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Section c82_. Let false:=False. Let false_ind:=False_ind. Variable dom:Set. Variable goal:Prop. Variable i:dom->dom->Prop. Variable l:dom->dom->Prop. Variable p:dom->dom->Prop. Variable a1 a1b1 a1c1 a2 a2b2 a2c2 ab ac b1 b1c1 b2 b2c2 bc c1 c2 o oa ob oc:dom. Hypothesis goal_normal:forall A:dom,(l A A)/\(i bc A)/\(i ac A)/\(i ab A)->goal. Hypothesis t1in2:(i a1 b2c2)/\(i b1 a2c2)/\(i c1 a2b2)->goal. Hypothesis t2in1:(i a2 b1c1)/\(i b2 a1c1)/\(i c2 a1b1)->goal. Hypothesis gap_a:(i a1 b2c2) \/ (i b2 a1c1). Hypothesis gap_b:(i b1 a2c2) \/ (i c2 a1b1). Hypothesis gap_c:(i c1 a2b2) \/ (i a2 b1c1). Hypothesis ia1b1:(i a1 a1b1). Hypothesis ib1a1:(i b1 a1b1). Hypothesis ia2b2:(i a2 a2b2). Hypothesis ib2a2:(i b2 a2b2). Hypothesis ia1c1:(i a1 a1c1). Hypothesis ic1a1:(i c1 a1c1). Hypothesis ia2c2:(i a2 a2c2). Hypothesis ic2a2:(i c2 a2c2). Hypothesis ic1b1:(i c1 b1c1). Hypothesis ib1c1:(i b1 b1c1). Hypothesis ic2b2:(i c2 b2c2). Hypothesis ib2c2:(i b2 b2c2). Hypothesis iooa:(i o oa). Hypothesis ioob:(i o ob). Hypothesis iooc:(i o oc). Hypothesis ia1oa:(i a1 oa). Hypothesis ia2oa:(i a2 oa). Hypothesis ib1ob:(i b1 ob). Hypothesis ib2ob:(i b2 ob). Hypothesis ic1oc:(i c1 oc). Hypothesis ic2oc:(i c2 oc). Hypothesis ibc1:(i bc b1c1). Hypothesis ibc2:(i bc b2c2). Hypothesis iac1:(i ac a1c1). Hypothesis iac2:(i ac a2c2). Hypothesis iab1:(i ab a1b1). Hypothesis iab2:(i ab a2b2). Hypothesis triangle1:forall A:dom,(i a1 A)/\(i b1 A)/\(i c1 A)->false. Hypothesis triangle2:forall A:dom,(i a2 A)/\(i b2 A)/\(i c2 A)->false. Hypothesis notaa:(p a2 a1)->false. Hypothesis notbb:(p b2 b1)->false. Hypothesis notcc:(p c2 c1)->false. Hypothesis notbc:(l b1c1 b2c2)->false. Hypothesis notac:(l a1c1 a2c2)->false. Hypothesis notab:(l a1b1 a2b2)->false. Hypothesis pref:forall A B:dom,(i A B)->(p A A). Hypothesis psym:forall A B:dom,(p A B)->(p B A). Hypothesis ptra:forall A B C:dom,(p A B)/\(p B C)->(p A C). Hypothesis lref:forall A B:dom,(i A B)->(l B B). Hypothesis lsym:forall A B:dom,(l A B)->(l B A). Hypothesis ltra:forall A B C:dom,(l A B)/\(l B C)->(l A C). Hypothesis pcon:forall A B C:dom,(p A B)/\(i B C)->(i A C). Hypothesis lcon:forall A B C:dom,(i A B)/\(l B C)->(i A C). Hypothesis unique:forall A B C D:dom,(i A C)/\(i A D)/\(i B C)/\(i B D)->(p A B) \/ (l C D). Lemma c82_1: (i a1 b2c2) \/ (i b2 a1c1). Proof. exact (gap_a). Qed. Lemma c82_2: (i a1 b2c2)->(i b1 a2c2) \/ (i c2 a1b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))=>gap_b). Qed. Lemma c82_3: (i a1 b2c2)->(i b1 a2c2)->(i c1 a2b2) \/ (i a2 b1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))=>gap_c). Qed. Lemma c82_4: (i a1 b2c2)->(i b1 a2c2)->(i c1 a2b2)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))=>(t1in2 (conj Via1b2c2 (conj Vib1a2c2 Vic1a2b2)))). Qed. Lemma c82_5: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(i a1 a1b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ia1b1). Qed. Lemma c82_6: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(i b1 a1b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ib1a1). Qed. Lemma c82_7: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(i a2 a2b2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ia2b2). Qed. Lemma c82_8: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(i b2 a2b2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ib2a2). Qed. Lemma c82_9: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(i a1 a1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ia1c1). Qed. Lemma c82_10: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(i c1 a1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ic1a1). Qed. Lemma c82_11: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(i a2 a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ia2c2). Qed. Lemma c82_12: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(i c2 a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ic2a2). Qed. Lemma c82_13: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(i c1 b1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ic1b1). Qed. Lemma c82_14: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(i b1 b1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ib1c1). Qed. Lemma c82_15: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(i c2 b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ic2b2). Qed. Lemma c82_16: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(i b2 b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ib2c2). Qed. Lemma c82_17: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(i o oa). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>iooa). Qed. Lemma c82_18: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(i o ob). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ioob). Qed. Lemma c82_19: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(i o oc). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>iooc). Qed. Lemma c82_20: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(i a1 oa). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ia1oa). Qed. Lemma c82_21: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(i a2 oa). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ia2oa). Qed. Lemma c82_22: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(i b1 ob). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ib1ob). Qed. Lemma c82_23: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(i b2 ob). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ib2ob). Qed. Lemma c82_24: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(i c1 oc). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ic1oc). Qed. Lemma c82_25: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(i c2 oc). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ic2oc). Qed. Lemma c82_26: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(i bc b1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ibc1). Qed. Lemma c82_27: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(i bc b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ibc2). Qed. Lemma c82_28: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(i ac a1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>iac1). Qed. Lemma c82_29: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(i ac a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>iac2). Qed. Lemma c82_30: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(i ab a1b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>iab1). Qed. Lemma c82_31: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(i ab a2b2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>iab2). Qed. Lemma c82_43: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>((lref b1 a2c2) Vib1a2c2)). Qed. Lemma c82_51: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2) \/ (l a2c2 b1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>((unique b1 a2 a2c2 b1c1) (conj Vib1a2c2 (conj (c82_14 Via1b2c2 Vib1a2c2 Via2b1c1) (conj (c82_11 Via1b2c2 Vib1a2c2 Via2b1c1) Via2b1c1))))). Qed. Lemma c82_52: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(p a2 b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))=>((psym b1 a2) Vpb1a2)). Qed. Lemma c82_53: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(i b1 a2b2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))=>((pcon b1 a2 a2b2) (conj Vpb1a2 (c82_7 Via1b2c2 Vib1a2c2 Via2b1c1)))). Qed. Lemma c82_54: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(i b1 oa). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))=>((pcon b1 a2 oa) (conj Vpb1a2 (c82_21 Via1b2c2 Vib1a2c2 Via2b1c1)))). Qed. Lemma c82_57: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(p a1 b1) \/ (l a1b1 oa). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))=>((unique a1 b1 a1b1 oa) (conj (c82_5 Via1b2c2 Vib1a2c2 Via2b1c1) (conj (c82_20 Via1b2c2 Vib1a2c2 Via2b1c1) (conj (c82_6 Via1b2c2 Vib1a2c2 Via2b1c1) (c82_54 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2)))))). Qed. Lemma c82_58: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(p a1 b1)->(p b1 a1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vpa1b1:(p a1 b1))=>((psym a1 b1) Vpa1b1)). Qed. Lemma c82_59: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(p a1 b1)->(p a2 a1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vpa1b1:(p a1 b1))=>((ptra a2 b1 a1) (conj (c82_52 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2) (c82_58 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vpa1b1)))). Qed. Lemma c82_60: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(p a1 b1)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vpa1b1:(p a1 b1))=>(notaa (c82_59 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vpa1b1))). Qed. Lemma c82_61: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(p a1 b1)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vpa1b1:(p a1 b1))=>((false_ind goal) (c82_60 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vpa1b1))). Qed. Lemma c82_62: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l oa a1b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))=>((lsym a1b1 oa) Vla1b1oa)). Qed. Lemma c82_63: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(i o a1b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))=>((lcon o oa a1b1) (conj (c82_17 Via1b2c2 Vib1a2c2 Via2b1c1) (c82_62 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa)))). Qed. Lemma c82_65: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o) \/ (l a1b1 ob). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))=>((unique b1 o a1b1 ob) (conj (c82_6 Via1b2c2 Vib1a2c2 Via2b1c1) (conj (c82_22 Via1b2c2 Vib1a2c2 Via2b1c1) (conj (c82_63 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa) (c82_18 Via1b2c2 Vib1a2c2 Via2b1c1)))))). Qed. Lemma c82_69: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(i b1 oc). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))=>((pcon b1 o oc) (conj Vpb1o (c82_19 Via1b2c2 Vib1a2c2 Via2b1c1)))). Qed. Lemma c82_74: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(p b1 c2) \/ (l a2c2 oc). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))=>((unique b1 c2 a2c2 oc) (conj Vib1a2c2 (conj (c82_69 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o) (conj (c82_12 Via1b2c2 Vib1a2c2 Via2b1c1) (c82_25 Via1b2c2 Vib1a2c2 Via2b1c1)))))). Qed. Lemma c82_80: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(p b1 c2)->(i b1 b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vpb1c2:(p b1 c2))=>((pcon b1 c2 b2c2) (conj Vpb1c2 (c82_15 Via1b2c2 Vib1a2c2 Via2b1c1)))). Qed. Lemma c82_81: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(p b1 c2)->(i a2 b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vpb1c2:(p b1 c2))=>((pcon a2 b1 b2c2) (conj (c82_52 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2) (c82_80 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vpb1c2)))). Qed. Lemma c82_82: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(p b1 c2)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vpb1c2:(p b1 c2))=>((triangle2 b2c2) (conj (c82_81 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vpb1c2) (conj (c82_16 Via1b2c2 Vib1a2c2 Via2b1c1) (c82_15 Via1b2c2 Vib1a2c2 Via2b1c1))))). Qed. Lemma c82_83: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(p b1 c2)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vpb1c2:(p b1 c2))=>((false_ind goal) (c82_82 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vpb1c2))). Qed. Lemma c82_84: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->(l oc a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))=>((lsym a2c2 oc) Vla2c2oc)). Qed. Lemma c82_85: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->(i c1 a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))=>((lcon c1 oc a2c2) (conj (c82_24 Via1b2c2 Vib1a2c2 Via2b1c1) (c82_84 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vla2c2oc)))). Qed. Lemma c82_87: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->(p b1 c1) \/ (l a2c2 b1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))=>((unique b1 c1 a2c2 b1c1) (conj Vib1a2c2 (conj (c82_14 Via1b2c2 Vib1a2c2 Via2b1c1) (conj (c82_85 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vla2c2oc) (c82_13 Via1b2c2 Vib1a2c2 Via2b1c1)))))). Qed. Lemma c82_93: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->(p b1 c1)->(i b1 a1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))(Vpb1c1:(p b1 c1))=>((pcon b1 c1 a1c1) (conj Vpb1c1 (c82_10 Via1b2c2 Vib1a2c2 Via2b1c1)))). Qed. Lemma c82_94: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->(p b1 c1)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))(Vpb1c1:(p b1 c1))=>((triangle1 a1c1) (conj (c82_9 Via1b2c2 Vib1a2c2 Via2b1c1) (conj (c82_93 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vla2c2oc Vpb1c1) (c82_10 Via1b2c2 Vib1a2c2 Via2b1c1))))). Qed. Lemma c82_95: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->(p b1 c1)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))(Vpb1c1:(p b1 c1))=>((false_ind goal) (c82_94 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vla2c2oc Vpb1c1))). Qed. Lemma c82_96: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->(l a2c2 b1c1)->(l b1c1 a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))(Vla2c2b1c1:(l a2c2 b1c1))=>((lsym a2c2 b1c1) Vla2c2b1c1)). Qed. Lemma c82_100: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->(l a2c2 b1c1)->(i bc a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))(Vla2c2b1c1:(l a2c2 b1c1))=>((lcon bc b1c1 a2c2) (conj (c82_26 Via1b2c2 Vib1a2c2 Via2b1c1) (c82_96 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vla2c2oc Vla2c2b1c1)))). Qed. Lemma c82_103: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->(l a2c2 b1c1)->(p b1 ab) \/ (l a1b1 a2b2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))(Vla2c2b1c1:(l a2c2 b1c1))=>((unique b1 ab a1b1 a2b2) (conj (c82_6 Via1b2c2 Vib1a2c2 Via2b1c1) (conj (c82_53 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2) (conj (c82_30 Via1b2c2 Vib1a2c2 Via2b1c1) (c82_31 Via1b2c2 Vib1a2c2 Via2b1c1)))))). Qed. Lemma c82_104: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->(l a2c2 b1c1)->(p b1 ab)->(p ab b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))(Vla2c2b1c1:(l a2c2 b1c1))(Vpb1ab:(p b1 ab))=>((psym b1 ab) Vpb1ab)). Qed. Lemma c82_109: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->(l a2c2 b1c1)->(p b1 ab)->(i ab a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))(Vla2c2b1c1:(l a2c2 b1c1))(Vpb1ab:(p b1 ab))=>((pcon ab b1 a2c2) (conj (c82_104 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vla2c2oc Vla2c2b1c1 Vpb1ab) Vib1a2c2))). Qed. Lemma c82_110: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->(l a2c2 b1c1)->(p b1 ab)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))(Vla2c2b1c1:(l a2c2 b1c1))(Vpb1ab:(p b1 ab))=>((goal_normal a2c2) (conj (c82_43 Via1b2c2 Vib1a2c2 Via2b1c1) (conj (c82_100 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vla2c2oc Vla2c2b1c1) (conj (c82_29 Via1b2c2 Vib1a2c2 Via2b1c1) (c82_109 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vla2c2oc Vla2c2b1c1 Vpb1ab)))))). Qed. Lemma c82_111: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->(l a2c2 b1c1)->(l a1b1 a2b2)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))(Vla2c2b1c1:(l a2c2 b1c1))(Vla1b1a2b2:(l a1b1 a2b2))=>(notab Vla1b1a2b2)). Qed. Lemma c82_112: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->(l a2c2 b1c1)->(l a1b1 a2b2)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))(Vla2c2b1c1:(l a2c2 b1c1))(Vla1b1a2b2:(l a1b1 a2b2))=>((false_ind goal) (c82_111 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vla2c2oc Vla2c2b1c1 Vla1b1a2b2))). Qed. Lemma c82_113: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->(l a2c2 b1c1)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))(Vla2c2b1c1:(l a2c2 b1c1))=>((or_ind ((c82_110 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vla2c2oc Vla2c2b1c1))((c82_112 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vla2c2oc Vla2c2b1c1)))(c82_103 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vla2c2oc Vla2c2b1c1))). Qed. Lemma c82_114: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))=>((or_ind ((c82_95 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vla2c2oc))((c82_113 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vla2c2oc)))(c82_87 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vla2c2oc))). Qed. Lemma c82_115: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))=>((or_ind ((c82_83 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o))((c82_114 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o)))(c82_74 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o))). Qed. Lemma c82_116: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(l ob a1b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))=>((lsym a1b1 ob) Vla1b1ob)). Qed. Lemma c82_120: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(i b2 a1b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))=>((lcon b2 ob a1b1) (conj (c82_23 Via1b2c2 Vib1a2c2 Via2b1c1) (c82_116 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob)))). Qed. Lemma c82_123: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(p a1 b2) \/ (l b2c2 a1b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))=>((unique a1 b2 b2c2 a1b1) (conj Via1b2c2 (conj (c82_5 Via1b2c2 Vib1a2c2 Via2b1c1) (conj (c82_16 Via1b2c2 Vib1a2c2 Via2b1c1) (c82_120 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob)))))). Qed. Lemma c82_125: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(p a1 b2)->(i a1 a2b2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))(Vpa1b2:(p a1 b2))=>((pcon a1 b2 a2b2) (conj Vpa1b2 (c82_8 Via1b2c2 Vib1a2c2 Via2b1c1)))). Qed. Lemma c82_127: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(p a1 b2)->(p a1 b1) \/ (l a1b1 a2b2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))(Vpa1b2:(p a1 b2))=>((unique a1 b1 a1b1 a2b2) (conj (c82_5 Via1b2c2 Vib1a2c2 Via2b1c1) (conj (c82_125 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob Vpa1b2) (conj (c82_6 Via1b2c2 Vib1a2c2 Via2b1c1) (c82_53 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2)))))). Qed. Lemma c82_128: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(p a1 b2)->(p a1 b1)->(p b1 a1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))(Vpa1b2:(p a1 b2))(Vpa1b1:(p a1 b1))=>((psym a1 b1) Vpa1b1)). Qed. Lemma c82_129: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(p a1 b2)->(p a1 b1)->(p a2 a1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))(Vpa1b2:(p a1 b2))(Vpa1b1:(p a1 b1))=>((ptra a2 b1 a1) (conj (c82_52 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2) (c82_128 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob Vpa1b2 Vpa1b1)))). Qed. Lemma c82_130: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(p a1 b2)->(p a1 b1)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))(Vpa1b2:(p a1 b2))(Vpa1b1:(p a1 b1))=>(notaa (c82_129 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob Vpa1b2 Vpa1b1))). Qed. Lemma c82_131: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(p a1 b2)->(p a1 b1)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))(Vpa1b2:(p a1 b2))(Vpa1b1:(p a1 b1))=>((false_ind goal) (c82_130 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob Vpa1b2 Vpa1b1))). Qed. Lemma c82_132: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(p a1 b2)->(l a1b1 a2b2)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))(Vpa1b2:(p a1 b2))(Vla1b1a2b2:(l a1b1 a2b2))=>(notab Vla1b1a2b2)). Qed. Lemma c82_133: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(p a1 b2)->(l a1b1 a2b2)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))(Vpa1b2:(p a1 b2))(Vla1b1a2b2:(l a1b1 a2b2))=>((false_ind goal) (c82_132 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob Vpa1b2 Vla1b1a2b2))). Qed. Lemma c82_134: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(p a1 b2)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))(Vpa1b2:(p a1 b2))=>((or_ind ((c82_131 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob Vpa1b2))((c82_133 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob Vpa1b2)))(c82_127 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob Vpa1b2))). Qed. Lemma c82_135: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(l b2c2 a1b1)->(l a1b1 b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))(Vlb2c2a1b1:(l b2c2 a1b1))=>((lsym b2c2 a1b1) Vlb2c2a1b1)). Qed. Lemma c82_140: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(l b2c2 a1b1)->(i b1 b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))(Vlb2c2a1b1:(l b2c2 a1b1))=>((lcon b1 a1b1 b2c2) (conj (c82_6 Via1b2c2 Vib1a2c2 Via2b1c1) (c82_135 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob Vlb2c2a1b1)))). Qed. Lemma c82_141: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(l b2c2 a1b1)->(i a2 b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))(Vlb2c2a1b1:(l b2c2 a1b1))=>((pcon a2 b1 b2c2) (conj (c82_52 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2) (c82_140 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob Vlb2c2a1b1)))). Qed. Lemma c82_142: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(l b2c2 a1b1)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))(Vlb2c2a1b1:(l b2c2 a1b1))=>((triangle2 b2c2) (conj (c82_141 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob Vlb2c2a1b1) (conj (c82_16 Via1b2c2 Vib1a2c2 Via2b1c1) (c82_15 Via1b2c2 Vib1a2c2 Via2b1c1))))). Qed. Lemma c82_143: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(l b2c2 a1b1)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))(Vlb2c2a1b1:(l b2c2 a1b1))=>((false_ind goal) (c82_142 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob Vlb2c2a1b1))). Qed. Lemma c82_144: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))=>((or_ind ((c82_134 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob))((c82_143 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob)))(c82_123 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob))). Qed. Lemma c82_145: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))=>((or_ind ((c82_115 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa))((c82_144 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa)))(c82_65 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa))). Qed. Lemma c82_146: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))=>((or_ind ((c82_61 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2))((c82_145 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2)))(c82_57 Via1b2c2 Vib1a2c2 Via2b1c1 Vpb1a2))). Qed. Lemma c82_147: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(l b1c1 a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))=>((lsym a2c2 b1c1) Vla2c2b1c1)). Qed. Lemma c82_150: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(i bc a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))=>((lcon bc b1c1 a2c2) (conj (c82_26 Via1b2c2 Vib1a2c2 Via2b1c1) (c82_147 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1)))). Qed. Lemma c82_151: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(i ac b1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))=>((lcon ac a2c2 b1c1) (conj (c82_29 Via1b2c2 Vib1a2c2 Via2b1c1) Vla2c2b1c1))). Qed. Lemma c82_152: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac) \/ (l a1c1 b1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))=>((unique c1 ac a1c1 b1c1) (conj (c82_10 Via1b2c2 Vib1a2c2 Via2b1c1) (conj (c82_13 Via1b2c2 Vib1a2c2 Via2b1c1) (conj (c82_28 Via1b2c2 Vib1a2c2 Via2b1c1) (c82_151 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1)))))). Qed. Lemma c82_153: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p ac c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))=>((psym c1 ac) Vpc1ac)). Qed. Lemma c82_154: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(i ac oc). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))=>((pcon ac c1 oc) (conj (c82_153 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac) (c82_24 Via1b2c2 Vib1a2c2 Via2b1c1)))). Qed. Lemma c82_155: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc) \/ (l a2c2 b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))=>((unique c2 bc a2c2 b2c2) (conj (c82_12 Via1b2c2 Vib1a2c2 Via2b1c1) (conj (c82_15 Via1b2c2 Vib1a2c2 Via2b1c1) (conj (c82_150 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1) (c82_27 Via1b2c2 Vib1a2c2 Via2b1c1)))))). Qed. Lemma c82_158: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(p c2 ac) \/ (l a2c2 oc). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))=>((unique c2 ac a2c2 oc) (conj (c82_12 Via1b2c2 Vib1a2c2 Via2b1c1) (conj (c82_25 Via1b2c2 Vib1a2c2 Via2b1c1) (conj (c82_29 Via1b2c2 Vib1a2c2 Via2b1c1) (c82_154 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac)))))). Qed. Lemma c82_159: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(p c2 ac)->(p ac c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vpc2ac:(p c2 ac))=>((psym c2 ac) Vpc2ac)). Qed. Lemma c82_160: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(p c2 ac)->(p c1 c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vpc2ac:(p c2 ac))=>((ptra c1 ac c2) (conj Vpc1ac (c82_159 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vpc2ac)))). Qed. Lemma c82_161: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(p c2 ac)->(p c2 c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vpc2ac:(p c2 ac))=>((psym c1 c2) (c82_160 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vpc2ac))). Qed. Lemma c82_162: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(p c2 ac)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vpc2ac:(p c2 ac))=>(notcc (c82_161 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vpc2ac))). Qed. Lemma c82_163: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(p c2 ac)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vpc2ac:(p c2 ac))=>((false_ind goal) (c82_162 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vpc2ac))). Qed. Lemma c82_164: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(l oc a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))=>((lsym a2c2 oc) Vla2c2oc)). Qed. Lemma c82_169: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(i o a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))=>((lcon o oc a2c2) (conj (c82_19 Via1b2c2 Vib1a2c2 Via2b1c1) (c82_164 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc)))). Qed. Lemma c82_171: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o) \/ (l a2c2 ob). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))=>((unique b1 o a2c2 ob) (conj Vib1a2c2 (conj (c82_22 Via1b2c2 Vib1a2c2 Via2b1c1) (conj (c82_169 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc) (c82_18 Via1b2c2 Vib1a2c2 Via2b1c1)))))). Qed. Lemma c82_173: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(i b1 oa). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))=>((pcon b1 o oa) (conj Vpb1o (c82_17 Via1b2c2 Vib1a2c2 Via2b1c1)))). Qed. Lemma c82_175: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2) \/ (l a2c2 oa). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))=>((unique b1 a2 a2c2 oa) (conj Vib1a2c2 (conj (c82_173 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o) (conj (c82_11 Via1b2c2 Vib1a2c2 Via2b1c1) (c82_21 Via1b2c2 Vib1a2c2 Via2b1c1)))))). Qed. Lemma c82_176: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2)->(p a2 b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))=>((psym b1 a2) Vpb1a2)). Qed. Lemma c82_179: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2)->(i b1 a2b2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))=>((pcon b1 a2 a2b2) (conj Vpb1a2 (c82_7 Via1b2c2 Vib1a2c2 Via2b1c1)))). Qed. Lemma c82_183: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2)->(p a1 b1) \/ (l a1b1 oa). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))=>((unique a1 b1 a1b1 oa) (conj (c82_5 Via1b2c2 Vib1a2c2 Via2b1c1) (conj (c82_20 Via1b2c2 Vib1a2c2 Via2b1c1) (conj (c82_6 Via1b2c2 Vib1a2c2 Via2b1c1) (c82_173 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o)))))). Qed. Lemma c82_184: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2)->(p a1 b1)->(p b1 a1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))(Vpa1b1:(p a1 b1))=>((psym a1 b1) Vpa1b1)). Qed. Lemma c82_187: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2)->(p a1 b1)->(p a2 a1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))(Vpa1b1:(p a1 b1))=>((ptra a2 b1 a1) (conj (c82_176 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vpb1a2) (c82_184 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vpb1a2 Vpa1b1)))). Qed. Lemma c82_188: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2)->(p a1 b1)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))(Vpa1b1:(p a1 b1))=>(notaa (c82_187 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vpb1a2 Vpa1b1))). Qed. Lemma c82_189: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2)->(p a1 b1)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))(Vpa1b1:(p a1 b1))=>((false_ind goal) (c82_188 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vpb1a2 Vpa1b1))). Qed. Lemma c82_192: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2)->(l a1b1 oa)->(p b1 ab) \/ (l a1b1 a2b2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))=>((unique b1 ab a1b1 a2b2) (conj (c82_6 Via1b2c2 Vib1a2c2 Via2b1c1) (conj (c82_179 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vpb1a2) (conj (c82_30 Via1b2c2 Vib1a2c2 Via2b1c1) (c82_31 Via1b2c2 Vib1a2c2 Via2b1c1)))))). Qed. Lemma c82_193: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2)->(l a1b1 oa)->(p b1 ab)->(p ab b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1ab:(p b1 ab))=>((psym b1 ab) Vpb1ab)). Qed. Lemma c82_198: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2)->(l a1b1 oa)->(p b1 ab)->(i ab a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1ab:(p b1 ab))=>((pcon ab b1 a2c2) (conj (c82_193 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vpb1a2 Vla1b1oa Vpb1ab) Vib1a2c2))). Qed. Lemma c82_199: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2)->(l a1b1 oa)->(p b1 ab)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1ab:(p b1 ab))=>((goal_normal a2c2) (conj (c82_43 Via1b2c2 Vib1a2c2 Via2b1c1) (conj (c82_150 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1) (conj (c82_29 Via1b2c2 Vib1a2c2 Via2b1c1) (c82_198 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vpb1a2 Vla1b1oa Vpb1ab)))))). Qed. Lemma c82_200: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2)->(l a1b1 oa)->(l a1b1 a2b2)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1a2b2:(l a1b1 a2b2))=>(notab Vla1b1a2b2)). Qed. Lemma c82_201: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2)->(l a1b1 oa)->(l a1b1 a2b2)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1a2b2:(l a1b1 a2b2))=>((false_ind goal) (c82_200 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vpb1a2 Vla1b1oa Vla1b1a2b2))). Qed. Lemma c82_202: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2)->(l a1b1 oa)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))=>((or_ind ((c82_199 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vpb1a2 Vla1b1oa))((c82_201 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vpb1a2 Vla1b1oa)))(c82_192 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vpb1a2 Vla1b1oa))). Qed. Lemma c82_203: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))=>((or_ind ((c82_189 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vpb1a2))((c82_202 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vpb1a2)))(c82_183 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vpb1a2))). Qed. Lemma c82_205: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(l a2c2 oa)->(l b1c1 oa). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vla2c2oa:(l a2c2 oa))=>((ltra b1c1 a2c2 oa) (conj (c82_147 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1) Vla2c2oa))). Qed. Lemma c82_211: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(l a2c2 oa)->(i c1 oa). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vla2c2oa:(l a2c2 oa))=>((lcon c1 b1c1 oa) (conj (c82_13 Via1b2c2 Vib1a2c2 Via2b1c1) (c82_205 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vla2c2oa)))). Qed. Lemma c82_212: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(l a2c2 oa)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vla2c2oa:(l a2c2 oa))=>((triangle1 oa) (conj (c82_20 Via1b2c2 Vib1a2c2 Via2b1c1) (conj (c82_173 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o) (c82_211 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vla2c2oa))))). Qed. Lemma c82_213: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(l a2c2 oa)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vla2c2oa:(l a2c2 oa))=>((false_ind goal) (c82_212 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vla2c2oa))). Qed. Lemma c82_214: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))=>((or_ind ((c82_203 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o))((c82_213 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o)))(c82_175 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o))). Qed. Lemma c82_216: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(l a2c2 ob)->(l b1c1 ob). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vla2c2ob:(l a2c2 ob))=>((ltra b1c1 a2c2 ob) (conj (c82_147 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1) Vla2c2ob))). Qed. Lemma c82_220: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(l a2c2 ob)->(i a2 ob). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vla2c2ob:(l a2c2 ob))=>((lcon a2 b1c1 ob) (conj Via2b1c1 (c82_216 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vla2c2ob)))). Qed. Lemma c82_221: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(l a2c2 ob)->(i c2 ob). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vla2c2ob:(l a2c2 ob))=>((lcon c2 a2c2 ob) (conj (c82_12 Via1b2c2 Vib1a2c2 Via2b1c1) Vla2c2ob))). Qed. Lemma c82_222: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(l a2c2 ob)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vla2c2ob:(l a2c2 ob))=>((triangle2 ob) (conj (c82_220 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vla2c2ob) (conj (c82_23 Via1b2c2 Vib1a2c2 Via2b1c1) (c82_221 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vla2c2ob))))). Qed. Lemma c82_223: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(l a2c2 ob)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vla2c2ob:(l a2c2 ob))=>((false_ind goal) (c82_222 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vla2c2ob))). Qed. Lemma c82_224: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))=>((or_ind ((c82_214 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc))((c82_223 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc)))(c82_171 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc))). Qed. Lemma c82_225: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))=>((or_ind ((c82_163 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc))((c82_224 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc)))(c82_158 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc))). Qed. Lemma c82_227: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(l a2c2 b2c2)->(l b1c1 b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vla2c2b2c2:(l a2c2 b2c2))=>((ltra b1c1 a2c2 b2c2) (conj (c82_147 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1) Vla2c2b2c2))). Qed. Lemma c82_228: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(l a2c2 b2c2)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vla2c2b2c2:(l a2c2 b2c2))=>(notbc (c82_227 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vla2c2b2c2))). Qed. Lemma c82_229: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(l a2c2 b2c2)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vla2c2b2c2:(l a2c2 b2c2))=>((false_ind goal) (c82_228 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vla2c2b2c2))). Qed. Lemma c82_230: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))=>((or_ind ((c82_225 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac))((c82_229 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac)))(c82_155 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac))). Qed. Lemma c82_231: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(l a1c1 b1c1)->(l b1c1 a1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vla1c1b1c1:(l a1c1 b1c1))=>((lsym a1c1 b1c1) Vla1c1b1c1)). Qed. Lemma c82_232: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(l a1c1 b1c1)->(l a2c2 a1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vla1c1b1c1:(l a1c1 b1c1))=>((ltra a2c2 b1c1 a1c1) (conj Vla2c2b1c1 (c82_231 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vla1c1b1c1)))). Qed. Lemma c82_233: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(l a1c1 b1c1)->(l a1c1 a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vla1c1b1c1:(l a1c1 b1c1))=>((lsym a2c2 a1c1) (c82_232 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vla1c1b1c1))). Qed. Lemma c82_234: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(l a1c1 b1c1)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vla1c1b1c1:(l a1c1 b1c1))=>(notac (c82_233 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vla1c1b1c1))). Qed. Lemma c82_235: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(l a1c1 b1c1)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vla1c1b1c1:(l a1c1 b1c1))=>((false_ind goal) (c82_234 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vla1c1b1c1))). Qed. Lemma c82_236: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))=>((or_ind ((c82_230 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1))((c82_235 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1)))(c82_152 Via1b2c2 Vib1a2c2 Via2b1c1 Vla2c2b1c1))). Qed. Lemma c82_237: (i a1 b2c2)->(i b1 a2c2)->(i a2 b1c1)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>((or_ind ((c82_146 Via1b2c2 Vib1a2c2 Via2b1c1))((c82_236 Via1b2c2 Vib1a2c2 Via2b1c1)))(c82_51 Via1b2c2 Vib1a2c2 Via2b1c1))). Qed. Lemma c82_238: (i a1 b2c2)->(i b1 a2c2)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vib1a2c2:(i b1 a2c2))=>((or_ind ((c82_4 Via1b2c2 Vib1a2c2))((c82_237 Via1b2c2 Vib1a2c2)))(c82_3 Via1b2c2 Vib1a2c2))). Qed. Lemma c82_239: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2) \/ (i a2 b1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))=>gap_c). Qed. Lemma c82_240: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(i a1 a1b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ia1b1). Qed. Lemma c82_241: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(i b1 a1b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ib1a1). Qed. Lemma c82_242: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(i a2 a2b2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ia2b2). Qed. Lemma c82_243: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(i b2 a2b2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ib2a2). Qed. Lemma c82_244: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(i a1 a1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ia1c1). Qed. Lemma c82_245: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(i c1 a1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ic1a1). Qed. Lemma c82_246: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(i a2 a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ia2c2). Qed. Lemma c82_247: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(i c2 a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ic2a2). Qed. Lemma c82_248: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(i c1 b1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ic1b1). Qed. Lemma c82_249: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(i b1 b1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ib1c1). Qed. Lemma c82_250: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(i c2 b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ic2b2). Qed. Lemma c82_251: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(i b2 b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ib2c2). Qed. Lemma c82_252: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(i o oa). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>iooa). Qed. Lemma c82_253: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(i o ob). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ioob). Qed. Lemma c82_254: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(i o oc). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>iooc). Qed. Lemma c82_255: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(i a1 oa). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ia1oa). Qed. Lemma c82_256: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(i a2 oa). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ia2oa). Qed. Lemma c82_257: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(i b1 ob). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ib1ob). Qed. Lemma c82_258: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(i b2 ob). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ib2ob). Qed. Lemma c82_259: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(i c1 oc). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ic1oc). Qed. Lemma c82_260: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(i c2 oc). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ic2oc). Qed. Lemma c82_261: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(i bc b1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ibc1). Qed. Lemma c82_262: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(i bc b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ibc2). Qed. Lemma c82_263: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(i ac a1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>iac1). Qed. Lemma c82_264: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(i ac a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>iac2). Qed. Lemma c82_265: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(i ab a1b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>iab1). Qed. Lemma c82_266: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(i ab a2b2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>iab2). Qed. Lemma c82_277: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>((lref a1 b2c2) Via1b2c2)). Qed. Lemma c82_278: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l a1b1 a1b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>((lref c2 a1b1) Vic2a1b1)). Qed. Lemma c82_286: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2) \/ (l b2c2 a1b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>((unique a1 c2 b2c2 a1b1) (conj Via1b2c2 (conj (c82_240 Via1b2c2 Vic2a1b1 Vic1a2b2) (conj (c82_250 Via1b2c2 Vic2a1b1 Vic1a2b2) Vic2a1b1))))). Qed. Lemma c82_287: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p c2 a1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))=>((psym a1 c2) Vpa1c2)). Qed. Lemma c82_288: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(i a1 a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))=>((pcon a1 c2 a2c2) (conj Vpa1c2 (c82_247 Via1b2c2 Vic2a1b1 Vic1a2b2)))). Qed. Lemma c82_289: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(i a1 oc). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))=>((pcon a1 c2 oc) (conj Vpa1c2 (c82_260 Via1b2c2 Vic2a1b1 Vic1a2b2)))). Qed. Lemma c82_290: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(i c2 a1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))=>((pcon c2 a1 a1c1) (conj (c82_287 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2) (c82_244 Via1b2c2 Vic2a1b1 Vic1a2b2)))). Qed. Lemma c82_292: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac) \/ (l a1c1 a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))=>((unique a1 ac a1c1 a2c2) (conj (c82_244 Via1b2c2 Vic2a1b1 Vic1a2b2) (conj (c82_288 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2) (conj (c82_263 Via1b2c2 Vic2a1b1 Vic1a2b2) (c82_264 Via1b2c2 Vic2a1b1 Vic1a2b2)))))). Qed. Lemma c82_293: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(p ac a1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))=>((psym a1 ac) Vpa1ac)). Qed. Lemma c82_297: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(i ac a1b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))=>((pcon ac a1 a1b1) (conj (c82_293 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac) (c82_240 Via1b2c2 Vic2a1b1 Vic1a2b2)))). Qed. Lemma c82_300: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(p a1 c1) \/ (l a1c1 oc). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))=>((unique a1 c1 a1c1 oc) (conj (c82_244 Via1b2c2 Vic2a1b1 Vic1a2b2) (conj (c82_289 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2) (conj (c82_245 Via1b2c2 Vic2a1b1 Vic1a2b2) (c82_259 Via1b2c2 Vic2a1b1 Vic1a2b2)))))). Qed. Lemma c82_302: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(p a1 c1)->(p c2 c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vpa1c1:(p a1 c1))=>((ptra c2 a1 c1) (conj (c82_287 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2) Vpa1c1))). Qed. Lemma c82_303: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(p a1 c1)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vpa1c1:(p a1 c1))=>(notcc (c82_302 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vpa1c1))). Qed. Lemma c82_304: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(p a1 c1)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vpa1c1:(p a1 c1))=>((false_ind goal) (c82_303 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vpa1c1))). Qed. Lemma c82_305: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l oc a1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))=>((lsym a1c1 oc) Vla1c1oc)). Qed. Lemma c82_306: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(i o a1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))=>((lcon o oc a1c1) (conj (c82_254 Via1b2c2 Vic2a1b1 Vic1a2b2) (c82_305 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc)))). Qed. Lemma c82_307: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o) \/ (l a1c1 oa). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))=>((unique a1 o a1c1 oa) (conj (c82_244 Via1b2c2 Vic2a1b1 Vic1a2b2) (conj (c82_255 Via1b2c2 Vic2a1b1 Vic1a2b2) (conj (c82_306 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc) (c82_252 Via1b2c2 Vic2a1b1 Vic1a2b2)))))). Qed. Lemma c82_313: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->(i a1 ob). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))=>((pcon a1 o ob) (conj Vpa1o (c82_253 Via1b2c2 Vic2a1b1 Vic1a2b2)))). Qed. Lemma c82_319: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->(p a1 b2) \/ (l b2c2 ob). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))=>((unique a1 b2 b2c2 ob) (conj Via1b2c2 (conj (c82_313 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc Vpa1o) (conj (c82_251 Via1b2c2 Vic2a1b1 Vic1a2b2) (c82_258 Via1b2c2 Vic2a1b1 Vic1a2b2)))))). Qed. Lemma c82_327: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->(p a1 b2)->(i a1 a2b2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vpa1b2:(p a1 b2))=>((pcon a1 b2 a2b2) (conj Vpa1b2 (c82_243 Via1b2c2 Vic2a1b1 Vic1a2b2)))). Qed. Lemma c82_328: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->(p a1 b2)->(i c2 a2b2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vpa1b2:(p a1 b2))=>((pcon c2 a1 a2b2) (conj (c82_287 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2) (c82_327 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc Vpa1o Vpa1b2)))). Qed. Lemma c82_329: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->(p a1 b2)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vpa1b2:(p a1 b2))=>((triangle2 a2b2) (conj (c82_242 Via1b2c2 Vic2a1b1 Vic1a2b2) (conj (c82_243 Via1b2c2 Vic2a1b1 Vic1a2b2) (c82_328 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc Vpa1o Vpa1b2))))). Qed. Lemma c82_330: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->(p a1 b2)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vpa1b2:(p a1 b2))=>((false_ind goal) (c82_329 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc Vpa1o Vpa1b2))). Qed. Lemma c82_331: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->(l b2c2 ob)->(l ob b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vlb2c2ob:(l b2c2 ob))=>((lsym b2c2 ob) Vlb2c2ob)). Qed. Lemma c82_332: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->(l b2c2 ob)->(i b1 b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vlb2c2ob:(l b2c2 ob))=>((lcon b1 ob b2c2) (conj (c82_257 Via1b2c2 Vic2a1b1 Vic1a2b2) (c82_331 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc Vpa1o Vlb2c2ob)))). Qed. Lemma c82_334: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->(l b2c2 ob)->(p a1 b1) \/ (l b2c2 a1b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vlb2c2ob:(l b2c2 ob))=>((unique a1 b1 b2c2 a1b1) (conj Via1b2c2 (conj (c82_240 Via1b2c2 Vic2a1b1 Vic1a2b2) (conj (c82_332 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc Vpa1o Vlb2c2ob) (c82_241 Via1b2c2 Vic2a1b1 Vic1a2b2)))))). Qed. Lemma c82_342: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->(l b2c2 ob)->(p a1 b1)->(i a1 b1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vlb2c2ob:(l b2c2 ob))(Vpa1b1:(p a1 b1))=>((pcon a1 b1 b1c1) (conj Vpa1b1 (c82_249 Via1b2c2 Vic2a1b1 Vic1a2b2)))). Qed. Lemma c82_343: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->(l b2c2 ob)->(p a1 b1)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vlb2c2ob:(l b2c2 ob))(Vpa1b1:(p a1 b1))=>((triangle1 b1c1) (conj (c82_342 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc Vpa1o Vlb2c2ob Vpa1b1) (conj (c82_249 Via1b2c2 Vic2a1b1 Vic1a2b2) (c82_248 Via1b2c2 Vic2a1b1 Vic1a2b2))))). Qed. Lemma c82_344: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->(l b2c2 ob)->(p a1 b1)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vlb2c2ob:(l b2c2 ob))(Vpa1b1:(p a1 b1))=>((false_ind goal) (c82_343 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc Vpa1o Vlb2c2ob Vpa1b1))). Qed. Lemma c82_349: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->(l b2c2 ob)->(l b2c2 a1b1)->(i bc a1b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vlb2c2ob:(l b2c2 ob))(Vlb2c2a1b1:(l b2c2 a1b1))=>((lcon bc b2c2 a1b1) (conj (c82_262 Via1b2c2 Vic2a1b1 Vic1a2b2) Vlb2c2a1b1))). Qed. Lemma c82_350: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->(l b2c2 ob)->(l b2c2 a1b1)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vlb2c2ob:(l b2c2 ob))(Vlb2c2a1b1:(l b2c2 a1b1))=>((goal_normal a1b1) (conj (c82_278 Via1b2c2 Vic2a1b1 Vic1a2b2) (conj (c82_349 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc Vpa1o Vlb2c2ob Vlb2c2a1b1) (conj (c82_297 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac) (c82_265 Via1b2c2 Vic2a1b1 Vic1a2b2)))))). Qed. Lemma c82_351: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->(l b2c2 ob)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vlb2c2ob:(l b2c2 ob))=>((or_ind ((c82_344 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc Vpa1o Vlb2c2ob))((c82_350 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc Vpa1o Vlb2c2ob)))(c82_334 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc Vpa1o Vlb2c2ob))). Qed. Lemma c82_352: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))=>((or_ind ((c82_330 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc Vpa1o))((c82_351 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc Vpa1o)))(c82_319 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc Vpa1o))). Qed. Lemma c82_353: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->(l oa a1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))=>((lsym a1c1 oa) Vla1c1oa)). Qed. Lemma c82_357: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->(i a2 a1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))=>((lcon a2 oa a1c1) (conj (c82_256 Via1b2c2 Vic2a1b1 Vic1a2b2) (c82_353 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc Vla1c1oa)))). Qed. Lemma c82_359: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->(p c1 a2) \/ (l a2b2 a1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))=>((unique c1 a2 a2b2 a1c1) (conj Vic1a2b2 (conj (c82_245 Via1b2c2 Vic2a1b1 Vic1a2b2) (conj (c82_242 Via1b2c2 Vic2a1b1 Vic1a2b2) (c82_357 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc Vla1c1oa)))))). Qed. Lemma c82_361: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->(p c1 a2)->(i c1 a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpc1a2:(p c1 a2))=>((pcon c1 a2 a2c2) (conj Vpc1a2 (c82_246 Via1b2c2 Vic2a1b1 Vic1a2b2)))). Qed. Lemma c82_363: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->(p c1 a2)->(p a1 c1) \/ (l a1c1 a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpc1a2:(p c1 a2))=>((unique a1 c1 a1c1 a2c2) (conj (c82_244 Via1b2c2 Vic2a1b1 Vic1a2b2) (conj (c82_288 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2) (conj (c82_245 Via1b2c2 Vic2a1b1 Vic1a2b2) (c82_361 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc Vla1c1oa Vpc1a2)))))). Qed. Lemma c82_365: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->(p c1 a2)->(p a1 c1)->(p c2 c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpc1a2:(p c1 a2))(Vpa1c1:(p a1 c1))=>((ptra c2 a1 c1) (conj (c82_287 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2) Vpa1c1))). Qed. Lemma c82_366: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->(p c1 a2)->(p a1 c1)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpc1a2:(p c1 a2))(Vpa1c1:(p a1 c1))=>(notcc (c82_365 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc Vla1c1oa Vpc1a2 Vpa1c1))). Qed. Lemma c82_367: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->(p c1 a2)->(p a1 c1)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpc1a2:(p c1 a2))(Vpa1c1:(p a1 c1))=>((false_ind goal) (c82_366 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc Vla1c1oa Vpc1a2 Vpa1c1))). Qed. Lemma c82_368: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->(p c1 a2)->(l a1c1 a2c2)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpc1a2:(p c1 a2))(Vla1c1a2c2:(l a1c1 a2c2))=>(notac Vla1c1a2c2)). Qed. Lemma c82_369: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->(p c1 a2)->(l a1c1 a2c2)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpc1a2:(p c1 a2))(Vla1c1a2c2:(l a1c1 a2c2))=>((false_ind goal) (c82_368 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc Vla1c1oa Vpc1a2 Vla1c1a2c2))). Qed. Lemma c82_370: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->(p c1 a2)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpc1a2:(p c1 a2))=>((or_ind ((c82_367 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc Vla1c1oa Vpc1a2))((c82_369 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc Vla1c1oa Vpc1a2)))(c82_363 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc Vla1c1oa Vpc1a2))). Qed. Lemma c82_376: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->(l a2b2 a1c1)->(i b2 a1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vla2b2a1c1:(l a2b2 a1c1))=>((lcon b2 a2b2 a1c1) (conj (c82_243 Via1b2c2 Vic2a1b1 Vic1a2b2) Vla2b2a1c1))). Qed. Lemma c82_377: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->(l a2b2 a1c1)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vla2b2a1c1:(l a2b2 a1c1))=>((triangle2 a1c1) (conj (c82_357 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc Vla1c1oa) (conj (c82_376 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc Vla1c1oa Vla2b2a1c1) (c82_290 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2))))). Qed. Lemma c82_378: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->(l a2b2 a1c1)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vla2b2a1c1:(l a2b2 a1c1))=>((false_ind goal) (c82_377 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc Vla1c1oa Vla2b2a1c1))). Qed. Lemma c82_379: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))=>((or_ind ((c82_370 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc Vla1c1oa))((c82_378 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc Vla1c1oa)))(c82_359 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc Vla1c1oa))). Qed. Lemma c82_380: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))=>((or_ind ((c82_352 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc))((c82_379 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc)))(c82_307 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac Vla1c1oc))). Qed. Lemma c82_381: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(p a1 ac)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))=>((or_ind ((c82_304 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac))((c82_380 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac)))(c82_300 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vpa1ac))). Qed. Lemma c82_382: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(l a1c1 a2c2)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vla1c1a2c2:(l a1c1 a2c2))=>(notac Vla1c1a2c2)). Qed. Lemma c82_383: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->(l a1c1 a2c2)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))(Vla1c1a2c2:(l a1c1 a2c2))=>((false_ind goal) (c82_382 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2 Vla1c1a2c2))). Qed. Lemma c82_384: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(p a1 c2)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpa1c2:(p a1 c2))=>((or_ind ((c82_381 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2))((c82_383 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2)))(c82_292 Via1b2c2 Vic2a1b1 Vic1a2b2 Vpa1c2))). Qed. Lemma c82_385: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(l a1b1 b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))=>((lsym b2c2 a1b1) Vlb2c2a1b1)). Qed. Lemma c82_387: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(i b2 a1b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))=>((lcon b2 b2c2 a1b1) (conj (c82_251 Via1b2c2 Vic2a1b1 Vic1a2b2) Vlb2c2a1b1))). Qed. Lemma c82_388: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(i bc a1b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))=>((lcon bc b2c2 a1b1) (conj (c82_262 Via1b2c2 Vic2a1b1 Vic1a2b2) Vlb2c2a1b1))). Qed. Lemma c82_389: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(i ab b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))=>((lcon ab a1b1 b2c2) (conj (c82_265 Via1b2c2 Vic2a1b1 Vic1a2b2) (c82_385 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1)))). Qed. Lemma c82_390: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc) \/ (l a1b1 b1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))=>((unique b1 bc a1b1 b1c1) (conj (c82_241 Via1b2c2 Vic2a1b1 Vic1a2b2) (conj (c82_249 Via1b2c2 Vic2a1b1 Vic1a2b2) (conj (c82_388 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1) (c82_261 Via1b2c2 Vic2a1b1 Vic1a2b2)))))). Qed. Lemma c82_393: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(p b1 b2) \/ (l a1b1 ob). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))=>((unique b1 b2 a1b1 ob) (conj (c82_241 Via1b2c2 Vic2a1b1 Vic1a2b2) (conj (c82_257 Via1b2c2 Vic2a1b1 Vic1a2b2) (conj (c82_387 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1) (c82_258 Via1b2c2 Vic2a1b1 Vic1a2b2)))))). Qed. Lemma c82_394: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(p b1 b2)->(p b2 b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vpb1b2:(p b1 b2))=>((psym b1 b2) Vpb1b2)). Qed. Lemma c82_395: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(p b1 b2)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vpb1b2:(p b1 b2))=>(notbb (c82_394 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vpb1b2))). Qed. Lemma c82_396: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(p b1 b2)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vpb1b2:(p b1 b2))=>((false_ind goal) (c82_395 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vpb1b2))). Qed. Lemma c82_398: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(l b2c2 ob). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))=>((ltra b2c2 a1b1 ob) (conj Vlb2c2a1b1 Vla1b1ob))). Qed. Lemma c82_399: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(l ob b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))=>((lsym b2c2 ob) (c82_398 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob))). Qed. Lemma c82_403: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(i o b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))=>((lcon o ob b2c2) (conj (c82_253 Via1b2c2 Vic2a1b1 Vic1a2b2) (c82_399 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob)))). Qed. Lemma c82_405: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o) \/ (l b2c2 oa). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))=>((unique a1 o b2c2 oa) (conj Via1b2c2 (conj (c82_255 Via1b2c2 Vic2a1b1 Vic1a2b2) (conj (c82_403 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob) (c82_252 Via1b2c2 Vic2a1b1 Vic1a2b2)))))). Qed. Lemma c82_407: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(i a1 oc). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))=>((pcon a1 o oc) (conj Vpa1o (c82_254 Via1b2c2 Vic2a1b1 Vic1a2b2)))). Qed. Lemma c82_409: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2) \/ (l b2c2 oc). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))=>((unique a1 c2 b2c2 oc) (conj Via1b2c2 (conj (c82_407 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o) (conj (c82_250 Via1b2c2 Vic2a1b1 Vic1a2b2) (c82_260 Via1b2c2 Vic2a1b1 Vic1a2b2)))))). Qed. Lemma c82_410: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(p c2 a1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))=>((psym a1 c2) Vpa1c2)). Qed. Lemma c82_413: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(i a1 a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))=>((pcon a1 c2 a2c2) (conj Vpa1c2 (c82_247 Via1b2c2 Vic2a1b1 Vic1a2b2)))). Qed. Lemma c82_417: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(p b2 ab) \/ (l a2b2 b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))=>((unique b2 ab a2b2 b2c2) (conj (c82_243 Via1b2c2 Vic2a1b1 Vic1a2b2) (conj (c82_251 Via1b2c2 Vic2a1b1 Vic1a2b2) (conj (c82_266 Via1b2c2 Vic2a1b1 Vic1a2b2) (c82_389 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1)))))). Qed. Lemma c82_419: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(p b2 ab)->(p a1 c1) \/ (l a1c1 oc). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vpb2ab:(p b2 ab))=>((unique a1 c1 a1c1 oc) (conj (c82_244 Via1b2c2 Vic2a1b1 Vic1a2b2) (conj (c82_407 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o) (conj (c82_245 Via1b2c2 Vic2a1b1 Vic1a2b2) (c82_259 Via1b2c2 Vic2a1b1 Vic1a2b2)))))). Qed. Lemma c82_423: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(p b2 ab)->(p a1 c1)->(p c2 c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vpb2ab:(p b2 ab))(Vpa1c1:(p a1 c1))=>((ptra c2 a1 c1) (conj (c82_410 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2) Vpa1c1))). Qed. Lemma c82_424: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(p b2 ab)->(p a1 c1)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vpb2ab:(p b2 ab))(Vpa1c1:(p a1 c1))=>(notcc (c82_423 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2 Vpb2ab Vpa1c1))). Qed. Lemma c82_425: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(p b2 ab)->(p a1 c1)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vpb2ab:(p b2 ab))(Vpa1c1:(p a1 c1))=>((false_ind goal) (c82_424 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2 Vpb2ab Vpa1c1))). Qed. Lemma c82_428: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(p b2 ab)->(l a1c1 oc)->(p a1 ac) \/ (l a1c1 a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))=>((unique a1 ac a1c1 a2c2) (conj (c82_244 Via1b2c2 Vic2a1b1 Vic1a2b2) (conj (c82_413 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2) (conj (c82_263 Via1b2c2 Vic2a1b1 Vic1a2b2) (c82_264 Via1b2c2 Vic2a1b1 Vic1a2b2)))))). Qed. Lemma c82_429: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(p b2 ab)->(l a1c1 oc)->(p a1 ac)->(p ac a1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vpa1ac:(p a1 ac))=>((psym a1 ac) Vpa1ac)). Qed. Lemma c82_434: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(p b2 ab)->(l a1c1 oc)->(p a1 ac)->(i ac b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vpa1ac:(p a1 ac))=>((pcon ac a1 b2c2) (conj (c82_429 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2 Vpb2ab Vla1c1oc Vpa1ac) Via1b2c2))). Qed. Lemma c82_435: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(p b2 ab)->(l a1c1 oc)->(p a1 ac)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vpa1ac:(p a1 ac))=>((goal_normal b2c2) (conj (c82_277 Via1b2c2 Vic2a1b1 Vic1a2b2) (conj (c82_262 Via1b2c2 Vic2a1b1 Vic1a2b2) (conj (c82_434 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2 Vpb2ab Vla1c1oc Vpa1ac) (c82_389 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1)))))). Qed. Lemma c82_436: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(p b2 ab)->(l a1c1 oc)->(l a1c1 a2c2)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vla1c1a2c2:(l a1c1 a2c2))=>(notac Vla1c1a2c2)). Qed. Lemma c82_437: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(p b2 ab)->(l a1c1 oc)->(l a1c1 a2c2)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vla1c1a2c2:(l a1c1 a2c2))=>((false_ind goal) (c82_436 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2 Vpb2ab Vla1c1oc Vla1c1a2c2))). Qed. Lemma c82_438: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(p b2 ab)->(l a1c1 oc)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))=>((or_ind ((c82_435 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2 Vpb2ab Vla1c1oc))((c82_437 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2 Vpb2ab Vla1c1oc)))(c82_428 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2 Vpb2ab Vla1c1oc))). Qed. Lemma c82_439: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(p b2 ab)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vpb2ab:(p b2 ab))=>((or_ind ((c82_425 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2 Vpb2ab))((c82_438 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2 Vpb2ab)))(c82_419 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2 Vpb2ab))). Qed. Lemma c82_440: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(l a2b2 b2c2)->(l b2c2 a2b2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vla2b2b2c2:(l a2b2 b2c2))=>((lsym a2b2 b2c2) Vla2b2b2c2)). Qed. Lemma c82_441: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(l a2b2 b2c2)->(l a1b1 a2b2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vla2b2b2c2:(l a2b2 b2c2))=>((ltra a1b1 b2c2 a2b2) (conj (c82_385 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1) (c82_440 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2 Vla2b2b2c2)))). Qed. Lemma c82_442: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(l a2b2 b2c2)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vla2b2b2c2:(l a2b2 b2c2))=>(notab (c82_441 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2 Vla2b2b2c2))). Qed. Lemma c82_443: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(l a2b2 b2c2)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vla2b2b2c2:(l a2b2 b2c2))=>((false_ind goal) (c82_442 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2 Vla2b2b2c2))). Qed. Lemma c82_444: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))=>((or_ind ((c82_439 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2))((c82_443 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2)))(c82_417 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2))). Qed. Lemma c82_446: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(l b2c2 oc)->(l a1b1 oc). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vlb2c2oc:(l b2c2 oc))=>((ltra a1b1 b2c2 oc) (conj (c82_385 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1) Vlb2c2oc))). Qed. Lemma c82_450: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(l b2c2 oc)->(i b1 oc). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vlb2c2oc:(l b2c2 oc))=>((lcon b1 a1b1 oc) (conj (c82_241 Via1b2c2 Vic2a1b1 Vic1a2b2) (c82_446 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vlb2c2oc)))). Qed. Lemma c82_451: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(l b2c2 oc)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vlb2c2oc:(l b2c2 oc))=>((triangle1 oc) (conj (c82_407 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o) (conj (c82_450 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vlb2c2oc) (c82_259 Via1b2c2 Vic2a1b1 Vic1a2b2))))). Qed. Lemma c82_452: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(l b2c2 oc)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vlb2c2oc:(l b2c2 oc))=>((false_ind goal) (c82_451 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vlb2c2oc))). Qed. Lemma c82_453: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))=>((or_ind ((c82_444 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o))((c82_452 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o)))(c82_409 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o))). Qed. Lemma c82_455: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(l b2c2 oa)->(l a1b1 oa). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vlb2c2oa:(l b2c2 oa))=>((ltra a1b1 b2c2 oa) (conj (c82_385 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1) Vlb2c2oa))). Qed. Lemma c82_459: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(l b2c2 oa)->(i c2 oa). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vlb2c2oa:(l b2c2 oa))=>((lcon c2 a1b1 oa) (conj Vic2a1b1 (c82_455 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vlb2c2oa)))). Qed. Lemma c82_462: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(l b2c2 oa)->(i b2 oa). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vlb2c2oa:(l b2c2 oa))=>((lcon b2 b2c2 oa) (conj (c82_251 Via1b2c2 Vic2a1b1 Vic1a2b2) Vlb2c2oa))). Qed. Lemma c82_463: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(l b2c2 oa)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vlb2c2oa:(l b2c2 oa))=>((triangle2 oa) (conj (c82_256 Via1b2c2 Vic2a1b1 Vic1a2b2) (conj (c82_462 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vlb2c2oa) (c82_459 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vlb2c2oa))))). Qed. Lemma c82_464: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(l b2c2 oa)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vlb2c2oa:(l b2c2 oa))=>((false_ind goal) (c82_463 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vlb2c2oa))). Qed. Lemma c82_465: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))=>((or_ind ((c82_453 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob))((c82_464 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob)))(c82_405 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc Vla1b1ob))). Qed. Lemma c82_466: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(p b1 bc)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))=>((or_ind ((c82_396 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc))((c82_465 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc)))(c82_393 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vpb1bc))). Qed. Lemma c82_468: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(l a1b1 b1c1)->(l b2c2 b1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vla1b1b1c1:(l a1b1 b1c1))=>((ltra b2c2 a1b1 b1c1) (conj Vlb2c2a1b1 Vla1b1b1c1))). Qed. Lemma c82_469: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(l a1b1 b1c1)->(l b1c1 b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vla1b1b1c1:(l a1b1 b1c1))=>((lsym b2c2 b1c1) (c82_468 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vla1b1b1c1))). Qed. Lemma c82_470: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(l a1b1 b1c1)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vla1b1b1c1:(l a1b1 b1c1))=>(notbc (c82_469 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vla1b1b1c1))). Qed. Lemma c82_471: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->(l a1b1 b1c1)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))(Vla1b1b1c1:(l a1b1 b1c1))=>((false_ind goal) (c82_470 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1 Vla1b1b1c1))). Qed. Lemma c82_472: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->(l b2c2 a1b1)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vlb2c2a1b1:(l b2c2 a1b1))=>((or_ind ((c82_466 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1))((c82_471 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1)))(c82_390 Via1b2c2 Vic2a1b1 Vic1a2b2 Vlb2c2a1b1))). Qed. Lemma c82_473: (i a1 b2c2)->(i c2 a1b1)->(i c1 a2b2)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>((or_ind ((c82_384 Via1b2c2 Vic2a1b1 Vic1a2b2))((c82_472 Via1b2c2 Vic2a1b1 Vic1a2b2)))(c82_286 Via1b2c2 Vic2a1b1 Vic1a2b2))). Qed. Lemma c82_474: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(i a1 a1b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>ia1b1). Qed. Lemma c82_475: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(i b1 a1b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>ib1a1). Qed. Lemma c82_476: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(i a2 a2b2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>ia2b2). Qed. Lemma c82_477: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(i b2 a2b2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>ib2a2). Qed. Lemma c82_478: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(i a1 a1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>ia1c1). Qed. Lemma c82_479: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(i c1 a1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>ic1a1). Qed. Lemma c82_480: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(i a2 a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>ia2c2). Qed. Lemma c82_481: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(i c2 a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>ic2a2). Qed. Lemma c82_482: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(i c1 b1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>ic1b1). Qed. Lemma c82_483: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(i b1 b1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>ib1c1). Qed. Lemma c82_484: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(i c2 b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>ic2b2). Qed. Lemma c82_485: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(i b2 b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>ib2c2). Qed. Lemma c82_486: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(i o oa). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>iooa). Qed. Lemma c82_487: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(i o ob). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>ioob). Qed. Lemma c82_488: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(i o oc). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>iooc). Qed. Lemma c82_489: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(i a1 oa). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>ia1oa). Qed. Lemma c82_490: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(i a2 oa). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>ia2oa). Qed. Lemma c82_491: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(i b1 ob). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>ib1ob). Qed. Lemma c82_492: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(i b2 ob). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>ib2ob). Qed. Lemma c82_493: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(i c1 oc). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>ic1oc). Qed. Lemma c82_494: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(i c2 oc). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>ic2oc). Qed. Lemma c82_495: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(i bc b1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>ibc1). Qed. Lemma c82_496: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(i bc b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>ibc2). Qed. Lemma c82_497: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(i ac a1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>iac1). Qed. Lemma c82_498: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(i ac a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>iac2). Qed. Lemma c82_499: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(i ab a1b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>iab1). Qed. Lemma c82_500: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(i ab a2b2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>iab2). Qed. Lemma c82_511: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>((lref a1 b2c2) Via1b2c2)). Qed. Lemma c82_512: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l a1b1 a1b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>((lref c2 a1b1) Vic2a1b1)). Qed. Lemma c82_520: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2) \/ (l b2c2 a1b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>((unique a1 c2 b2c2 a1b1) (conj Via1b2c2 (conj (c82_474 Via1b2c2 Vic2a1b1 Via2b1c1) (conj (c82_484 Via1b2c2 Vic2a1b1 Via2b1c1) Vic2a1b1))))). Qed. Lemma c82_521: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p c2 a1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))=>((psym a1 c2) Vpa1c2)). Qed. Lemma c82_522: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(i a1 a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))=>((pcon a1 c2 a2c2) (conj Vpa1c2 (c82_481 Via1b2c2 Vic2a1b1 Via2b1c1)))). Qed. Lemma c82_523: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(i a1 oc). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))=>((pcon a1 c2 oc) (conj Vpa1c2 (c82_494 Via1b2c2 Vic2a1b1 Via2b1c1)))). Qed. Lemma c82_526: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac) \/ (l a1c1 a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))=>((unique a1 ac a1c1 a2c2) (conj (c82_478 Via1b2c2 Vic2a1b1 Via2b1c1) (conj (c82_522 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2) (conj (c82_497 Via1b2c2 Vic2a1b1 Via2b1c1) (c82_498 Via1b2c2 Vic2a1b1 Via2b1c1)))))). Qed. Lemma c82_527: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(p ac a1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))=>((psym a1 ac) Vpa1ac)). Qed. Lemma c82_531: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(i ac a1b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))=>((pcon ac a1 a1b1) (conj (c82_527 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac) (c82_474 Via1b2c2 Vic2a1b1 Via2b1c1)))). Qed. Lemma c82_534: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(p a1 c1) \/ (l a1c1 oc). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))=>((unique a1 c1 a1c1 oc) (conj (c82_478 Via1b2c2 Vic2a1b1 Via2b1c1) (conj (c82_523 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2) (conj (c82_479 Via1b2c2 Vic2a1b1 Via2b1c1) (c82_493 Via1b2c2 Vic2a1b1 Via2b1c1)))))). Qed. Lemma c82_536: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(p a1 c1)->(p c2 c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vpa1c1:(p a1 c1))=>((ptra c2 a1 c1) (conj (c82_521 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2) Vpa1c1))). Qed. Lemma c82_537: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(p a1 c1)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vpa1c1:(p a1 c1))=>(notcc (c82_536 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vpa1c1))). Qed. Lemma c82_538: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(p a1 c1)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vpa1c1:(p a1 c1))=>((false_ind goal) (c82_537 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vpa1c1))). Qed. Lemma c82_539: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l oc a1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))=>((lsym a1c1 oc) Vla1c1oc)). Qed. Lemma c82_540: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(i o a1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))=>((lcon o oc a1c1) (conj (c82_488 Via1b2c2 Vic2a1b1 Via2b1c1) (c82_539 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc)))). Qed. Lemma c82_541: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o) \/ (l a1c1 oa). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))=>((unique a1 o a1c1 oa) (conj (c82_478 Via1b2c2 Vic2a1b1 Via2b1c1) (conj (c82_489 Via1b2c2 Vic2a1b1 Via2b1c1) (conj (c82_540 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc) (c82_486 Via1b2c2 Vic2a1b1 Via2b1c1)))))). Qed. Lemma c82_547: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->(i a1 ob). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))=>((pcon a1 o ob) (conj Vpa1o (c82_487 Via1b2c2 Vic2a1b1 Via2b1c1)))). Qed. Lemma c82_553: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->(p a1 b2) \/ (l b2c2 ob). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))=>((unique a1 b2 b2c2 ob) (conj Via1b2c2 (conj (c82_547 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc Vpa1o) (conj (c82_485 Via1b2c2 Vic2a1b1 Via2b1c1) (c82_492 Via1b2c2 Vic2a1b1 Via2b1c1)))))). Qed. Lemma c82_561: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->(p a1 b2)->(i a1 a2b2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vpa1b2:(p a1 b2))=>((pcon a1 b2 a2b2) (conj Vpa1b2 (c82_477 Via1b2c2 Vic2a1b1 Via2b1c1)))). Qed. Lemma c82_562: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->(p a1 b2)->(i c2 a2b2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vpa1b2:(p a1 b2))=>((pcon c2 a1 a2b2) (conj (c82_521 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2) (c82_561 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc Vpa1o Vpa1b2)))). Qed. Lemma c82_563: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->(p a1 b2)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vpa1b2:(p a1 b2))=>((triangle2 a2b2) (conj (c82_476 Via1b2c2 Vic2a1b1 Via2b1c1) (conj (c82_477 Via1b2c2 Vic2a1b1 Via2b1c1) (c82_562 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc Vpa1o Vpa1b2))))). Qed. Lemma c82_564: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->(p a1 b2)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vpa1b2:(p a1 b2))=>((false_ind goal) (c82_563 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc Vpa1o Vpa1b2))). Qed. Lemma c82_565: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->(l b2c2 ob)->(l ob b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vlb2c2ob:(l b2c2 ob))=>((lsym b2c2 ob) Vlb2c2ob)). Qed. Lemma c82_566: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->(l b2c2 ob)->(i b1 b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vlb2c2ob:(l b2c2 ob))=>((lcon b1 ob b2c2) (conj (c82_491 Via1b2c2 Vic2a1b1 Via2b1c1) (c82_565 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc Vpa1o Vlb2c2ob)))). Qed. Lemma c82_568: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->(l b2c2 ob)->(p a1 b1) \/ (l b2c2 a1b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vlb2c2ob:(l b2c2 ob))=>((unique a1 b1 b2c2 a1b1) (conj Via1b2c2 (conj (c82_474 Via1b2c2 Vic2a1b1 Via2b1c1) (conj (c82_566 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc Vpa1o Vlb2c2ob) (c82_475 Via1b2c2 Vic2a1b1 Via2b1c1)))))). Qed. Lemma c82_576: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->(l b2c2 ob)->(p a1 b1)->(i a1 b1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vlb2c2ob:(l b2c2 ob))(Vpa1b1:(p a1 b1))=>((pcon a1 b1 b1c1) (conj Vpa1b1 (c82_483 Via1b2c2 Vic2a1b1 Via2b1c1)))). Qed. Lemma c82_577: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->(l b2c2 ob)->(p a1 b1)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vlb2c2ob:(l b2c2 ob))(Vpa1b1:(p a1 b1))=>((triangle1 b1c1) (conj (c82_576 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc Vpa1o Vlb2c2ob Vpa1b1) (conj (c82_483 Via1b2c2 Vic2a1b1 Via2b1c1) (c82_482 Via1b2c2 Vic2a1b1 Via2b1c1))))). Qed. Lemma c82_578: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->(l b2c2 ob)->(p a1 b1)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vlb2c2ob:(l b2c2 ob))(Vpa1b1:(p a1 b1))=>((false_ind goal) (c82_577 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc Vpa1o Vlb2c2ob Vpa1b1))). Qed. Lemma c82_583: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->(l b2c2 ob)->(l b2c2 a1b1)->(i bc a1b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vlb2c2ob:(l b2c2 ob))(Vlb2c2a1b1:(l b2c2 a1b1))=>((lcon bc b2c2 a1b1) (conj (c82_496 Via1b2c2 Vic2a1b1 Via2b1c1) Vlb2c2a1b1))). Qed. Lemma c82_584: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->(l b2c2 ob)->(l b2c2 a1b1)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vlb2c2ob:(l b2c2 ob))(Vlb2c2a1b1:(l b2c2 a1b1))=>((goal_normal a1b1) (conj (c82_512 Via1b2c2 Vic2a1b1 Via2b1c1) (conj (c82_583 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc Vpa1o Vlb2c2ob Vlb2c2a1b1) (conj (c82_531 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac) (c82_499 Via1b2c2 Vic2a1b1 Via2b1c1)))))). Qed. Lemma c82_585: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->(l b2c2 ob)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))(Vlb2c2ob:(l b2c2 ob))=>((or_ind ((c82_578 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc Vpa1o Vlb2c2ob))((c82_584 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc Vpa1o Vlb2c2ob)))(c82_568 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc Vpa1o Vlb2c2ob))). Qed. Lemma c82_586: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(p a1 o)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vpa1o:(p a1 o))=>((or_ind ((c82_564 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc Vpa1o))((c82_585 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc Vpa1o)))(c82_553 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc Vpa1o))). Qed. Lemma c82_590: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->(i c1 oa). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))=>((lcon c1 a1c1 oa) (conj (c82_479 Via1b2c2 Vic2a1b1 Via2b1c1) Vla1c1oa))). Qed. Lemma c82_593: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->(p a2 c1) \/ (l b1c1 oa). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))=>((unique a2 c1 b1c1 oa) (conj Via2b1c1 (conj (c82_490 Via1b2c2 Vic2a1b1 Via2b1c1) (conj (c82_482 Via1b2c2 Vic2a1b1 Via2b1c1) (c82_590 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc Vla1c1oa)))))). Qed. Lemma c82_594: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->(p a2 c1)->(p c1 a2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpa2c1:(p a2 c1))=>((psym a2 c1) Vpa2c1)). Qed. Lemma c82_596: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->(p a2 c1)->(i c1 a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpa2c1:(p a2 c1))=>((pcon c1 a2 a2c2) (conj (c82_594 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc Vla1c1oa Vpa2c1) (c82_480 Via1b2c2 Vic2a1b1 Via2b1c1)))). Qed. Lemma c82_597: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->(p a2 c1)->(p a1 c1) \/ (l a1c1 a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpa2c1:(p a2 c1))=>((unique a1 c1 a1c1 a2c2) (conj (c82_478 Via1b2c2 Vic2a1b1 Via2b1c1) (conj (c82_522 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2) (conj (c82_479 Via1b2c2 Vic2a1b1 Via2b1c1) (c82_596 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc Vla1c1oa Vpa2c1)))))). Qed. Lemma c82_599: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->(p a2 c1)->(p a1 c1)->(p c2 c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpa2c1:(p a2 c1))(Vpa1c1:(p a1 c1))=>((ptra c2 a1 c1) (conj (c82_521 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2) Vpa1c1))). Qed. Lemma c82_600: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->(p a2 c1)->(p a1 c1)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpa2c1:(p a2 c1))(Vpa1c1:(p a1 c1))=>(notcc (c82_599 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc Vla1c1oa Vpa2c1 Vpa1c1))). Qed. Lemma c82_601: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->(p a2 c1)->(p a1 c1)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpa2c1:(p a2 c1))(Vpa1c1:(p a1 c1))=>((false_ind goal) (c82_600 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc Vla1c1oa Vpa2c1 Vpa1c1))). Qed. Lemma c82_602: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->(p a2 c1)->(l a1c1 a2c2)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpa2c1:(p a2 c1))(Vla1c1a2c2:(l a1c1 a2c2))=>(notac Vla1c1a2c2)). Qed. Lemma c82_603: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->(p a2 c1)->(l a1c1 a2c2)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpa2c1:(p a2 c1))(Vla1c1a2c2:(l a1c1 a2c2))=>((false_ind goal) (c82_602 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc Vla1c1oa Vpa2c1 Vla1c1a2c2))). Qed. Lemma c82_604: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->(p a2 c1)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vpa2c1:(p a2 c1))=>((or_ind ((c82_601 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc Vla1c1oa Vpa2c1))((c82_603 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc Vla1c1oa Vpa2c1)))(c82_597 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc Vla1c1oa Vpa2c1))). Qed. Lemma c82_605: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->(l b1c1 oa)->(l oa b1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vlb1c1oa:(l b1c1 oa))=>((lsym b1c1 oa) Vlb1c1oa)). Qed. Lemma c82_606: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->(l b1c1 oa)->(l a1c1 b1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vlb1c1oa:(l b1c1 oa))=>((ltra a1c1 oa b1c1) (conj Vla1c1oa (c82_605 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc Vla1c1oa Vlb1c1oa)))). Qed. Lemma c82_610: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->(l b1c1 oa)->(i a1 b1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vlb1c1oa:(l b1c1 oa))=>((lcon a1 a1c1 b1c1) (conj (c82_478 Via1b2c2 Vic2a1b1 Via2b1c1) (c82_606 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc Vla1c1oa Vlb1c1oa)))). Qed. Lemma c82_611: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->(l b1c1 oa)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vlb1c1oa:(l b1c1 oa))=>((triangle1 b1c1) (conj (c82_610 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc Vla1c1oa Vlb1c1oa) (conj (c82_483 Via1b2c2 Vic2a1b1 Via2b1c1) (c82_482 Via1b2c2 Vic2a1b1 Via2b1c1))))). Qed. Lemma c82_612: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->(l b1c1 oa)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))(Vlb1c1oa:(l b1c1 oa))=>((false_ind goal) (c82_611 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc Vla1c1oa Vlb1c1oa))). Qed. Lemma c82_613: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->(l a1c1 oa)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))(Vla1c1oa:(l a1c1 oa))=>((or_ind ((c82_604 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc Vla1c1oa))((c82_612 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc Vla1c1oa)))(c82_593 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc Vla1c1oa))). Qed. Lemma c82_614: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->(l a1c1 oc)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))(Vla1c1oc:(l a1c1 oc))=>((or_ind ((c82_586 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc))((c82_613 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc)))(c82_541 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac Vla1c1oc))). Qed. Lemma c82_615: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(p a1 ac)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vpa1ac:(p a1 ac))=>((or_ind ((c82_538 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac))((c82_614 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac)))(c82_534 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vpa1ac))). Qed. Lemma c82_616: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(l a1c1 a2c2)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vla1c1a2c2:(l a1c1 a2c2))=>(notac Vla1c1a2c2)). Qed. Lemma c82_617: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->(l a1c1 a2c2)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))(Vla1c1a2c2:(l a1c1 a2c2))=>((false_ind goal) (c82_616 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2 Vla1c1a2c2))). Qed. Lemma c82_618: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(p a1 c2)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vpa1c2:(p a1 c2))=>((or_ind ((c82_615 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2))((c82_617 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2)))(c82_526 Via1b2c2 Vic2a1b1 Via2b1c1 Vpa1c2))). Qed. Lemma c82_619: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(l a1b1 b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))=>((lsym b2c2 a1b1) Vlb2c2a1b1)). Qed. Lemma c82_621: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(i b2 a1b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))=>((lcon b2 b2c2 a1b1) (conj (c82_485 Via1b2c2 Vic2a1b1 Via2b1c1) Vlb2c2a1b1))). Qed. Lemma c82_622: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(i bc a1b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))=>((lcon bc b2c2 a1b1) (conj (c82_496 Via1b2c2 Vic2a1b1 Via2b1c1) Vlb2c2a1b1))). Qed. Lemma c82_623: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(i ab b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))=>((lcon ab a1b1 b2c2) (conj (c82_499 Via1b2c2 Vic2a1b1 Via2b1c1) (c82_619 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1)))). Qed. Lemma c82_624: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc) \/ (l a1b1 b1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))=>((unique b1 bc a1b1 b1c1) (conj (c82_475 Via1b2c2 Vic2a1b1 Via2b1c1) (conj (c82_483 Via1b2c2 Vic2a1b1 Via2b1c1) (conj (c82_622 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1) (c82_495 Via1b2c2 Vic2a1b1 Via2b1c1)))))). Qed. Lemma c82_627: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(p b1 b2) \/ (l a1b1 ob). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))=>((unique b1 b2 a1b1 ob) (conj (c82_475 Via1b2c2 Vic2a1b1 Via2b1c1) (conj (c82_491 Via1b2c2 Vic2a1b1 Via2b1c1) (conj (c82_621 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1) (c82_492 Via1b2c2 Vic2a1b1 Via2b1c1)))))). Qed. Lemma c82_628: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(p b1 b2)->(p b2 b1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vpb1b2:(p b1 b2))=>((psym b1 b2) Vpb1b2)). Qed. Lemma c82_629: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(p b1 b2)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vpb1b2:(p b1 b2))=>(notbb (c82_628 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vpb1b2))). Qed. Lemma c82_630: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(p b1 b2)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vpb1b2:(p b1 b2))=>((false_ind goal) (c82_629 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vpb1b2))). Qed. Lemma c82_632: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(l b2c2 ob). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))=>((ltra b2c2 a1b1 ob) (conj Vlb2c2a1b1 Vla1b1ob))). Qed. Lemma c82_633: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(l ob b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))=>((lsym b2c2 ob) (c82_632 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob))). Qed. Lemma c82_637: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(i o b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))=>((lcon o ob b2c2) (conj (c82_487 Via1b2c2 Vic2a1b1 Via2b1c1) (c82_633 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob)))). Qed. Lemma c82_639: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o) \/ (l b2c2 oa). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))=>((unique a1 o b2c2 oa) (conj Via1b2c2 (conj (c82_489 Via1b2c2 Vic2a1b1 Via2b1c1) (conj (c82_637 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob) (c82_486 Via1b2c2 Vic2a1b1 Via2b1c1)))))). Qed. Lemma c82_641: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(i a1 oc). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))=>((pcon a1 o oc) (conj Vpa1o (c82_488 Via1b2c2 Vic2a1b1 Via2b1c1)))). Qed. Lemma c82_643: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2) \/ (l b2c2 oc). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))=>((unique a1 c2 b2c2 oc) (conj Via1b2c2 (conj (c82_641 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o) (conj (c82_484 Via1b2c2 Vic2a1b1 Via2b1c1) (c82_494 Via1b2c2 Vic2a1b1 Via2b1c1)))))). Qed. Lemma c82_644: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(p c2 a1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))=>((psym a1 c2) Vpa1c2)). Qed. Lemma c82_647: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(i a1 a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))=>((pcon a1 c2 a2c2) (conj Vpa1c2 (c82_481 Via1b2c2 Vic2a1b1 Via2b1c1)))). Qed. Lemma c82_651: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(p b2 ab) \/ (l a2b2 b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))=>((unique b2 ab a2b2 b2c2) (conj (c82_477 Via1b2c2 Vic2a1b1 Via2b1c1) (conj (c82_485 Via1b2c2 Vic2a1b1 Via2b1c1) (conj (c82_500 Via1b2c2 Vic2a1b1 Via2b1c1) (c82_623 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1)))))). Qed. Lemma c82_653: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(p b2 ab)->(p a1 c1) \/ (l a1c1 oc). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vpb2ab:(p b2 ab))=>((unique a1 c1 a1c1 oc) (conj (c82_478 Via1b2c2 Vic2a1b1 Via2b1c1) (conj (c82_641 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o) (conj (c82_479 Via1b2c2 Vic2a1b1 Via2b1c1) (c82_493 Via1b2c2 Vic2a1b1 Via2b1c1)))))). Qed. Lemma c82_657: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(p b2 ab)->(p a1 c1)->(p c2 c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vpb2ab:(p b2 ab))(Vpa1c1:(p a1 c1))=>((ptra c2 a1 c1) (conj (c82_644 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2) Vpa1c1))). Qed. Lemma c82_658: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(p b2 ab)->(p a1 c1)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vpb2ab:(p b2 ab))(Vpa1c1:(p a1 c1))=>(notcc (c82_657 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2 Vpb2ab Vpa1c1))). Qed. Lemma c82_659: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(p b2 ab)->(p a1 c1)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vpb2ab:(p b2 ab))(Vpa1c1:(p a1 c1))=>((false_ind goal) (c82_658 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2 Vpb2ab Vpa1c1))). Qed. Lemma c82_662: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(p b2 ab)->(l a1c1 oc)->(p a1 ac) \/ (l a1c1 a2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))=>((unique a1 ac a1c1 a2c2) (conj (c82_478 Via1b2c2 Vic2a1b1 Via2b1c1) (conj (c82_647 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2) (conj (c82_497 Via1b2c2 Vic2a1b1 Via2b1c1) (c82_498 Via1b2c2 Vic2a1b1 Via2b1c1)))))). Qed. Lemma c82_663: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(p b2 ab)->(l a1c1 oc)->(p a1 ac)->(p ac a1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vpa1ac:(p a1 ac))=>((psym a1 ac) Vpa1ac)). Qed. Lemma c82_668: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(p b2 ab)->(l a1c1 oc)->(p a1 ac)->(i ac b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vpa1ac:(p a1 ac))=>((pcon ac a1 b2c2) (conj (c82_663 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2 Vpb2ab Vla1c1oc Vpa1ac) Via1b2c2))). Qed. Lemma c82_669: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(p b2 ab)->(l a1c1 oc)->(p a1 ac)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vpa1ac:(p a1 ac))=>((goal_normal b2c2) (conj (c82_511 Via1b2c2 Vic2a1b1 Via2b1c1) (conj (c82_496 Via1b2c2 Vic2a1b1 Via2b1c1) (conj (c82_668 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2 Vpb2ab Vla1c1oc Vpa1ac) (c82_623 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1)))))). Qed. Lemma c82_670: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(p b2 ab)->(l a1c1 oc)->(l a1c1 a2c2)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vla1c1a2c2:(l a1c1 a2c2))=>(notac Vla1c1a2c2)). Qed. Lemma c82_671: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(p b2 ab)->(l a1c1 oc)->(l a1c1 a2c2)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))(Vla1c1a2c2:(l a1c1 a2c2))=>((false_ind goal) (c82_670 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2 Vpb2ab Vla1c1oc Vla1c1a2c2))). Qed. Lemma c82_672: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(p b2 ab)->(l a1c1 oc)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vpb2ab:(p b2 ab))(Vla1c1oc:(l a1c1 oc))=>((or_ind ((c82_669 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2 Vpb2ab Vla1c1oc))((c82_671 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2 Vpb2ab Vla1c1oc)))(c82_662 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2 Vpb2ab Vla1c1oc))). Qed. Lemma c82_673: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(p b2 ab)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vpb2ab:(p b2 ab))=>((or_ind ((c82_659 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2 Vpb2ab))((c82_672 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2 Vpb2ab)))(c82_653 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2 Vpb2ab))). Qed. Lemma c82_674: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(l a2b2 b2c2)->(l b2c2 a2b2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vla2b2b2c2:(l a2b2 b2c2))=>((lsym a2b2 b2c2) Vla2b2b2c2)). Qed. Lemma c82_675: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(l a2b2 b2c2)->(l a1b1 a2b2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vla2b2b2c2:(l a2b2 b2c2))=>((ltra a1b1 b2c2 a2b2) (conj (c82_619 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1) (c82_674 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2 Vla2b2b2c2)))). Qed. Lemma c82_676: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(l a2b2 b2c2)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vla2b2b2c2:(l a2b2 b2c2))=>(notab (c82_675 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2 Vla2b2b2c2))). Qed. Lemma c82_677: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->(l a2b2 b2c2)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))(Vla2b2b2c2:(l a2b2 b2c2))=>((false_ind goal) (c82_676 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2 Vla2b2b2c2))). Qed. Lemma c82_678: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(p a1 c2)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vpa1c2:(p a1 c2))=>((or_ind ((c82_673 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2))((c82_677 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2)))(c82_651 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vpa1c2))). Qed. Lemma c82_680: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(l b2c2 oc)->(l a1b1 oc). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vlb2c2oc:(l b2c2 oc))=>((ltra a1b1 b2c2 oc) (conj (c82_619 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1) Vlb2c2oc))). Qed. Lemma c82_684: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(l b2c2 oc)->(i b1 oc). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vlb2c2oc:(l b2c2 oc))=>((lcon b1 a1b1 oc) (conj (c82_475 Via1b2c2 Vic2a1b1 Via2b1c1) (c82_680 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vlb2c2oc)))). Qed. Lemma c82_685: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(l b2c2 oc)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vlb2c2oc:(l b2c2 oc))=>((triangle1 oc) (conj (c82_641 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o) (conj (c82_684 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vlb2c2oc) (c82_493 Via1b2c2 Vic2a1b1 Via2b1c1))))). Qed. Lemma c82_686: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->(l b2c2 oc)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))(Vlb2c2oc:(l b2c2 oc))=>((false_ind goal) (c82_685 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o Vlb2c2oc))). Qed. Lemma c82_687: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(p a1 o)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vpa1o:(p a1 o))=>((or_ind ((c82_678 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o))((c82_686 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o)))(c82_643 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vpa1o))). Qed. Lemma c82_689: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(l b2c2 oa)->(l a1b1 oa). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vlb2c2oa:(l b2c2 oa))=>((ltra a1b1 b2c2 oa) (conj (c82_619 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1) Vlb2c2oa))). Qed. Lemma c82_693: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(l b2c2 oa)->(i c2 oa). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vlb2c2oa:(l b2c2 oa))=>((lcon c2 a1b1 oa) (conj Vic2a1b1 (c82_689 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vlb2c2oa)))). Qed. Lemma c82_696: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(l b2c2 oa)->(i b2 oa). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vlb2c2oa:(l b2c2 oa))=>((lcon b2 b2c2 oa) (conj (c82_485 Via1b2c2 Vic2a1b1 Via2b1c1) Vlb2c2oa))). Qed. Lemma c82_697: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(l b2c2 oa)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vlb2c2oa:(l b2c2 oa))=>((triangle2 oa) (conj (c82_490 Via1b2c2 Vic2a1b1 Via2b1c1) (conj (c82_696 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vlb2c2oa) (c82_693 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vlb2c2oa))))). Qed. Lemma c82_698: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->(l b2c2 oa)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))(Vlb2c2oa:(l b2c2 oa))=>((false_ind goal) (c82_697 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob Vlb2c2oa))). Qed. Lemma c82_699: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->(l a1b1 ob)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))(Vla1b1ob:(l a1b1 ob))=>((or_ind ((c82_687 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob))((c82_698 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob)))(c82_639 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc Vla1b1ob))). Qed. Lemma c82_700: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(p b1 bc)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vpb1bc:(p b1 bc))=>((or_ind ((c82_630 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc))((c82_699 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc)))(c82_627 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vpb1bc))). Qed. Lemma c82_702: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(l a1b1 b1c1)->(l b2c2 b1c1). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vla1b1b1c1:(l a1b1 b1c1))=>((ltra b2c2 a1b1 b1c1) (conj Vlb2c2a1b1 Vla1b1b1c1))). Qed. Lemma c82_703: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(l a1b1 b1c1)->(l b1c1 b2c2). Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vla1b1b1c1:(l a1b1 b1c1))=>((lsym b2c2 b1c1) (c82_702 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vla1b1b1c1))). Qed. Lemma c82_704: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(l a1b1 b1c1)->false. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vla1b1b1c1:(l a1b1 b1c1))=>(notbc (c82_703 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vla1b1b1c1))). Qed. Lemma c82_705: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->(l a1b1 b1c1)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))(Vla1b1b1c1:(l a1b1 b1c1))=>((false_ind goal) (c82_704 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1 Vla1b1b1c1))). Qed. Lemma c82_706: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->(l b2c2 a1b1)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))(Vlb2c2a1b1:(l b2c2 a1b1))=>((or_ind ((c82_700 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1))((c82_705 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1)))(c82_624 Via1b2c2 Vic2a1b1 Via2b1c1 Vlb2c2a1b1))). Qed. Lemma c82_707: (i a1 b2c2)->(i c2 a1b1)->(i a2 b1c1)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>((or_ind ((c82_618 Via1b2c2 Vic2a1b1 Via2b1c1))((c82_706 Via1b2c2 Vic2a1b1 Via2b1c1)))(c82_520 Via1b2c2 Vic2a1b1 Via2b1c1))). Qed. Lemma c82_708: (i a1 b2c2)->(i c2 a1b1)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))(Vic2a1b1:(i c2 a1b1))=>((or_ind ((c82_473 Via1b2c2 Vic2a1b1))((c82_707 Via1b2c2 Vic2a1b1)))(c82_239 Via1b2c2 Vic2a1b1))). Qed. Lemma c82_709: (i a1 b2c2)->goal. Proof. exact (fun (Via1b2c2:(i a1 b2c2))=>((or_ind ((c82_238 Via1b2c2))((c82_708 Via1b2c2)))(c82_2 Via1b2c2))). Qed. Lemma c82_710: (i b2 a1c1)->(i b1 a2c2) \/ (i c2 a1b1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))=>gap_b). Qed. Lemma c82_711: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2) \/ (i a2 b1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))=>gap_c). Qed. Lemma c82_712: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(i a1 a1b1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))=>ia1b1). Qed. Lemma c82_713: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(i b1 a1b1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))=>ib1a1). Qed. Lemma c82_714: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(i a2 a2b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))=>ia2b2). Qed. Lemma c82_715: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(i b2 a2b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))=>ib2a2). Qed. Lemma c82_716: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(i a1 a1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))=>ia1c1). Qed. Lemma c82_717: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(i c1 a1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))=>ic1a1). Qed. Lemma c82_718: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(i a2 a2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))=>ia2c2). Qed. Lemma c82_719: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(i c2 a2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))=>ic2a2). Qed. Lemma c82_720: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(i c1 b1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))=>ic1b1). Qed. Lemma c82_721: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(i b1 b1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))=>ib1c1). Qed. Lemma c82_722: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(i c2 b2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))=>ic2b2). Qed. Lemma c82_723: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(i b2 b2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))=>ib2c2). Qed. Lemma c82_724: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(i o oa). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))=>iooa). Qed. Lemma c82_725: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(i o ob). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))=>ioob). Qed. Lemma c82_726: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(i o oc). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))=>iooc). Qed. Lemma c82_727: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(i a1 oa). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))=>ia1oa). Qed. Lemma c82_728: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(i a2 oa). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))=>ia2oa). Qed. Lemma c82_729: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(i b1 ob). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))=>ib1ob). Qed. Lemma c82_730: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(i b2 ob). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))=>ib2ob). Qed. Lemma c82_731: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(i c1 oc). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))=>ic1oc). Qed. Lemma c82_732: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(i c2 oc). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))=>ic2oc). Qed. Lemma c82_733: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(i bc b1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))=>ibc1). Qed. Lemma c82_734: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(i bc b2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))=>ibc2). Qed. Lemma c82_735: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(i ac a1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))=>iac1). Qed. Lemma c82_736: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(i ac a2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))=>iac2). Qed. Lemma c82_737: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(i ab a1b1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))=>iab1). Qed. Lemma c82_738: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(i ab a2b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))=>iab2). Qed. Lemma c82_751: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a2b2 a2b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))=>((lref c1 a2b2) Vic1a2b2)). Qed. Lemma c82_758: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1) \/ (l a1c1 a2b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))=>((unique b2 c1 a1c1 a2b2) (conj Vib2a1c1 (conj (c82_715 Vib2a1c1 Vib1a2c2 Vic1a2b2) (conj (c82_717 Vib2a1c1 Vib1a2c2 Vic1a2b2) Vic1a2b2))))). Qed. Lemma c82_759: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))=>((psym b2 c1) Vpb2c1)). Qed. Lemma c82_760: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(i b2 b1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))=>((pcon b2 c1 b1c1) (conj Vpb2c1 (c82_720 Vib2a1c1 Vib1a2c2 Vic1a2b2)))). Qed. Lemma c82_762: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(i c1 b2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))=>((pcon c1 b2 b2c2) (conj (c82_759 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1) (c82_723 Vib2a1c1 Vib1a2c2 Vic1a2b2)))). Qed. Lemma c82_763: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(i c1 ob). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))=>((pcon c1 b2 ob) (conj (c82_759 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1) (c82_730 Vib2a1c1 Vib1a2c2 Vic1a2b2)))). Qed. Lemma c82_764: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc) \/ (l b1c1 b2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))=>((unique c1 bc b1c1 b2c2) (conj (c82_720 Vib2a1c1 Vib1a2c2 Vic1a2b2) (conj (c82_762 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1) (conj (c82_733 Vib2a1c1 Vib1a2c2 Vic1a2b2) (c82_734 Vib2a1c1 Vib1a2c2 Vic1a2b2)))))). Qed. Lemma c82_765: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(p bc c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))=>((psym c1 bc) Vpc1bc)). Qed. Lemma c82_768: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(i bc a2b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))=>((pcon bc c1 a2b2) (conj (c82_765 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc) Vic1a2b2))). Qed. Lemma c82_772: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(p c1 b1) \/ (l b1c1 ob). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))=>((unique c1 b1 b1c1 ob) (conj (c82_720 Vib2a1c1 Vib1a2c2 Vic1a2b2) (conj (c82_763 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1) (conj (c82_721 Vib2a1c1 Vib1a2c2 Vic1a2b2) (c82_729 Vib2a1c1 Vib1a2c2 Vic1a2b2)))))). Qed. Lemma c82_774: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(p c1 b1)->(p b2 b1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vpc1b1:(p c1 b1))=>((ptra b2 c1 b1) (conj Vpb2c1 Vpc1b1))). Qed. Lemma c82_775: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(p c1 b1)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vpc1b1:(p c1 b1))=>(notbb (c82_774 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vpc1b1))). Qed. Lemma c82_776: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(p c1 b1)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vpc1b1:(p c1 b1))=>((false_ind goal) (c82_775 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vpc1b1))). Qed. Lemma c82_777: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l ob b1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))=>((lsym b1c1 ob) Vlb1c1ob)). Qed. Lemma c82_778: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(i o b1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))=>((lcon o ob b1c1) (conj (c82_725 Vib2a1c1 Vib1a2c2 Vic1a2b2) (c82_777 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob)))). Qed. Lemma c82_779: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o) \/ (l b1c1 oc). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))=>((unique c1 o b1c1 oc) (conj (c82_720 Vib2a1c1 Vib1a2c2 Vic1a2b2) (conj (c82_731 Vib2a1c1 Vib1a2c2 Vic1a2b2) (conj (c82_778 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob) (c82_726 Vib2a1c1 Vib1a2c2 Vic1a2b2)))))). Qed. Lemma c82_785: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(i c1 oa). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))=>((pcon c1 o oa) (conj Vpc1o (c82_724 Vib2a1c1 Vib1a2c2 Vic1a2b2)))). Qed. Lemma c82_786: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(i b2 oa). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))=>((pcon b2 c1 oa) (conj Vpb2c1 (c82_785 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o)))). Qed. Lemma c82_791: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(p b2 a1) \/ (l a1c1 oa). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))=>((unique b2 a1 a1c1 oa) (conj Vib2a1c1 (conj (c82_786 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o) (conj (c82_716 Vib2a1c1 Vib1a2c2 Vic1a2b2) (c82_727 Vib2a1c1 Vib1a2c2 Vic1a2b2)))))). Qed. Lemma c82_799: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(p b2 a1)->(i b2 a1b1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))(Vpb2a1:(p b2 a1))=>((pcon b2 a1 a1b1) (conj Vpb2a1 (c82_712 Vib2a1c1 Vib1a2c2 Vic1a2b2)))). Qed. Lemma c82_800: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(p b2 a1)->(i c1 a1b1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))(Vpb2a1:(p b2 a1))=>((pcon c1 b2 a1b1) (conj (c82_759 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1) (c82_799 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o Vpb2a1)))). Qed. Lemma c82_801: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(p b2 a1)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))(Vpb2a1:(p b2 a1))=>((triangle1 a1b1) (conj (c82_712 Vib2a1c1 Vib1a2c2 Vic1a2b2) (conj (c82_713 Vib2a1c1 Vib1a2c2 Vic1a2b2) (c82_800 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o Vpb2a1))))). Qed. Lemma c82_802: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(p b2 a1)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))(Vpb2a1:(p b2 a1))=>((false_ind goal) (c82_801 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o Vpb2a1))). Qed. Lemma c82_803: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(l a1c1 oa)->(l oa a1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))(Vla1c1oa:(l a1c1 oa))=>((lsym a1c1 oa) Vla1c1oa)). Qed. Lemma c82_804: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(l a1c1 oa)->(i a2 a1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))(Vla1c1oa:(l a1c1 oa))=>((lcon a2 oa a1c1) (conj (c82_728 Vib2a1c1 Vib1a2c2 Vic1a2b2) (c82_803 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o Vla1c1oa)))). Qed. Lemma c82_806: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(l a1c1 oa)->(p b2 a2) \/ (l a1c1 a2b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))(Vla1c1oa:(l a1c1 oa))=>((unique b2 a2 a1c1 a2b2) (conj Vib2a1c1 (conj (c82_715 Vib2a1c1 Vib1a2c2 Vic1a2b2) (conj (c82_804 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o Vla1c1oa) (c82_714 Vib2a1c1 Vib1a2c2 Vic1a2b2)))))). Qed. Lemma c82_814: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(l a1c1 oa)->(p b2 a2)->(i b2 a2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))(Vla1c1oa:(l a1c1 oa))(Vpb2a2:(p b2 a2))=>((pcon b2 a2 a2c2) (conj Vpb2a2 (c82_718 Vib2a1c1 Vib1a2c2 Vic1a2b2)))). Qed. Lemma c82_815: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(l a1c1 oa)->(p b2 a2)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))(Vla1c1oa:(l a1c1 oa))(Vpb2a2:(p b2 a2))=>((triangle2 a2c2) (conj (c82_718 Vib2a1c1 Vib1a2c2 Vic1a2b2) (conj (c82_814 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o Vla1c1oa Vpb2a2) (c82_719 Vib2a1c1 Vib1a2c2 Vic1a2b2))))). Qed. Lemma c82_816: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(l a1c1 oa)->(p b2 a2)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))(Vla1c1oa:(l a1c1 oa))(Vpb2a2:(p b2 a2))=>((false_ind goal) (c82_815 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o Vla1c1oa Vpb2a2))). Qed. Lemma c82_821: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(l a1c1 oa)->(l a1c1 a2b2)->(i ac a2b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))(Vla1c1oa:(l a1c1 oa))(Vla1c1a2b2:(l a1c1 a2b2))=>((lcon ac a1c1 a2b2) (conj (c82_735 Vib2a1c1 Vib1a2c2 Vic1a2b2) Vla1c1a2b2))). Qed. Lemma c82_822: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(l a1c1 oa)->(l a1c1 a2b2)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))(Vla1c1oa:(l a1c1 oa))(Vla1c1a2b2:(l a1c1 a2b2))=>((goal_normal a2b2) (conj (c82_751 Vib2a1c1 Vib1a2c2 Vic1a2b2) (conj (c82_768 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc) (conj (c82_821 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o Vla1c1oa Vla1c1a2b2) (c82_738 Vib2a1c1 Vib1a2c2 Vic1a2b2)))))). Qed. Lemma c82_823: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(l a1c1 oa)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))(Vla1c1oa:(l a1c1 oa))=>((or_ind ((c82_816 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o Vla1c1oa))((c82_822 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o Vla1c1oa)))(c82_806 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o Vla1c1oa))). Qed. Lemma c82_824: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))=>((or_ind ((c82_802 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o))((c82_823 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o)))(c82_791 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o))). Qed. Lemma c82_825: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l b1c1 oc)->(l oc b1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vlb1c1oc:(l b1c1 oc))=>((lsym b1c1 oc) Vlb1c1oc)). Qed. Lemma c82_829: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l b1c1 oc)->(i c2 b1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vlb1c1oc:(l b1c1 oc))=>((lcon c2 oc b1c1) (conj (c82_732 Vib2a1c1 Vib1a2c2 Vic1a2b2) (c82_825 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vlb1c1oc)))). Qed. Lemma c82_831: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l b1c1 oc)->(p b1 c2) \/ (l a2c2 b1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vlb1c1oc:(l b1c1 oc))=>((unique b1 c2 a2c2 b1c1) (conj Vib1a2c2 (conj (c82_721 Vib2a1c1 Vib1a2c2 Vic1a2b2) (conj (c82_719 Vib2a1c1 Vib1a2c2 Vic1a2b2) (c82_829 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vlb1c1oc)))))). Qed. Lemma c82_833: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l b1c1 oc)->(p b1 c2)->(i b1 b2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vlb1c1oc:(l b1c1 oc))(Vpb1c2:(p b1 c2))=>((pcon b1 c2 b2c2) (conj Vpb1c2 (c82_722 Vib2a1c1 Vib1a2c2 Vic1a2b2)))). Qed. Lemma c82_835: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l b1c1 oc)->(p b1 c2)->(p c1 b1) \/ (l b1c1 b2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vlb1c1oc:(l b1c1 oc))(Vpb1c2:(p b1 c2))=>((unique c1 b1 b1c1 b2c2) (conj (c82_720 Vib2a1c1 Vib1a2c2 Vic1a2b2) (conj (c82_762 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1) (conj (c82_721 Vib2a1c1 Vib1a2c2 Vic1a2b2) (c82_833 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vlb1c1oc Vpb1c2)))))). Qed. Lemma c82_837: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l b1c1 oc)->(p b1 c2)->(p c1 b1)->(p b2 b1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vlb1c1oc:(l b1c1 oc))(Vpb1c2:(p b1 c2))(Vpc1b1:(p c1 b1))=>((ptra b2 c1 b1) (conj Vpb2c1 Vpc1b1))). Qed. Lemma c82_838: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l b1c1 oc)->(p b1 c2)->(p c1 b1)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vlb1c1oc:(l b1c1 oc))(Vpb1c2:(p b1 c2))(Vpc1b1:(p c1 b1))=>(notbb (c82_837 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vlb1c1oc Vpb1c2 Vpc1b1))). Qed. Lemma c82_839: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l b1c1 oc)->(p b1 c2)->(p c1 b1)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vlb1c1oc:(l b1c1 oc))(Vpb1c2:(p b1 c2))(Vpc1b1:(p c1 b1))=>((false_ind goal) (c82_838 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vlb1c1oc Vpb1c2 Vpc1b1))). Qed. Lemma c82_840: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l b1c1 oc)->(p b1 c2)->(l b1c1 b2c2)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vlb1c1oc:(l b1c1 oc))(Vpb1c2:(p b1 c2))(Vlb1c1b2c2:(l b1c1 b2c2))=>(notbc Vlb1c1b2c2)). Qed. Lemma c82_841: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l b1c1 oc)->(p b1 c2)->(l b1c1 b2c2)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vlb1c1oc:(l b1c1 oc))(Vpb1c2:(p b1 c2))(Vlb1c1b2c2:(l b1c1 b2c2))=>((false_ind goal) (c82_840 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vlb1c1oc Vpb1c2 Vlb1c1b2c2))). Qed. Lemma c82_842: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l b1c1 oc)->(p b1 c2)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vlb1c1oc:(l b1c1 oc))(Vpb1c2:(p b1 c2))=>((or_ind ((c82_839 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vlb1c1oc Vpb1c2))((c82_841 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vlb1c1oc Vpb1c2)))(c82_835 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vlb1c1oc Vpb1c2))). Qed. Lemma c82_848: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l b1c1 oc)->(l a2c2 b1c1)->(i a2 b1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vlb1c1oc:(l b1c1 oc))(Vla2c2b1c1:(l a2c2 b1c1))=>((lcon a2 a2c2 b1c1) (conj (c82_718 Vib2a1c1 Vib1a2c2 Vic1a2b2) Vla2c2b1c1))). Qed. Lemma c82_849: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l b1c1 oc)->(l a2c2 b1c1)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vlb1c1oc:(l b1c1 oc))(Vla2c2b1c1:(l a2c2 b1c1))=>((triangle2 b1c1) (conj (c82_848 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vlb1c1oc Vla2c2b1c1) (conj (c82_760 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1) (c82_829 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vlb1c1oc))))). Qed. Lemma c82_850: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l b1c1 oc)->(l a2c2 b1c1)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vlb1c1oc:(l b1c1 oc))(Vla2c2b1c1:(l a2c2 b1c1))=>((false_ind goal) (c82_849 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vlb1c1oc Vla2c2b1c1))). Qed. Lemma c82_851: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l b1c1 oc)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vlb1c1oc:(l b1c1 oc))=>((or_ind ((c82_842 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vlb1c1oc))((c82_850 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vlb1c1oc)))(c82_831 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vlb1c1oc))). Qed. Lemma c82_852: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))=>((or_ind ((c82_824 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob))((c82_851 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob)))(c82_779 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob))). Qed. Lemma c82_853: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))=>((or_ind ((c82_776 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc))((c82_852 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc)))(c82_772 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vpc1bc))). Qed. Lemma c82_854: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(l b1c1 b2c2)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vlb1c1b2c2:(l b1c1 b2c2))=>(notbc Vlb1c1b2c2)). Qed. Lemma c82_855: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->(l b1c1 b2c2)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vlb1c1b2c2:(l b1c1 b2c2))=>((false_ind goal) (c82_854 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1 Vlb1c1b2c2))). Qed. Lemma c82_856: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(p b2 c1)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))=>((or_ind ((c82_853 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1))((c82_855 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1)))(c82_764 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vpb2c1))). Qed. Lemma c82_857: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(l a2b2 a1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))=>((lsym a1c1 a2b2) Vla1c1a2b2)). Qed. Lemma c82_860: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(i ac a2b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))=>((lcon ac a1c1 a2b2) (conj (c82_735 Vib2a1c1 Vib1a2c2 Vic1a2b2) Vla1c1a2b2))). Qed. Lemma c82_861: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(i ab a1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))=>((lcon ab a2b2 a1c1) (conj (c82_738 Vib2a1c1 Vib1a2c2 Vic1a2b2) (c82_857 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2)))). Qed. Lemma c82_862: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab) \/ (l a1b1 a1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))=>((unique a1 ab a1b1 a1c1) (conj (c82_712 Vib2a1c1 Vib1a2c2 Vic1a2b2) (conj (c82_716 Vib2a1c1 Vib1a2c2 Vic1a2b2) (conj (c82_737 Vib2a1c1 Vib1a2c2 Vic1a2b2) (c82_861 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2)))))). Qed. Lemma c82_863: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p ab a1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))=>((psym a1 ab) Vpa1ab)). Qed. Lemma c82_864: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(i ab oa). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))=>((pcon ab a1 oa) (conj (c82_863 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab) (c82_727 Vib2a1c1 Vib1a2c2 Vic1a2b2)))). Qed. Lemma c82_865: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac) \/ (l a2b2 a2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))=>((unique a2 ac a2b2 a2c2) (conj (c82_714 Vib2a1c1 Vib1a2c2 Vic1a2b2) (conj (c82_718 Vib2a1c1 Vib1a2c2 Vic1a2b2) (conj (c82_860 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2) (c82_736 Vib2a1c1 Vib1a2c2 Vic1a2b2)))))). Qed. Lemma c82_868: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(p a2 ab) \/ (l a2b2 oa). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))=>((unique a2 ab a2b2 oa) (conj (c82_714 Vib2a1c1 Vib1a2c2 Vic1a2b2) (conj (c82_728 Vib2a1c1 Vib1a2c2 Vic1a2b2) (conj (c82_738 Vib2a1c1 Vib1a2c2 Vic1a2b2) (c82_864 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab)))))). Qed. Lemma c82_869: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(p a2 ab)->(p ab a2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vpa2ab:(p a2 ab))=>((psym a2 ab) Vpa2ab)). Qed. Lemma c82_870: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(p a2 ab)->(p a1 a2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vpa2ab:(p a2 ab))=>((ptra a1 ab a2) (conj Vpa1ab (c82_869 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vpa2ab)))). Qed. Lemma c82_871: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(p a2 ab)->(p a2 a1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vpa2ab:(p a2 ab))=>((psym a1 a2) (c82_870 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vpa2ab))). Qed. Lemma c82_872: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(p a2 ab)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vpa2ab:(p a2 ab))=>(notaa (c82_871 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vpa2ab))). Qed. Lemma c82_873: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(p a2 ab)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vpa2ab:(p a2 ab))=>((false_ind goal) (c82_872 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vpa2ab))). Qed. Lemma c82_875: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(l a1c1 oa). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))=>((ltra a1c1 a2b2 oa) (conj Vla1c1a2b2 Vla2b2oa))). Qed. Lemma c82_876: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(l oa a1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))=>((lsym a1c1 oa) (c82_875 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa))). Qed. Lemma c82_880: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(i o a1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))=>((lcon o oa a1c1) (conj (c82_724 Vib2a1c1 Vib1a2c2 Vic1a2b2) (c82_876 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa)))). Qed. Lemma c82_881: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o) \/ (l a1c1 ob). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))=>((unique b2 o a1c1 ob) (conj Vib2a1c1 (conj (c82_730 Vib2a1c1 Vib1a2c2 Vic1a2b2) (conj (c82_880 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa) (c82_725 Vib2a1c1 Vib1a2c2 Vic1a2b2)))))). Qed. Lemma c82_883: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->(i b2 oc). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))=>((pcon b2 o oc) (conj Vpb2o (c82_726 Vib2a1c1 Vib1a2c2 Vic1a2b2)))). Qed. Lemma c82_885: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->(p b2 c1) \/ (l a1c1 oc). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))=>((unique b2 c1 a1c1 oc) (conj Vib2a1c1 (conj (c82_883 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o) (conj (c82_717 Vib2a1c1 Vib1a2c2 Vic1a2b2) (c82_731 Vib2a1c1 Vib1a2c2 Vic1a2b2)))))). Qed. Lemma c82_886: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->(p b2 c1)->(p c1 b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2c1:(p b2 c1))=>((psym b2 c1) Vpb2c1)). Qed. Lemma c82_891: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->(p b2 c1)->(i c1 b2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2c1:(p b2 c1))=>((pcon c1 b2 b2c2) (conj (c82_886 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o Vpb2c1) (c82_723 Vib2a1c1 Vib1a2c2 Vic1a2b2)))). Qed. Lemma c82_893: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->(p b2 c1)->(p c1 bc) \/ (l b1c1 b2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2c1:(p b2 c1))=>((unique c1 bc b1c1 b2c2) (conj (c82_720 Vib2a1c1 Vib1a2c2 Vic1a2b2) (conj (c82_891 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o Vpb2c1) (conj (c82_733 Vib2a1c1 Vib1a2c2 Vic1a2b2) (c82_734 Vib2a1c1 Vib1a2c2 Vic1a2b2)))))). Qed. Lemma c82_894: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->(p b2 c1)->(p c1 bc)->(p bc c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))=>((psym c1 bc) Vpc1bc)). Qed. Lemma c82_899: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->(p b2 c1)->(p c1 bc)->(i bc a2b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))=>((pcon bc c1 a2b2) (conj (c82_894 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o Vpb2c1 Vpc1bc) Vic1a2b2))). Qed. Lemma c82_900: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->(p b2 c1)->(p c1 bc)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))=>((goal_normal a2b2) (conj (c82_751 Vib2a1c1 Vib1a2c2 Vic1a2b2) (conj (c82_899 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o Vpb2c1 Vpc1bc) (conj (c82_860 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2) (c82_738 Vib2a1c1 Vib1a2c2 Vic1a2b2)))))). Qed. Lemma c82_901: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->(p b2 c1)->(l b1c1 b2c2)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2c1:(p b2 c1))(Vlb1c1b2c2:(l b1c1 b2c2))=>(notbc Vlb1c1b2c2)). Qed. Lemma c82_902: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->(p b2 c1)->(l b1c1 b2c2)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2c1:(p b2 c1))(Vlb1c1b2c2:(l b1c1 b2c2))=>((false_ind goal) (c82_901 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o Vpb2c1 Vlb1c1b2c2))). Qed. Lemma c82_903: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->(p b2 c1)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2c1:(p b2 c1))=>((or_ind ((c82_900 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o Vpb2c1))((c82_902 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o Vpb2c1)))(c82_893 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o Vpb2c1))). Qed. Lemma c82_905: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->(l a1c1 oc)->(l a2b2 oc). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vla1c1oc:(l a1c1 oc))=>((ltra a2b2 a1c1 oc) (conj (c82_857 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2) Vla1c1oc))). Qed. Lemma c82_909: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->(l a1c1 oc)->(i a2 oc). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vla1c1oc:(l a1c1 oc))=>((lcon a2 a2b2 oc) (conj (c82_714 Vib2a1c1 Vib1a2c2 Vic1a2b2) (c82_905 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o Vla1c1oc)))). Qed. Lemma c82_910: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->(l a1c1 oc)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vla1c1oc:(l a1c1 oc))=>((triangle2 oc) (conj (c82_909 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o Vla1c1oc) (conj (c82_883 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o) (c82_732 Vib2a1c1 Vib1a2c2 Vic1a2b2))))). Qed. Lemma c82_911: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->(l a1c1 oc)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vla1c1oc:(l a1c1 oc))=>((false_ind goal) (c82_910 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o Vla1c1oc))). Qed. Lemma c82_912: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))=>((or_ind ((c82_903 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o))((c82_911 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o)))(c82_885 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o))). Qed. Lemma c82_914: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(l a1c1 ob)->(l a2b2 ob). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vla1c1ob:(l a1c1 ob))=>((ltra a2b2 a1c1 ob) (conj (c82_857 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2) Vla1c1ob))). Qed. Lemma c82_918: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(l a1c1 ob)->(i c1 ob). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vla1c1ob:(l a1c1 ob))=>((lcon c1 a2b2 ob) (conj Vic1a2b2 (c82_914 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vla1c1ob)))). Qed. Lemma c82_921: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(l a1c1 ob)->(i a1 ob). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vla1c1ob:(l a1c1 ob))=>((lcon a1 a1c1 ob) (conj (c82_716 Vib2a1c1 Vib1a2c2 Vic1a2b2) Vla1c1ob))). Qed. Lemma c82_922: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(l a1c1 ob)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vla1c1ob:(l a1c1 ob))=>((triangle1 ob) (conj (c82_921 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vla1c1ob) (conj (c82_729 Vib2a1c1 Vib1a2c2 Vic1a2b2) (c82_918 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vla1c1ob))))). Qed. Lemma c82_923: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(l a1c1 ob)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vla1c1ob:(l a1c1 ob))=>((false_ind goal) (c82_922 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vla1c1ob))). Qed. Lemma c82_924: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))=>((or_ind ((c82_912 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa))((c82_923 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa)))(c82_881 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa))). Qed. Lemma c82_925: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))=>((or_ind ((c82_873 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac))((c82_924 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac)))(c82_868 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac))). Qed. Lemma c82_927: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(l a2b2 a2c2)->(l a1c1 a2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vla2b2a2c2:(l a2b2 a2c2))=>((ltra a1c1 a2b2 a2c2) (conj Vla1c1a2b2 Vla2b2a2c2))). Qed. Lemma c82_928: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(l a2b2 a2c2)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vla2b2a2c2:(l a2b2 a2c2))=>(notac (c82_927 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vla2b2a2c2))). Qed. Lemma c82_929: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(l a2b2 a2c2)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vla2b2a2c2:(l a2b2 a2c2))=>((false_ind goal) (c82_928 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vla2b2a2c2))). Qed. Lemma c82_930: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))=>((or_ind ((c82_925 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab))((c82_929 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab)))(c82_865 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vpa1ab))). Qed. Lemma c82_931: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(l a1b1 a1c1)->(l a1c1 a1b1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vla1b1a1c1:(l a1b1 a1c1))=>((lsym a1b1 a1c1) Vla1b1a1c1)). Qed. Lemma c82_932: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(l a1b1 a1c1)->(l a2b2 a1b1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vla1b1a1c1:(l a1b1 a1c1))=>((ltra a2b2 a1c1 a1b1) (conj (c82_857 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2) (c82_931 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vla1b1a1c1)))). Qed. Lemma c82_933: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(l a1b1 a1c1)->(l a1b1 a2b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vla1b1a1c1:(l a1b1 a1c1))=>((lsym a2b2 a1b1) (c82_932 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vla1b1a1c1))). Qed. Lemma c82_934: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(l a1b1 a1c1)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vla1b1a1c1:(l a1b1 a1c1))=>(notab (c82_933 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vla1b1a1c1))). Qed. Lemma c82_935: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->(l a1b1 a1c1)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vla1b1a1c1:(l a1b1 a1c1))=>((false_ind goal) (c82_934 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2 Vla1b1a1c1))). Qed. Lemma c82_936: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->(l a1c1 a2b2)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))=>((or_ind ((c82_930 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2))((c82_935 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2)))(c82_862 Vib2a1c1 Vib1a2c2 Vic1a2b2 Vla1c1a2b2))). Qed. Lemma c82_937: (i b2 a1c1)->(i b1 a2c2)->(i c1 a2b2)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Vic1a2b2:(i c1 a2b2))=>((or_ind ((c82_856 Vib2a1c1 Vib1a2c2 Vic1a2b2))((c82_936 Vib2a1c1 Vib1a2c2 Vic1a2b2)))(c82_758 Vib2a1c1 Vib1a2c2 Vic1a2b2))). Qed. Lemma c82_938: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(i a1 a1b1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ia1b1). Qed. Lemma c82_939: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(i b1 a1b1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ib1a1). Qed. Lemma c82_940: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(i a2 a2b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ia2b2). Qed. Lemma c82_941: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(i b2 a2b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ib2a2). Qed. Lemma c82_942: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(i a1 a1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ia1c1). Qed. Lemma c82_943: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(i c1 a1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ic1a1). Qed. Lemma c82_944: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(i a2 a2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ia2c2). Qed. Lemma c82_945: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(i c2 a2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ic2a2). Qed. Lemma c82_946: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(i c1 b1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ic1b1). Qed. Lemma c82_947: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(i b1 b1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ib1c1). Qed. Lemma c82_948: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(i c2 b2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ic2b2). Qed. Lemma c82_949: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(i b2 b2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ib2c2). Qed. Lemma c82_950: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(i o oa). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>iooa). Qed. Lemma c82_951: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(i o ob). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ioob). Qed. Lemma c82_952: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(i o oc). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>iooc). Qed. Lemma c82_953: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(i a1 oa). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ia1oa). Qed. Lemma c82_954: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(i a2 oa). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ia2oa). Qed. Lemma c82_955: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(i b1 ob). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ib1ob). Qed. Lemma c82_956: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(i b2 ob). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ib2ob). Qed. Lemma c82_957: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(i c1 oc). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ic1oc). Qed. Lemma c82_958: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(i c2 oc). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ic2oc). Qed. Lemma c82_959: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(i bc b1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ibc1). Qed. Lemma c82_960: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(i bc b2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>ibc2). Qed. Lemma c82_961: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(i ac a1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>iac1). Qed. Lemma c82_962: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(i ac a2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>iac2). Qed. Lemma c82_963: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(i ab a1b1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>iab1). Qed. Lemma c82_964: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(i ab a2b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>iab2). Qed. Lemma c82_976: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 a2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>((lref b1 a2c2) Vib1a2c2)). Qed. Lemma c82_984: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2) \/ (l a2c2 b1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>((unique b1 a2 a2c2 b1c1) (conj Vib1a2c2 (conj (c82_947 Vib2a1c1 Vib1a2c2 Via2b1c1) (conj (c82_944 Vib2a1c1 Vib1a2c2 Via2b1c1) Via2b1c1))))). Qed. Lemma c82_985: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(p a2 b1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))=>((psym b1 a2) Vpb1a2)). Qed. Lemma c82_986: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(i b1 a2b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))=>((pcon b1 a2 a2b2) (conj Vpb1a2 (c82_940 Vib2a1c1 Vib1a2c2 Via2b1c1)))). Qed. Lemma c82_987: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(i b1 oa). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))=>((pcon b1 a2 oa) (conj Vpb1a2 (c82_954 Vib2a1c1 Vib1a2c2 Via2b1c1)))). Qed. Lemma c82_990: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(p a1 b1) \/ (l a1b1 oa). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))=>((unique a1 b1 a1b1 oa) (conj (c82_938 Vib2a1c1 Vib1a2c2 Via2b1c1) (conj (c82_953 Vib2a1c1 Vib1a2c2 Via2b1c1) (conj (c82_939 Vib2a1c1 Vib1a2c2 Via2b1c1) (c82_987 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2)))))). Qed. Lemma c82_991: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(p a1 b1)->(p b1 a1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vpa1b1:(p a1 b1))=>((psym a1 b1) Vpa1b1)). Qed. Lemma c82_992: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(p a1 b1)->(p a2 a1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vpa1b1:(p a1 b1))=>((ptra a2 b1 a1) (conj (c82_985 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2) (c82_991 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vpa1b1)))). Qed. Lemma c82_993: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(p a1 b1)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vpa1b1:(p a1 b1))=>(notaa (c82_992 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vpa1b1))). Qed. Lemma c82_994: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(p a1 b1)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vpa1b1:(p a1 b1))=>((false_ind goal) (c82_993 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vpa1b1))). Qed. Lemma c82_995: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l oa a1b1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))=>((lsym a1b1 oa) Vla1b1oa)). Qed. Lemma c82_996: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(i o a1b1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))=>((lcon o oa a1b1) (conj (c82_950 Vib2a1c1 Vib1a2c2 Via2b1c1) (c82_995 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa)))). Qed. Lemma c82_998: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o) \/ (l a1b1 ob). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))=>((unique b1 o a1b1 ob) (conj (c82_939 Vib2a1c1 Vib1a2c2 Via2b1c1) (conj (c82_955 Vib2a1c1 Vib1a2c2 Via2b1c1) (conj (c82_996 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa) (c82_951 Vib2a1c1 Vib1a2c2 Via2b1c1)))))). Qed. Lemma c82_1002: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(i b1 oc). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))=>((pcon b1 o oc) (conj Vpb1o (c82_952 Vib2a1c1 Vib1a2c2 Via2b1c1)))). Qed. Lemma c82_1007: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(p b1 c2) \/ (l a2c2 oc). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))=>((unique b1 c2 a2c2 oc) (conj Vib1a2c2 (conj (c82_1002 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o) (conj (c82_945 Vib2a1c1 Vib1a2c2 Via2b1c1) (c82_958 Vib2a1c1 Vib1a2c2 Via2b1c1)))))). Qed. Lemma c82_1013: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(p b1 c2)->(i b1 b2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vpb1c2:(p b1 c2))=>((pcon b1 c2 b2c2) (conj Vpb1c2 (c82_948 Vib2a1c1 Vib1a2c2 Via2b1c1)))). Qed. Lemma c82_1014: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(p b1 c2)->(i a2 b2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vpb1c2:(p b1 c2))=>((pcon a2 b1 b2c2) (conj (c82_985 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2) (c82_1013 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vpb1c2)))). Qed. Lemma c82_1015: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(p b1 c2)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vpb1c2:(p b1 c2))=>((triangle2 b2c2) (conj (c82_1014 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vpb1c2) (conj (c82_949 Vib2a1c1 Vib1a2c2 Via2b1c1) (c82_948 Vib2a1c1 Vib1a2c2 Via2b1c1))))). Qed. Lemma c82_1016: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(p b1 c2)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vpb1c2:(p b1 c2))=>((false_ind goal) (c82_1015 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vpb1c2))). Qed. Lemma c82_1017: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->(l oc a2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))=>((lsym a2c2 oc) Vla2c2oc)). Qed. Lemma c82_1018: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->(i c1 a2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))=>((lcon c1 oc a2c2) (conj (c82_957 Vib2a1c1 Vib1a2c2 Via2b1c1) (c82_1017 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vla2c2oc)))). Qed. Lemma c82_1020: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->(p b1 c1) \/ (l a2c2 b1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))=>((unique b1 c1 a2c2 b1c1) (conj Vib1a2c2 (conj (c82_947 Vib2a1c1 Vib1a2c2 Via2b1c1) (conj (c82_1018 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vla2c2oc) (c82_946 Vib2a1c1 Vib1a2c2 Via2b1c1)))))). Qed. Lemma c82_1026: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->(p b1 c1)->(i b1 a1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))(Vpb1c1:(p b1 c1))=>((pcon b1 c1 a1c1) (conj Vpb1c1 (c82_943 Vib2a1c1 Vib1a2c2 Via2b1c1)))). Qed. Lemma c82_1027: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->(p b1 c1)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))(Vpb1c1:(p b1 c1))=>((triangle1 a1c1) (conj (c82_942 Vib2a1c1 Vib1a2c2 Via2b1c1) (conj (c82_1026 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vla2c2oc Vpb1c1) (c82_943 Vib2a1c1 Vib1a2c2 Via2b1c1))))). Qed. Lemma c82_1028: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->(p b1 c1)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))(Vpb1c1:(p b1 c1))=>((false_ind goal) (c82_1027 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vla2c2oc Vpb1c1))). Qed. Lemma c82_1029: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->(l a2c2 b1c1)->(l b1c1 a2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))(Vla2c2b1c1:(l a2c2 b1c1))=>((lsym a2c2 b1c1) Vla2c2b1c1)). Qed. Lemma c82_1033: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->(l a2c2 b1c1)->(i bc a2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))(Vla2c2b1c1:(l a2c2 b1c1))=>((lcon bc b1c1 a2c2) (conj (c82_959 Vib2a1c1 Vib1a2c2 Via2b1c1) (c82_1029 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vla2c2oc Vla2c2b1c1)))). Qed. Lemma c82_1036: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->(l a2c2 b1c1)->(p b1 ab) \/ (l a1b1 a2b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))(Vla2c2b1c1:(l a2c2 b1c1))=>((unique b1 ab a1b1 a2b2) (conj (c82_939 Vib2a1c1 Vib1a2c2 Via2b1c1) (conj (c82_986 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2) (conj (c82_963 Vib2a1c1 Vib1a2c2 Via2b1c1) (c82_964 Vib2a1c1 Vib1a2c2 Via2b1c1)))))). Qed. Lemma c82_1037: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->(l a2c2 b1c1)->(p b1 ab)->(p ab b1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))(Vla2c2b1c1:(l a2c2 b1c1))(Vpb1ab:(p b1 ab))=>((psym b1 ab) Vpb1ab)). Qed. Lemma c82_1042: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->(l a2c2 b1c1)->(p b1 ab)->(i ab a2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))(Vla2c2b1c1:(l a2c2 b1c1))(Vpb1ab:(p b1 ab))=>((pcon ab b1 a2c2) (conj (c82_1037 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vla2c2oc Vla2c2b1c1 Vpb1ab) Vib1a2c2))). Qed. Lemma c82_1043: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->(l a2c2 b1c1)->(p b1 ab)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))(Vla2c2b1c1:(l a2c2 b1c1))(Vpb1ab:(p b1 ab))=>((goal_normal a2c2) (conj (c82_976 Vib2a1c1 Vib1a2c2 Via2b1c1) (conj (c82_1033 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vla2c2oc Vla2c2b1c1) (conj (c82_962 Vib2a1c1 Vib1a2c2 Via2b1c1) (c82_1042 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vla2c2oc Vla2c2b1c1 Vpb1ab)))))). Qed. Lemma c82_1044: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->(l a2c2 b1c1)->(l a1b1 a2b2)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))(Vla2c2b1c1:(l a2c2 b1c1))(Vla1b1a2b2:(l a1b1 a2b2))=>(notab Vla1b1a2b2)). Qed. Lemma c82_1045: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->(l a2c2 b1c1)->(l a1b1 a2b2)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))(Vla2c2b1c1:(l a2c2 b1c1))(Vla1b1a2b2:(l a1b1 a2b2))=>((false_ind goal) (c82_1044 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vla2c2oc Vla2c2b1c1 Vla1b1a2b2))). Qed. Lemma c82_1046: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->(l a2c2 b1c1)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))(Vla2c2b1c1:(l a2c2 b1c1))=>((or_ind ((c82_1043 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vla2c2oc Vla2c2b1c1))((c82_1045 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vla2c2oc Vla2c2b1c1)))(c82_1036 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vla2c2oc Vla2c2b1c1))). Qed. Lemma c82_1047: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->(l a2c2 oc)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))(Vla2c2oc:(l a2c2 oc))=>((or_ind ((c82_1028 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vla2c2oc))((c82_1046 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vla2c2oc)))(c82_1020 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o Vla2c2oc))). Qed. Lemma c82_1048: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(p b1 o)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1o:(p b1 o))=>((or_ind ((c82_1016 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o))((c82_1047 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o)))(c82_1007 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vpb1o))). Qed. Lemma c82_1052: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(i a1 ob). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))=>((lcon a1 a1b1 ob) (conj (c82_938 Vib2a1c1 Vib1a2c2 Via2b1c1) Vla1b1ob))). Qed. Lemma c82_1056: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(p b2 a1) \/ (l a1c1 ob). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))=>((unique b2 a1 a1c1 ob) (conj Vib2a1c1 (conj (c82_956 Vib2a1c1 Vib1a2c2 Via2b1c1) (conj (c82_942 Vib2a1c1 Vib1a2c2 Via2b1c1) (c82_1052 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob)))))). Qed. Lemma c82_1057: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(p b2 a1)->(p a1 b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))(Vpb2a1:(p b2 a1))=>((psym b2 a1) Vpb2a1)). Qed. Lemma c82_1058: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(p b2 a1)->(i a1 a2b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))(Vpb2a1:(p b2 a1))=>((pcon a1 b2 a2b2) (conj (c82_1057 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob Vpb2a1) (c82_941 Vib2a1c1 Vib1a2c2 Via2b1c1)))). Qed. Lemma c82_1060: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(p b2 a1)->(p a1 b1) \/ (l a1b1 a2b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))(Vpb2a1:(p b2 a1))=>((unique a1 b1 a1b1 a2b2) (conj (c82_938 Vib2a1c1 Vib1a2c2 Via2b1c1) (conj (c82_1058 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob Vpb2a1) (conj (c82_939 Vib2a1c1 Vib1a2c2 Via2b1c1) (c82_986 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2)))))). Qed. Lemma c82_1061: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(p b2 a1)->(p a1 b1)->(p b1 a1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))(Vpb2a1:(p b2 a1))(Vpa1b1:(p a1 b1))=>((psym a1 b1) Vpa1b1)). Qed. Lemma c82_1062: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(p b2 a1)->(p a1 b1)->(p a2 a1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))(Vpb2a1:(p b2 a1))(Vpa1b1:(p a1 b1))=>((ptra a2 b1 a1) (conj (c82_985 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2) (c82_1061 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob Vpb2a1 Vpa1b1)))). Qed. Lemma c82_1063: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(p b2 a1)->(p a1 b1)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))(Vpb2a1:(p b2 a1))(Vpa1b1:(p a1 b1))=>(notaa (c82_1062 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob Vpb2a1 Vpa1b1))). Qed. Lemma c82_1064: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(p b2 a1)->(p a1 b1)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))(Vpb2a1:(p b2 a1))(Vpa1b1:(p a1 b1))=>((false_ind goal) (c82_1063 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob Vpb2a1 Vpa1b1))). Qed. Lemma c82_1065: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(p b2 a1)->(l a1b1 a2b2)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))(Vpb2a1:(p b2 a1))(Vla1b1a2b2:(l a1b1 a2b2))=>(notab Vla1b1a2b2)). Qed. Lemma c82_1066: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(p b2 a1)->(l a1b1 a2b2)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))(Vpb2a1:(p b2 a1))(Vla1b1a2b2:(l a1b1 a2b2))=>((false_ind goal) (c82_1065 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob Vpb2a1 Vla1b1a2b2))). Qed. Lemma c82_1067: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(p b2 a1)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))(Vpb2a1:(p b2 a1))=>((or_ind ((c82_1064 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob Vpb2a1))((c82_1066 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob Vpb2a1)))(c82_1060 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob Vpb2a1))). Qed. Lemma c82_1068: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(l a1c1 ob)->(l ob a1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))(Vla1c1ob:(l a1c1 ob))=>((lsym a1c1 ob) Vla1c1ob)). Qed. Lemma c82_1069: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(l a1c1 ob)->(l a1b1 a1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))(Vla1c1ob:(l a1c1 ob))=>((ltra a1b1 ob a1c1) (conj Vla1b1ob (c82_1068 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob Vla1c1ob)))). Qed. Lemma c82_1073: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(l a1c1 ob)->(i b1 a1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))(Vla1c1ob:(l a1c1 ob))=>((lcon b1 a1b1 a1c1) (conj (c82_939 Vib2a1c1 Vib1a2c2 Via2b1c1) (c82_1069 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob Vla1c1ob)))). Qed. Lemma c82_1074: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(l a1c1 ob)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))(Vla1c1ob:(l a1c1 ob))=>((triangle1 a1c1) (conj (c82_942 Vib2a1c1 Vib1a2c2 Via2b1c1) (conj (c82_1073 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob Vla1c1ob) (c82_943 Vib2a1c1 Vib1a2c2 Via2b1c1))))). Qed. Lemma c82_1075: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->(l a1c1 ob)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))(Vla1c1ob:(l a1c1 ob))=>((false_ind goal) (c82_1074 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob Vla1c1ob))). Qed. Lemma c82_1076: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->(l a1b1 ob)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1ob:(l a1b1 ob))=>((or_ind ((c82_1067 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob))((c82_1075 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob)))(c82_1056 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa Vla1b1ob))). Qed. Lemma c82_1077: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->(l a1b1 oa)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))=>((or_ind ((c82_1048 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa))((c82_1076 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa)))(c82_998 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2 Vla1b1oa))). Qed. Lemma c82_1078: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(p b1 a2)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vpb1a2:(p b1 a2))=>((or_ind ((c82_994 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2))((c82_1077 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2)))(c82_990 Vib2a1c1 Vib1a2c2 Via2b1c1 Vpb1a2))). Qed. Lemma c82_1079: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(l b1c1 a2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))=>((lsym a2c2 b1c1) Vla2c2b1c1)). Qed. Lemma c82_1082: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(i bc a2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))=>((lcon bc b1c1 a2c2) (conj (c82_959 Vib2a1c1 Vib1a2c2 Via2b1c1) (c82_1079 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1)))). Qed. Lemma c82_1083: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(i ac b1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))=>((lcon ac a2c2 b1c1) (conj (c82_962 Vib2a1c1 Vib1a2c2 Via2b1c1) Vla2c2b1c1))). Qed. Lemma c82_1084: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac) \/ (l a1c1 b1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))=>((unique c1 ac a1c1 b1c1) (conj (c82_943 Vib2a1c1 Vib1a2c2 Via2b1c1) (conj (c82_946 Vib2a1c1 Vib1a2c2 Via2b1c1) (conj (c82_961 Vib2a1c1 Vib1a2c2 Via2b1c1) (c82_1083 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1)))))). Qed. Lemma c82_1085: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p ac c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))=>((psym c1 ac) Vpc1ac)). Qed. Lemma c82_1086: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(i ac oc). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))=>((pcon ac c1 oc) (conj (c82_1085 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac) (c82_957 Vib2a1c1 Vib1a2c2 Via2b1c1)))). Qed. Lemma c82_1087: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc) \/ (l a2c2 b2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))=>((unique c2 bc a2c2 b2c2) (conj (c82_945 Vib2a1c1 Vib1a2c2 Via2b1c1) (conj (c82_948 Vib2a1c1 Vib1a2c2 Via2b1c1) (conj (c82_1082 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1) (c82_960 Vib2a1c1 Vib1a2c2 Via2b1c1)))))). Qed. Lemma c82_1090: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(p c2 ac) \/ (l a2c2 oc). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))=>((unique c2 ac a2c2 oc) (conj (c82_945 Vib2a1c1 Vib1a2c2 Via2b1c1) (conj (c82_958 Vib2a1c1 Vib1a2c2 Via2b1c1) (conj (c82_962 Vib2a1c1 Vib1a2c2 Via2b1c1) (c82_1086 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac)))))). Qed. Lemma c82_1091: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(p c2 ac)->(p ac c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vpc2ac:(p c2 ac))=>((psym c2 ac) Vpc2ac)). Qed. Lemma c82_1092: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(p c2 ac)->(p c1 c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vpc2ac:(p c2 ac))=>((ptra c1 ac c2) (conj Vpc1ac (c82_1091 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vpc2ac)))). Qed. Lemma c82_1093: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(p c2 ac)->(p c2 c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vpc2ac:(p c2 ac))=>((psym c1 c2) (c82_1092 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vpc2ac))). Qed. Lemma c82_1094: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(p c2 ac)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vpc2ac:(p c2 ac))=>(notcc (c82_1093 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vpc2ac))). Qed. Lemma c82_1095: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(p c2 ac)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vpc2ac:(p c2 ac))=>((false_ind goal) (c82_1094 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vpc2ac))). Qed. Lemma c82_1096: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(l oc a2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))=>((lsym a2c2 oc) Vla2c2oc)). Qed. Lemma c82_1101: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(i o a2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))=>((lcon o oc a2c2) (conj (c82_952 Vib2a1c1 Vib1a2c2 Via2b1c1) (c82_1096 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc)))). Qed. Lemma c82_1103: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o) \/ (l a2c2 ob). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))=>((unique b1 o a2c2 ob) (conj Vib1a2c2 (conj (c82_955 Vib2a1c1 Vib1a2c2 Via2b1c1) (conj (c82_1101 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc) (c82_951 Vib2a1c1 Vib1a2c2 Via2b1c1)))))). Qed. Lemma c82_1105: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(i b1 oa). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))=>((pcon b1 o oa) (conj Vpb1o (c82_950 Vib2a1c1 Vib1a2c2 Via2b1c1)))). Qed. Lemma c82_1107: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2) \/ (l a2c2 oa). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))=>((unique b1 a2 a2c2 oa) (conj Vib1a2c2 (conj (c82_1105 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o) (conj (c82_944 Vib2a1c1 Vib1a2c2 Via2b1c1) (c82_954 Vib2a1c1 Vib1a2c2 Via2b1c1)))))). Qed. Lemma c82_1108: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2)->(p a2 b1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))=>((psym b1 a2) Vpb1a2)). Qed. Lemma c82_1111: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2)->(i b1 a2b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))=>((pcon b1 a2 a2b2) (conj Vpb1a2 (c82_940 Vib2a1c1 Vib1a2c2 Via2b1c1)))). Qed. Lemma c82_1115: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2)->(p a1 b1) \/ (l a1b1 oa). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))=>((unique a1 b1 a1b1 oa) (conj (c82_938 Vib2a1c1 Vib1a2c2 Via2b1c1) (conj (c82_953 Vib2a1c1 Vib1a2c2 Via2b1c1) (conj (c82_939 Vib2a1c1 Vib1a2c2 Via2b1c1) (c82_1105 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o)))))). Qed. Lemma c82_1116: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2)->(p a1 b1)->(p b1 a1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))(Vpa1b1:(p a1 b1))=>((psym a1 b1) Vpa1b1)). Qed. Lemma c82_1119: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2)->(p a1 b1)->(p a2 a1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))(Vpa1b1:(p a1 b1))=>((ptra a2 b1 a1) (conj (c82_1108 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vpb1a2) (c82_1116 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vpb1a2 Vpa1b1)))). Qed. Lemma c82_1120: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2)->(p a1 b1)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))(Vpa1b1:(p a1 b1))=>(notaa (c82_1119 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vpb1a2 Vpa1b1))). Qed. Lemma c82_1121: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2)->(p a1 b1)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))(Vpa1b1:(p a1 b1))=>((false_ind goal) (c82_1120 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vpb1a2 Vpa1b1))). Qed. Lemma c82_1124: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2)->(l a1b1 oa)->(p b1 ab) \/ (l a1b1 a2b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))=>((unique b1 ab a1b1 a2b2) (conj (c82_939 Vib2a1c1 Vib1a2c2 Via2b1c1) (conj (c82_1111 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vpb1a2) (conj (c82_963 Vib2a1c1 Vib1a2c2 Via2b1c1) (c82_964 Vib2a1c1 Vib1a2c2 Via2b1c1)))))). Qed. Lemma c82_1125: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2)->(l a1b1 oa)->(p b1 ab)->(p ab b1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1ab:(p b1 ab))=>((psym b1 ab) Vpb1ab)). Qed. Lemma c82_1130: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2)->(l a1b1 oa)->(p b1 ab)->(i ab a2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1ab:(p b1 ab))=>((pcon ab b1 a2c2) (conj (c82_1125 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vpb1a2 Vla1b1oa Vpb1ab) Vib1a2c2))). Qed. Lemma c82_1131: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2)->(l a1b1 oa)->(p b1 ab)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vpb1ab:(p b1 ab))=>((goal_normal a2c2) (conj (c82_976 Vib2a1c1 Vib1a2c2 Via2b1c1) (conj (c82_1082 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1) (conj (c82_962 Vib2a1c1 Vib1a2c2 Via2b1c1) (c82_1130 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vpb1a2 Vla1b1oa Vpb1ab)))))). Qed. Lemma c82_1132: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2)->(l a1b1 oa)->(l a1b1 a2b2)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1a2b2:(l a1b1 a2b2))=>(notab Vla1b1a2b2)). Qed. Lemma c82_1133: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2)->(l a1b1 oa)->(l a1b1 a2b2)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))(Vla1b1a2b2:(l a1b1 a2b2))=>((false_ind goal) (c82_1132 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vpb1a2 Vla1b1oa Vla1b1a2b2))). Qed. Lemma c82_1134: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2)->(l a1b1 oa)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))(Vla1b1oa:(l a1b1 oa))=>((or_ind ((c82_1131 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vpb1a2 Vla1b1oa))((c82_1133 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vpb1a2 Vla1b1oa)))(c82_1124 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vpb1a2 Vla1b1oa))). Qed. Lemma c82_1135: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(p b1 a2)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vpb1a2:(p b1 a2))=>((or_ind ((c82_1121 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vpb1a2))((c82_1134 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vpb1a2)))(c82_1115 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vpb1a2))). Qed. Lemma c82_1137: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(l a2c2 oa)->(l b1c1 oa). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vla2c2oa:(l a2c2 oa))=>((ltra b1c1 a2c2 oa) (conj (c82_1079 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1) Vla2c2oa))). Qed. Lemma c82_1143: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(l a2c2 oa)->(i c1 oa). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vla2c2oa:(l a2c2 oa))=>((lcon c1 b1c1 oa) (conj (c82_946 Vib2a1c1 Vib1a2c2 Via2b1c1) (c82_1137 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vla2c2oa)))). Qed. Lemma c82_1144: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(l a2c2 oa)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vla2c2oa:(l a2c2 oa))=>((triangle1 oa) (conj (c82_953 Vib2a1c1 Vib1a2c2 Via2b1c1) (conj (c82_1105 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o) (c82_1143 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vla2c2oa))))). Qed. Lemma c82_1145: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->(l a2c2 oa)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))(Vla2c2oa:(l a2c2 oa))=>((false_ind goal) (c82_1144 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o Vla2c2oa))). Qed. Lemma c82_1146: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(p b1 o)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vpb1o:(p b1 o))=>((or_ind ((c82_1135 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o))((c82_1145 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o)))(c82_1107 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vpb1o))). Qed. Lemma c82_1148: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(l a2c2 ob)->(l b1c1 ob). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vla2c2ob:(l a2c2 ob))=>((ltra b1c1 a2c2 ob) (conj (c82_1079 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1) Vla2c2ob))). Qed. Lemma c82_1152: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(l a2c2 ob)->(i a2 ob). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vla2c2ob:(l a2c2 ob))=>((lcon a2 b1c1 ob) (conj Via2b1c1 (c82_1148 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vla2c2ob)))). Qed. Lemma c82_1153: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(l a2c2 ob)->(i c2 ob). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vla2c2ob:(l a2c2 ob))=>((lcon c2 a2c2 ob) (conj (c82_945 Vib2a1c1 Vib1a2c2 Via2b1c1) Vla2c2ob))). Qed. Lemma c82_1154: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(l a2c2 ob)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vla2c2ob:(l a2c2 ob))=>((triangle2 ob) (conj (c82_1152 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vla2c2ob) (conj (c82_956 Vib2a1c1 Vib1a2c2 Via2b1c1) (c82_1153 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vla2c2ob))))). Qed. Lemma c82_1155: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->(l a2c2 ob)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))(Vla2c2ob:(l a2c2 ob))=>((false_ind goal) (c82_1154 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc Vla2c2ob))). Qed. Lemma c82_1156: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->(l a2c2 oc)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))(Vla2c2oc:(l a2c2 oc))=>((or_ind ((c82_1146 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc))((c82_1155 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc)))(c82_1103 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc Vla2c2oc))). Qed. Lemma c82_1157: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(p c2 bc)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vpc2bc:(p c2 bc))=>((or_ind ((c82_1095 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc))((c82_1156 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc)))(c82_1090 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vpc2bc))). Qed. Lemma c82_1159: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(l a2c2 b2c2)->(l b1c1 b2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vla2c2b2c2:(l a2c2 b2c2))=>((ltra b1c1 a2c2 b2c2) (conj (c82_1079 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1) Vla2c2b2c2))). Qed. Lemma c82_1160: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(l a2c2 b2c2)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vla2c2b2c2:(l a2c2 b2c2))=>(notbc (c82_1159 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vla2c2b2c2))). Qed. Lemma c82_1161: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->(l a2c2 b2c2)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))(Vla2c2b2c2:(l a2c2 b2c2))=>((false_ind goal) (c82_1160 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac Vla2c2b2c2))). Qed. Lemma c82_1162: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(p c1 ac)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vpc1ac:(p c1 ac))=>((or_ind ((c82_1157 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac))((c82_1161 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac)))(c82_1087 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vpc1ac))). Qed. Lemma c82_1163: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(l a1c1 b1c1)->(l b1c1 a1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vla1c1b1c1:(l a1c1 b1c1))=>((lsym a1c1 b1c1) Vla1c1b1c1)). Qed. Lemma c82_1164: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(l a1c1 b1c1)->(l a2c2 a1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vla1c1b1c1:(l a1c1 b1c1))=>((ltra a2c2 b1c1 a1c1) (conj Vla2c2b1c1 (c82_1163 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vla1c1b1c1)))). Qed. Lemma c82_1165: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(l a1c1 b1c1)->(l a1c1 a2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vla1c1b1c1:(l a1c1 b1c1))=>((lsym a2c2 a1c1) (c82_1164 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vla1c1b1c1))). Qed. Lemma c82_1166: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(l a1c1 b1c1)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vla1c1b1c1:(l a1c1 b1c1))=>(notac (c82_1165 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vla1c1b1c1))). Qed. Lemma c82_1167: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->(l a1c1 b1c1)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))(Vla1c1b1c1:(l a1c1 b1c1))=>((false_ind goal) (c82_1166 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1 Vla1c1b1c1))). Qed. Lemma c82_1168: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->(l a2c2 b1c1)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))(Vla2c2b1c1:(l a2c2 b1c1))=>((or_ind ((c82_1162 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1))((c82_1167 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1)))(c82_1084 Vib2a1c1 Vib1a2c2 Via2b1c1 Vla2c2b1c1))). Qed. Lemma c82_1169: (i b2 a1c1)->(i b1 a2c2)->(i a2 b1c1)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))(Via2b1c1:(i a2 b1c1))=>((or_ind ((c82_1078 Vib2a1c1 Vib1a2c2 Via2b1c1))((c82_1168 Vib2a1c1 Vib1a2c2 Via2b1c1)))(c82_984 Vib2a1c1 Vib1a2c2 Via2b1c1))). Qed. Lemma c82_1170: (i b2 a1c1)->(i b1 a2c2)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vib1a2c2:(i b1 a2c2))=>((or_ind ((c82_937 Vib2a1c1 Vib1a2c2))((c82_1169 Vib2a1c1 Vib1a2c2)))(c82_711 Vib2a1c1 Vib1a2c2))). Qed. Lemma c82_1171: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2) \/ (i a2 b1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))=>gap_c). Qed. Lemma c82_1172: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(i a1 a1b1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ia1b1). Qed. Lemma c82_1173: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(i b1 a1b1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ib1a1). Qed. Lemma c82_1174: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(i a2 a2b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ia2b2). Qed. Lemma c82_1175: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(i b2 a2b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ib2a2). Qed. Lemma c82_1176: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(i a1 a1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ia1c1). Qed. Lemma c82_1177: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(i c1 a1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ic1a1). Qed. Lemma c82_1178: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(i a2 a2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ia2c2). Qed. Lemma c82_1179: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(i c2 a2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ic2a2). Qed. Lemma c82_1180: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(i c1 b1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ic1b1). Qed. Lemma c82_1181: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(i b1 b1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ib1c1). Qed. Lemma c82_1182: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(i c2 b2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ic2b2). Qed. Lemma c82_1183: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(i b2 b2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ib2c2). Qed. Lemma c82_1184: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(i o oa). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>iooa). Qed. Lemma c82_1185: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(i o ob). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ioob). Qed. Lemma c82_1186: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(i o oc). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>iooc). Qed. Lemma c82_1187: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(i a1 oa). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ia1oa). Qed. Lemma c82_1188: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(i a2 oa). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ia2oa). Qed. Lemma c82_1189: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(i b1 ob). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ib1ob). Qed. Lemma c82_1190: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(i b2 ob). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ib2ob). Qed. Lemma c82_1191: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(i c1 oc). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ic1oc). Qed. Lemma c82_1192: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(i c2 oc). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ic2oc). Qed. Lemma c82_1193: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(i bc b1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ibc1). Qed. Lemma c82_1194: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(i bc b2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>ibc2). Qed. Lemma c82_1195: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(i ac a1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>iac1). Qed. Lemma c82_1196: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(i ac a2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>iac2). Qed. Lemma c82_1197: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(i ab a1b1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>iab1). Qed. Lemma c82_1198: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(i ab a2b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>iab2). Qed. Lemma c82_1211: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a2b2 a2b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>((lref c1 a2b2) Vic1a2b2)). Qed. Lemma c82_1218: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1) \/ (l a1c1 a2b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>((unique b2 c1 a1c1 a2b2) (conj Vib2a1c1 (conj (c82_1175 Vib2a1c1 Vic2a1b1 Vic1a2b2) (conj (c82_1177 Vib2a1c1 Vic2a1b1 Vic1a2b2) Vic1a2b2))))). Qed. Lemma c82_1219: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))=>((psym b2 c1) Vpb2c1)). Qed. Lemma c82_1222: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(i c1 b2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))=>((pcon c1 b2 b2c2) (conj (c82_1219 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1) (c82_1183 Vib2a1c1 Vic2a1b1 Vic1a2b2)))). Qed. Lemma c82_1223: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(i c1 ob). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))=>((pcon c1 b2 ob) (conj (c82_1219 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1) (c82_1190 Vib2a1c1 Vic2a1b1 Vic1a2b2)))). Qed. Lemma c82_1224: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc) \/ (l b1c1 b2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))=>((unique c1 bc b1c1 b2c2) (conj (c82_1180 Vib2a1c1 Vic2a1b1 Vic1a2b2) (conj (c82_1222 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1) (conj (c82_1193 Vib2a1c1 Vic2a1b1 Vic1a2b2) (c82_1194 Vib2a1c1 Vic2a1b1 Vic1a2b2)))))). Qed. Lemma c82_1225: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(p bc c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))=>((psym c1 bc) Vpc1bc)). Qed. Lemma c82_1228: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(i bc a2b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))=>((pcon bc c1 a2b2) (conj (c82_1225 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc) Vic1a2b2))). Qed. Lemma c82_1232: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(p c1 b1) \/ (l b1c1 ob). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))=>((unique c1 b1 b1c1 ob) (conj (c82_1180 Vib2a1c1 Vic2a1b1 Vic1a2b2) (conj (c82_1223 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1) (conj (c82_1181 Vib2a1c1 Vic2a1b1 Vic1a2b2) (c82_1189 Vib2a1c1 Vic2a1b1 Vic1a2b2)))))). Qed. Lemma c82_1234: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(p c1 b1)->(p b2 b1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vpc1b1:(p c1 b1))=>((ptra b2 c1 b1) (conj Vpb2c1 Vpc1b1))). Qed. Lemma c82_1235: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(p c1 b1)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vpc1b1:(p c1 b1))=>(notbb (c82_1234 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vpc1b1))). Qed. Lemma c82_1236: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(p c1 b1)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vpc1b1:(p c1 b1))=>((false_ind goal) (c82_1235 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vpc1b1))). Qed. Lemma c82_1237: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l ob b1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))=>((lsym b1c1 ob) Vlb1c1ob)). Qed. Lemma c82_1238: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(i o b1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))=>((lcon o ob b1c1) (conj (c82_1185 Vib2a1c1 Vic2a1b1 Vic1a2b2) (c82_1237 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob)))). Qed. Lemma c82_1239: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o) \/ (l b1c1 oc). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))=>((unique c1 o b1c1 oc) (conj (c82_1180 Vib2a1c1 Vic2a1b1 Vic1a2b2) (conj (c82_1191 Vib2a1c1 Vic2a1b1 Vic1a2b2) (conj (c82_1238 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob) (c82_1186 Vib2a1c1 Vic2a1b1 Vic1a2b2)))))). Qed. Lemma c82_1245: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(i c1 oa). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))=>((pcon c1 o oa) (conj Vpc1o (c82_1184 Vib2a1c1 Vic2a1b1 Vic1a2b2)))). Qed. Lemma c82_1246: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(i b2 oa). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))=>((pcon b2 c1 oa) (conj Vpb2c1 (c82_1245 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o)))). Qed. Lemma c82_1251: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(p b2 a1) \/ (l a1c1 oa). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))=>((unique b2 a1 a1c1 oa) (conj Vib2a1c1 (conj (c82_1246 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o) (conj (c82_1176 Vib2a1c1 Vic2a1b1 Vic1a2b2) (c82_1187 Vib2a1c1 Vic2a1b1 Vic1a2b2)))))). Qed. Lemma c82_1259: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(p b2 a1)->(i b2 a1b1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))(Vpb2a1:(p b2 a1))=>((pcon b2 a1 a1b1) (conj Vpb2a1 (c82_1172 Vib2a1c1 Vic2a1b1 Vic1a2b2)))). Qed. Lemma c82_1260: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(p b2 a1)->(i c1 a1b1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))(Vpb2a1:(p b2 a1))=>((pcon c1 b2 a1b1) (conj (c82_1219 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1) (c82_1259 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o Vpb2a1)))). Qed. Lemma c82_1261: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(p b2 a1)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))(Vpb2a1:(p b2 a1))=>((triangle1 a1b1) (conj (c82_1172 Vib2a1c1 Vic2a1b1 Vic1a2b2) (conj (c82_1173 Vib2a1c1 Vic2a1b1 Vic1a2b2) (c82_1260 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o Vpb2a1))))). Qed. Lemma c82_1262: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(p b2 a1)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))(Vpb2a1:(p b2 a1))=>((false_ind goal) (c82_1261 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o Vpb2a1))). Qed. Lemma c82_1263: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(l a1c1 oa)->(l oa a1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))(Vla1c1oa:(l a1c1 oa))=>((lsym a1c1 oa) Vla1c1oa)). Qed. Lemma c82_1264: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(l a1c1 oa)->(i a2 a1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))(Vla1c1oa:(l a1c1 oa))=>((lcon a2 oa a1c1) (conj (c82_1188 Vib2a1c1 Vic2a1b1 Vic1a2b2) (c82_1263 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o Vla1c1oa)))). Qed. Lemma c82_1266: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(l a1c1 oa)->(p b2 a2) \/ (l a1c1 a2b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))(Vla1c1oa:(l a1c1 oa))=>((unique b2 a2 a1c1 a2b2) (conj Vib2a1c1 (conj (c82_1175 Vib2a1c1 Vic2a1b1 Vic1a2b2) (conj (c82_1264 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o Vla1c1oa) (c82_1174 Vib2a1c1 Vic2a1b1 Vic1a2b2)))))). Qed. Lemma c82_1274: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(l a1c1 oa)->(p b2 a2)->(i b2 a2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))(Vla1c1oa:(l a1c1 oa))(Vpb2a2:(p b2 a2))=>((pcon b2 a2 a2c2) (conj Vpb2a2 (c82_1178 Vib2a1c1 Vic2a1b1 Vic1a2b2)))). Qed. Lemma c82_1275: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(l a1c1 oa)->(p b2 a2)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))(Vla1c1oa:(l a1c1 oa))(Vpb2a2:(p b2 a2))=>((triangle2 a2c2) (conj (c82_1178 Vib2a1c1 Vic2a1b1 Vic1a2b2) (conj (c82_1274 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o Vla1c1oa Vpb2a2) (c82_1179 Vib2a1c1 Vic2a1b1 Vic1a2b2))))). Qed. Lemma c82_1276: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(l a1c1 oa)->(p b2 a2)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))(Vla1c1oa:(l a1c1 oa))(Vpb2a2:(p b2 a2))=>((false_ind goal) (c82_1275 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o Vla1c1oa Vpb2a2))). Qed. Lemma c82_1281: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(l a1c1 oa)->(l a1c1 a2b2)->(i ac a2b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))(Vla1c1oa:(l a1c1 oa))(Vla1c1a2b2:(l a1c1 a2b2))=>((lcon ac a1c1 a2b2) (conj (c82_1195 Vib2a1c1 Vic2a1b1 Vic1a2b2) Vla1c1a2b2))). Qed. Lemma c82_1282: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(l a1c1 oa)->(l a1c1 a2b2)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))(Vla1c1oa:(l a1c1 oa))(Vla1c1a2b2:(l a1c1 a2b2))=>((goal_normal a2b2) (conj (c82_1211 Vib2a1c1 Vic2a1b1 Vic1a2b2) (conj (c82_1228 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc) (conj (c82_1281 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o Vla1c1oa Vla1c1a2b2) (c82_1198 Vib2a1c1 Vic2a1b1 Vic1a2b2)))))). Qed. Lemma c82_1283: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->(l a1c1 oa)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))(Vla1c1oa:(l a1c1 oa))=>((or_ind ((c82_1276 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o Vla1c1oa))((c82_1282 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o Vla1c1oa)))(c82_1266 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o Vla1c1oa))). Qed. Lemma c82_1284: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(p c1 o)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vpc1o:(p c1 o))=>((or_ind ((c82_1262 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o))((c82_1283 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o)))(c82_1251 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vpc1o))). Qed. Lemma c82_1288: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l b1c1 oc)->(i b1 oc). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vlb1c1oc:(l b1c1 oc))=>((lcon b1 b1c1 oc) (conj (c82_1181 Vib2a1c1 Vic2a1b1 Vic1a2b2) Vlb1c1oc))). Qed. Lemma c82_1291: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l b1c1 oc)->(p c2 b1) \/ (l a1b1 oc). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vlb1c1oc:(l b1c1 oc))=>((unique c2 b1 a1b1 oc) (conj Vic2a1b1 (conj (c82_1192 Vib2a1c1 Vic2a1b1 Vic1a2b2) (conj (c82_1173 Vib2a1c1 Vic2a1b1 Vic1a2b2) (c82_1288 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vlb1c1oc)))))). Qed. Lemma c82_1292: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l b1c1 oc)->(p c2 b1)->(p b1 c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vlb1c1oc:(l b1c1 oc))(Vpc2b1:(p c2 b1))=>((psym c2 b1) Vpc2b1)). Qed. Lemma c82_1294: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l b1c1 oc)->(p c2 b1)->(i b1 b2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vlb1c1oc:(l b1c1 oc))(Vpc2b1:(p c2 b1))=>((pcon b1 c2 b2c2) (conj (c82_1292 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vlb1c1oc Vpc2b1) (c82_1182 Vib2a1c1 Vic2a1b1 Vic1a2b2)))). Qed. Lemma c82_1295: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l b1c1 oc)->(p c2 b1)->(p c1 b1) \/ (l b1c1 b2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vlb1c1oc:(l b1c1 oc))(Vpc2b1:(p c2 b1))=>((unique c1 b1 b1c1 b2c2) (conj (c82_1180 Vib2a1c1 Vic2a1b1 Vic1a2b2) (conj (c82_1222 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1) (conj (c82_1181 Vib2a1c1 Vic2a1b1 Vic1a2b2) (c82_1294 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vlb1c1oc Vpc2b1)))))). Qed. Lemma c82_1297: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l b1c1 oc)->(p c2 b1)->(p c1 b1)->(p b2 b1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vlb1c1oc:(l b1c1 oc))(Vpc2b1:(p c2 b1))(Vpc1b1:(p c1 b1))=>((ptra b2 c1 b1) (conj Vpb2c1 Vpc1b1))). Qed. Lemma c82_1298: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l b1c1 oc)->(p c2 b1)->(p c1 b1)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vlb1c1oc:(l b1c1 oc))(Vpc2b1:(p c2 b1))(Vpc1b1:(p c1 b1))=>(notbb (c82_1297 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vlb1c1oc Vpc2b1 Vpc1b1))). Qed. Lemma c82_1299: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l b1c1 oc)->(p c2 b1)->(p c1 b1)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vlb1c1oc:(l b1c1 oc))(Vpc2b1:(p c2 b1))(Vpc1b1:(p c1 b1))=>((false_ind goal) (c82_1298 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vlb1c1oc Vpc2b1 Vpc1b1))). Qed. Lemma c82_1300: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l b1c1 oc)->(p c2 b1)->(l b1c1 b2c2)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vlb1c1oc:(l b1c1 oc))(Vpc2b1:(p c2 b1))(Vlb1c1b2c2:(l b1c1 b2c2))=>(notbc Vlb1c1b2c2)). Qed. Lemma c82_1301: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l b1c1 oc)->(p c2 b1)->(l b1c1 b2c2)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vlb1c1oc:(l b1c1 oc))(Vpc2b1:(p c2 b1))(Vlb1c1b2c2:(l b1c1 b2c2))=>((false_ind goal) (c82_1300 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vlb1c1oc Vpc2b1 Vlb1c1b2c2))). Qed. Lemma c82_1302: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l b1c1 oc)->(p c2 b1)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vlb1c1oc:(l b1c1 oc))(Vpc2b1:(p c2 b1))=>((or_ind ((c82_1299 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vlb1c1oc Vpc2b1))((c82_1301 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vlb1c1oc Vpc2b1)))(c82_1295 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vlb1c1oc Vpc2b1))). Qed. Lemma c82_1308: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l b1c1 oc)->(l a1b1 oc)->(i a1 oc). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vlb1c1oc:(l b1c1 oc))(Vla1b1oc:(l a1b1 oc))=>((lcon a1 a1b1 oc) (conj (c82_1172 Vib2a1c1 Vic2a1b1 Vic1a2b2) Vla1b1oc))). Qed. Lemma c82_1309: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l b1c1 oc)->(l a1b1 oc)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vlb1c1oc:(l b1c1 oc))(Vla1b1oc:(l a1b1 oc))=>((triangle1 oc) (conj (c82_1308 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vlb1c1oc Vla1b1oc) (conj (c82_1288 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vlb1c1oc) (c82_1191 Vib2a1c1 Vic2a1b1 Vic1a2b2))))). Qed. Lemma c82_1310: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l b1c1 oc)->(l a1b1 oc)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vlb1c1oc:(l b1c1 oc))(Vla1b1oc:(l a1b1 oc))=>((false_ind goal) (c82_1309 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vlb1c1oc Vla1b1oc))). Qed. Lemma c82_1311: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->(l b1c1 oc)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))(Vlb1c1oc:(l b1c1 oc))=>((or_ind ((c82_1302 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vlb1c1oc))((c82_1310 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vlb1c1oc)))(c82_1291 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob Vlb1c1oc))). Qed. Lemma c82_1312: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->(l b1c1 ob)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))(Vlb1c1ob:(l b1c1 ob))=>((or_ind ((c82_1284 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob))((c82_1311 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob)))(c82_1239 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc Vlb1c1ob))). Qed. Lemma c82_1313: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(p c1 bc)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))=>((or_ind ((c82_1236 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc))((c82_1312 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc)))(c82_1232 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vpc1bc))). Qed. Lemma c82_1314: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(l b1c1 b2c2)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vlb1c1b2c2:(l b1c1 b2c2))=>(notbc Vlb1c1b2c2)). Qed. Lemma c82_1315: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->(l b1c1 b2c2)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))(Vlb1c1b2c2:(l b1c1 b2c2))=>((false_ind goal) (c82_1314 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1 Vlb1c1b2c2))). Qed. Lemma c82_1316: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(p b2 c1)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vpb2c1:(p b2 c1))=>((or_ind ((c82_1313 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1))((c82_1315 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1)))(c82_1224 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vpb2c1))). Qed. Lemma c82_1317: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(l a2b2 a1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))=>((lsym a1c1 a2b2) Vla1c1a2b2)). Qed. Lemma c82_1320: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(i ac a2b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))=>((lcon ac a1c1 a2b2) (conj (c82_1195 Vib2a1c1 Vic2a1b1 Vic1a2b2) Vla1c1a2b2))). Qed. Lemma c82_1321: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(i ab a1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))=>((lcon ab a2b2 a1c1) (conj (c82_1198 Vib2a1c1 Vic2a1b1 Vic1a2b2) (c82_1317 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2)))). Qed. Lemma c82_1322: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab) \/ (l a1b1 a1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))=>((unique a1 ab a1b1 a1c1) (conj (c82_1172 Vib2a1c1 Vic2a1b1 Vic1a2b2) (conj (c82_1176 Vib2a1c1 Vic2a1b1 Vic1a2b2) (conj (c82_1197 Vib2a1c1 Vic2a1b1 Vic1a2b2) (c82_1321 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2)))))). Qed. Lemma c82_1323: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p ab a1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))=>((psym a1 ab) Vpa1ab)). Qed. Lemma c82_1324: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(i ab oa). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))=>((pcon ab a1 oa) (conj (c82_1323 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab) (c82_1187 Vib2a1c1 Vic2a1b1 Vic1a2b2)))). Qed. Lemma c82_1325: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac) \/ (l a2b2 a2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))=>((unique a2 ac a2b2 a2c2) (conj (c82_1174 Vib2a1c1 Vic2a1b1 Vic1a2b2) (conj (c82_1178 Vib2a1c1 Vic2a1b1 Vic1a2b2) (conj (c82_1320 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2) (c82_1196 Vib2a1c1 Vic2a1b1 Vic1a2b2)))))). Qed. Lemma c82_1328: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(p a2 ab) \/ (l a2b2 oa). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))=>((unique a2 ab a2b2 oa) (conj (c82_1174 Vib2a1c1 Vic2a1b1 Vic1a2b2) (conj (c82_1188 Vib2a1c1 Vic2a1b1 Vic1a2b2) (conj (c82_1198 Vib2a1c1 Vic2a1b1 Vic1a2b2) (c82_1324 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab)))))). Qed. Lemma c82_1329: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(p a2 ab)->(p ab a2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vpa2ab:(p a2 ab))=>((psym a2 ab) Vpa2ab)). Qed. Lemma c82_1330: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(p a2 ab)->(p a1 a2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vpa2ab:(p a2 ab))=>((ptra a1 ab a2) (conj Vpa1ab (c82_1329 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vpa2ab)))). Qed. Lemma c82_1331: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(p a2 ab)->(p a2 a1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vpa2ab:(p a2 ab))=>((psym a1 a2) (c82_1330 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vpa2ab))). Qed. Lemma c82_1332: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(p a2 ab)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vpa2ab:(p a2 ab))=>(notaa (c82_1331 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vpa2ab))). Qed. Lemma c82_1333: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(p a2 ab)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vpa2ab:(p a2 ab))=>((false_ind goal) (c82_1332 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vpa2ab))). Qed. Lemma c82_1335: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(l a1c1 oa). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))=>((ltra a1c1 a2b2 oa) (conj Vla1c1a2b2 Vla2b2oa))). Qed. Lemma c82_1336: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(l oa a1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))=>((lsym a1c1 oa) (c82_1335 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa))). Qed. Lemma c82_1340: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(i o a1c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))=>((lcon o oa a1c1) (conj (c82_1184 Vib2a1c1 Vic2a1b1 Vic1a2b2) (c82_1336 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa)))). Qed. Lemma c82_1341: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o) \/ (l a1c1 ob). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))=>((unique b2 o a1c1 ob) (conj Vib2a1c1 (conj (c82_1190 Vib2a1c1 Vic2a1b1 Vic1a2b2) (conj (c82_1340 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa) (c82_1185 Vib2a1c1 Vic2a1b1 Vic1a2b2)))))). Qed. Lemma c82_1343: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->(i b2 oc). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))=>((pcon b2 o oc) (conj Vpb2o (c82_1186 Vib2a1c1 Vic2a1b1 Vic1a2b2)))). Qed. Lemma c82_1345: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->(p b2 c1) \/ (l a1c1 oc). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))=>((unique b2 c1 a1c1 oc) (conj Vib2a1c1 (conj (c82_1343 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o) (conj (c82_1177 Vib2a1c1 Vic2a1b1 Vic1a2b2) (c82_1191 Vib2a1c1 Vic2a1b1 Vic1a2b2)))))). Qed. Lemma c82_1346: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->(p b2 c1)->(p c1 b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2c1:(p b2 c1))=>((psym b2 c1) Vpb2c1)). Qed. Lemma c82_1351: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->(p b2 c1)->(i c1 b2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2c1:(p b2 c1))=>((pcon c1 b2 b2c2) (conj (c82_1346 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o Vpb2c1) (c82_1183 Vib2a1c1 Vic2a1b1 Vic1a2b2)))). Qed. Lemma c82_1353: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->(p b2 c1)->(p c1 bc) \/ (l b1c1 b2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2c1:(p b2 c1))=>((unique c1 bc b1c1 b2c2) (conj (c82_1180 Vib2a1c1 Vic2a1b1 Vic1a2b2) (conj (c82_1351 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o Vpb2c1) (conj (c82_1193 Vib2a1c1 Vic2a1b1 Vic1a2b2) (c82_1194 Vib2a1c1 Vic2a1b1 Vic1a2b2)))))). Qed. Lemma c82_1354: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->(p b2 c1)->(p c1 bc)->(p bc c1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))=>((psym c1 bc) Vpc1bc)). Qed. Lemma c82_1359: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->(p b2 c1)->(p c1 bc)->(i bc a2b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))=>((pcon bc c1 a2b2) (conj (c82_1354 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o Vpb2c1 Vpc1bc) Vic1a2b2))). Qed. Lemma c82_1360: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->(p b2 c1)->(p c1 bc)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2c1:(p b2 c1))(Vpc1bc:(p c1 bc))=>((goal_normal a2b2) (conj (c82_1211 Vib2a1c1 Vic2a1b1 Vic1a2b2) (conj (c82_1359 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o Vpb2c1 Vpc1bc) (conj (c82_1320 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2) (c82_1198 Vib2a1c1 Vic2a1b1 Vic1a2b2)))))). Qed. Lemma c82_1361: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->(p b2 c1)->(l b1c1 b2c2)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2c1:(p b2 c1))(Vlb1c1b2c2:(l b1c1 b2c2))=>(notbc Vlb1c1b2c2)). Qed. Lemma c82_1362: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->(p b2 c1)->(l b1c1 b2c2)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2c1:(p b2 c1))(Vlb1c1b2c2:(l b1c1 b2c2))=>((false_ind goal) (c82_1361 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o Vpb2c1 Vlb1c1b2c2))). Qed. Lemma c82_1363: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->(p b2 c1)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vpb2c1:(p b2 c1))=>((or_ind ((c82_1360 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o Vpb2c1))((c82_1362 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o Vpb2c1)))(c82_1353 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o Vpb2c1))). Qed. Lemma c82_1365: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->(l a1c1 oc)->(l a2b2 oc). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vla1c1oc:(l a1c1 oc))=>((ltra a2b2 a1c1 oc) (conj (c82_1317 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2) Vla1c1oc))). Qed. Lemma c82_1369: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->(l a1c1 oc)->(i a2 oc). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vla1c1oc:(l a1c1 oc))=>((lcon a2 a2b2 oc) (conj (c82_1174 Vib2a1c1 Vic2a1b1 Vic1a2b2) (c82_1365 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o Vla1c1oc)))). Qed. Lemma c82_1370: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->(l a1c1 oc)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vla1c1oc:(l a1c1 oc))=>((triangle2 oc) (conj (c82_1369 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o Vla1c1oc) (conj (c82_1343 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o) (c82_1192 Vib2a1c1 Vic2a1b1 Vic1a2b2))))). Qed. Lemma c82_1371: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->(l a1c1 oc)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))(Vla1c1oc:(l a1c1 oc))=>((false_ind goal) (c82_1370 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o Vla1c1oc))). Qed. Lemma c82_1372: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(p b2 o)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vpb2o:(p b2 o))=>((or_ind ((c82_1363 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o))((c82_1371 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o)))(c82_1345 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vpb2o))). Qed. Lemma c82_1374: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(l a1c1 ob)->(l a2b2 ob). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vla1c1ob:(l a1c1 ob))=>((ltra a2b2 a1c1 ob) (conj (c82_1317 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2) Vla1c1ob))). Qed. Lemma c82_1378: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(l a1c1 ob)->(i c1 ob). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vla1c1ob:(l a1c1 ob))=>((lcon c1 a2b2 ob) (conj Vic1a2b2 (c82_1374 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vla1c1ob)))). Qed. Lemma c82_1381: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(l a1c1 ob)->(i a1 ob). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vla1c1ob:(l a1c1 ob))=>((lcon a1 a1c1 ob) (conj (c82_1176 Vib2a1c1 Vic2a1b1 Vic1a2b2) Vla1c1ob))). Qed. Lemma c82_1382: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(l a1c1 ob)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vla1c1ob:(l a1c1 ob))=>((triangle1 ob) (conj (c82_1381 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vla1c1ob) (conj (c82_1189 Vib2a1c1 Vic2a1b1 Vic1a2b2) (c82_1378 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vla1c1ob))))). Qed. Lemma c82_1383: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->(l a1c1 ob)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))(Vla1c1ob:(l a1c1 ob))=>((false_ind goal) (c82_1382 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa Vla1c1ob))). Qed. Lemma c82_1384: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->(l a2b2 oa)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))(Vla2b2oa:(l a2b2 oa))=>((or_ind ((c82_1372 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa))((c82_1383 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa)))(c82_1341 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac Vla2b2oa))). Qed. Lemma c82_1385: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(p a2 ac)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vpa2ac:(p a2 ac))=>((or_ind ((c82_1333 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac))((c82_1384 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac)))(c82_1328 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vpa2ac))). Qed. Lemma c82_1387: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(l a2b2 a2c2)->(l a1c1 a2c2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vla2b2a2c2:(l a2b2 a2c2))=>((ltra a1c1 a2b2 a2c2) (conj Vla1c1a2b2 Vla2b2a2c2))). Qed. Lemma c82_1388: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(l a2b2 a2c2)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vla2b2a2c2:(l a2b2 a2c2))=>(notac (c82_1387 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vla2b2a2c2))). Qed. Lemma c82_1389: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->(l a2b2 a2c2)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))(Vla2b2a2c2:(l a2b2 a2c2))=>((false_ind goal) (c82_1388 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab Vla2b2a2c2))). Qed. Lemma c82_1390: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(p a1 ab)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vpa1ab:(p a1 ab))=>((or_ind ((c82_1385 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab))((c82_1389 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab)))(c82_1325 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vpa1ab))). Qed. Lemma c82_1391: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(l a1b1 a1c1)->(l a1c1 a1b1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vla1b1a1c1:(l a1b1 a1c1))=>((lsym a1b1 a1c1) Vla1b1a1c1)). Qed. Lemma c82_1392: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(l a1b1 a1c1)->(l a2b2 a1b1). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vla1b1a1c1:(l a1b1 a1c1))=>((ltra a2b2 a1c1 a1b1) (conj (c82_1317 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2) (c82_1391 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vla1b1a1c1)))). Qed. Lemma c82_1393: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(l a1b1 a1c1)->(l a1b1 a2b2). Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vla1b1a1c1:(l a1b1 a1c1))=>((lsym a2b2 a1b1) (c82_1392 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vla1b1a1c1))). Qed. Lemma c82_1394: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(l a1b1 a1c1)->false. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vla1b1a1c1:(l a1b1 a1c1))=>(notab (c82_1393 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vla1b1a1c1))). Qed. Lemma c82_1395: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->(l a1b1 a1c1)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))(Vla1b1a1c1:(l a1b1 a1c1))=>((false_ind goal) (c82_1394 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2 Vla1b1a1c1))). Qed. Lemma c82_1396: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->(l a1c1 a2b2)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))(Vla1c1a2b2:(l a1c1 a2b2))=>((or_ind ((c82_1390 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2))((c82_1395 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2)))(c82_1322 Vib2a1c1 Vic2a1b1 Vic1a2b2 Vla1c1a2b2))). Qed. Lemma c82_1397: (i b2 a1c1)->(i c2 a1b1)->(i c1 a2b2)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Vic1a2b2:(i c1 a2b2))=>((or_ind ((c82_1316 Vib2a1c1 Vic2a1b1 Vic1a2b2))((c82_1396 Vib2a1c1 Vic2a1b1 Vic1a2b2)))(c82_1218 Vib2a1c1 Vic2a1b1 Vic1a2b2))). Qed. Lemma c82_1398: (i b2 a1c1)->(i c2 a1b1)->(i a2 b1c1)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))(Via2b1c1:(i a2 b1c1))=>(t2in1 (conj Via2b1c1 (conj Vib2a1c1 Vic2a1b1)))). Qed. Lemma c82_1399: (i b2 a1c1)->(i c2 a1b1)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))(Vic2a1b1:(i c2 a1b1))=>((or_ind ((c82_1397 Vib2a1c1 Vic2a1b1))((c82_1398 Vib2a1c1 Vic2a1b1)))(c82_1171 Vib2a1c1 Vic2a1b1))). Qed. Lemma c82_1400: (i b2 a1c1)->goal. Proof. exact (fun (Vib2a1c1:(i b2 a1c1))=>((or_ind ((c82_1170 Vib2a1c1))((c82_1399 Vib2a1c1)))(c82_710 Vib2a1c1))). Qed. Lemma c82_1401: goal. Proof. exact (((or_ind (c82_709)(c82_1400))c82_1)). Qed. Check c82_1401. End c82_.