->(el m r)->(ep c e)->(el l q)->(el p l)->(el p q). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vellq:(el l q))(Velpl:(el p l))=>((lsym q p) (p1p2_2523 Vplcm Velmr Vepce Vellq Velpl))). Qed. Lemma p1p2_2525: (pl c m)->(el m r)->(ep c e)->(el l q)->(el p l)->goal. Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vellq:(el l q))(Velpl:(el p l))=>(goal2 (p1p2_2524 Vplcm Velmr Vepce Vellq Velpl))). Qed. Lemma p1p2_2526: (pl c m)->(el m r)->(ep c e)->(el l q)->goal. Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))(Vellq:(el l q))=>((or_ind ((p1p2_2521 Vplcm Velmr Vepce Vellq))((p1p2_2525 Vplcm Velmr Vepce Vellq)))(p1p2_2510 Vplcm Velmr Vepce Vellq))). Qed. Lemma p1p2_2527: (pl c m)->(el m r)->(ep c e)->goal. Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Vepce:(ep c e))=>((or_ind ((p1p2_2506 Vplcm Velmr Vepce))((p1p2_2526 Vplcm Velmr Vepce)))(p1p2_2372 Vplcm Velmr Vepce))). Qed. Lemma p1p2_2528: (pl c m)->(el m r)->(el o r)->(el r o). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Velor:(el o r))=>((lsym o r) Velor)). Qed. Lemma p1p2_2529: (pl c m)->(el m r)->(el o r)->(el m o). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Velor:(el o r))=>((ltra m r o) (conj Velmr (p1p2_2528 Vplcm Velmr Velor)))). Qed. Lemma p1p2_2530: (pl c m)->(el m r)->(el o r)->(el o m). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Velor:(el o r))=>((lsym m o) (p1p2_2529 Vplcm Velmr Velor))). Qed. Lemma p1p2_2534: (pl c m)->(el m r)->(el o r)->(pl g m). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Velor:(el o r))=>((lcon g o m) (conj p1p2_24 (p1p2_2530 Vplcm Velmr Velor)))). Qed. Lemma p1p2_2536: (pl c m)->(el m r)->(el o r)->(ep f g) \/ (el n m). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Velor:(el o r))=>((unique n m f g) (conj p1p2_15 (conj p1p2_22 (conj p1p2_23 (p1p2_2534 Vplcm Velmr Velor)))))). Qed. Lemma p1p2_2537: (pl c m)->(el m r)->(el o r)->(ep f g)->(ep g f). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Velor:(el o r))(Vepfg:(ep f g))=>((psym f g) Vepfg)). Qed. Lemma p1p2_2539: (pl c m)->(el m r)->(el o r)->(ep f g)->(ep f i) \/ (el s m). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Velor:(el o r))(Vepfg:(ep f g))=>((unique s m f i) (conj p1p2_20 (conj p1p2_22 (conj p1p2_28 (p1p2_2367 Vplcm Velmr)))))). Qed. Lemma p1p2_2540: (pl c m)->(el m r)->(el o r)->(ep f g)->(ep f i)->(ep i f). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Velor:(el o r))(Vepfg:(ep f g))(Vepfi:(ep f i))=>((psym f i) Vepfi)). Qed. Lemma p1p2_2544: (pl c m)->(el m r)->(el o r)->(ep f g)->(ep f i)->(exists A:dom,(pl a A)/\(pl d A)). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Velor:(el o r))(Vepfg:(ep f g))(Vepfi:(ep f i))=>((line a d) (conj p1p2_29 p1p2_30))). Qed. Lemma p1p2_2546: (pl c m)->(el m r)->(el o r)->(ep f g)->(ep f i)->forall C0:dom,(pl a C0)->(pl d C0)->(exists A:dom,(pl b A)/\(pl e A)). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Velor:(el o r))(Vepfg:(ep f g))(Vepfi:(ep f i))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))=>((line b e) (conj p1p2_31 p1p2_33))). Qed. Lemma p1p2_2548: (pl c m)->(el m r)->(el o r)->(ep f g)->(ep f i)->forall C0:dom,(pl a C0)->(pl d C0)->forall C1:dom,(pl b C1)->(pl e C1)->(exists A:dom,(pl c A)/\(pl h A)). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Velor:(el o r))(Vepfg:(ep f g))(Vepfi:(ep f i))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))(C1:dom)(VplbC1:(pl b C1))(VpleC1:(pl e C1))=>((line c h) (conj p1p2_32 p1p2_36))). Qed. Lemma p1p2_2550: (pl c m)->(el m r)->(el o r)->(ep f g)->(ep f i)->forall C0:dom,(pl a C0)->(pl d C0)->forall C1:dom,(pl b C1)->(pl e C1)->forall C2:dom,(pl c C2)->(pl h C2)->(exists A:dom,(pl f A)/\(pl h A)). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Velor:(el o r))(Vepfg:(ep f g))(Vepfi:(ep f i))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))(C1:dom)(VplbC1:(pl b C1))(VpleC1:(pl e C1))(C2:dom)(VplcC2:(pl c C2))(VplhC2:(pl h C2))=>((line f h) (conj p1p2_34 p1p2_36))). Qed. Lemma p1p2_2551: (pl c m)->(el m r)->(el o r)->(ep f g)->(ep f i)->forall C0:dom,(pl a C0)->(pl d C0)->forall C1:dom,(pl b C1)->(pl e C1)->forall C2:dom,(pl c C2)->(pl h C2)->forall C3:dom,(pl f C3)->(pl h C3)->(el C3 C3). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Velor:(el o r))(Vepfg:(ep f g))(Vepfi:(ep f i))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))(C1:dom)(VplbC1:(pl b C1))(VpleC1:(pl e C1))(C2:dom)(VplcC2:(pl c C2))(VplhC2:(pl h C2))(C3:dom)(VplfC3:(pl f C3))(VplhC3:(pl h C3))=>((lref f C3) VplfC3)). Qed. Lemma p1p2_2552: (pl c m)->(el m r)->(el o r)->(ep f g)->(ep f i)->forall C0:dom,(pl a C0)->(pl d C0)->forall C1:dom,(pl b C1)->(pl e C1)->forall C2:dom,(pl c C2)->(pl h C2)->forall C3:dom,(pl f C3)->(pl h C3)->(pl g C3). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Velor:(el o r))(Vepfg:(ep f g))(Vepfi:(ep f i))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))(C1:dom)(VplbC1:(pl b C1))(VpleC1:(pl e C1))(C2:dom)(VplcC2:(pl c C2))(VplhC2:(pl h C2))(C3:dom)(VplfC3:(pl f C3))(VplhC3:(pl h C3))=>((pcon g f C3) (conj (p1p2_2537 Vplcm Velmr Velor Vepfg) VplfC3))). Qed. Lemma p1p2_2553: (pl c m)->(el m r)->(el o r)->(ep f g)->(ep f i)->forall C0:dom,(pl a C0)->(pl d C0)->forall C1:dom,(pl b C1)->(pl e C1)->forall C2:dom,(pl c C2)->(pl h C2)->forall C3:dom,(pl f C3)->(pl h C3)->(pl i C3). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Velor:(el o r))(Vepfg:(ep f g))(Vepfi:(ep f i))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))(C1:dom)(VplbC1:(pl b C1))(VpleC1:(pl e C1))(C2:dom)(VplcC2:(pl c C2))(VplhC2:(pl h C2))(C3:dom)(VplfC3:(pl f C3))(VplhC3:(pl h C3))=>((pcon i f C3) (conj (p1p2_2540 Vplcm Velmr Velor Vepfg Vepfi) VplfC3))). Qed. Lemma p1p2_2554: (pl c m)->(el m r)->(el o r)->(ep f g)->(ep f i)->forall C0:dom,(pl a C0)->(pl d C0)->forall C1:dom,(pl b C1)->(pl e C1)->forall C2:dom,(pl c C2)->(pl h C2)->forall C3:dom,(pl f C3)->(pl h C3)->goal. Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Velor:(el o r))(Vepfg:(ep f g))(Vepfi:(ep f i))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))(C1:dom)(VplbC1:(pl b C1))(VpleC1:(pl e C1))(C2:dom)(VplcC2:(pl c C2))(VplhC2:(pl h C2))(C3:dom)(VplfC3:(pl f C3))(VplhC3:(pl h C3))=>((goal4 C3) (conj (p1p2_2551 Vplcm Velmr Velor Vepfg Vepfi C0 VplaC0 VpldC0 C1 VplbC1 VpleC1 C2 VplcC2 VplhC2 C3 VplfC3 VplhC3) (conj (p1p2_2552 Vplcm Velmr Velor Vepfg Vepfi C0 VplaC0 VpldC0 C1 VplbC1 VpleC1 C2 VplcC2 VplhC2 C3 VplfC3 VplhC3) (conj VplhC3 (p1p2_2553 Vplcm Velmr Velor Vepfg Vepfi C0 VplaC0 VpldC0 C1 VplbC1 VpleC1 C2 VplcC2 VplhC2 C3 VplfC3 VplhC3)))))). Qed. Lemma p1p2_2555: (pl c m)->(el m r)->(el o r)->(ep f g)->(ep f i)->forall C0:dom,(pl a C0)->(pl d C0)->forall C1:dom,(pl b C1)->(pl e C1)->forall C2:dom,(pl c C2)->(pl h C2)->goal. Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Velor:(el o r))(Vepfg:(ep f g))(Vepfi:(ep f i))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))(C1:dom)(VplbC1:(pl b C1))(VpleC1:(pl e C1))(C2:dom)(VplcC2:(pl c C2))(VplhC2:(pl h C2))=>((ex_ind (P:=fun C3:dom=>(pl f C3)/\(pl h C3))(fun C3:dom=>(and_ind (p1p2_2554 Vplcm Velmr Velor Vepfg Vepfi C0 VplaC0 VpldC0 C1 VplbC1 VpleC1 C2 VplcC2 VplhC2 C3))))(p1p2_2550 Vplcm Velmr Velor Vepfg Vepfi C0 VplaC0 VpldC0 C1 VplbC1 VpleC1 C2 VplcC2 VplhC2))). Qed. Lemma p1p2_2556: (pl c m)->(el m r)->(el o r)->(ep f g)->(ep f i)->forall C0:dom,(pl a C0)->(pl d C0)->forall C1:dom,(pl b C1)->(pl e C1)->goal. Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Velor:(el o r))(Vepfg:(ep f g))(Vepfi:(ep f i))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))(C1:dom)(VplbC1:(pl b C1))(VpleC1:(pl e C1))=>((ex_ind (P:=fun C2:dom=>(pl c C2)/\(pl h C2))(fun C2:dom=>(and_ind (p1p2_2555 Vplcm Velmr Velor Vepfg Vepfi C0 VplaC0 VpldC0 C1 VplbC1 VpleC1 C2))))(p1p2_2548 Vplcm Velmr Velor Vepfg Vepfi C0 VplaC0 VpldC0 C1 VplbC1 VpleC1))). Qed. Lemma p1p2_2557: (pl c m)->(el m r)->(el o r)->(ep f g)->(ep f i)->forall C0:dom,(pl a C0)->(pl d C0)->goal. Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Velor:(el o r))(Vepfg:(ep f g))(Vepfi:(ep f i))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))=>((ex_ind (P:=fun C1:dom=>(pl b C1)/\(pl e C1))(fun C1:dom=>(and_ind (p1p2_2556 Vplcm Velmr Velor Vepfg Vepfi C0 VplaC0 VpldC0 C1))))(p1p2_2546 Vplcm Velmr Velor Vepfg Vepfi C0 VplaC0 VpldC0))). Qed. Lemma p1p2_2558: (pl c m)->(el m r)->(el o r)->(ep f g)->(ep f i)->goal. Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Velor:(el o r))(Vepfg:(ep f g))(Vepfi:(ep f i))=>((ex_ind (P:=fun C0:dom=>(pl a C0)/\(pl d C0))(fun C0:dom=>(and_ind (p1p2_2557 Vplcm Velmr Velor Vepfg Vepfi C0))))(p1p2_2544 Vplcm Velmr Velor Vepfg Vepfi))). Qed. Lemma p1p2_2559: (pl c m)->(el m r)->(el o r)->(ep f g)->(el s m)->(el m s). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Velor:(el o r))(Vepfg:(ep f g))(Velsm:(el s m))=>((lsym s m) Velsm)). Qed. Lemma p1p2_2560: (pl c m)->(el m r)->(el o r)->(ep f g)->(el s m)->(el r s). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Velor:(el o r))(Vepfg:(ep f g))(Velsm:(el s m))=>((ltra r m s) (conj (p1p2_2364 Vplcm Velmr) (p1p2_2559 Vplcm Velmr Velor Vepfg Velsm)))). Qed. Lemma p1p2_2561: (pl c m)->(el m r)->(el o r)->(ep f g)->(el s m)->(el s r). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Velor:(el o r))(Vepfg:(ep f g))(Velsm:(el s m))=>((lsym r s) (p1p2_2560 Vplcm Velmr Velor Vepfg Velsm))). Qed. Lemma p1p2_2562: (pl c m)->(el m r)->(el o r)->(ep f g)->(el s m)->goal. Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Velor:(el o r))(Vepfg:(ep f g))(Velsm:(el s m))=>(goal3 (p1p2_2561 Vplcm Velmr Velor Vepfg Velsm))). Qed. Lemma p1p2_2563: (pl c m)->(el m r)->(el o r)->(ep f g)->goal. Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Velor:(el o r))(Vepfg:(ep f g))=>((or_ind ((p1p2_2558 Vplcm Velmr Velor Vepfg))((p1p2_2562 Vplcm Velmr Velor Vepfg)))(p1p2_2539 Vplcm Velmr Velor Vepfg))). Qed. Lemma p1p2_2564: (pl c m)->(el m r)->(el o r)->(el n m)->(el m n). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Velor:(el o r))(Velnm:(el n m))=>((lsym n m) Velnm)). Qed. Lemma p1p2_2565: (pl c m)->(el m r)->(el o r)->(el n m)->(el r n). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Velor:(el o r))(Velnm:(el n m))=>((ltra r m n) (conj (p1p2_2364 Vplcm Velmr) (p1p2_2564 Vplcm Velmr Velor Velnm)))). Qed. Lemma p1p2_2567: (pl c m)->(el m r)->(el o r)->(el n m)->(el o n). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Velor:(el o r))(Velnm:(el n m))=>((ltra o r n) (conj Velor (p1p2_2565 Vplcm Velmr Velor Velnm)))). Qed. Lemma p1p2_2568: (pl c m)->(el m r)->(el o r)->(el n m)->(el n o). Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Velor:(el o r))(Velnm:(el n m))=>((lsym o n) (p1p2_2567 Vplcm Velmr Velor Velnm))). Qed. Lemma p1p2_2569: (pl c m)->(el m r)->(el o r)->(el n m)->goal. Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Velor:(el o r))(Velnm:(el n m))=>(goal1 (p1p2_2568 Vplcm Velmr Velor Velnm))). Qed. Lemma p1p2_2570: (pl c m)->(el m r)->(el o r)->goal. Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))(Velor:(el o r))=>((or_ind ((p1p2_2563 Vplcm Velmr Velor))((p1p2_2569 Vplcm Velmr Velor)))(p1p2_2536 Vplcm Velmr Velor))). Qed. Lemma p1p2_2571: (pl c m)->(el m r)->goal. Proof. exact (fun (Vplcm:(pl c m))(Velmr:(el m r))=>((or_ind ((p1p2_2527 Vplcm Velmr))((p1p2_2570 Vplcm Velmr)))(p1p2_2368 Vplcm Velmr))). Qed. Lemma p1p2_2572: (pl c m)->goal. Proof. exact (fun (Vplcm:(pl c m))=>((or_ind ((p1p2_2363 Vplcm))((p1p2_2571 Vplcm)))(p1p2_1711 Vplcm))). Qed. Lemma p1p2_2573: (pl d l)->(ep b d) \/ (el p l). Proof. exact (fun (Vpldl:(pl d l))=>((unique p l b d) (conj p1p2_9 (conj p1p2_13 (conj p1p2_17 Vpldl))))). Qed. Lemma p1p2_2574: (pl d l)->(ep b d)->(ep d b). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))=>((psym b d) Vepbd)). Qed. Lemma p1p2_2576: (pl d l)->(ep b d)->(pl b r). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))=>((pcon b d r) (conj Vepbd p1p2_19))). Qed. Lemma p1p2_2577: (pl d l)->(ep b d)->(pl d n). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))=>((pcon d b n) (conj (p1p2_2574 Vpldl Vepbd) p1p2_7))). Qed. Lemma p1p2_2578: (pl d l)->(ep b d)->(ep d f) \/ (el m n). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))=>((unique m n d f) (conj p1p2_6 (conj (p1p2_2577 Vpldl Vepbd) (conj p1p2_22 p1p2_15))))). Qed. Lemma p1p2_2582: (pl d l)->(ep b d)->(ep d f)->(pl d s). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))=>((pcon d f s) (conj Vepdf p1p2_20))). Qed. Lemma p1p2_2583: (pl d l)->(ep b d)->(ep d f)->(pl b s). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))=>((pcon b d s) (conj Vepbd (p1p2_2582 Vpldl Vepbd Vepdf)))). Qed. Lemma p1p2_2587: (pl d l)->(ep b d)->(ep d f)->(ep a b) \/ (el l s). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))=>((unique l s a b) (conj p1p2_5 (conj p1p2_12 (conj p1p2_13 (p1p2_2583 Vpldl Vepbd Vepdf)))))). Qed. Lemma p1p2_2588: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep b a). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))=>((psym a b) Vepab)). Qed. Lemma p1p2_2593: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(pl a n). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))=>((pcon a b n) (conj Vepab p1p2_7))). Qed. Lemma p1p2_2594: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(pl a p). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))=>((pcon a b p) (conj Vepab p1p2_9))). Qed. Lemma p1p2_2596: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(pl a r). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))=>((pcon a b r) (conj Vepab (p1p2_2576 Vpldl Vepbd)))). Qed. Lemma p1p2_2597: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(pl b q). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))=>((pcon b a q) (conj (p1p2_2588 Vpldl Vepbd Vepdf Vepab) p1p2_10))). Qed. Lemma p1p2_2598: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(pl d q). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))=>((pcon d b q) (conj (p1p2_2574 Vpldl Vepbd) (p1p2_2597 Vpldl Vepbd Vepdf Vepab)))). Qed. Lemma p1p2_2600: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c) \/ (el l r). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))=>((unique l r a c) (conj p1p2_5 (conj (p1p2_2596 Vpldl Vepbd Vepdf Vepab) (conj p1p2_21 p1p2_11))))). Qed. Lemma p1p2_2608: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(pl a o). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))=>((pcon a c o) (conj Vepac p1p2_8))). Qed. Lemma p1p2_2609: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(pl b o). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))=>((pcon b a o) (conj (p1p2_2588 Vpldl Vepbd Vepdf Vepab) (p1p2_2608 Vpldl Vepbd Vepdf Vepab Vepac)))). Qed. Lemma p1p2_2610: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(pl d o). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))=>((pcon d b o) (conj (p1p2_2574 Vpldl Vepbd) (p1p2_2609 Vpldl Vepbd Vepdf Vepab Vepac)))). Qed. Lemma p1p2_2617: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(ep d e) \/ (el m q). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))=>((unique m q d e) (conj p1p2_6 (conj (p1p2_2598 Vpldl Vepbd Vepdf Vepab) (conj p1p2_14 p1p2_18))))). Qed. Lemma p1p2_2632: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(ep d e)->(ep b g) \/ (el n o). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Vepde:(ep d e))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_2609 Vpldl Vepbd Vepdf Vepab Vepac) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_2633: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(ep d e)->(ep b g)->(ep g b). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_2647: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(ep d e)->(ep b g)->(pl g r). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))=>((pcon g b r) (conj (p1p2_2633 Vpldl Vepbd Vepdf Vepab Vepac Vepde Vepbg) (p1p2_2576 Vpldl Vepbd)))). Qed. Lemma p1p2_2650: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(ep d e)->(ep b g)->(ep b h) \/ (el p q). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))=>((unique p q b h) (conj p1p2_9 (conj (p1p2_2597 Vpldl Vepbd Vepdf Vepab) (conj p1p2_25 p1p2_26))))). Qed. Lemma p1p2_2651: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(ep d e)->(ep b g)->(ep b h)->(ep h b). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))(Vepbh:(ep b h))=>((psym b h) Vepbh)). Qed. Lemma p1p2_2667: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(ep d e)->(ep b g)->(ep b h)->(pl h r). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))(Vepbh:(ep b h))=>((pcon h b r) (conj (p1p2_2651 Vpldl Vepbd Vepdf Vepab Vepac Vepde Vepbg Vepbh) (p1p2_2576 Vpldl Vepbd)))). Qed. Lemma p1p2_2668: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(ep d e)->(ep b g)->(ep b h)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))(Vepbh:(ep b h))=>((goal4 r) (conj p1p2_44 (conj (p1p2_2647 Vpldl Vepbd Vepdf Vepab Vepac Vepde Vepbg) (conj (p1p2_2667 Vpldl Vepbd Vepdf Vepab Vepac Vepde Vepbg Vepbh) p1p2_27))))). Qed. Lemma p1p2_2669: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(ep d e)->(ep b g)->(el p q)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))(Velpq:(el p q))=>(goal2 Velpq)). Qed. Lemma p1p2_2670: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(ep d e)->(ep b g)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))=>((or_ind ((p1p2_2668 Vpldl Vepbd Vepdf Vepab Vepac Vepde Vepbg))((p1p2_2669 Vpldl Vepbd Vepdf Vepab Vepac Vepde Vepbg)))(p1p2_2650 Vpldl Vepbd Vepdf Vepab Vepac Vepde Vepbg))). Qed. Lemma p1p2_2671: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(ep d e)->(el n o)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Vepde:(ep d e))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_2672: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(ep d e)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Vepde:(ep d e))=>((or_ind ((p1p2_2670 Vpldl Vepbd Vepdf Vepab Vepac Vepde))((p1p2_2671 Vpldl Vepbd Vepdf Vepab Vepac Vepde)))(p1p2_2632 Vpldl Vepbd Vepdf Vepab Vepac Vepde))). Qed. Lemma p1p2_2673: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(el q m). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))=>((lsym m q) Velmq)). Qed. Lemma p1p2_2674: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(pl h m). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))=>((lcon h q m) (conj p1p2_26 (p1p2_2673 Vpldl Vepbd Vepdf Vepab Vepac Velmq)))). Qed. Lemma p1p2_2675: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h) \/ (el m p). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))=>((unique m p d h) (conj p1p2_6 (conj p1p2_17 (conj (p1p2_2674 Vpldl Vepbd Vepdf Vepab Vepac Velmq) p1p2_25))))). Qed. Lemma p1p2_2676: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(ep h d). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))=>((psym d h) Vepdh)). Qed. Lemma p1p2_2685: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(pl h r). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))=>((pcon h d r) (conj (p1p2_2676 Vpldl Vepbd Vepdf Vepab Vepac Velmq Vepdh) p1p2_19))). Qed. Lemma p1p2_2690: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(ep d e) \/ (el m o). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))=>((unique m o d e) (conj p1p2_6 (conj (p1p2_2610 Vpldl Vepbd Vepdf Vepab Vepac) (conj p1p2_14 p1p2_16))))). Qed. Lemma p1p2_2707: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(ep d e)->(ep b g) \/ (el n o). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Vepde:(ep d e))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_2609 Vpldl Vepbd Vepdf Vepab Vepac) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_2708: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(ep d e)->(ep b g)->(ep g b). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Vepde:(ep d e))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_2724: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(ep d e)->(ep b g)->(pl g r). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Vepde:(ep d e))(Vepbg:(ep b g))=>((pcon g b r) (conj (p1p2_2708 Vpldl Vepbd Vepdf Vepab Vepac Velmq Vepdh Vepde Vepbg) (p1p2_2576 Vpldl Vepbd)))). Qed. Lemma p1p2_2725: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(ep d e)->(ep b g)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Vepde:(ep d e))(Vepbg:(ep b g))=>((goal4 r) (conj p1p2_44 (conj (p1p2_2724 Vpldl Vepbd Vepdf Vepab Vepac Velmq Vepdh Vepde Vepbg) (conj (p1p2_2685 Vpldl Vepbd Vepdf Vepab Vepac Velmq Vepdh) p1p2_27))))). Qed. Lemma p1p2_2726: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(ep d e)->(el n o)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Vepde:(ep d e))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_2727: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(ep d e)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Vepde:(ep d e))=>((or_ind ((p1p2_2725 Vpldl Vepbd Vepdf Vepab Vepac Velmq Vepdh Vepde))((p1p2_2726 Vpldl Vepbd Vepdf Vepab Vepac Velmq Vepdh Vepde)))(p1p2_2707 Vpldl Vepbd Vepdf Vepab Vepac Velmq Vepdh Vepde))). Qed. Lemma p1p2_2728: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(el m o)->(el o m). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Velmo:(el m o))=>((lsym m o) Velmo)). Qed. Lemma p1p2_2731: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(el m o)->(pl g m). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Velmo:(el m o))=>((lcon g o m) (conj p1p2_24 (p1p2_2728 Vpldl Vepbd Vepdf Vepab Vepac Velmq Vepdh Velmo)))). Qed. Lemma p1p2_2733: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(el m o)->(ep d g) \/ (el m n). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Velmo:(el m o))=>((unique m n d g) (conj p1p2_6 (conj (p1p2_2577 Vpldl Vepbd) (conj (p1p2_2731 Vpldl Vepbd Vepdf Vepab Vepac Velmq Vepdh Velmo) p1p2_23))))). Qed. Lemma p1p2_2734: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(el m o)->(ep d g)->(ep g d). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Velmo:(el m o))(Vepdg:(ep d g))=>((psym d g) Vepdg)). Qed. Lemma p1p2_2746: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(el m o)->(ep d g)->(pl g r). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Velmo:(el m o))(Vepdg:(ep d g))=>((pcon g d r) (conj (p1p2_2734 Vpldl Vepbd Vepdf Vepab Vepac Velmq Vepdh Velmo Vepdg) p1p2_19))). Qed. Lemma p1p2_2747: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(el m o)->(ep d g)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Velmo:(el m o))(Vepdg:(ep d g))=>((goal4 r) (conj p1p2_44 (conj (p1p2_2746 Vpldl Vepbd Vepdf Vepab Vepac Velmq Vepdh Velmo Vepdg) (conj (p1p2_2685 Vpldl Vepbd Vepdf Vepab Vepac Velmq Vepdh) p1p2_27))))). Qed. Lemma p1p2_2751: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(el m o)->(el m n)->(el o n). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Velmo:(el m o))(Velmn:(el m n))=>((ltra o m n) (conj (p1p2_2728 Vpldl Vepbd Vepdf Vepab Vepac Velmq Vepdh Velmo) Velmn))). Qed. Lemma p1p2_2752: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(el m o)->(el m n)->(el n o). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Velmo:(el m o))(Velmn:(el m n))=>((lsym o n) (p1p2_2751 Vpldl Vepbd Vepdf Vepab Vepac Velmq Vepdh Velmo Velmn))). Qed. Lemma p1p2_2753: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(el m o)->(el m n)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Velmo:(el m o))(Velmn:(el m n))=>(goal1 (p1p2_2752 Vpldl Vepbd Vepdf Vepab Vepac Velmq Vepdh Velmo Velmn))). Qed. Lemma p1p2_2754: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->(el m o)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Velmo:(el m o))=>((or_ind ((p1p2_2747 Vpldl Vepbd Vepdf Vepab Vepac Velmq Vepdh Velmo))((p1p2_2753 Vpldl Vepbd Vepdf Vepab Vepac Velmq Vepdh Velmo)))(p1p2_2733 Vpldl Vepbd Vepdf Vepab Vepac Velmq Vepdh Velmo))). Qed. Lemma p1p2_2755: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(ep d h)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))=>((or_ind ((p1p2_2727 Vpldl Vepbd Vepdf Vepab Vepac Velmq Vepdh))((p1p2_2754 Vpldl Vepbd Vepdf Vepab Vepac Velmq Vepdh)))(p1p2_2690 Vpldl Vepbd Vepdf Vepab Vepac Velmq Vepdh))). Qed. Lemma p1p2_2757: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(el m p)->(el q p). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Velmp:(el m p))=>((ltra q m p) (conj (p1p2_2673 Vpldl Vepbd Vepdf Vepab Vepac Velmq) Velmp))). Qed. Lemma p1p2_2758: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(el m p)->(el p q). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Velmp:(el m p))=>((lsym q p) (p1p2_2757 Vpldl Vepbd Vepdf Vepab Vepac Velmq Velmp))). Qed. Lemma p1p2_2759: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(el m q)->(el m p)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))(Velmp:(el m p))=>(goal2 (p1p2_2758 Vpldl Vepbd Vepdf Vepab Vepac Velmq Velmp))). Qed. Lemma p1p2_2760: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->(el m q)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))(Velmq:(el m q))=>((or_ind ((p1p2_2755 Vpldl Vepbd Vepdf Vepab Vepac Velmq))((p1p2_2759 Vpldl Vepbd Vepdf Vepab Vepac Velmq)))(p1p2_2675 Vpldl Vepbd Vepdf Vepab Vepac Velmq))). Qed. Lemma p1p2_2761: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(ep a c)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepac:(ep a c))=>((or_ind ((p1p2_2672 Vpldl Vepbd Vepdf Vepab Vepac))((p1p2_2760 Vpldl Vepbd Vepdf Vepab Vepac)))(p1p2_2617 Vpldl Vepbd Vepdf Vepab Vepac))). Qed. Lemma p1p2_2762: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(el r l). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))=>((lsym l r) Vellr)). Qed. Lemma p1p2_2763: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(pl i l). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))=>((lcon i r l) (conj p1p2_27 (p1p2_2762 Vpldl Vepbd Vepdf Vepab Vellr)))). Qed. Lemma p1p2_2764: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i) \/ (el l s). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))=>((unique l s a i) (conj p1p2_5 (conj p1p2_12 (conj (p1p2_2763 Vpldl Vepbd Vepdf Vepab Vellr) p1p2_28))))). Qed. Lemma p1p2_2765: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep i a). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))=>((psym a i) Vepai)). Qed. Lemma p1p2_2772: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(pl i q). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))=>((pcon i a q) (conj (p1p2_2765 Vpldl Vepbd Vepdf Vepab Vellr Vepai) p1p2_10))). Qed. Lemma p1p2_2773: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(pl i n). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))=>((pcon i a n) (conj (p1p2_2765 Vpldl Vepbd Vepdf Vepab Vellr Vepai) (p1p2_2593 Vpldl Vepbd Vepdf Vepab)))). Qed. Lemma p1p2_2774: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(pl i p). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))=>((pcon i a p) (conj (p1p2_2765 Vpldl Vepbd Vepdf Vepab Vellr Vepai) (p1p2_2594 Vpldl Vepbd Vepdf Vepab)))). Qed. Lemma p1p2_2776: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e) \/ (el m q). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))=>((unique m q d e) (conj p1p2_6 (conj (p1p2_2598 Vpldl Vepbd Vepdf Vepab) (conj p1p2_14 p1p2_18))))). Qed. Lemma p1p2_2786: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(pl d o). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))=>((pcon d e o) (conj Vepde p1p2_16))). Qed. Lemma p1p2_2787: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(pl b o). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))=>((pcon b d o) (conj Vepbd (p1p2_2786 Vpldl Vepbd Vepdf Vepab Vellr Vepai Vepde)))). Qed. Lemma p1p2_2789: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(pl a o). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))=>((pcon a b o) (conj Vepab (p1p2_2787 Vpldl Vepbd Vepdf Vepab Vellr Vepai Vepde)))). Qed. Lemma p1p2_2796: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(ep a c) \/ (el l o). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))=>((unique l o a c) (conj p1p2_5 (conj (p1p2_2789 Vpldl Vepbd Vepdf Vepab Vellr Vepai Vepde) (conj p1p2_21 p1p2_8))))). Qed. Lemma p1p2_2813: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(ep a c)->(ep b g) \/ (el n o). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vepac:(ep a c))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_2787 Vpldl Vepbd Vepdf Vepab Vellr Vepai Vepde) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_2814: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(ep a c)->(ep b g)->(ep g b). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vepac:(ep a c))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_2827: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(ep a c)->(ep b g)->(pl g p). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vepac:(ep a c))(Vepbg:(ep b g))=>((pcon g b p) (conj (p1p2_2814 Vpldl Vepbd Vepdf Vepab Vellr Vepai Vepde Vepac Vepbg) p1p2_9))). Qed. Lemma p1p2_2828: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(ep a c)->(ep b g)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vepac:(ep a c))(Vepbg:(ep b g))=>((goal4 p) (conj p1p2_42 (conj (p1p2_2827 Vpldl Vepbd Vepdf Vepab Vellr Vepai Vepde Vepac Vepbg) (conj p1p2_25 (p1p2_2774 Vpldl Vepbd Vepdf Vepab Vellr Vepai)))))). Qed. Lemma p1p2_2829: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(ep a c)->(el n o)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vepac:(ep a c))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_2830: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(ep a c)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vepac:(ep a c))=>((or_ind ((p1p2_2828 Vpldl Vepbd Vepdf Vepab Vellr Vepai Vepde Vepac))((p1p2_2829 Vpldl Vepbd Vepdf Vepab Vellr Vepai Vepde Vepac)))(p1p2_2813 Vpldl Vepbd Vepdf Vepab Vellr Vepai Vepde Vepac))). Qed. Lemma p1p2_2831: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(el l o)->(el o l). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vello:(el l o))=>((lsym l o) Vello)). Qed. Lemma p1p2_2834: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(el l o)->(pl g l). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vello:(el l o))=>((lcon g o l) (conj p1p2_24 (p1p2_2831 Vpldl Vepbd Vepdf Vepab Vellr Vepai Vepde Vello)))). Qed. Lemma p1p2_2836: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(el l o)->(ep a g) \/ (el l n). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vello:(el l o))=>((unique l n a g) (conj p1p2_5 (conj (p1p2_2593 Vpldl Vepbd Vepdf Vepab) (conj (p1p2_2834 Vpldl Vepbd Vepdf Vepab Vellr Vepai Vepde Vello) p1p2_23))))). Qed. Lemma p1p2_2837: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(el l o)->(ep a g)->(ep g a). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vello:(el l o))(Vepag:(ep a g))=>((psym a g) Vepag)). Qed. Lemma p1p2_2848: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(el l o)->(ep a g)->(pl g q). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vello:(el l o))(Vepag:(ep a g))=>((pcon g a q) (conj (p1p2_2837 Vpldl Vepbd Vepdf Vepab Vellr Vepai Vepde Vello Vepag) p1p2_10))). Qed. Lemma p1p2_2849: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(el l o)->(ep a g)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vello:(el l o))(Vepag:(ep a g))=>((goal4 q) (conj p1p2_43 (conj (p1p2_2848 Vpldl Vepbd Vepdf Vepab Vellr Vepai Vepde Vello Vepag) (conj p1p2_26 (p1p2_2772 Vpldl Vepbd Vepdf Vepab Vellr Vepai)))))). Qed. Lemma p1p2_2853: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(el l o)->(el l n)->(el o n). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vello:(el l o))(Velln:(el l n))=>((ltra o l n) (conj (p1p2_2831 Vpldl Vepbd Vepdf Vepab Vellr Vepai Vepde Vello) Velln))). Qed. Lemma p1p2_2854: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(el l o)->(el l n)->(el n o). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vello:(el l o))(Velln:(el l n))=>((lsym o n) (p1p2_2853 Vpldl Vepbd Vepdf Vepab Vellr Vepai Vepde Vello Velln))). Qed. Lemma p1p2_2855: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(el l o)->(el l n)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vello:(el l o))(Velln:(el l n))=>(goal1 (p1p2_2854 Vpldl Vepbd Vepdf Vepab Vellr Vepai Vepde Vello Velln))). Qed. Lemma p1p2_2856: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->(el l o)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vello:(el l o))=>((or_ind ((p1p2_2849 Vpldl Vepbd Vepdf Vepab Vellr Vepai Vepde Vello))((p1p2_2855 Vpldl Vepbd Vepdf Vepab Vellr Vepai Vepde Vello)))(p1p2_2836 Vpldl Vepbd Vepdf Vepab Vellr Vepai Vepde Vello))). Qed. Lemma p1p2_2857: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(ep d e)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))=>((or_ind ((p1p2_2830 Vpldl Vepbd Vepdf Vepab Vellr Vepai Vepde))((p1p2_2856 Vpldl Vepbd Vepdf Vepab Vellr Vepai Vepde)))(p1p2_2796 Vpldl Vepbd Vepdf Vepab Vellr Vepai Vepde))). Qed. Lemma p1p2_2858: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(el m q)->(el q m). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Velmq:(el m q))=>((lsym m q) Velmq)). Qed. Lemma p1p2_2859: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(el m q)->(pl h m). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Velmq:(el m q))=>((lcon h q m) (conj p1p2_26 (p1p2_2858 Vpldl Vepbd Vepdf Vepab Vellr Vepai Velmq)))). Qed. Lemma p1p2_2860: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(el m q)->(ep d h) \/ (el m p). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Velmq:(el m q))=>((unique m p d h) (conj p1p2_6 (conj p1p2_17 (conj (p1p2_2859 Vpldl Vepbd Vepdf Vepab Vellr Vepai Velmq) p1p2_25))))). Qed. Lemma p1p2_2861: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(el m q)->(ep d h)->(ep h d). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Velmq:(el m q))(Vepdh:(ep d h))=>((psym d h) Vepdh)). Qed. Lemma p1p2_2872: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(el m q)->(ep d h)->(pl h n). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Velmq:(el m q))(Vepdh:(ep d h))=>((pcon h d n) (conj (p1p2_2861 Vpldl Vepbd Vepdf Vepab Vellr Vepai Velmq Vepdh) (p1p2_2577 Vpldl Vepbd)))). Qed. Lemma p1p2_2873: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(el m q)->(ep d h)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Velmq:(el m q))(Vepdh:(ep d h))=>((goal4 n) (conj p1p2_40 (conj p1p2_23 (conj (p1p2_2872 Vpldl Vepbd Vepdf Vepab Vellr Vepai Velmq Vepdh) (p1p2_2773 Vpldl Vepbd Vepdf Vepab Vellr Vepai)))))). Qed. Lemma p1p2_2875: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(el m q)->(el m p)->(el q p). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Velmq:(el m q))(Velmp:(el m p))=>((ltra q m p) (conj (p1p2_2858 Vpldl Vepbd Vepdf Vepab Vellr Vepai Velmq) Velmp))). Qed. Lemma p1p2_2876: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(el m q)->(el m p)->(el p q). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Velmq:(el m q))(Velmp:(el m p))=>((lsym q p) (p1p2_2875 Vpldl Vepbd Vepdf Vepab Vellr Vepai Velmq Velmp))). Qed. Lemma p1p2_2877: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(el m q)->(el m p)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Velmq:(el m q))(Velmp:(el m p))=>(goal2 (p1p2_2876 Vpldl Vepbd Vepdf Vepab Vellr Vepai Velmq Velmp))). Qed. Lemma p1p2_2878: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->(el m q)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))(Velmq:(el m q))=>((or_ind ((p1p2_2873 Vpldl Vepbd Vepdf Vepab Vellr Vepai Velmq))((p1p2_2877 Vpldl Vepbd Vepdf Vepab Vellr Vepai Velmq)))(p1p2_2860 Vpldl Vepbd Vepdf Vepab Vellr Vepai Velmq))). Qed. Lemma p1p2_2879: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(ep a i)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vepai:(ep a i))=>((or_ind ((p1p2_2857 Vpldl Vepbd Vepdf Vepab Vellr Vepai))((p1p2_2878 Vpldl Vepbd Vepdf Vepab Vellr Vepai)))(p1p2_2776 Vpldl Vepbd Vepdf Vepab Vellr Vepai))). Qed. Lemma p1p2_2881: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(el l s)->(el r s). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vells:(el l s))=>((ltra r l s) (conj (p1p2_2762 Vpldl Vepbd Vepdf Vepab Vellr) Vells))). Qed. Lemma p1p2_2882: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(el l s)->(el s r). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vells:(el l s))=>((lsym r s) (p1p2_2881 Vpldl Vepbd Vepdf Vepab Vellr Vells))). Qed. Lemma p1p2_2883: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->(el l s)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))(Vells:(el l s))=>(goal3 (p1p2_2882 Vpldl Vepbd Vepdf Vepab Vellr Vells))). Qed. Lemma p1p2_2884: (pl d l)->(ep b d)->(ep d f)->(ep a b)->(el l r)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellr:(el l r))=>((or_ind ((p1p2_2879 Vpldl Vepbd Vepdf Vepab Vellr))((p1p2_2883 Vpldl Vepbd Vepdf Vepab Vellr)))(p1p2_2764 Vpldl Vepbd Vepdf Vepab Vellr))). Qed. Lemma p1p2_2885: (pl d l)->(ep b d)->(ep d f)->(ep a b)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))=>((or_ind ((p1p2_2761 Vpldl Vepbd Vepdf Vepab))((p1p2_2884 Vpldl Vepbd Vepdf Vepab)))(p1p2_2600 Vpldl Vepbd Vepdf Vepab))). Qed. Lemma p1p2_2886: (pl d l)->(ep b d)->(ep d f)->(el l s)->(el s l). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))=>((lsym l s) Vells)). Qed. Lemma p1p2_2888: (pl d l)->(ep b d)->(ep d f)->(el l s)->(pl i l). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))=>((lcon i s l) (conj p1p2_28 (p1p2_2886 Vpldl Vepbd Vepdf Vells)))). Qed. Lemma p1p2_2889: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d) \/ (el r l). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))=>((unique r l c d) (conj p1p2_11 (conj p1p2_21 (conj p1p2_19 Vpldl))))). Qed. Lemma p1p2_2890: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(ep d c). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))=>((psym c d) Vepcd)). Qed. Lemma p1p2_2896: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(pl c p). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))=>((pcon c d p) (conj Vepcd p1p2_17))). Qed. Lemma p1p2_2898: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(pl d o). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))=>((pcon d c o) (conj (p1p2_2890 Vpldl Vepbd Vepdf Vells Vepcd) p1p2_8))). Qed. Lemma p1p2_2899: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(pl b o). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))=>((pcon b d o) (conj Vepbd (p1p2_2898 Vpldl Vepbd Vepdf Vells Vepcd)))). Qed. Lemma p1p2_2901: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(ep d e) \/ (el m o). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))=>((unique m o d e) (conj p1p2_6 (conj (p1p2_2898 Vpldl Vepbd Vepdf Vells Vepcd) (conj p1p2_14 p1p2_16))))). Qed. Lemma p1p2_2909: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(pl d q). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))=>((pcon d e q) (conj Vepde p1p2_18))). Qed. Lemma p1p2_2910: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(pl b q). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))=>((pcon b d q) (conj Vepbd (p1p2_2909 Vpldl Vepbd Vepdf Vells Vepcd Vepde)))). Qed. Lemma p1p2_2918: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(ep a b) \/ (el l q). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))=>((unique l q a b) (conj p1p2_5 (conj p1p2_10 (conj p1p2_13 (p1p2_2910 Vpldl Vepbd Vepdf Vells Vepcd Vepde)))))). Qed. Lemma p1p2_2929: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(ep a b)->(pl a p). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))=>((pcon a b p) (conj Vepab p1p2_9))). Qed. Lemma p1p2_2931: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(ep a b)->(pl a r). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))=>((pcon a b r) (conj Vepab (p1p2_2576 Vpldl Vepbd)))). Qed. Lemma p1p2_2933: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(ep a b)->(ep a i) \/ (el l r). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))=>((unique l r a i) (conj p1p2_5 (conj (p1p2_2931 Vpldl Vepbd Vepdf Vells Vepcd Vepde Vepab) (conj (p1p2_2888 Vpldl Vepbd Vepdf Vells) p1p2_27))))). Qed. Lemma p1p2_2934: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(ep a b)->(ep a i)->(ep i a). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepai:(ep a i))=>((psym a i) Vepai)). Qed. Lemma p1p2_2947: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(ep a b)->(ep a i)->(pl i p). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepai:(ep a i))=>((pcon i a p) (conj (p1p2_2934 Vpldl Vepbd Vepdf Vells Vepcd Vepde Vepab Vepai) (p1p2_2929 Vpldl Vepbd Vepdf Vells Vepcd Vepde Vepab)))). Qed. Lemma p1p2_2950: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(ep a b)->(ep a i)->(ep b g) \/ (el n o). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepai:(ep a i))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_2899 Vpldl Vepbd Vepdf Vells Vepcd) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_2951: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(ep a b)->(ep a i)->(ep b g)->(ep g b). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepai:(ep a i))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_2964: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(ep a b)->(ep a i)->(ep b g)->(pl g p). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepai:(ep a i))(Vepbg:(ep b g))=>((pcon g b p) (conj (p1p2_2951 Vpldl Vepbd Vepdf Vells Vepcd Vepde Vepab Vepai Vepbg) p1p2_9))). Qed. Lemma p1p2_2965: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(ep a b)->(ep a i)->(ep b g)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepai:(ep a i))(Vepbg:(ep b g))=>((goal4 p) (conj p1p2_42 (conj (p1p2_2964 Vpldl Vepbd Vepdf Vells Vepcd Vepde Vepab Vepai Vepbg) (conj p1p2_25 (p1p2_2947 Vpldl Vepbd Vepdf Vells Vepcd Vepde Vepab Vepai)))))). Qed. Lemma p1p2_2966: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(ep a b)->(ep a i)->(el n o)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepai:(ep a i))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_2967: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(ep a b)->(ep a i)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepai:(ep a i))=>((or_ind ((p1p2_2965 Vpldl Vepbd Vepdf Vells Vepcd Vepde Vepab Vepai))((p1p2_2966 Vpldl Vepbd Vepdf Vells Vepcd Vepde Vepab Vepai)))(p1p2_2950 Vpldl Vepbd Vepdf Vells Vepcd Vepde Vepab Vepai))). Qed. Lemma p1p2_2969: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(ep a b)->(el l r)->(el s r). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vellr:(el l r))=>((ltra s l r) (conj (p1p2_2886 Vpldl Vepbd Vepdf Vells) Vellr))). Qed. Lemma p1p2_2970: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(ep a b)->(el l r)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vellr:(el l r))=>(goal3 (p1p2_2969 Vpldl Vepbd Vepdf Vells Vepcd Vepde Vepab Vellr))). Qed. Lemma p1p2_2971: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(ep a b)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))=>((or_ind ((p1p2_2967 Vpldl Vepbd Vepdf Vells Vepcd Vepde Vepab))((p1p2_2970 Vpldl Vepbd Vepdf Vells Vepcd Vepde Vepab)))(p1p2_2933 Vpldl Vepbd Vepdf Vells Vepcd Vepde Vepab))). Qed. Lemma p1p2_2972: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(el l q)->(el q l). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))=>((lsym l q) Vellq)). Qed. Lemma p1p2_2975: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(el l q)->(pl h l). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))=>((lcon h q l) (conj p1p2_26 (p1p2_2972 Vpldl Vepbd Vepdf Vells Vepcd Vepde Vellq)))). Qed. Lemma p1p2_2978: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(el l q)->(ep b g) \/ (el n o). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_2899 Vpldl Vepbd Vepdf Vells Vepcd) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_2979: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(el l q)->(ep b g)->(ep g b). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_2989: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(el l q)->(ep b g)->(pl g l). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Vepbg:(ep b g))=>((pcon g b l) (conj (p1p2_2979 Vpldl Vepbd Vepdf Vells Vepcd Vepde Vellq Vepbg) p1p2_13))). Qed. Lemma p1p2_2990: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(el l q)->(ep b g)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Vepbg:(ep b g))=>((goal4 l) (conj p1p2_38 (conj (p1p2_2989 Vpldl Vepbd Vepdf Vells Vepcd Vepde Vellq Vepbg) (conj (p1p2_2975 Vpldl Vepbd Vepdf Vells Vepcd Vepde Vellq) (p1p2_2888 Vpldl Vepbd Vepdf Vells)))))). Qed. Lemma p1p2_2991: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(el l q)->(el n o)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_2992: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(ep d e)->(el l q)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))=>((or_ind ((p1p2_2990 Vpldl Vepbd Vepdf Vells Vepcd Vepde Vellq))((p1p2_2991 Vpldl Vepbd Vepdf Vells Vepcd Vepde Vellq)))(p1p2_2978 Vpldl Vepbd Vepdf Vells Vepcd Vepde Vellq))). Qed. Lemma p1p2_2993: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(ep d e)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Vepde:(ep d e))=>((or_ind ((p1p2_2971 Vpldl Vepbd Vepdf Vells Vepcd Vepde))((p1p2_2992 Vpldl Vepbd Vepdf Vells Vepcd Vepde)))(p1p2_2918 Vpldl Vepbd Vepdf Vells Vepcd Vepde))). Qed. Lemma p1p2_2994: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(el m o)->(el o m). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))=>((lsym m o) Velmo)). Qed. Lemma p1p2_2995: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(el m o)->(pl g m). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))=>((lcon g o m) (conj p1p2_24 (p1p2_2994 Vpldl Vepbd Vepdf Vells Vepcd Velmo)))). Qed. Lemma p1p2_2996: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(el m o)->(ep d g) \/ (el m n). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))=>((unique m n d g) (conj p1p2_6 (conj (p1p2_2577 Vpldl Vepbd) (conj (p1p2_2995 Vpldl Vepbd Vepdf Vells Vepcd Velmo) p1p2_23))))). Qed. Lemma p1p2_2997: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(el m o)->(ep d g)->(ep g d). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))(Vepdg:(ep d g))=>((psym d g) Vepdg)). Qed. Lemma p1p2_3004: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(el m o)->(ep d g)->(pl g p). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))(Vepdg:(ep d g))=>((pcon g d p) (conj (p1p2_2997 Vpldl Vepbd Vepdf Vells Vepcd Velmo Vepdg) p1p2_17))). Qed. Lemma p1p2_3008: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(el m o)->(ep d g)->(ep c i) \/ (el r l). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))(Vepdg:(ep d g))=>((unique r l c i) (conj p1p2_11 (conj p1p2_21 (conj p1p2_27 (p1p2_2888 Vpldl Vepbd Vepdf Vells)))))). Qed. Lemma p1p2_3009: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(el m o)->(ep d g)->(ep c i)->(ep i c). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))(Vepdg:(ep d g))(Vepci:(ep c i))=>((psym c i) Vepci)). Qed. Lemma p1p2_3020: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(el m o)->(ep d g)->(ep c i)->(pl i p). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))(Vepdg:(ep d g))(Vepci:(ep c i))=>((pcon i c p) (conj (p1p2_3009 Vpldl Vepbd Vepdf Vells Vepcd Velmo Vepdg Vepci) (p1p2_2896 Vpldl Vepbd Vepdf Vells Vepcd)))). Qed. Lemma p1p2_3021: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(el m o)->(ep d g)->(ep c i)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))(Vepdg:(ep d g))(Vepci:(ep c i))=>((goal4 p) (conj p1p2_42 (conj (p1p2_3004 Vpldl Vepbd Vepdf Vells Vepcd Velmo Vepdg) (conj p1p2_25 (p1p2_3020 Vpldl Vepbd Vepdf Vells Vepcd Velmo Vepdg Vepci)))))). Qed. Lemma p1p2_3022: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(el m o)->(ep d g)->(el r l)->(el l r). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))(Vepdg:(ep d g))(Velrl:(el r l))=>((lsym r l) Velrl)). Qed. Lemma p1p2_3023: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(el m o)->(ep d g)->(el r l)->(el s r). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))(Vepdg:(ep d g))(Velrl:(el r l))=>((ltra s l r) (conj (p1p2_2886 Vpldl Vepbd Vepdf Vells) (p1p2_3022 Vpldl Vepbd Vepdf Vells Vepcd Velmo Vepdg Velrl)))). Qed. Lemma p1p2_3024: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(el m o)->(ep d g)->(el r l)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))(Vepdg:(ep d g))(Velrl:(el r l))=>(goal3 (p1p2_3023 Vpldl Vepbd Vepdf Vells Vepcd Velmo Vepdg Velrl))). Qed. Lemma p1p2_3025: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(el m o)->(ep d g)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))(Vepdg:(ep d g))=>((or_ind ((p1p2_3021 Vpldl Vepbd Vepdf Vells Vepcd Velmo Vepdg))((p1p2_3024 Vpldl Vepbd Vepdf Vells Vepcd Velmo Vepdg)))(p1p2_3008 Vpldl Vepbd Vepdf Vells Vepcd Velmo Vepdg))). Qed. Lemma p1p2_3027: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(el m o)->(el m n)->(el o n). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))(Velmn:(el m n))=>((ltra o m n) (conj (p1p2_2994 Vpldl Vepbd Vepdf Vells Vepcd Velmo) Velmn))). Qed. Lemma p1p2_3028: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(el m o)->(el m n)->(el n o). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))(Velmn:(el m n))=>((lsym o n) (p1p2_3027 Vpldl Vepbd Vepdf Vells Vepcd Velmo Velmn))). Qed. Lemma p1p2_3029: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(el m o)->(el m n)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))(Velmn:(el m n))=>(goal1 (p1p2_3028 Vpldl Vepbd Vepdf Vells Vepcd Velmo Velmn))). Qed. Lemma p1p2_3030: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->(el m o)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))(Velmo:(el m o))=>((or_ind ((p1p2_3025 Vpldl Vepbd Vepdf Vells Vepcd Velmo))((p1p2_3029 Vpldl Vepbd Vepdf Vells Vepcd Velmo)))(p1p2_2996 Vpldl Vepbd Vepdf Vells Vepcd Velmo))). Qed. Lemma p1p2_3031: (pl d l)->(ep b d)->(ep d f)->(el l s)->(ep c d)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepcd:(ep c d))=>((or_ind ((p1p2_2993 Vpldl Vepbd Vepdf Vells Vepcd))((p1p2_3030 Vpldl Vepbd Vepdf Vells Vepcd)))(p1p2_2901 Vpldl Vepbd Vepdf Vells Vepcd))). Qed. Lemma p1p2_3032: (pl d l)->(ep b d)->(ep d f)->(el l s)->(el r l)->(el l r). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Velrl:(el r l))=>((lsym r l) Velrl)). Qed. Lemma p1p2_3033: (pl d l)->(ep b d)->(ep d f)->(el l s)->(el r l)->(el s r). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Velrl:(el r l))=>((ltra s l r) (conj (p1p2_2886 Vpldl Vepbd Vepdf Vells) (p1p2_3032 Vpldl Vepbd Vepdf Vells Velrl)))). Qed. Lemma p1p2_3034: (pl d l)->(ep b d)->(ep d f)->(el l s)->(el r l)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Velrl:(el r l))=>(goal3 (p1p2_3033 Vpldl Vepbd Vepdf Vells Velrl))). Qed. Lemma p1p2_3035: (pl d l)->(ep b d)->(ep d f)->(el l s)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))=>((or_ind ((p1p2_3031 Vpldl Vepbd Vepdf Vells))((p1p2_3034 Vpldl Vepbd Vepdf Vells)))(p1p2_2889 Vpldl Vepbd Vepdf Vells))). Qed. Lemma p1p2_3036: (pl d l)->(ep b d)->(ep d f)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Vepdf:(ep d f))=>((or_ind ((p1p2_2885 Vpldl Vepbd Vepdf))((p1p2_3035 Vpldl Vepbd Vepdf)))(p1p2_2587 Vpldl Vepbd Vepdf))). Qed. Lemma p1p2_3037: (pl d l)->(ep b d)->(el m n)->(el n m). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))=>((lsym m n) Velmn)). Qed. Lemma p1p2_3039: (pl d l)->(ep b d)->(el m n)->(pl g m). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))=>((lcon g n m) (conj p1p2_23 (p1p2_3037 Vpldl Vepbd Velmn)))). Qed. Lemma p1p2_3040: (pl d l)->(ep b d)->(el m n)->(ep c d) \/ (el r l). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))=>((unique r l c d) (conj p1p2_11 (conj p1p2_21 (conj p1p2_19 Vpldl))))). Qed. Lemma p1p2_3041: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d c). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))=>((psym c d) Vepcd)). Qed. Lemma p1p2_3047: (pl d l)->(ep b d)->(el m n)->(ep c d)->(pl d o). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))=>((pcon d c o) (conj (p1p2_3041 Vpldl Vepbd Velmn Vepcd) p1p2_8))). Qed. Lemma p1p2_3049: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e) \/ (el m o). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))=>((unique m o d e) (conj p1p2_6 (conj (p1p2_3047 Vpldl Vepbd Velmn Vepcd) (conj p1p2_14 p1p2_16))))). Qed. Lemma p1p2_3055: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(pl d q). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))=>((pcon d e q) (conj Vepde p1p2_18))). Qed. Lemma p1p2_3056: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(pl b q). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))=>((pcon b d q) (conj Vepbd (p1p2_3055 Vpldl Vepbd Velmn Vepcd Vepde)))). Qed. Lemma p1p2_3061: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(ep a b) \/ (el l q). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))=>((unique l q a b) (conj p1p2_5 (conj p1p2_10 (conj p1p2_13 (p1p2_3056 Vpldl Vepbd Velmn Vepcd Vepde)))))). Qed. Lemma p1p2_3062: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep b a). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))=>((psym a b) Vepab)). Qed. Lemma p1p2_3074: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(pl b s). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))=>((pcon b a s) (conj (p1p2_3062 Vpldl Vepbd Velmn Vepcd Vepde Vepab) p1p2_12))). Qed. Lemma p1p2_3075: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(pl d s). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))=>((pcon d b s) (conj (p1p2_2574 Vpldl Vepbd) (p1p2_3074 Vpldl Vepbd Velmn Vepcd Vepde Vepab)))). Qed. Lemma p1p2_3078: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g) \/ (el m o). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))=>((unique m o d g) (conj p1p2_6 (conj (p1p2_3047 Vpldl Vepbd Velmn Vepcd) (conj (p1p2_3039 Vpldl Vepbd Velmn) p1p2_24))))). Qed. Lemma p1p2_3079: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(ep g d). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))=>((psym d g) Vepdg)). Qed. Lemma p1p2_3088: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(pl g p). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))=>((pcon g d p) (conj (p1p2_3079 Vpldl Vepbd Velmn Vepcd Vepde Vepab Vepdg) p1p2_17))). Qed. Lemma p1p2_3089: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(pl g r). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))=>((pcon g d r) (conj (p1p2_3079 Vpldl Vepbd Velmn Vepcd Vepde Vepab Vepdg) p1p2_19))). Qed. Lemma p1p2_3093: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(ep d f) \/ (el m s). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))=>((unique m s d f) (conj p1p2_6 (conj (p1p2_3075 Vpldl Vepbd Velmn Vepcd Vepde Vepab) (conj p1p2_22 p1p2_20))))). Qed. Lemma p1p2_3110: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(ep d f)->(ep b h) \/ (el p q). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))(Vepdf:(ep d f))=>((unique p q b h) (conj p1p2_9 (conj (p1p2_3056 Vpldl Vepbd Velmn Vepcd Vepde) (conj p1p2_25 p1p2_26))))). Qed. Lemma p1p2_3111: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(ep d f)->(ep b h)->(ep h b). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))(Vepdf:(ep d f))(Vepbh:(ep b h))=>((psym b h) Vepbh)). Qed. Lemma p1p2_3127: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(ep d f)->(ep b h)->(pl h r). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))(Vepdf:(ep d f))(Vepbh:(ep b h))=>((pcon h b r) (conj (p1p2_3111 Vpldl Vepbd Velmn Vepcd Vepde Vepab Vepdg Vepdf Vepbh) (p1p2_2576 Vpldl Vepbd)))). Qed. Lemma p1p2_3128: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(ep d f)->(ep b h)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))(Vepdf:(ep d f))(Vepbh:(ep b h))=>((goal4 r) (conj p1p2_44 (conj (p1p2_3089 Vpldl Vepbd Velmn Vepcd Vepde Vepab Vepdg) (conj (p1p2_3127 Vpldl Vepbd Velmn Vepcd Vepde Vepab Vepdg Vepdf Vepbh) p1p2_27))))). Qed. Lemma p1p2_3129: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(ep d f)->(el p q)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))(Vepdf:(ep d f))(Velpq:(el p q))=>(goal2 Velpq)). Qed. Lemma p1p2_3130: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(ep d f)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))(Vepdf:(ep d f))=>((or_ind ((p1p2_3128 Vpldl Vepbd Velmn Vepcd Vepde Vepab Vepdg Vepdf))((p1p2_3129 Vpldl Vepbd Velmn Vepcd Vepde Vepab Vepdg Vepdf)))(p1p2_3110 Vpldl Vepbd Velmn Vepcd Vepde Vepab Vepdg Vepdf))). Qed. Lemma p1p2_3131: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(el m s)->(el s m). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))(Velms:(el m s))=>((lsym m s) Velms)). Qed. Lemma p1p2_3134: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(el m s)->(pl i m). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))(Velms:(el m s))=>((lcon i s m) (conj p1p2_28 (p1p2_3131 Vpldl Vepbd Velmn Vepcd Vepde Vepab Vepdg Velms)))). Qed. Lemma p1p2_3136: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(el m s)->(ep d i) \/ (el m r). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))(Velms:(el m s))=>((unique m r d i) (conj p1p2_6 (conj p1p2_19 (conj (p1p2_3134 Vpldl Vepbd Velmn Vepcd Vepde Vepab Vepdg Velms) p1p2_27))))). Qed. Lemma p1p2_3137: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(el m s)->(ep d i)->(ep i d). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))(Velms:(el m s))(Vepdi:(ep d i))=>((psym d i) Vepdi)). Qed. Lemma p1p2_3148: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(el m s)->(ep d i)->(pl i p). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))(Velms:(el m s))(Vepdi:(ep d i))=>((pcon i d p) (conj (p1p2_3137 Vpldl Vepbd Velmn Vepcd Vepde Vepab Vepdg Velms Vepdi) p1p2_17))). Qed. Lemma p1p2_3149: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(el m s)->(ep d i)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))(Velms:(el m s))(Vepdi:(ep d i))=>((goal4 p) (conj p1p2_42 (conj (p1p2_3088 Vpldl Vepbd Velmn Vepcd Vepde Vepab Vepdg) (conj p1p2_25 (p1p2_3148 Vpldl Vepbd Velmn Vepcd Vepde Vepab Vepdg Velms Vepdi)))))). Qed. Lemma p1p2_3153: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(el m s)->(el m r)->(el s r). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))(Velms:(el m s))(Velmr:(el m r))=>((ltra s m r) (conj (p1p2_3131 Vpldl Vepbd Velmn Vepcd Vepde Vepab Vepdg Velms) Velmr))). Qed. Lemma p1p2_3154: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(el m s)->(el m r)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))(Velms:(el m s))(Velmr:(el m r))=>(goal3 (p1p2_3153 Vpldl Vepbd Velmn Vepcd Vepde Vepab Vepdg Velms Velmr))). Qed. Lemma p1p2_3155: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->(el m s)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))(Velms:(el m s))=>((or_ind ((p1p2_3149 Vpldl Vepbd Velmn Vepcd Vepde Vepab Vepdg Velms))((p1p2_3154 Vpldl Vepbd Velmn Vepcd Vepde Vepab Vepdg Velms)))(p1p2_3136 Vpldl Vepbd Velmn Vepcd Vepde Vepab Vepdg Velms))). Qed. Lemma p1p2_3156: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(ep d g)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdg:(ep d g))=>((or_ind ((p1p2_3130 Vpldl Vepbd Velmn Vepcd Vepde Vepab Vepdg))((p1p2_3155 Vpldl Vepbd Velmn Vepcd Vepde Vepab Vepdg)))(p1p2_3093 Vpldl Vepbd Velmn Vepcd Vepde Vepab Vepdg))). Qed. Lemma p1p2_3158: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(el m o)->(el n o). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Velmo:(el m o))=>((ltra n m o) (conj (p1p2_3037 Vpldl Vepbd Velmn) Velmo))). Qed. Lemma p1p2_3159: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(ep a b)->(el m o)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Velmo:(el m o))=>(goal1 (p1p2_3158 Vpldl Vepbd Velmn Vepcd Vepde Vepab Velmo))). Qed. Lemma p1p2_3160: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(ep a b)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))=>((or_ind ((p1p2_3156 Vpldl Vepbd Velmn Vepcd Vepde Vepab))((p1p2_3159 Vpldl Vepbd Velmn Vepcd Vepde Vepab)))(p1p2_3078 Vpldl Vepbd Velmn Vepcd Vepde Vepab))). Qed. Lemma p1p2_3161: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(el l q)->(el q l). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))=>((lsym l q) Vellq)). Qed. Lemma p1p2_3162: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(el l q)->(pl h l). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))=>((lcon h q l) (conj p1p2_26 (p1p2_3161 Vpldl Vepbd Velmn Vepcd Vepde Vellq)))). Qed. Lemma p1p2_3163: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(el l q)->(ep d g) \/ (el m o). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))=>((unique m o d g) (conj p1p2_6 (conj (p1p2_3047 Vpldl Vepbd Velmn Vepcd) (conj (p1p2_3039 Vpldl Vepbd Velmn) p1p2_24))))). Qed. Lemma p1p2_3164: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(el l q)->(ep d g)->(ep g d). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Vepdg:(ep d g))=>((psym d g) Vepdg)). Qed. Lemma p1p2_3172: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(el l q)->(ep d g)->(pl g r). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Vepdg:(ep d g))=>((pcon g d r) (conj (p1p2_3164 Vpldl Vepbd Velmn Vepcd Vepde Vellq Vepdg) p1p2_19))). Qed. Lemma p1p2_3175: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(el l q)->(ep d g)->(ep b h) \/ (el p l). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Vepdg:(ep d g))=>((unique p l b h) (conj p1p2_9 (conj p1p2_13 (conj p1p2_25 (p1p2_3162 Vpldl Vepbd Velmn Vepcd Vepde Vellq)))))). Qed. Lemma p1p2_3176: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(el l q)->(ep d g)->(ep b h)->(ep h b). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Vepdg:(ep d g))(Vepbh:(ep b h))=>((psym b h) Vepbh)). Qed. Lemma p1p2_3187: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(el l q)->(ep d g)->(ep b h)->(pl h r). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Vepdg:(ep d g))(Vepbh:(ep b h))=>((pcon h b r) (conj (p1p2_3176 Vpldl Vepbd Velmn Vepcd Vepde Vellq Vepdg Vepbh) (p1p2_2576 Vpldl Vepbd)))). Qed. Lemma p1p2_3188: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(el l q)->(ep d g)->(ep b h)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Vepdg:(ep d g))(Vepbh:(ep b h))=>((goal4 r) (conj p1p2_44 (conj (p1p2_3172 Vpldl Vepbd Velmn Vepcd Vepde Vellq Vepdg) (conj (p1p2_3187 Vpldl Vepbd Velmn Vepcd Vepde Vellq Vepdg Vepbh) p1p2_27))))). Qed. Lemma p1p2_3189: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(el l q)->(ep d g)->(el p l)->(el l p). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Vepdg:(ep d g))(Velpl:(el p l))=>((lsym p l) Velpl)). Qed. Lemma p1p2_3190: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(el l q)->(ep d g)->(el p l)->(el q p). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Vepdg:(ep d g))(Velpl:(el p l))=>((ltra q l p) (conj (p1p2_3161 Vpldl Vepbd Velmn Vepcd Vepde Vellq) (p1p2_3189 Vpldl Vepbd Velmn Vepcd Vepde Vellq Vepdg Velpl)))). Qed. Lemma p1p2_3191: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(el l q)->(ep d g)->(el p l)->(el p q). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Vepdg:(ep d g))(Velpl:(el p l))=>((lsym q p) (p1p2_3190 Vpldl Vepbd Velmn Vepcd Vepde Vellq Vepdg Velpl))). Qed. Lemma p1p2_3192: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(el l q)->(ep d g)->(el p l)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Vepdg:(ep d g))(Velpl:(el p l))=>(goal2 (p1p2_3191 Vpldl Vepbd Velmn Vepcd Vepde Vellq Vepdg Velpl))). Qed. Lemma p1p2_3193: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(el l q)->(ep d g)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Vepdg:(ep d g))=>((or_ind ((p1p2_3188 Vpldl Vepbd Velmn Vepcd Vepde Vellq Vepdg))((p1p2_3192 Vpldl Vepbd Velmn Vepcd Vepde Vellq Vepdg)))(p1p2_3175 Vpldl Vepbd Velmn Vepcd Vepde Vellq Vepdg))). Qed. Lemma p1p2_3195: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(el l q)->(el m o)->(el n o). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Velmo:(el m o))=>((ltra n m o) (conj (p1p2_3037 Vpldl Vepbd Velmn) Velmo))). Qed. Lemma p1p2_3196: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(el l q)->(el m o)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Velmo:(el m o))=>(goal1 (p1p2_3195 Vpldl Vepbd Velmn Vepcd Vepde Vellq Velmo))). Qed. Lemma p1p2_3197: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->(el l q)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))=>((or_ind ((p1p2_3193 Vpldl Vepbd Velmn Vepcd Vepde Vellq))((p1p2_3196 Vpldl Vepbd Velmn Vepcd Vepde Vellq)))(p1p2_3163 Vpldl Vepbd Velmn Vepcd Vepde Vellq))). Qed. Lemma p1p2_3198: (pl d l)->(ep b d)->(el m n)->(ep c d)->(ep d e)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Vepde:(ep d e))=>((or_ind ((p1p2_3160 Vpldl Vepbd Velmn Vepcd Vepde))((p1p2_3197 Vpldl Vepbd Velmn Vepcd Vepde)))(p1p2_3061 Vpldl Vepbd Velmn Vepcd Vepde))). Qed. Lemma p1p2_3200: (pl d l)->(ep b d)->(el m n)->(ep c d)->(el m o)->(el n o). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Velmo:(el m o))=>((ltra n m o) (conj (p1p2_3037 Vpldl Vepbd Velmn) Velmo))). Qed. Lemma p1p2_3201: (pl d l)->(ep b d)->(el m n)->(ep c d)->(el m o)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))(Velmo:(el m o))=>(goal1 (p1p2_3200 Vpldl Vepbd Velmn Vepcd Velmo))). Qed. Lemma p1p2_3202: (pl d l)->(ep b d)->(el m n)->(ep c d)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Vepcd:(ep c d))=>((or_ind ((p1p2_3198 Vpldl Vepbd Velmn Vepcd))((p1p2_3201 Vpldl Vepbd Velmn Vepcd)))(p1p2_3049 Vpldl Vepbd Velmn Vepcd))). Qed. Lemma p1p2_3205: (pl d l)->(ep b d)->(el m n)->(el r l)->(pl i l). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Velrl:(el r l))=>((lcon i r l) (conj p1p2_27 Velrl))). Qed. Lemma p1p2_3206: (pl d l)->(ep b d)->(el m n)->(el r l)->(ep a i) \/ (el l s). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Velrl:(el r l))=>((unique l s a i) (conj p1p2_5 (conj p1p2_12 (conj (p1p2_3205 Vpldl Vepbd Velmn Velrl) p1p2_28))))). Qed. Lemma p1p2_3207: (pl d l)->(ep b d)->(el m n)->(el r l)->(ep a i)->(ep i a). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Velrl:(el r l))(Vepai:(ep a i))=>((psym a i) Vepai)). Qed. Lemma p1p2_3208: (pl d l)->(ep b d)->(el m n)->(el r l)->(ep a i)->(pl i q). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Velrl:(el r l))(Vepai:(ep a i))=>((pcon i a q) (conj (p1p2_3207 Vpldl Vepbd Velmn Velrl Vepai) p1p2_10))). Qed. Lemma p1p2_3209: (pl d l)->(ep b d)->(el m n)->(el r l)->(ep a i)->(ep e g) \/ (el m o). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Velrl:(el r l))(Vepai:(ep a i))=>((unique m o e g) (conj p1p2_14 (conj p1p2_16 (conj (p1p2_3039 Vpldl Vepbd Velmn) p1p2_24))))). Qed. Lemma p1p2_3210: (pl d l)->(ep b d)->(el m n)->(el r l)->(ep a i)->(ep e g)->(ep g e). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Velrl:(el r l))(Vepai:(ep a i))(Vepeg:(ep e g))=>((psym e g) Vepeg)). Qed. Lemma p1p2_3211: (pl d l)->(ep b d)->(el m n)->(el r l)->(ep a i)->(ep e g)->(pl g q). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Velrl:(el r l))(Vepai:(ep a i))(Vepeg:(ep e g))=>((pcon g e q) (conj (p1p2_3210 Vpldl Vepbd Velmn Velrl Vepai Vepeg) p1p2_18))). Qed. Lemma p1p2_3212: (pl d l)->(ep b d)->(el m n)->(el r l)->(ep a i)->(ep e g)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Velrl:(el r l))(Vepai:(ep a i))(Vepeg:(ep e g))=>((goal4 q) (conj p1p2_43 (conj (p1p2_3211 Vpldl Vepbd Velmn Velrl Vepai Vepeg) (conj p1p2_26 (p1p2_3208 Vpldl Vepbd Velmn Velrl Vepai)))))). Qed. Lemma p1p2_3214: (pl d l)->(ep b d)->(el m n)->(el r l)->(ep a i)->(el m o)->(el n o). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Velrl:(el r l))(Vepai:(ep a i))(Velmo:(el m o))=>((ltra n m o) (conj (p1p2_3037 Vpldl Vepbd Velmn) Velmo))). Qed. Lemma p1p2_3215: (pl d l)->(ep b d)->(el m n)->(el r l)->(ep a i)->(el m o)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Velrl:(el r l))(Vepai:(ep a i))(Velmo:(el m o))=>(goal1 (p1p2_3214 Vpldl Vepbd Velmn Velrl Vepai Velmo))). Qed. Lemma p1p2_3216: (pl d l)->(ep b d)->(el m n)->(el r l)->(ep a i)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Velrl:(el r l))(Vepai:(ep a i))=>((or_ind ((p1p2_3212 Vpldl Vepbd Velmn Velrl Vepai))((p1p2_3215 Vpldl Vepbd Velmn Velrl Vepai)))(p1p2_3209 Vpldl Vepbd Velmn Velrl Vepai))). Qed. Lemma p1p2_3218: (pl d l)->(ep b d)->(el m n)->(el r l)->(el l s)->(el r s). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Velrl:(el r l))(Vells:(el l s))=>((ltra r l s) (conj Velrl Vells))). Qed. Lemma p1p2_3219: (pl d l)->(ep b d)->(el m n)->(el r l)->(el l s)->(el s r). Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Velrl:(el r l))(Vells:(el l s))=>((lsym r s) (p1p2_3218 Vpldl Vepbd Velmn Velrl Vells))). Qed. Lemma p1p2_3220: (pl d l)->(ep b d)->(el m n)->(el r l)->(el l s)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Velrl:(el r l))(Vells:(el l s))=>(goal3 (p1p2_3219 Vpldl Vepbd Velmn Velrl Vells))). Qed. Lemma p1p2_3221: (pl d l)->(ep b d)->(el m n)->(el r l)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))(Velrl:(el r l))=>((or_ind ((p1p2_3216 Vpldl Vepbd Velmn Velrl))((p1p2_3220 Vpldl Vepbd Velmn Velrl)))(p1p2_3206 Vpldl Vepbd Velmn Velrl))). Qed. Lemma p1p2_3222: (pl d l)->(ep b d)->(el m n)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))(Velmn:(el m n))=>((or_ind ((p1p2_3202 Vpldl Vepbd Velmn))((p1p2_3221 Vpldl Vepbd Velmn)))(p1p2_3040 Vpldl Vepbd Velmn))). Qed. Lemma p1p2_3223: (pl d l)->(ep b d)->goal. Proof. exact (fun (Vpldl:(pl d l))(Vepbd:(ep b d))=>((or_ind ((p1p2_3036 Vpldl Vepbd))((p1p2_3222 Vpldl Vepbd)))(p1p2_2578 Vpldl Vepbd))). Qed. Lemma p1p2_3227: (pl d l)->(el p l)->(pl h l). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))=>((lcon h p l) (conj p1p2_25 Velpl))). Qed. Lemma p1p2_3228: (pl d l)->(el p l)->(ep a h) \/ (el l q). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))=>((unique l q a h) (conj p1p2_5 (conj p1p2_10 (conj (p1p2_3227 Vpldl Velpl) p1p2_26))))). Qed. Lemma p1p2_3229: (pl d l)->(el p l)->(ep a h)->(ep h a). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))=>((psym a h) Vepah)). Qed. Lemma p1p2_3230: (pl d l)->(el p l)->(ep a h)->(pl h s). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))=>((pcon h a s) (conj (p1p2_3229 Vpldl Velpl Vepah) p1p2_12))). Qed. Lemma p1p2_3231: (pl d l)->(el p l)->(ep a h)->(ep c d) \/ (el r l). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))=>((unique r l c d) (conj p1p2_11 (conj p1p2_21 (conj p1p2_19 Vpldl))))). Qed. Lemma p1p2_3232: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d c). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))=>((psym c d) Vepcd)). Qed. Lemma p1p2_3234: (pl d l)->(el p l)->(ep a h)->(ep c d)->(pl d o). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))=>((pcon d c o) (conj (p1p2_3232 Vpldl Velpl Vepah Vepcd) p1p2_8))). Qed. Lemma p1p2_3235: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e) \/ (el m o). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))=>((unique m o d e) (conj p1p2_6 (conj (p1p2_3234 Vpldl Velpl Vepah Vepcd) (conj p1p2_14 p1p2_16))))). Qed. Lemma p1p2_3239: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(pl d q). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))=>((pcon d e q) (conj Vepde p1p2_18))). Qed. Lemma p1p2_3240: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(pl c q). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))=>((pcon c d q) (conj Vepcd (p1p2_3239 Vpldl Velpl Vepah Vepcd Vepde)))). Qed. Lemma p1p2_3244: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c) \/ (el l q). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))=>((unique l q a c) (conj p1p2_5 (conj p1p2_10 (conj p1p2_21 (p1p2_3240 Vpldl Velpl Vepah Vepcd Vepde)))))). Qed. Lemma p1p2_3245: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(ep c a). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))=>((psym a c) Vepac)). Qed. Lemma p1p2_3256: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(pl a o). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))=>((pcon a c o) (conj Vepac p1p2_8))). Qed. Lemma p1p2_3257: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(pl h o). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))=>((pcon h a o) (conj (p1p2_3229 Vpldl Velpl Vepah) (p1p2_3256 Vpldl Velpl Vepah Vepcd Vepde Vepac)))). Qed. Lemma p1p2_3262: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(pl c s). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))=>((pcon c a s) (conj (p1p2_3245 Vpldl Velpl Vepah Vepcd Vepde Vepac) p1p2_12))). Qed. Lemma p1p2_3263: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(pl d s). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))=>((pcon d c s) (conj (p1p2_3232 Vpldl Velpl Vepah Vepcd) (p1p2_3262 Vpldl Velpl Vepah Vepcd Vepde Vepac)))). Qed. Lemma p1p2_3265: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(ep d f) \/ (el m s). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))=>((unique m s d f) (conj p1p2_6 (conj (p1p2_3263 Vpldl Velpl Vepah Vepcd Vepde Vepac) (conj p1p2_22 p1p2_20))))). Qed. Lemma p1p2_3275: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(ep d f)->(pl d n). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Vepdf:(ep d f))=>((pcon d f n) (conj Vepdf p1p2_15))). Qed. Lemma p1p2_3276: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(ep d f)->(pl c n). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Vepdf:(ep d f))=>((pcon c d n) (conj Vepcd (p1p2_3275 Vpldl Velpl Vepah Vepcd Vepde Vepac Vepdf)))). Qed. Lemma p1p2_3278: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(ep d f)->(pl a n). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Vepdf:(ep d f))=>((pcon a c n) (conj Vepac (p1p2_3276 Vpldl Velpl Vepah Vepcd Vepde Vepac Vepdf)))). Qed. Lemma p1p2_3285: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(ep d f)->(ep a b) \/ (el l n). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Vepdf:(ep d f))=>((unique l n a b) (conj p1p2_5 (conj (p1p2_3278 Vpldl Velpl Vepah Vepcd Vepde Vepac Vepdf) (conj p1p2_13 p1p2_7))))). Qed. Lemma p1p2_3286: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(ep d f)->(ep a b)->(ep b a). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Vepdf:(ep d f))(Vepab:(ep a b))=>((psym a b) Vepab)). Qed. Lemma p1p2_3298: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(ep d f)->(ep a b)->(pl b s). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Vepdf:(ep d f))(Vepab:(ep a b))=>((pcon b a s) (conj (p1p2_3286 Vpldl Velpl Vepah Vepcd Vepde Vepac Vepdf Vepab) p1p2_12))). Qed. Lemma p1p2_3299: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(ep d f)->(ep a b)->(pl b o). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Vepdf:(ep d f))(Vepab:(ep a b))=>((pcon b a o) (conj (p1p2_3286 Vpldl Velpl Vepah Vepcd Vepde Vepac Vepdf Vepab) (p1p2_3256 Vpldl Velpl Vepah Vepcd Vepde Vepac)))). Qed. Lemma p1p2_3302: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(ep d f)->(ep a b)->(ep b g) \/ (el n o). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Vepdf:(ep d f))(Vepab:(ep a b))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_3299 Vpldl Velpl Vepah Vepcd Vepde Vepac Vepdf Vepab) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_3303: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(ep d f)->(ep a b)->(ep b g)->(ep g b). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_3319: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(ep d f)->(ep a b)->(ep b g)->(pl g s). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepbg:(ep b g))=>((pcon g b s) (conj (p1p2_3303 Vpldl Velpl Vepah Vepcd Vepde Vepac Vepdf Vepab Vepbg) (p1p2_3298 Vpldl Velpl Vepah Vepcd Vepde Vepac Vepdf Vepab)))). Qed. Lemma p1p2_3320: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(ep d f)->(ep a b)->(ep b g)->goal. Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepbg:(ep b g))=>((goal4 s) (conj p1p2_45 (conj (p1p2_3319 Vpldl Velpl Vepah Vepcd Vepde Vepac Vepdf Vepab Vepbg) (conj (p1p2_3230 Vpldl Velpl Vepah) p1p2_28))))). Qed. Lemma p1p2_3321: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(ep d f)->(ep a b)->(el n o)->goal. Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Vepdf:(ep d f))(Vepab:(ep a b))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_3322: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(ep d f)->(ep a b)->goal. Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Vepdf:(ep d f))(Vepab:(ep a b))=>((or_ind ((p1p2_3320 Vpldl Velpl Vepah Vepcd Vepde Vepac Vepdf Vepab))((p1p2_3321 Vpldl Velpl Vepah Vepcd Vepde Vepac Vepdf Vepab)))(p1p2_3302 Vpldl Velpl Vepah Vepcd Vepde Vepac Vepdf Vepab))). Qed. Lemma p1p2_3323: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(ep d f)->(el l n)->(el n l). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Vepdf:(ep d f))(Velln:(el l n))=>((lsym l n) Velln)). Qed. Lemma p1p2_3326: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(ep d f)->(el l n)->(pl g l). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Vepdf:(ep d f))(Velln:(el l n))=>((lcon g n l) (conj p1p2_23 (p1p2_3323 Vpldl Velpl Vepah Vepcd Vepde Vepac Vepdf Velln)))). Qed. Lemma p1p2_3328: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(ep d f)->(el l n)->(ep a g) \/ (el l o). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Vepdf:(ep d f))(Velln:(el l n))=>((unique l o a g) (conj p1p2_5 (conj (p1p2_3256 Vpldl Velpl Vepah Vepcd Vepde Vepac) (conj (p1p2_3326 Vpldl Velpl Vepah Vepcd Vepde Vepac Vepdf Velln) p1p2_24))))). Qed. Lemma p1p2_3329: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(ep d f)->(el l n)->(ep a g)->(ep g a). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Vepdf:(ep d f))(Velln:(el l n))(Vepag:(ep a g))=>((psym a g) Vepag)). Qed. Lemma p1p2_3341: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(ep d f)->(el l n)->(ep a g)->(pl g s). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Vepdf:(ep d f))(Velln:(el l n))(Vepag:(ep a g))=>((pcon g a s) (conj (p1p2_3329 Vpldl Velpl Vepah Vepcd Vepde Vepac Vepdf Velln Vepag) p1p2_12))). Qed. Lemma p1p2_3342: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(ep d f)->(el l n)->(ep a g)->goal. Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Vepdf:(ep d f))(Velln:(el l n))(Vepag:(ep a g))=>((goal4 s) (conj p1p2_45 (conj (p1p2_3341 Vpldl Velpl Vepah Vepcd Vepde Vepac Vepdf Velln Vepag) (conj (p1p2_3230 Vpldl Velpl Vepah) p1p2_28))))). Qed. Lemma p1p2_3346: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(ep d f)->(el l n)->(el l o)->(el n o). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Vepdf:(ep d f))(Velln:(el l n))(Vello:(el l o))=>((ltra n l o) (conj (p1p2_3323 Vpldl Velpl Vepah Vepcd Vepde Vepac Vepdf Velln) Vello))). Qed. Lemma p1p2_3347: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(ep d f)->(el l n)->(el l o)->goal. Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Vepdf:(ep d f))(Velln:(el l n))(Vello:(el l o))=>(goal1 (p1p2_3346 Vpldl Velpl Vepah Vepcd Vepde Vepac Vepdf Velln Vello))). Qed. Lemma p1p2_3348: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(ep d f)->(el l n)->goal. Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Vepdf:(ep d f))(Velln:(el l n))=>((or_ind ((p1p2_3342 Vpldl Velpl Vepah Vepcd Vepde Vepac Vepdf Velln))((p1p2_3347 Vpldl Velpl Vepah Vepcd Vepde Vepac Vepdf Velln)))(p1p2_3328 Vpldl Velpl Vepah Vepcd Vepde Vepac Vepdf Velln))). Qed. Lemma p1p2_3349: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(ep d f)->goal. Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Vepdf:(ep d f))=>((or_ind ((p1p2_3322 Vpldl Velpl Vepah Vepcd Vepde Vepac Vepdf))((p1p2_3348 Vpldl Velpl Vepah Vepcd Vepde Vepac Vepdf)))(p1p2_3285 Vpldl Velpl Vepah Vepcd Vepde Vepac Vepdf))). Qed. Lemma p1p2_3350: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(el m s)->(el s m). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Velms:(el m s))=>((lsym m s) Velms)). Qed. Lemma p1p2_3351: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(el m s)->(pl i m). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Velms:(el m s))=>((lcon i s m) (conj p1p2_28 (p1p2_3350 Vpldl Velpl Vepah Vepcd Vepde Vepac Velms)))). Qed. Lemma p1p2_3352: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(el m s)->(ep d i) \/ (el m r). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Velms:(el m s))=>((unique m r d i) (conj p1p2_6 (conj p1p2_19 (conj (p1p2_3351 Vpldl Velpl Vepah Vepcd Vepde Vepac Velms) p1p2_27))))). Qed. Lemma p1p2_3353: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(el m s)->(ep d i)->(ep i d). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Velms:(el m s))(Vepdi:(ep d i))=>((psym d i) Vepdi)). Qed. Lemma p1p2_3364: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(el m s)->(ep d i)->(pl i o). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Velms:(el m s))(Vepdi:(ep d i))=>((pcon i d o) (conj (p1p2_3353 Vpldl Velpl Vepah Vepcd Vepde Vepac Velms Vepdi) (p1p2_3234 Vpldl Velpl Vepah Vepcd)))). Qed. Lemma p1p2_3365: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(el m s)->(ep d i)->goal. Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Velms:(el m s))(Vepdi:(ep d i))=>((goal4 o) (conj p1p2_41 (conj p1p2_24 (conj (p1p2_3257 Vpldl Velpl Vepah Vepcd Vepde Vepac) (p1p2_3364 Vpldl Velpl Vepah Vepcd Vepde Vepac Velms Vepdi)))))). Qed. Lemma p1p2_3367: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(el m s)->(el m r)->(el s r). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Velms:(el m s))(Velmr:(el m r))=>((ltra s m r) (conj (p1p2_3350 Vpldl Velpl Vepah Vepcd Vepde Vepac Velms) Velmr))). Qed. Lemma p1p2_3368: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(el m s)->(el m r)->goal. Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Velms:(el m s))(Velmr:(el m r))=>(goal3 (p1p2_3367 Vpldl Velpl Vepah Vepcd Vepde Vepac Velms Velmr))). Qed. Lemma p1p2_3369: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->(el m s)->goal. Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))(Velms:(el m s))=>((or_ind ((p1p2_3365 Vpldl Velpl Vepah Vepcd Vepde Vepac Velms))((p1p2_3368 Vpldl Velpl Vepah Vepcd Vepde Vepac Velms)))(p1p2_3352 Vpldl Velpl Vepah Vepcd Vepde Vepac Velms))). Qed. Lemma p1p2_3370: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(ep a c)->goal. Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepac:(ep a c))=>((or_ind ((p1p2_3349 Vpldl Velpl Vepah Vepcd Vepde Vepac))((p1p2_3369 Vpldl Velpl Vepah Vepcd Vepde Vepac)))(p1p2_3265 Vpldl Velpl Vepah Vepcd Vepde Vepac))). Qed. Lemma p1p2_3372: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(el l q)->(el p q). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))=>((ltra p l q) (conj Velpl Vellq))). Qed. Lemma p1p2_3373: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->(el l q)->goal. Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))=>(goal2 (p1p2_3372 Vpldl Velpl Vepah Vepcd Vepde Vellq))). Qed. Lemma p1p2_3374: (pl d l)->(el p l)->(ep a h)->(ep c d)->(ep d e)->goal. Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Vepde:(ep d e))=>((or_ind ((p1p2_3370 Vpldl Velpl Vepah Vepcd Vepde))((p1p2_3373 Vpldl Velpl Vepah Vepcd Vepde)))(p1p2_3244 Vpldl Velpl Vepah Vepcd Vepde))). Qed. Lemma p1p2_3375: (pl d l)->(el p l)->(ep a h)->(ep c d)->(el m o)->(el o m). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Velmo:(el m o))=>((lsym m o) Velmo)). Qed. Lemma p1p2_3377: (pl d l)->(el p l)->(ep a h)->(ep c d)->(el m o)->(pl g m). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Velmo:(el m o))=>((lcon g o m) (conj p1p2_24 (p1p2_3375 Vpldl Velpl Vepah Vepcd Velmo)))). Qed. Lemma p1p2_3378: (pl d l)->(el p l)->(ep a h)->(ep c d)->(el m o)->(ep f g) \/ (el n m). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Velmo:(el m o))=>((unique n m f g) (conj p1p2_15 (conj p1p2_22 (conj p1p2_23 (p1p2_3377 Vpldl Velpl Vepah Vepcd Velmo)))))). Qed. Lemma p1p2_3379: (pl d l)->(el p l)->(ep a h)->(ep c d)->(el m o)->(ep f g)->(ep g f). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Velmo:(el m o))(Vepfg:(ep f g))=>((psym f g) Vepfg)). Qed. Lemma p1p2_3380: (pl d l)->(el p l)->(ep a h)->(ep c d)->(el m o)->(ep f g)->(pl g s). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Velmo:(el m o))(Vepfg:(ep f g))=>((pcon g f s) (conj (p1p2_3379 Vpldl Velpl Vepah Vepcd Velmo Vepfg) p1p2_20))). Qed. Lemma p1p2_3381: (pl d l)->(el p l)->(ep a h)->(ep c d)->(el m o)->(ep f g)->goal. Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Velmo:(el m o))(Vepfg:(ep f g))=>((goal4 s) (conj p1p2_45 (conj (p1p2_3380 Vpldl Velpl Vepah Vepcd Velmo Vepfg) (conj (p1p2_3230 Vpldl Velpl Vepah) p1p2_28))))). Qed. Lemma p1p2_3382: (pl d l)->(el p l)->(ep a h)->(ep c d)->(el m o)->(el n m)->(el m n). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Velmo:(el m o))(Velnm:(el n m))=>((lsym n m) Velnm)). Qed. Lemma p1p2_3383: (pl d l)->(el p l)->(ep a h)->(ep c d)->(el m o)->(el n m)->(el o n). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Velmo:(el m o))(Velnm:(el n m))=>((ltra o m n) (conj (p1p2_3375 Vpldl Velpl Vepah Vepcd Velmo) (p1p2_3382 Vpldl Velpl Vepah Vepcd Velmo Velnm)))). Qed. Lemma p1p2_3384: (pl d l)->(el p l)->(ep a h)->(ep c d)->(el m o)->(el n m)->(el n o). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Velmo:(el m o))(Velnm:(el n m))=>((lsym o n) (p1p2_3383 Vpldl Velpl Vepah Vepcd Velmo Velnm))). Qed. Lemma p1p2_3385: (pl d l)->(el p l)->(ep a h)->(ep c d)->(el m o)->(el n m)->goal. Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Velmo:(el m o))(Velnm:(el n m))=>(goal1 (p1p2_3384 Vpldl Velpl Vepah Vepcd Velmo Velnm))). Qed. Lemma p1p2_3386: (pl d l)->(el p l)->(ep a h)->(ep c d)->(el m o)->goal. Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))(Velmo:(el m o))=>((or_ind ((p1p2_3381 Vpldl Velpl Vepah Vepcd Velmo))((p1p2_3385 Vpldl Velpl Vepah Vepcd Velmo)))(p1p2_3378 Vpldl Velpl Vepah Vepcd Velmo))). Qed. Lemma p1p2_3387: (pl d l)->(el p l)->(ep a h)->(ep c d)->goal. Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Vepcd:(ep c d))=>((or_ind ((p1p2_3374 Vpldl Velpl Vepah Vepcd))((p1p2_3386 Vpldl Velpl Vepah Vepcd)))(p1p2_3235 Vpldl Velpl Vepah Vepcd))). Qed. Lemma p1p2_3394: (pl d l)->(el p l)->(ep a h)->(el r l)->(pl i l). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Velrl:(el r l))=>((lcon i r l) (conj p1p2_27 Velrl))). Qed. Lemma p1p2_3396: (pl d l)->(el p l)->(ep a h)->(el r l)->(ep a i) \/ (el l s). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Velrl:(el r l))=>((unique l s a i) (conj p1p2_5 (conj p1p2_12 (conj (p1p2_3394 Vpldl Velpl Vepah Velrl) p1p2_28))))). Qed. Lemma p1p2_3397: (pl d l)->(el p l)->(ep a h)->(el r l)->(ep a i)->(ep i a). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Velrl:(el r l))(Vepai:(ep a i))=>((psym a i) Vepai)). Qed. Lemma p1p2_3401: (pl d l)->(el p l)->(ep a h)->(el r l)->(ep a i)->(exists A:dom,(pl a A)/\(pl g A)). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Velrl:(el r l))(Vepai:(ep a i))=>((line a g) (conj p1p2_29 p1p2_35))). Qed. Lemma p1p2_3402: (pl d l)->(el p l)->(ep a h)->(el r l)->(ep a i)->forall C0:dom,(pl a C0)->(pl g C0)->(el C0 C0). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Velrl:(el r l))(Vepai:(ep a i))(C0:dom)(VplaC0:(pl a C0))(VplgC0:(pl g C0))=>((lref a C0) VplaC0)). Qed. Lemma p1p2_3403: (pl d l)->(el p l)->(ep a h)->(el r l)->(ep a i)->forall C0:dom,(pl a C0)->(pl g C0)->(pl h C0). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Velrl:(el r l))(Vepai:(ep a i))(C0:dom)(VplaC0:(pl a C0))(VplgC0:(pl g C0))=>((pcon h a C0) (conj (p1p2_3229 Vpldl Velpl Vepah) VplaC0))). Qed. Lemma p1p2_3404: (pl d l)->(el p l)->(ep a h)->(el r l)->(ep a i)->forall C0:dom,(pl a C0)->(pl g C0)->(pl i C0). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Velrl:(el r l))(Vepai:(ep a i))(C0:dom)(VplaC0:(pl a C0))(VplgC0:(pl g C0))=>((pcon i a C0) (conj (p1p2_3397 Vpldl Velpl Vepah Velrl Vepai) VplaC0))). Qed. Lemma p1p2_3405: (pl d l)->(el p l)->(ep a h)->(el r l)->(ep a i)->forall C0:dom,(pl a C0)->(pl g C0)->goal. Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Velrl:(el r l))(Vepai:(ep a i))(C0:dom)(VplaC0:(pl a C0))(VplgC0:(pl g C0))=>((goal4 C0) (conj (p1p2_3402 Vpldl Velpl Vepah Velrl Vepai C0 VplaC0 VplgC0) (conj VplgC0 (conj (p1p2_3403 Vpldl Velpl Vepah Velrl Vepai C0 VplaC0 VplgC0) (p1p2_3404 Vpldl Velpl Vepah Velrl Vepai C0 VplaC0 VplgC0)))))). Qed. Lemma p1p2_3406: (pl d l)->(el p l)->(ep a h)->(el r l)->(ep a i)->goal. Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Velrl:(el r l))(Vepai:(ep a i))=>((ex_ind (P:=fun C0:dom=>(pl a C0)/\(pl g C0))(fun C0:dom=>(and_ind (p1p2_3405 Vpldl Velpl Vepah Velrl Vepai C0))))(p1p2_3401 Vpldl Velpl Vepah Velrl Vepai))). Qed. Lemma p1p2_3410: (pl d l)->(el p l)->(ep a h)->(el r l)->(el l s)->(el r s). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Velrl:(el r l))(Vells:(el l s))=>((ltra r l s) (conj Velrl Vells))). Qed. Lemma p1p2_3411: (pl d l)->(el p l)->(ep a h)->(el r l)->(el l s)->(el s r). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Velrl:(el r l))(Vells:(el l s))=>((lsym r s) (p1p2_3410 Vpldl Velpl Vepah Velrl Vells))). Qed. Lemma p1p2_3412: (pl d l)->(el p l)->(ep a h)->(el r l)->(el l s)->goal. Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Velrl:(el r l))(Vells:(el l s))=>(goal3 (p1p2_3411 Vpldl Velpl Vepah Velrl Vells))). Qed. Lemma p1p2_3413: (pl d l)->(el p l)->(ep a h)->(el r l)->goal. Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))(Velrl:(el r l))=>((or_ind ((p1p2_3406 Vpldl Velpl Vepah Velrl))((p1p2_3412 Vpldl Velpl Vepah Velrl)))(p1p2_3396 Vpldl Velpl Vepah Velrl))). Qed. Lemma p1p2_3414: (pl d l)->(el p l)->(ep a h)->goal. Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vepah:(ep a h))=>((or_ind ((p1p2_3387 Vpldl Velpl Vepah))((p1p2_3413 Vpldl Velpl Vepah)))(p1p2_3231 Vpldl Velpl Vepah))). Qed. Lemma p1p2_3416: (pl d l)->(el p l)->(el l q)->(el p q). Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vellq:(el l q))=>((ltra p l q) (conj Velpl Vellq))). Qed. Lemma p1p2_3417: (pl d l)->(el p l)->(el l q)->goal. Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))(Vellq:(el l q))=>(goal2 (p1p2_3416 Vpldl Velpl Vellq))). Qed. Lemma p1p2_3418: (pl d l)->(el p l)->goal. Proof. exact (fun (Vpldl:(pl d l))(Velpl:(el p l))=>((or_ind ((p1p2_3414 Vpldl Velpl))((p1p2_3417 Vpldl Velpl)))(p1p2_3228 Vpldl Velpl))). Qed. Lemma p1p2_3419: (pl d l)->goal. Proof. exact (fun (Vpldl:(pl d l))=>((or_ind ((p1p2_3223 Vpldl))((p1p2_3418 Vpldl)))(p1p2_2573 Vpldl))). Qed. Lemma p1p2_3420: (pl e l)->(ep a e) \/ (el l q). Proof. exact (fun (Vplel:(pl e l))=>((unique l q a e) (conj p1p2_5 (conj p1p2_10 (conj Vplel p1p2_18))))). Qed. Lemma p1p2_3421: (pl e l)->(ep a e)->(ep e a). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))=>((psym a e) Vepae)). Qed. Lemma p1p2_3422: (pl e l)->(ep a e)->(pl a m). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))=>((pcon a e m) (conj Vepae p1p2_14))). Qed. Lemma p1p2_3423: (pl e l)->(ep a e)->(pl a o). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))=>((pcon a e o) (conj Vepae p1p2_16))). Qed. Lemma p1p2_3424: (pl e l)->(ep a e)->(pl e s). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))=>((pcon e a s) (conj (p1p2_3421 Vplel Vepae) p1p2_12))). Qed. Lemma p1p2_3425: (pl e l)->(ep a e)->(ep a c) \/ (el l o). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))=>((unique l o a c) (conj p1p2_5 (conj (p1p2_3423 Vplel Vepae) (conj p1p2_21 p1p2_8))))). Qed. Lemma p1p2_3426: (pl e l)->(ep a e)->(ep a c)->(ep c a). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))=>((psym a c) Vepac)). Qed. Lemma p1p2_3429: (pl e l)->(ep a e)->(ep a c)->(pl a r). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))=>((pcon a c r) (conj Vepac p1p2_11))). Qed. Lemma p1p2_3430: (pl e l)->(ep a e)->(ep a c)->(pl e r). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))=>((pcon e a r) (conj (p1p2_3421 Vplel Vepae) (p1p2_3429 Vplel Vepae Vepac)))). Qed. Lemma p1p2_3431: (pl e l)->(ep a e)->(ep a c)->(pl c q). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))=>((pcon c a q) (conj (p1p2_3426 Vplel Vepae Vepac) p1p2_10))). Qed. Lemma p1p2_3432: (pl e l)->(ep a e)->(ep a c)->(pl c s). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))=>((pcon c a s) (conj (p1p2_3426 Vplel Vepae Vepac) p1p2_12))). Qed. Lemma p1p2_3434: (pl e l)->(ep a e)->(ep a c)->(ep d e) \/ (el m r). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))=>((unique m r d e) (conj p1p2_6 (conj p1p2_19 (conj p1p2_14 (p1p2_3430 Vplel Vepae Vepac)))))). Qed. Lemma p1p2_3435: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep e d). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))=>((psym d e) Vepde)). Qed. Lemma p1p2_3440: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(pl d o). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))=>((pcon d e o) (conj Vepde p1p2_16))). Qed. Lemma p1p2_3443: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(pl d s). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))=>((pcon d e s) (conj Vepde (p1p2_3424 Vplel Vepae)))). Qed. Lemma p1p2_3444: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(pl e p). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))=>((pcon e d p) (conj (p1p2_3435 Vplel Vepae Vepac Vepde) p1p2_17))). Qed. Lemma p1p2_3445: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(pl a p). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))=>((pcon a e p) (conj Vepae (p1p2_3444 Vplel Vepae Vepac Vepde)))). Qed. Lemma p1p2_3447: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b) \/ (el l p). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))=>((unique l p a b) (conj p1p2_5 (conj (p1p2_3445 Vplel Vepae Vepac Vepde) (conj p1p2_13 p1p2_9))))). Qed. Lemma p1p2_3448: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(ep b a). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))=>((psym a b) Vepab)). Qed. Lemma p1p2_3455: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(pl a n). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))=>((pcon a b n) (conj Vepab p1p2_7))). Qed. Lemma p1p2_3456: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(pl e n). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))=>((pcon e a n) (conj (p1p2_3421 Vplel Vepae) (p1p2_3455 Vplel Vepae Vepac Vepde Vepab)))). Qed. Lemma p1p2_3458: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(pl d n). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))=>((pcon d e n) (conj Vepde (p1p2_3456 Vplel Vepae Vepac Vepde Vepab)))). Qed. Lemma p1p2_3459: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(pl b q). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))=>((pcon b a q) (conj (p1p2_3448 Vplel Vepae Vepac Vepde Vepab) p1p2_10))). Qed. Lemma p1p2_3460: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(pl b s). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))=>((pcon b a s) (conj (p1p2_3448 Vplel Vepae Vepac Vepde Vepab) p1p2_12))). Qed. Lemma p1p2_3462: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(pl b o). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))=>((pcon b a o) (conj (p1p2_3448 Vplel Vepae Vepac Vepde Vepab) (p1p2_3423 Vplel Vepae)))). Qed. Lemma p1p2_3464: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(ep d f) \/ (el m s). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))=>((unique m s d f) (conj p1p2_6 (conj (p1p2_3443 Vplel Vepae Vepac Vepde) (conj p1p2_22 p1p2_20))))). Qed. Lemma p1p2_3479: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(ep d f)->(ep b g) \/ (el n o). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdf:(ep d f))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_3462 Vplel Vepae Vepac Vepde Vepab) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_3480: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(ep d f)->(ep b g)->(ep g b). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_3494: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(ep d f)->(ep b g)->(pl g s). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepbg:(ep b g))=>((pcon g b s) (conj (p1p2_3480 Vplel Vepae Vepac Vepde Vepab Vepdf Vepbg) (p1p2_3460 Vplel Vepae Vepac Vepde Vepab)))). Qed. Lemma p1p2_3497: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(ep d f)->(ep b g)->(ep b h) \/ (el p q). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepbg:(ep b g))=>((unique p q b h) (conj p1p2_9 (conj (p1p2_3459 Vplel Vepae Vepac Vepde Vepab) (conj p1p2_25 p1p2_26))))). Qed. Lemma p1p2_3498: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(ep d f)->(ep b g)->(ep b h)->(ep h b). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepbg:(ep b g))(Vepbh:(ep b h))=>((psym b h) Vepbh)). Qed. Lemma p1p2_3513: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(ep d f)->(ep b g)->(ep b h)->(pl h s). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepbg:(ep b g))(Vepbh:(ep b h))=>((pcon h b s) (conj (p1p2_3498 Vplel Vepae Vepac Vepde Vepab Vepdf Vepbg Vepbh) (p1p2_3460 Vplel Vepae Vepac Vepde Vepab)))). Qed. Lemma p1p2_3514: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(ep d f)->(ep b g)->(ep b h)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepbg:(ep b g))(Vepbh:(ep b h))=>((goal4 s) (conj p1p2_45 (conj (p1p2_3494 Vplel Vepae Vepac Vepde Vepab Vepdf Vepbg) (conj (p1p2_3513 Vplel Vepae Vepac Vepde Vepab Vepdf Vepbg Vepbh) p1p2_28))))). Qed. Lemma p1p2_3515: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(ep d f)->(ep b g)->(el p q)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepbg:(ep b g))(Velpq:(el p q))=>(goal2 Velpq)). Qed. Lemma p1p2_3516: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(ep d f)->(ep b g)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepbg:(ep b g))=>((or_ind ((p1p2_3514 Vplel Vepae Vepac Vepde Vepab Vepdf Vepbg))((p1p2_3515 Vplel Vepae Vepac Vepde Vepab Vepdf Vepbg)))(p1p2_3497 Vplel Vepae Vepac Vepde Vepab Vepdf Vepbg))). Qed. Lemma p1p2_3517: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(ep d f)->(el n o)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdf:(ep d f))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_3518: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(ep d f)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Vepdf:(ep d f))=>((or_ind ((p1p2_3516 Vplel Vepae Vepac Vepde Vepab Vepdf))((p1p2_3517 Vplel Vepae Vepac Vepde Vepab Vepdf)))(p1p2_3479 Vplel Vepae Vepac Vepde Vepab Vepdf))). Qed. Lemma p1p2_3519: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(el s m). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))=>((lsym m s) Velms)). Qed. Lemma p1p2_3520: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(pl i m). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))=>((lcon i s m) (conj p1p2_28 (p1p2_3519 Vplel Vepae Vepac Vepde Vepab Velms)))). Qed. Lemma p1p2_3521: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i) \/ (el m r). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))=>((unique m r d i) (conj p1p2_6 (conj p1p2_19 (conj (p1p2_3520 Vplel Vepae Vepac Vepde Vepab Velms) p1p2_27))))). Qed. Lemma p1p2_3522: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(ep i d). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))=>((psym d i) Vepdi)). Qed. Lemma p1p2_3531: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(pl i p). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))=>((pcon i d p) (conj (p1p2_3522 Vplel Vepae Vepac Vepde Vepab Velms Vepdi) p1p2_17))). Qed. Lemma p1p2_3536: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(ep d f) \/ (el m n). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))=>((unique m n d f) (conj p1p2_6 (conj (p1p2_3458 Vplel Vepae Vepac Vepde Vepab) (conj p1p2_22 p1p2_15))))). Qed. Lemma p1p2_3553: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(ep d f)->(ep b g) \/ (el n o). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Vepdf:(ep d f))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_3462 Vplel Vepae Vepac Vepde Vepab) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_3554: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(ep d f)->(ep b g)->(ep g b). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Vepdf:(ep d f))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_3567: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(ep d f)->(ep b g)->(pl g p). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Vepdf:(ep d f))(Vepbg:(ep b g))=>((pcon g b p) (conj (p1p2_3554 Vplel Vepae Vepac Vepde Vepab Velms Vepdi Vepdf Vepbg) p1p2_9))). Qed. Lemma p1p2_3568: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(ep d f)->(ep b g)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Vepdf:(ep d f))(Vepbg:(ep b g))=>((goal4 p) (conj p1p2_42 (conj (p1p2_3567 Vplel Vepae Vepac Vepde Vepab Velms Vepdi Vepdf Vepbg) (conj p1p2_25 (p1p2_3531 Vplel Vepae Vepac Vepde Vepab Velms Vepdi)))))). Qed. Lemma p1p2_3569: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(ep d f)->(el n o)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Vepdf:(ep d f))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_3570: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(ep d f)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Vepdf:(ep d f))=>((or_ind ((p1p2_3568 Vplel Vepae Vepac Vepde Vepab Velms Vepdi Vepdf))((p1p2_3569 Vplel Vepae Vepac Vepde Vepab Velms Vepdi Vepdf)))(p1p2_3553 Vplel Vepae Vepac Vepde Vepab Velms Vepdi Vepdf))). Qed. Lemma p1p2_3571: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(el m n)->(el n m). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Velmn:(el m n))=>((lsym m n) Velmn)). Qed. Lemma p1p2_3574: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(el m n)->(pl g m). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Velmn:(el m n))=>((lcon g n m) (conj p1p2_23 (p1p2_3571 Vplel Vepae Vepac Vepde Vepab Velms Vepdi Velmn)))). Qed. Lemma p1p2_3576: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(el m n)->(ep d g) \/ (el m o). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Velmn:(el m n))=>((unique m o d g) (conj p1p2_6 (conj (p1p2_3440 Vplel Vepae Vepac Vepde) (conj (p1p2_3574 Vplel Vepae Vepac Vepde Vepab Velms Vepdi Velmn) p1p2_24))))). Qed. Lemma p1p2_3577: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(el m n)->(ep d g)->(ep g d). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Velmn:(el m n))(Vepdg:(ep d g))=>((psym d g) Vepdg)). Qed. Lemma p1p2_3588: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(el m n)->(ep d g)->(pl g p). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Velmn:(el m n))(Vepdg:(ep d g))=>((pcon g d p) (conj (p1p2_3577 Vplel Vepae Vepac Vepde Vepab Velms Vepdi Velmn Vepdg) p1p2_17))). Qed. Lemma p1p2_3589: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(el m n)->(ep d g)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Velmn:(el m n))(Vepdg:(ep d g))=>((goal4 p) (conj p1p2_42 (conj (p1p2_3588 Vplel Vepae Vepac Vepde Vepab Velms Vepdi Velmn Vepdg) (conj p1p2_25 (p1p2_3531 Vplel Vepae Vepac Vepde Vepab Velms Vepdi)))))). Qed. Lemma p1p2_3593: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(el m n)->(el m o)->(el n o). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Velmn:(el m n))(Velmo:(el m o))=>((ltra n m o) (conj (p1p2_3571 Vplel Vepae Vepac Vepde Vepab Velms Vepdi Velmn) Velmo))). Qed. Lemma p1p2_3594: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(el m n)->(el m o)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Velmn:(el m n))(Velmo:(el m o))=>(goal1 (p1p2_3593 Vplel Vepae Vepac Vepde Vepab Velms Vepdi Velmn Velmo))). Qed. Lemma p1p2_3595: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->(el m n)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))(Velmn:(el m n))=>((or_ind ((p1p2_3589 Vplel Vepae Vepac Vepde Vepab Velms Vepdi Velmn))((p1p2_3594 Vplel Vepae Vepac Vepde Vepab Velms Vepdi Velmn)))(p1p2_3576 Vplel Vepae Vepac Vepde Vepab Velms Vepdi Velmn))). Qed. Lemma p1p2_3596: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(ep d i)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Vepdi:(ep d i))=>((or_ind ((p1p2_3570 Vplel Vepae Vepac Vepde Vepab Velms Vepdi))((p1p2_3595 Vplel Vepae Vepac Vepde Vepab Velms Vepdi)))(p1p2_3536 Vplel Vepae Vepac Vepde Vepab Velms Vepdi))). Qed. Lemma p1p2_3598: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(el m r)->(el s r). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Velmr:(el m r))=>((ltra s m r) (conj (p1p2_3519 Vplel Vepae Vepac Vepde Vepab Velms) Velmr))). Qed. Lemma p1p2_3599: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->(el m r)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))(Velmr:(el m r))=>(goal3 (p1p2_3598 Vplel Vepae Vepac Vepde Vepab Velms Velmr))). Qed. Lemma p1p2_3600: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el m s)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velms:(el m s))=>((or_ind ((p1p2_3596 Vplel Vepae Vepac Vepde Vepab Velms))((p1p2_3599 Vplel Vepae Vepac Vepde Vepab Velms)))(p1p2_3521 Vplel Vepae Vepac Vepde Vepab Velms))). Qed. Lemma p1p2_3601: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))=>((or_ind ((p1p2_3518 Vplel Vepae Vepac Vepde Vepab))((p1p2_3600 Vplel Vepae Vepac Vepde Vepab)))(p1p2_3464 Vplel Vepae Vepac Vepde Vepab))). Qed. Lemma p1p2_3602: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(el p l). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))=>((lsym l p) Vellp)). Qed. Lemma p1p2_3603: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(pl h l). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))=>((lcon h p l) (conj p1p2_25 (p1p2_3602 Vplel Vepae Vepac Vepde Vellp)))). Qed. Lemma p1p2_3604: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h) \/ (el l q). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))=>((unique l q a h) (conj p1p2_5 (conj p1p2_10 (conj (p1p2_3603 Vplel Vepae Vepac Vepde Vellp) p1p2_26))))). Qed. Lemma p1p2_3605: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep h a). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))=>((psym a h) Vepah)). Qed. Lemma p1p2_3612: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(pl h s). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))=>((pcon h a s) (conj (p1p2_3605 Vplel Vepae Vepac Vepde Vellp Vepah) p1p2_12))). Qed. Lemma p1p2_3614: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(pl h o). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))=>((pcon h a o) (conj (p1p2_3605 Vplel Vepae Vepac Vepde Vellp Vepah) (p1p2_3423 Vplel Vepae)))). Qed. Lemma p1p2_3616: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f) \/ (el m s). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))=>((unique m s d f) (conj p1p2_6 (conj (p1p2_3443 Vplel Vepae Vepac Vepde) (conj p1p2_22 p1p2_20))))). Qed. Lemma p1p2_3626: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(pl d n). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))=>((pcon d f n) (conj Vepdf p1p2_15))). Qed. Lemma p1p2_3627: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(pl e n). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))=>((pcon e d n) (conj (p1p2_3435 Vplel Vepae Vepac Vepde) (p1p2_3626 Vplel Vepae Vepac Vepde Vellp Vepah Vepdf)))). Qed. Lemma p1p2_3628: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(pl a n). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))=>((pcon a e n) (conj Vepae (p1p2_3627 Vplel Vepae Vepac Vepde Vellp Vepah Vepdf)))). Qed. Lemma p1p2_3636: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(ep a b) \/ (el l n). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))=>((unique l n a b) (conj p1p2_5 (conj (p1p2_3628 Vplel Vepae Vepac Vepde Vellp Vepah Vepdf) (conj p1p2_13 p1p2_7))))). Qed. Lemma p1p2_3637: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(ep a b)->(ep b a). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Vepab:(ep a b))=>((psym a b) Vepab)). Qed. Lemma p1p2_3649: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(ep a b)->(pl b s). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Vepab:(ep a b))=>((pcon b a s) (conj (p1p2_3637 Vplel Vepae Vepac Vepde Vellp Vepah Vepdf Vepab) p1p2_12))). Qed. Lemma p1p2_3651: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(ep a b)->(pl b o). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Vepab:(ep a b))=>((pcon b a o) (conj (p1p2_3637 Vplel Vepae Vepac Vepde Vellp Vepah Vepdf Vepab) (p1p2_3423 Vplel Vepae)))). Qed. Lemma p1p2_3653: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(ep a b)->(ep b g) \/ (el n o). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Vepab:(ep a b))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_3651 Vplel Vepae Vepac Vepde Vellp Vepah Vepdf Vepab) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_3654: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(ep a b)->(ep b g)->(ep g b). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_3670: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(ep a b)->(ep b g)->(pl g s). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepbg:(ep b g))=>((pcon g b s) (conj (p1p2_3654 Vplel Vepae Vepac Vepde Vellp Vepah Vepdf Vepab Vepbg) (p1p2_3649 Vplel Vepae Vepac Vepde Vellp Vepah Vepdf Vepab)))). Qed. Lemma p1p2_3671: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(ep a b)->(ep b g)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepbg:(ep b g))=>((goal4 s) (conj p1p2_45 (conj (p1p2_3670 Vplel Vepae Vepac Vepde Vellp Vepah Vepdf Vepab Vepbg) (conj (p1p2_3612 Vplel Vepae Vepac Vepde Vellp Vepah) p1p2_28))))). Qed. Lemma p1p2_3672: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(ep a b)->(el n o)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Vepab:(ep a b))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_3673: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(ep a b)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Vepab:(ep a b))=>((or_ind ((p1p2_3671 Vplel Vepae Vepac Vepde Vellp Vepah Vepdf Vepab))((p1p2_3672 Vplel Vepae Vepac Vepde Vellp Vepah Vepdf Vepab)))(p1p2_3653 Vplel Vepae Vepac Vepde Vellp Vepah Vepdf Vepab))). Qed. Lemma p1p2_3674: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(el l n)->(el n l). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Velln:(el l n))=>((lsym l n) Velln)). Qed. Lemma p1p2_3677: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(el l n)->(pl g l). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Velln:(el l n))=>((lcon g n l) (conj p1p2_23 (p1p2_3674 Vplel Vepae Vepac Vepde Vellp Vepah Vepdf Velln)))). Qed. Lemma p1p2_3679: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(el l n)->(ep a g) \/ (el l o). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Velln:(el l n))=>((unique l o a g) (conj p1p2_5 (conj (p1p2_3423 Vplel Vepae) (conj (p1p2_3677 Vplel Vepae Vepac Vepde Vellp Vepah Vepdf Velln) p1p2_24))))). Qed. Lemma p1p2_3680: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(el l n)->(ep a g)->(ep g a). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Velln:(el l n))(Vepag:(ep a g))=>((psym a g) Vepag)). Qed. Lemma p1p2_3692: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(el l n)->(ep a g)->(pl g s). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Velln:(el l n))(Vepag:(ep a g))=>((pcon g a s) (conj (p1p2_3680 Vplel Vepae Vepac Vepde Vellp Vepah Vepdf Velln Vepag) p1p2_12))). Qed. Lemma p1p2_3693: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(el l n)->(ep a g)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Velln:(el l n))(Vepag:(ep a g))=>((goal4 s) (conj p1p2_45 (conj (p1p2_3692 Vplel Vepae Vepac Vepde Vellp Vepah Vepdf Velln Vepag) (conj (p1p2_3612 Vplel Vepae Vepac Vepde Vellp Vepah) p1p2_28))))). Qed. Lemma p1p2_3697: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(el l n)->(el l o)->(el n o). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Velln:(el l n))(Vello:(el l o))=>((ltra n l o) (conj (p1p2_3674 Vplel Vepae Vepac Vepde Vellp Vepah Vepdf Velln) Vello))). Qed. Lemma p1p2_3698: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(el l n)->(el l o)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Velln:(el l n))(Vello:(el l o))=>(goal1 (p1p2_3697 Vplel Vepae Vepac Vepde Vellp Vepah Vepdf Velln Vello))). Qed. Lemma p1p2_3699: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->(el l n)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))(Velln:(el l n))=>((or_ind ((p1p2_3693 Vplel Vepae Vepac Vepde Vellp Vepah Vepdf Velln))((p1p2_3698 Vplel Vepae Vepac Vepde Vellp Vepah Vepdf Velln)))(p1p2_3679 Vplel Vepae Vepac Vepde Vellp Vepah Vepdf Velln))). Qed. Lemma p1p2_3700: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep d f)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Vepdf:(ep d f))=>((or_ind ((p1p2_3673 Vplel Vepae Vepac Vepde Vellp Vepah Vepdf))((p1p2_3699 Vplel Vepae Vepac Vepde Vellp Vepah Vepdf)))(p1p2_3636 Vplel Vepae Vepac Vepde Vellp Vepah Vepdf))). Qed. Lemma p1p2_3701: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(el m s)->(el s m). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Velms:(el m s))=>((lsym m s) Velms)). Qed. Lemma p1p2_3702: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(el m s)->(pl i m). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Velms:(el m s))=>((lcon i s m) (conj p1p2_28 (p1p2_3701 Vplel Vepae Vepac Vepde Vellp Vepah Velms)))). Qed. Lemma p1p2_3703: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(el m s)->(ep d i) \/ (el m r). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Velms:(el m s))=>((unique m r d i) (conj p1p2_6 (conj p1p2_19 (conj (p1p2_3702 Vplel Vepae Vepac Vepde Vellp Vepah Velms) p1p2_27))))). Qed. Lemma p1p2_3704: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(el m s)->(ep d i)->(ep i d). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Velms:(el m s))(Vepdi:(ep d i))=>((psym d i) Vepdi)). Qed. Lemma p1p2_3714: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(el m s)->(ep d i)->(pl i o). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Velms:(el m s))(Vepdi:(ep d i))=>((pcon i d o) (conj (p1p2_3704 Vplel Vepae Vepac Vepde Vellp Vepah Velms Vepdi) (p1p2_3440 Vplel Vepae Vepac Vepde)))). Qed. Lemma p1p2_3715: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(el m s)->(ep d i)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Velms:(el m s))(Vepdi:(ep d i))=>((goal4 o) (conj p1p2_41 (conj p1p2_24 (conj (p1p2_3614 Vplel Vepae Vepac Vepde Vellp Vepah) (p1p2_3714 Vplel Vepae Vepac Vepde Vellp Vepah Velms Vepdi)))))). Qed. Lemma p1p2_3717: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(el m s)->(el m r)->(el s r). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Velms:(el m s))(Velmr:(el m r))=>((ltra s m r) (conj (p1p2_3701 Vplel Vepae Vepac Vepde Vellp Vepah Velms) Velmr))). Qed. Lemma p1p2_3718: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(el m s)->(el m r)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Velms:(el m s))(Velmr:(el m r))=>(goal3 (p1p2_3717 Vplel Vepae Vepac Vepde Vellp Vepah Velms Velmr))). Qed. Lemma p1p2_3719: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(el m s)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))(Velms:(el m s))=>((or_ind ((p1p2_3715 Vplel Vepae Vepac Vepde Vellp Vepah Velms))((p1p2_3718 Vplel Vepae Vepac Vepde Vellp Vepah Velms)))(p1p2_3703 Vplel Vepae Vepac Vepde Vellp Vepah Velms))). Qed. Lemma p1p2_3720: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))=>((or_ind ((p1p2_3700 Vplel Vepae Vepac Vepde Vellp Vepah))((p1p2_3719 Vplel Vepae Vepac Vepde Vellp Vepah)))(p1p2_3616 Vplel Vepae Vepac Vepde Vellp Vepah))). Qed. Lemma p1p2_3722: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(el l q)->(el p q). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vellq:(el l q))=>((ltra p l q) (conj (p1p2_3602 Vplel Vepae Vepac Vepde Vellp) Vellq))). Qed. Lemma p1p2_3723: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(el l q)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vellq:(el l q))=>(goal2 (p1p2_3722 Vplel Vepae Vepac Vepde Vellp Vellq))). Qed. Lemma p1p2_3724: (pl e l)->(ep a e)->(ep a c)->(ep d e)->(el l p)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))=>((or_ind ((p1p2_3720 Vplel Vepae Vepac Vepde Vellp))((p1p2_3723 Vplel Vepae Vepac Vepde Vellp)))(p1p2_3604 Vplel Vepae Vepac Vepde Vellp))). Qed. Lemma p1p2_3725: (pl e l)->(ep a e)->(ep a c)->(ep d e)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))=>((or_ind ((p1p2_3601 Vplel Vepae Vepac Vepde))((p1p2_3724 Vplel Vepae Vepac Vepde)))(p1p2_3447 Vplel Vepae Vepac Vepde))). Qed. Lemma p1p2_3727: (pl e l)->(ep a e)->(ep a c)->(el m r)->(pl f r). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))=>((lcon f m r) (conj p1p2_22 Velmr))). Qed. Lemma p1p2_3729: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i) \/ (el r s). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))=>((unique r s c i) (conj p1p2_11 (conj (p1p2_3432 Vplel Vepae Vepac) (conj p1p2_27 p1p2_28))))). Qed. Lemma p1p2_3730: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep i c). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))=>((psym c i) Vepci)). Qed. Lemma p1p2_3737: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(pl i q). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))=>((pcon i c q) (conj (p1p2_3730 Vplel Vepae Vepac Velmr Vepci) (p1p2_3431 Vplel Vepae Vepac)))). Qed. Lemma p1p2_3738: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f) \/ (el r s). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))=>((unique r s c f) (conj p1p2_11 (conj (p1p2_3432 Vplel Vepae Vepac) (conj (p1p2_3727 Vplel Vepae Vepac Velmr) p1p2_20))))). Qed. Lemma p1p2_3746: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(pl c n). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))=>((pcon c f n) (conj Vepcf p1p2_15))). Qed. Lemma p1p2_3747: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(pl a n). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))=>((pcon a c n) (conj Vepac (p1p2_3746 Vplel Vepae Vepac Velmr Vepci Vepcf)))). Qed. Lemma p1p2_3753: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b) \/ (el l n). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))=>((unique l n a b) (conj p1p2_5 (conj (p1p2_3747 Vplel Vepae Vepac Velmr Vepci Vepcf) (conj p1p2_13 p1p2_7))))). Qed. Lemma p1p2_3754: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(ep b a). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))=>((psym a b) Vepab)). Qed. Lemma p1p2_3763: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(pl a p). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))=>((pcon a b p) (conj Vepab p1p2_9))). Qed. Lemma p1p2_3764: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(pl e p). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))=>((pcon e a p) (conj (p1p2_3421 Vplel Vepae) (p1p2_3763 Vplel Vepae Vepac Velmr Vepci Vepcf Vepab)))). Qed. Lemma p1p2_3765: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(pl c p). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))=>((pcon c a p) (conj (p1p2_3426 Vplel Vepae Vepac) (p1p2_3763 Vplel Vepae Vepac Velmr Vepci Vepcf Vepab)))). Qed. Lemma p1p2_3766: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(pl i p). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))=>((pcon i c p) (conj (p1p2_3730 Vplel Vepae Vepac Velmr Vepci) (p1p2_3765 Vplel Vepae Vepac Velmr Vepci Vepcf Vepab)))). Qed. Lemma p1p2_3771: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(pl b o). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))=>((pcon b a o) (conj (p1p2_3754 Vplel Vepae Vepac Velmr Vepci Vepcf Vepab) (p1p2_3423 Vplel Vepae)))). Qed. Lemma p1p2_3773: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(ep d e) \/ (el m p). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))=>((unique m p d e) (conj p1p2_6 (conj p1p2_17 (conj p1p2_14 (p1p2_3764 Vplel Vepae Vepac Velmr Vepci Vepcf Vepab)))))). Qed. Lemma p1p2_3790: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(ep d e)->(ep b g) \/ (el n o). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Vepde:(ep d e))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_3771 Vplel Vepae Vepac Velmr Vepci Vepcf Vepab) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_3791: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(ep d e)->(ep b g)->(ep g b). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Vepde:(ep d e))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_3804: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(ep d e)->(ep b g)->(pl g p). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Vepde:(ep d e))(Vepbg:(ep b g))=>((pcon g b p) (conj (p1p2_3791 Vplel Vepae Vepac Velmr Vepci Vepcf Vepab Vepde Vepbg) p1p2_9))). Qed. Lemma p1p2_3805: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(ep d e)->(ep b g)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Vepde:(ep d e))(Vepbg:(ep b g))=>((goal4 p) (conj p1p2_42 (conj (p1p2_3804 Vplel Vepae Vepac Velmr Vepci Vepcf Vepab Vepde Vepbg) (conj p1p2_25 (p1p2_3766 Vplel Vepae Vepac Velmr Vepci Vepcf Vepab)))))). Qed. Lemma p1p2_3806: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(ep d e)->(el n o)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Vepde:(ep d e))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_3807: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(ep d e)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Vepde:(ep d e))=>((or_ind ((p1p2_3805 Vplel Vepae Vepac Velmr Vepci Vepcf Vepab Vepde))((p1p2_3806 Vplel Vepae Vepac Velmr Vepci Vepcf Vepab Vepde)))(p1p2_3790 Vplel Vepae Vepac Velmr Vepci Vepcf Vepab Vepde))). Qed. Lemma p1p2_3813: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(el m p)->(ep b g) \/ (el n o). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Velmp:(el m p))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_3771 Vplel Vepae Vepac Velmr Vepci Vepcf Vepab) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_3814: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(el m p)->(ep b g)->(ep g b). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_3825: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(el m p)->(ep b g)->(pl g p). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbg:(ep b g))=>((pcon g b p) (conj (p1p2_3814 Vplel Vepae Vepac Velmr Vepci Vepcf Vepab Velmp Vepbg) p1p2_9))). Qed. Lemma p1p2_3826: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(el m p)->(ep b g)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbg:(ep b g))=>((goal4 p) (conj p1p2_42 (conj (p1p2_3825 Vplel Vepae Vepac Velmr Vepci Vepcf Vepab Velmp Vepbg) (conj p1p2_25 (p1p2_3766 Vplel Vepae Vepac Velmr Vepci Vepcf Vepab)))))). Qed. Lemma p1p2_3827: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(el m p)->(el n o)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Velmp:(el m p))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_3828: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->(el m p)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))(Velmp:(el m p))=>((or_ind ((p1p2_3826 Vplel Vepae Vepac Velmr Vepci Vepcf Vepab Velmp))((p1p2_3827 Vplel Vepae Vepac Velmr Vepci Vepcf Vepab Velmp)))(p1p2_3813 Vplel Vepae Vepac Velmr Vepci Vepcf Vepab Velmp))). Qed. Lemma p1p2_3829: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(ep a b)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Vepab:(ep a b))=>((or_ind ((p1p2_3807 Vplel Vepae Vepac Velmr Vepci Vepcf Vepab))((p1p2_3828 Vplel Vepae Vepac Velmr Vepci Vepcf Vepab)))(p1p2_3773 Vplel Vepae Vepac Velmr Vepci Vepcf Vepab))). Qed. Lemma p1p2_3830: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(el l n)->(el n l). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Velln:(el l n))=>((lsym l n) Velln)). Qed. Lemma p1p2_3831: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(el l n)->(pl g l). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Velln:(el l n))=>((lcon g n l) (conj p1p2_23 (p1p2_3830 Vplel Vepae Vepac Velmr Vepci Vepcf Velln)))). Qed. Lemma p1p2_3832: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(el l n)->(ep a g) \/ (el l o). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Velln:(el l n))=>((unique l o a g) (conj p1p2_5 (conj (p1p2_3423 Vplel Vepae) (conj (p1p2_3831 Vplel Vepae Vepac Velmr Vepci Vepcf Velln) p1p2_24))))). Qed. Lemma p1p2_3833: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(el l n)->(ep a g)->(ep g a). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Velln:(el l n))(Vepag:(ep a g))=>((psym a g) Vepag)). Qed. Lemma p1p2_3842: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(el l n)->(ep a g)->(pl g q). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Velln:(el l n))(Vepag:(ep a g))=>((pcon g a q) (conj (p1p2_3833 Vplel Vepae Vepac Velmr Vepci Vepcf Velln Vepag) p1p2_10))). Qed. Lemma p1p2_3843: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(el l n)->(ep a g)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Velln:(el l n))(Vepag:(ep a g))=>((goal4 q) (conj p1p2_43 (conj (p1p2_3842 Vplel Vepae Vepac Velmr Vepci Vepcf Velln Vepag) (conj p1p2_26 (p1p2_3737 Vplel Vepae Vepac Velmr Vepci)))))). Qed. Lemma p1p2_3845: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(el l n)->(el l o)->(el n o). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Velln:(el l n))(Vello:(el l o))=>((ltra n l o) (conj (p1p2_3830 Vplel Vepae Vepac Velmr Vepci Vepcf Velln) Vello))). Qed. Lemma p1p2_3846: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(el l n)->(el l o)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Velln:(el l n))(Vello:(el l o))=>(goal1 (p1p2_3845 Vplel Vepae Vepac Velmr Vepci Vepcf Velln Vello))). Qed. Lemma p1p2_3847: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->(el l n)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))(Velln:(el l n))=>((or_ind ((p1p2_3843 Vplel Vepae Vepac Velmr Vepci Vepcf Velln))((p1p2_3846 Vplel Vepae Vepac Velmr Vepci Vepcf Velln)))(p1p2_3832 Vplel Vepae Vepac Velmr Vepci Vepcf Velln))). Qed. Lemma p1p2_3848: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep c f)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Vepcf:(ep c f))=>((or_ind ((p1p2_3829 Vplel Vepae Vepac Velmr Vepci Vepcf))((p1p2_3847 Vplel Vepae Vepac Velmr Vepci Vepcf)))(p1p2_3753 Vplel Vepae Vepac Velmr Vepci Vepcf))). Qed. Lemma p1p2_3849: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(el r s)->(el s r). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Velrs:(el r s))=>((lsym r s) Velrs)). Qed. Lemma p1p2_3850: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(el r s)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))(Velrs:(el r s))=>(goal3 (p1p2_3849 Vplel Vepae Vepac Velmr Vepci Velrs))). Qed. Lemma p1p2_3851: (pl e l)->(ep a e)->(ep a c)->(el m r)->(ep c i)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))=>((or_ind ((p1p2_3848 Vplel Vepae Vepac Velmr Vepci))((p1p2_3850 Vplel Vepae Vepac Velmr Vepci)))(p1p2_3738 Vplel Vepae Vepac Velmr Vepci))). Qed. Lemma p1p2_3852: (pl e l)->(ep a e)->(ep a c)->(el m r)->(el r s)->(el s r). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Velrs:(el r s))=>((lsym r s) Velrs)). Qed. Lemma p1p2_3853: (pl e l)->(ep a e)->(ep a c)->(el m r)->(el r s)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Velrs:(el r s))=>(goal3 (p1p2_3852 Vplel Vepae Vepac Velmr Velrs))). Qed. Lemma p1p2_3854: (pl e l)->(ep a e)->(ep a c)->(el m r)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))=>((or_ind ((p1p2_3851 Vplel Vepae Vepac Velmr))((p1p2_3853 Vplel Vepae Vepac Velmr)))(p1p2_3729 Vplel Vepae Vepac Velmr))). Qed. Lemma p1p2_3855: (pl e l)->(ep a e)->(ep a c)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vepac:(ep a c))=>((or_ind ((p1p2_3725 Vplel Vepae Vepac))((p1p2_3854 Vplel Vepae Vepac)))(p1p2_3434 Vplel Vepae Vepac))). Qed. Lemma p1p2_3856: (pl e l)->(ep a e)->(el l o)->(el o l). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))=>((lsym l o) Vello)). Qed. Lemma p1p2_3858: (pl e l)->(ep a e)->(el l o)->(pl g l). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))=>((lcon g o l) (conj p1p2_24 (p1p2_3856 Vplel Vepae Vello)))). Qed. Lemma p1p2_3859: (pl e l)->(ep a e)->(el l o)->(ep b g) \/ (el n l). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))=>((unique n l b g) (conj p1p2_7 (conj p1p2_13 (conj p1p2_23 (p1p2_3858 Vplel Vepae Vello)))))). Qed. Lemma p1p2_3860: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep g b). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_3861: (pl e l)->(ep a e)->(el l o)->(ep b g)->(pl g p). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))=>((pcon g b p) (conj (p1p2_3860 Vplel Vepae Vello Vepbg) p1p2_9))). Qed. Lemma p1p2_3862: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f) \/ (el s m). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))=>((unique s m a f) (conj p1p2_12 (conj (p1p2_3422 Vplel Vepae) (conj p1p2_20 p1p2_22))))). Qed. Lemma p1p2_3866: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(pl a n). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))=>((pcon a f n) (conj Vepaf p1p2_15))). Qed. Lemma p1p2_3871: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b) \/ (el l n). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))=>((unique l n a b) (conj p1p2_5 (conj (p1p2_3866 Vplel Vepae Vello Vepbg Vepaf) (conj p1p2_13 p1p2_7))))). Qed. Lemma p1p2_3872: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep b a). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))=>((psym a b) Vepab)). Qed. Lemma p1p2_3883: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(pl a p). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))=>((pcon a b p) (conj Vepab p1p2_9))). Qed. Lemma p1p2_3884: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(pl e p). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))=>((pcon e a p) (conj (p1p2_3421 Vplel Vepae) (p1p2_3883 Vplel Vepae Vello Vepbg Vepaf Vepab)))). Qed. Lemma p1p2_3886: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(pl b q). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))=>((pcon b a q) (conj (p1p2_3872 Vplel Vepae Vello Vepbg Vepaf Vepab) p1p2_10))). Qed. Lemma p1p2_3887: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(pl g q). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))=>((pcon g b q) (conj (p1p2_3860 Vplel Vepae Vello Vepbg) (p1p2_3886 Vplel Vepae Vello Vepbg Vepaf Vepab)))). Qed. Lemma p1p2_3888: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(pl b s). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))=>((pcon b a s) (conj (p1p2_3872 Vplel Vepae Vello Vepbg Vepaf Vepab) p1p2_12))). Qed. Lemma p1p2_3889: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(pl g s). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))=>((pcon g b s) (conj (p1p2_3860 Vplel Vepae Vello Vepbg) (p1p2_3888 Vplel Vepae Vello Vepbg Vepaf Vepab)))). Qed. Lemma p1p2_3892: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e) \/ (el m p). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))=>((unique m p d e) (conj p1p2_6 (conj p1p2_17 (conj p1p2_14 (p1p2_3884 Vplel Vepae Vello Vepbg Vepaf Vepab)))))). Qed. Lemma p1p2_3893: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(ep e d). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))=>((psym d e) Vepde)). Qed. Lemma p1p2_3907: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(pl e r). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))=>((pcon e d r) (conj (p1p2_3893 Vplel Vepae Vello Vepbg Vepaf Vepab Vepde) p1p2_19))). Qed. Lemma p1p2_3908: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(pl a r). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))=>((pcon a e r) (conj Vepae (p1p2_3907 Vplel Vepae Vello Vepbg Vepaf Vepab Vepde)))). Qed. Lemma p1p2_3912: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(ep a c) \/ (el l r). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))=>((unique l r a c) (conj p1p2_5 (conj (p1p2_3908 Vplel Vepae Vello Vepbg Vepaf Vepab Vepde) (conj p1p2_21 p1p2_11))))). Qed. Lemma p1p2_3929: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(ep a c)->(ep b h) \/ (el p q). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vepac:(ep a c))=>((unique p q b h) (conj p1p2_9 (conj (p1p2_3886 Vplel Vepae Vello Vepbg Vepaf Vepab) (conj p1p2_25 p1p2_26))))). Qed. Lemma p1p2_3930: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(ep a c)->(ep b h)->(ep h b). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vepac:(ep a c))(Vepbh:(ep b h))=>((psym b h) Vepbh)). Qed. Lemma p1p2_3946: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(ep a c)->(ep b h)->(pl h s). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vepac:(ep a c))(Vepbh:(ep b h))=>((pcon h b s) (conj (p1p2_3930 Vplel Vepae Vello Vepbg Vepaf Vepab Vepde Vepac Vepbh) (p1p2_3888 Vplel Vepae Vello Vepbg Vepaf Vepab)))). Qed. Lemma p1p2_3947: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(ep a c)->(ep b h)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vepac:(ep a c))(Vepbh:(ep b h))=>((goal4 s) (conj p1p2_45 (conj (p1p2_3889 Vplel Vepae Vello Vepbg Vepaf Vepab) (conj (p1p2_3946 Vplel Vepae Vello Vepbg Vepaf Vepab Vepde Vepac Vepbh) p1p2_28))))). Qed. Lemma p1p2_3948: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(ep a c)->(el p q)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vepac:(ep a c))(Velpq:(el p q))=>(goal2 Velpq)). Qed. Lemma p1p2_3949: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(ep a c)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vepac:(ep a c))=>((or_ind ((p1p2_3947 Vplel Vepae Vello Vepbg Vepaf Vepab Vepde Vepac))((p1p2_3948 Vplel Vepae Vello Vepbg Vepaf Vepab Vepde Vepac)))(p1p2_3929 Vplel Vepae Vello Vepbg Vepaf Vepab Vepde Vepac))). Qed. Lemma p1p2_3950: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(el l r)->(el r l). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vellr:(el l r))=>((lsym l r) Vellr)). Qed. Lemma p1p2_3953: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(el l r)->(pl i l). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vellr:(el l r))=>((lcon i r l) (conj p1p2_27 (p1p2_3950 Vplel Vepae Vello Vepbg Vepaf Vepab Vepde Vellr)))). Qed. Lemma p1p2_3955: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(el l r)->(ep a i) \/ (el l s). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vellr:(el l r))=>((unique l s a i) (conj p1p2_5 (conj p1p2_12 (conj (p1p2_3953 Vplel Vepae Vello Vepbg Vepaf Vepab Vepde Vellr) p1p2_28))))). Qed. Lemma p1p2_3956: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(el l r)->(ep a i)->(ep i a). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vellr:(el l r))(Vepai:(ep a i))=>((psym a i) Vepai)). Qed. Lemma p1p2_3967: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(el l r)->(ep a i)->(pl i q). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vellr:(el l r))(Vepai:(ep a i))=>((pcon i a q) (conj (p1p2_3956 Vplel Vepae Vello Vepbg Vepaf Vepab Vepde Vellr Vepai) p1p2_10))). Qed. Lemma p1p2_3968: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(el l r)->(ep a i)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vellr:(el l r))(Vepai:(ep a i))=>((goal4 q) (conj p1p2_43 (conj (p1p2_3887 Vplel Vepae Vello Vepbg Vepaf Vepab) (conj p1p2_26 (p1p2_3967 Vplel Vepae Vello Vepbg Vepaf Vepab Vepde Vellr Vepai)))))). Qed. Lemma p1p2_3972: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(el l r)->(el l s)->(el r s). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vellr:(el l r))(Vells:(el l s))=>((ltra r l s) (conj (p1p2_3950 Vplel Vepae Vello Vepbg Vepaf Vepab Vepde Vellr) Vells))). Qed. Lemma p1p2_3973: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(el l r)->(el l s)->(el s r). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vellr:(el l r))(Vells:(el l s))=>((lsym r s) (p1p2_3972 Vplel Vepae Vello Vepbg Vepaf Vepab Vepde Vellr Vells))). Qed. Lemma p1p2_3974: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(el l r)->(el l s)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vellr:(el l r))(Vells:(el l s))=>(goal3 (p1p2_3973 Vplel Vepae Vello Vepbg Vepaf Vepab Vepde Vellr Vells))). Qed. Lemma p1p2_3975: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->(el l r)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))(Vellr:(el l r))=>((or_ind ((p1p2_3968 Vplel Vepae Vello Vepbg Vepaf Vepab Vepde Vellr))((p1p2_3974 Vplel Vepae Vello Vepbg Vepaf Vepab Vepde Vellr)))(p1p2_3955 Vplel Vepae Vello Vepbg Vepaf Vepab Vepde Vellr))). Qed. Lemma p1p2_3976: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(ep d e)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepde:(ep d e))=>((or_ind ((p1p2_3949 Vplel Vepae Vello Vepbg Vepaf Vepab Vepde))((p1p2_3975 Vplel Vepae Vello Vepbg Vepaf Vepab Vepde)))(p1p2_3912 Vplel Vepae Vello Vepbg Vepaf Vepab Vepde))). Qed. Lemma p1p2_3979: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(el m p)->(ep b h) \/ (el p q). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))=>((unique p q b h) (conj p1p2_9 (conj (p1p2_3886 Vplel Vepae Vello Vepbg Vepaf Vepab) (conj p1p2_25 p1p2_26))))). Qed. Lemma p1p2_3980: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep h b). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))=>((psym b h) Vepbh)). Qed. Lemma p1p2_3992: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(pl h s). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))=>((pcon h b s) (conj (p1p2_3980 Vplel Vepae Vello Vepbg Vepaf Vepab Velmp Vepbh) (p1p2_3888 Vplel Vepae Vello Vepbg Vepaf Vepab)))). Qed. Lemma p1p2_3993: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(el m p)->(ep b h)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))=>((goal4 s) (conj p1p2_45 (conj (p1p2_3889 Vplel Vepae Vello Vepbg Vepaf Vepab) (conj (p1p2_3992 Vplel Vepae Vello Vepbg Vepaf Vepab Velmp Vepbh) p1p2_28))))). Qed. Lemma p1p2_3994: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(el m p)->(el p q)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Velpq:(el p q))=>(goal2 Velpq)). Qed. Lemma p1p2_3995: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->(el m p)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))=>((or_ind ((p1p2_3993 Vplel Vepae Vello Vepbg Vepaf Vepab Velmp))((p1p2_3994 Vplel Vepae Vello Vepbg Vepaf Vepab Velmp)))(p1p2_3979 Vplel Vepae Vello Vepbg Vepaf Vepab Velmp))). Qed. Lemma p1p2_3996: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(ep a b)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Vepab:(ep a b))=>((or_ind ((p1p2_3976 Vplel Vepae Vello Vepbg Vepaf Vepab))((p1p2_3995 Vplel Vepae Vello Vepbg Vepaf Vepab)))(p1p2_3892 Vplel Vepae Vello Vepbg Vepaf Vepab))). Qed. Lemma p1p2_3998: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(el l n)->(el o n). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Velln:(el l n))=>((ltra o l n) (conj (p1p2_3856 Vplel Vepae Vello) Velln))). Qed. Lemma p1p2_3999: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(el l n)->(el n o). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Velln:(el l n))=>((lsym o n) (p1p2_3998 Vplel Vepae Vello Vepbg Vepaf Velln))). Qed. Lemma p1p2_4000: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->(el l n)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))(Velln:(el l n))=>(goal1 (p1p2_3999 Vplel Vepae Vello Vepbg Vepaf Velln))). Qed. Lemma p1p2_4001: (pl e l)->(ep a e)->(el l o)->(ep b g)->(ep a f)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Vepaf:(ep a f))=>((or_ind ((p1p2_3996 Vplel Vepae Vello Vepbg Vepaf))((p1p2_4000 Vplel Vepae Vello Vepbg Vepaf)))(p1p2_3871 Vplel Vepae Vello Vepbg Vepaf))). Qed. Lemma p1p2_4004: (pl e l)->(ep a e)->(el l o)->(ep b g)->(el s m)->(pl i m). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Velsm:(el s m))=>((lcon i s m) (conj p1p2_28 Velsm))). Qed. Lemma p1p2_4005: (pl e l)->(ep a e)->(el l o)->(ep b g)->(el s m)->(ep d i) \/ (el m r). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Velsm:(el s m))=>((unique m r d i) (conj p1p2_6 (conj p1p2_19 (conj (p1p2_4004 Vplel Vepae Vello Vepbg Velsm) p1p2_27))))). Qed. Lemma p1p2_4006: (pl e l)->(ep a e)->(el l o)->(ep b g)->(el s m)->(ep d i)->(ep i d). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Velsm:(el s m))(Vepdi:(ep d i))=>((psym d i) Vepdi)). Qed. Lemma p1p2_4007: (pl e l)->(ep a e)->(el l o)->(ep b g)->(el s m)->(ep d i)->(pl i p). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Velsm:(el s m))(Vepdi:(ep d i))=>((pcon i d p) (conj (p1p2_4006 Vplel Vepae Vello Vepbg Velsm Vepdi) p1p2_17))). Qed. Lemma p1p2_4008: (pl e l)->(ep a e)->(el l o)->(ep b g)->(el s m)->(ep d i)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Velsm:(el s m))(Vepdi:(ep d i))=>((goal4 p) (conj p1p2_42 (conj (p1p2_3861 Vplel Vepae Vello Vepbg) (conj p1p2_25 (p1p2_4007 Vplel Vepae Vello Vepbg Velsm Vepdi)))))). Qed. Lemma p1p2_4010: (pl e l)->(ep a e)->(el l o)->(ep b g)->(el s m)->(el m r)->(el s r). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Velsm:(el s m))(Velmr:(el m r))=>((ltra s m r) (conj Velsm Velmr))). Qed. Lemma p1p2_4011: (pl e l)->(ep a e)->(el l o)->(ep b g)->(el s m)->(el m r)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Velsm:(el s m))(Velmr:(el m r))=>(goal3 (p1p2_4010 Vplel Vepae Vello Vepbg Velsm Velmr))). Qed. Lemma p1p2_4012: (pl e l)->(ep a e)->(el l o)->(ep b g)->(el s m)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))(Velsm:(el s m))=>((or_ind ((p1p2_4008 Vplel Vepae Vello Vepbg Velsm))((p1p2_4011 Vplel Vepae Vello Vepbg Velsm)))(p1p2_4005 Vplel Vepae Vello Vepbg Velsm))). Qed. Lemma p1p2_4013: (pl e l)->(ep a e)->(el l o)->(ep b g)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Vepbg:(ep b g))=>((or_ind ((p1p2_4001 Vplel Vepae Vello Vepbg))((p1p2_4012 Vplel Vepae Vello Vepbg)))(p1p2_3862 Vplel Vepae Vello Vepbg))). Qed. Lemma p1p2_4014: (pl e l)->(ep a e)->(el l o)->(el n l)->(el l n). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Velnl:(el n l))=>((lsym n l) Velnl)). Qed. Lemma p1p2_4015: (pl e l)->(ep a e)->(el l o)->(el n l)->(el o n). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Velnl:(el n l))=>((ltra o l n) (conj (p1p2_3856 Vplel Vepae Vello) (p1p2_4014 Vplel Vepae Vello Velnl)))). Qed. Lemma p1p2_4016: (pl e l)->(ep a e)->(el l o)->(el n l)->(el n o). Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Velnl:(el n l))=>((lsym o n) (p1p2_4015 Vplel Vepae Vello Velnl))). Qed. Lemma p1p2_4017: (pl e l)->(ep a e)->(el l o)->(el n l)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))(Velnl:(el n l))=>(goal1 (p1p2_4016 Vplel Vepae Vello Velnl))). Qed. Lemma p1p2_4018: (pl e l)->(ep a e)->(el l o)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))(Vello:(el l o))=>((or_ind ((p1p2_4013 Vplel Vepae Vello))((p1p2_4017 Vplel Vepae Vello)))(p1p2_3859 Vplel Vepae Vello))). Qed. Lemma p1p2_4019: (pl e l)->(ep a e)->goal. Proof. exact (fun (Vplel:(pl e l))(Vepae:(ep a e))=>((or_ind ((p1p2_3855 Vplel Vepae))((p1p2_4018 Vplel Vepae)))(p1p2_3425 Vplel Vepae))). Qed. Lemma p1p2_4020: (pl e l)->(el l q)->(el q l). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))=>((lsym l q) Vellq)). Qed. Lemma p1p2_4023: (pl e l)->(el l q)->(pl h l). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))=>((lcon h q l) (conj p1p2_26 (p1p2_4020 Vplel Vellq)))). Qed. Lemma p1p2_4024: (pl e l)->(el l q)->(ep c e) \/ (el o l). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))=>((unique o l c e) (conj p1p2_8 (conj p1p2_21 (conj p1p2_16 Vplel))))). Qed. Lemma p1p2_4025: (pl e l)->(el l q)->(ep c e)->(ep e c). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))=>((psym c e) Vepce)). Qed. Lemma p1p2_4027: (pl e l)->(el l q)->(ep c e)->(pl e r). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))=>((pcon e c r) (conj (p1p2_4025 Vplel Vellq Vepce) p1p2_11))). Qed. Lemma p1p2_4028: (pl e l)->(el l q)->(ep c e)->(ep d e) \/ (el m r). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))=>((unique m r d e) (conj p1p2_6 (conj p1p2_19 (conj p1p2_14 (p1p2_4027 Vplel Vellq Vepce)))))). Qed. Lemma p1p2_4032: (pl e l)->(el l q)->(ep c e)->(ep d e)->(pl d o). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))=>((pcon d e o) (conj Vepde p1p2_16))). Qed. Lemma p1p2_4034: (pl e l)->(el l q)->(ep c e)->(ep d e)->(pl d l). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))=>((pcon d e l) (conj Vepde Vplel))). Qed. Lemma p1p2_4037: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d) \/ (el p l). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))=>((unique p l b d) (conj p1p2_9 (conj p1p2_13 (conj p1p2_17 (p1p2_4034 Vplel Vellq Vepce Vepde)))))). Qed. Lemma p1p2_4038: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(ep d b). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))=>((psym b d) Vepbd)). Qed. Lemma p1p2_4044: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(pl b r). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))=>((pcon b d r) (conj Vepbd p1p2_19))). Qed. Lemma p1p2_4045: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(pl b o). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))=>((pcon b d o) (conj Vepbd (p1p2_4032 Vplel Vellq Vepce Vepde)))). Qed. Lemma p1p2_4046: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(pl d n). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))=>((pcon d b n) (conj (p1p2_4038 Vplel Vellq Vepce Vepde Vepbd) p1p2_7))). Qed. Lemma p1p2_4049: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(ep d f) \/ (el m n). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))=>((unique m n d f) (conj p1p2_6 (conj (p1p2_4046 Vplel Vellq Vepce Vepde Vepbd) (conj p1p2_22 p1p2_15))))). Qed. Lemma p1p2_4057: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(ep d f)->(pl d s). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Vepdf:(ep d f))=>((pcon d f s) (conj Vepdf p1p2_20))). Qed. Lemma p1p2_4060: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(ep d f)->(pl b s). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Vepdf:(ep d f))=>((pcon b d s) (conj Vepbd (p1p2_4057 Vplel Vellq Vepce Vepde Vepbd Vepdf)))). Qed. Lemma p1p2_4066: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(ep d f)->(ep a b) \/ (el l s). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Vepdf:(ep d f))=>((unique l s a b) (conj p1p2_5 (conj p1p2_12 (conj p1p2_13 (p1p2_4060 Vplel Vellq Vepce Vepde Vepbd Vepdf)))))). Qed. Lemma p1p2_4077: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(ep d f)->(ep a b)->(pl a p). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))=>((pcon a b p) (conj Vepab p1p2_9))). Qed. Lemma p1p2_4079: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(ep d f)->(ep a b)->(pl a r). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))=>((pcon a b r) (conj Vepab (p1p2_4044 Vplel Vellq Vepce Vepde Vepbd)))). Qed. Lemma p1p2_4081: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(ep d f)->(ep a b)->(ep a h) \/ (el l p). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))=>((unique l p a h) (conj p1p2_5 (conj (p1p2_4077 Vplel Vellq Vepce Vepde Vepbd Vepdf Vepab) (conj (p1p2_4023 Vplel Vellq) p1p2_25))))). Qed. Lemma p1p2_4082: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(ep d f)->(ep a b)->(ep a h)->(ep h a). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepah:(ep a h))=>((psym a h) Vepah)). Qed. Lemma p1p2_4096: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(ep d f)->(ep a b)->(ep a h)->(pl h r). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepah:(ep a h))=>((pcon h a r) (conj (p1p2_4082 Vplel Vellq Vepce Vepde Vepbd Vepdf Vepab Vepah) (p1p2_4079 Vplel Vellq Vepce Vepde Vepbd Vepdf Vepab)))). Qed. Lemma p1p2_4098: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(ep d f)->(ep a b)->(ep a h)->(ep b g) \/ (el n o). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepah:(ep a h))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_4045 Vplel Vellq Vepce Vepde Vepbd) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_4099: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(ep d f)->(ep a b)->(ep a h)->(ep b g)->(ep g b). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepah:(ep a h))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_4116: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(ep d f)->(ep a b)->(ep a h)->(ep b g)->(pl g r). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepah:(ep a h))(Vepbg:(ep b g))=>((pcon g b r) (conj (p1p2_4099 Vplel Vellq Vepce Vepde Vepbd Vepdf Vepab Vepah Vepbg) (p1p2_4044 Vplel Vellq Vepce Vepde Vepbd)))). Qed. Lemma p1p2_4117: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(ep d f)->(ep a b)->(ep a h)->(ep b g)->goal. Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepah:(ep a h))(Vepbg:(ep b g))=>((goal4 r) (conj p1p2_44 (conj (p1p2_4116 Vplel Vellq Vepce Vepde Vepbd Vepdf Vepab Vepah Vepbg) (conj (p1p2_4096 Vplel Vellq Vepce Vepde Vepbd Vepdf Vepab Vepah) p1p2_27))))). Qed. Lemma p1p2_4118: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(ep d f)->(ep a b)->(ep a h)->(el n o)->goal. Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepah:(ep a h))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_4119: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(ep d f)->(ep a b)->(ep a h)->goal. Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vepah:(ep a h))=>((or_ind ((p1p2_4117 Vplel Vellq Vepce Vepde Vepbd Vepdf Vepab Vepah))((p1p2_4118 Vplel Vellq Vepce Vepde Vepbd Vepdf Vepab Vepah)))(p1p2_4098 Vplel Vellq Vepce Vepde Vepbd Vepdf Vepab Vepah))). Qed. Lemma p1p2_4121: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(ep d f)->(ep a b)->(el l p)->(el q p). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellp:(el l p))=>((ltra q l p) (conj (p1p2_4020 Vplel Vellq) Vellp))). Qed. Lemma p1p2_4122: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(ep d f)->(ep a b)->(el l p)->(el p q). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellp:(el l p))=>((lsym q p) (p1p2_4121 Vplel Vellq Vepce Vepde Vepbd Vepdf Vepab Vellp))). Qed. Lemma p1p2_4123: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(ep d f)->(ep a b)->(el l p)->goal. Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))(Vellp:(el l p))=>(goal2 (p1p2_4122 Vplel Vellq Vepce Vepde Vepbd Vepdf Vepab Vellp))). Qed. Lemma p1p2_4124: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(ep d f)->(ep a b)->goal. Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vepab:(ep a b))=>((or_ind ((p1p2_4119 Vplel Vellq Vepce Vepde Vepbd Vepdf Vepab))((p1p2_4123 Vplel Vellq Vepce Vepde Vepbd Vepdf Vepab)))(p1p2_4081 Vplel Vellq Vepce Vepde Vepbd Vepdf Vepab))). Qed. Lemma p1p2_4125: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(ep d f)->(el l s)->(el s l). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))=>((lsym l s) Vells)). Qed. Lemma p1p2_4129: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(ep d f)->(el l s)->(pl i l). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))=>((lcon i s l) (conj p1p2_28 (p1p2_4125 Vplel Vellq Vepce Vepde Vepbd Vepdf Vells)))). Qed. Lemma p1p2_4131: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(ep d f)->(el l s)->(ep b g) \/ (el n o). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_4045 Vplel Vellq Vepce Vepde Vepbd) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_4132: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(ep d f)->(el l s)->(ep b g)->(ep g b). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_4142: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(ep d f)->(el l s)->(ep b g)->(pl g l). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepbg:(ep b g))=>((pcon g b l) (conj (p1p2_4132 Vplel Vellq Vepce Vepde Vepbd Vepdf Vells Vepbg) p1p2_13))). Qed. Lemma p1p2_4143: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(ep d f)->(el l s)->(ep b g)->goal. Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Vepbg:(ep b g))=>((goal4 l) (conj p1p2_38 (conj (p1p2_4142 Vplel Vellq Vepce Vepde Vepbd Vepdf Vells Vepbg) (conj (p1p2_4023 Vplel Vellq) (p1p2_4129 Vplel Vellq Vepce Vepde Vepbd Vepdf Vells)))))). Qed. Lemma p1p2_4144: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(ep d f)->(el l s)->(el n o)->goal. Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_4145: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(ep d f)->(el l s)->goal. Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Vepdf:(ep d f))(Vells:(el l s))=>((or_ind ((p1p2_4143 Vplel Vellq Vepce Vepde Vepbd Vepdf Vells))((p1p2_4144 Vplel Vellq Vepce Vepde Vepbd Vepdf Vells)))(p1p2_4131 Vplel Vellq Vepce Vepde Vepbd Vepdf Vells))). Qed. Lemma p1p2_4146: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(ep d f)->goal. Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Vepdf:(ep d f))=>((or_ind ((p1p2_4124 Vplel Vellq Vepce Vepde Vepbd Vepdf))((p1p2_4145 Vplel Vellq Vepce Vepde Vepbd Vepdf)))(p1p2_4066 Vplel Vellq Vepce Vepde Vepbd Vepdf))). Qed. Lemma p1p2_4147: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(el m n)->(el n m). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Velmn:(el m n))=>((lsym m n) Velmn)). Qed. Lemma p1p2_4148: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(el m n)->(pl g m). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Velmn:(el m n))=>((lcon g n m) (conj p1p2_23 (p1p2_4147 Vplel Vellq Vepce Vepde Vepbd Velmn)))). Qed. Lemma p1p2_4149: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(el m n)->(ep d g) \/ (el m o). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Velmn:(el m n))=>((unique m o d g) (conj p1p2_6 (conj (p1p2_4032 Vplel Vellq Vepce Vepde) (conj (p1p2_4148 Vplel Vellq Vepce Vepde Vepbd Velmn) p1p2_24))))). Qed. Lemma p1p2_4150: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(el m n)->(ep d g)->(ep g d). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Velmn:(el m n))(Vepdg:(ep d g))=>((psym d g) Vepdg)). Qed. Lemma p1p2_4158: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(el m n)->(ep d g)->(pl g r). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Velmn:(el m n))(Vepdg:(ep d g))=>((pcon g d r) (conj (p1p2_4150 Vplel Vellq Vepce Vepde Vepbd Velmn Vepdg) p1p2_19))). Qed. Lemma p1p2_4161: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(el m n)->(ep d g)->(ep b h) \/ (el p l). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Velmn:(el m n))(Vepdg:(ep d g))=>((unique p l b h) (conj p1p2_9 (conj p1p2_13 (conj p1p2_25 (p1p2_4023 Vplel Vellq)))))). Qed. Lemma p1p2_4162: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(el m n)->(ep d g)->(ep b h)->(ep h b). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Velmn:(el m n))(Vepdg:(ep d g))(Vepbh:(ep b h))=>((psym b h) Vepbh)). Qed. Lemma p1p2_4173: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(el m n)->(ep d g)->(ep b h)->(pl h r). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Velmn:(el m n))(Vepdg:(ep d g))(Vepbh:(ep b h))=>((pcon h b r) (conj (p1p2_4162 Vplel Vellq Vepce Vepde Vepbd Velmn Vepdg Vepbh) (p1p2_4044 Vplel Vellq Vepce Vepde Vepbd)))). Qed. Lemma p1p2_4174: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(el m n)->(ep d g)->(ep b h)->goal. Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Velmn:(el m n))(Vepdg:(ep d g))(Vepbh:(ep b h))=>((goal4 r) (conj p1p2_44 (conj (p1p2_4158 Vplel Vellq Vepce Vepde Vepbd Velmn Vepdg) (conj (p1p2_4173 Vplel Vellq Vepce Vepde Vepbd Velmn Vepdg Vepbh) p1p2_27))))). Qed. Lemma p1p2_4175: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(el m n)->(ep d g)->(el p l)->(el l p). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Velmn:(el m n))(Vepdg:(ep d g))(Velpl:(el p l))=>((lsym p l) Velpl)). Qed. Lemma p1p2_4176: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(el m n)->(ep d g)->(el p l)->(el q p). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Velmn:(el m n))(Vepdg:(ep d g))(Velpl:(el p l))=>((ltra q l p) (conj (p1p2_4020 Vplel Vellq) (p1p2_4175 Vplel Vellq Vepce Vepde Vepbd Velmn Vepdg Velpl)))). Qed. Lemma p1p2_4177: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(el m n)->(ep d g)->(el p l)->(el p q). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Velmn:(el m n))(Vepdg:(ep d g))(Velpl:(el p l))=>((lsym q p) (p1p2_4176 Vplel Vellq Vepce Vepde Vepbd Velmn Vepdg Velpl))). Qed. Lemma p1p2_4178: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(el m n)->(ep d g)->(el p l)->goal. Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Velmn:(el m n))(Vepdg:(ep d g))(Velpl:(el p l))=>(goal2 (p1p2_4177 Vplel Vellq Vepce Vepde Vepbd Velmn Vepdg Velpl))). Qed. Lemma p1p2_4179: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(el m n)->(ep d g)->goal. Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Velmn:(el m n))(Vepdg:(ep d g))=>((or_ind ((p1p2_4174 Vplel Vellq Vepce Vepde Vepbd Velmn Vepdg))((p1p2_4178 Vplel Vellq Vepce Vepde Vepbd Velmn Vepdg)))(p1p2_4161 Vplel Vellq Vepce Vepde Vepbd Velmn Vepdg))). Qed. Lemma p1p2_4181: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(el m n)->(el m o)->(el n o). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Velmn:(el m n))(Velmo:(el m o))=>((ltra n m o) (conj (p1p2_4147 Vplel Vellq Vepce Vepde Vepbd Velmn) Velmo))). Qed. Lemma p1p2_4182: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(el m n)->(el m o)->goal. Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Velmn:(el m n))(Velmo:(el m o))=>(goal1 (p1p2_4181 Vplel Vellq Vepce Vepde Vepbd Velmn Velmo))). Qed. Lemma p1p2_4183: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->(el m n)->goal. Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))(Velmn:(el m n))=>((or_ind ((p1p2_4179 Vplel Vellq Vepce Vepde Vepbd Velmn))((p1p2_4182 Vplel Vellq Vepce Vepde Vepbd Velmn)))(p1p2_4149 Vplel Vellq Vepce Vepde Vepbd Velmn))). Qed. Lemma p1p2_4184: (pl e l)->(el l q)->(ep c e)->(ep d e)->(ep b d)->goal. Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Vepbd:(ep b d))=>((or_ind ((p1p2_4146 Vplel Vellq Vepce Vepde Vepbd))((p1p2_4183 Vplel Vellq Vepce Vepde Vepbd)))(p1p2_4049 Vplel Vellq Vepce Vepde Vepbd))). Qed. Lemma p1p2_4185: (pl e l)->(el l q)->(ep c e)->(ep d e)->(el p l)->(el l p). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Velpl:(el p l))=>((lsym p l) Velpl)). Qed. Lemma p1p2_4186: (pl e l)->(el l q)->(ep c e)->(ep d e)->(el p l)->(el q p). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Velpl:(el p l))=>((ltra q l p) (conj (p1p2_4020 Vplel Vellq) (p1p2_4185 Vplel Vellq Vepce Vepde Velpl)))). Qed. Lemma p1p2_4187: (pl e l)->(el l q)->(ep c e)->(ep d e)->(el p l)->(el p q). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Velpl:(el p l))=>((lsym q p) (p1p2_4186 Vplel Vellq Vepce Vepde Velpl))). Qed. Lemma p1p2_4188: (pl e l)->(el l q)->(ep c e)->(ep d e)->(el p l)->goal. Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))(Velpl:(el p l))=>(goal2 (p1p2_4187 Vplel Vellq Vepce Vepde Velpl))). Qed. Lemma p1p2_4189: (pl e l)->(el l q)->(ep c e)->(ep d e)->goal. Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Vepde:(ep d e))=>((or_ind ((p1p2_4184 Vplel Vellq Vepce Vepde))((p1p2_4188 Vplel Vellq Vepce Vepde)))(p1p2_4037 Vplel Vellq Vepce Vepde))). Qed. Lemma p1p2_4190: (pl e l)->(el l q)->(ep c e)->(el m r)->(el r m). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Velmr:(el m r))=>((lsym m r) Velmr)). Qed. Lemma p1p2_4192: (pl e l)->(el l q)->(ep c e)->(el m r)->(pl i m). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Velmr:(el m r))=>((lcon i r m) (conj p1p2_27 (p1p2_4190 Vplel Vellq Vepce Velmr)))). Qed. Lemma p1p2_4193: (pl e l)->(el l q)->(ep c e)->(el m r)->(ep b h) \/ (el p l). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Velmr:(el m r))=>((unique p l b h) (conj p1p2_9 (conj p1p2_13 (conj p1p2_25 (p1p2_4023 Vplel Vellq)))))). Qed. Lemma p1p2_4194: (pl e l)->(el l q)->(ep c e)->(el m r)->(ep b h)->(ep h b). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Velmr:(el m r))(Vepbh:(ep b h))=>((psym b h) Vepbh)). Qed. Lemma p1p2_4195: (pl e l)->(el l q)->(ep c e)->(el m r)->(ep b h)->(pl h n). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Velmr:(el m r))(Vepbh:(ep b h))=>((pcon h b n) (conj (p1p2_4194 Vplel Vellq Vepce Velmr Vepbh) p1p2_7))). Qed. Lemma p1p2_4196: (pl e l)->(el l q)->(ep c e)->(el m r)->(ep b h)->(ep f i) \/ (el s m). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Velmr:(el m r))(Vepbh:(ep b h))=>((unique s m f i) (conj p1p2_20 (conj p1p2_22 (conj p1p2_28 (p1p2_4192 Vplel Vellq Vepce Velmr)))))). Qed. Lemma p1p2_4197: (pl e l)->(el l q)->(ep c e)->(el m r)->(ep b h)->(ep f i)->(ep i f). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Velmr:(el m r))(Vepbh:(ep b h))(Vepfi:(ep f i))=>((psym f i) Vepfi)). Qed. Lemma p1p2_4198: (pl e l)->(el l q)->(ep c e)->(el m r)->(ep b h)->(ep f i)->(pl i n). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Velmr:(el m r))(Vepbh:(ep b h))(Vepfi:(ep f i))=>((pcon i f n) (conj (p1p2_4197 Vplel Vellq Vepce Velmr Vepbh Vepfi) p1p2_15))). Qed. Lemma p1p2_4199: (pl e l)->(el l q)->(ep c e)->(el m r)->(ep b h)->(ep f i)->goal. Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Velmr:(el m r))(Vepbh:(ep b h))(Vepfi:(ep f i))=>((goal4 n) (conj p1p2_40 (conj p1p2_23 (conj (p1p2_4195 Vplel Vellq Vepce Velmr Vepbh) (p1p2_4198 Vplel Vellq Vepce Velmr Vepbh Vepfi)))))). Qed. Lemma p1p2_4200: (pl e l)->(el l q)->(ep c e)->(el m r)->(ep b h)->(el s m)->(el m s). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Velmr:(el m r))(Vepbh:(ep b h))(Velsm:(el s m))=>((lsym s m) Velsm)). Qed. Lemma p1p2_4201: (pl e l)->(el l q)->(ep c e)->(el m r)->(ep b h)->(el s m)->(el r s). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Velmr:(el m r))(Vepbh:(ep b h))(Velsm:(el s m))=>((ltra r m s) (conj (p1p2_4190 Vplel Vellq Vepce Velmr) (p1p2_4200 Vplel Vellq Vepce Velmr Vepbh Velsm)))). Qed. Lemma p1p2_4202: (pl e l)->(el l q)->(ep c e)->(el m r)->(ep b h)->(el s m)->(el s r). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Velmr:(el m r))(Vepbh:(ep b h))(Velsm:(el s m))=>((lsym r s) (p1p2_4201 Vplel Vellq Vepce Velmr Vepbh Velsm))). Qed. Lemma p1p2_4203: (pl e l)->(el l q)->(ep c e)->(el m r)->(ep b h)->(el s m)->goal. Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Velmr:(el m r))(Vepbh:(ep b h))(Velsm:(el s m))=>(goal3 (p1p2_4202 Vplel Vellq Vepce Velmr Vepbh Velsm))). Qed. Lemma p1p2_4204: (pl e l)->(el l q)->(ep c e)->(el m r)->(ep b h)->goal. Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Velmr:(el m r))(Vepbh:(ep b h))=>((or_ind ((p1p2_4199 Vplel Vellq Vepce Velmr Vepbh))((p1p2_4203 Vplel Vellq Vepce Velmr Vepbh)))(p1p2_4196 Vplel Vellq Vepce Velmr Vepbh))). Qed. Lemma p1p2_4205: (pl e l)->(el l q)->(ep c e)->(el m r)->(el p l)->(el l p). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Velmr:(el m r))(Velpl:(el p l))=>((lsym p l) Velpl)). Qed. Lemma p1p2_4206: (pl e l)->(el l q)->(ep c e)->(el m r)->(el p l)->(el q p). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Velmr:(el m r))(Velpl:(el p l))=>((ltra q l p) (conj (p1p2_4020 Vplel Vellq) (p1p2_4205 Vplel Vellq Vepce Velmr Velpl)))). Qed. Lemma p1p2_4207: (pl e l)->(el l q)->(ep c e)->(el m r)->(el p l)->(el p q). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Velmr:(el m r))(Velpl:(el p l))=>((lsym q p) (p1p2_4206 Vplel Vellq Vepce Velmr Velpl))). Qed. Lemma p1p2_4208: (pl e l)->(el l q)->(ep c e)->(el m r)->(el p l)->goal. Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Velmr:(el m r))(Velpl:(el p l))=>(goal2 (p1p2_4207 Vplel Vellq Vepce Velmr Velpl))). Qed. Lemma p1p2_4209: (pl e l)->(el l q)->(ep c e)->(el m r)->goal. Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))(Velmr:(el m r))=>((or_ind ((p1p2_4204 Vplel Vellq Vepce Velmr))((p1p2_4208 Vplel Vellq Vepce Velmr)))(p1p2_4193 Vplel Vellq Vepce Velmr))). Qed. Lemma p1p2_4210: (pl e l)->(el l q)->(ep c e)->goal. Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Vepce:(ep c e))=>((or_ind ((p1p2_4189 Vplel Vellq Vepce))((p1p2_4209 Vplel Vellq Vepce)))(p1p2_4028 Vplel Vellq Vepce))). Qed. Lemma p1p2_4216: (pl e l)->(el l q)->(el o l)->(pl g l). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Velol:(el o l))=>((lcon g o l) (conj p1p2_24 Velol))). Qed. Lemma p1p2_4219: (pl e l)->(el l q)->(el o l)->(ep b g) \/ (el n l). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Velol:(el o l))=>((unique n l b g) (conj p1p2_7 (conj p1p2_13 (conj p1p2_23 (p1p2_4216 Vplel Vellq Velol)))))). Qed. Lemma p1p2_4220: (pl e l)->(el l q)->(el o l)->(ep b g)->(ep g b). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Velol:(el o l))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_4222: (pl e l)->(el l q)->(el o l)->(ep b g)->(ep b h) \/ (el p l). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Velol:(el o l))(Vepbg:(ep b g))=>((unique p l b h) (conj p1p2_9 (conj p1p2_13 (conj p1p2_25 (p1p2_4023 Vplel Vellq)))))). Qed. Lemma p1p2_4223: (pl e l)->(el l q)->(el o l)->(ep b g)->(ep b h)->(ep h b). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Velol:(el o l))(Vepbg:(ep b g))(Vepbh:(ep b h))=>((psym b h) Vepbh)). Qed. Lemma p1p2_4227: (pl e l)->(el l q)->(el o l)->(ep b g)->(ep b h)->(exists A:dom,(pl a A)/\(pl d A)). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Velol:(el o l))(Vepbg:(ep b g))(Vepbh:(ep b h))=>((line a d) (conj p1p2_29 p1p2_30))). Qed. Lemma p1p2_4229: (pl e l)->(el l q)->(el o l)->(ep b g)->(ep b h)->forall C0:dom,(pl a C0)->(pl d C0)->(exists A:dom,(pl b A)/\(pl i A)). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Velol:(el o l))(Vepbg:(ep b g))(Vepbh:(ep b h))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))=>((line b i) (conj p1p2_31 p1p2_37))). Qed. Lemma p1p2_4230: (pl e l)->(el l q)->(el o l)->(ep b g)->(ep b h)->forall C0:dom,(pl a C0)->(pl d C0)->forall C1:dom,(pl b C1)->(pl i C1)->(el C1 C1). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Velol:(el o l))(Vepbg:(ep b g))(Vepbh:(ep b h))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))(C1:dom)(VplbC1:(pl b C1))(VpliC1:(pl i C1))=>((lref b C1) VplbC1)). Qed. Lemma p1p2_4231: (pl e l)->(el l q)->(el o l)->(ep b g)->(ep b h)->forall C0:dom,(pl a C0)->(pl d C0)->forall C1:dom,(pl b C1)->(pl i C1)->(pl g C1). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Velol:(el o l))(Vepbg:(ep b g))(Vepbh:(ep b h))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))(C1:dom)(VplbC1:(pl b C1))(VpliC1:(pl i C1))=>((pcon g b C1) (conj (p1p2_4220 Vplel Vellq Velol Vepbg) VplbC1))). Qed. Lemma p1p2_4232: (pl e l)->(el l q)->(el o l)->(ep b g)->(ep b h)->forall C0:dom,(pl a C0)->(pl d C0)->forall C1:dom,(pl b C1)->(pl i C1)->(pl h C1). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Velol:(el o l))(Vepbg:(ep b g))(Vepbh:(ep b h))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))(C1:dom)(VplbC1:(pl b C1))(VpliC1:(pl i C1))=>((pcon h b C1) (conj (p1p2_4223 Vplel Vellq Velol Vepbg Vepbh) VplbC1))). Qed. Lemma p1p2_4233: (pl e l)->(el l q)->(el o l)->(ep b g)->(ep b h)->forall C0:dom,(pl a C0)->(pl d C0)->forall C1:dom,(pl b C1)->(pl i C1)->goal. Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Velol:(el o l))(Vepbg:(ep b g))(Vepbh:(ep b h))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))(C1:dom)(VplbC1:(pl b C1))(VpliC1:(pl i C1))=>((goal4 C1) (conj (p1p2_4230 Vplel Vellq Velol Vepbg Vepbh C0 VplaC0 VpldC0 C1 VplbC1 VpliC1) (conj (p1p2_4231 Vplel Vellq Velol Vepbg Vepbh C0 VplaC0 VpldC0 C1 VplbC1 VpliC1) (conj (p1p2_4232 Vplel Vellq Velol Vepbg Vepbh C0 VplaC0 VpldC0 C1 VplbC1 VpliC1) VpliC1))))). Qed. Lemma p1p2_4234: (pl e l)->(el l q)->(el o l)->(ep b g)->(ep b h)->forall C0:dom,(pl a C0)->(pl d C0)->goal. Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Velol:(el o l))(Vepbg:(ep b g))(Vepbh:(ep b h))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))=>((ex_ind (P:=fun C1:dom=>(pl b C1)/\(pl i C1))(fun C1:dom=>(and_ind (p1p2_4233 Vplel Vellq Velol Vepbg Vepbh C0 VplaC0 VpldC0 C1))))(p1p2_4229 Vplel Vellq Velol Vepbg Vepbh C0 VplaC0 VpldC0))). Qed. Lemma p1p2_4235: (pl e l)->(el l q)->(el o l)->(ep b g)->(ep b h)->goal. Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Velol:(el o l))(Vepbg:(ep b g))(Vepbh:(ep b h))=>((ex_ind (P:=fun C0:dom=>(pl a C0)/\(pl d C0))(fun C0:dom=>(and_ind (p1p2_4234 Vplel Vellq Velol Vepbg Vepbh C0))))(p1p2_4227 Vplel Vellq Velol Vepbg Vepbh))). Qed. Lemma p1p2_4236: (pl e l)->(el l q)->(el o l)->(ep b g)->(el p l)->(el l p). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Velol:(el o l))(Vepbg:(ep b g))(Velpl:(el p l))=>((lsym p l) Velpl)). Qed. Lemma p1p2_4237: (pl e l)->(el l q)->(el o l)->(ep b g)->(el p l)->(el q p). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Velol:(el o l))(Vepbg:(ep b g))(Velpl:(el p l))=>((ltra q l p) (conj (p1p2_4020 Vplel Vellq) (p1p2_4236 Vplel Vellq Velol Vepbg Velpl)))). Qed. Lemma p1p2_4238: (pl e l)->(el l q)->(el o l)->(ep b g)->(el p l)->(el p q). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Velol:(el o l))(Vepbg:(ep b g))(Velpl:(el p l))=>((lsym q p) (p1p2_4237 Vplel Vellq Velol Vepbg Velpl))). Qed. Lemma p1p2_4239: (pl e l)->(el l q)->(el o l)->(ep b g)->(el p l)->goal. Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Velol:(el o l))(Vepbg:(ep b g))(Velpl:(el p l))=>(goal2 (p1p2_4238 Vplel Vellq Velol Vepbg Velpl))). Qed. Lemma p1p2_4240: (pl e l)->(el l q)->(el o l)->(ep b g)->goal. Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Velol:(el o l))(Vepbg:(ep b g))=>((or_ind ((p1p2_4235 Vplel Vellq Velol Vepbg))((p1p2_4239 Vplel Vellq Velol Vepbg)))(p1p2_4222 Vplel Vellq Velol Vepbg))). Qed. Lemma p1p2_4241: (pl e l)->(el l q)->(el o l)->(el n l)->(el l n). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Velol:(el o l))(Velnl:(el n l))=>((lsym n l) Velnl)). Qed. Lemma p1p2_4244: (pl e l)->(el l q)->(el o l)->(el n l)->(el o n). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Velol:(el o l))(Velnl:(el n l))=>((ltra o l n) (conj Velol (p1p2_4241 Vplel Vellq Velol Velnl)))). Qed. Lemma p1p2_4245: (pl e l)->(el l q)->(el o l)->(el n l)->(el n o). Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Velol:(el o l))(Velnl:(el n l))=>((lsym o n) (p1p2_4244 Vplel Vellq Velol Velnl))). Qed. Lemma p1p2_4246: (pl e l)->(el l q)->(el o l)->(el n l)->goal. Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Velol:(el o l))(Velnl:(el n l))=>(goal1 (p1p2_4245 Vplel Vellq Velol Velnl))). Qed. Lemma p1p2_4247: (pl e l)->(el l q)->(el o l)->goal. Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))(Velol:(el o l))=>((or_ind ((p1p2_4240 Vplel Vellq Velol))((p1p2_4246 Vplel Vellq Velol)))(p1p2_4219 Vplel Vellq Velol))). Qed. Lemma p1p2_4248: (pl e l)->(el l q)->goal. Proof. exact (fun (Vplel:(pl e l))(Vellq:(el l q))=>((or_ind ((p1p2_4210 Vplel Vellq))((p1p2_4247 Vplel Vellq)))(p1p2_4024 Vplel Vellq))). Qed. Lemma p1p2_4249: (pl e l)->goal. Proof. exact (fun (Vplel:(pl e l))=>((or_ind ((p1p2_4019 Vplel))((p1p2_4248 Vplel)))(p1p2_3420 Vplel))). Qed. Lemma p1p2_4250: (pl f l)->(ep a f) \/ (el l s). Proof. exact (fun (Vplfl:(pl f l))=>((unique l s a f) (conj p1p2_5 (conj p1p2_12 (conj Vplfl p1p2_20))))). Qed. Lemma p1p2_4251: (pl f l)->(ep a f)->(ep f a). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))=>((psym a f) Vepaf)). Qed. Lemma p1p2_4252: (pl f l)->(ep a f)->(pl a n). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))=>((pcon a f n) (conj Vepaf p1p2_15))). Qed. Lemma p1p2_4253: (pl f l)->(ep a f)->(pl a m). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))=>((pcon a f m) (conj Vepaf p1p2_22))). Qed. Lemma p1p2_4254: (pl f l)->(ep a f)->(pl f q). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))=>((pcon f a q) (conj (p1p2_4251 Vplfl Vepaf) p1p2_10))). Qed. Lemma p1p2_4255: (pl f l)->(ep a f)->(ep a b) \/ (el l n). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))=>((unique l n a b) (conj p1p2_5 (conj (p1p2_4252 Vplfl Vepaf) (conj p1p2_13 p1p2_7))))). Qed. Lemma p1p2_4256: (pl f l)->(ep a f)->(ep a b)->(ep b a). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))=>((psym a b) Vepab)). Qed. Lemma p1p2_4259: (pl f l)->(ep a f)->(ep a b)->(pl a p). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))=>((pcon a b p) (conj Vepab p1p2_9))). Qed. Lemma p1p2_4260: (pl f l)->(ep a f)->(ep a b)->(pl f p). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))=>((pcon f a p) (conj (p1p2_4251 Vplfl Vepaf) (p1p2_4259 Vplfl Vepaf Vepab)))). Qed. Lemma p1p2_4261: (pl f l)->(ep a f)->(ep a b)->(pl b q). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))=>((pcon b a q) (conj (p1p2_4256 Vplfl Vepaf Vepab) p1p2_10))). Qed. Lemma p1p2_4262: (pl f l)->(ep a f)->(ep a b)->(pl b s). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))=>((pcon b a s) (conj (p1p2_4256 Vplfl Vepaf Vepab) p1p2_12))). Qed. Lemma p1p2_4264: (pl f l)->(ep a f)->(ep a b)->(ep d f) \/ (el m p). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))=>((unique m p d f) (conj p1p2_6 (conj p1p2_17 (conj p1p2_22 (p1p2_4260 Vplfl Vepaf Vepab)))))). Qed. Lemma p1p2_4265: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep f d). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))=>((psym d f) Vepdf)). Qed. Lemma p1p2_4270: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(pl d n). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))=>((pcon d f n) (conj Vepdf p1p2_15))). Qed. Lemma p1p2_4271: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(pl d s). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))=>((pcon d f s) (conj Vepdf p1p2_20))). Qed. Lemma p1p2_4273: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(pl d q). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))=>((pcon d f q) (conj Vepdf (p1p2_4254 Vplfl Vepaf)))). Qed. Lemma p1p2_4274: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(pl f r). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))=>((pcon f d r) (conj (p1p2_4265 Vplfl Vepaf Vepab Vepdf) p1p2_19))). Qed. Lemma p1p2_4275: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(pl a r). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))=>((pcon a f r) (conj Vepaf (p1p2_4274 Vplfl Vepaf Vepab Vepdf)))). Qed. Lemma p1p2_4277: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c) \/ (el l r). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))=>((unique l r a c) (conj p1p2_5 (conj (p1p2_4275 Vplfl Vepaf Vepab Vepdf) (conj p1p2_21 p1p2_11))))). Qed. Lemma p1p2_4285: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(pl a o). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))=>((pcon a c o) (conj Vepac p1p2_8))). Qed. Lemma p1p2_4286: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(pl f o). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))=>((pcon f a o) (conj (p1p2_4251 Vplfl Vepaf) (p1p2_4285 Vplfl Vepaf Vepab Vepdf Vepac)))). Qed. Lemma p1p2_4287: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(pl b o). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))=>((pcon b a o) (conj (p1p2_4256 Vplfl Vepaf Vepab) (p1p2_4285 Vplfl Vepaf Vepab Vepdf Vepac)))). Qed. Lemma p1p2_4288: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(pl d o). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))=>((pcon d f o) (conj Vepdf (p1p2_4286 Vplfl Vepaf Vepab Vepdf Vepac)))). Qed. Lemma p1p2_4294: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(ep d e) \/ (el m q). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))=>((unique m q d e) (conj p1p2_6 (conj (p1p2_4273 Vplfl Vepaf Vepab Vepdf) (conj p1p2_14 p1p2_18))))). Qed. Lemma p1p2_4309: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(ep d e)->(ep b g) \/ (el n o). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Vepde:(ep d e))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_4287 Vplfl Vepaf Vepab Vepdf Vepac) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_4310: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(ep d e)->(ep b g)->(ep g b). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_4324: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(ep d e)->(ep b g)->(pl g s). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))=>((pcon g b s) (conj (p1p2_4310 Vplfl Vepaf Vepab Vepdf Vepac Vepde Vepbg) (p1p2_4262 Vplfl Vepaf Vepab)))). Qed. Lemma p1p2_4327: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(ep d e)->(ep b g)->(ep b h) \/ (el p q). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))=>((unique p q b h) (conj p1p2_9 (conj (p1p2_4261 Vplfl Vepaf Vepab) (conj p1p2_25 p1p2_26))))). Qed. Lemma p1p2_4328: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(ep d e)->(ep b g)->(ep b h)->(ep h b). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))(Vepbh:(ep b h))=>((psym b h) Vepbh)). Qed. Lemma p1p2_4343: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(ep d e)->(ep b g)->(ep b h)->(pl h s). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))(Vepbh:(ep b h))=>((pcon h b s) (conj (p1p2_4328 Vplfl Vepaf Vepab Vepdf Vepac Vepde Vepbg Vepbh) (p1p2_4262 Vplfl Vepaf Vepab)))). Qed. Lemma p1p2_4344: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(ep d e)->(ep b g)->(ep b h)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))(Vepbh:(ep b h))=>((goal4 s) (conj p1p2_45 (conj (p1p2_4324 Vplfl Vepaf Vepab Vepdf Vepac Vepde Vepbg) (conj (p1p2_4343 Vplfl Vepaf Vepab Vepdf Vepac Vepde Vepbg Vepbh) p1p2_28))))). Qed. Lemma p1p2_4345: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(ep d e)->(ep b g)->(el p q)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))(Velpq:(el p q))=>(goal2 Velpq)). Qed. Lemma p1p2_4346: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(ep d e)->(ep b g)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))=>((or_ind ((p1p2_4344 Vplfl Vepaf Vepab Vepdf Vepac Vepde Vepbg))((p1p2_4345 Vplfl Vepaf Vepab Vepdf Vepac Vepde Vepbg)))(p1p2_4327 Vplfl Vepaf Vepab Vepdf Vepac Vepde Vepbg))). Qed. Lemma p1p2_4347: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(ep d e)->(el n o)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Vepde:(ep d e))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_4348: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(ep d e)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Vepde:(ep d e))=>((or_ind ((p1p2_4346 Vplfl Vepaf Vepab Vepdf Vepac Vepde))((p1p2_4347 Vplfl Vepaf Vepab Vepdf Vepac Vepde)))(p1p2_4309 Vplfl Vepaf Vepab Vepdf Vepac Vepde))). Qed. Lemma p1p2_4349: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m q)->(el q m). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmq:(el m q))=>((lsym m q) Velmq)). Qed. Lemma p1p2_4350: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m q)->(pl h m). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmq:(el m q))=>((lcon h q m) (conj p1p2_26 (p1p2_4349 Vplfl Vepaf Vepab Vepdf Vepac Velmq)))). Qed. Lemma p1p2_4351: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m q)->(ep d h) \/ (el m p). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmq:(el m q))=>((unique m p d h) (conj p1p2_6 (conj p1p2_17 (conj (p1p2_4350 Vplfl Vepaf Vepab Vepdf Vepac Velmq) p1p2_25))))). Qed. Lemma p1p2_4352: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m q)->(ep d h)->(ep h d). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))=>((psym d h) Vepdh)). Qed. Lemma p1p2_4361: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m q)->(ep d h)->(pl h r). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))=>((pcon h d r) (conj (p1p2_4352 Vplfl Vepaf Vepab Vepdf Vepac Velmq Vepdh) p1p2_19))). Qed. Lemma p1p2_4363: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m q)->(ep d h)->(pl h s). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))=>((pcon h d s) (conj (p1p2_4352 Vplfl Vepaf Vepab Vepdf Vepac Velmq Vepdh) (p1p2_4271 Vplfl Vepaf Vepab Vepdf)))). Qed. Lemma p1p2_4366: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m q)->(ep d h)->(ep d e) \/ (el m o). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))=>((unique m o d e) (conj p1p2_6 (conj (p1p2_4288 Vplfl Vepaf Vepab Vepdf Vepac) (conj p1p2_14 p1p2_16))))). Qed. Lemma p1p2_4383: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m q)->(ep d h)->(ep d e)->(ep b g) \/ (el n o). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Vepde:(ep d e))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_4287 Vplfl Vepaf Vepab Vepdf Vepac) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_4384: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m q)->(ep d h)->(ep d e)->(ep b g)->(ep g b). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Vepde:(ep d e))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_4400: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m q)->(ep d h)->(ep d e)->(ep b g)->(pl g s). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Vepde:(ep d e))(Vepbg:(ep b g))=>((pcon g b s) (conj (p1p2_4384 Vplfl Vepaf Vepab Vepdf Vepac Velmq Vepdh Vepde Vepbg) (p1p2_4262 Vplfl Vepaf Vepab)))). Qed. Lemma p1p2_4401: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m q)->(ep d h)->(ep d e)->(ep b g)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Vepde:(ep d e))(Vepbg:(ep b g))=>((goal4 s) (conj p1p2_45 (conj (p1p2_4400 Vplfl Vepaf Vepab Vepdf Vepac Velmq Vepdh Vepde Vepbg) (conj (p1p2_4363 Vplfl Vepaf Vepab Vepdf Vepac Velmq Vepdh) p1p2_28))))). Qed. Lemma p1p2_4402: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m q)->(ep d h)->(ep d e)->(el n o)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Vepde:(ep d e))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_4403: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m q)->(ep d h)->(ep d e)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Vepde:(ep d e))=>((or_ind ((p1p2_4401 Vplfl Vepaf Vepab Vepdf Vepac Velmq Vepdh Vepde))((p1p2_4402 Vplfl Vepaf Vepab Vepdf Vepac Velmq Vepdh Vepde)))(p1p2_4383 Vplfl Vepaf Vepab Vepdf Vepac Velmq Vepdh Vepde))). Qed. Lemma p1p2_4404: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m q)->(ep d h)->(el m o)->(el o m). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Velmo:(el m o))=>((lsym m o) Velmo)). Qed. Lemma p1p2_4407: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m q)->(ep d h)->(el m o)->(pl g m). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Velmo:(el m o))=>((lcon g o m) (conj p1p2_24 (p1p2_4404 Vplfl Vepaf Vepab Vepdf Vepac Velmq Vepdh Velmo)))). Qed. Lemma p1p2_4409: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m q)->(ep d h)->(el m o)->(ep d g) \/ (el m n). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Velmo:(el m o))=>((unique m n d g) (conj p1p2_6 (conj (p1p2_4270 Vplfl Vepaf Vepab Vepdf) (conj (p1p2_4407 Vplfl Vepaf Vepab Vepdf Vepac Velmq Vepdh Velmo) p1p2_23))))). Qed. Lemma p1p2_4410: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m q)->(ep d h)->(el m o)->(ep d g)->(ep g d). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Velmo:(el m o))(Vepdg:(ep d g))=>((psym d g) Vepdg)). Qed. Lemma p1p2_4422: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m q)->(ep d h)->(el m o)->(ep d g)->(pl g r). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Velmo:(el m o))(Vepdg:(ep d g))=>((pcon g d r) (conj (p1p2_4410 Vplfl Vepaf Vepab Vepdf Vepac Velmq Vepdh Velmo Vepdg) p1p2_19))). Qed. Lemma p1p2_4423: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m q)->(ep d h)->(el m o)->(ep d g)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Velmo:(el m o))(Vepdg:(ep d g))=>((goal4 r) (conj p1p2_44 (conj (p1p2_4422 Vplfl Vepaf Vepab Vepdf Vepac Velmq Vepdh Velmo Vepdg) (conj (p1p2_4361 Vplfl Vepaf Vepab Vepdf Vepac Velmq Vepdh) p1p2_27))))). Qed. Lemma p1p2_4427: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m q)->(ep d h)->(el m o)->(el m n)->(el o n). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Velmo:(el m o))(Velmn:(el m n))=>((ltra o m n) (conj (p1p2_4404 Vplfl Vepaf Vepab Vepdf Vepac Velmq Vepdh Velmo) Velmn))). Qed. Lemma p1p2_4428: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m q)->(ep d h)->(el m o)->(el m n)->(el n o). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Velmo:(el m o))(Velmn:(el m n))=>((lsym o n) (p1p2_4427 Vplfl Vepaf Vepab Vepdf Vepac Velmq Vepdh Velmo Velmn))). Qed. Lemma p1p2_4429: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m q)->(ep d h)->(el m o)->(el m n)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Velmo:(el m o))(Velmn:(el m n))=>(goal1 (p1p2_4428 Vplfl Vepaf Vepab Vepdf Vepac Velmq Vepdh Velmo Velmn))). Qed. Lemma p1p2_4430: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m q)->(ep d h)->(el m o)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))(Velmo:(el m o))=>((or_ind ((p1p2_4423 Vplfl Vepaf Vepab Vepdf Vepac Velmq Vepdh Velmo))((p1p2_4429 Vplfl Vepaf Vepab Vepdf Vepac Velmq Vepdh Velmo)))(p1p2_4409 Vplfl Vepaf Vepab Vepdf Vepac Velmq Vepdh Velmo))). Qed. Lemma p1p2_4431: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m q)->(ep d h)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmq:(el m q))(Vepdh:(ep d h))=>((or_ind ((p1p2_4403 Vplfl Vepaf Vepab Vepdf Vepac Velmq Vepdh))((p1p2_4430 Vplfl Vepaf Vepab Vepdf Vepac Velmq Vepdh)))(p1p2_4366 Vplfl Vepaf Vepab Vepdf Vepac Velmq Vepdh))). Qed. Lemma p1p2_4433: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m q)->(el m p)->(el q p). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmq:(el m q))(Velmp:(el m p))=>((ltra q m p) (conj (p1p2_4349 Vplfl Vepaf Vepab Vepdf Vepac Velmq) Velmp))). Qed. Lemma p1p2_4434: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m q)->(el m p)->(el p q). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmq:(el m q))(Velmp:(el m p))=>((lsym q p) (p1p2_4433 Vplfl Vepaf Vepab Vepdf Vepac Velmq Velmp))). Qed. Lemma p1p2_4435: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m q)->(el m p)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmq:(el m q))(Velmp:(el m p))=>(goal2 (p1p2_4434 Vplfl Vepaf Vepab Vepdf Vepac Velmq Velmp))). Qed. Lemma p1p2_4436: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->(el m q)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))(Velmq:(el m q))=>((or_ind ((p1p2_4431 Vplfl Vepaf Vepab Vepdf Vepac Velmq))((p1p2_4435 Vplfl Vepaf Vepab Vepdf Vepac Velmq)))(p1p2_4351 Vplfl Vepaf Vepab Vepdf Vepac Velmq))). Qed. Lemma p1p2_4437: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(ep a c)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vepac:(ep a c))=>((or_ind ((p1p2_4348 Vplfl Vepaf Vepab Vepdf Vepac))((p1p2_4436 Vplfl Vepaf Vepab Vepdf Vepac)))(p1p2_4294 Vplfl Vepaf Vepab Vepdf Vepac))). Qed. Lemma p1p2_4438: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(el r l). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))=>((lsym l r) Vellr)). Qed. Lemma p1p2_4439: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(pl i l). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))=>((lcon i r l) (conj p1p2_27 (p1p2_4438 Vplfl Vepaf Vepab Vepdf Vellr)))). Qed. Lemma p1p2_4440: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i) \/ (el l s). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))=>((unique l s a i) (conj p1p2_5 (conj p1p2_12 (conj (p1p2_4439 Vplfl Vepaf Vepab Vepdf Vellr) p1p2_28))))). Qed. Lemma p1p2_4441: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(ep i a). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))=>((psym a i) Vepai)). Qed. Lemma p1p2_4448: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(pl i q). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))=>((pcon i a q) (conj (p1p2_4441 Vplfl Vepaf Vepab Vepdf Vellr Vepai) p1p2_10))). Qed. Lemma p1p2_4449: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(pl i n). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))=>((pcon i a n) (conj (p1p2_4441 Vplfl Vepaf Vepab Vepdf Vellr Vepai) (p1p2_4252 Vplfl Vepaf)))). Qed. Lemma p1p2_4451: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(pl i p). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))=>((pcon i a p) (conj (p1p2_4441 Vplfl Vepaf Vepab Vepdf Vellr Vepai) (p1p2_4259 Vplfl Vepaf Vepab)))). Qed. Lemma p1p2_4452: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(ep d e) \/ (el m q). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))=>((unique m q d e) (conj p1p2_6 (conj (p1p2_4273 Vplfl Vepaf Vepab Vepdf) (conj p1p2_14 p1p2_18))))). Qed. Lemma p1p2_4462: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(ep d e)->(pl d o). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))=>((pcon d e o) (conj Vepde p1p2_16))). Qed. Lemma p1p2_4463: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(ep d e)->(pl f o). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))=>((pcon f d o) (conj (p1p2_4265 Vplfl Vepaf Vepab Vepdf) (p1p2_4462 Vplfl Vepaf Vepab Vepdf Vellr Vepai Vepde)))). Qed. Lemma p1p2_4464: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(ep d e)->(pl a o). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))=>((pcon a f o) (conj Vepaf (p1p2_4463 Vplfl Vepaf Vepab Vepdf Vellr Vepai Vepde)))). Qed. Lemma p1p2_4465: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(ep d e)->(pl b o). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))=>((pcon b a o) (conj (p1p2_4256 Vplfl Vepaf Vepab) (p1p2_4464 Vplfl Vepaf Vepab Vepdf Vellr Vepai Vepde)))). Qed. Lemma p1p2_4472: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(ep d e)->(ep a c) \/ (el l o). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))=>((unique l o a c) (conj p1p2_5 (conj (p1p2_4464 Vplfl Vepaf Vepab Vepdf Vellr Vepai Vepde) (conj p1p2_21 p1p2_8))))). Qed. Lemma p1p2_4489: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(ep d e)->(ep a c)->(ep b g) \/ (el n o). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vepac:(ep a c))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_4465 Vplfl Vepaf Vepab Vepdf Vellr Vepai Vepde) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_4490: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(ep d e)->(ep a c)->(ep b g)->(ep g b). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vepac:(ep a c))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_4503: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(ep d e)->(ep a c)->(ep b g)->(pl g p). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vepac:(ep a c))(Vepbg:(ep b g))=>((pcon g b p) (conj (p1p2_4490 Vplfl Vepaf Vepab Vepdf Vellr Vepai Vepde Vepac Vepbg) p1p2_9))). Qed. Lemma p1p2_4504: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(ep d e)->(ep a c)->(ep b g)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vepac:(ep a c))(Vepbg:(ep b g))=>((goal4 p) (conj p1p2_42 (conj (p1p2_4503 Vplfl Vepaf Vepab Vepdf Vellr Vepai Vepde Vepac Vepbg) (conj p1p2_25 (p1p2_4451 Vplfl Vepaf Vepab Vepdf Vellr Vepai)))))). Qed. Lemma p1p2_4505: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(ep d e)->(ep a c)->(el n o)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vepac:(ep a c))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_4506: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(ep d e)->(ep a c)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vepac:(ep a c))=>((or_ind ((p1p2_4504 Vplfl Vepaf Vepab Vepdf Vellr Vepai Vepde Vepac))((p1p2_4505 Vplfl Vepaf Vepab Vepdf Vellr Vepai Vepde Vepac)))(p1p2_4489 Vplfl Vepaf Vepab Vepdf Vellr Vepai Vepde Vepac))). Qed. Lemma p1p2_4507: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(ep d e)->(el l o)->(el o l). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vello:(el l o))=>((lsym l o) Vello)). Qed. Lemma p1p2_4510: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(ep d e)->(el l o)->(pl g l). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vello:(el l o))=>((lcon g o l) (conj p1p2_24 (p1p2_4507 Vplfl Vepaf Vepab Vepdf Vellr Vepai Vepde Vello)))). Qed. Lemma p1p2_4512: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(ep d e)->(el l o)->(ep a g) \/ (el l n). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vello:(el l o))=>((unique l n a g) (conj p1p2_5 (conj (p1p2_4252 Vplfl Vepaf) (conj (p1p2_4510 Vplfl Vepaf Vepab Vepdf Vellr Vepai Vepde Vello) p1p2_23))))). Qed. Lemma p1p2_4513: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(ep d e)->(el l o)->(ep a g)->(ep g a). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vello:(el l o))(Vepag:(ep a g))=>((psym a g) Vepag)). Qed. Lemma p1p2_4524: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(ep d e)->(el l o)->(ep a g)->(pl g q). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vello:(el l o))(Vepag:(ep a g))=>((pcon g a q) (conj (p1p2_4513 Vplfl Vepaf Vepab Vepdf Vellr Vepai Vepde Vello Vepag) p1p2_10))). Qed. Lemma p1p2_4525: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(ep d e)->(el l o)->(ep a g)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vello:(el l o))(Vepag:(ep a g))=>((goal4 q) (conj p1p2_43 (conj (p1p2_4524 Vplfl Vepaf Vepab Vepdf Vellr Vepai Vepde Vello Vepag) (conj p1p2_26 (p1p2_4448 Vplfl Vepaf Vepab Vepdf Vellr Vepai)))))). Qed. Lemma p1p2_4529: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(ep d e)->(el l o)->(el l n)->(el o n). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vello:(el l o))(Velln:(el l n))=>((ltra o l n) (conj (p1p2_4507 Vplfl Vepaf Vepab Vepdf Vellr Vepai Vepde Vello) Velln))). Qed. Lemma p1p2_4530: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(ep d e)->(el l o)->(el l n)->(el n o). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vello:(el l o))(Velln:(el l n))=>((lsym o n) (p1p2_4529 Vplfl Vepaf Vepab Vepdf Vellr Vepai Vepde Vello Velln))). Qed. Lemma p1p2_4531: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(ep d e)->(el l o)->(el l n)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vello:(el l o))(Velln:(el l n))=>(goal1 (p1p2_4530 Vplfl Vepaf Vepab Vepdf Vellr Vepai Vepde Vello Velln))). Qed. Lemma p1p2_4532: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(ep d e)->(el l o)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))(Vello:(el l o))=>((or_ind ((p1p2_4525 Vplfl Vepaf Vepab Vepdf Vellr Vepai Vepde Vello))((p1p2_4531 Vplfl Vepaf Vepab Vepdf Vellr Vepai Vepde Vello)))(p1p2_4512 Vplfl Vepaf Vepab Vepdf Vellr Vepai Vepde Vello))). Qed. Lemma p1p2_4533: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(ep d e)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Vepde:(ep d e))=>((or_ind ((p1p2_4506 Vplfl Vepaf Vepab Vepdf Vellr Vepai Vepde))((p1p2_4532 Vplfl Vepaf Vepab Vepdf Vellr Vepai Vepde)))(p1p2_4472 Vplfl Vepaf Vepab Vepdf Vellr Vepai Vepde))). Qed. Lemma p1p2_4534: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(el m q)->(el q m). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Velmq:(el m q))=>((lsym m q) Velmq)). Qed. Lemma p1p2_4535: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(el m q)->(pl h m). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Velmq:(el m q))=>((lcon h q m) (conj p1p2_26 (p1p2_4534 Vplfl Vepaf Vepab Vepdf Vellr Vepai Velmq)))). Qed. Lemma p1p2_4536: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(el m q)->(ep d h) \/ (el m p). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Velmq:(el m q))=>((unique m p d h) (conj p1p2_6 (conj p1p2_17 (conj (p1p2_4535 Vplfl Vepaf Vepab Vepdf Vellr Vepai Velmq) p1p2_25))))). Qed. Lemma p1p2_4537: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(el m q)->(ep d h)->(ep h d). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Velmq:(el m q))(Vepdh:(ep d h))=>((psym d h) Vepdh)). Qed. Lemma p1p2_4547: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(el m q)->(ep d h)->(pl h n). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Velmq:(el m q))(Vepdh:(ep d h))=>((pcon h d n) (conj (p1p2_4537 Vplfl Vepaf Vepab Vepdf Vellr Vepai Velmq Vepdh) (p1p2_4270 Vplfl Vepaf Vepab Vepdf)))). Qed. Lemma p1p2_4548: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(el m q)->(ep d h)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Velmq:(el m q))(Vepdh:(ep d h))=>((goal4 n) (conj p1p2_40 (conj p1p2_23 (conj (p1p2_4547 Vplfl Vepaf Vepab Vepdf Vellr Vepai Velmq Vepdh) (p1p2_4449 Vplfl Vepaf Vepab Vepdf Vellr Vepai)))))). Qed. Lemma p1p2_4550: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(el m q)->(el m p)->(el q p). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Velmq:(el m q))(Velmp:(el m p))=>((ltra q m p) (conj (p1p2_4534 Vplfl Vepaf Vepab Vepdf Vellr Vepai Velmq) Velmp))). Qed. Lemma p1p2_4551: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(el m q)->(el m p)->(el p q). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Velmq:(el m q))(Velmp:(el m p))=>((lsym q p) (p1p2_4550 Vplfl Vepaf Vepab Vepdf Vellr Vepai Velmq Velmp))). Qed. Lemma p1p2_4552: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(el m q)->(el m p)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Velmq:(el m q))(Velmp:(el m p))=>(goal2 (p1p2_4551 Vplfl Vepaf Vepab Vepdf Vellr Vepai Velmq Velmp))). Qed. Lemma p1p2_4553: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->(el m q)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))(Velmq:(el m q))=>((or_ind ((p1p2_4548 Vplfl Vepaf Vepab Vepdf Vellr Vepai Velmq))((p1p2_4552 Vplfl Vepaf Vepab Vepdf Vellr Vepai Velmq)))(p1p2_4536 Vplfl Vepaf Vepab Vepdf Vellr Vepai Velmq))). Qed. Lemma p1p2_4554: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(ep a i)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vepai:(ep a i))=>((or_ind ((p1p2_4533 Vplfl Vepaf Vepab Vepdf Vellr Vepai))((p1p2_4553 Vplfl Vepaf Vepab Vepdf Vellr Vepai)))(p1p2_4452 Vplfl Vepaf Vepab Vepdf Vellr Vepai))). Qed. Lemma p1p2_4556: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(el l s)->(el r s). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vells:(el l s))=>((ltra r l s) (conj (p1p2_4438 Vplfl Vepaf Vepab Vepdf Vellr) Vells))). Qed. Lemma p1p2_4557: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(el l s)->(el s r). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vells:(el l s))=>((lsym r s) (p1p2_4556 Vplfl Vepaf Vepab Vepdf Vellr Vells))). Qed. Lemma p1p2_4558: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->(el l s)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))(Vells:(el l s))=>(goal3 (p1p2_4557 Vplfl Vepaf Vepab Vepdf Vellr Vells))). Qed. Lemma p1p2_4559: (pl f l)->(ep a f)->(ep a b)->(ep d f)->(el l r)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))(Vellr:(el l r))=>((or_ind ((p1p2_4554 Vplfl Vepaf Vepab Vepdf Vellr))((p1p2_4558 Vplfl Vepaf Vepab Vepdf Vellr)))(p1p2_4440 Vplfl Vepaf Vepab Vepdf Vellr))). Qed. Lemma p1p2_4560: (pl f l)->(ep a f)->(ep a b)->(ep d f)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Vepdf:(ep d f))=>((or_ind ((p1p2_4437 Vplfl Vepaf Vepab Vepdf))((p1p2_4559 Vplfl Vepaf Vepab Vepdf)))(p1p2_4277 Vplfl Vepaf Vepab Vepdf))). Qed. Lemma p1p2_4561: (pl f l)->(ep a f)->(ep a b)->(el m p)->(el p m). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))=>((lsym m p) Velmp)). Qed. Lemma p1p2_4562: (pl f l)->(ep a f)->(ep a b)->(el m p)->(pl e p). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))=>((lcon e m p) (conj p1p2_14 Velmp))). Qed. Lemma p1p2_4564: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h) \/ (el p q). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))=>((unique p q b h) (conj p1p2_9 (conj (p1p2_4261 Vplfl Vepaf Vepab) (conj p1p2_25 p1p2_26))))). Qed. Lemma p1p2_4565: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep h b). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))=>((psym b h) Vepbh)). Qed. Lemma p1p2_4572: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(pl h s). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))=>((pcon h b s) (conj (p1p2_4565 Vplfl Vepaf Vepab Velmp Vepbh) (p1p2_4262 Vplfl Vepaf Vepab)))). Qed. Lemma p1p2_4573: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e) \/ (el p q). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))=>((unique p q b e) (conj p1p2_9 (conj (p1p2_4261 Vplfl Vepaf Vepab) (conj (p1p2_4562 Vplfl Vepaf Vepab Velmp) p1p2_18))))). Qed. Lemma p1p2_4574: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(ep e b). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))=>((psym b e) Vepbe)). Qed. Lemma p1p2_4581: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(pl b o). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))=>((pcon b e o) (conj Vepbe p1p2_16))). Qed. Lemma p1p2_4582: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(pl a o). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))=>((pcon a b o) (conj Vepab (p1p2_4581 Vplfl Vepaf Vepab Velmp Vepbh Vepbe)))). Qed. Lemma p1p2_4588: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(ep a c) \/ (el l o). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))=>((unique l o a c) (conj p1p2_5 (conj (p1p2_4582 Vplfl Vepaf Vepab Velmp Vepbh Vepbe) (conj p1p2_21 p1p2_8))))). Qed. Lemma p1p2_4598: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(ep a c)->(pl a r). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))=>((pcon a c r) (conj Vepac p1p2_11))). Qed. Lemma p1p2_4600: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(ep a c)->(pl b r). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))=>((pcon b a r) (conj (p1p2_4256 Vplfl Vepaf Vepab) (p1p2_4598 Vplfl Vepaf Vepab Velmp Vepbh Vepbe Vepac)))). Qed. Lemma p1p2_4602: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(ep a c)->(pl e r). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))=>((pcon e b r) (conj (p1p2_4574 Vplfl Vepaf Vepab Velmp Vepbh Vepbe) (p1p2_4600 Vplfl Vepaf Vepab Velmp Vepbh Vepbe Vepac)))). Qed. Lemma p1p2_4608: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(ep a c)->(ep d e) \/ (el m r). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))=>((unique m r d e) (conj p1p2_6 (conj p1p2_19 (conj p1p2_14 (p1p2_4602 Vplfl Vepaf Vepab Velmp Vepbh Vepbe Vepac)))))). Qed. Lemma p1p2_4625: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(ep a c)->(ep d e)->(ep b g) \/ (el n o). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))(Vepde:(ep d e))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_4581 Vplfl Vepaf Vepab Velmp Vepbh Vepbe) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_4626: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(ep a c)->(ep d e)->(ep b g)->(ep g b). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_4642: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(ep a c)->(ep d e)->(ep b g)->(pl g s). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))=>((pcon g b s) (conj (p1p2_4626 Vplfl Vepaf Vepab Velmp Vepbh Vepbe Vepac Vepde Vepbg) (p1p2_4262 Vplfl Vepaf Vepab)))). Qed. Lemma p1p2_4643: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(ep a c)->(ep d e)->(ep b g)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepbg:(ep b g))=>((goal4 s) (conj p1p2_45 (conj (p1p2_4642 Vplfl Vepaf Vepab Velmp Vepbh Vepbe Vepac Vepde Vepbg) (conj (p1p2_4572 Vplfl Vepaf Vepab Velmp Vepbh) p1p2_28))))). Qed. Lemma p1p2_4644: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(ep a c)->(ep d e)->(el n o)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))(Vepde:(ep d e))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_4645: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(ep a c)->(ep d e)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))(Vepde:(ep d e))=>((or_ind ((p1p2_4643 Vplfl Vepaf Vepab Velmp Vepbh Vepbe Vepac Vepde))((p1p2_4644 Vplfl Vepaf Vepab Velmp Vepbh Vepbe Vepac Vepde)))(p1p2_4625 Vplfl Vepaf Vepab Velmp Vepbh Vepbe Vepac Vepde))). Qed. Lemma p1p2_4647: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(ep a c)->(el m r)->(el p r). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))(Velmr:(el m r))=>((ltra p m r) (conj (p1p2_4561 Vplfl Vepaf Vepab Velmp) Velmr))). Qed. Lemma p1p2_4648: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(ep a c)->(el m r)->(el r p). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))(Velmr:(el m r))=>((lsym p r) (p1p2_4647 Vplfl Vepaf Vepab Velmp Vepbh Vepbe Vepac Velmr))). Qed. Lemma p1p2_4650: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(ep a c)->(el m r)->(pl i p). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))(Velmr:(el m r))=>((lcon i r p) (conj p1p2_27 (p1p2_4648 Vplfl Vepaf Vepab Velmp Vepbh Vepbe Vepac Velmr)))). Qed. Lemma p1p2_4651: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(ep a c)->(el m r)->(ep b g) \/ (el n o). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))(Velmr:(el m r))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_4581 Vplfl Vepaf Vepab Velmp Vepbh Vepbe) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_4652: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(ep a c)->(el m r)->(ep b g)->(ep g b). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))(Velmr:(el m r))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_4663: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(ep a c)->(el m r)->(ep b g)->(pl g p). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))(Velmr:(el m r))(Vepbg:(ep b g))=>((pcon g b p) (conj (p1p2_4652 Vplfl Vepaf Vepab Velmp Vepbh Vepbe Vepac Velmr Vepbg) p1p2_9))). Qed. Lemma p1p2_4664: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(ep a c)->(el m r)->(ep b g)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))(Velmr:(el m r))(Vepbg:(ep b g))=>((goal4 p) (conj p1p2_42 (conj (p1p2_4663 Vplfl Vepaf Vepab Velmp Vepbh Vepbe Vepac Velmr Vepbg) (conj p1p2_25 (p1p2_4650 Vplfl Vepaf Vepab Velmp Vepbh Vepbe Vepac Velmr)))))). Qed. Lemma p1p2_4665: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(ep a c)->(el m r)->(el n o)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))(Velmr:(el m r))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_4666: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(ep a c)->(el m r)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))(Velmr:(el m r))=>((or_ind ((p1p2_4664 Vplfl Vepaf Vepab Velmp Vepbh Vepbe Vepac Velmr))((p1p2_4665 Vplfl Vepaf Vepab Velmp Vepbh Vepbe Vepac Velmr)))(p1p2_4651 Vplfl Vepaf Vepab Velmp Vepbh Vepbe Vepac Velmr))). Qed. Lemma p1p2_4667: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(ep a c)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vepac:(ep a c))=>((or_ind ((p1p2_4645 Vplfl Vepaf Vepab Velmp Vepbh Vepbe Vepac))((p1p2_4666 Vplfl Vepaf Vepab Velmp Vepbh Vepbe Vepac)))(p1p2_4608 Vplfl Vepaf Vepab Velmp Vepbh Vepbe Vepac))). Qed. Lemma p1p2_4668: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(el l o)->(el o l). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vello:(el l o))=>((lsym l o) Vello)). Qed. Lemma p1p2_4669: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(el l o)->(pl g l). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vello:(el l o))=>((lcon g o l) (conj p1p2_24 (p1p2_4668 Vplfl Vepaf Vepab Velmp Vepbh Vepbe Vello)))). Qed. Lemma p1p2_4670: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(el l o)->(ep a g) \/ (el l n). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vello:(el l o))=>((unique l n a g) (conj p1p2_5 (conj (p1p2_4252 Vplfl Vepaf) (conj (p1p2_4669 Vplfl Vepaf Vepab Velmp Vepbh Vepbe Vello) p1p2_23))))). Qed. Lemma p1p2_4671: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(el l o)->(ep a g)->(ep g a). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vello:(el l o))(Vepag:(ep a g))=>((psym a g) Vepag)). Qed. Lemma p1p2_4681: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(el l o)->(ep a g)->(pl g s). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vello:(el l o))(Vepag:(ep a g))=>((pcon g a s) (conj (p1p2_4671 Vplfl Vepaf Vepab Velmp Vepbh Vepbe Vello Vepag) p1p2_12))). Qed. Lemma p1p2_4682: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(el l o)->(ep a g)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vello:(el l o))(Vepag:(ep a g))=>((goal4 s) (conj p1p2_45 (conj (p1p2_4681 Vplfl Vepaf Vepab Velmp Vepbh Vepbe Vello Vepag) (conj (p1p2_4572 Vplfl Vepaf Vepab Velmp Vepbh) p1p2_28))))). Qed. Lemma p1p2_4684: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(el l o)->(el l n)->(el o n). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vello:(el l o))(Velln:(el l n))=>((ltra o l n) (conj (p1p2_4668 Vplfl Vepaf Vepab Velmp Vepbh Vepbe Vello) Velln))). Qed. Lemma p1p2_4685: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(el l o)->(el l n)->(el n o). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vello:(el l o))(Velln:(el l n))=>((lsym o n) (p1p2_4684 Vplfl Vepaf Vepab Velmp Vepbh Vepbe Vello Velln))). Qed. Lemma p1p2_4686: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(el l o)->(el l n)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vello:(el l o))(Velln:(el l n))=>(goal1 (p1p2_4685 Vplfl Vepaf Vepab Velmp Vepbh Vepbe Vello Velln))). Qed. Lemma p1p2_4687: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->(el l o)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))(Vello:(el l o))=>((or_ind ((p1p2_4682 Vplfl Vepaf Vepab Velmp Vepbh Vepbe Vello))((p1p2_4686 Vplfl Vepaf Vepab Velmp Vepbh Vepbe Vello)))(p1p2_4670 Vplfl Vepaf Vepab Velmp Vepbh Vepbe Vello))). Qed. Lemma p1p2_4688: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(ep b e)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Vepbe:(ep b e))=>((or_ind ((p1p2_4667 Vplfl Vepaf Vepab Velmp Vepbh Vepbe))((p1p2_4687 Vplfl Vepaf Vepab Velmp Vepbh Vepbe)))(p1p2_4588 Vplfl Vepaf Vepab Velmp Vepbh Vepbe))). Qed. Lemma p1p2_4689: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->(el p q)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))(Velpq:(el p q))=>(goal2 Velpq)). Qed. Lemma p1p2_4690: (pl f l)->(ep a f)->(ep a b)->(el m p)->(ep b h)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Vepbh:(ep b h))=>((or_ind ((p1p2_4688 Vplfl Vepaf Vepab Velmp Vepbh))((p1p2_4689 Vplfl Vepaf Vepab Velmp Vepbh)))(p1p2_4573 Vplfl Vepaf Vepab Velmp Vepbh))). Qed. Lemma p1p2_4691: (pl f l)->(ep a f)->(ep a b)->(el m p)->(el p q)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))(Velpq:(el p q))=>(goal2 Velpq)). Qed. Lemma p1p2_4692: (pl f l)->(ep a f)->(ep a b)->(el m p)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))(Velmp:(el m p))=>((or_ind ((p1p2_4690 Vplfl Vepaf Vepab Velmp))((p1p2_4691 Vplfl Vepaf Vepab Velmp)))(p1p2_4564 Vplfl Vepaf Vepab Velmp))). Qed. Lemma p1p2_4693: (pl f l)->(ep a f)->(ep a b)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Vepab:(ep a b))=>((or_ind ((p1p2_4560 Vplfl Vepaf Vepab))((p1p2_4692 Vplfl Vepaf Vepab)))(p1p2_4264 Vplfl Vepaf Vepab))). Qed. Lemma p1p2_4694: (pl f l)->(ep a f)->(el l n)->(el n l). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))=>((lsym l n) Velln)). Qed. Lemma p1p2_4696: (pl f l)->(ep a f)->(el l n)->(pl g l). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))=>((lcon g n l) (conj p1p2_23 (p1p2_4694 Vplfl Vepaf Velln)))). Qed. Lemma p1p2_4697: (pl f l)->(ep a f)->(el l n)->(ep c g) \/ (el o l). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))=>((unique o l c g) (conj p1p2_8 (conj p1p2_21 (conj p1p2_24 (p1p2_4696 Vplfl Vepaf Velln)))))). Qed. Lemma p1p2_4698: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep g c). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))=>((psym c g) Vepcg)). Qed. Lemma p1p2_4699: (pl f l)->(ep a f)->(el l n)->(ep c g)->(pl g r). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))=>((pcon g c r) (conj (p1p2_4698 Vplfl Vepaf Velln Vepcg) p1p2_11))). Qed. Lemma p1p2_4700: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e) \/ (el q m). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))=>((unique q m a e) (conj p1p2_10 (conj (p1p2_4253 Vplfl Vepaf) (conj p1p2_18 p1p2_14))))). Qed. Lemma p1p2_4701: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep e a). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))=>((psym a e) Vepae)). Qed. Lemma p1p2_4704: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(pl a o). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))=>((pcon a e o) (conj Vepae p1p2_16))). Qed. Lemma p1p2_4709: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c) \/ (el l o). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))=>((unique l o a c) (conj p1p2_5 (conj (p1p2_4704 Vplfl Vepaf Velln Vepcg Vepae) (conj p1p2_21 p1p2_8))))). Qed. Lemma p1p2_4710: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(ep c a). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))=>((psym a c) Vepac)). Qed. Lemma p1p2_4721: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(pl a r). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))=>((pcon a c r) (conj Vepac p1p2_11))). Qed. Lemma p1p2_4723: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(pl e r). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))=>((pcon e a r) (conj (p1p2_4701 Vplfl Vepaf Velln Vepcg Vepae) (p1p2_4721 Vplfl Vepaf Velln Vepcg Vepae Vepac)))). Qed. Lemma p1p2_4724: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(pl c q). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))=>((pcon c a q) (conj (p1p2_4710 Vplfl Vepaf Velln Vepcg Vepae Vepac) p1p2_10))). Qed. Lemma p1p2_4725: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(pl g q). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))=>((pcon g c q) (conj (p1p2_4698 Vplfl Vepaf Velln Vepcg) (p1p2_4724 Vplfl Vepaf Velln Vepcg Vepae Vepac)))). Qed. Lemma p1p2_4726: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(pl c s). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))=>((pcon c a s) (conj (p1p2_4710 Vplfl Vepaf Velln Vepcg Vepae Vepac) p1p2_12))). Qed. Lemma p1p2_4727: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(pl g s). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))=>((pcon g c s) (conj (p1p2_4698 Vplfl Vepaf Velln Vepcg) (p1p2_4726 Vplfl Vepaf Velln Vepcg Vepae Vepac)))). Qed. Lemma p1p2_4730: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(ep d e) \/ (el m r). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))=>((unique m r d e) (conj p1p2_6 (conj p1p2_19 (conj p1p2_14 (p1p2_4723 Vplfl Vepaf Velln Vepcg Vepae Vepac)))))). Qed. Lemma p1p2_4731: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(ep d e)->(ep e d). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))=>((psym d e) Vepde)). Qed. Lemma p1p2_4745: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(ep d e)->(pl e p). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))=>((pcon e d p) (conj (p1p2_4731 Vplfl Vepaf Velln Vepcg Vepae Vepac Vepde) p1p2_17))). Qed. Lemma p1p2_4746: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(ep d e)->(pl a p). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))=>((pcon a e p) (conj Vepae (p1p2_4745 Vplfl Vepaf Velln Vepcg Vepae Vepac Vepde)))). Qed. Lemma p1p2_4750: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(ep d e)->(ep a b) \/ (el l p). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))=>((unique l p a b) (conj p1p2_5 (conj (p1p2_4746 Vplfl Vepaf Velln Vepcg Vepae Vepac Vepde) (conj p1p2_13 p1p2_9))))). Qed. Lemma p1p2_4751: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(ep b a). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))=>((psym a b) Vepab)). Qed. Lemma p1p2_4762: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(pl b q). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))=>((pcon b a q) (conj (p1p2_4751 Vplfl Vepaf Velln Vepcg Vepae Vepac Vepde Vepab) p1p2_10))). Qed. Lemma p1p2_4763: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(pl b s). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))=>((pcon b a s) (conj (p1p2_4751 Vplfl Vepaf Velln Vepcg Vepae Vepac Vepde Vepab) p1p2_12))). Qed. Lemma p1p2_4767: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(ep b h) \/ (el p q). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))=>((unique p q b h) (conj p1p2_9 (conj (p1p2_4762 Vplfl Vepaf Velln Vepcg Vepae Vepac Vepde Vepab) (conj p1p2_25 p1p2_26))))). Qed. Lemma p1p2_4768: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(ep b h)->(ep h b). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Vepbh:(ep b h))=>((psym b h) Vepbh)). Qed. Lemma p1p2_4783: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(ep b h)->(pl h s). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Vepbh:(ep b h))=>((pcon h b s) (conj (p1p2_4768 Vplfl Vepaf Velln Vepcg Vepae Vepac Vepde Vepab Vepbh) (p1p2_4763 Vplfl Vepaf Velln Vepcg Vepae Vepac Vepde Vepab)))). Qed. Lemma p1p2_4784: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(ep b h)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Vepbh:(ep b h))=>((goal4 s) (conj p1p2_45 (conj (p1p2_4727 Vplfl Vepaf Velln Vepcg Vepae Vepac) (conj (p1p2_4783 Vplfl Vepaf Velln Vepcg Vepae Vepac Vepde Vepab Vepbh) p1p2_28))))). Qed. Lemma p1p2_4785: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->(el p q)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))(Velpq:(el p q))=>(goal2 Velpq)). Qed. Lemma p1p2_4786: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(ep d e)->(ep a b)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vepab:(ep a b))=>((or_ind ((p1p2_4784 Vplfl Vepaf Velln Vepcg Vepae Vepac Vepde Vepab))((p1p2_4785 Vplfl Vepaf Velln Vepcg Vepae Vepac Vepde Vepab)))(p1p2_4767 Vplfl Vepaf Velln Vepcg Vepae Vepac Vepde Vepab))). Qed. Lemma p1p2_4787: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(el p l). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))=>((lsym l p) Vellp)). Qed. Lemma p1p2_4790: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(pl h l). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))=>((lcon h p l) (conj p1p2_25 (p1p2_4787 Vplfl Vepaf Velln Vepcg Vepae Vepac Vepde Vellp)))). Qed. Lemma p1p2_4792: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h) \/ (el l q). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))=>((unique l q a h) (conj p1p2_5 (conj p1p2_10 (conj (p1p2_4790 Vplfl Vepaf Velln Vepcg Vepae Vepac Vepde Vellp) p1p2_26))))). Qed. Lemma p1p2_4793: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(ep h a). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))=>((psym a h) Vepah)). Qed. Lemma p1p2_4804: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->(pl h s). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))=>((pcon h a s) (conj (p1p2_4793 Vplfl Vepaf Velln Vepcg Vepae Vepac Vepde Vellp Vepah) p1p2_12))). Qed. Lemma p1p2_4805: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(ep a h)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vepah:(ep a h))=>((goal4 s) (conj p1p2_45 (conj (p1p2_4727 Vplfl Vepaf Velln Vepcg Vepae Vepac) (conj (p1p2_4804 Vplfl Vepaf Velln Vepcg Vepae Vepac Vepde Vellp Vepah) p1p2_28))))). Qed. Lemma p1p2_4809: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(el l q)->(el p q). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vellq:(el l q))=>((ltra p l q) (conj (p1p2_4787 Vplfl Vepaf Velln Vepcg Vepae Vepac Vepde Vellp) Vellq))). Qed. Lemma p1p2_4810: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(ep d e)->(el l p)->(el l q)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))(Vellq:(el l q))=>(goal2 (p1p2_4809 Vplfl Vepaf Velln Vepcg Vepae Vepac Vepde Vellp Vellq))). Qed. Lemma p1p2_4811: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(ep d e)->(el l p)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))(Vellp:(el l p))=>((or_ind ((p1p2_4805 Vplfl Vepaf Velln Vepcg Vepae Vepac Vepde Vellp))((p1p2_4810 Vplfl Vepaf Velln Vepcg Vepae Vepac Vepde Vellp)))(p1p2_4792 Vplfl Vepaf Velln Vepcg Vepae Vepac Vepde Vellp))). Qed. Lemma p1p2_4812: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(ep d e)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))(Vepde:(ep d e))=>((or_ind ((p1p2_4786 Vplfl Vepaf Velln Vepcg Vepae Vepac Vepde))((p1p2_4811 Vplfl Vepaf Velln Vepcg Vepae Vepac Vepde)))(p1p2_4750 Vplfl Vepaf Velln Vepcg Vepae Vepac Vepde))). Qed. Lemma p1p2_4815: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(el m r)->(ep c i) \/ (el r s). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))=>((unique r s c i) (conj p1p2_11 (conj (p1p2_4726 Vplfl Vepaf Velln Vepcg Vepae Vepac) (conj p1p2_27 p1p2_28))))). Qed. Lemma p1p2_4816: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(ep i c). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))=>((psym c i) Vepci)). Qed. Lemma p1p2_4828: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(el m r)->(ep c i)->(pl i q). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))=>((pcon i c q) (conj (p1p2_4816 Vplfl Vepaf Velln Vepcg Vepae Vepac Velmr Vepci) (p1p2_4724 Vplfl Vepaf Velln Vepcg Vepae Vepac)))). Qed. Lemma p1p2_4829: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(el m r)->(ep c i)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Vepci:(ep c i))=>((goal4 q) (conj p1p2_43 (conj (p1p2_4725 Vplfl Vepaf Velln Vepcg Vepae Vepac) (conj p1p2_26 (p1p2_4828 Vplfl Vepaf Velln Vepcg Vepae Vepac Velmr Vepci)))))). Qed. Lemma p1p2_4830: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(el m r)->(el r s)->(el s r). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Velrs:(el r s))=>((lsym r s) Velrs)). Qed. Lemma p1p2_4831: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(el m r)->(el r s)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))(Velrs:(el r s))=>(goal3 (p1p2_4830 Vplfl Vepaf Velln Vepcg Vepae Vepac Velmr Velrs))). Qed. Lemma p1p2_4832: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->(el m r)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))(Velmr:(el m r))=>((or_ind ((p1p2_4829 Vplfl Vepaf Velln Vepcg Vepae Vepac Velmr))((p1p2_4831 Vplfl Vepaf Velln Vepcg Vepae Vepac Velmr)))(p1p2_4815 Vplfl Vepaf Velln Vepcg Vepae Vepac Velmr))). Qed. Lemma p1p2_4833: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(ep a c)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vepac:(ep a c))=>((or_ind ((p1p2_4812 Vplfl Vepaf Velln Vepcg Vepae Vepac))((p1p2_4832 Vplfl Vepaf Velln Vepcg Vepae Vepac)))(p1p2_4730 Vplfl Vepaf Velln Vepcg Vepae Vepac))). Qed. Lemma p1p2_4835: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(el l o)->(el n o). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vello:(el l o))=>((ltra n l o) (conj (p1p2_4694 Vplfl Vepaf Velln) Vello))). Qed. Lemma p1p2_4836: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->(el l o)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))(Vello:(el l o))=>(goal1 (p1p2_4835 Vplfl Vepaf Velln Vepcg Vepae Vello))). Qed. Lemma p1p2_4837: (pl f l)->(ep a f)->(el l n)->(ep c g)->(ep a e)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Vepae:(ep a e))=>((or_ind ((p1p2_4833 Vplfl Vepaf Velln Vepcg Vepae))((p1p2_4836 Vplfl Vepaf Velln Vepcg Vepae)))(p1p2_4709 Vplfl Vepaf Velln Vepcg Vepae))). Qed. Lemma p1p2_4840: (pl f l)->(ep a f)->(el l n)->(ep c g)->(el q m)->(pl h m). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Velqm:(el q m))=>((lcon h q m) (conj p1p2_26 Velqm))). Qed. Lemma p1p2_4841: (pl f l)->(ep a f)->(el l n)->(ep c g)->(el q m)->(ep d h) \/ (el m p). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Velqm:(el q m))=>((unique m p d h) (conj p1p2_6 (conj p1p2_17 (conj (p1p2_4840 Vplfl Vepaf Velln Vepcg Velqm) p1p2_25))))). Qed. Lemma p1p2_4842: (pl f l)->(ep a f)->(el l n)->(ep c g)->(el q m)->(ep d h)->(ep h d). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Velqm:(el q m))(Vepdh:(ep d h))=>((psym d h) Vepdh)). Qed. Lemma p1p2_4843: (pl f l)->(ep a f)->(el l n)->(ep c g)->(el q m)->(ep d h)->(pl h r). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Velqm:(el q m))(Vepdh:(ep d h))=>((pcon h d r) (conj (p1p2_4842 Vplfl Vepaf Velln Vepcg Velqm Vepdh) p1p2_19))). Qed. Lemma p1p2_4844: (pl f l)->(ep a f)->(el l n)->(ep c g)->(el q m)->(ep d h)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Velqm:(el q m))(Vepdh:(ep d h))=>((goal4 r) (conj p1p2_44 (conj (p1p2_4699 Vplfl Vepaf Velln Vepcg) (conj (p1p2_4843 Vplfl Vepaf Velln Vepcg Velqm Vepdh) p1p2_27))))). Qed. Lemma p1p2_4846: (pl f l)->(ep a f)->(el l n)->(ep c g)->(el q m)->(el m p)->(el q p). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Velqm:(el q m))(Velmp:(el m p))=>((ltra q m p) (conj Velqm Velmp))). Qed. Lemma p1p2_4847: (pl f l)->(ep a f)->(el l n)->(ep c g)->(el q m)->(el m p)->(el p q). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Velqm:(el q m))(Velmp:(el m p))=>((lsym q p) (p1p2_4846 Vplfl Vepaf Velln Vepcg Velqm Velmp))). Qed. Lemma p1p2_4848: (pl f l)->(ep a f)->(el l n)->(ep c g)->(el q m)->(el m p)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Velqm:(el q m))(Velmp:(el m p))=>(goal2 (p1p2_4847 Vplfl Vepaf Velln Vepcg Velqm Velmp))). Qed. Lemma p1p2_4849: (pl f l)->(ep a f)->(el l n)->(ep c g)->(el q m)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))(Velqm:(el q m))=>((or_ind ((p1p2_4844 Vplfl Vepaf Velln Vepcg Velqm))((p1p2_4848 Vplfl Vepaf Velln Vepcg Velqm)))(p1p2_4841 Vplfl Vepaf Velln Vepcg Velqm))). Qed. Lemma p1p2_4850: (pl f l)->(ep a f)->(el l n)->(ep c g)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Vepcg:(ep c g))=>((or_ind ((p1p2_4837 Vplfl Vepaf Velln Vepcg))((p1p2_4849 Vplfl Vepaf Velln Vepcg)))(p1p2_4700 Vplfl Vepaf Velln Vepcg))). Qed. Lemma p1p2_4851: (pl f l)->(ep a f)->(el l n)->(el o l)->(el l o). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Velol:(el o l))=>((lsym o l) Velol)). Qed. Lemma p1p2_4852: (pl f l)->(ep a f)->(el l n)->(el o l)->(el n o). Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Velol:(el o l))=>((ltra n l o) (conj (p1p2_4694 Vplfl Vepaf Velln) (p1p2_4851 Vplfl Vepaf Velln Velol)))). Qed. Lemma p1p2_4853: (pl f l)->(ep a f)->(el l n)->(el o l)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))(Velol:(el o l))=>(goal1 (p1p2_4852 Vplfl Vepaf Velln Velol))). Qed. Lemma p1p2_4854: (pl f l)->(ep a f)->(el l n)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))(Velln:(el l n))=>((or_ind ((p1p2_4850 Vplfl Vepaf Velln))((p1p2_4853 Vplfl Vepaf Velln)))(p1p2_4697 Vplfl Vepaf Velln))). Qed. Lemma p1p2_4855: (pl f l)->(ep a f)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vepaf:(ep a f))=>((or_ind ((p1p2_4693 Vplfl Vepaf))((p1p2_4854 Vplfl Vepaf)))(p1p2_4255 Vplfl Vepaf))). Qed. Lemma p1p2_4856: (pl f l)->(el l s)->(el s l). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))=>((lsym l s) Vells)). Qed. Lemma p1p2_4859: (pl f l)->(el l s)->(pl i l). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))=>((lcon i s l) (conj p1p2_28 (p1p2_4856 Vplfl Vells)))). Qed. Lemma p1p2_4860: (pl f l)->(el l s)->(ep b f) \/ (el n l). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))=>((unique n l b f) (conj p1p2_7 (conj p1p2_13 (conj p1p2_15 Vplfl))))). Qed. Lemma p1p2_4861: (pl f l)->(el l s)->(ep b f)->(ep f b). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))=>((psym b f) Vepbf)). Qed. Lemma p1p2_4863: (pl f l)->(el l s)->(ep b f)->(pl f p). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))=>((pcon f b p) (conj (p1p2_4861 Vplfl Vells Vepbf) p1p2_9))). Qed. Lemma p1p2_4864: (pl f l)->(el l s)->(ep b f)->(ep d f) \/ (el m p). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))=>((unique m p d f) (conj p1p2_6 (conj p1p2_17 (conj p1p2_22 (p1p2_4863 Vplfl Vells Vepbf)))))). Qed. Lemma p1p2_4865: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep f d). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))=>((psym d f) Vepdf)). Qed. Lemma p1p2_4868: (pl f l)->(el l s)->(ep b f)->(ep d f)->(pl d n). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))=>((pcon d f n) (conj Vepdf p1p2_15))). Qed. Lemma p1p2_4870: (pl f l)->(el l s)->(ep b f)->(ep d f)->(pl d l). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))=>((pcon d f l) (conj Vepdf Vplfl))). Qed. Lemma p1p2_4871: (pl f l)->(el l s)->(ep b f)->(ep d f)->(pl f r). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))=>((pcon f d r) (conj (p1p2_4865 Vplfl Vells Vepbf Vepdf) p1p2_19))). Qed. Lemma p1p2_4872: (pl f l)->(el l s)->(ep b f)->(ep d f)->(pl b r). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))=>((pcon b f r) (conj Vepbf (p1p2_4871 Vplfl Vells Vepbf Vepdf)))). Qed. Lemma p1p2_4873: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d) \/ (el r l). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))=>((unique r l c d) (conj p1p2_11 (conj p1p2_21 (conj p1p2_19 (p1p2_4870 Vplfl Vells Vepbf Vepdf)))))). Qed. Lemma p1p2_4874: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(ep d c). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))=>((psym c d) Vepcd)). Qed. Lemma p1p2_4880: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(pl c p). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))=>((pcon c d p) (conj Vepcd p1p2_17))). Qed. Lemma p1p2_4882: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(pl d o). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))=>((pcon d c o) (conj (p1p2_4874 Vplfl Vells Vepbf Vepdf Vepcd) p1p2_8))). Qed. Lemma p1p2_4883: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(pl f o). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))=>((pcon f d o) (conj (p1p2_4865 Vplfl Vells Vepbf Vepdf) (p1p2_4882 Vplfl Vells Vepbf Vepdf Vepcd)))). Qed. Lemma p1p2_4884: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(pl b o). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))=>((pcon b f o) (conj Vepbf (p1p2_4883 Vplfl Vells Vepbf Vepdf Vepcd)))). Qed. Lemma p1p2_4885: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(ep d e) \/ (el m o). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))=>((unique m o d e) (conj p1p2_6 (conj (p1p2_4882 Vplfl Vells Vepbf Vepdf Vepcd) (conj p1p2_14 p1p2_16))))). Qed. Lemma p1p2_4893: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(ep d e)->(pl d q). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Vepde:(ep d e))=>((pcon d e q) (conj Vepde p1p2_18))). Qed. Lemma p1p2_4894: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(ep d e)->(pl f q). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Vepde:(ep d e))=>((pcon f d q) (conj (p1p2_4865 Vplfl Vells Vepbf Vepdf) (p1p2_4893 Vplfl Vells Vepbf Vepdf Vepcd Vepde)))). Qed. Lemma p1p2_4895: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(ep d e)->(pl b q). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Vepde:(ep d e))=>((pcon b f q) (conj Vepbf (p1p2_4894 Vplfl Vells Vepbf Vepdf Vepcd Vepde)))). Qed. Lemma p1p2_4902: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(ep d e)->(ep a b) \/ (el l q). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Vepde:(ep d e))=>((unique l q a b) (conj p1p2_5 (conj p1p2_10 (conj p1p2_13 (p1p2_4895 Vplfl Vells Vepbf Vepdf Vepcd Vepde)))))). Qed. Lemma p1p2_4913: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(ep d e)->(ep a b)->(pl a p). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))=>((pcon a b p) (conj Vepab p1p2_9))). Qed. Lemma p1p2_4915: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(ep d e)->(ep a b)->(pl a r). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))=>((pcon a b r) (conj Vepab (p1p2_4872 Vplfl Vells Vepbf Vepdf)))). Qed. Lemma p1p2_4917: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(ep d e)->(ep a b)->(ep a i) \/ (el l r). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))=>((unique l r a i) (conj p1p2_5 (conj (p1p2_4915 Vplfl Vells Vepbf Vepdf Vepcd Vepde Vepab) (conj (p1p2_4859 Vplfl Vells) p1p2_27))))). Qed. Lemma p1p2_4918: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(ep d e)->(ep a b)->(ep a i)->(ep i a). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepai:(ep a i))=>((psym a i) Vepai)). Qed. Lemma p1p2_4931: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(ep d e)->(ep a b)->(ep a i)->(pl i p). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepai:(ep a i))=>((pcon i a p) (conj (p1p2_4918 Vplfl Vells Vepbf Vepdf Vepcd Vepde Vepab Vepai) (p1p2_4913 Vplfl Vells Vepbf Vepdf Vepcd Vepde Vepab)))). Qed. Lemma p1p2_4934: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(ep d e)->(ep a b)->(ep a i)->(ep b g) \/ (el n o). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepai:(ep a i))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_4884 Vplfl Vells Vepbf Vepdf Vepcd) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_4935: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(ep d e)->(ep a b)->(ep a i)->(ep b g)->(ep g b). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepai:(ep a i))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_4948: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(ep d e)->(ep a b)->(ep a i)->(ep b g)->(pl g p). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepai:(ep a i))(Vepbg:(ep b g))=>((pcon g b p) (conj (p1p2_4935 Vplfl Vells Vepbf Vepdf Vepcd Vepde Vepab Vepai Vepbg) p1p2_9))). Qed. Lemma p1p2_4949: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(ep d e)->(ep a b)->(ep a i)->(ep b g)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepai:(ep a i))(Vepbg:(ep b g))=>((goal4 p) (conj p1p2_42 (conj (p1p2_4948 Vplfl Vells Vepbf Vepdf Vepcd Vepde Vepab Vepai Vepbg) (conj p1p2_25 (p1p2_4931 Vplfl Vells Vepbf Vepdf Vepcd Vepde Vepab Vepai)))))). Qed. Lemma p1p2_4950: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(ep d e)->(ep a b)->(ep a i)->(el n o)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepai:(ep a i))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_4951: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(ep d e)->(ep a b)->(ep a i)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vepai:(ep a i))=>((or_ind ((p1p2_4949 Vplfl Vells Vepbf Vepdf Vepcd Vepde Vepab Vepai))((p1p2_4950 Vplfl Vells Vepbf Vepdf Vepcd Vepde Vepab Vepai)))(p1p2_4934 Vplfl Vells Vepbf Vepdf Vepcd Vepde Vepab Vepai))). Qed. Lemma p1p2_4953: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(ep d e)->(ep a b)->(el l r)->(el s r). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vellr:(el l r))=>((ltra s l r) (conj (p1p2_4856 Vplfl Vells) Vellr))). Qed. Lemma p1p2_4954: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(ep d e)->(ep a b)->(el l r)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))(Vellr:(el l r))=>(goal3 (p1p2_4953 Vplfl Vells Vepbf Vepdf Vepcd Vepde Vepab Vellr))). Qed. Lemma p1p2_4955: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(ep d e)->(ep a b)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Vepde:(ep d e))(Vepab:(ep a b))=>((or_ind ((p1p2_4951 Vplfl Vells Vepbf Vepdf Vepcd Vepde Vepab))((p1p2_4954 Vplfl Vells Vepbf Vepdf Vepcd Vepde Vepab)))(p1p2_4917 Vplfl Vells Vepbf Vepdf Vepcd Vepde Vepab))). Qed. Lemma p1p2_4956: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(ep d e)->(el l q)->(el q l). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))=>((lsym l q) Vellq)). Qed. Lemma p1p2_4959: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(ep d e)->(el l q)->(pl h l). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))=>((lcon h q l) (conj p1p2_26 (p1p2_4956 Vplfl Vells Vepbf Vepdf Vepcd Vepde Vellq)))). Qed. Lemma p1p2_4962: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(ep d e)->(el l q)->(ep b g) \/ (el n o). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))=>((unique n o b g) (conj p1p2_7 (conj (p1p2_4884 Vplfl Vells Vepbf Vepdf Vepcd) (conj p1p2_23 p1p2_24))))). Qed. Lemma p1p2_4963: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(ep d e)->(el l q)->(ep b g)->(ep g b). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Vepbg:(ep b g))=>((psym b g) Vepbg)). Qed. Lemma p1p2_4973: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(ep d e)->(el l q)->(ep b g)->(pl g l). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Vepbg:(ep b g))=>((pcon g b l) (conj (p1p2_4963 Vplfl Vells Vepbf Vepdf Vepcd Vepde Vellq Vepbg) p1p2_13))). Qed. Lemma p1p2_4974: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(ep d e)->(el l q)->(ep b g)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Vepbg:(ep b g))=>((goal4 l) (conj p1p2_38 (conj (p1p2_4973 Vplfl Vells Vepbf Vepdf Vepcd Vepde Vellq Vepbg) (conj (p1p2_4959 Vplfl Vells Vepbf Vepdf Vepcd Vepde Vellq) (p1p2_4859 Vplfl Vells)))))). Qed. Lemma p1p2_4975: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(ep d e)->(el l q)->(el n o)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))(Velno:(el n o))=>(goal1 Velno)). Qed. Lemma p1p2_4976: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(ep d e)->(el l q)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Vepde:(ep d e))(Vellq:(el l q))=>((or_ind ((p1p2_4974 Vplfl Vells Vepbf Vepdf Vepcd Vepde Vellq))((p1p2_4975 Vplfl Vells Vepbf Vepdf Vepcd Vepde Vellq)))(p1p2_4962 Vplfl Vells Vepbf Vepdf Vepcd Vepde Vellq))). Qed. Lemma p1p2_4977: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(ep d e)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Vepde:(ep d e))=>((or_ind ((p1p2_4955 Vplfl Vells Vepbf Vepdf Vepcd Vepde))((p1p2_4976 Vplfl Vells Vepbf Vepdf Vepcd Vepde)))(p1p2_4902 Vplfl Vells Vepbf Vepdf Vepcd Vepde))). Qed. Lemma p1p2_4978: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(el m o)->(el o m). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Velmo:(el m o))=>((lsym m o) Velmo)). Qed. Lemma p1p2_4979: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(el m o)->(pl g m). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Velmo:(el m o))=>((lcon g o m) (conj p1p2_24 (p1p2_4978 Vplfl Vells Vepbf Vepdf Vepcd Velmo)))). Qed. Lemma p1p2_4980: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(el m o)->(ep d g) \/ (el m n). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Velmo:(el m o))=>((unique m n d g) (conj p1p2_6 (conj (p1p2_4868 Vplfl Vells Vepbf Vepdf) (conj (p1p2_4979 Vplfl Vells Vepbf Vepdf Vepcd Velmo) p1p2_23))))). Qed. Lemma p1p2_4981: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(el m o)->(ep d g)->(ep g d). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Velmo:(el m o))(Vepdg:(ep d g))=>((psym d g) Vepdg)). Qed. Lemma p1p2_4988: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(el m o)->(ep d g)->(pl g p). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Velmo:(el m o))(Vepdg:(ep d g))=>((pcon g d p) (conj (p1p2_4981 Vplfl Vells Vepbf Vepdf Vepcd Velmo Vepdg) p1p2_17))). Qed. Lemma p1p2_4992: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(el m o)->(ep d g)->(ep c i) \/ (el r l). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Velmo:(el m o))(Vepdg:(ep d g))=>((unique r l c i) (conj p1p2_11 (conj p1p2_21 (conj p1p2_27 (p1p2_4859 Vplfl Vells)))))). Qed. Lemma p1p2_4993: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(el m o)->(ep d g)->(ep c i)->(ep i c). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Velmo:(el m o))(Vepdg:(ep d g))(Vepci:(ep c i))=>((psym c i) Vepci)). Qed. Lemma p1p2_5004: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(el m o)->(ep d g)->(ep c i)->(pl i p). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Velmo:(el m o))(Vepdg:(ep d g))(Vepci:(ep c i))=>((pcon i c p) (conj (p1p2_4993 Vplfl Vells Vepbf Vepdf Vepcd Velmo Vepdg Vepci) (p1p2_4880 Vplfl Vells Vepbf Vepdf Vepcd)))). Qed. Lemma p1p2_5005: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(el m o)->(ep d g)->(ep c i)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Velmo:(el m o))(Vepdg:(ep d g))(Vepci:(ep c i))=>((goal4 p) (conj p1p2_42 (conj (p1p2_4988 Vplfl Vells Vepbf Vepdf Vepcd Velmo Vepdg) (conj p1p2_25 (p1p2_5004 Vplfl Vells Vepbf Vepdf Vepcd Velmo Vepdg Vepci)))))). Qed. Lemma p1p2_5006: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(el m o)->(ep d g)->(el r l)->(el l r). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Velmo:(el m o))(Vepdg:(ep d g))(Velrl:(el r l))=>((lsym r l) Velrl)). Qed. Lemma p1p2_5007: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(el m o)->(ep d g)->(el r l)->(el s r). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Velmo:(el m o))(Vepdg:(ep d g))(Velrl:(el r l))=>((ltra s l r) (conj (p1p2_4856 Vplfl Vells) (p1p2_5006 Vplfl Vells Vepbf Vepdf Vepcd Velmo Vepdg Velrl)))). Qed. Lemma p1p2_5008: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(el m o)->(ep d g)->(el r l)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Velmo:(el m o))(Vepdg:(ep d g))(Velrl:(el r l))=>(goal3 (p1p2_5007 Vplfl Vells Vepbf Vepdf Vepcd Velmo Vepdg Velrl))). Qed. Lemma p1p2_5009: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(el m o)->(ep d g)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Velmo:(el m o))(Vepdg:(ep d g))=>((or_ind ((p1p2_5005 Vplfl Vells Vepbf Vepdf Vepcd Velmo Vepdg))((p1p2_5008 Vplfl Vells Vepbf Vepdf Vepcd Velmo Vepdg)))(p1p2_4992 Vplfl Vells Vepbf Vepdf Vepcd Velmo Vepdg))). Qed. Lemma p1p2_5011: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(el m o)->(el m n)->(el o n). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Velmo:(el m o))(Velmn:(el m n))=>((ltra o m n) (conj (p1p2_4978 Vplfl Vells Vepbf Vepdf Vepcd Velmo) Velmn))). Qed. Lemma p1p2_5012: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(el m o)->(el m n)->(el n o). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Velmo:(el m o))(Velmn:(el m n))=>((lsym o n) (p1p2_5011 Vplfl Vells Vepbf Vepdf Vepcd Velmo Velmn))). Qed. Lemma p1p2_5013: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(el m o)->(el m n)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Velmo:(el m o))(Velmn:(el m n))=>(goal1 (p1p2_5012 Vplfl Vells Vepbf Vepdf Vepcd Velmo Velmn))). Qed. Lemma p1p2_5014: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->(el m o)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))(Velmo:(el m o))=>((or_ind ((p1p2_5009 Vplfl Vells Vepbf Vepdf Vepcd Velmo))((p1p2_5013 Vplfl Vells Vepbf Vepdf Vepcd Velmo)))(p1p2_4980 Vplfl Vells Vepbf Vepdf Vepcd Velmo))). Qed. Lemma p1p2_5015: (pl f l)->(el l s)->(ep b f)->(ep d f)->(ep c d)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Vepcd:(ep c d))=>((or_ind ((p1p2_4977 Vplfl Vells Vepbf Vepdf Vepcd))((p1p2_5014 Vplfl Vells Vepbf Vepdf Vepcd)))(p1p2_4885 Vplfl Vells Vepbf Vepdf Vepcd))). Qed. Lemma p1p2_5016: (pl f l)->(el l s)->(ep b f)->(ep d f)->(el r l)->(el l r). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Velrl:(el r l))=>((lsym r l) Velrl)). Qed. Lemma p1p2_5017: (pl f l)->(el l s)->(ep b f)->(ep d f)->(el r l)->(el s r). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Velrl:(el r l))=>((ltra s l r) (conj (p1p2_4856 Vplfl Vells) (p1p2_5016 Vplfl Vells Vepbf Vepdf Velrl)))). Qed. Lemma p1p2_5018: (pl f l)->(el l s)->(ep b f)->(ep d f)->(el r l)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))(Velrl:(el r l))=>(goal3 (p1p2_5017 Vplfl Vells Vepbf Vepdf Velrl))). Qed. Lemma p1p2_5019: (pl f l)->(el l s)->(ep b f)->(ep d f)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Vepdf:(ep d f))=>((or_ind ((p1p2_5015 Vplfl Vells Vepbf Vepdf))((p1p2_5018 Vplfl Vells Vepbf Vepdf)))(p1p2_4873 Vplfl Vells Vepbf Vepdf))). Qed. Lemma p1p2_5020: (pl f l)->(el l s)->(ep b f)->(el m p)->(el p m). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Velmp:(el m p))=>((lsym m p) Velmp)). Qed. Lemma p1p2_5022: (pl f l)->(el l s)->(ep b f)->(el m p)->(pl h m). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Velmp:(el m p))=>((lcon h p m) (conj p1p2_25 (p1p2_5020 Vplfl Vells Vepbf Velmp)))). Qed. Lemma p1p2_5023: (pl f l)->(el l s)->(ep b f)->(el m p)->(ep c i) \/ (el r l). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Velmp:(el m p))=>((unique r l c i) (conj p1p2_11 (conj p1p2_21 (conj p1p2_27 (p1p2_4859 Vplfl Vells)))))). Qed. Lemma p1p2_5024: (pl f l)->(el l s)->(ep b f)->(el m p)->(ep c i)->(ep i c). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Velmp:(el m p))(Vepci:(ep c i))=>((psym c i) Vepci)). Qed. Lemma p1p2_5025: (pl f l)->(el l s)->(ep b f)->(el m p)->(ep c i)->(pl i o). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Velmp:(el m p))(Vepci:(ep c i))=>((pcon i c o) (conj (p1p2_5024 Vplfl Vells Vepbf Velmp Vepci) p1p2_8))). Qed. Lemma p1p2_5026: (pl f l)->(el l s)->(ep b f)->(el m p)->(ep c i)->(ep e h) \/ (el m q). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Velmp:(el m p))(Vepci:(ep c i))=>((unique m q e h) (conj p1p2_14 (conj p1p2_18 (conj (p1p2_5022 Vplfl Vells Vepbf Velmp) p1p2_26))))). Qed. Lemma p1p2_5027: (pl f l)->(el l s)->(ep b f)->(el m p)->(ep c i)->(ep e h)->(ep h e). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Velmp:(el m p))(Vepci:(ep c i))(Vepeh:(ep e h))=>((psym e h) Vepeh)). Qed. Lemma p1p2_5028: (pl f l)->(el l s)->(ep b f)->(el m p)->(ep c i)->(ep e h)->(pl h o). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Velmp:(el m p))(Vepci:(ep c i))(Vepeh:(ep e h))=>((pcon h e o) (conj (p1p2_5027 Vplfl Vells Vepbf Velmp Vepci Vepeh) p1p2_16))). Qed. Lemma p1p2_5029: (pl f l)->(el l s)->(ep b f)->(el m p)->(ep c i)->(ep e h)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Velmp:(el m p))(Vepci:(ep c i))(Vepeh:(ep e h))=>((goal4 o) (conj p1p2_41 (conj p1p2_24 (conj (p1p2_5028 Vplfl Vells Vepbf Velmp Vepci Vepeh) (p1p2_5025 Vplfl Vells Vepbf Velmp Vepci)))))). Qed. Lemma p1p2_5031: (pl f l)->(el l s)->(ep b f)->(el m p)->(ep c i)->(el m q)->(el p q). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Velmp:(el m p))(Vepci:(ep c i))(Velmq:(el m q))=>((ltra p m q) (conj (p1p2_5020 Vplfl Vells Vepbf Velmp) Velmq))). Qed. Lemma p1p2_5032: (pl f l)->(el l s)->(ep b f)->(el m p)->(ep c i)->(el m q)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Velmp:(el m p))(Vepci:(ep c i))(Velmq:(el m q))=>(goal2 (p1p2_5031 Vplfl Vells Vepbf Velmp Vepci Velmq))). Qed. Lemma p1p2_5033: (pl f l)->(el l s)->(ep b f)->(el m p)->(ep c i)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Velmp:(el m p))(Vepci:(ep c i))=>((or_ind ((p1p2_5029 Vplfl Vells Vepbf Velmp Vepci))((p1p2_5032 Vplfl Vells Vepbf Velmp Vepci)))(p1p2_5026 Vplfl Vells Vepbf Velmp Vepci))). Qed. Lemma p1p2_5034: (pl f l)->(el l s)->(ep b f)->(el m p)->(el r l)->(el l r). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Velmp:(el m p))(Velrl:(el r l))=>((lsym r l) Velrl)). Qed. Lemma p1p2_5035: (pl f l)->(el l s)->(ep b f)->(el m p)->(el r l)->(el s r). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Velmp:(el m p))(Velrl:(el r l))=>((ltra s l r) (conj (p1p2_4856 Vplfl Vells) (p1p2_5034 Vplfl Vells Vepbf Velmp Velrl)))). Qed. Lemma p1p2_5036: (pl f l)->(el l s)->(ep b f)->(el m p)->(el r l)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Velmp:(el m p))(Velrl:(el r l))=>(goal3 (p1p2_5035 Vplfl Vells Vepbf Velmp Velrl))). Qed. Lemma p1p2_5037: (pl f l)->(el l s)->(ep b f)->(el m p)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))(Velmp:(el m p))=>((or_ind ((p1p2_5033 Vplfl Vells Vepbf Velmp))((p1p2_5036 Vplfl Vells Vepbf Velmp)))(p1p2_5023 Vplfl Vells Vepbf Velmp))). Qed. Lemma p1p2_5038: (pl f l)->(el l s)->(ep b f)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Vepbf:(ep b f))=>((or_ind ((p1p2_5019 Vplfl Vells Vepbf))((p1p2_5037 Vplfl Vells Vepbf)))(p1p2_4864 Vplfl Vells Vepbf))). Qed. Lemma p1p2_5044: (pl f l)->(el l s)->(el n l)->(pl g l). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Velnl:(el n l))=>((lcon g n l) (conj p1p2_23 Velnl))). Qed. Lemma p1p2_5047: (pl f l)->(el l s)->(el n l)->(ep c g) \/ (el o l). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Velnl:(el n l))=>((unique o l c g) (conj p1p2_8 (conj p1p2_21 (conj p1p2_24 (p1p2_5044 Vplfl Vells Velnl)))))). Qed. Lemma p1p2_5048: (pl f l)->(el l s)->(el n l)->(ep c g)->(ep g c). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Velnl:(el n l))(Vepcg:(ep c g))=>((psym c g) Vepcg)). Qed. Lemma p1p2_5050: (pl f l)->(el l s)->(el n l)->(ep c g)->(ep c i) \/ (el r l). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Velnl:(el n l))(Vepcg:(ep c g))=>((unique r l c i) (conj p1p2_11 (conj p1p2_21 (conj p1p2_27 (p1p2_4859 Vplfl Vells)))))). Qed. Lemma p1p2_5051: (pl f l)->(el l s)->(el n l)->(ep c g)->(ep c i)->(ep i c). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Velnl:(el n l))(Vepcg:(ep c g))(Vepci:(ep c i))=>((psym c i) Vepci)). Qed. Lemma p1p2_5055: (pl f l)->(el l s)->(el n l)->(ep c g)->(ep c i)->(exists A:dom,(pl a A)/\(pl d A)). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Velnl:(el n l))(Vepcg:(ep c g))(Vepci:(ep c i))=>((line a d) (conj p1p2_29 p1p2_30))). Qed. Lemma p1p2_5057: (pl f l)->(el l s)->(el n l)->(ep c g)->(ep c i)->forall C0:dom,(pl a C0)->(pl d C0)->(exists A:dom,(pl b A)/\(pl e A)). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Velnl:(el n l))(Vepcg:(ep c g))(Vepci:(ep c i))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))=>((line b e) (conj p1p2_31 p1p2_33))). Qed. Lemma p1p2_5059: (pl f l)->(el l s)->(el n l)->(ep c g)->(ep c i)->forall C0:dom,(pl a C0)->(pl d C0)->forall C1:dom,(pl b C1)->(pl e C1)->(exists A:dom,(pl c A)/\(pl h A)). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Velnl:(el n l))(Vepcg:(ep c g))(Vepci:(ep c i))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))(C1:dom)(VplbC1:(pl b C1))(VpleC1:(pl e C1))=>((line c h) (conj p1p2_32 p1p2_36))). Qed. Lemma p1p2_5060: (pl f l)->(el l s)->(el n l)->(ep c g)->(ep c i)->forall C0:dom,(pl a C0)->(pl d C0)->forall C1:dom,(pl b C1)->(pl e C1)->forall C2:dom,(pl c C2)->(pl h C2)->(el C2 C2). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Velnl:(el n l))(Vepcg:(ep c g))(Vepci:(ep c i))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))(C1:dom)(VplbC1:(pl b C1))(VpleC1:(pl e C1))(C2:dom)(VplcC2:(pl c C2))(VplhC2:(pl h C2))=>((lref c C2) VplcC2)). Qed. Lemma p1p2_5061: (pl f l)->(el l s)->(el n l)->(ep c g)->(ep c i)->forall C0:dom,(pl a C0)->(pl d C0)->forall C1:dom,(pl b C1)->(pl e C1)->forall C2:dom,(pl c C2)->(pl h C2)->(pl g C2). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Velnl:(el n l))(Vepcg:(ep c g))(Vepci:(ep c i))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))(C1:dom)(VplbC1:(pl b C1))(VpleC1:(pl e C1))(C2:dom)(VplcC2:(pl c C2))(VplhC2:(pl h C2))=>((pcon g c C2) (conj (p1p2_5048 Vplfl Vells Velnl Vepcg) VplcC2))). Qed. Lemma p1p2_5062: (pl f l)->(el l s)->(el n l)->(ep c g)->(ep c i)->forall C0:dom,(pl a C0)->(pl d C0)->forall C1:dom,(pl b C1)->(pl e C1)->forall C2:dom,(pl c C2)->(pl h C2)->(pl i C2). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Velnl:(el n l))(Vepcg:(ep c g))(Vepci:(ep c i))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))(C1:dom)(VplbC1:(pl b C1))(VpleC1:(pl e C1))(C2:dom)(VplcC2:(pl c C2))(VplhC2:(pl h C2))=>((pcon i c C2) (conj (p1p2_5051 Vplfl Vells Velnl Vepcg Vepci) VplcC2))). Qed. Lemma p1p2_5063: (pl f l)->(el l s)->(el n l)->(ep c g)->(ep c i)->forall C0:dom,(pl a C0)->(pl d C0)->forall C1:dom,(pl b C1)->(pl e C1)->forall C2:dom,(pl c C2)->(pl h C2)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Velnl:(el n l))(Vepcg:(ep c g))(Vepci:(ep c i))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))(C1:dom)(VplbC1:(pl b C1))(VpleC1:(pl e C1))(C2:dom)(VplcC2:(pl c C2))(VplhC2:(pl h C2))=>((goal4 C2) (conj (p1p2_5060 Vplfl Vells Velnl Vepcg Vepci C0 VplaC0 VpldC0 C1 VplbC1 VpleC1 C2 VplcC2 VplhC2) (conj (p1p2_5061 Vplfl Vells Velnl Vepcg Vepci C0 VplaC0 VpldC0 C1 VplbC1 VpleC1 C2 VplcC2 VplhC2) (conj VplhC2 (p1p2_5062 Vplfl Vells Velnl Vepcg Vepci C0 VplaC0 VpldC0 C1 VplbC1 VpleC1 C2 VplcC2 VplhC2)))))). Qed. Lemma p1p2_5064: (pl f l)->(el l s)->(el n l)->(ep c g)->(ep c i)->forall C0:dom,(pl a C0)->(pl d C0)->forall C1:dom,(pl b C1)->(pl e C1)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Velnl:(el n l))(Vepcg:(ep c g))(Vepci:(ep c i))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))(C1:dom)(VplbC1:(pl b C1))(VpleC1:(pl e C1))=>((ex_ind (P:=fun C2:dom=>(pl c C2)/\(pl h C2))(fun C2:dom=>(and_ind (p1p2_5063 Vplfl Vells Velnl Vepcg Vepci C0 VplaC0 VpldC0 C1 VplbC1 VpleC1 C2))))(p1p2_5059 Vplfl Vells Velnl Vepcg Vepci C0 VplaC0 VpldC0 C1 VplbC1 VpleC1))). Qed. Lemma p1p2_5065: (pl f l)->(el l s)->(el n l)->(ep c g)->(ep c i)->forall C0:dom,(pl a C0)->(pl d C0)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Velnl:(el n l))(Vepcg:(ep c g))(Vepci:(ep c i))(C0:dom)(VplaC0:(pl a C0))(VpldC0:(pl d C0))=>((ex_ind (P:=fun C1:dom=>(pl b C1)/\(pl e C1))(fun C1:dom=>(and_ind (p1p2_5064 Vplfl Vells Velnl Vepcg Vepci C0 VplaC0 VpldC0 C1))))(p1p2_5057 Vplfl Vells Velnl Vepcg Vepci C0 VplaC0 VpldC0))). Qed. Lemma p1p2_5066: (pl f l)->(el l s)->(el n l)->(ep c g)->(ep c i)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Velnl:(el n l))(Vepcg:(ep c g))(Vepci:(ep c i))=>((ex_ind (P:=fun C0:dom=>(pl a C0)/\(pl d C0))(fun C0:dom=>(and_ind (p1p2_5065 Vplfl Vells Velnl Vepcg Vepci C0))))(p1p2_5055 Vplfl Vells Velnl Vepcg Vepci))). Qed. Lemma p1p2_5067: (pl f l)->(el l s)->(el n l)->(ep c g)->(el r l)->(el l r). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Velnl:(el n l))(Vepcg:(ep c g))(Velrl:(el r l))=>((lsym r l) Velrl)). Qed. Lemma p1p2_5068: (pl f l)->(el l s)->(el n l)->(ep c g)->(el r l)->(el s r). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Velnl:(el n l))(Vepcg:(ep c g))(Velrl:(el r l))=>((ltra s l r) (conj (p1p2_4856 Vplfl Vells) (p1p2_5067 Vplfl Vells Velnl Vepcg Velrl)))). Qed. Lemma p1p2_5069: (pl f l)->(el l s)->(el n l)->(ep c g)->(el r l)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Velnl:(el n l))(Vepcg:(ep c g))(Velrl:(el r l))=>(goal3 (p1p2_5068 Vplfl Vells Velnl Vepcg Velrl))). Qed. Lemma p1p2_5070: (pl f l)->(el l s)->(el n l)->(ep c g)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Velnl:(el n l))(Vepcg:(ep c g))=>((or_ind ((p1p2_5066 Vplfl Vells Velnl Vepcg))((p1p2_5069 Vplfl Vells Velnl Vepcg)))(p1p2_5050 Vplfl Vells Velnl Vepcg))). Qed. Lemma p1p2_5071: (pl f l)->(el l s)->(el n l)->(el o l)->(el l o). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Velnl:(el n l))(Velol:(el o l))=>((lsym o l) Velol)). Qed. Lemma p1p2_5074: (pl f l)->(el l s)->(el n l)->(el o l)->(el n o). Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Velnl:(el n l))(Velol:(el o l))=>((ltra n l o) (conj Velnl (p1p2_5071 Vplfl Vells Velnl Velol)))). Qed. Lemma p1p2_5075: (pl f l)->(el l s)->(el n l)->(el o l)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Velnl:(el n l))(Velol:(el o l))=>(goal1 (p1p2_5074 Vplfl Vells Velnl Velol))). Qed. Lemma p1p2_5076: (pl f l)->(el l s)->(el n l)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))(Velnl:(el n l))=>((or_ind ((p1p2_5070 Vplfl Vells Velnl))((p1p2_5075 Vplfl Vells Velnl)))(p1p2_5047 Vplfl Vells Velnl))). Qed. Lemma p1p2_5077: (pl f l)->(el l s)->goal. Proof. exact (fun (Vplfl:(pl f l))(Vells:(el l s))=>((or_ind ((p1p2_5038 Vplfl Vells))((p1p2_5076 Vplfl Vells)))(p1p2_4860 Vplfl Vells))). Qed. Lemma p1p2_5078: (pl f l)->goal. Proof. exact (fun (Vplfl:(pl f l))=>((or_ind ((p1p2_4855 Vplfl))((p1p2_5077 Vplfl)))(p1p2_4250 Vplfl))). Qed. Lemma p1p2_5079: goal. Proof. exact (((or_ind (ex_ind (P:=fun C0:dom=>(col g h i C0))(fun C0:dom=>((p1p2_51 C0))))(or_ind (p1p2_852)(or_ind (p1p2_1710)(or_ind (p1p2_2572)(or_ind (p1p2_3419)(or_ind (p1p2_4249)(p1p2_5078)))))))p1p2_46)). Qed. Check p1p2_5079. End p1p2_.