%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWV164+1 : TPTP v8.1.0. Bugfixed v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n004.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Wed Jul 20 23:03:10 EDT 2022 % Result : Theorem 90.44s 90.70s % Output : Proof 90.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SWV164+1 : TPTP v8.1.0. Bugfixed v3.3.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.14/0.34 % Computer : n004.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Thu Jun 16 01:12:54 EDT 2022 % 0.14/0.35 % CPUTime : % 90.44/90.70 (* PROOF-FOUND *) % 90.44/90.70 % SZS status Theorem % 90.44/90.70 (* BEGIN-PROOF *) % 90.44/90.70 % SZS output start Proof % 90.44/90.70 Theorem cl5_nebula_norm_0014 : (((leq (n0) (pv10))/\((leq (pv10) (n135299))/\(forall A : zenon_U, (((leq (n0) A)/\(leq A (pred (pv10))))->((sum (n0) (n4) (a_select3 (q) A (tptp_sum_index))) = (n1))))))->(forall B : zenon_U, (((leq (n0) B)/\(leq B (tptp_minus_1)))->((a_select3 (q) (pv10) B) = (divide (divide (times (exp (divide (divide (times (minus (a_select2 (x) (pv10)) (a_select2 (mu) B)) (minus (a_select2 (x) (pv10)) (a_select2 (mu) B))) (tptp_minus_2)) (times (a_select2 (sigma) B) (a_select2 (sigma) B)))) (a_select2 (rho) B)) (times (sqrt (times (n2) (tptp_pi))) (a_select2 (sigma) B))) (sum (n0) (n4) (divide (times (exp (divide (divide (times (minus (a_select2 (x) (pv10)) (a_select2 (mu) (tptp_sum_index))) (minus (a_select2 (x) (pv10)) (a_select2 (mu) (tptp_sum_index)))) (tptp_minus_2)) (times (a_select2 (sigma) (tptp_sum_index)) (a_select2 (sigma) (tptp_sum_index))))) (a_select2 (rho) (tptp_sum_index))) (times (sqrt (times (n2) (tptp_pi))) (a_select2 (sigma) (tptp_sum_index)))))))))). % 90.44/90.70 Proof. % 90.44/90.70 assert (zenon_L1_ : (~((n3) = (n3))) -> False). % 90.44/90.70 do 0 intro. intros zenon_H64. % 90.44/90.70 apply zenon_H64. apply refl_equal. % 90.44/90.70 (* end of lemma zenon_L1_ *) % 90.44/90.70 assert (zenon_L2_ : (~((n2) = (n2))) -> False). % 90.44/90.70 do 0 intro. intros zenon_H65. % 90.44/90.70 apply zenon_H65. apply refl_equal. % 90.44/90.70 (* end of lemma zenon_L2_ *) % 90.44/90.70 assert (zenon_L3_ : (~((n1) = (n1))) -> False). % 90.44/90.70 do 0 intro. intros zenon_H66. % 90.44/90.70 apply zenon_H66. apply refl_equal. % 90.44/90.70 (* end of lemma zenon_L3_ *) % 90.44/90.70 assert (zenon_L4_ : (~((n0) = (n0))) -> False). % 90.44/90.70 do 0 intro. intros zenon_H67. % 90.44/90.70 apply zenon_H67. apply refl_equal. % 90.44/90.70 (* end of lemma zenon_L4_ *) % 90.44/90.70 assert (zenon_L5_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (~(leq (n0) zenon_TB_ec)) -> False). % 90.44/90.70 do 1 intro. intros zenon_H68 zenon_H69. % 90.44/90.70 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H6b. % 90.44/90.70 generalize (zenon_H6b zenon_TB_ec). zenon_intro zenon_H6c. % 90.44/90.70 apply (zenon_equiv_s _ _ zenon_H6c); [ zenon_intro zenon_H69; zenon_intro zenon_H6e | zenon_intro zenon_H6d; zenon_intro zenon_H68 ]. % 90.44/90.70 exact (zenon_H6e zenon_H68). % 90.44/90.70 exact (zenon_H69 zenon_H6d). % 90.44/90.70 (* end of lemma zenon_L5_ *) % 90.44/90.70 assert (zenon_L6_ : (~((n4) = (n4))) -> False). % 90.44/90.70 do 0 intro. intros zenon_H6f. % 90.44/90.70 apply zenon_H6f. apply refl_equal. % 90.44/90.70 (* end of lemma zenon_L6_ *) % 90.44/90.70 assert (zenon_L7_ : (~(gt (n1) (succ (tptp_minus_1)))) -> False). % 90.44/90.70 do 0 intro. intros zenon_H70. % 90.44/90.70 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 90.44/90.70 cut ((gt (n1) (n0)) = (gt (n1) (succ (tptp_minus_1)))). % 90.44/90.70 intro zenon_D_pnotp. % 90.44/90.70 apply zenon_H70. % 90.44/90.70 rewrite <- zenon_D_pnotp. % 90.44/90.70 exact gt_1_0. % 90.44/90.70 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.44/90.70 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.44/90.70 congruence. % 90.44/90.70 apply zenon_H66. apply refl_equal. % 90.44/90.70 exact (zenon_H72 zenon_H71). % 90.44/90.70 apply zenon_H72. apply sym_equal. exact succ_tptp_minus_1. % 90.44/90.70 (* end of lemma zenon_L7_ *) % 90.44/90.70 assert (zenon_L8_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n2) (succ (tptp_minus_1)))) -> False). % 90.44/90.70 do 0 intro. intros zenon_H73 zenon_H74. % 90.44/90.70 elim (classic (gt (n1) (succ (tptp_minus_1)))); [ zenon_intro zenon_H75 | zenon_intro zenon_H70 ]. % 90.44/90.70 generalize (zenon_H73 (n2)). zenon_intro zenon_H76. % 90.44/90.70 generalize (zenon_H76 (n1)). zenon_intro zenon_H77. % 90.44/90.70 generalize (zenon_H77 (succ (tptp_minus_1))). zenon_intro zenon_H78. % 90.44/90.70 apply (zenon_imply_s _ _ zenon_H78); [ zenon_intro zenon_H7a | zenon_intro zenon_H79 ]. % 90.44/90.70 exact (zenon_H7a gt_2_1). % 90.44/90.70 apply (zenon_imply_s _ _ zenon_H79); [ zenon_intro zenon_H70 | zenon_intro zenon_H7b ]. % 90.44/90.70 exact (zenon_H70 zenon_H75). % 90.44/90.70 exact (zenon_H74 zenon_H7b). % 90.44/90.70 apply (zenon_L7_); trivial. % 90.44/90.70 (* end of lemma zenon_L8_ *) % 90.44/90.70 assert (zenon_L9_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n3) (succ (tptp_minus_1)))) -> False). % 90.44/90.70 do 0 intro. intros zenon_H73 zenon_H7c. % 90.44/90.70 elim (classic (gt (n2) (succ (tptp_minus_1)))); [ zenon_intro zenon_H7b | zenon_intro zenon_H74 ]. % 90.44/90.70 generalize (zenon_H73 (n3)). zenon_intro zenon_H7d. % 90.44/90.70 generalize (zenon_H7d (n2)). zenon_intro zenon_H7e. % 90.44/90.70 generalize (zenon_H7e (succ (tptp_minus_1))). zenon_intro zenon_H7f. % 90.44/90.70 apply (zenon_imply_s _ _ zenon_H7f); [ zenon_intro zenon_H81 | zenon_intro zenon_H80 ]. % 90.44/90.70 exact (zenon_H81 gt_3_2). % 90.44/90.70 apply (zenon_imply_s _ _ zenon_H80); [ zenon_intro zenon_H74 | zenon_intro zenon_H82 ]. % 90.44/90.70 exact (zenon_H74 zenon_H7b). % 90.44/90.70 exact (zenon_H7c zenon_H82). % 90.44/90.70 apply (zenon_L8_); trivial. % 90.44/90.70 (* end of lemma zenon_L9_ *) % 90.44/90.70 assert (zenon_L10_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n4) (succ (tptp_minus_1)))) -> False). % 90.44/90.70 do 0 intro. intros zenon_H73 zenon_H83. % 90.44/90.70 elim (classic (gt (n3) (succ (tptp_minus_1)))); [ zenon_intro zenon_H82 | zenon_intro zenon_H7c ]. % 90.44/90.70 generalize (zenon_H73 (n4)). zenon_intro zenon_H84. % 90.44/90.70 generalize (zenon_H84 (n3)). zenon_intro zenon_H85. % 90.44/90.70 generalize (zenon_H85 (succ (tptp_minus_1))). zenon_intro zenon_H86. % 90.44/90.70 apply (zenon_imply_s _ _ zenon_H86); [ zenon_intro zenon_H88 | zenon_intro zenon_H87 ]. % 90.44/90.70 exact (zenon_H88 gt_4_3). % 90.44/90.70 apply (zenon_imply_s _ _ zenon_H87); [ zenon_intro zenon_H7c | zenon_intro zenon_H89 ]. % 90.44/90.70 exact (zenon_H7c zenon_H82). % 90.44/90.70 exact (zenon_H83 zenon_H89). % 90.44/90.70 apply (zenon_L9_); trivial. % 90.44/90.70 (* end of lemma zenon_L10_ *) % 90.44/90.70 assert (zenon_L11_ : (~((succ (n3)) = (succ (succ (succ (succ (n0))))))) -> False). % 90.44/90.70 do 0 intro. intros zenon_H8a. % 90.44/90.70 cut (((n3) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 90.44/90.70 congruence. % 90.44/90.70 apply zenon_H8b. apply sym_equal. exact successor_3. % 90.44/90.70 (* end of lemma zenon_L11_ *) % 90.44/90.70 assert (zenon_L12_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n3)) (succ (tptp_minus_1)))) -> False). % 90.44/90.70 do 0 intro. intros zenon_H73 zenon_H8c. % 90.44/90.70 elim (classic (gt (n4) (succ (tptp_minus_1)))); [ zenon_intro zenon_H89 | zenon_intro zenon_H83 ]. % 90.44/90.70 elim (classic (gt (succ (succ (succ (succ (n0))))) (succ (tptp_minus_1)))); [ zenon_intro zenon_H8d | zenon_intro zenon_H8e ]. % 90.44/90.70 cut ((gt (succ (succ (succ (succ (n0))))) (succ (tptp_minus_1))) = (gt (succ (n3)) (succ (tptp_minus_1)))). % 90.44/90.70 intro zenon_D_pnotp. % 90.44/90.70 apply zenon_H8c. % 90.44/90.70 rewrite <- zenon_D_pnotp. % 90.44/90.70 exact zenon_H8d. % 90.44/90.70 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.44/90.70 cut (((succ (succ (succ (succ (n0))))) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_H90]. % 90.44/90.70 congruence. % 90.44/90.70 elim (classic ((succ (n3)) = (succ (n3)))); [ zenon_intro zenon_H91 | zenon_intro zenon_H92 ]. % 90.44/90.70 cut (((succ (n3)) = (succ (n3))) = ((succ (succ (succ (succ (n0))))) = (succ (n3)))). % 90.44/90.70 intro zenon_D_pnotp. % 90.44/90.70 apply zenon_H90. % 90.44/90.70 rewrite <- zenon_D_pnotp. % 90.44/90.70 exact zenon_H91. % 90.44/90.70 cut (((succ (n3)) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_H92]. % 90.44/90.70 cut (((succ (n3)) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_H8a]. % 90.44/90.70 congruence. % 90.44/90.70 apply (zenon_L11_); trivial. % 90.44/90.70 apply zenon_H92. apply refl_equal. % 90.44/90.70 apply zenon_H92. apply refl_equal. % 90.44/90.70 apply zenon_H8f. apply refl_equal. % 90.44/90.70 cut ((gt (n4) (succ (tptp_minus_1))) = (gt (succ (succ (succ (succ (n0))))) (succ (tptp_minus_1)))). % 90.44/90.70 intro zenon_D_pnotp. % 90.44/90.70 apply zenon_H8e. % 90.44/90.70 rewrite <- zenon_D_pnotp. % 90.44/90.70 exact zenon_H89. % 90.44/90.70 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.44/90.70 cut (((n4) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_H93]. % 90.44/90.70 congruence. % 90.44/90.70 elim (classic ((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0))))))); [ zenon_intro zenon_H94 | zenon_intro zenon_H95 ]. % 90.44/90.70 cut (((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0)))))) = ((n4) = (succ (succ (succ (succ (n0))))))). % 90.44/90.70 intro zenon_D_pnotp. % 90.44/90.70 apply zenon_H93. % 90.44/90.70 rewrite <- zenon_D_pnotp. % 90.44/90.70 exact zenon_H94. % 90.44/90.70 cut (((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_H95]. % 90.44/90.70 cut (((succ (succ (succ (succ (n0))))) = (n4))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 90.44/90.70 congruence. % 90.44/90.70 exact (zenon_H96 successor_4). % 90.44/90.70 apply zenon_H95. apply refl_equal. % 90.44/90.70 apply zenon_H95. apply refl_equal. % 90.44/90.70 apply zenon_H8f. apply refl_equal. % 90.44/90.70 apply (zenon_L10_); trivial. % 90.44/90.70 (* end of lemma zenon_L12_ *) % 90.44/90.70 assert (zenon_L13_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(leq zenon_TB_ec (n3))) -> False). % 90.44/90.70 do 1 intro. intros zenon_H73 zenon_H97 zenon_H98. % 90.44/90.70 generalize (leq_succ_gt_equiv zenon_TB_ec). zenon_intro zenon_H99. % 90.44/90.70 generalize (zenon_H99 (n3)). zenon_intro zenon_H9a. % 90.44/90.70 apply (zenon_equiv_s _ _ zenon_H9a); [ zenon_intro zenon_H98; zenon_intro zenon_H9d | zenon_intro zenon_H9c; zenon_intro zenon_H9b ]. % 90.44/90.70 elim (classic ((~((succ (n3)) = (succ (tptp_minus_1))))/\(~(gt (succ (n3)) (succ (tptp_minus_1)))))); [ zenon_intro zenon_H9e | zenon_intro zenon_H9f ]. % 90.44/90.70 apply (zenon_and_s _ _ zenon_H9e). zenon_intro zenon_Ha0. zenon_intro zenon_H8c. % 90.44/90.70 apply (zenon_L12_); trivial. % 90.44/90.70 cut ((gt (succ (tptp_minus_1)) zenon_TB_ec) = (gt (succ (n3)) zenon_TB_ec)). % 90.44/90.70 intro zenon_D_pnotp. % 90.44/90.70 apply zenon_H9d. % 90.44/90.70 rewrite <- zenon_D_pnotp. % 90.44/90.70 exact zenon_H97. % 90.44/90.70 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.44/90.70 cut (((succ (tptp_minus_1)) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 90.44/90.70 congruence. % 90.44/90.70 apply (zenon_notand_s _ _ zenon_H9f); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Ha3 ]. % 90.44/90.70 apply zenon_Ha4. zenon_intro zenon_Ha5. % 90.44/90.70 elim (classic ((succ (n3)) = (succ (n3)))); [ zenon_intro zenon_H91 | zenon_intro zenon_H92 ]. % 90.44/90.70 cut (((succ (n3)) = (succ (n3))) = ((succ (tptp_minus_1)) = (succ (n3)))). % 90.44/90.70 intro zenon_D_pnotp. % 90.44/90.70 apply zenon_Ha2. % 90.44/90.70 rewrite <- zenon_D_pnotp. % 90.44/90.70 exact zenon_H91. % 90.44/90.70 cut (((succ (n3)) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_H92]. % 90.44/90.70 cut (((succ (n3)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 90.44/90.70 congruence. % 90.44/90.70 exact (zenon_Ha0 zenon_Ha5). % 90.44/90.70 apply zenon_H92. apply refl_equal. % 90.44/90.70 apply zenon_H92. apply refl_equal. % 90.44/90.70 apply zenon_Ha3. zenon_intro zenon_Ha6. % 90.44/90.70 generalize (zenon_H73 (succ (n3))). zenon_intro zenon_Ha7. % 90.44/90.70 generalize (zenon_Ha7 (succ (tptp_minus_1))). zenon_intro zenon_Ha8. % 90.44/90.70 generalize (zenon_Ha8 zenon_TB_ec). zenon_intro zenon_Ha9. % 90.44/90.70 apply (zenon_imply_s _ _ zenon_Ha9); [ zenon_intro zenon_H8c | zenon_intro zenon_Haa ]. % 90.44/90.70 exact (zenon_H8c zenon_Ha6). % 90.44/90.70 apply (zenon_imply_s _ _ zenon_Haa); [ zenon_intro zenon_Hab | zenon_intro zenon_H9b ]. % 90.44/90.70 exact (zenon_Hab zenon_H97). % 90.44/90.70 exact (zenon_H9d zenon_H9b). % 90.44/90.70 apply zenon_Ha1. apply refl_equal. % 90.44/90.70 exact (zenon_H98 zenon_H9c). % 90.44/90.70 (* end of lemma zenon_L13_ *) % 90.44/90.70 assert (zenon_L14_ : forall (zenon_TB_ec : zenon_U), (~(gt (succ (tptp_minus_1)) (n1))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (zenon_TB_ec = (n1)) -> False). % 90.44/90.70 do 1 intro. intros zenon_Hac zenon_H97 zenon_Had. % 90.44/90.70 cut ((gt (succ (tptp_minus_1)) zenon_TB_ec) = (gt (succ (tptp_minus_1)) (n1))). % 90.44/90.70 intro zenon_D_pnotp. % 90.44/90.70 apply zenon_Hac. % 90.44/90.70 rewrite <- zenon_D_pnotp. % 90.44/90.70 exact zenon_H97. % 90.44/90.70 cut ((zenon_TB_ec = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hae]. % 90.44/90.70 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.44/90.70 congruence. % 90.44/90.70 apply zenon_H8f. apply refl_equal. % 90.44/90.70 exact (zenon_Hae zenon_Had). % 90.44/90.70 (* end of lemma zenon_L14_ *) % 90.44/90.70 assert (zenon_L15_ : (~(gt (succ (n0)) (succ (tptp_minus_1)))) -> False). % 90.52/90.70 do 0 intro. intros zenon_Haf. % 90.52/90.70 elim (classic (gt (n1) (succ (tptp_minus_1)))); [ zenon_intro zenon_H75 | zenon_intro zenon_H70 ]. % 90.52/90.70 cut ((gt (n1) (succ (tptp_minus_1))) = (gt (succ (n0)) (succ (tptp_minus_1)))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_Haf. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_H75. % 90.52/90.70 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.70 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 90.52/90.70 congruence. % 90.52/90.70 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 90.52/90.70 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_Hb0. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_Hb1. % 90.52/90.70 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.70 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.70 congruence. % 90.52/90.70 exact (zenon_Hb3 successor_1). % 90.52/90.70 apply zenon_Hb2. apply refl_equal. % 90.52/90.70 apply zenon_Hb2. apply refl_equal. % 90.52/90.70 apply zenon_H8f. apply refl_equal. % 90.52/90.70 apply (zenon_L7_); trivial. % 90.52/90.70 (* end of lemma zenon_L15_ *) % 90.52/90.70 assert (zenon_L16_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n0))) -> (~(zenon_TB_ec = (n1))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> False). % 90.52/90.70 do 1 intro. intros zenon_H73 zenon_H68 zenon_H97 zenon_Hb4 zenon_Hae zenon_Hb5 zenon_Hb6. % 90.52/90.70 generalize (finite_domain_3 zenon_TB_ec). zenon_intro zenon_Hb7. % 90.52/90.70 apply (zenon_imply_s _ _ zenon_Hb7); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 90.52/90.70 apply (zenon_notand_s _ _ zenon_Hb9); [ zenon_intro zenon_H69 | zenon_intro zenon_H98 ]. % 90.52/90.70 apply (zenon_L5_ zenon_TB_ec); trivial. % 90.52/90.70 apply (zenon_L13_ zenon_TB_ec); trivial. % 90.52/90.70 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 90.52/90.70 exact (zenon_Hb4 zenon_Hbb). % 90.52/90.70 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_Had | zenon_intro zenon_Hbc ]. % 90.52/90.70 exact (zenon_Hae zenon_Had). % 90.52/90.70 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hbd ]. % 90.52/90.70 exact (zenon_Hb5 zenon_Hbe). % 90.52/90.70 exact (zenon_Hb6 zenon_Hbd). % 90.52/90.70 (* end of lemma zenon_L16_ *) % 90.52/90.70 assert (zenon_L17_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (n0))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n1))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> False). % 90.52/90.70 do 1 intro. intros zenon_H73 zenon_Hbf zenon_H68 zenon_H97 zenon_Hae zenon_Hb5 zenon_Hb6. % 90.52/90.70 elim (classic (zenon_TB_ec = (n0))); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hb4 ]. % 90.52/90.70 cut ((gt (succ (tptp_minus_1)) zenon_TB_ec) = (gt (succ (tptp_minus_1)) (n0))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_Hbf. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_H97. % 90.52/90.70 cut ((zenon_TB_ec = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hb4]. % 90.52/90.70 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.70 congruence. % 90.52/90.70 apply zenon_H8f. apply refl_equal. % 90.52/90.70 exact (zenon_Hb4 zenon_Hbb). % 90.52/90.70 apply (zenon_L16_ zenon_TB_ec); trivial. % 90.52/90.70 (* end of lemma zenon_L17_ *) % 90.52/90.70 assert (zenon_L18_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n1))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> (~(gt (succ (tptp_minus_1)) (succ (tptp_minus_1)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.70 do 1 intro. intros zenon_H68 zenon_H97 zenon_Hae zenon_Hb5 zenon_Hb6 zenon_Hc0 zenon_H73. % 90.52/90.70 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 90.52/90.70 elim (classic (gt (succ (tptp_minus_1)) (n0))); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hbf ]. % 90.52/90.70 cut ((gt (succ (tptp_minus_1)) (n0)) = (gt (succ (tptp_minus_1)) (succ (tptp_minus_1)))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_Hc0. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_Hc1. % 90.52/90.70 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.70 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.70 congruence. % 90.52/90.70 apply zenon_H8f. apply refl_equal. % 90.52/90.70 exact (zenon_H72 zenon_H71). % 90.52/90.70 apply (zenon_L17_ zenon_TB_ec); trivial. % 90.52/90.70 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.70 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_H72. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_Hc2. % 90.52/90.70 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.70 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.70 congruence. % 90.52/90.70 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.70 apply zenon_H8f. apply refl_equal. % 90.52/90.70 apply zenon_H8f. apply refl_equal. % 90.52/90.70 (* end of lemma zenon_L18_ *) % 90.52/90.70 assert (zenon_L19_ : forall (zenon_TB_ec : zenon_U), (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n1))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (~(gt zenon_TB_ec (succ (tptp_minus_1)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.70 do 1 intro. intros zenon_Hb6 zenon_Hb5 zenon_Hae zenon_H97 zenon_H68 zenon_Hc4 zenon_H73. % 90.52/90.70 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 90.52/90.70 elim (classic (gt (succ (tptp_minus_1)) (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hc0 ]. % 90.52/90.70 elim (classic (gt (n0) (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hc7 ]. % 90.52/90.70 cut ((gt (n0) (succ (tptp_minus_1))) = (gt zenon_TB_ec (succ (tptp_minus_1)))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_Hc4. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_Hc6. % 90.52/90.70 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.70 cut (((n0) = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Hc8]. % 90.52/90.70 congruence. % 90.52/90.70 elim (classic (zenon_TB_ec = zenon_TB_ec)); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Ha1 ]. % 90.52/90.70 cut ((zenon_TB_ec = zenon_TB_ec) = ((n0) = zenon_TB_ec)). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_Hc8. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_Hc9. % 90.52/90.70 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.70 cut ((zenon_TB_ec = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hb4]. % 90.52/90.70 congruence. % 90.52/90.70 apply (zenon_L16_ zenon_TB_ec); trivial. % 90.52/90.70 apply zenon_Ha1. apply refl_equal. % 90.52/90.70 apply zenon_Ha1. apply refl_equal. % 90.52/90.70 apply zenon_H8f. apply refl_equal. % 90.52/90.70 cut ((gt (succ (tptp_minus_1)) (succ (tptp_minus_1))) = (gt (n0) (succ (tptp_minus_1)))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_Hc7. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_Hc5. % 90.52/90.70 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.70 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.70 congruence. % 90.52/90.70 elim (classic ((n0) = (n0))); [ zenon_intro zenon_Hca | zenon_intro zenon_H67 ]. % 90.52/90.70 cut (((n0) = (n0)) = ((succ (tptp_minus_1)) = (n0))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_Hc3. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_Hca. % 90.52/90.70 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.70 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.70 congruence. % 90.52/90.70 exact (zenon_H72 zenon_H71). % 90.52/90.70 apply zenon_H67. apply refl_equal. % 90.52/90.70 apply zenon_H67. apply refl_equal. % 90.52/90.70 apply zenon_H8f. apply refl_equal. % 90.52/90.70 apply (zenon_L18_ zenon_TB_ec); trivial. % 90.52/90.70 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.70 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_H72. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_Hc2. % 90.52/90.70 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.70 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.70 congruence. % 90.52/90.70 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.70 apply zenon_H8f. apply refl_equal. % 90.52/90.70 apply zenon_H8f. apply refl_equal. % 90.52/90.70 (* end of lemma zenon_L19_ *) % 90.52/90.70 assert (zenon_L20_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt zenon_TB_ec (n0))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n1))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.70 do 1 intro. intros zenon_H73 zenon_Hcb zenon_Hb6 zenon_Hb5 zenon_Hae zenon_H97 zenon_H68. % 90.52/90.70 elim (classic (gt zenon_TB_ec (succ (tptp_minus_1)))); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hc4 ]. % 90.52/90.70 cut ((gt zenon_TB_ec (succ (tptp_minus_1))) = (gt zenon_TB_ec (n0))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_Hcb. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_Hcc. % 90.52/90.70 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.70 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.70 congruence. % 90.52/90.70 apply zenon_Ha1. apply refl_equal. % 90.52/90.70 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.70 apply (zenon_L19_ zenon_TB_ec); trivial. % 90.52/90.70 (* end of lemma zenon_L20_ *) % 90.52/90.70 assert (zenon_L21_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (sum (n0) (tptp_minus_1) zenon_E))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n1))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.70 do 1 intro. intros zenon_H73 zenon_Hcd zenon_Hce zenon_Hb6 zenon_Hb5 zenon_Hae zenon_H97 zenon_H68. % 90.52/90.70 elim (classic (gt zenon_TB_ec (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd0 ]. % 90.52/90.70 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.70 generalize (zenon_Hd1 zenon_TB_ec). zenon_intro zenon_Hd2. % 90.52/90.70 generalize (zenon_Hd2 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_Hd3. % 90.52/90.70 apply (zenon_imply_s _ _ zenon_Hd3); [ zenon_intro zenon_Hab | zenon_intro zenon_Hd4 ]. % 90.52/90.70 exact (zenon_Hab zenon_H97). % 90.52/90.70 apply (zenon_imply_s _ _ zenon_Hd4); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hd5 ]. % 90.52/90.70 exact (zenon_Hd0 zenon_Hcf). % 90.52/90.70 exact (zenon_Hcd zenon_Hd5). % 90.52/90.70 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 90.52/90.70 elim (classic (gt zenon_TB_ec (n0))); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hcb ]. % 90.52/90.70 cut ((gt zenon_TB_ec (n0)) = (gt zenon_TB_ec (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_Hd0. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_Hd8. % 90.52/90.70 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 90.52/90.70 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.70 congruence. % 90.52/90.70 apply zenon_Ha1. apply refl_equal. % 90.52/90.70 exact (zenon_Hd7 zenon_Hd6). % 90.52/90.70 apply (zenon_L20_ zenon_TB_ec); trivial. % 90.52/90.70 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd9 | zenon_intro zenon_Hda ]. % 90.52/90.70 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_Hd7. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_Hd9. % 90.52/90.70 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.70 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 90.52/90.70 congruence. % 90.52/90.70 exact (zenon_Hdb zenon_Hce). % 90.52/90.70 apply zenon_Hda. apply refl_equal. % 90.52/90.70 apply zenon_Hda. apply refl_equal. % 90.52/90.70 (* end of lemma zenon_L21_ *) % 90.52/90.70 assert (zenon_L22_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n1))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.70 do 1 intro. intros zenon_H73 zenon_Hdc zenon_Hce zenon_Hb6 zenon_Hb5 zenon_Hae zenon_H97 zenon_H68. % 90.52/90.70 elim (classic (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hde ]. % 90.52/90.70 cut ((gt (n0) (sum (n0) (tptp_minus_1) zenon_E)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_Hdc. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_Hdd. % 90.52/90.70 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.70 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 90.52/90.70 congruence. % 90.52/90.70 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd9 | zenon_intro zenon_Hda ]. % 90.52/90.70 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_Hd7. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_Hd9. % 90.52/90.70 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.70 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 90.52/90.70 congruence. % 90.52/90.70 exact (zenon_Hdb zenon_Hce). % 90.52/90.70 apply zenon_Hda. apply refl_equal. % 90.52/90.70 apply zenon_Hda. apply refl_equal. % 90.52/90.70 apply zenon_Hda. apply refl_equal. % 90.52/90.70 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 90.52/90.70 elim (classic (gt (succ (tptp_minus_1)) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd5 | zenon_intro zenon_Hcd ]. % 90.52/90.70 cut ((gt (succ (tptp_minus_1)) (sum (n0) (tptp_minus_1) zenon_E)) = (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_Hde. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_Hd5. % 90.52/90.70 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.70 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.70 congruence. % 90.52/90.70 elim (classic ((n0) = (n0))); [ zenon_intro zenon_Hca | zenon_intro zenon_H67 ]. % 90.52/90.70 cut (((n0) = (n0)) = ((succ (tptp_minus_1)) = (n0))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_Hc3. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_Hca. % 90.52/90.70 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.70 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.70 congruence. % 90.52/90.70 exact (zenon_H72 zenon_H71). % 90.52/90.70 apply zenon_H67. apply refl_equal. % 90.52/90.70 apply zenon_H67. apply refl_equal. % 90.52/90.70 apply zenon_Hda. apply refl_equal. % 90.52/90.70 apply (zenon_L21_ zenon_TB_ec); trivial. % 90.52/90.70 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.70 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_H72. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_Hc2. % 90.52/90.70 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.70 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.70 congruence. % 90.52/90.70 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.70 apply zenon_H8f. apply refl_equal. % 90.52/90.70 apply zenon_H8f. apply refl_equal. % 90.52/90.70 (* end of lemma zenon_L22_ *) % 90.52/90.70 assert (zenon_L23_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n1))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (n0))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False). % 90.52/90.70 do 1 intro. intros zenon_H68 zenon_H97 zenon_Hae zenon_Hb5 zenon_Hb6 zenon_H73 zenon_Hdf zenon_Hce. % 90.52/90.70 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 90.52/90.70 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))); [ zenon_intro zenon_He0 | zenon_intro zenon_He1 ]. % 90.52/90.70 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (n0)) = (gt (n0) (n0))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_Hdf. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_He0. % 90.52/90.70 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.70 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 90.52/90.70 congruence. % 90.52/90.70 elim (classic ((n0) = (n0))); [ zenon_intro zenon_Hca | zenon_intro zenon_H67 ]. % 90.52/90.70 cut (((n0) = (n0)) = ((sum (n0) (tptp_minus_1) zenon_E) = (n0))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_Hdb. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_Hca. % 90.52/90.70 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.70 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 90.52/90.70 congruence. % 90.52/90.70 exact (zenon_Hd7 zenon_Hd6). % 90.52/90.70 apply zenon_H67. apply refl_equal. % 90.52/90.70 apply zenon_H67. apply refl_equal. % 90.52/90.70 apply zenon_H67. apply refl_equal. % 90.52/90.70 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_He2 | zenon_intro zenon_Hdc ]. % 90.52/90.70 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_He1. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_He2. % 90.52/90.70 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 90.52/90.70 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.70 congruence. % 90.52/90.70 apply zenon_Hda. apply refl_equal. % 90.52/90.70 exact (zenon_Hdb zenon_Hce). % 90.52/90.70 apply (zenon_L22_ zenon_TB_ec); trivial. % 90.52/90.70 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd9 | zenon_intro zenon_Hda ]. % 90.52/90.70 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_Hd7. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_Hd9. % 90.52/90.70 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.70 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 90.52/90.70 congruence. % 90.52/90.70 exact (zenon_Hdb zenon_Hce). % 90.52/90.70 apply zenon_Hda. apply refl_equal. % 90.52/90.70 apply zenon_Hda. apply refl_equal. % 90.52/90.70 (* end of lemma zenon_L23_ *) % 90.52/90.70 assert (zenon_L24_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~((succ (n0)) = (succ zenon_TB_ec))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n1))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.70 do 1 intro. intros zenon_H73 zenon_He3 zenon_Hb6 zenon_Hb5 zenon_Hae zenon_H97 zenon_H68. % 90.52/90.70 cut (((n0) = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Hc8]. % 90.52/90.70 congruence. % 90.52/90.70 generalize (finite_domain_3 zenon_TB_ec). zenon_intro zenon_Hb7. % 90.52/90.70 apply (zenon_imply_s _ _ zenon_Hb7); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 90.52/90.70 apply (zenon_notand_s _ _ zenon_Hb9); [ zenon_intro zenon_H69 | zenon_intro zenon_H98 ]. % 90.52/90.70 apply (zenon_L5_ zenon_TB_ec); trivial. % 90.52/90.70 apply (zenon_L13_ zenon_TB_ec); trivial. % 90.52/90.70 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 90.52/90.70 apply zenon_Hc8. apply sym_equal. exact zenon_Hbb. % 90.52/90.70 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_Had | zenon_intro zenon_Hbc ]. % 90.52/90.70 exact (zenon_Hae zenon_Had). % 90.52/90.70 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hbd ]. % 90.52/90.70 exact (zenon_Hb5 zenon_Hbe). % 90.52/90.70 exact (zenon_Hb6 zenon_Hbd). % 90.52/90.70 (* end of lemma zenon_L24_ *) % 90.52/90.70 assert (zenon_L25_ : (~((tptp_minus_1) = (tptp_minus_1))) -> False). % 90.52/90.70 do 0 intro. intros zenon_He4. % 90.52/90.70 apply zenon_He4. apply refl_equal. % 90.52/90.70 (* end of lemma zenon_L25_ *) % 90.52/90.70 assert (zenon_L26_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n1))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> (~((tptp_minus_1) = (n0))) -> (~((tptp_minus_1) = (n1))) -> (~((tptp_minus_1) = (n2))) -> (~((tptp_minus_1) = (n3))) -> False). % 90.52/90.70 do 1 intro. intros zenon_H73 zenon_H68 zenon_H97 zenon_Hae zenon_Hb5 zenon_Hb6 zenon_He5 zenon_He6 zenon_He7 zenon_He8. % 90.52/90.70 generalize (finite_domain_3 zenon_TB_ec). zenon_intro zenon_Hb7. % 90.52/90.70 apply (zenon_imply_s _ _ zenon_Hb7); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 90.52/90.70 apply (zenon_notand_s _ _ zenon_Hb9); [ zenon_intro zenon_H69 | zenon_intro zenon_H98 ]. % 90.52/90.70 apply (zenon_L5_ zenon_TB_ec); trivial. % 90.52/90.70 apply (zenon_L13_ zenon_TB_ec); trivial. % 90.52/90.70 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 90.52/90.70 generalize (finite_domain_3 (tptp_minus_1)). zenon_intro zenon_He9. % 90.52/90.70 apply (zenon_imply_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 90.52/90.70 apply (zenon_notand_s _ _ zenon_Heb); [ zenon_intro zenon_Hed | zenon_intro zenon_Hec ]. % 90.52/90.70 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H6b. % 90.52/90.70 generalize (zenon_H6b (tptp_minus_1)). zenon_intro zenon_Hee. % 90.52/90.70 apply (zenon_equiv_s _ _ zenon_Hee); [ zenon_intro zenon_Hed; zenon_intro zenon_Hbf | zenon_intro zenon_Hef; zenon_intro zenon_Hc1 ]. % 90.52/90.70 apply (zenon_L17_ zenon_TB_ec); trivial. % 90.52/90.70 exact (zenon_Hed zenon_Hef). % 90.52/90.70 generalize (leq_succ_gt_equiv (tptp_minus_1)). zenon_intro zenon_Hf0. % 90.52/90.70 generalize (zenon_Hf0 (n3)). zenon_intro zenon_Hf1. % 90.52/90.70 apply (zenon_equiv_s _ _ zenon_Hf1); [ zenon_intro zenon_Hec; zenon_intro zenon_Hf4 | zenon_intro zenon_Hf3; zenon_intro zenon_Hf2 ]. % 90.52/90.70 elim (classic ((~((succ (n3)) = (n0)))/\(~(gt (succ (n3)) (n0))))); [ zenon_intro zenon_Hf5 | zenon_intro zenon_Hf6 ]. % 90.52/90.70 apply (zenon_and_s _ _ zenon_Hf5). zenon_intro zenon_Hf8. zenon_intro zenon_Hf7. % 90.52/90.70 elim (classic ((~((succ (n3)) = (succ (tptp_minus_1))))/\(~(gt (succ (n3)) (succ (tptp_minus_1)))))); [ zenon_intro zenon_H9e | zenon_intro zenon_H9f ]. % 90.52/90.70 apply (zenon_and_s _ _ zenon_H9e). zenon_intro zenon_Ha0. zenon_intro zenon_H8c. % 90.52/90.70 apply (zenon_L12_); trivial. % 90.52/90.70 cut ((gt (succ (tptp_minus_1)) zenon_TB_ec) = (gt (succ (n3)) (n0))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_Hf7. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_H97. % 90.52/90.70 cut ((zenon_TB_ec = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hb4]. % 90.52/90.70 cut (((succ (tptp_minus_1)) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 90.52/90.70 congruence. % 90.52/90.70 apply (zenon_notand_s _ _ zenon_H9f); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Ha3 ]. % 90.52/90.70 apply zenon_Ha4. zenon_intro zenon_Ha5. % 90.52/90.70 elim (classic ((succ (n3)) = (succ (n3)))); [ zenon_intro zenon_H91 | zenon_intro zenon_H92 ]. % 90.52/90.70 cut (((succ (n3)) = (succ (n3))) = ((succ (tptp_minus_1)) = (succ (n3)))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_Ha2. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_H91. % 90.52/90.70 cut (((succ (n3)) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_H92]. % 90.52/90.70 cut (((succ (n3)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 90.52/90.70 congruence. % 90.52/90.70 exact (zenon_Ha0 zenon_Ha5). % 90.52/90.70 apply zenon_H92. apply refl_equal. % 90.52/90.70 apply zenon_H92. apply refl_equal. % 90.52/90.70 apply zenon_Ha3. zenon_intro zenon_Ha6. % 90.52/90.70 generalize (zenon_H73 (succ (n3))). zenon_intro zenon_Ha7. % 90.52/90.70 generalize (zenon_Ha7 (succ (tptp_minus_1))). zenon_intro zenon_Ha8. % 90.52/90.70 generalize (zenon_Ha8 zenon_TB_ec). zenon_intro zenon_Ha9. % 90.52/90.70 apply (zenon_imply_s _ _ zenon_Ha9); [ zenon_intro zenon_H8c | zenon_intro zenon_Haa ]. % 90.52/90.70 exact (zenon_H8c zenon_Ha6). % 90.52/90.70 apply (zenon_imply_s _ _ zenon_Haa); [ zenon_intro zenon_Hab | zenon_intro zenon_H9b ]. % 90.52/90.70 exact (zenon_Hab zenon_H97). % 90.52/90.70 cut ((gt (succ (n3)) zenon_TB_ec) = (gt (succ (n3)) (n0))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_Hf7. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_H9b. % 90.52/90.70 cut ((zenon_TB_ec = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hb4]. % 90.52/90.70 cut (((succ (n3)) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_H92]. % 90.52/90.70 congruence. % 90.52/90.70 apply zenon_H92. apply refl_equal. % 90.52/90.70 exact (zenon_Hb4 zenon_Hbb). % 90.52/90.70 exact (zenon_Hb4 zenon_Hbb). % 90.52/90.70 cut ((gt (n0) (tptp_minus_1)) = (gt (succ (n3)) (tptp_minus_1))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_Hf4. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact gt_0_tptp_minus_1. % 90.52/90.70 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_He4]. % 90.52/90.70 cut (((n0) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_Hf9]. % 90.52/90.70 congruence. % 90.52/90.70 apply (zenon_notand_s _ _ zenon_Hf6); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hfa ]. % 90.52/90.70 apply zenon_Hfb. zenon_intro zenon_Hfc. % 90.52/90.70 elim (classic ((succ (n3)) = (succ (n3)))); [ zenon_intro zenon_H91 | zenon_intro zenon_H92 ]. % 90.52/90.70 cut (((succ (n3)) = (succ (n3))) = ((n0) = (succ (n3)))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_Hf9. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_H91. % 90.52/90.70 cut (((succ (n3)) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_H92]. % 90.52/90.70 cut (((succ (n3)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 90.52/90.70 congruence. % 90.52/90.70 exact (zenon_Hf8 zenon_Hfc). % 90.52/90.70 apply zenon_H92. apply refl_equal. % 90.52/90.70 apply zenon_H92. apply refl_equal. % 90.52/90.70 apply zenon_Hfa. zenon_intro zenon_Hfd. % 90.52/90.70 generalize (zenon_H73 (succ (n3))). zenon_intro zenon_Ha7. % 90.52/90.70 generalize (zenon_Ha7 (n0)). zenon_intro zenon_Hfe. % 90.52/90.70 generalize (zenon_Hfe (tptp_minus_1)). zenon_intro zenon_Hff. % 90.52/90.70 apply (zenon_imply_s _ _ zenon_Hff); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H100 ]. % 90.52/90.70 exact (zenon_Hf7 zenon_Hfd). % 90.52/90.70 apply (zenon_imply_s _ _ zenon_H100); [ zenon_intro zenon_H101 | zenon_intro zenon_Hf2 ]. % 90.52/90.70 exact (zenon_H101 gt_0_tptp_minus_1). % 90.52/90.70 exact (zenon_Hf4 zenon_Hf2). % 90.52/90.70 apply zenon_He4. apply refl_equal. % 90.52/90.70 exact (zenon_Hec zenon_Hf3). % 90.52/90.70 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H103 | zenon_intro zenon_H102 ]. % 90.52/90.70 exact (zenon_He5 zenon_H103). % 90.52/90.70 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H105 | zenon_intro zenon_H104 ]. % 90.52/90.70 exact (zenon_He6 zenon_H105). % 90.52/90.70 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_H107 | zenon_intro zenon_H106 ]. % 90.52/90.70 exact (zenon_He7 zenon_H107). % 90.52/90.70 exact (zenon_He8 zenon_H106). % 90.52/90.70 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_Had | zenon_intro zenon_Hbc ]. % 90.52/90.70 exact (zenon_Hae zenon_Had). % 90.52/90.70 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hbd ]. % 90.52/90.70 exact (zenon_Hb5 zenon_Hbe). % 90.52/90.70 exact (zenon_Hb6 zenon_Hbd). % 90.52/90.70 (* end of lemma zenon_L26_ *) % 90.52/90.70 assert (zenon_L27_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~((succ (tptp_minus_1)) = (succ (n0)))) -> (~((tptp_minus_1) = (n3))) -> (~((tptp_minus_1) = (n2))) -> (~((tptp_minus_1) = (n1))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n1))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.70 do 1 intro. intros zenon_H73 zenon_H108 zenon_He8 zenon_He7 zenon_He6 zenon_Hb6 zenon_Hb5 zenon_Hae zenon_H97 zenon_H68. % 90.52/90.70 cut (((tptp_minus_1) = (n0))); [idtac | apply NNPP; zenon_intro zenon_He5]. % 90.52/90.70 congruence. % 90.52/90.70 apply (zenon_L26_ zenon_TB_ec); trivial. % 90.52/90.70 (* end of lemma zenon_L27_ *) % 90.52/90.70 assert (zenon_L28_ : forall (zenon_TB_ec : zenon_U), (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n1))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (~(gt zenon_TB_ec (succ (n0)))) -> (~((tptp_minus_1) = (n1))) -> (~((tptp_minus_1) = (n2))) -> (~((tptp_minus_1) = (n3))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.70 do 1 intro. intros zenon_Hb6 zenon_Hb5 zenon_Hae zenon_H97 zenon_H68 zenon_H109 zenon_He6 zenon_He7 zenon_He8 zenon_H73. % 90.52/90.70 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 90.52/90.70 elim (classic (gt zenon_TB_ec (n0))); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hcb ]. % 90.52/90.70 elim (classic (gt zenon_TB_ec (succ (tptp_minus_1)))); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hc4 ]. % 90.52/90.70 cut ((gt zenon_TB_ec (succ (tptp_minus_1))) = (gt zenon_TB_ec (succ (n0)))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_H109. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_Hcc. % 90.52/90.70 cut (((succ (tptp_minus_1)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 90.52/90.70 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.70 congruence. % 90.52/90.70 apply zenon_Ha1. apply refl_equal. % 90.52/90.70 apply (zenon_L27_ zenon_TB_ec); trivial. % 90.52/90.70 cut ((gt zenon_TB_ec (n0)) = (gt zenon_TB_ec (succ (tptp_minus_1)))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_Hc4. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_Hd8. % 90.52/90.70 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.70 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.70 congruence. % 90.52/90.70 apply zenon_Ha1. apply refl_equal. % 90.52/90.70 exact (zenon_H72 zenon_H71). % 90.52/90.70 apply (zenon_L20_ zenon_TB_ec); trivial. % 90.52/90.70 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.70 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_H72. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_Hc2. % 90.52/90.70 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.70 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.70 congruence. % 90.52/90.70 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.70 apply zenon_H8f. apply refl_equal. % 90.52/90.70 apply zenon_H8f. apply refl_equal. % 90.52/90.70 (* end of lemma zenon_L28_ *) % 90.52/90.70 assert (zenon_L29_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (succ (n0)))) -> (~((tptp_minus_1) = (n1))) -> (~((tptp_minus_1) = (n2))) -> (~((tptp_minus_1) = (n3))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n1))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.70 do 1 intro. intros zenon_H73 zenon_H10a zenon_He6 zenon_He7 zenon_He8 zenon_Hb6 zenon_Hb5 zenon_Hae zenon_H97 zenon_H68. % 90.52/90.70 elim (classic (gt zenon_TB_ec (succ (n0)))); [ zenon_intro zenon_H10b | zenon_intro zenon_H109 ]. % 90.52/90.70 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.70 generalize (zenon_Hd1 zenon_TB_ec). zenon_intro zenon_Hd2. % 90.52/90.70 generalize (zenon_Hd2 (succ (n0))). zenon_intro zenon_H10c. % 90.52/90.70 apply (zenon_imply_s _ _ zenon_H10c); [ zenon_intro zenon_Hab | zenon_intro zenon_H10d ]. % 90.52/90.70 exact (zenon_Hab zenon_H97). % 90.52/90.70 apply (zenon_imply_s _ _ zenon_H10d); [ zenon_intro zenon_H109 | zenon_intro zenon_H10e ]. % 90.52/90.70 exact (zenon_H109 zenon_H10b). % 90.52/90.70 exact (zenon_H10a zenon_H10e). % 90.52/90.70 apply (zenon_L28_ zenon_TB_ec); trivial. % 90.52/90.70 (* end of lemma zenon_L29_ *) % 90.52/90.70 assert (zenon_L30_ : forall (zenon_TB_ec : zenon_U), (~((tptp_minus_1) = (n1))) -> (~((tptp_minus_1) = (n2))) -> (~((tptp_minus_1) = (n3))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n1))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (~(gt (tptp_minus_1) (succ (n0)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.70 do 1 intro. intros zenon_He6 zenon_He7 zenon_He8 zenon_Hb6 zenon_Hb5 zenon_Hae zenon_H97 zenon_H68 zenon_H10f zenon_H73. % 90.52/90.70 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 90.52/90.70 elim (classic (gt (succ (tptp_minus_1)) (succ (n0)))); [ zenon_intro zenon_H10e | zenon_intro zenon_H10a ]. % 90.52/90.70 elim (classic (gt (n0) (succ (n0)))); [ zenon_intro zenon_H110 | zenon_intro zenon_H111 ]. % 90.52/90.70 cut ((gt (n0) (succ (n0))) = (gt (tptp_minus_1) (succ (n0)))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_H10f. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_H110. % 90.52/90.70 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.70 cut (((n0) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H112]. % 90.52/90.70 congruence. % 90.52/90.70 elim (classic ((tptp_minus_1) = (tptp_minus_1))); [ zenon_intro zenon_H113 | zenon_intro zenon_He4 ]. % 90.52/90.70 cut (((tptp_minus_1) = (tptp_minus_1)) = ((n0) = (tptp_minus_1))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_H112. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_H113. % 90.52/90.70 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_He4]. % 90.52/90.70 cut (((tptp_minus_1) = (n0))); [idtac | apply NNPP; zenon_intro zenon_He5]. % 90.52/90.70 congruence. % 90.52/90.70 apply (zenon_L26_ zenon_TB_ec); trivial. % 90.52/90.70 apply zenon_He4. apply refl_equal. % 90.52/90.70 apply zenon_He4. apply refl_equal. % 90.52/90.70 apply zenon_Hb2. apply refl_equal. % 90.52/90.70 cut ((gt (succ (tptp_minus_1)) (succ (n0))) = (gt (n0) (succ (n0)))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_H111. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_H10e. % 90.52/90.70 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.70 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.70 congruence. % 90.52/90.70 elim (classic ((n0) = (n0))); [ zenon_intro zenon_Hca | zenon_intro zenon_H67 ]. % 90.52/90.70 cut (((n0) = (n0)) = ((succ (tptp_minus_1)) = (n0))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_Hc3. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_Hca. % 90.52/90.70 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.70 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.70 congruence. % 90.52/90.70 exact (zenon_H72 zenon_H71). % 90.52/90.70 apply zenon_H67. apply refl_equal. % 90.52/90.70 apply zenon_H67. apply refl_equal. % 90.52/90.70 apply zenon_Hb2. apply refl_equal. % 90.52/90.70 apply (zenon_L29_ zenon_TB_ec); trivial. % 90.52/90.70 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.70 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_H72. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_Hc2. % 90.52/90.70 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.70 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.70 congruence. % 90.52/90.70 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.70 apply zenon_H8f. apply refl_equal. % 90.52/90.70 apply zenon_H8f. apply refl_equal. % 90.52/90.70 (* end of lemma zenon_L30_ *) % 90.52/90.70 assert (zenon_L31_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (succ (n0)))) -> (~((tptp_minus_1) = (n3))) -> (~((tptp_minus_1) = (n2))) -> (~((tptp_minus_1) = (n1))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n1))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.70 do 1 intro. intros zenon_H73 zenon_H111 zenon_He8 zenon_He7 zenon_He6 zenon_Hb6 zenon_Hb5 zenon_Hae zenon_H97 zenon_H68. % 90.52/90.70 elim (classic (gt (tptp_minus_1) (succ (n0)))); [ zenon_intro zenon_H114 | zenon_intro zenon_H10f ]. % 90.52/90.70 generalize (zenon_H73 (n0)). zenon_intro zenon_H115. % 90.52/90.70 generalize (zenon_H115 (tptp_minus_1)). zenon_intro zenon_H116. % 90.52/90.70 generalize (zenon_H116 (succ (n0))). zenon_intro zenon_H117. % 90.52/90.70 apply (zenon_imply_s _ _ zenon_H117); [ zenon_intro zenon_H101 | zenon_intro zenon_H118 ]. % 90.52/90.70 exact (zenon_H101 gt_0_tptp_minus_1). % 90.52/90.70 apply (zenon_imply_s _ _ zenon_H118); [ zenon_intro zenon_H10f | zenon_intro zenon_H110 ]. % 90.52/90.70 exact (zenon_H10f zenon_H114). % 90.52/90.70 exact (zenon_H111 zenon_H110). % 90.52/90.70 apply (zenon_L30_ zenon_TB_ec); trivial. % 90.52/90.70 (* end of lemma zenon_L31_ *) % 90.52/90.70 assert (zenon_L32_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n0)) (succ (n0)))) -> (~((tptp_minus_1) = (n1))) -> (~((tptp_minus_1) = (n2))) -> (~((tptp_minus_1) = (n3))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n1))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.70 do 1 intro. intros zenon_H73 zenon_H119 zenon_He6 zenon_He7 zenon_He8 zenon_Hb6 zenon_Hb5 zenon_Hae zenon_H97 zenon_H68. % 90.52/90.70 elim (classic ((~((succ (n0)) = (succ zenon_TB_ec)))/\(~(gt (succ (n0)) (succ zenon_TB_ec))))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 90.52/90.70 apply (zenon_and_s _ _ zenon_H11a). zenon_intro zenon_He3. zenon_intro zenon_H11c. % 90.52/90.70 apply (zenon_L24_ zenon_TB_ec); trivial. % 90.52/90.70 elim (classic (gt (n0) (succ (n0)))); [ zenon_intro zenon_H110 | zenon_intro zenon_H111 ]. % 90.52/90.70 generalize (zenon_H73 (succ zenon_TB_ec)). zenon_intro zenon_H11d. % 90.52/90.70 generalize (zenon_H11d (n0)). zenon_intro zenon_H11e. % 90.52/90.70 generalize (zenon_H11e (succ (n0))). zenon_intro zenon_H11f. % 90.52/90.70 apply (zenon_imply_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 90.52/90.70 exact (zenon_H6e zenon_H68). % 90.52/90.70 apply (zenon_imply_s _ _ zenon_H120); [ zenon_intro zenon_H111 | zenon_intro zenon_H121 ]. % 90.52/90.70 exact (zenon_H111 zenon_H110). % 90.52/90.70 cut ((gt (succ zenon_TB_ec) (succ (n0))) = (gt (succ (n0)) (succ (n0)))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_H119. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_H121. % 90.52/90.70 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.70 cut (((succ zenon_TB_ec) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H122]. % 90.52/90.70 congruence. % 90.52/90.70 apply (zenon_notand_s _ _ zenon_H11b); [ zenon_intro zenon_H124 | zenon_intro zenon_H123 ]. % 90.52/90.70 apply zenon_H124. zenon_intro zenon_H125. % 90.52/90.70 apply zenon_H122. apply sym_equal. exact zenon_H125. % 90.52/90.70 apply zenon_H123. zenon_intro zenon_H126. % 90.52/90.70 generalize (zenon_H73 (succ (n0))). zenon_intro zenon_H127. % 90.52/90.70 generalize (zenon_H127 (succ zenon_TB_ec)). zenon_intro zenon_H128. % 90.52/90.70 generalize (zenon_H128 (succ (n0))). zenon_intro zenon_H129. % 90.52/90.70 apply (zenon_imply_s _ _ zenon_H129); [ zenon_intro zenon_H11c | zenon_intro zenon_H12a ]. % 90.52/90.70 exact (zenon_H11c zenon_H126). % 90.52/90.70 apply (zenon_imply_s _ _ zenon_H12a); [ zenon_intro zenon_H12c | zenon_intro zenon_H12b ]. % 90.52/90.70 exact (zenon_H12c zenon_H121). % 90.52/90.70 exact (zenon_H119 zenon_H12b). % 90.52/90.70 apply zenon_Hb2. apply refl_equal. % 90.52/90.70 apply (zenon_L31_ zenon_TB_ec); trivial. % 90.52/90.70 (* end of lemma zenon_L32_ *) % 90.52/90.70 assert (zenon_L33_ : forall (zenon_TB_ec : zenon_U), (~((tptp_minus_1) = (n3))) -> (~((tptp_minus_1) = (n2))) -> (~((tptp_minus_1) = (n1))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n1))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (n1))) -> False). % 90.52/90.70 do 1 intro. intros zenon_He8 zenon_He7 zenon_He6 zenon_H68 zenon_H97 zenon_Hae zenon_Hb5 zenon_Hb6 zenon_H73 zenon_H12d. % 90.52/90.70 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_H12e | zenon_intro zenon_Hb0 ]. % 90.52/90.70 elim (classic (gt (succ (n0)) (n1))); [ zenon_intro zenon_H12f | zenon_intro zenon_H130 ]. % 90.52/90.70 cut ((gt (succ (n0)) (n1)) = (gt (n1) (n1))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_H12d. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_H12f. % 90.52/90.70 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.70 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.70 congruence. % 90.52/90.70 elim (classic ((n1) = (n1))); [ zenon_intro zenon_H131 | zenon_intro zenon_H66 ]. % 90.52/90.70 cut (((n1) = (n1)) = ((succ (n0)) = (n1))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_Hb3. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_H131. % 90.52/90.70 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.70 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 90.52/90.70 congruence. % 90.52/90.70 exact (zenon_Hb0 zenon_H12e). % 90.52/90.70 apply zenon_H66. apply refl_equal. % 90.52/90.70 apply zenon_H66. apply refl_equal. % 90.52/90.70 apply zenon_H66. apply refl_equal. % 90.52/90.70 elim (classic (gt (succ (n0)) (succ (n0)))); [ zenon_intro zenon_H12b | zenon_intro zenon_H119 ]. % 90.52/90.70 cut ((gt (succ (n0)) (succ (n0))) = (gt (succ (n0)) (n1))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_H130. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_H12b. % 90.52/90.70 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.70 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.70 congruence. % 90.52/90.70 apply zenon_Hb2. apply refl_equal. % 90.52/90.70 exact (zenon_Hb3 successor_1). % 90.52/90.70 apply (zenon_L32_ zenon_TB_ec); trivial. % 90.52/90.70 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 90.52/90.70 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_Hb0. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_Hb1. % 90.52/90.70 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.70 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.70 congruence. % 90.52/90.70 exact (zenon_Hb3 successor_1). % 90.52/90.70 apply zenon_Hb2. apply refl_equal. % 90.52/90.70 apply zenon_Hb2. apply refl_equal. % 90.52/90.70 (* end of lemma zenon_L33_ *) % 90.52/90.70 assert (zenon_L34_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (tptp_minus_1) (n1))) -> (~((tptp_minus_1) = (n3))) -> (~((tptp_minus_1) = (n2))) -> (~((tptp_minus_1) = (n1))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n1))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.70 do 1 intro. intros zenon_H73 zenon_H132 zenon_He8 zenon_He7 zenon_He6 zenon_Hb6 zenon_Hb5 zenon_Hae zenon_H97 zenon_H68. % 90.52/90.70 elim (classic (gt (tptp_minus_1) (succ (n0)))); [ zenon_intro zenon_H114 | zenon_intro zenon_H10f ]. % 90.52/90.70 cut ((gt (tptp_minus_1) (succ (n0))) = (gt (tptp_minus_1) (n1))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_H132. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_H114. % 90.52/90.70 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.70 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_He4]. % 90.52/90.70 congruence. % 90.52/90.70 apply zenon_He4. apply refl_equal. % 90.52/90.70 exact (zenon_Hb3 successor_1). % 90.52/90.70 apply (zenon_L30_ zenon_TB_ec); trivial. % 90.52/90.70 (* end of lemma zenon_L34_ *) % 90.52/90.70 assert (zenon_L35_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (n1))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n1))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> (~((tptp_minus_1) = (n2))) -> (~((tptp_minus_1) = (n3))) -> False). % 90.52/90.70 do 1 intro. intros zenon_H73 zenon_H133 zenon_H68 zenon_H97 zenon_Hae zenon_Hb5 zenon_Hb6 zenon_He7 zenon_He8. % 90.52/90.70 elim (classic ((tptp_minus_1) = (n1))); [ zenon_intro zenon_H105 | zenon_intro zenon_He6 ]. % 90.52/90.70 cut ((gt (n0) (tptp_minus_1)) = (gt (n0) (n1))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_H133. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact gt_0_tptp_minus_1. % 90.52/90.70 cut (((tptp_minus_1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_He6]. % 90.52/90.70 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.70 congruence. % 90.52/90.70 apply zenon_H67. apply refl_equal. % 90.52/90.70 exact (zenon_He6 zenon_H105). % 90.52/90.70 elim (classic (gt (tptp_minus_1) (n1))); [ zenon_intro zenon_H134 | zenon_intro zenon_H132 ]. % 90.52/90.70 generalize (zenon_H73 (n0)). zenon_intro zenon_H115. % 90.52/90.70 generalize (zenon_H115 (tptp_minus_1)). zenon_intro zenon_H116. % 90.52/90.70 generalize (zenon_H116 (n1)). zenon_intro zenon_H135. % 90.52/90.70 apply (zenon_imply_s _ _ zenon_H135); [ zenon_intro zenon_H101 | zenon_intro zenon_H136 ]. % 90.52/90.70 exact (zenon_H101 gt_0_tptp_minus_1). % 90.52/90.70 apply (zenon_imply_s _ _ zenon_H136); [ zenon_intro zenon_H132 | zenon_intro zenon_H137 ]. % 90.52/90.70 exact (zenon_H132 zenon_H134). % 90.52/90.70 exact (zenon_H133 zenon_H137). % 90.52/90.70 apply (zenon_L34_ zenon_TB_ec); trivial. % 90.52/90.70 (* end of lemma zenon_L35_ *) % 90.52/90.70 assert (zenon_L36_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (n1))) -> (~((tptp_minus_1) = (n3))) -> (~((tptp_minus_1) = (n2))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n1))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.70 do 1 intro. intros zenon_H73 zenon_H12d zenon_He8 zenon_He7 zenon_Hb6 zenon_Hb5 zenon_Hae zenon_H97 zenon_H68. % 90.52/90.70 elim (classic (gt (n0) (n1))); [ zenon_intro zenon_H137 | zenon_intro zenon_H133 ]. % 90.52/90.70 generalize (zenon_H73 (n1)). zenon_intro zenon_H138. % 90.52/90.70 generalize (zenon_H138 (n0)). zenon_intro zenon_H139. % 90.52/90.70 generalize (zenon_H139 (n1)). zenon_intro zenon_H13a. % 90.52/90.70 apply (zenon_imply_s _ _ zenon_H13a); [ zenon_intro zenon_H13c | zenon_intro zenon_H13b ]. % 90.52/90.70 exact (zenon_H13c gt_1_0). % 90.52/90.70 apply (zenon_imply_s _ _ zenon_H13b); [ zenon_intro zenon_H133 | zenon_intro zenon_H13d ]. % 90.52/90.70 exact (zenon_H133 zenon_H137). % 90.52/90.70 exact (zenon_H12d zenon_H13d). % 90.52/90.70 apply (zenon_L35_ zenon_TB_ec); trivial. % 90.52/90.70 (* end of lemma zenon_L36_ *) % 90.52/90.70 assert (zenon_L37_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n0)) (succ (n0)))) -> (~((tptp_minus_1) = (n3))) -> (~((tptp_minus_1) = (n2))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n1))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.70 do 1 intro. intros zenon_H73 zenon_H119 zenon_He8 zenon_He7 zenon_Hb6 zenon_Hb5 zenon_Hae zenon_H97 zenon_H68. % 90.52/90.70 elim (classic (gt (n1) (succ (n0)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 90.52/90.70 cut ((gt (n1) (succ (n0))) = (gt (succ (n0)) (succ (n0)))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_H119. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_H13e. % 90.52/90.70 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.70 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 90.52/90.70 congruence. % 90.52/90.70 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 90.52/90.70 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_Hb0. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_Hb1. % 90.52/90.70 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.70 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.70 congruence. % 90.52/90.70 exact (zenon_Hb3 successor_1). % 90.52/90.70 apply zenon_Hb2. apply refl_equal. % 90.52/90.70 apply zenon_Hb2. apply refl_equal. % 90.52/90.70 apply zenon_Hb2. apply refl_equal. % 90.52/90.70 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_H12e | zenon_intro zenon_Hb0 ]. % 90.52/90.70 elim (classic (gt (n1) (n1))); [ zenon_intro zenon_H13d | zenon_intro zenon_H12d ]. % 90.52/90.70 cut ((gt (n1) (n1)) = (gt (n1) (succ (n0)))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_H13f. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_H13d. % 90.52/90.70 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 90.52/90.70 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.70 congruence. % 90.52/90.70 apply zenon_H66. apply refl_equal. % 90.52/90.70 exact (zenon_Hb0 zenon_H12e). % 90.52/90.70 apply (zenon_L36_ zenon_TB_ec); trivial. % 90.52/90.70 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 90.52/90.70 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_Hb0. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_Hb1. % 90.52/90.70 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.70 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.70 congruence. % 90.52/90.70 exact (zenon_Hb3 successor_1). % 90.52/90.70 apply zenon_Hb2. apply refl_equal. % 90.52/90.70 apply zenon_Hb2. apply refl_equal. % 90.52/90.70 (* end of lemma zenon_L37_ *) % 90.52/90.70 assert (zenon_L38_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (succ (n0)))) -> (~((tptp_minus_1) = (n3))) -> (~((tptp_minus_1) = (n2))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n1))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.70 do 1 intro. intros zenon_H73 zenon_H111 zenon_He8 zenon_He7 zenon_Hb6 zenon_Hb5 zenon_Hae zenon_H97 zenon_H68. % 90.52/90.70 elim (classic (gt (tptp_minus_1) (succ (n0)))); [ zenon_intro zenon_H114 | zenon_intro zenon_H10f ]. % 90.52/90.70 generalize (zenon_H73 (n0)). zenon_intro zenon_H115. % 90.52/90.70 generalize (zenon_H115 (tptp_minus_1)). zenon_intro zenon_H116. % 90.52/90.70 generalize (zenon_H116 (succ (n0))). zenon_intro zenon_H117. % 90.52/90.70 apply (zenon_imply_s _ _ zenon_H117); [ zenon_intro zenon_H101 | zenon_intro zenon_H118 ]. % 90.52/90.70 exact (zenon_H101 gt_0_tptp_minus_1). % 90.52/90.70 apply (zenon_imply_s _ _ zenon_H118); [ zenon_intro zenon_H10f | zenon_intro zenon_H110 ]. % 90.52/90.70 exact (zenon_H10f zenon_H114). % 90.52/90.70 exact (zenon_H111 zenon_H110). % 90.52/90.70 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_H12e | zenon_intro zenon_Hb0 ]. % 90.52/90.70 elim (classic (gt (tptp_minus_1) (n1))); [ zenon_intro zenon_H134 | zenon_intro zenon_H132 ]. % 90.52/90.70 cut ((gt (tptp_minus_1) (n1)) = (gt (tptp_minus_1) (succ (n0)))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_H10f. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_H134. % 90.52/90.70 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 90.52/90.70 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_He4]. % 90.52/90.70 congruence. % 90.52/90.70 apply zenon_He4. apply refl_equal. % 90.52/90.70 exact (zenon_Hb0 zenon_H12e). % 90.52/90.70 elim (classic (gt (succ (n0)) (succ (n0)))); [ zenon_intro zenon_H12b | zenon_intro zenon_H119 ]. % 90.52/90.70 elim (classic (gt (n1) (succ (n0)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 90.52/90.70 cut ((gt (n1) (succ (n0))) = (gt (tptp_minus_1) (succ (n0)))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_H10f. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_H13e. % 90.52/90.70 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.70 cut (((n1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H140]. % 90.52/90.70 congruence. % 90.52/90.70 elim (classic ((tptp_minus_1) = (tptp_minus_1))); [ zenon_intro zenon_H113 | zenon_intro zenon_He4 ]. % 90.52/90.70 cut (((tptp_minus_1) = (tptp_minus_1)) = ((n1) = (tptp_minus_1))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_H140. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_H113. % 90.52/90.70 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_He4]. % 90.52/90.70 cut (((tptp_minus_1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_He6]. % 90.52/90.70 congruence. % 90.52/90.70 apply (zenon_L34_ zenon_TB_ec); trivial. % 90.52/90.70 apply zenon_He4. apply refl_equal. % 90.52/90.70 apply zenon_He4. apply refl_equal. % 90.52/90.70 apply zenon_Hb2. apply refl_equal. % 90.52/90.70 cut ((gt (succ (n0)) (succ (n0))) = (gt (n1) (succ (n0)))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_H13f. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_H12b. % 90.52/90.70 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.70 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.70 congruence. % 90.52/90.70 elim (classic ((n1) = (n1))); [ zenon_intro zenon_H131 | zenon_intro zenon_H66 ]. % 90.52/90.70 cut (((n1) = (n1)) = ((succ (n0)) = (n1))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_Hb3. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_H131. % 90.52/90.70 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.70 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 90.52/90.70 congruence. % 90.52/90.70 exact (zenon_Hb0 zenon_H12e). % 90.52/90.70 apply zenon_H66. apply refl_equal. % 90.52/90.70 apply zenon_H66. apply refl_equal. % 90.52/90.70 apply zenon_Hb2. apply refl_equal. % 90.52/90.70 apply (zenon_L37_ zenon_TB_ec); trivial. % 90.52/90.70 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 90.52/90.70 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))). % 90.52/90.70 intro zenon_D_pnotp. % 90.52/90.70 apply zenon_Hb0. % 90.52/90.70 rewrite <- zenon_D_pnotp. % 90.52/90.70 exact zenon_Hb1. % 90.52/90.70 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.70 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.70 congruence. % 90.52/90.70 exact (zenon_Hb3 successor_1). % 90.52/90.70 apply zenon_Hb2. apply refl_equal. % 90.52/90.70 apply zenon_Hb2. apply refl_equal. % 90.52/90.70 (* end of lemma zenon_L38_ *) % 90.52/90.71 assert (zenon_L39_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~((tptp_minus_1) = (n2))) -> (~((tptp_minus_1) = (n3))) -> (~(gt (succ (tptp_minus_1)) (succ (n0)))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n1))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> False). % 90.52/90.71 do 1 intro. intros zenon_H73 zenon_He7 zenon_He8 zenon_H10a zenon_H68 zenon_H97 zenon_Hae zenon_Hb5 zenon_Hb6. % 90.52/90.71 elim (classic (gt (succ (tptp_minus_1)) (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hc0 ]. % 90.52/90.71 elim (classic (gt (succ (tptp_minus_1)) (n0))); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hbf ]. % 90.52/90.71 elim (classic (gt (n0) (succ (n0)))); [ zenon_intro zenon_H110 | zenon_intro zenon_H111 ]. % 90.52/90.71 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.71 generalize (zenon_Hd1 (n0)). zenon_intro zenon_H141. % 90.52/90.71 generalize (zenon_H141 (succ (n0))). zenon_intro zenon_H142. % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H142); [ zenon_intro zenon_Hbf | zenon_intro zenon_H143 ]. % 90.52/90.71 exact (zenon_Hbf zenon_Hc1). % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H143); [ zenon_intro zenon_H111 | zenon_intro zenon_H10e ]. % 90.52/90.71 exact (zenon_H111 zenon_H110). % 90.52/90.71 exact (zenon_H10a zenon_H10e). % 90.52/90.71 apply (zenon_L38_ zenon_TB_ec); trivial. % 90.52/90.71 cut ((gt (succ (tptp_minus_1)) (succ (tptp_minus_1))) = (gt (succ (tptp_minus_1)) (n0))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_Hbf. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_Hc5. % 90.52/90.71 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.71 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.71 congruence. % 90.52/90.71 apply zenon_H8f. apply refl_equal. % 90.52/90.71 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.71 apply (zenon_L18_ zenon_TB_ec); trivial. % 90.52/90.71 (* end of lemma zenon_L39_ *) % 90.52/90.71 assert (zenon_L40_ : forall (zenon_TB_ec : zenon_U), (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n1))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (~(gt zenon_TB_ec (succ (n0)))) -> (~((tptp_minus_1) = (n2))) -> (~((tptp_minus_1) = (n3))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.71 do 1 intro. intros zenon_Hb6 zenon_Hb5 zenon_Hae zenon_H97 zenon_H68 zenon_H109 zenon_He7 zenon_He8 zenon_H73. % 90.52/90.71 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 90.52/90.71 elim (classic (gt zenon_TB_ec (n0))); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hcb ]. % 90.52/90.71 elim (classic (gt zenon_TB_ec (succ (tptp_minus_1)))); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hc4 ]. % 90.52/90.71 elim (classic (gt (succ (tptp_minus_1)) (succ (n0)))); [ zenon_intro zenon_H10e | zenon_intro zenon_H10a ]. % 90.52/90.71 generalize (zenon_H73 zenon_TB_ec). zenon_intro zenon_H144. % 90.52/90.71 generalize (zenon_H144 (succ (tptp_minus_1))). zenon_intro zenon_H145. % 90.52/90.71 generalize (zenon_H145 (succ (n0))). zenon_intro zenon_H146. % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H146); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H147 ]. % 90.52/90.71 exact (zenon_Hc4 zenon_Hcc). % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H147); [ zenon_intro zenon_H10a | zenon_intro zenon_H10b ]. % 90.52/90.71 exact (zenon_H10a zenon_H10e). % 90.52/90.71 exact (zenon_H109 zenon_H10b). % 90.52/90.71 apply (zenon_L39_ zenon_TB_ec); trivial. % 90.52/90.71 cut ((gt zenon_TB_ec (n0)) = (gt zenon_TB_ec (succ (tptp_minus_1)))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_Hc4. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_Hd8. % 90.52/90.71 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.71 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.71 congruence. % 90.52/90.71 apply zenon_Ha1. apply refl_equal. % 90.52/90.71 exact (zenon_H72 zenon_H71). % 90.52/90.71 apply (zenon_L20_ zenon_TB_ec); trivial. % 90.52/90.71 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.71 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H72. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_Hc2. % 90.52/90.71 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.71 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.71 congruence. % 90.52/90.71 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.71 apply zenon_H8f. apply refl_equal. % 90.52/90.71 apply zenon_H8f. apply refl_equal. % 90.52/90.71 (* end of lemma zenon_L40_ *) % 90.52/90.71 assert (zenon_L41_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt zenon_TB_ec (n1))) -> (~((tptp_minus_1) = (n2))) -> (~((tptp_minus_1) = (n3))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n1))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.71 do 1 intro. intros zenon_H73 zenon_H148 zenon_He7 zenon_He8 zenon_Hb6 zenon_Hb5 zenon_Hae zenon_H97 zenon_H68. % 90.52/90.71 elim (classic (gt zenon_TB_ec (succ (n0)))); [ zenon_intro zenon_H10b | zenon_intro zenon_H109 ]. % 90.52/90.71 cut ((gt zenon_TB_ec (succ (n0))) = (gt zenon_TB_ec (n1))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H148. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H10b. % 90.52/90.71 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.71 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.71 congruence. % 90.52/90.71 apply zenon_Ha1. apply refl_equal. % 90.52/90.71 exact (zenon_Hb3 successor_1). % 90.52/90.71 apply (zenon_L40_ zenon_TB_ec); trivial. % 90.52/90.71 (* end of lemma zenon_L41_ *) % 90.52/90.71 assert (zenon_L42_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (n2))) -> (~(gt zenon_TB_ec (n1))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n1))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> (~((tptp_minus_1) = (n3))) -> False). % 90.52/90.71 do 1 intro. intros zenon_H73 zenon_H149 zenon_H148 zenon_H68 zenon_H97 zenon_Hae zenon_Hb5 zenon_Hb6 zenon_He8. % 90.52/90.71 elim (classic ((tptp_minus_1) = (n2))); [ zenon_intro zenon_H107 | zenon_intro zenon_He7 ]. % 90.52/90.71 cut ((gt (n0) (tptp_minus_1)) = (gt (n0) (n2))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H149. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact gt_0_tptp_minus_1. % 90.52/90.71 cut (((tptp_minus_1) = (n2))); [idtac | apply NNPP; zenon_intro zenon_He7]. % 90.52/90.71 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.71 congruence. % 90.52/90.71 apply zenon_H67. apply refl_equal. % 90.52/90.71 exact (zenon_He7 zenon_H107). % 90.52/90.71 apply (zenon_L41_ zenon_TB_ec); trivial. % 90.52/90.71 (* end of lemma zenon_L42_ *) % 90.52/90.71 assert (zenon_L43_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (n2))) -> (~((tptp_minus_1) = (n3))) -> (~(gt zenon_TB_ec (n1))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n1))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.71 do 1 intro. intros zenon_H73 zenon_H14a zenon_He8 zenon_H148 zenon_Hb6 zenon_Hb5 zenon_Hae zenon_H97 zenon_H68. % 90.52/90.71 elim (classic (gt (n0) (n2))); [ zenon_intro zenon_H14b | zenon_intro zenon_H149 ]. % 90.52/90.71 generalize (zenon_H73 (n1)). zenon_intro zenon_H138. % 90.52/90.71 generalize (zenon_H138 (n0)). zenon_intro zenon_H139. % 90.52/90.71 generalize (zenon_H139 (n2)). zenon_intro zenon_H14c. % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H14c); [ zenon_intro zenon_H13c | zenon_intro zenon_H14d ]. % 90.52/90.71 exact (zenon_H13c gt_1_0). % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H14d); [ zenon_intro zenon_H149 | zenon_intro zenon_H14e ]. % 90.52/90.71 exact (zenon_H149 zenon_H14b). % 90.52/90.71 exact (zenon_H14a zenon_H14e). % 90.52/90.71 apply (zenon_L42_ zenon_TB_ec); trivial. % 90.52/90.71 (* end of lemma zenon_L43_ *) % 90.52/90.71 assert (zenon_L44_ : forall (zenon_TB_ec : zenon_U), (~((tptp_minus_1) = (n3))) -> (~(gt zenon_TB_ec (n1))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n1))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (n1))) -> False). % 90.52/90.71 do 1 intro. intros zenon_He8 zenon_H148 zenon_Hb6 zenon_Hb5 zenon_Hae zenon_H97 zenon_H68 zenon_H73 zenon_H12d. % 90.52/90.71 elim (classic ((~((n1) = (n2)))/\(~(gt (n1) (n2))))); [ zenon_intro zenon_H14f | zenon_intro zenon_H150 ]. % 90.52/90.71 apply (zenon_and_s _ _ zenon_H14f). zenon_intro zenon_H151. zenon_intro zenon_H14a. % 90.52/90.71 apply (zenon_L43_ zenon_TB_ec); trivial. % 90.52/90.71 cut ((gt (n2) (n1)) = (gt (n1) (n1))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H12d. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact gt_2_1. % 90.52/90.71 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.71 cut (((n2) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H152]. % 90.52/90.71 congruence. % 90.52/90.71 apply (zenon_notand_s _ _ zenon_H150); [ zenon_intro zenon_H154 | zenon_intro zenon_H153 ]. % 90.52/90.71 apply zenon_H154. zenon_intro zenon_H155. % 90.52/90.71 elim (classic ((n1) = (n1))); [ zenon_intro zenon_H131 | zenon_intro zenon_H66 ]. % 90.52/90.71 cut (((n1) = (n1)) = ((n2) = (n1))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H152. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H131. % 90.52/90.71 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.71 cut (((n1) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H151]. % 90.52/90.71 congruence. % 90.52/90.71 exact (zenon_H151 zenon_H155). % 90.52/90.71 apply zenon_H66. apply refl_equal. % 90.52/90.71 apply zenon_H66. apply refl_equal. % 90.52/90.71 apply zenon_H153. zenon_intro zenon_H14e. % 90.52/90.71 generalize (zenon_H73 (n1)). zenon_intro zenon_H138. % 90.52/90.71 generalize (zenon_H138 (n2)). zenon_intro zenon_H156. % 90.52/90.71 generalize (zenon_H156 (n1)). zenon_intro zenon_H157. % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H157); [ zenon_intro zenon_H14a | zenon_intro zenon_H158 ]. % 90.52/90.71 exact (zenon_H14a zenon_H14e). % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H158); [ zenon_intro zenon_H7a | zenon_intro zenon_H13d ]. % 90.52/90.71 exact (zenon_H7a gt_2_1). % 90.52/90.71 exact (zenon_H12d zenon_H13d). % 90.52/90.71 apply zenon_H66. apply refl_equal. % 90.52/90.71 (* end of lemma zenon_L44_ *) % 90.52/90.71 assert (zenon_L45_ : forall (zenon_TB_ec : zenon_U), (~((tptp_minus_1) = (n3))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (n1))) -> False). % 90.52/90.71 do 1 intro. intros zenon_He8 zenon_Hb6 zenon_Hb5 zenon_H97 zenon_H68 zenon_H73 zenon_H12d. % 90.52/90.71 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_H12e | zenon_intro zenon_Hb0 ]. % 90.52/90.71 elim (classic (gt (succ (n0)) (n1))); [ zenon_intro zenon_H12f | zenon_intro zenon_H130 ]. % 90.52/90.71 cut ((gt (succ (n0)) (n1)) = (gt (n1) (n1))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H12d. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H12f. % 90.52/90.71 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.71 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.71 congruence. % 90.52/90.71 elim (classic ((n1) = (n1))); [ zenon_intro zenon_H131 | zenon_intro zenon_H66 ]. % 90.52/90.71 cut (((n1) = (n1)) = ((succ (n0)) = (n1))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_Hb3. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H131. % 90.52/90.71 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.71 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 90.52/90.71 congruence. % 90.52/90.71 exact (zenon_Hb0 zenon_H12e). % 90.52/90.71 apply zenon_H66. apply refl_equal. % 90.52/90.71 apply zenon_H66. apply refl_equal. % 90.52/90.71 apply zenon_H66. apply refl_equal. % 90.52/90.71 elim (classic ((~((succ (n0)) = (succ (tptp_minus_1))))/\(~(gt (succ (n0)) (succ (tptp_minus_1)))))); [ zenon_intro zenon_H159 | zenon_intro zenon_H15a ]. % 90.52/90.71 apply (zenon_and_s _ _ zenon_H159). zenon_intro zenon_H15b. zenon_intro zenon_Haf. % 90.52/90.71 apply (zenon_L15_); trivial. % 90.52/90.71 elim (classic (zenon_TB_ec = (n1))); [ zenon_intro zenon_Had | zenon_intro zenon_Hae ]. % 90.52/90.71 cut ((gt (succ (tptp_minus_1)) zenon_TB_ec) = (gt (succ (n0)) (n1))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H130. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H97. % 90.52/90.71 cut ((zenon_TB_ec = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hae]. % 90.52/90.71 cut (((succ (tptp_minus_1)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 90.52/90.71 congruence. % 90.52/90.71 apply (zenon_notand_s _ _ zenon_H15a); [ zenon_intro zenon_H15d | zenon_intro zenon_H15c ]. % 90.52/90.71 apply zenon_H15d. zenon_intro zenon_H15e. % 90.52/90.71 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 90.52/90.71 cut (((succ (n0)) = (succ (n0))) = ((succ (tptp_minus_1)) = (succ (n0)))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H108. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_Hb1. % 90.52/90.71 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.71 cut (((succ (n0)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H15b]. % 90.52/90.71 congruence. % 90.52/90.71 exact (zenon_H15b zenon_H15e). % 90.52/90.71 apply zenon_Hb2. apply refl_equal. % 90.52/90.71 apply zenon_Hb2. apply refl_equal. % 90.52/90.71 apply zenon_H15c. zenon_intro zenon_H15f. % 90.52/90.71 generalize (zenon_H73 (succ (n0))). zenon_intro zenon_H127. % 90.52/90.71 generalize (zenon_H127 (succ (tptp_minus_1))). zenon_intro zenon_H160. % 90.52/90.71 generalize (zenon_H160 zenon_TB_ec). zenon_intro zenon_H161. % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H161); [ zenon_intro zenon_Haf | zenon_intro zenon_H162 ]. % 90.52/90.71 exact (zenon_Haf zenon_H15f). % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H162); [ zenon_intro zenon_Hab | zenon_intro zenon_H163 ]. % 90.52/90.71 exact (zenon_Hab zenon_H97). % 90.52/90.71 cut ((gt (succ (n0)) zenon_TB_ec) = (gt (succ (n0)) (n1))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H130. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H163. % 90.52/90.71 cut ((zenon_TB_ec = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hae]. % 90.52/90.71 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.71 congruence. % 90.52/90.71 apply zenon_Hb2. apply refl_equal. % 90.52/90.71 exact (zenon_Hae zenon_Had). % 90.52/90.71 exact (zenon_Hae zenon_Had). % 90.52/90.71 elim (classic (gt zenon_TB_ec (n1))); [ zenon_intro zenon_H164 | zenon_intro zenon_H148 ]. % 90.52/90.71 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.71 generalize (zenon_Hd1 zenon_TB_ec). zenon_intro zenon_Hd2. % 90.52/90.71 generalize (zenon_Hd2 (n1)). zenon_intro zenon_H165. % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H165); [ zenon_intro zenon_Hab | zenon_intro zenon_H166 ]. % 90.52/90.71 exact (zenon_Hab zenon_H97). % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H166); [ zenon_intro zenon_H148 | zenon_intro zenon_H167 ]. % 90.52/90.71 exact (zenon_H148 zenon_H164). % 90.52/90.71 cut ((gt (succ (tptp_minus_1)) (n1)) = (gt (succ (n0)) (n1))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H130. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H167. % 90.52/90.71 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.71 cut (((succ (tptp_minus_1)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 90.52/90.71 congruence. % 90.52/90.71 apply (zenon_notand_s _ _ zenon_H15a); [ zenon_intro zenon_H15d | zenon_intro zenon_H15c ]. % 90.52/90.71 apply zenon_H15d. zenon_intro zenon_H15e. % 90.52/90.71 apply zenon_H108. apply sym_equal. exact zenon_H15e. % 90.52/90.71 apply zenon_H15c. zenon_intro zenon_H15f. % 90.52/90.71 generalize (zenon_H73 (succ (n0))). zenon_intro zenon_H127. % 90.52/90.71 generalize (zenon_H127 (succ (tptp_minus_1))). zenon_intro zenon_H160. % 90.52/90.71 generalize (zenon_H160 (n1)). zenon_intro zenon_H168. % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H168); [ zenon_intro zenon_Haf | zenon_intro zenon_H169 ]. % 90.52/90.71 exact (zenon_Haf zenon_H15f). % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H169); [ zenon_intro zenon_Hac | zenon_intro zenon_H12f ]. % 90.52/90.71 exact (zenon_Hac zenon_H167). % 90.52/90.71 exact (zenon_H130 zenon_H12f). % 90.52/90.71 apply zenon_H66. apply refl_equal. % 90.52/90.71 apply (zenon_L44_ zenon_TB_ec); trivial. % 90.52/90.71 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 90.52/90.71 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_Hb0. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_Hb1. % 90.52/90.71 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.71 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.71 congruence. % 90.52/90.71 exact (zenon_Hb3 successor_1). % 90.52/90.71 apply zenon_Hb2. apply refl_equal. % 90.52/90.71 apply zenon_Hb2. apply refl_equal. % 90.52/90.71 (* end of lemma zenon_L45_ *) % 90.52/90.71 assert (zenon_L46_ : forall (zenon_TB_ec : zenon_U), (~((tptp_minus_1) = (n1))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (tptp_minus_1) (n1))) -> (~((tptp_minus_1) = (n3))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n1))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.71 do 1 intro. intros zenon_He6 zenon_H73 zenon_H132 zenon_He8 zenon_Hb6 zenon_Hb5 zenon_Hae zenon_H97 zenon_H68. % 90.52/90.71 elim (classic ((~((tptp_minus_1) = (n2)))/\(~(gt (tptp_minus_1) (n2))))); [ zenon_intro zenon_H16a | zenon_intro zenon_H16b ]. % 90.52/90.71 apply (zenon_and_s _ _ zenon_H16a). zenon_intro zenon_He7. zenon_intro zenon_H16c. % 90.52/90.71 apply (zenon_L34_ zenon_TB_ec); trivial. % 90.52/90.71 cut ((gt (n2) (n1)) = (gt (tptp_minus_1) (n1))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H132. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact gt_2_1. % 90.52/90.71 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.71 cut (((n2) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H16d]. % 90.52/90.71 congruence. % 90.52/90.71 apply (zenon_notand_s _ _ zenon_H16b); [ zenon_intro zenon_H16f | zenon_intro zenon_H16e ]. % 90.52/90.71 apply zenon_H16f. zenon_intro zenon_H107. % 90.52/90.71 elim (classic ((tptp_minus_1) = (tptp_minus_1))); [ zenon_intro zenon_H113 | zenon_intro zenon_He4 ]. % 90.52/90.71 cut (((tptp_minus_1) = (tptp_minus_1)) = ((n2) = (tptp_minus_1))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H16d. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H113. % 90.52/90.71 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_He4]. % 90.52/90.71 cut (((tptp_minus_1) = (n2))); [idtac | apply NNPP; zenon_intro zenon_He7]. % 90.52/90.71 congruence. % 90.52/90.71 exact (zenon_He7 zenon_H107). % 90.52/90.71 apply zenon_He4. apply refl_equal. % 90.52/90.71 apply zenon_He4. apply refl_equal. % 90.52/90.71 apply zenon_H16e. zenon_intro zenon_H170. % 90.52/90.71 generalize (zenon_H73 (tptp_minus_1)). zenon_intro zenon_H171. % 90.52/90.71 generalize (zenon_H171 (n2)). zenon_intro zenon_H172. % 90.52/90.71 generalize (zenon_H172 (n1)). zenon_intro zenon_H173. % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H173); [ zenon_intro zenon_H16c | zenon_intro zenon_H174 ]. % 90.52/90.71 exact (zenon_H16c zenon_H170). % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H174); [ zenon_intro zenon_H7a | zenon_intro zenon_H134 ]. % 90.52/90.71 exact (zenon_H7a gt_2_1). % 90.52/90.71 exact (zenon_H132 zenon_H134). % 90.52/90.71 apply zenon_H66. apply refl_equal. % 90.52/90.71 (* end of lemma zenon_L46_ *) % 90.52/90.71 assert (zenon_L47_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n0)) (succ (n0)))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n1))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> (~(gt zenon_TB_ec (n1))) -> (~((tptp_minus_1) = (n3))) -> False). % 90.52/90.71 do 1 intro. intros zenon_H73 zenon_H119 zenon_H68 zenon_H97 zenon_Hae zenon_Hb5 zenon_Hb6 zenon_H148 zenon_He8. % 90.52/90.71 elim (classic (gt (n1) (succ (n0)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 90.52/90.71 cut ((gt (n1) (succ (n0))) = (gt (succ (n0)) (succ (n0)))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H119. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H13e. % 90.52/90.71 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.71 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 90.52/90.71 congruence. % 90.52/90.71 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 90.52/90.71 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_Hb0. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_Hb1. % 90.52/90.71 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.71 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.71 congruence. % 90.52/90.71 exact (zenon_Hb3 successor_1). % 90.52/90.71 apply zenon_Hb2. apply refl_equal. % 90.52/90.71 apply zenon_Hb2. apply refl_equal. % 90.52/90.71 apply zenon_Hb2. apply refl_equal. % 90.52/90.71 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_H12e | zenon_intro zenon_Hb0 ]. % 90.52/90.71 elim (classic (gt (n1) (n1))); [ zenon_intro zenon_H13d | zenon_intro zenon_H12d ]. % 90.52/90.71 cut ((gt (n1) (n1)) = (gt (n1) (succ (n0)))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H13f. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H13d. % 90.52/90.71 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 90.52/90.71 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.71 congruence. % 90.52/90.71 apply zenon_H66. apply refl_equal. % 90.52/90.71 exact (zenon_Hb0 zenon_H12e). % 90.52/90.71 apply (zenon_L44_ zenon_TB_ec); trivial. % 90.52/90.71 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 90.52/90.71 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_Hb0. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_Hb1. % 90.52/90.71 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.71 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.71 congruence. % 90.52/90.71 exact (zenon_Hb3 successor_1). % 90.52/90.71 apply zenon_Hb2. apply refl_equal. % 90.52/90.71 apply zenon_Hb2. apply refl_equal. % 90.52/90.71 (* end of lemma zenon_L47_ *) % 90.52/90.71 assert (zenon_L48_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (succ (n0)))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n1))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> (~((tptp_minus_1) = (n3))) -> (~(gt zenon_TB_ec (n1))) -> False). % 90.52/90.71 do 1 intro. intros zenon_H73 zenon_H111 zenon_H68 zenon_H97 zenon_Hae zenon_Hb5 zenon_Hb6 zenon_He8 zenon_H148. % 90.52/90.71 elim (classic (gt (tptp_minus_1) (succ (n0)))); [ zenon_intro zenon_H114 | zenon_intro zenon_H10f ]. % 90.52/90.71 generalize (zenon_H73 (n0)). zenon_intro zenon_H115. % 90.52/90.71 generalize (zenon_H115 (tptp_minus_1)). zenon_intro zenon_H116. % 90.52/90.71 generalize (zenon_H116 (succ (n0))). zenon_intro zenon_H117. % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H117); [ zenon_intro zenon_H101 | zenon_intro zenon_H118 ]. % 90.52/90.71 exact (zenon_H101 gt_0_tptp_minus_1). % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H118); [ zenon_intro zenon_H10f | zenon_intro zenon_H110 ]. % 90.52/90.71 exact (zenon_H10f zenon_H114). % 90.52/90.71 exact (zenon_H111 zenon_H110). % 90.52/90.71 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_H12e | zenon_intro zenon_Hb0 ]. % 90.52/90.71 elim (classic (gt (tptp_minus_1) (n1))); [ zenon_intro zenon_H134 | zenon_intro zenon_H132 ]. % 90.52/90.71 cut ((gt (tptp_minus_1) (n1)) = (gt (tptp_minus_1) (succ (n0)))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H10f. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H134. % 90.52/90.71 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 90.52/90.71 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_He4]. % 90.52/90.71 congruence. % 90.52/90.71 apply zenon_He4. apply refl_equal. % 90.52/90.71 exact (zenon_Hb0 zenon_H12e). % 90.52/90.71 elim (classic (gt (succ (n0)) (succ (n0)))); [ zenon_intro zenon_H12b | zenon_intro zenon_H119 ]. % 90.52/90.71 elim (classic (gt (n1) (succ (n0)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 90.52/90.71 cut ((gt (n1) (succ (n0))) = (gt (tptp_minus_1) (succ (n0)))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H10f. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H13e. % 90.52/90.71 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.71 cut (((n1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H140]. % 90.52/90.71 congruence. % 90.52/90.71 elim (classic ((tptp_minus_1) = (tptp_minus_1))); [ zenon_intro zenon_H113 | zenon_intro zenon_He4 ]. % 90.52/90.71 cut (((tptp_minus_1) = (tptp_minus_1)) = ((n1) = (tptp_minus_1))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H140. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H113. % 90.52/90.71 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_He4]. % 90.52/90.71 cut (((tptp_minus_1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_He6]. % 90.52/90.71 congruence. % 90.52/90.71 apply (zenon_L46_ zenon_TB_ec); trivial. % 90.52/90.71 apply zenon_He4. apply refl_equal. % 90.52/90.71 apply zenon_He4. apply refl_equal. % 90.52/90.71 apply zenon_Hb2. apply refl_equal. % 90.52/90.71 cut ((gt (succ (n0)) (succ (n0))) = (gt (n1) (succ (n0)))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H13f. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H12b. % 90.52/90.71 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.71 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.71 congruence. % 90.52/90.71 elim (classic ((n1) = (n1))); [ zenon_intro zenon_H131 | zenon_intro zenon_H66 ]. % 90.52/90.71 cut (((n1) = (n1)) = ((succ (n0)) = (n1))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_Hb3. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H131. % 90.52/90.71 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.71 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 90.52/90.71 congruence. % 90.52/90.71 exact (zenon_Hb0 zenon_H12e). % 90.52/90.71 apply zenon_H66. apply refl_equal. % 90.52/90.71 apply zenon_H66. apply refl_equal. % 90.52/90.71 apply zenon_Hb2. apply refl_equal. % 90.52/90.71 apply (zenon_L47_ zenon_TB_ec); trivial. % 90.52/90.71 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 90.52/90.71 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_Hb0. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_Hb1. % 90.52/90.71 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.71 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.71 congruence. % 90.52/90.71 exact (zenon_Hb3 successor_1). % 90.52/90.71 apply zenon_Hb2. apply refl_equal. % 90.52/90.71 apply zenon_Hb2. apply refl_equal. % 90.52/90.71 (* end of lemma zenon_L48_ *) % 90.52/90.71 assert (zenon_L49_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt zenon_TB_ec (n1))) -> (~((tptp_minus_1) = (n3))) -> (~(gt (succ (tptp_minus_1)) (succ (n0)))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n1))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> False). % 90.52/90.71 do 1 intro. intros zenon_H73 zenon_H148 zenon_He8 zenon_H10a zenon_H68 zenon_H97 zenon_Hae zenon_Hb5 zenon_Hb6. % 90.52/90.71 elim (classic (gt (succ (tptp_minus_1)) (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hc0 ]. % 90.52/90.71 elim (classic (gt (succ (tptp_minus_1)) (n0))); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hbf ]. % 90.52/90.71 elim (classic (gt (n0) (succ (n0)))); [ zenon_intro zenon_H110 | zenon_intro zenon_H111 ]. % 90.52/90.71 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.71 generalize (zenon_Hd1 (n0)). zenon_intro zenon_H141. % 90.52/90.71 generalize (zenon_H141 (succ (n0))). zenon_intro zenon_H142. % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H142); [ zenon_intro zenon_Hbf | zenon_intro zenon_H143 ]. % 90.52/90.71 exact (zenon_Hbf zenon_Hc1). % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H143); [ zenon_intro zenon_H111 | zenon_intro zenon_H10e ]. % 90.52/90.71 exact (zenon_H111 zenon_H110). % 90.52/90.71 exact (zenon_H10a zenon_H10e). % 90.52/90.71 apply (zenon_L48_ zenon_TB_ec); trivial. % 90.52/90.71 cut ((gt (succ (tptp_minus_1)) (succ (tptp_minus_1))) = (gt (succ (tptp_minus_1)) (n0))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_Hbf. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_Hc5. % 90.52/90.71 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.71 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.71 congruence. % 90.52/90.71 apply zenon_H8f. apply refl_equal. % 90.52/90.71 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.71 apply (zenon_L18_ zenon_TB_ec); trivial. % 90.52/90.71 (* end of lemma zenon_L49_ *) % 90.52/90.71 assert (zenon_L50_ : forall (zenon_TB_ec : zenon_U), (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n1))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (~(gt zenon_TB_ec (succ (n0)))) -> (~(gt zenon_TB_ec (n1))) -> (~((tptp_minus_1) = (n3))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.71 do 1 intro. intros zenon_Hb6 zenon_Hb5 zenon_Hae zenon_H97 zenon_H68 zenon_H109 zenon_H148 zenon_He8 zenon_H73. % 90.52/90.71 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 90.52/90.71 elim (classic (gt zenon_TB_ec (n0))); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hcb ]. % 90.52/90.71 elim (classic (gt zenon_TB_ec (succ (tptp_minus_1)))); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hc4 ]. % 90.52/90.71 elim (classic (gt (succ (tptp_minus_1)) (succ (n0)))); [ zenon_intro zenon_H10e | zenon_intro zenon_H10a ]. % 90.52/90.71 generalize (zenon_H73 zenon_TB_ec). zenon_intro zenon_H144. % 90.52/90.71 generalize (zenon_H144 (succ (tptp_minus_1))). zenon_intro zenon_H145. % 90.52/90.71 generalize (zenon_H145 (succ (n0))). zenon_intro zenon_H146. % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H146); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H147 ]. % 90.52/90.71 exact (zenon_Hc4 zenon_Hcc). % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H147); [ zenon_intro zenon_H10a | zenon_intro zenon_H10b ]. % 90.52/90.71 exact (zenon_H10a zenon_H10e). % 90.52/90.71 exact (zenon_H109 zenon_H10b). % 90.52/90.71 apply (zenon_L49_ zenon_TB_ec); trivial. % 90.52/90.71 cut ((gt zenon_TB_ec (n0)) = (gt zenon_TB_ec (succ (tptp_minus_1)))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_Hc4. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_Hd8. % 90.52/90.71 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.71 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.71 congruence. % 90.52/90.71 apply zenon_Ha1. apply refl_equal. % 90.52/90.71 exact (zenon_H72 zenon_H71). % 90.52/90.71 apply (zenon_L20_ zenon_TB_ec); trivial. % 90.52/90.71 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.71 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H72. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_Hc2. % 90.52/90.71 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.71 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.71 congruence. % 90.52/90.71 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.71 apply zenon_H8f. apply refl_equal. % 90.52/90.71 apply zenon_H8f. apply refl_equal. % 90.52/90.71 (* end of lemma zenon_L50_ *) % 90.52/90.71 assert (zenon_L51_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt zenon_TB_ec (n1))) -> (~((tptp_minus_1) = (n3))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n1))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.71 do 1 intro. intros zenon_H73 zenon_H148 zenon_He8 zenon_Hb6 zenon_Hb5 zenon_Hae zenon_H97 zenon_H68. % 90.52/90.71 elim (classic (gt zenon_TB_ec (succ (n0)))); [ zenon_intro zenon_H10b | zenon_intro zenon_H109 ]. % 90.52/90.71 cut ((gt zenon_TB_ec (succ (n0))) = (gt zenon_TB_ec (n1))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H148. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H10b. % 90.52/90.71 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.71 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.71 congruence. % 90.52/90.71 apply zenon_Ha1. apply refl_equal. % 90.52/90.71 exact (zenon_Hb3 successor_1). % 90.52/90.71 apply (zenon_L50_ zenon_TB_ec); trivial. % 90.52/90.71 (* end of lemma zenon_L51_ *) % 90.52/90.71 assert (zenon_L52_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (n3))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n1))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> (~(gt zenon_TB_ec (n1))) -> False). % 90.52/90.71 do 1 intro. intros zenon_H73 zenon_H175 zenon_H68 zenon_H97 zenon_Hae zenon_Hb5 zenon_Hb6 zenon_H148. % 90.52/90.71 elim (classic ((tptp_minus_1) = (n3))); [ zenon_intro zenon_H106 | zenon_intro zenon_He8 ]. % 90.52/90.71 cut ((gt (n0) (tptp_minus_1)) = (gt (n0) (n3))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H175. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact gt_0_tptp_minus_1. % 90.52/90.71 cut (((tptp_minus_1) = (n3))); [idtac | apply NNPP; zenon_intro zenon_He8]. % 90.52/90.71 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.71 congruence. % 90.52/90.71 apply zenon_H67. apply refl_equal. % 90.52/90.71 exact (zenon_He8 zenon_H106). % 90.52/90.71 apply (zenon_L51_ zenon_TB_ec); trivial. % 90.52/90.71 (* end of lemma zenon_L52_ *) % 90.52/90.71 assert (zenon_L53_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (n3))) -> (~(gt zenon_TB_ec (n1))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n1))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.71 do 1 intro. intros zenon_H73 zenon_H176 zenon_H148 zenon_Hb6 zenon_Hb5 zenon_Hae zenon_H97 zenon_H68. % 90.52/90.71 elim (classic (gt (n0) (n3))); [ zenon_intro zenon_H177 | zenon_intro zenon_H175 ]. % 90.52/90.71 generalize (zenon_H73 (n1)). zenon_intro zenon_H138. % 90.52/90.71 generalize (zenon_H138 (n0)). zenon_intro zenon_H139. % 90.52/90.71 generalize (zenon_H139 (n3)). zenon_intro zenon_H178. % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H178); [ zenon_intro zenon_H13c | zenon_intro zenon_H179 ]. % 90.52/90.71 exact (zenon_H13c gt_1_0). % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H179); [ zenon_intro zenon_H175 | zenon_intro zenon_H17a ]. % 90.52/90.71 exact (zenon_H175 zenon_H177). % 90.52/90.71 exact (zenon_H176 zenon_H17a). % 90.52/90.71 apply (zenon_L52_ zenon_TB_ec); trivial. % 90.52/90.71 (* end of lemma zenon_L53_ *) % 90.52/90.71 assert (zenon_L54_ : forall (zenon_TB_ec : zenon_U), (~(gt zenon_TB_ec (n1))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n1))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (n1))) -> False). % 90.52/90.71 do 1 intro. intros zenon_H148 zenon_Hb6 zenon_Hb5 zenon_Hae zenon_H97 zenon_H68 zenon_H73 zenon_H12d. % 90.52/90.71 elim (classic ((~((n1) = (n3)))/\(~(gt (n1) (n3))))); [ zenon_intro zenon_H17b | zenon_intro zenon_H17c ]. % 90.52/90.71 apply (zenon_and_s _ _ zenon_H17b). zenon_intro zenon_H17d. zenon_intro zenon_H176. % 90.52/90.71 apply (zenon_L53_ zenon_TB_ec); trivial. % 90.52/90.71 cut ((gt (n3) (n1)) = (gt (n1) (n1))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H12d. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact gt_3_1. % 90.52/90.71 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.71 cut (((n3) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 90.52/90.71 congruence. % 90.52/90.71 apply (zenon_notand_s _ _ zenon_H17c); [ zenon_intro zenon_H180 | zenon_intro zenon_H17f ]. % 90.52/90.71 apply zenon_H180. zenon_intro zenon_H181. % 90.52/90.71 elim (classic ((n1) = (n1))); [ zenon_intro zenon_H131 | zenon_intro zenon_H66 ]. % 90.52/90.71 cut (((n1) = (n1)) = ((n3) = (n1))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H17e. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H131. % 90.52/90.71 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.71 cut (((n1) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H17d]. % 90.52/90.71 congruence. % 90.52/90.71 exact (zenon_H17d zenon_H181). % 90.52/90.71 apply zenon_H66. apply refl_equal. % 90.52/90.71 apply zenon_H66. apply refl_equal. % 90.52/90.71 apply zenon_H17f. zenon_intro zenon_H17a. % 90.52/90.71 generalize (zenon_H73 (n1)). zenon_intro zenon_H138. % 90.52/90.71 generalize (zenon_H138 (n3)). zenon_intro zenon_H182. % 90.52/90.71 generalize (zenon_H182 (n1)). zenon_intro zenon_H183. % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H183); [ zenon_intro zenon_H176 | zenon_intro zenon_H184 ]. % 90.52/90.71 exact (zenon_H176 zenon_H17a). % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H184); [ zenon_intro zenon_H185 | zenon_intro zenon_H13d ]. % 90.52/90.71 exact (zenon_H185 gt_3_1). % 90.52/90.71 exact (zenon_H12d zenon_H13d). % 90.52/90.71 apply zenon_H66. apply refl_equal. % 90.52/90.71 (* end of lemma zenon_L54_ *) % 90.52/90.71 assert (zenon_L55_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n0)) (succ (n0)))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n1))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> (~(gt zenon_TB_ec (n1))) -> False). % 90.52/90.71 do 1 intro. intros zenon_H73 zenon_H119 zenon_H68 zenon_H97 zenon_Hae zenon_Hb5 zenon_Hb6 zenon_H148. % 90.52/90.71 elim (classic (gt (n1) (succ (n0)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 90.52/90.71 cut ((gt (n1) (succ (n0))) = (gt (succ (n0)) (succ (n0)))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H119. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H13e. % 90.52/90.71 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.71 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 90.52/90.71 congruence. % 90.52/90.71 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 90.52/90.71 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_Hb0. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_Hb1. % 90.52/90.71 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.71 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.71 congruence. % 90.52/90.71 exact (zenon_Hb3 successor_1). % 90.52/90.71 apply zenon_Hb2. apply refl_equal. % 90.52/90.71 apply zenon_Hb2. apply refl_equal. % 90.52/90.71 apply zenon_Hb2. apply refl_equal. % 90.52/90.71 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_H12e | zenon_intro zenon_Hb0 ]. % 90.52/90.71 elim (classic (gt (n1) (n1))); [ zenon_intro zenon_H13d | zenon_intro zenon_H12d ]. % 90.52/90.71 cut ((gt (n1) (n1)) = (gt (n1) (succ (n0)))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H13f. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H13d. % 90.52/90.71 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 90.52/90.71 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.71 congruence. % 90.52/90.71 apply zenon_H66. apply refl_equal. % 90.52/90.71 exact (zenon_Hb0 zenon_H12e). % 90.52/90.71 apply (zenon_L54_ zenon_TB_ec); trivial. % 90.52/90.71 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 90.52/90.71 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_Hb0. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_Hb1. % 90.52/90.71 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.71 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.71 congruence. % 90.52/90.71 exact (zenon_Hb3 successor_1). % 90.52/90.71 apply zenon_Hb2. apply refl_equal. % 90.52/90.71 apply zenon_Hb2. apply refl_equal. % 90.52/90.71 (* end of lemma zenon_L55_ *) % 90.52/90.71 assert (zenon_L56_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n1))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> (~(gt zenon_TB_ec (n1))) -> (~(gt (tptp_minus_1) (succ (n0)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.71 do 1 intro. intros zenon_H68 zenon_H97 zenon_Hae zenon_Hb5 zenon_Hb6 zenon_H148 zenon_H10f zenon_H73. % 90.52/90.71 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_H12e | zenon_intro zenon_Hb0 ]. % 90.52/90.71 elim (classic (gt (tptp_minus_1) (n1))); [ zenon_intro zenon_H134 | zenon_intro zenon_H132 ]. % 90.52/90.71 cut ((gt (tptp_minus_1) (n1)) = (gt (tptp_minus_1) (succ (n0)))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H10f. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H134. % 90.52/90.71 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 90.52/90.71 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_He4]. % 90.52/90.71 congruence. % 90.52/90.71 apply zenon_He4. apply refl_equal. % 90.52/90.71 exact (zenon_Hb0 zenon_H12e). % 90.52/90.71 elim (classic (gt (succ (n0)) (succ (n0)))); [ zenon_intro zenon_H12b | zenon_intro zenon_H119 ]. % 90.52/90.71 elim (classic (gt (n1) (succ (n0)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 90.52/90.71 cut ((gt (n1) (succ (n0))) = (gt (tptp_minus_1) (succ (n0)))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H10f. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H13e. % 90.52/90.71 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.71 cut (((n1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H140]. % 90.52/90.71 congruence. % 90.52/90.71 elim (classic ((tptp_minus_1) = (tptp_minus_1))); [ zenon_intro zenon_H113 | zenon_intro zenon_He4 ]. % 90.52/90.71 cut (((tptp_minus_1) = (tptp_minus_1)) = ((n1) = (tptp_minus_1))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H140. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H113. % 90.52/90.71 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_He4]. % 90.52/90.71 cut (((tptp_minus_1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_He6]. % 90.52/90.71 congruence. % 90.52/90.71 elim (classic ((~((tptp_minus_1) = (n3)))/\(~(gt (tptp_minus_1) (n3))))); [ zenon_intro zenon_H186 | zenon_intro zenon_H187 ]. % 90.52/90.71 apply (zenon_and_s _ _ zenon_H186). zenon_intro zenon_He8. zenon_intro zenon_H188. % 90.52/90.71 apply (zenon_L46_ zenon_TB_ec); trivial. % 90.52/90.71 cut ((gt (n3) (n1)) = (gt (tptp_minus_1) (n1))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H132. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact gt_3_1. % 90.52/90.71 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.71 cut (((n3) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 90.52/90.71 congruence. % 90.52/90.71 apply (zenon_notand_s _ _ zenon_H187); [ zenon_intro zenon_H18b | zenon_intro zenon_H18a ]. % 90.52/90.71 apply zenon_H18b. zenon_intro zenon_H106. % 90.52/90.71 elim (classic ((tptp_minus_1) = (tptp_minus_1))); [ zenon_intro zenon_H113 | zenon_intro zenon_He4 ]. % 90.52/90.71 cut (((tptp_minus_1) = (tptp_minus_1)) = ((n3) = (tptp_minus_1))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H189. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H113. % 90.52/90.71 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_He4]. % 90.52/90.71 cut (((tptp_minus_1) = (n3))); [idtac | apply NNPP; zenon_intro zenon_He8]. % 90.52/90.71 congruence. % 90.52/90.71 exact (zenon_He8 zenon_H106). % 90.52/90.71 apply zenon_He4. apply refl_equal. % 90.52/90.71 apply zenon_He4. apply refl_equal. % 90.52/90.71 apply zenon_H18a. zenon_intro zenon_H18c. % 90.52/90.71 generalize (zenon_H73 (tptp_minus_1)). zenon_intro zenon_H171. % 90.52/90.71 generalize (zenon_H171 (n3)). zenon_intro zenon_H18d. % 90.52/90.71 generalize (zenon_H18d (n1)). zenon_intro zenon_H18e. % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H18e); [ zenon_intro zenon_H188 | zenon_intro zenon_H18f ]. % 90.52/90.71 exact (zenon_H188 zenon_H18c). % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H18f); [ zenon_intro zenon_H185 | zenon_intro zenon_H134 ]. % 90.52/90.71 exact (zenon_H185 gt_3_1). % 90.52/90.71 exact (zenon_H132 zenon_H134). % 90.52/90.71 apply zenon_H66. apply refl_equal. % 90.52/90.71 apply zenon_He4. apply refl_equal. % 90.52/90.71 apply zenon_He4. apply refl_equal. % 90.52/90.71 apply zenon_Hb2. apply refl_equal. % 90.52/90.71 cut ((gt (succ (n0)) (succ (n0))) = (gt (n1) (succ (n0)))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H13f. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H12b. % 90.52/90.71 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.71 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.71 congruence. % 90.52/90.71 elim (classic ((n1) = (n1))); [ zenon_intro zenon_H131 | zenon_intro zenon_H66 ]. % 90.52/90.71 cut (((n1) = (n1)) = ((succ (n0)) = (n1))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_Hb3. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H131. % 90.52/90.71 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.71 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 90.52/90.71 congruence. % 90.52/90.71 exact (zenon_Hb0 zenon_H12e). % 90.52/90.71 apply zenon_H66. apply refl_equal. % 90.52/90.71 apply zenon_H66. apply refl_equal. % 90.52/90.71 apply zenon_Hb2. apply refl_equal. % 90.52/90.71 apply (zenon_L55_ zenon_TB_ec); trivial. % 90.52/90.71 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 90.52/90.71 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_Hb0. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_Hb1. % 90.52/90.71 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.71 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.71 congruence. % 90.52/90.71 exact (zenon_Hb3 successor_1). % 90.52/90.71 apply zenon_Hb2. apply refl_equal. % 90.52/90.71 apply zenon_Hb2. apply refl_equal. % 90.52/90.71 (* end of lemma zenon_L56_ *) % 90.52/90.71 assert (zenon_L57_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n0)) (succ (n0)))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> (~((tptp_minus_1) = (n3))) -> False). % 90.52/90.71 do 1 intro. intros zenon_H73 zenon_H119 zenon_H68 zenon_H97 zenon_Hb5 zenon_Hb6 zenon_He8. % 90.52/90.71 elim (classic (gt (n1) (succ (n0)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 90.52/90.71 cut ((gt (n1) (succ (n0))) = (gt (succ (n0)) (succ (n0)))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H119. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H13e. % 90.52/90.71 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.71 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 90.52/90.71 congruence. % 90.52/90.71 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 90.52/90.71 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_Hb0. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_Hb1. % 90.52/90.71 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.71 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.71 congruence. % 90.52/90.71 exact (zenon_Hb3 successor_1). % 90.52/90.71 apply zenon_Hb2. apply refl_equal. % 90.52/90.71 apply zenon_Hb2. apply refl_equal. % 90.52/90.71 apply zenon_Hb2. apply refl_equal. % 90.52/90.71 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_H12e | zenon_intro zenon_Hb0 ]. % 90.52/90.71 elim (classic (gt (n1) (n1))); [ zenon_intro zenon_H13d | zenon_intro zenon_H12d ]. % 90.52/90.71 cut ((gt (n1) (n1)) = (gt (n1) (succ (n0)))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H13f. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H13d. % 90.52/90.71 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 90.52/90.71 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.71 congruence. % 90.52/90.71 apply zenon_H66. apply refl_equal. % 90.52/90.71 exact (zenon_Hb0 zenon_H12e). % 90.52/90.71 apply (zenon_L45_ zenon_TB_ec); trivial. % 90.52/90.71 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 90.52/90.71 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_Hb0. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_Hb1. % 90.52/90.71 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.71 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.71 congruence. % 90.52/90.71 exact (zenon_Hb3 successor_1). % 90.52/90.71 apply zenon_Hb2. apply refl_equal. % 90.52/90.71 apply zenon_Hb2. apply refl_equal. % 90.52/90.71 (* end of lemma zenon_L57_ *) % 90.52/90.71 assert (zenon_L58_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> (~(gt (tptp_minus_1) (succ (n0)))) -> (~(gt (succ (tptp_minus_1)) (succ (n0)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.71 do 1 intro. intros zenon_H68 zenon_H97 zenon_Hb5 zenon_Hb6 zenon_H10f zenon_H10a zenon_H73. % 90.52/90.71 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_H12e | zenon_intro zenon_Hb0 ]. % 90.52/90.71 elim (classic (gt (succ (tptp_minus_1)) (n1))); [ zenon_intro zenon_H167 | zenon_intro zenon_Hac ]. % 90.52/90.71 cut ((gt (succ (tptp_minus_1)) (n1)) = (gt (succ (tptp_minus_1)) (succ (n0)))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H10a. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H167. % 90.52/90.71 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 90.52/90.71 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.71 congruence. % 90.52/90.71 apply zenon_H8f. apply refl_equal. % 90.52/90.71 exact (zenon_Hb0 zenon_H12e). % 90.52/90.71 elim (classic (zenon_TB_ec = (n1))); [ zenon_intro zenon_Had | zenon_intro zenon_Hae ]. % 90.52/90.71 cut ((gt (succ (tptp_minus_1)) zenon_TB_ec) = (gt (succ (tptp_minus_1)) (n1))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_Hac. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H97. % 90.52/90.71 cut ((zenon_TB_ec = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hae]. % 90.52/90.71 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.71 congruence. % 90.52/90.71 apply zenon_H8f. apply refl_equal. % 90.52/90.71 exact (zenon_Hae zenon_Had). % 90.52/90.71 elim (classic (gt zenon_TB_ec (n1))); [ zenon_intro zenon_H164 | zenon_intro zenon_H148 ]. % 90.52/90.71 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.71 generalize (zenon_Hd1 zenon_TB_ec). zenon_intro zenon_Hd2. % 90.52/90.71 generalize (zenon_Hd2 (n1)). zenon_intro zenon_H165. % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H165); [ zenon_intro zenon_Hab | zenon_intro zenon_H166 ]. % 90.52/90.71 exact (zenon_Hab zenon_H97). % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H166); [ zenon_intro zenon_H148 | zenon_intro zenon_H167 ]. % 90.52/90.71 exact (zenon_H148 zenon_H164). % 90.52/90.71 exact (zenon_Hac zenon_H167). % 90.52/90.71 apply (zenon_L56_ zenon_TB_ec); trivial. % 90.52/90.71 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 90.52/90.71 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_Hb0. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_Hb1. % 90.52/90.71 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.71 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.71 congruence. % 90.52/90.71 exact (zenon_Hb3 successor_1). % 90.52/90.71 apply zenon_Hb2. apply refl_equal. % 90.52/90.71 apply zenon_Hb2. apply refl_equal. % 90.52/90.71 (* end of lemma zenon_L58_ *) % 90.52/90.71 assert (zenon_L59_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> (~(gt (tptp_minus_1) (succ (n0)))) -> (~(gt (n0) (succ (n0)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.71 do 1 intro. intros zenon_H68 zenon_H97 zenon_Hb5 zenon_Hb6 zenon_H10f zenon_H111 zenon_H73. % 90.52/90.71 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 90.52/90.71 elim (classic (gt (succ (tptp_minus_1)) (succ (n0)))); [ zenon_intro zenon_H10e | zenon_intro zenon_H10a ]. % 90.52/90.71 cut ((gt (succ (tptp_minus_1)) (succ (n0))) = (gt (n0) (succ (n0)))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H111. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H10e. % 90.52/90.71 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.71 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.71 congruence. % 90.52/90.71 elim (classic ((n0) = (n0))); [ zenon_intro zenon_Hca | zenon_intro zenon_H67 ]. % 90.52/90.71 cut (((n0) = (n0)) = ((succ (tptp_minus_1)) = (n0))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_Hc3. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_Hca. % 90.52/90.71 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.71 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.71 congruence. % 90.52/90.71 exact (zenon_H72 zenon_H71). % 90.52/90.71 apply zenon_H67. apply refl_equal. % 90.52/90.71 apply zenon_H67. apply refl_equal. % 90.52/90.71 apply zenon_Hb2. apply refl_equal. % 90.52/90.71 apply (zenon_L58_ zenon_TB_ec); trivial. % 90.52/90.71 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.71 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H72. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_Hc2. % 90.52/90.71 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.71 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.71 congruence. % 90.52/90.71 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.71 apply zenon_H8f. apply refl_equal. % 90.52/90.71 apply zenon_H8f. apply refl_equal. % 90.52/90.71 (* end of lemma zenon_L59_ *) % 90.52/90.71 assert (zenon_L60_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (succ (n0)))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> False). % 90.52/90.71 do 1 intro. intros zenon_H73 zenon_H111 zenon_H68 zenon_H97 zenon_Hb5 zenon_Hb6. % 90.52/90.71 elim (classic (gt (tptp_minus_1) (succ (n0)))); [ zenon_intro zenon_H114 | zenon_intro zenon_H10f ]. % 90.52/90.71 generalize (zenon_H73 (n0)). zenon_intro zenon_H115. % 90.52/90.71 generalize (zenon_H115 (tptp_minus_1)). zenon_intro zenon_H116. % 90.52/90.71 generalize (zenon_H116 (succ (n0))). zenon_intro zenon_H117. % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H117); [ zenon_intro zenon_H101 | zenon_intro zenon_H118 ]. % 90.52/90.71 exact (zenon_H101 gt_0_tptp_minus_1). % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H118); [ zenon_intro zenon_H10f | zenon_intro zenon_H110 ]. % 90.52/90.71 exact (zenon_H10f zenon_H114). % 90.52/90.71 exact (zenon_H111 zenon_H110). % 90.52/90.71 apply (zenon_L59_ zenon_TB_ec); trivial. % 90.52/90.71 (* end of lemma zenon_L60_ *) % 90.52/90.71 assert (zenon_L61_ : forall (zenon_TB_ec : zenon_U), (~((tptp_minus_1) = (n3))) -> (~(gt zenon_TB_ec (n1))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (tptp_minus_1) (n0))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n1))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> False). % 90.52/90.71 do 1 intro. intros zenon_He8 zenon_H148 zenon_H73 zenon_H190 zenon_H68 zenon_H97 zenon_Hae zenon_Hb5 zenon_Hb6. % 90.52/90.71 elim (classic ((~((tptp_minus_1) = (n2)))/\(~(gt (tptp_minus_1) (n2))))); [ zenon_intro zenon_H16a | zenon_intro zenon_H16b ]. % 90.52/90.71 apply (zenon_and_s _ _ zenon_H16a). zenon_intro zenon_He7. zenon_intro zenon_H16c. % 90.52/90.71 apply (zenon_L41_ zenon_TB_ec); trivial. % 90.52/90.71 cut ((gt (n2) (n0)) = (gt (tptp_minus_1) (n0))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H190. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact gt_2_0. % 90.52/90.71 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.71 cut (((n2) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H16d]. % 90.52/90.71 congruence. % 90.52/90.71 apply (zenon_notand_s _ _ zenon_H16b); [ zenon_intro zenon_H16f | zenon_intro zenon_H16e ]. % 90.52/90.71 apply zenon_H16f. zenon_intro zenon_H107. % 90.52/90.71 elim (classic ((tptp_minus_1) = (tptp_minus_1))); [ zenon_intro zenon_H113 | zenon_intro zenon_He4 ]. % 90.52/90.71 cut (((tptp_minus_1) = (tptp_minus_1)) = ((n2) = (tptp_minus_1))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H16d. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H113. % 90.52/90.71 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_He4]. % 90.52/90.71 cut (((tptp_minus_1) = (n2))); [idtac | apply NNPP; zenon_intro zenon_He7]. % 90.52/90.71 congruence. % 90.52/90.71 exact (zenon_He7 zenon_H107). % 90.52/90.71 apply zenon_He4. apply refl_equal. % 90.52/90.71 apply zenon_He4. apply refl_equal. % 90.52/90.71 apply zenon_H16e. zenon_intro zenon_H170. % 90.52/90.71 generalize (zenon_H73 (tptp_minus_1)). zenon_intro zenon_H171. % 90.52/90.71 generalize (zenon_H171 (n2)). zenon_intro zenon_H172. % 90.52/90.71 generalize (zenon_H172 (n0)). zenon_intro zenon_H191. % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H191); [ zenon_intro zenon_H16c | zenon_intro zenon_H192 ]. % 90.52/90.71 exact (zenon_H16c zenon_H170). % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H192); [ zenon_intro zenon_H194 | zenon_intro zenon_H193 ]. % 90.52/90.71 exact (zenon_H194 gt_2_0). % 90.52/90.71 exact (zenon_H190 zenon_H193). % 90.52/90.71 apply zenon_H67. apply refl_equal. % 90.52/90.71 (* end of lemma zenon_L61_ *) % 90.52/90.71 assert (zenon_L62_ : forall (zenon_TB_ec : zenon_U), (~(gt zenon_TB_ec (n1))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (tptp_minus_1) (n0))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n1))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> False). % 90.52/90.71 do 1 intro. intros zenon_H148 zenon_H73 zenon_H190 zenon_H68 zenon_H97 zenon_Hae zenon_Hb5 zenon_Hb6. % 90.52/90.71 elim (classic ((~((tptp_minus_1) = (n3)))/\(~(gt (tptp_minus_1) (n3))))); [ zenon_intro zenon_H186 | zenon_intro zenon_H187 ]. % 90.52/90.71 apply (zenon_and_s _ _ zenon_H186). zenon_intro zenon_He8. zenon_intro zenon_H188. % 90.52/90.71 apply (zenon_L61_ zenon_TB_ec); trivial. % 90.52/90.71 cut ((gt (n3) (n0)) = (gt (tptp_minus_1) (n0))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H190. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact gt_3_0. % 90.52/90.71 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.71 cut (((n3) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 90.52/90.71 congruence. % 90.52/90.71 apply (zenon_notand_s _ _ zenon_H187); [ zenon_intro zenon_H18b | zenon_intro zenon_H18a ]. % 90.52/90.71 apply zenon_H18b. zenon_intro zenon_H106. % 90.52/90.71 elim (classic ((tptp_minus_1) = (tptp_minus_1))); [ zenon_intro zenon_H113 | zenon_intro zenon_He4 ]. % 90.52/90.71 cut (((tptp_minus_1) = (tptp_minus_1)) = ((n3) = (tptp_minus_1))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H189. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H113. % 90.52/90.71 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_He4]. % 90.52/90.71 cut (((tptp_minus_1) = (n3))); [idtac | apply NNPP; zenon_intro zenon_He8]. % 90.52/90.71 congruence. % 90.52/90.71 exact (zenon_He8 zenon_H106). % 90.52/90.71 apply zenon_He4. apply refl_equal. % 90.52/90.71 apply zenon_He4. apply refl_equal. % 90.52/90.71 apply zenon_H18a. zenon_intro zenon_H18c. % 90.52/90.71 generalize (zenon_H73 (tptp_minus_1)). zenon_intro zenon_H171. % 90.52/90.71 generalize (zenon_H171 (n3)). zenon_intro zenon_H18d. % 90.52/90.71 generalize (zenon_H18d (n0)). zenon_intro zenon_H195. % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H195); [ zenon_intro zenon_H188 | zenon_intro zenon_H196 ]. % 90.52/90.71 exact (zenon_H188 zenon_H18c). % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H196); [ zenon_intro zenon_H197 | zenon_intro zenon_H193 ]. % 90.52/90.71 exact (zenon_H197 gt_3_0). % 90.52/90.71 exact (zenon_H190 zenon_H193). % 90.52/90.71 apply zenon_H67. apply refl_equal. % 90.52/90.71 (* end of lemma zenon_L62_ *) % 90.52/90.71 assert (zenon_L63_ : forall (zenon_TB_ec : zenon_U), (~(gt (tptp_minus_1) (n0))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt zenon_TB_ec (n0))) -> False). % 90.52/90.71 do 1 intro. intros zenon_H190 zenon_Hb6 zenon_Hb5 zenon_H97 zenon_H68 zenon_H73 zenon_Hcb. % 90.52/90.71 elim (classic ((~(zenon_TB_ec = (n1)))/\(~(gt zenon_TB_ec (n1))))); [ zenon_intro zenon_H198 | zenon_intro zenon_H199 ]. % 90.52/90.71 apply (zenon_and_s _ _ zenon_H198). zenon_intro zenon_Hae. zenon_intro zenon_H148. % 90.52/90.71 apply (zenon_L62_ zenon_TB_ec); trivial. % 90.52/90.71 cut ((gt (n1) (n0)) = (gt zenon_TB_ec (n0))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_Hcb. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact gt_1_0. % 90.52/90.71 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.71 cut (((n1) = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 90.52/90.71 congruence. % 90.52/90.71 apply (zenon_notand_s _ _ zenon_H199); [ zenon_intro zenon_H19c | zenon_intro zenon_H19b ]. % 90.52/90.71 apply zenon_H19c. zenon_intro zenon_Had. % 90.52/90.71 elim (classic (zenon_TB_ec = zenon_TB_ec)); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Ha1 ]. % 90.52/90.71 cut ((zenon_TB_ec = zenon_TB_ec) = ((n1) = zenon_TB_ec)). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H19a. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_Hc9. % 90.52/90.71 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.71 cut ((zenon_TB_ec = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hae]. % 90.52/90.71 congruence. % 90.52/90.71 exact (zenon_Hae zenon_Had). % 90.52/90.71 apply zenon_Ha1. apply refl_equal. % 90.52/90.71 apply zenon_Ha1. apply refl_equal. % 90.52/90.71 apply zenon_H19b. zenon_intro zenon_H164. % 90.52/90.71 generalize (zenon_H73 zenon_TB_ec). zenon_intro zenon_H144. % 90.52/90.71 generalize (zenon_H144 (n1)). zenon_intro zenon_H19d. % 90.52/90.71 generalize (zenon_H19d (n0)). zenon_intro zenon_H19e. % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H19e); [ zenon_intro zenon_H148 | zenon_intro zenon_H19f ]. % 90.52/90.71 exact (zenon_H148 zenon_H164). % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H19f); [ zenon_intro zenon_H13c | zenon_intro zenon_Hd8 ]. % 90.52/90.71 exact (zenon_H13c gt_1_0). % 90.52/90.71 exact (zenon_Hcb zenon_Hd8). % 90.52/90.71 apply zenon_H67. apply refl_equal. % 90.52/90.71 (* end of lemma zenon_L63_ *) % 90.52/90.71 assert (zenon_L64_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (sum (n0) (tptp_minus_1) zenon_E))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (tptp_minus_1) (n0))) -> False). % 90.52/90.71 do 1 intro. intros zenon_H73 zenon_Hcd zenon_H68 zenon_H97 zenon_Hb5 zenon_Hb6 zenon_Hce zenon_H190. % 90.52/90.71 elim (classic (gt zenon_TB_ec (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd0 ]. % 90.52/90.71 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.71 generalize (zenon_Hd1 zenon_TB_ec). zenon_intro zenon_Hd2. % 90.52/90.71 generalize (zenon_Hd2 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_Hd3. % 90.52/90.71 apply (zenon_imply_s _ _ zenon_Hd3); [ zenon_intro zenon_Hab | zenon_intro zenon_Hd4 ]. % 90.52/90.71 exact (zenon_Hab zenon_H97). % 90.52/90.71 apply (zenon_imply_s _ _ zenon_Hd4); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hd5 ]. % 90.52/90.71 exact (zenon_Hd0 zenon_Hcf). % 90.52/90.71 exact (zenon_Hcd zenon_Hd5). % 90.52/90.71 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 90.52/90.71 elim (classic (gt zenon_TB_ec (n0))); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hcb ]. % 90.52/90.71 cut ((gt zenon_TB_ec (n0)) = (gt zenon_TB_ec (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_Hd0. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_Hd8. % 90.52/90.71 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 90.52/90.71 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.71 congruence. % 90.52/90.71 apply zenon_Ha1. apply refl_equal. % 90.52/90.71 exact (zenon_Hd7 zenon_Hd6). % 90.52/90.71 apply (zenon_L63_ zenon_TB_ec); trivial. % 90.52/90.71 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd9 | zenon_intro zenon_Hda ]. % 90.52/90.71 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_Hd7. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_Hd9. % 90.52/90.71 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.71 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 90.52/90.71 congruence. % 90.52/90.71 exact (zenon_Hdb zenon_Hce). % 90.52/90.71 apply zenon_Hda. apply refl_equal. % 90.52/90.71 apply zenon_Hda. apply refl_equal. % 90.52/90.71 (* end of lemma zenon_L64_ *) % 90.52/90.71 assert (zenon_L65_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (tptp_minus_1) (n0))) -> (~(gt (n0) (sum (n0) (tptp_minus_1) zenon_E))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.71 do 1 intro. intros zenon_H68 zenon_H97 zenon_Hb5 zenon_Hb6 zenon_Hce zenon_H190 zenon_Hde zenon_H73. % 90.52/90.71 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 90.52/90.71 elim (classic (gt (succ (tptp_minus_1)) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd5 | zenon_intro zenon_Hcd ]. % 90.52/90.71 cut ((gt (succ (tptp_minus_1)) (sum (n0) (tptp_minus_1) zenon_E)) = (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_Hde. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_Hd5. % 90.52/90.71 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.71 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.71 congruence. % 90.52/90.71 elim (classic ((n0) = (n0))); [ zenon_intro zenon_Hca | zenon_intro zenon_H67 ]. % 90.52/90.71 cut (((n0) = (n0)) = ((succ (tptp_minus_1)) = (n0))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_Hc3. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_Hca. % 90.52/90.71 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.71 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.71 congruence. % 90.52/90.71 exact (zenon_H72 zenon_H71). % 90.52/90.71 apply zenon_H67. apply refl_equal. % 90.52/90.71 apply zenon_H67. apply refl_equal. % 90.52/90.71 apply zenon_Hda. apply refl_equal. % 90.52/90.71 apply (zenon_L64_ zenon_TB_ec); trivial. % 90.52/90.71 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.71 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H72. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_Hc2. % 90.52/90.71 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.71 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.71 congruence. % 90.52/90.71 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.71 apply zenon_H8f. apply refl_equal. % 90.52/90.71 apply zenon_H8f. apply refl_equal. % 90.52/90.71 (* end of lemma zenon_L65_ *) % 90.52/90.71 assert (zenon_L66_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (tptp_minus_1) (n0))) -> False). % 90.52/90.71 do 1 intro. intros zenon_H73 zenon_Hdc zenon_H68 zenon_H97 zenon_Hb5 zenon_Hb6 zenon_Hce zenon_H190. % 90.52/90.71 elim (classic (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hde ]. % 90.52/90.71 cut ((gt (n0) (sum (n0) (tptp_minus_1) zenon_E)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_Hdc. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_Hdd. % 90.52/90.71 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.71 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 90.52/90.71 congruence. % 90.52/90.71 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd9 | zenon_intro zenon_Hda ]. % 90.52/90.71 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_Hd7. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_Hd9. % 90.52/90.71 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.71 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 90.52/90.71 congruence. % 90.52/90.71 exact (zenon_Hdb zenon_Hce). % 90.52/90.71 apply zenon_Hda. apply refl_equal. % 90.52/90.71 apply zenon_Hda. apply refl_equal. % 90.52/90.71 apply zenon_Hda. apply refl_equal. % 90.52/90.71 apply (zenon_L65_ zenon_TB_ec); trivial. % 90.52/90.71 (* end of lemma zenon_L66_ *) % 90.52/90.71 assert (zenon_L67_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (n1))) -> (~(gt (tptp_minus_1) (n0))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.71 do 1 intro. intros zenon_H73 zenon_H1a0 zenon_H190 zenon_Hce zenon_Hb6 zenon_Hb5 zenon_H97 zenon_H68. % 90.52/90.71 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (n0)))); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H1a2 ]. % 90.52/90.71 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (succ (n0))) = (gt (sum (n0) (tptp_minus_1) zenon_E) (n1))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H1a0. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_H1a1. % 90.52/90.71 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.71 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.71 congruence. % 90.52/90.71 apply zenon_Hda. apply refl_equal. % 90.52/90.71 exact (zenon_Hb3 successor_1). % 90.52/90.71 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_He2 | zenon_intro zenon_Hdc ]. % 90.52/90.71 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))); [ zenon_intro zenon_He0 | zenon_intro zenon_He1 ]. % 90.52/90.71 elim (classic (gt (n0) (succ (n0)))); [ zenon_intro zenon_H110 | zenon_intro zenon_H111 ]. % 90.52/90.71 generalize (zenon_H73 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H1a3. % 90.52/90.71 generalize (zenon_H1a3 (n0)). zenon_intro zenon_H1a4. % 90.52/90.71 generalize (zenon_H1a4 (succ (n0))). zenon_intro zenon_H1a5. % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H1a5); [ zenon_intro zenon_He1 | zenon_intro zenon_H1a6 ]. % 90.52/90.71 exact (zenon_He1 zenon_He0). % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H1a6); [ zenon_intro zenon_H111 | zenon_intro zenon_H1a1 ]. % 90.52/90.71 exact (zenon_H111 zenon_H110). % 90.52/90.71 exact (zenon_H1a2 zenon_H1a1). % 90.52/90.71 apply (zenon_L60_ zenon_TB_ec); trivial. % 90.52/90.71 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_He1. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_He2. % 90.52/90.71 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 90.52/90.71 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.71 congruence. % 90.52/90.71 apply zenon_Hda. apply refl_equal. % 90.52/90.71 exact (zenon_Hdb zenon_Hce). % 90.52/90.71 apply (zenon_L66_ zenon_TB_ec); trivial. % 90.52/90.71 (* end of lemma zenon_L67_ *) % 90.52/90.71 assert (zenon_L68_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (tptp_minus_1) (n0))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (n0))) -> False). % 90.52/90.71 do 1 intro. intros zenon_H68 zenon_H97 zenon_Hb5 zenon_Hb6 zenon_Hce zenon_H190 zenon_H73 zenon_He1. % 90.52/90.71 elim (classic ((~((sum (n0) (tptp_minus_1) zenon_E) = (n1)))/\(~(gt (sum (n0) (tptp_minus_1) zenon_E) (n1))))); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H1a8 ]. % 90.52/90.71 apply (zenon_and_s _ _ zenon_H1a7). zenon_intro zenon_H1a9. zenon_intro zenon_H1a0. % 90.52/90.71 apply (zenon_L67_ zenon_TB_ec); trivial. % 90.52/90.71 cut ((gt (n1) (n0)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_He1. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact gt_1_0. % 90.52/90.71 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.71 cut (((n1) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1aa]. % 90.52/90.71 congruence. % 90.52/90.71 apply (zenon_notand_s _ _ zenon_H1a8); [ zenon_intro zenon_H1ac | zenon_intro zenon_H1ab ]. % 90.52/90.71 apply zenon_H1ac. zenon_intro zenon_H1ad. % 90.52/90.71 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd9 | zenon_intro zenon_Hda ]. % 90.52/90.71 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n1) = (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_H1aa. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_Hd9. % 90.52/90.71 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.71 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 90.52/90.71 congruence. % 90.52/90.71 exact (zenon_H1a9 zenon_H1ad). % 90.52/90.71 apply zenon_Hda. apply refl_equal. % 90.52/90.71 apply zenon_Hda. apply refl_equal. % 90.52/90.71 apply zenon_H1ab. zenon_intro zenon_H1ae. % 90.52/90.71 generalize (zenon_H73 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H1a3. % 90.52/90.71 generalize (zenon_H1a3 (n1)). zenon_intro zenon_H1af. % 90.52/90.71 generalize (zenon_H1af (n0)). zenon_intro zenon_H1b0. % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H1b0); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H1b1 ]. % 90.52/90.71 exact (zenon_H1a0 zenon_H1ae). % 90.52/90.71 apply (zenon_imply_s _ _ zenon_H1b1); [ zenon_intro zenon_H13c | zenon_intro zenon_He0 ]. % 90.52/90.71 exact (zenon_H13c gt_1_0). % 90.52/90.71 exact (zenon_He1 zenon_He0). % 90.52/90.71 apply zenon_H67. apply refl_equal. % 90.52/90.71 (* end of lemma zenon_L68_ *) % 90.52/90.71 assert (zenon_L69_ : forall (zenon_TB_ec : zenon_U), (~(gt (tptp_minus_1) (n0))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (n0))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False). % 90.52/90.71 do 1 intro. intros zenon_H190 zenon_Hb6 zenon_Hb5 zenon_H97 zenon_H68 zenon_H73 zenon_Hdf zenon_Hce. % 90.52/90.71 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 90.52/90.71 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))); [ zenon_intro zenon_He0 | zenon_intro zenon_He1 ]. % 90.52/90.71 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (n0)) = (gt (n0) (n0))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_Hdf. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_He0. % 90.52/90.71 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.71 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 90.52/90.71 congruence. % 90.52/90.71 elim (classic ((n0) = (n0))); [ zenon_intro zenon_Hca | zenon_intro zenon_H67 ]. % 90.52/90.71 cut (((n0) = (n0)) = ((sum (n0) (tptp_minus_1) zenon_E) = (n0))). % 90.52/90.71 intro zenon_D_pnotp. % 90.52/90.71 apply zenon_Hdb. % 90.52/90.71 rewrite <- zenon_D_pnotp. % 90.52/90.71 exact zenon_Hca. % 90.52/90.71 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.71 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 90.52/90.71 congruence. % 90.52/90.71 exact (zenon_Hd7 zenon_Hd6). % 90.52/90.71 apply zenon_H67. apply refl_equal. % 90.52/90.71 apply zenon_H67. apply refl_equal. % 90.52/90.71 apply zenon_H67. apply refl_equal. % 90.52/90.72 apply (zenon_L68_ zenon_TB_ec); trivial. % 90.52/90.72 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd9 | zenon_intro zenon_Hda ]. % 90.52/90.72 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_Hd7. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_Hd9. % 90.52/90.72 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.72 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 90.52/90.72 congruence. % 90.52/90.72 exact (zenon_Hdb zenon_Hce). % 90.52/90.72 apply zenon_Hda. apply refl_equal. % 90.52/90.72 apply zenon_Hda. apply refl_equal. % 90.52/90.72 (* end of lemma zenon_L69_ *) % 90.52/90.72 assert (zenon_L70_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (n0))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.72 do 1 intro. intros zenon_H73 zenon_Hdf zenon_Hce zenon_Hb6 zenon_Hb5 zenon_H97 zenon_H68. % 90.52/90.72 elim (classic (gt (tptp_minus_1) (n0))); [ zenon_intro zenon_H193 | zenon_intro zenon_H190 ]. % 90.52/90.72 generalize (zenon_H73 (n0)). zenon_intro zenon_H115. % 90.52/90.72 generalize (zenon_H115 (tptp_minus_1)). zenon_intro zenon_H116. % 90.52/90.72 generalize (zenon_H116 (n0)). zenon_intro zenon_H1b2. % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H1b2); [ zenon_intro zenon_H101 | zenon_intro zenon_H1b3 ]. % 90.52/90.72 exact (zenon_H101 gt_0_tptp_minus_1). % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H1b3); [ zenon_intro zenon_H190 | zenon_intro zenon_H1b4 ]. % 90.52/90.72 exact (zenon_H190 zenon_H193). % 90.52/90.72 exact (zenon_Hdf zenon_H1b4). % 90.52/90.72 apply (zenon_L69_ zenon_TB_ec); trivial. % 90.52/90.72 (* end of lemma zenon_L70_ *) % 90.52/90.72 assert (zenon_L71_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(leq (tptp_minus_1) (n0))) -> False). % 90.52/90.72 do 0 intro. intros zenon_H73 zenon_H1b5. % 90.52/90.72 generalize (leq_succ_gt_equiv (tptp_minus_1)). zenon_intro zenon_Hf0. % 90.52/90.72 generalize (zenon_Hf0 (n0)). zenon_intro zenon_H1b6. % 90.52/90.72 apply (zenon_equiv_s _ _ zenon_H1b6); [ zenon_intro zenon_H1b5; zenon_intro zenon_H1b9 | zenon_intro zenon_H1b8; zenon_intro zenon_H1b7 ]. % 90.52/90.72 elim (classic ((~((succ (n0)) = (n1)))/\(~(gt (succ (n0)) (n1))))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 90.52/90.72 apply (zenon_and_s _ _ zenon_H1ba). zenon_intro zenon_Hb3. zenon_intro zenon_H130. % 90.52/90.72 exact (zenon_Hb3 successor_1). % 90.52/90.72 cut ((gt (n1) (tptp_minus_1)) = (gt (succ (n0)) (tptp_minus_1))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H1b9. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact gt_1_tptp_minus_1. % 90.52/90.72 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_He4]. % 90.52/90.72 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 90.52/90.72 congruence. % 90.52/90.72 apply (zenon_notand_s _ _ zenon_H1bb); [ zenon_intro zenon_H1bd | zenon_intro zenon_H1bc ]. % 90.52/90.72 apply zenon_H1bd. zenon_intro successor_1. % 90.52/90.72 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 90.52/90.72 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_Hb0. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_Hb1. % 90.52/90.72 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.72 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.72 congruence. % 90.52/90.72 exact (zenon_Hb3 successor_1). % 90.52/90.72 apply zenon_Hb2. apply refl_equal. % 90.52/90.72 apply zenon_Hb2. apply refl_equal. % 90.52/90.72 apply zenon_H1bc. zenon_intro zenon_H12f. % 90.52/90.72 generalize (zenon_H73 (succ (n0))). zenon_intro zenon_H127. % 90.52/90.72 generalize (zenon_H127 (n1)). zenon_intro zenon_H1be. % 90.52/90.72 generalize (zenon_H1be (tptp_minus_1)). zenon_intro zenon_H1bf. % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H1bf); [ zenon_intro zenon_H130 | zenon_intro zenon_H1c0 ]. % 90.52/90.72 exact (zenon_H130 zenon_H12f). % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H1c0); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H1b7 ]. % 90.52/90.72 exact (zenon_H1c1 gt_1_tptp_minus_1). % 90.52/90.72 exact (zenon_H1b9 zenon_H1b7). % 90.52/90.72 apply zenon_He4. apply refl_equal. % 90.52/90.72 exact (zenon_H1b5 zenon_H1b8). % 90.52/90.72 (* end of lemma zenon_L71_ *) % 90.52/90.72 assert (zenon_L72_ : (~((succ (tptp_minus_1)) = (succ (n0)))) -> ((tptp_minus_1) = (n0)) -> False). % 90.52/90.72 do 0 intro. intros zenon_H108 zenon_H103. % 90.52/90.72 cut (((tptp_minus_1) = (n0))); [idtac | apply NNPP; zenon_intro zenon_He5]. % 90.52/90.72 congruence. % 90.52/90.72 exact (zenon_He5 zenon_H103). % 90.52/90.72 (* end of lemma zenon_L72_ *) % 90.52/90.72 assert (zenon_L73_ : forall (zenon_TB_ec : zenon_U), ((tptp_minus_1) = (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(leq zenon_TB_ec (n0))) -> False). % 90.52/90.72 do 1 intro. intros zenon_H103 zenon_H97 zenon_H1c2. % 90.52/90.72 generalize (leq_succ_gt_equiv zenon_TB_ec). zenon_intro zenon_H99. % 90.52/90.72 generalize (zenon_H99 (n0)). zenon_intro zenon_H1c3. % 90.52/90.72 apply (zenon_equiv_s _ _ zenon_H1c3); [ zenon_intro zenon_H1c2; zenon_intro zenon_H1c5 | zenon_intro zenon_H1c4; zenon_intro zenon_H163 ]. % 90.52/90.72 cut ((gt (succ (tptp_minus_1)) zenon_TB_ec) = (gt (succ (n0)) zenon_TB_ec)). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H1c5. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_H97. % 90.52/90.72 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.72 cut (((succ (tptp_minus_1)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 90.52/90.72 congruence. % 90.52/90.72 apply (zenon_L72_); trivial. % 90.52/90.72 apply zenon_Ha1. apply refl_equal. % 90.52/90.72 exact (zenon_H1c2 zenon_H1c4). % 90.52/90.72 (* end of lemma zenon_L73_ *) % 90.52/90.72 assert (zenon_L74_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> ((tptp_minus_1) = (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~((n0) = zenon_TB_ec)) -> False). % 90.52/90.72 do 1 intro. intros zenon_H68 zenon_H103 zenon_H97 zenon_Hc8. % 90.52/90.72 generalize (finite_domain_0 zenon_TB_ec). zenon_intro zenon_H1c6. % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H1c6); [ zenon_intro zenon_H1c7 | zenon_intro zenon_Hbb ]. % 90.52/90.72 apply (zenon_notand_s _ _ zenon_H1c7); [ zenon_intro zenon_H69 | zenon_intro zenon_H1c2 ]. % 90.52/90.72 apply (zenon_L5_ zenon_TB_ec); trivial. % 90.52/90.72 apply (zenon_L73_ zenon_TB_ec); trivial. % 90.52/90.72 apply zenon_Hc8. apply sym_equal. exact zenon_Hbb. % 90.52/90.72 (* end of lemma zenon_L74_ *) % 90.52/90.72 assert (zenon_L75_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~((succ (n0)) = (succ zenon_TB_ec))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.72 do 1 intro. intros zenon_H73 zenon_He3 zenon_Hb6 zenon_Hb5 zenon_H97 zenon_H68. % 90.52/90.72 cut (((n0) = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Hc8]. % 90.52/90.72 congruence. % 90.52/90.72 generalize (finite_domain_3 zenon_TB_ec). zenon_intro zenon_Hb7. % 90.52/90.72 apply (zenon_imply_s _ _ zenon_Hb7); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 90.52/90.72 apply (zenon_notand_s _ _ zenon_Hb9); [ zenon_intro zenon_H69 | zenon_intro zenon_H98 ]. % 90.52/90.72 apply (zenon_L5_ zenon_TB_ec); trivial. % 90.52/90.72 apply (zenon_L13_ zenon_TB_ec); trivial. % 90.52/90.72 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 90.52/90.72 apply zenon_Hc8. apply sym_equal. exact zenon_Hbb. % 90.52/90.72 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_Had | zenon_intro zenon_Hbc ]. % 90.52/90.72 generalize (finite_domain_0 (tptp_minus_1)). zenon_intro zenon_H1c8. % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H1c8); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H103 ]. % 90.52/90.72 apply (zenon_notand_s _ _ zenon_H1c9); [ zenon_intro zenon_Hed | zenon_intro zenon_H1b5 ]. % 90.52/90.72 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H6b. % 90.52/90.72 generalize (zenon_H6b (tptp_minus_1)). zenon_intro zenon_Hee. % 90.52/90.72 apply (zenon_equiv_s _ _ zenon_Hee); [ zenon_intro zenon_Hed; zenon_intro zenon_Hbf | zenon_intro zenon_Hef; zenon_intro zenon_Hc1 ]. % 90.52/90.72 elim (classic ((~((succ (tptp_minus_1)) = (n1)))/\(~(gt (succ (tptp_minus_1)) (n1))))); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1cb ]. % 90.52/90.72 apply (zenon_and_s _ _ zenon_H1ca). zenon_intro zenon_H1cc. zenon_intro zenon_Hac. % 90.52/90.72 apply (zenon_L14_ zenon_TB_ec); trivial. % 90.52/90.72 cut ((gt (n1) (n0)) = (gt (succ (tptp_minus_1)) (n0))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_Hbf. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact gt_1_0. % 90.52/90.72 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.72 cut (((n1) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H1cd]. % 90.52/90.72 congruence. % 90.52/90.72 apply (zenon_notand_s _ _ zenon_H1cb); [ zenon_intro zenon_H1cf | zenon_intro zenon_H1ce ]. % 90.52/90.72 apply zenon_H1cf. zenon_intro zenon_H1d0. % 90.52/90.72 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.72 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n1) = (succ (tptp_minus_1)))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H1cd. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_Hc2. % 90.52/90.72 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.72 cut (((succ (tptp_minus_1)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H1cc]. % 90.52/90.72 congruence. % 90.52/90.72 exact (zenon_H1cc zenon_H1d0). % 90.52/90.72 apply zenon_H8f. apply refl_equal. % 90.52/90.72 apply zenon_H8f. apply refl_equal. % 90.52/90.72 apply zenon_H1ce. zenon_intro zenon_H167. % 90.52/90.72 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.72 generalize (zenon_Hd1 (n1)). zenon_intro zenon_H1d1. % 90.52/90.72 generalize (zenon_H1d1 (n0)). zenon_intro zenon_H1d2. % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H1d2); [ zenon_intro zenon_Hac | zenon_intro zenon_H1d3 ]. % 90.52/90.72 exact (zenon_Hac zenon_H167). % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H1d3); [ zenon_intro zenon_H13c | zenon_intro zenon_Hc1 ]. % 90.52/90.72 exact (zenon_H13c gt_1_0). % 90.52/90.72 exact (zenon_Hbf zenon_Hc1). % 90.52/90.72 apply zenon_H67. apply refl_equal. % 90.52/90.72 exact (zenon_Hed zenon_Hef). % 90.52/90.72 apply (zenon_L71_); trivial. % 90.52/90.72 apply (zenon_L74_ zenon_TB_ec); trivial. % 90.52/90.72 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hbd ]. % 90.52/90.72 exact (zenon_Hb5 zenon_Hbe). % 90.52/90.72 exact (zenon_Hb6 zenon_Hbd). % 90.52/90.72 (* end of lemma zenon_L75_ *) % 90.52/90.72 assert (zenon_L76_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> (~((tptp_minus_1) = (n3))) -> (~(gt (n1) (succ zenon_TB_ec))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.72 do 1 intro. intros zenon_H68 zenon_H97 zenon_Hb5 zenon_Hb6 zenon_He8 zenon_H1d4 zenon_H73. % 90.52/90.72 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_H12e | zenon_intro zenon_Hb0 ]. % 90.52/90.72 elim (classic (gt (n1) (n1))); [ zenon_intro zenon_H13d | zenon_intro zenon_H12d ]. % 90.52/90.72 elim (classic (gt (n1) (succ (n0)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 90.52/90.72 cut ((gt (n1) (succ (n0))) = (gt (n1) (succ zenon_TB_ec))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H1d4. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_H13e. % 90.52/90.72 cut (((succ (n0)) = (succ zenon_TB_ec))); [idtac | apply NNPP; zenon_intro zenon_He3]. % 90.52/90.72 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.72 congruence. % 90.52/90.72 apply zenon_H66. apply refl_equal. % 90.52/90.72 apply (zenon_L75_ zenon_TB_ec); trivial. % 90.52/90.72 cut ((gt (n1) (n1)) = (gt (n1) (succ (n0)))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H13f. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_H13d. % 90.52/90.72 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 90.52/90.72 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.72 congruence. % 90.52/90.72 apply zenon_H66. apply refl_equal. % 90.52/90.72 exact (zenon_Hb0 zenon_H12e). % 90.52/90.72 apply (zenon_L45_ zenon_TB_ec); trivial. % 90.52/90.72 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 90.52/90.72 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_Hb0. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_Hb1. % 90.52/90.72 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.72 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.72 congruence. % 90.52/90.72 exact (zenon_Hb3 successor_1). % 90.52/90.72 apply zenon_Hb2. apply refl_equal. % 90.52/90.72 apply zenon_Hb2. apply refl_equal. % 90.52/90.72 (* end of lemma zenon_L76_ *) % 90.52/90.72 assert (zenon_L77_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (succ (n0)))) -> (~(gt (succ (tptp_minus_1)) (succ (n0)))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.72 do 1 intro. intros zenon_H73 zenon_H111 zenon_H10a zenon_Hb6 zenon_Hb5 zenon_H97 zenon_H68. % 90.52/90.72 elim (classic (gt (tptp_minus_1) (succ (n0)))); [ zenon_intro zenon_H114 | zenon_intro zenon_H10f ]. % 90.52/90.72 generalize (zenon_H73 (n0)). zenon_intro zenon_H115. % 90.52/90.72 generalize (zenon_H115 (tptp_minus_1)). zenon_intro zenon_H116. % 90.52/90.72 generalize (zenon_H116 (succ (n0))). zenon_intro zenon_H117. % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H117); [ zenon_intro zenon_H101 | zenon_intro zenon_H118 ]. % 90.52/90.72 exact (zenon_H101 gt_0_tptp_minus_1). % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H118); [ zenon_intro zenon_H10f | zenon_intro zenon_H110 ]. % 90.52/90.72 exact (zenon_H10f zenon_H114). % 90.52/90.72 exact (zenon_H111 zenon_H110). % 90.52/90.72 apply (zenon_L58_ zenon_TB_ec); trivial. % 90.52/90.72 (* end of lemma zenon_L77_ *) % 90.52/90.72 assert (zenon_L78_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> (~(gt (succ (tptp_minus_1)) (succ (n0)))) -> False). % 90.52/90.72 do 1 intro. intros zenon_H73 zenon_H68 zenon_H97 zenon_Hb5 zenon_Hb6 zenon_H10a. % 90.52/90.72 elim (classic (gt (n0) (succ (n0)))); [ zenon_intro zenon_H110 | zenon_intro zenon_H111 ]. % 90.52/90.72 cut ((gt (n0) (succ (n0))) = (gt (succ (tptp_minus_1)) (succ (n0)))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H10a. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_H110. % 90.52/90.72 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.72 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.72 congruence. % 90.52/90.72 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.72 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H72. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_Hc2. % 90.52/90.72 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.72 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.72 congruence. % 90.52/90.72 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.72 apply zenon_H8f. apply refl_equal. % 90.52/90.72 apply zenon_H8f. apply refl_equal. % 90.52/90.72 apply zenon_Hb2. apply refl_equal. % 90.52/90.72 apply (zenon_L77_ zenon_TB_ec); trivial. % 90.52/90.72 (* end of lemma zenon_L78_ *) % 90.52/90.72 assert (zenon_L79_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (succ zenon_TB_ec))) -> (~((tptp_minus_1) = (n3))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.72 do 1 intro. intros zenon_H73 zenon_H1d5 zenon_He8 zenon_Hb6 zenon_Hb5 zenon_H97 zenon_H68. % 90.52/90.72 elim (classic (gt (succ (tptp_minus_1)) (succ (n0)))); [ zenon_intro zenon_H10e | zenon_intro zenon_H10a ]. % 90.52/90.72 elim (classic (gt (succ (tptp_minus_1)) (n1))); [ zenon_intro zenon_H167 | zenon_intro zenon_Hac ]. % 90.52/90.72 elim (classic (gt (n1) (succ zenon_TB_ec))); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H1d4 ]. % 90.52/90.72 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.72 generalize (zenon_Hd1 (n1)). zenon_intro zenon_H1d1. % 90.52/90.72 generalize (zenon_H1d1 (succ zenon_TB_ec)). zenon_intro zenon_H1d7. % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H1d7); [ zenon_intro zenon_Hac | zenon_intro zenon_H1d8 ]. % 90.52/90.72 exact (zenon_Hac zenon_H167). % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H1d8); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1d9 ]. % 90.52/90.72 exact (zenon_H1d4 zenon_H1d6). % 90.52/90.72 exact (zenon_H1d5 zenon_H1d9). % 90.52/90.72 apply (zenon_L76_ zenon_TB_ec); trivial. % 90.52/90.72 cut ((gt (succ (tptp_minus_1)) (succ (n0))) = (gt (succ (tptp_minus_1)) (n1))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_Hac. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_H10e. % 90.52/90.72 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.72 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.72 congruence. % 90.52/90.72 apply zenon_H8f. apply refl_equal. % 90.52/90.72 exact (zenon_Hb3 successor_1). % 90.52/90.72 apply (zenon_L78_ zenon_TB_ec); trivial. % 90.52/90.72 (* end of lemma zenon_L79_ *) % 90.52/90.72 assert (zenon_L80_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~((tptp_minus_1) = (n3))) -> (~(gt zenon_TB_ec (n1))) -> (~(gt (succ (tptp_minus_1)) (n2))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n1))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> False). % 90.52/90.72 do 1 intro. intros zenon_H73 zenon_He8 zenon_H148 zenon_H1da zenon_H68 zenon_H97 zenon_Hae zenon_Hb5 zenon_Hb6. % 90.52/90.72 elim (classic (gt (succ (tptp_minus_1)) (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hc0 ]. % 90.52/90.72 elim (classic (gt (succ (tptp_minus_1)) (n0))); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hbf ]. % 90.52/90.72 elim (classic (gt (n0) (n2))); [ zenon_intro zenon_H14b | zenon_intro zenon_H149 ]. % 90.52/90.72 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.72 generalize (zenon_Hd1 (n0)). zenon_intro zenon_H141. % 90.52/90.72 generalize (zenon_H141 (n2)). zenon_intro zenon_H1db. % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H1db); [ zenon_intro zenon_Hbf | zenon_intro zenon_H1dc ]. % 90.52/90.72 exact (zenon_Hbf zenon_Hc1). % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H1dc); [ zenon_intro zenon_H149 | zenon_intro zenon_H1dd ]. % 90.52/90.72 exact (zenon_H149 zenon_H14b). % 90.52/90.72 exact (zenon_H1da zenon_H1dd). % 90.52/90.72 apply (zenon_L42_ zenon_TB_ec); trivial. % 90.52/90.72 cut ((gt (succ (tptp_minus_1)) (succ (tptp_minus_1))) = (gt (succ (tptp_minus_1)) (n0))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_Hbf. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_Hc5. % 90.52/90.72 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.72 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.72 congruence. % 90.52/90.72 apply zenon_H8f. apply refl_equal. % 90.52/90.72 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.72 apply (zenon_L18_ zenon_TB_ec); trivial. % 90.52/90.72 (* end of lemma zenon_L80_ *) % 90.52/90.72 assert (zenon_L81_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> (~((tptp_minus_1) = (n3))) -> (~(gt (succ (tptp_minus_1)) (n2))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt zenon_TB_ec (n0))) -> False). % 90.52/90.72 do 1 intro. intros zenon_H68 zenon_H97 zenon_Hb5 zenon_Hb6 zenon_He8 zenon_H1da zenon_H73 zenon_Hcb. % 90.52/90.72 elim (classic ((~(zenon_TB_ec = (n1)))/\(~(gt zenon_TB_ec (n1))))); [ zenon_intro zenon_H198 | zenon_intro zenon_H199 ]. % 90.52/90.72 apply (zenon_and_s _ _ zenon_H198). zenon_intro zenon_Hae. zenon_intro zenon_H148. % 90.52/90.72 apply (zenon_L80_ zenon_TB_ec); trivial. % 90.52/90.72 cut ((gt (n1) (n0)) = (gt zenon_TB_ec (n0))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_Hcb. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact gt_1_0. % 90.52/90.72 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.72 cut (((n1) = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 90.52/90.72 congruence. % 90.52/90.72 apply (zenon_notand_s _ _ zenon_H199); [ zenon_intro zenon_H19c | zenon_intro zenon_H19b ]. % 90.52/90.72 apply zenon_H19c. zenon_intro zenon_Had. % 90.52/90.72 elim (classic (zenon_TB_ec = zenon_TB_ec)); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Ha1 ]. % 90.52/90.72 cut ((zenon_TB_ec = zenon_TB_ec) = ((n1) = zenon_TB_ec)). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H19a. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_Hc9. % 90.52/90.72 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.72 cut ((zenon_TB_ec = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hae]. % 90.52/90.72 congruence. % 90.52/90.72 exact (zenon_Hae zenon_Had). % 90.52/90.72 apply zenon_Ha1. apply refl_equal. % 90.52/90.72 apply zenon_Ha1. apply refl_equal. % 90.52/90.72 apply zenon_H19b. zenon_intro zenon_H164. % 90.52/90.72 generalize (zenon_H73 zenon_TB_ec). zenon_intro zenon_H144. % 90.52/90.72 generalize (zenon_H144 (n1)). zenon_intro zenon_H19d. % 90.52/90.72 generalize (zenon_H19d (n0)). zenon_intro zenon_H19e. % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H19e); [ zenon_intro zenon_H148 | zenon_intro zenon_H19f ]. % 90.52/90.72 exact (zenon_H148 zenon_H164). % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H19f); [ zenon_intro zenon_H13c | zenon_intro zenon_Hd8 ]. % 90.52/90.72 exact (zenon_H13c gt_1_0). % 90.52/90.72 exact (zenon_Hcb zenon_Hd8). % 90.52/90.72 apply zenon_H67. apply refl_equal. % 90.52/90.72 (* end of lemma zenon_L81_ *) % 90.52/90.72 assert (zenon_L82_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (sum (n0) (tptp_minus_1) zenon_E))) -> (~(gt (succ (tptp_minus_1)) (n2))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~((tptp_minus_1) = (n3))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.72 do 1 intro. intros zenon_H73 zenon_Hcd zenon_H1da zenon_Hce zenon_He8 zenon_Hb6 zenon_Hb5 zenon_H97 zenon_H68. % 90.52/90.72 elim (classic (gt zenon_TB_ec (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd0 ]. % 90.52/90.72 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.72 generalize (zenon_Hd1 zenon_TB_ec). zenon_intro zenon_Hd2. % 90.52/90.72 generalize (zenon_Hd2 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_Hd3. % 90.52/90.72 apply (zenon_imply_s _ _ zenon_Hd3); [ zenon_intro zenon_Hab | zenon_intro zenon_Hd4 ]. % 90.52/90.72 exact (zenon_Hab zenon_H97). % 90.52/90.72 apply (zenon_imply_s _ _ zenon_Hd4); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hd5 ]. % 90.52/90.72 exact (zenon_Hd0 zenon_Hcf). % 90.52/90.72 exact (zenon_Hcd zenon_Hd5). % 90.52/90.72 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 90.52/90.72 elim (classic (gt zenon_TB_ec (n0))); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hcb ]. % 90.52/90.72 cut ((gt zenon_TB_ec (n0)) = (gt zenon_TB_ec (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_Hd0. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_Hd8. % 90.52/90.72 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 90.52/90.72 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.72 congruence. % 90.52/90.72 apply zenon_Ha1. apply refl_equal. % 90.52/90.72 exact (zenon_Hd7 zenon_Hd6). % 90.52/90.72 apply (zenon_L81_ zenon_TB_ec); trivial. % 90.52/90.72 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd9 | zenon_intro zenon_Hda ]. % 90.52/90.72 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_Hd7. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_Hd9. % 90.52/90.72 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.72 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 90.52/90.72 congruence. % 90.52/90.72 exact (zenon_Hdb zenon_Hce). % 90.52/90.72 apply zenon_Hda. apply refl_equal. % 90.52/90.72 apply zenon_Hda. apply refl_equal. % 90.52/90.72 (* end of lemma zenon_L82_ *) % 90.52/90.72 assert (zenon_L83_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))) -> (~(gt (succ (tptp_minus_1)) (n2))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~((tptp_minus_1) = (n3))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.72 do 1 intro. intros zenon_H73 zenon_Hdc zenon_H1da zenon_Hce zenon_He8 zenon_Hb6 zenon_Hb5 zenon_H97 zenon_H68. % 90.52/90.72 elim (classic (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hde ]. % 90.52/90.72 cut ((gt (n0) (sum (n0) (tptp_minus_1) zenon_E)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_Hdc. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_Hdd. % 90.52/90.72 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.72 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 90.52/90.72 congruence. % 90.52/90.72 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd9 | zenon_intro zenon_Hda ]. % 90.52/90.72 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_Hd7. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_Hd9. % 90.52/90.72 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.72 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 90.52/90.72 congruence. % 90.52/90.72 exact (zenon_Hdb zenon_Hce). % 90.52/90.72 apply zenon_Hda. apply refl_equal. % 90.52/90.72 apply zenon_Hda. apply refl_equal. % 90.52/90.72 apply zenon_Hda. apply refl_equal. % 90.52/90.72 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 90.52/90.72 elim (classic (gt (succ (tptp_minus_1)) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd5 | zenon_intro zenon_Hcd ]. % 90.52/90.72 cut ((gt (succ (tptp_minus_1)) (sum (n0) (tptp_minus_1) zenon_E)) = (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_Hde. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_Hd5. % 90.52/90.72 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.72 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.72 congruence. % 90.52/90.72 elim (classic ((n0) = (n0))); [ zenon_intro zenon_Hca | zenon_intro zenon_H67 ]. % 90.52/90.72 cut (((n0) = (n0)) = ((succ (tptp_minus_1)) = (n0))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_Hc3. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_Hca. % 90.52/90.72 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.72 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.72 congruence. % 90.52/90.72 exact (zenon_H72 zenon_H71). % 90.52/90.72 apply zenon_H67. apply refl_equal. % 90.52/90.72 apply zenon_H67. apply refl_equal. % 90.52/90.72 apply zenon_Hda. apply refl_equal. % 90.52/90.72 apply (zenon_L82_ zenon_TB_ec); trivial. % 90.52/90.72 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.72 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H72. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_Hc2. % 90.52/90.72 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.72 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.72 congruence. % 90.52/90.72 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.72 apply zenon_H8f. apply refl_equal. % 90.52/90.72 apply zenon_H8f. apply refl_equal. % 90.52/90.72 (* end of lemma zenon_L83_ *) % 90.52/90.72 assert (zenon_L84_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (n0))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> (~((tptp_minus_1) = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (succ (tptp_minus_1)) (n2))) -> False). % 90.52/90.72 do 1 intro. intros zenon_H73 zenon_He1 zenon_H68 zenon_H97 zenon_Hb5 zenon_Hb6 zenon_He8 zenon_Hce zenon_H1da. % 90.52/90.72 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_He2 | zenon_intro zenon_Hdc ]. % 90.52/90.72 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_He1. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_He2. % 90.52/90.72 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 90.52/90.72 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.72 congruence. % 90.52/90.72 apply zenon_Hda. apply refl_equal. % 90.52/90.72 exact (zenon_Hdb zenon_Hce). % 90.52/90.72 apply (zenon_L83_ zenon_TB_ec); trivial. % 90.52/90.72 (* end of lemma zenon_L84_ *) % 90.52/90.72 assert (zenon_L85_ : forall (zenon_TB_ec : zenon_U), (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (~((tptp_minus_1) = (n3))) -> (~(gt (n0) (succ zenon_TB_ec))) -> (~(gt (succ (tptp_minus_1)) (n2))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False). % 90.52/90.72 do 1 intro. intros zenon_Hb6 zenon_Hb5 zenon_H97 zenon_H68 zenon_He8 zenon_H1de zenon_H1da zenon_H73 zenon_Hce. % 90.52/90.72 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 90.52/90.72 elim (classic (gt (n0) (n0))); [ zenon_intro zenon_H1b4 | zenon_intro zenon_Hdf ]. % 90.52/90.72 elim (classic (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hde ]. % 90.52/90.72 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (succ zenon_TB_ec))); [ zenon_intro zenon_H1df | zenon_intro zenon_H1e0 ]. % 90.52/90.72 generalize (zenon_H73 (n0)). zenon_intro zenon_H115. % 90.52/90.72 generalize (zenon_H115 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H1e1. % 90.52/90.72 generalize (zenon_H1e1 (succ zenon_TB_ec)). zenon_intro zenon_H1e2. % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H1e2); [ zenon_intro zenon_Hde | zenon_intro zenon_H1e3 ]. % 90.52/90.72 exact (zenon_Hde zenon_Hdd). % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H1e3); [ zenon_intro zenon_H1e0 | zenon_intro zenon_H1e4 ]. % 90.52/90.72 exact (zenon_H1e0 zenon_H1df). % 90.52/90.72 exact (zenon_H1de zenon_H1e4). % 90.52/90.72 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 90.52/90.72 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))); [ zenon_intro zenon_He0 | zenon_intro zenon_He1 ]. % 90.52/90.72 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (tptp_minus_1)))); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e6 ]. % 90.52/90.72 elim (classic (gt (succ (tptp_minus_1)) (succ zenon_TB_ec))); [ zenon_intro zenon_H1d9 | zenon_intro zenon_H1d5 ]. % 90.52/90.72 generalize (zenon_H73 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H1a3. % 90.52/90.72 generalize (zenon_H1a3 (succ (tptp_minus_1))). zenon_intro zenon_H1e7. % 90.52/90.72 generalize (zenon_H1e7 (succ zenon_TB_ec)). zenon_intro zenon_H1e8. % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H1e8); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H1e9 ]. % 90.52/90.72 exact (zenon_H1e6 zenon_H1e5). % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H1e9); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H1df ]. % 90.52/90.72 exact (zenon_H1d5 zenon_H1d9). % 90.52/90.72 exact (zenon_H1e0 zenon_H1df). % 90.52/90.72 apply (zenon_L79_ zenon_TB_ec); trivial. % 90.52/90.72 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (n0)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (tptp_minus_1)))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H1e6. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_He0. % 90.52/90.72 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.72 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.72 congruence. % 90.52/90.72 apply zenon_Hda. apply refl_equal. % 90.52/90.72 exact (zenon_H72 zenon_H71). % 90.52/90.72 apply (zenon_L84_ zenon_TB_ec); trivial. % 90.52/90.72 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.72 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H72. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_Hc2. % 90.52/90.72 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.72 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.72 congruence. % 90.52/90.72 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.72 apply zenon_H8f. apply refl_equal. % 90.52/90.72 apply zenon_H8f. apply refl_equal. % 90.52/90.72 cut ((gt (n0) (n0)) = (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_Hde. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_H1b4. % 90.52/90.72 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 90.52/90.72 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.72 congruence. % 90.52/90.72 apply zenon_H67. apply refl_equal. % 90.52/90.72 exact (zenon_Hd7 zenon_Hd6). % 90.52/90.72 apply (zenon_L70_ zenon_TB_ec); trivial. % 90.52/90.72 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd9 | zenon_intro zenon_Hda ]. % 90.52/90.72 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_Hd7. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_Hd9. % 90.52/90.72 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.72 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 90.52/90.72 congruence. % 90.52/90.72 exact (zenon_Hdb zenon_Hce). % 90.52/90.72 apply zenon_Hda. apply refl_equal. % 90.52/90.72 apply zenon_Hda. apply refl_equal. % 90.52/90.72 (* end of lemma zenon_L85_ *) % 90.52/90.72 assert (zenon_L86_ : forall (zenon_TB_ec : zenon_U), (~((tptp_minus_1) = (n3))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ zenon_TB_ec))) -> (~(gt (succ (tptp_minus_1)) (succ (succ (n0))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.72 do 1 intro. intros zenon_He8 zenon_H68 zenon_H97 zenon_Hb5 zenon_Hb6 zenon_Hce zenon_H1de zenon_H1ea zenon_H73. % 90.52/90.72 elim (classic ((n2) = (succ (succ (n0))))); [ zenon_intro zenon_H1eb | zenon_intro zenon_H1ec ]. % 90.52/90.72 elim (classic (gt (succ (tptp_minus_1)) (n2))); [ zenon_intro zenon_H1dd | zenon_intro zenon_H1da ]. % 90.52/90.72 cut ((gt (succ (tptp_minus_1)) (n2)) = (gt (succ (tptp_minus_1)) (succ (succ (n0))))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H1ea. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_H1dd. % 90.52/90.72 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ec]. % 90.52/90.72 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.72 congruence. % 90.52/90.72 apply zenon_H8f. apply refl_equal. % 90.52/90.72 exact (zenon_H1ec zenon_H1eb). % 90.52/90.72 apply (zenon_L85_ zenon_TB_ec); trivial. % 90.52/90.72 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1ee ]. % 90.52/90.72 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((n2) = (succ (succ (n0))))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H1ec. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_H1ed. % 90.52/90.72 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 90.52/90.72 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 90.52/90.72 congruence. % 90.52/90.72 exact (zenon_H1ef successor_2). % 90.52/90.72 apply zenon_H1ee. apply refl_equal. % 90.52/90.72 apply zenon_H1ee. apply refl_equal. % 90.52/90.72 (* end of lemma zenon_L86_ *) % 90.52/90.72 assert (zenon_L87_ : forall (zenon_TB_ec : zenon_U), (~(gt (n1) (succ (succ (n0))))) -> (~(gt (n0) (succ zenon_TB_ec))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (~((tptp_minus_1) = (n3))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.72 do 1 intro. intros zenon_H1f0 zenon_H1de zenon_Hce zenon_Hb6 zenon_Hb5 zenon_H97 zenon_H68 zenon_He8 zenon_H73. % 90.52/90.72 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 90.52/90.72 elim (classic (gt (n1) (succ (tptp_minus_1)))); [ zenon_intro zenon_H75 | zenon_intro zenon_H70 ]. % 90.52/90.72 elim (classic (gt (succ (tptp_minus_1)) (succ (succ (n0))))); [ zenon_intro zenon_H1f1 | zenon_intro zenon_H1ea ]. % 90.52/90.72 generalize (zenon_H73 (n1)). zenon_intro zenon_H138. % 90.52/90.72 generalize (zenon_H138 (succ (tptp_minus_1))). zenon_intro zenon_H1f2. % 90.52/90.72 generalize (zenon_H1f2 (succ (succ (n0)))). zenon_intro zenon_H1f3. % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H1f3); [ zenon_intro zenon_H70 | zenon_intro zenon_H1f4 ]. % 90.52/90.72 exact (zenon_H70 zenon_H75). % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H1f4); [ zenon_intro zenon_H1ea | zenon_intro zenon_H1f5 ]. % 90.52/90.72 exact (zenon_H1ea zenon_H1f1). % 90.52/90.72 exact (zenon_H1f0 zenon_H1f5). % 90.52/90.72 apply (zenon_L86_ zenon_TB_ec); trivial. % 90.52/90.72 cut ((gt (n1) (n0)) = (gt (n1) (succ (tptp_minus_1)))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H70. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact gt_1_0. % 90.52/90.72 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.72 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.72 congruence. % 90.52/90.72 apply zenon_H66. apply refl_equal. % 90.52/90.72 exact (zenon_H72 zenon_H71). % 90.52/90.72 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.72 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H72. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_Hc2. % 90.52/90.72 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.72 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.72 congruence. % 90.52/90.72 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.72 apply zenon_H8f. apply refl_equal. % 90.52/90.72 apply zenon_H8f. apply refl_equal. % 90.52/90.72 (* end of lemma zenon_L87_ *) % 90.52/90.72 assert (zenon_L88_ : (~(gt (n2) (succ (n0)))) -> False). % 90.52/90.72 do 0 intro. intros zenon_H1f6. % 90.52/90.72 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_H12e | zenon_intro zenon_Hb0 ]. % 90.52/90.72 cut ((gt (n2) (n1)) = (gt (n2) (succ (n0)))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H1f6. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact gt_2_1. % 90.52/90.72 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 90.52/90.72 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 90.52/90.72 congruence. % 90.52/90.72 apply zenon_H65. apply refl_equal. % 90.52/90.72 exact (zenon_Hb0 zenon_H12e). % 90.52/90.72 apply zenon_Hb0. apply sym_equal. exact successor_1. % 90.52/90.72 (* end of lemma zenon_L88_ *) % 90.52/90.72 assert (zenon_L89_ : (~(gt (succ (succ (n0))) (succ (n0)))) -> False). % 90.52/90.72 do 0 intro. intros zenon_H1f7. % 90.52/90.72 elim (classic (gt (n2) (succ (n0)))); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H1f6 ]. % 90.52/90.72 cut ((gt (n2) (succ (n0))) = (gt (succ (succ (n0))) (succ (n0)))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H1f7. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_H1f8. % 90.52/90.72 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.72 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ec]. % 90.52/90.72 congruence. % 90.52/90.72 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1ee ]. % 90.52/90.72 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((n2) = (succ (succ (n0))))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H1ec. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_H1ed. % 90.52/90.72 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 90.52/90.72 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 90.52/90.72 congruence. % 90.52/90.72 exact (zenon_H1ef successor_2). % 90.52/90.72 apply zenon_H1ee. apply refl_equal. % 90.52/90.72 apply zenon_H1ee. apply refl_equal. % 90.52/90.72 apply zenon_Hb2. apply refl_equal. % 90.52/90.72 apply (zenon_L88_); trivial. % 90.52/90.72 (* end of lemma zenon_L89_ *) % 90.52/90.72 assert (zenon_L90_ : forall (zenon_TB_ec : zenon_U), (~((tptp_minus_1) = (n3))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ zenon_TB_ec))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n2) (n2))) -> False). % 90.52/90.72 do 1 intro. intros zenon_He8 zenon_H68 zenon_H97 zenon_Hb5 zenon_Hb6 zenon_Hce zenon_H1de zenon_H73 zenon_H1f9. % 90.52/90.72 elim (classic ((n2) = (succ (succ (n0))))); [ zenon_intro zenon_H1eb | zenon_intro zenon_H1ec ]. % 90.52/90.72 elim (classic (gt (succ (succ (n0))) (n2))); [ zenon_intro zenon_H1fa | zenon_intro zenon_H1fb ]. % 90.52/90.72 cut ((gt (succ (succ (n0))) (n2)) = (gt (n2) (n2))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H1f9. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_H1fa. % 90.52/90.72 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 90.52/90.72 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 90.52/90.72 congruence. % 90.52/90.72 elim (classic ((n2) = (n2))); [ zenon_intro zenon_H1fc | zenon_intro zenon_H65 ]. % 90.52/90.72 cut (((n2) = (n2)) = ((succ (succ (n0))) = (n2))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H1ef. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_H1fc. % 90.52/90.72 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 90.52/90.72 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ec]. % 90.52/90.72 congruence. % 90.52/90.72 exact (zenon_H1ec zenon_H1eb). % 90.52/90.72 apply zenon_H65. apply refl_equal. % 90.52/90.72 apply zenon_H65. apply refl_equal. % 90.52/90.72 apply zenon_H65. apply refl_equal. % 90.52/90.72 elim (classic (gt (succ (succ (n0))) (succ (succ (n0))))); [ zenon_intro zenon_H1fd | zenon_intro zenon_H1fe ]. % 90.52/90.72 cut ((gt (succ (succ (n0))) (succ (succ (n0)))) = (gt (succ (succ (n0))) (n2))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H1fb. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_H1fd. % 90.52/90.72 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 90.52/90.72 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 90.52/90.72 congruence. % 90.52/90.72 apply zenon_H1ee. apply refl_equal. % 90.52/90.72 exact (zenon_H1ef successor_2). % 90.52/90.72 elim (classic (gt (succ (succ (n0))) (succ (n0)))); [ zenon_intro zenon_H1ff | zenon_intro zenon_H1f7 ]. % 90.52/90.72 elim (classic (gt (succ (succ (n0))) (n1))); [ zenon_intro zenon_H200 | zenon_intro zenon_H201 ]. % 90.52/90.72 elim (classic (gt (n1) (succ (succ (n0))))); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H1f0 ]. % 90.52/90.72 generalize (zenon_H73 (succ (succ (n0)))). zenon_intro zenon_H202. % 90.52/90.72 generalize (zenon_H202 (n1)). zenon_intro zenon_H203. % 90.52/90.72 generalize (zenon_H203 (succ (succ (n0)))). zenon_intro zenon_H204. % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H204); [ zenon_intro zenon_H201 | zenon_intro zenon_H205 ]. % 90.52/90.72 exact (zenon_H201 zenon_H200). % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H205); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H1fd ]. % 90.52/90.72 exact (zenon_H1f0 zenon_H1f5). % 90.52/90.72 exact (zenon_H1fe zenon_H1fd). % 90.52/90.72 apply (zenon_L87_ zenon_TB_ec); trivial. % 90.52/90.72 cut ((gt (succ (succ (n0))) (succ (n0))) = (gt (succ (succ (n0))) (n1))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H201. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_H1ff. % 90.52/90.72 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.72 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 90.52/90.72 congruence. % 90.52/90.72 apply zenon_H1ee. apply refl_equal. % 90.52/90.72 exact (zenon_Hb3 successor_1). % 90.52/90.72 apply (zenon_L89_); trivial. % 90.52/90.72 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1ee ]. % 90.52/90.72 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((n2) = (succ (succ (n0))))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H1ec. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_H1ed. % 90.52/90.72 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 90.52/90.72 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 90.52/90.72 congruence. % 90.52/90.72 exact (zenon_H1ef successor_2). % 90.52/90.72 apply zenon_H1ee. apply refl_equal. % 90.52/90.72 apply zenon_H1ee. apply refl_equal. % 90.52/90.72 (* end of lemma zenon_L90_ *) % 90.52/90.72 assert (zenon_L91_ : (~(gt (n3) (succ (succ (n0))))) -> False). % 90.52/90.72 do 0 intro. intros zenon_H206. % 90.52/90.72 elim (classic ((n2) = (succ (succ (n0))))); [ zenon_intro zenon_H1eb | zenon_intro zenon_H1ec ]. % 90.52/90.72 cut ((gt (n3) (n2)) = (gt (n3) (succ (succ (n0))))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H206. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact gt_3_2. % 90.52/90.72 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ec]. % 90.52/90.72 cut (((n3) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 90.52/90.72 congruence. % 90.52/90.72 apply zenon_H64. apply refl_equal. % 90.52/90.72 exact (zenon_H1ec zenon_H1eb). % 90.52/90.72 apply zenon_H1ec. apply sym_equal. exact successor_2. % 90.52/90.72 (* end of lemma zenon_L91_ *) % 90.52/90.72 assert (zenon_L92_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n2) (n3))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n1))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> (~(gt zenon_TB_ec (n1))) -> False). % 90.52/90.72 do 1 intro. intros zenon_H73 zenon_H207 zenon_H68 zenon_H97 zenon_Hae zenon_Hb5 zenon_Hb6 zenon_H148. % 90.52/90.72 elim (classic (gt (n1) (n3))); [ zenon_intro zenon_H17a | zenon_intro zenon_H176 ]. % 90.52/90.72 generalize (zenon_H73 (n2)). zenon_intro zenon_H76. % 90.52/90.72 generalize (zenon_H76 (n1)). zenon_intro zenon_H77. % 90.52/90.72 generalize (zenon_H77 (n3)). zenon_intro zenon_H208. % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H208); [ zenon_intro zenon_H7a | zenon_intro zenon_H209 ]. % 90.52/90.72 exact (zenon_H7a gt_2_1). % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H209); [ zenon_intro zenon_H176 | zenon_intro zenon_H20a ]. % 90.52/90.72 exact (zenon_H176 zenon_H17a). % 90.52/90.72 exact (zenon_H207 zenon_H20a). % 90.52/90.72 apply (zenon_L53_ zenon_TB_ec); trivial. % 90.52/90.72 (* end of lemma zenon_L92_ *) % 90.52/90.72 assert (zenon_L93_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n1))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> (~(gt zenon_TB_ec (n1))) -> (~(gt (n2) (succ (succ (succ (n0)))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.72 do 1 intro. intros zenon_H68 zenon_H97 zenon_Hae zenon_Hb5 zenon_Hb6 zenon_H148 zenon_H20b zenon_H73. % 90.52/90.72 elim (classic ((n3) = (succ (succ (succ (n0)))))); [ zenon_intro zenon_H20c | zenon_intro zenon_H8b ]. % 90.52/90.72 elim (classic (gt (n2) (n3))); [ zenon_intro zenon_H20a | zenon_intro zenon_H207 ]. % 90.52/90.72 cut ((gt (n2) (n3)) = (gt (n2) (succ (succ (succ (n0)))))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H20b. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_H20a. % 90.52/90.72 cut (((n3) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 90.52/90.72 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 90.52/90.72 congruence. % 90.52/90.72 apply zenon_H65. apply refl_equal. % 90.52/90.72 exact (zenon_H8b zenon_H20c). % 90.52/90.72 apply (zenon_L92_ zenon_TB_ec); trivial. % 90.52/90.72 elim (classic ((succ (succ (succ (n0)))) = (succ (succ (succ (n0)))))); [ zenon_intro zenon_H20d | zenon_intro zenon_H20e ]. % 90.52/90.72 cut (((succ (succ (succ (n0)))) = (succ (succ (succ (n0))))) = ((n3) = (succ (succ (succ (n0)))))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H8b. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_H20d. % 90.52/90.72 cut (((succ (succ (succ (n0)))) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H20e]. % 90.52/90.72 cut (((succ (succ (succ (n0)))) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H20f]. % 90.52/90.72 congruence. % 90.52/90.72 exact (zenon_H20f successor_3). % 90.52/90.72 apply zenon_H20e. apply refl_equal. % 90.52/90.72 apply zenon_H20e. apply refl_equal. % 90.52/90.72 (* end of lemma zenon_L93_ *) % 90.52/90.72 assert (zenon_L94_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (succ (n0))) (succ (succ (succ (n0)))))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n1))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> (~(gt zenon_TB_ec (n1))) -> False). % 90.52/90.72 do 1 intro. intros zenon_H73 zenon_H210 zenon_H68 zenon_H97 zenon_Hae zenon_Hb5 zenon_Hb6 zenon_H148. % 90.52/90.72 elim (classic (gt (n2) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H211 | zenon_intro zenon_H20b ]. % 90.52/90.72 cut ((gt (n2) (succ (succ (succ (n0))))) = (gt (succ (succ (n0))) (succ (succ (succ (n0)))))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H210. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_H211. % 90.52/90.72 cut (((succ (succ (succ (n0)))) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H20e]. % 90.52/90.72 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ec]. % 90.52/90.72 congruence. % 90.52/90.72 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1ee ]. % 90.52/90.72 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((n2) = (succ (succ (n0))))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H1ec. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_H1ed. % 90.52/90.72 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 90.52/90.72 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 90.52/90.72 congruence. % 90.52/90.72 exact (zenon_H1ef successor_2). % 90.52/90.72 apply zenon_H1ee. apply refl_equal. % 90.52/90.72 apply zenon_H1ee. apply refl_equal. % 90.52/90.72 apply zenon_H20e. apply refl_equal. % 90.52/90.72 apply (zenon_L93_ zenon_TB_ec); trivial. % 90.52/90.72 (* end of lemma zenon_L94_ *) % 90.52/90.72 assert (zenon_L95_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n1))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> (~(gt zenon_TB_ec (n1))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n2) (n2))) -> False). % 90.52/90.72 do 1 intro. intros zenon_H68 zenon_H97 zenon_Hae zenon_Hb5 zenon_Hb6 zenon_H148 zenon_H73 zenon_H1f9. % 90.52/90.72 elim (classic ((~((n2) = (n3)))/\(~(gt (n2) (n3))))); [ zenon_intro zenon_H212 | zenon_intro zenon_H213 ]. % 90.52/90.72 apply (zenon_and_s _ _ zenon_H212). zenon_intro zenon_H214. zenon_intro zenon_H207. % 90.52/90.72 apply (zenon_L92_ zenon_TB_ec); trivial. % 90.52/90.72 cut ((gt (n3) (n2)) = (gt (n2) (n2))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H1f9. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact gt_3_2. % 90.52/90.72 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 90.52/90.72 cut (((n3) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H215]. % 90.52/90.72 congruence. % 90.52/90.72 apply (zenon_notand_s _ _ zenon_H213); [ zenon_intro zenon_H217 | zenon_intro zenon_H216 ]. % 90.52/90.72 apply zenon_H217. zenon_intro zenon_H218. % 90.52/90.72 elim (classic ((n2) = (n2))); [ zenon_intro zenon_H1fc | zenon_intro zenon_H65 ]. % 90.52/90.72 cut (((n2) = (n2)) = ((n3) = (n2))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H215. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_H1fc. % 90.52/90.72 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 90.52/90.72 cut (((n2) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H214]. % 90.52/90.72 congruence. % 90.52/90.72 exact (zenon_H214 zenon_H218). % 90.52/90.72 apply zenon_H65. apply refl_equal. % 90.52/90.72 apply zenon_H65. apply refl_equal. % 90.52/90.72 apply zenon_H216. zenon_intro zenon_H20a. % 90.52/90.72 generalize (zenon_H73 (n2)). zenon_intro zenon_H76. % 90.52/90.72 generalize (zenon_H76 (n3)). zenon_intro zenon_H219. % 90.52/90.72 generalize (zenon_H219 (n2)). zenon_intro zenon_H21a. % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H21a); [ zenon_intro zenon_H207 | zenon_intro zenon_H21b ]. % 90.52/90.72 exact (zenon_H207 zenon_H20a). % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H21b); [ zenon_intro zenon_H81 | zenon_intro zenon_H21c ]. % 90.52/90.72 exact (zenon_H81 gt_3_2). % 90.52/90.72 exact (zenon_H1f9 zenon_H21c). % 90.52/90.72 apply zenon_H65. apply refl_equal. % 90.52/90.72 (* end of lemma zenon_L95_ *) % 90.52/90.72 assert (zenon_L96_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n1))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> (~(gt zenon_TB_ec (n1))) -> (~(gt (succ (tptp_minus_1)) (succ (succ (succ (n0)))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.72 do 1 intro. intros zenon_H68 zenon_H97 zenon_Hae zenon_Hb5 zenon_Hb6 zenon_H148 zenon_H21d zenon_H73. % 90.52/90.72 elim (classic ((n2) = (succ (succ (n0))))); [ zenon_intro zenon_H1eb | zenon_intro zenon_H1ec ]. % 90.52/90.72 elim (classic (gt (succ (tptp_minus_1)) (n2))); [ zenon_intro zenon_H1dd | zenon_intro zenon_H1da ]. % 90.52/90.72 elim (classic (gt (succ (tptp_minus_1)) (succ (succ (n0))))); [ zenon_intro zenon_H1f1 | zenon_intro zenon_H1ea ]. % 90.52/90.72 elim (classic (gt (succ (succ (n0))) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H21e | zenon_intro zenon_H210 ]. % 90.52/90.72 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.72 generalize (zenon_Hd1 (succ (succ (n0)))). zenon_intro zenon_H21f. % 90.52/90.72 generalize (zenon_H21f (succ (succ (succ (n0))))). zenon_intro zenon_H220. % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H220); [ zenon_intro zenon_H1ea | zenon_intro zenon_H221 ]. % 90.52/90.72 exact (zenon_H1ea zenon_H1f1). % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H221); [ zenon_intro zenon_H210 | zenon_intro zenon_H222 ]. % 90.52/90.72 exact (zenon_H210 zenon_H21e). % 90.52/90.72 exact (zenon_H21d zenon_H222). % 90.52/90.72 apply (zenon_L94_ zenon_TB_ec); trivial. % 90.52/90.72 cut ((gt (succ (tptp_minus_1)) (n2)) = (gt (succ (tptp_minus_1)) (succ (succ (n0))))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H1ea. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_H1dd. % 90.52/90.72 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ec]. % 90.52/90.72 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.72 congruence. % 90.52/90.72 apply zenon_H8f. apply refl_equal. % 90.52/90.72 exact (zenon_H1ec zenon_H1eb). % 90.52/90.72 elim (classic ((~((succ (tptp_minus_1)) = (n3)))/\(~(gt (succ (tptp_minus_1)) (n3))))); [ zenon_intro zenon_H223 | zenon_intro zenon_H224 ]. % 90.52/90.72 apply (zenon_and_s _ _ zenon_H223). zenon_intro zenon_H226. zenon_intro zenon_H225. % 90.52/90.72 elim (classic (gt (succ (tptp_minus_1)) (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hc0 ]. % 90.52/90.72 elim (classic (gt (succ (tptp_minus_1)) (n0))); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hbf ]. % 90.52/90.72 elim (classic (gt (n0) (n3))); [ zenon_intro zenon_H177 | zenon_intro zenon_H175 ]. % 90.52/90.72 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.72 generalize (zenon_Hd1 (n0)). zenon_intro zenon_H141. % 90.52/90.72 generalize (zenon_H141 (n3)). zenon_intro zenon_H227. % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H227); [ zenon_intro zenon_Hbf | zenon_intro zenon_H228 ]. % 90.52/90.72 exact (zenon_Hbf zenon_Hc1). % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H228); [ zenon_intro zenon_H175 | zenon_intro zenon_H229 ]. % 90.52/90.72 exact (zenon_H175 zenon_H177). % 90.52/90.72 exact (zenon_H225 zenon_H229). % 90.52/90.72 apply (zenon_L52_ zenon_TB_ec); trivial. % 90.52/90.72 cut ((gt (succ (tptp_minus_1)) (succ (tptp_minus_1))) = (gt (succ (tptp_minus_1)) (n0))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_Hbf. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_Hc5. % 90.52/90.72 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.72 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.72 congruence. % 90.52/90.72 apply zenon_H8f. apply refl_equal. % 90.52/90.72 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.72 apply (zenon_L18_ zenon_TB_ec); trivial. % 90.52/90.72 cut ((gt (n3) (n2)) = (gt (succ (tptp_minus_1)) (n2))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H1da. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact gt_3_2. % 90.52/90.72 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 90.52/90.72 cut (((n3) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H22a]. % 90.52/90.72 congruence. % 90.52/90.72 apply (zenon_notand_s _ _ zenon_H224); [ zenon_intro zenon_H22c | zenon_intro zenon_H22b ]. % 90.52/90.72 apply zenon_H22c. zenon_intro zenon_H22d. % 90.52/90.72 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.72 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n3) = (succ (tptp_minus_1)))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H22a. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_Hc2. % 90.52/90.72 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.72 cut (((succ (tptp_minus_1)) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H226]. % 90.52/90.72 congruence. % 90.52/90.72 exact (zenon_H226 zenon_H22d). % 90.52/90.72 apply zenon_H8f. apply refl_equal. % 90.52/90.72 apply zenon_H8f. apply refl_equal. % 90.52/90.72 apply zenon_H22b. zenon_intro zenon_H229. % 90.52/90.72 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.72 generalize (zenon_Hd1 (n3)). zenon_intro zenon_H22e. % 90.52/90.72 generalize (zenon_H22e (n2)). zenon_intro zenon_H22f. % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H22f); [ zenon_intro zenon_H225 | zenon_intro zenon_H230 ]. % 90.52/90.72 exact (zenon_H225 zenon_H229). % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H230); [ zenon_intro zenon_H81 | zenon_intro zenon_H1dd ]. % 90.52/90.72 exact (zenon_H81 gt_3_2). % 90.52/90.72 exact (zenon_H1da zenon_H1dd). % 90.52/90.72 apply zenon_H65. apply refl_equal. % 90.52/90.72 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1ee ]. % 90.52/90.72 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((n2) = (succ (succ (n0))))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H1ec. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_H1ed. % 90.52/90.72 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 90.52/90.72 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 90.52/90.72 congruence. % 90.52/90.72 exact (zenon_H1ef successor_2). % 90.52/90.72 apply zenon_H1ee. apply refl_equal. % 90.52/90.72 apply zenon_H1ee. apply refl_equal. % 90.52/90.72 (* end of lemma zenon_L96_ *) % 90.52/90.72 assert (zenon_L97_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (succ (succ (n0))))) -> (~(gt zenon_TB_ec (n1))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n1))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.72 do 1 intro. intros zenon_H73 zenon_H1ea zenon_H148 zenon_Hb6 zenon_Hb5 zenon_Hae zenon_H97 zenon_H68. % 90.52/90.72 elim (classic (gt (succ (tptp_minus_1)) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H222 | zenon_intro zenon_H21d ]. % 90.52/90.72 elim (classic (gt (succ (tptp_minus_1)) (n3))); [ zenon_intro zenon_H229 | zenon_intro zenon_H225 ]. % 90.52/90.72 elim (classic (gt (n3) (succ (succ (n0))))); [ zenon_intro zenon_H231 | zenon_intro zenon_H206 ]. % 90.52/90.72 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.72 generalize (zenon_Hd1 (n3)). zenon_intro zenon_H22e. % 90.52/90.72 generalize (zenon_H22e (succ (succ (n0)))). zenon_intro zenon_H232. % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H232); [ zenon_intro zenon_H225 | zenon_intro zenon_H233 ]. % 90.52/90.72 exact (zenon_H225 zenon_H229). % 90.52/90.72 apply (zenon_imply_s _ _ zenon_H233); [ zenon_intro zenon_H206 | zenon_intro zenon_H1f1 ]. % 90.52/90.72 exact (zenon_H206 zenon_H231). % 90.52/90.72 exact (zenon_H1ea zenon_H1f1). % 90.52/90.72 apply (zenon_L91_); trivial. % 90.52/90.72 cut ((gt (succ (tptp_minus_1)) (succ (succ (succ (n0))))) = (gt (succ (tptp_minus_1)) (n3))). % 90.52/90.72 intro zenon_D_pnotp. % 90.52/90.72 apply zenon_H225. % 90.52/90.72 rewrite <- zenon_D_pnotp. % 90.52/90.72 exact zenon_H222. % 90.52/90.72 cut (((succ (succ (succ (n0)))) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H20f]. % 90.52/90.72 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.72 congruence. % 90.52/90.72 apply zenon_H8f. apply refl_equal. % 90.52/90.72 exact (zenon_H20f successor_3). % 90.52/90.72 apply (zenon_L96_ zenon_TB_ec); trivial. % 90.52/90.72 (* end of lemma zenon_L97_ *) % 90.52/90.72 assert (zenon_L98_ : forall (zenon_TB_ec : zenon_U), (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n1))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (~(gt zenon_TB_ec (succ (succ (n0))))) -> (~(gt zenon_TB_ec (n1))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.72 do 1 intro. intros zenon_Hb6 zenon_Hb5 zenon_Hae zenon_H97 zenon_H68 zenon_H234 zenon_H148 zenon_H73. % 90.52/90.72 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 90.52/90.72 elim (classic (gt zenon_TB_ec (n0))); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hcb ]. % 90.52/90.72 elim (classic (gt zenon_TB_ec (succ (tptp_minus_1)))); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hc4 ]. % 90.52/90.72 elim (classic (gt (succ (tptp_minus_1)) (succ (succ (n0))))); [ zenon_intro zenon_H1f1 | zenon_intro zenon_H1ea ]. % 90.52/90.73 generalize (zenon_H73 zenon_TB_ec). zenon_intro zenon_H144. % 90.52/90.73 generalize (zenon_H144 (succ (tptp_minus_1))). zenon_intro zenon_H145. % 90.52/90.73 generalize (zenon_H145 (succ (succ (n0)))). zenon_intro zenon_H235. % 90.52/90.73 apply (zenon_imply_s _ _ zenon_H235); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H236 ]. % 90.52/90.73 exact (zenon_Hc4 zenon_Hcc). % 90.52/90.73 apply (zenon_imply_s _ _ zenon_H236); [ zenon_intro zenon_H1ea | zenon_intro zenon_H237 ]. % 90.52/90.73 exact (zenon_H1ea zenon_H1f1). % 90.52/90.73 exact (zenon_H234 zenon_H237). % 90.52/90.73 apply (zenon_L97_ zenon_TB_ec); trivial. % 90.52/90.73 cut ((gt zenon_TB_ec (n0)) = (gt zenon_TB_ec (succ (tptp_minus_1)))). % 90.52/90.73 intro zenon_D_pnotp. % 90.52/90.73 apply zenon_Hc4. % 90.52/90.73 rewrite <- zenon_D_pnotp. % 90.52/90.73 exact zenon_Hd8. % 90.52/90.73 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.73 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.73 congruence. % 90.52/90.73 apply zenon_Ha1. apply refl_equal. % 90.52/90.73 exact (zenon_H72 zenon_H71). % 90.52/90.73 apply (zenon_L20_ zenon_TB_ec); trivial. % 90.52/90.73 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.73 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))). % 90.52/90.73 intro zenon_D_pnotp. % 90.52/90.73 apply zenon_H72. % 90.52/90.73 rewrite <- zenon_D_pnotp. % 90.52/90.73 exact zenon_Hc2. % 90.52/90.73 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.73 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.73 congruence. % 90.52/90.73 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.73 apply zenon_H8f. apply refl_equal. % 90.52/90.73 apply zenon_H8f. apply refl_equal. % 90.52/90.73 (* end of lemma zenon_L98_ *) % 90.52/90.73 assert (zenon_L99_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> (~(gt zenon_TB_ec (succ (succ (n0))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt zenon_TB_ec (n0))) -> False). % 90.52/90.73 do 1 intro. intros zenon_H68 zenon_H97 zenon_Hb5 zenon_Hb6 zenon_H234 zenon_H73 zenon_Hcb. % 90.52/90.73 elim (classic ((~(zenon_TB_ec = (n1)))/\(~(gt zenon_TB_ec (n1))))); [ zenon_intro zenon_H198 | zenon_intro zenon_H199 ]. % 90.52/90.73 apply (zenon_and_s _ _ zenon_H198). zenon_intro zenon_Hae. zenon_intro zenon_H148. % 90.52/90.73 apply (zenon_L98_ zenon_TB_ec); trivial. % 90.52/90.73 cut ((gt (n1) (n0)) = (gt zenon_TB_ec (n0))). % 90.52/90.73 intro zenon_D_pnotp. % 90.52/90.73 apply zenon_Hcb. % 90.52/90.73 rewrite <- zenon_D_pnotp. % 90.52/90.73 exact gt_1_0. % 90.52/90.73 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.73 cut (((n1) = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 90.52/90.73 congruence. % 90.52/90.73 apply (zenon_notand_s _ _ zenon_H199); [ zenon_intro zenon_H19c | zenon_intro zenon_H19b ]. % 90.52/90.73 apply zenon_H19c. zenon_intro zenon_Had. % 90.52/90.73 elim (classic (zenon_TB_ec = zenon_TB_ec)); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Ha1 ]. % 90.52/90.73 cut ((zenon_TB_ec = zenon_TB_ec) = ((n1) = zenon_TB_ec)). % 90.52/90.73 intro zenon_D_pnotp. % 90.52/90.73 apply zenon_H19a. % 90.52/90.73 rewrite <- zenon_D_pnotp. % 90.52/90.73 exact zenon_Hc9. % 90.52/90.73 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.73 cut ((zenon_TB_ec = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hae]. % 90.52/90.73 congruence. % 90.52/90.73 exact (zenon_Hae zenon_Had). % 90.52/90.73 apply zenon_Ha1. apply refl_equal. % 90.52/90.73 apply zenon_Ha1. apply refl_equal. % 90.52/90.73 apply zenon_H19b. zenon_intro zenon_H164. % 90.52/90.73 generalize (zenon_H73 zenon_TB_ec). zenon_intro zenon_H144. % 90.52/90.73 generalize (zenon_H144 (n1)). zenon_intro zenon_H19d. % 90.52/90.73 generalize (zenon_H19d (n0)). zenon_intro zenon_H19e. % 90.52/90.73 apply (zenon_imply_s _ _ zenon_H19e); [ zenon_intro zenon_H148 | zenon_intro zenon_H19f ]. % 90.52/90.73 exact (zenon_H148 zenon_H164). % 90.52/90.73 apply (zenon_imply_s _ _ zenon_H19f); [ zenon_intro zenon_H13c | zenon_intro zenon_Hd8 ]. % 90.52/90.73 exact (zenon_H13c gt_1_0). % 90.52/90.73 exact (zenon_Hcb zenon_Hd8). % 90.52/90.73 apply zenon_H67. apply refl_equal. % 90.52/90.73 (* end of lemma zenon_L99_ *) % 90.52/90.73 assert (zenon_L100_ : forall (zenon_TB_ec : zenon_U), (~(gt zenon_TB_ec (succ (succ (n0))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (~(gt (n0) (succ zenon_TB_ec))) -> (~((tptp_minus_1) = (n3))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.74 do 1 intro. intros zenon_H234 zenon_Hce zenon_Hb6 zenon_Hb5 zenon_H97 zenon_H68 zenon_H1de zenon_He8 zenon_H73. % 90.52/90.74 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 90.52/90.74 elim (classic (gt zenon_TB_ec (n0))); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hcb ]. % 90.52/90.74 elim (classic (gt zenon_TB_ec (succ (tptp_minus_1)))); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hc4 ]. % 90.52/90.74 elim (classic (gt (succ (tptp_minus_1)) (succ (succ (n0))))); [ zenon_intro zenon_H1f1 | zenon_intro zenon_H1ea ]. % 90.52/90.74 generalize (zenon_H73 zenon_TB_ec). zenon_intro zenon_H144. % 90.52/90.74 generalize (zenon_H144 (succ (tptp_minus_1))). zenon_intro zenon_H145. % 90.52/90.74 generalize (zenon_H145 (succ (succ (n0)))). zenon_intro zenon_H235. % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H235); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H236 ]. % 90.52/90.74 exact (zenon_Hc4 zenon_Hcc). % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H236); [ zenon_intro zenon_H1ea | zenon_intro zenon_H237 ]. % 90.52/90.74 exact (zenon_H1ea zenon_H1f1). % 90.52/90.74 exact (zenon_H234 zenon_H237). % 90.52/90.74 apply (zenon_L86_ zenon_TB_ec); trivial. % 90.52/90.74 cut ((gt zenon_TB_ec (n0)) = (gt zenon_TB_ec (succ (tptp_minus_1)))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_Hc4. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_Hd8. % 90.52/90.74 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.74 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.74 congruence. % 90.52/90.74 apply zenon_Ha1. apply refl_equal. % 90.52/90.74 exact (zenon_H72 zenon_H71). % 90.52/90.74 apply (zenon_L99_ zenon_TB_ec); trivial. % 90.52/90.74 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.74 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H72. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_Hc2. % 90.52/90.74 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.74 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.74 congruence. % 90.52/90.74 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.74 apply zenon_H8f. apply refl_equal. % 90.52/90.74 apply zenon_H8f. apply refl_equal. % 90.52/90.74 (* end of lemma zenon_L100_ *) % 90.52/90.74 assert (zenon_L101_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt zenon_TB_ec (n2))) -> (~(gt (n0) (succ zenon_TB_ec))) -> (~((tptp_minus_1) = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.74 do 1 intro. intros zenon_H73 zenon_H238 zenon_H1de zenon_He8 zenon_Hce zenon_Hb6 zenon_Hb5 zenon_H97 zenon_H68. % 90.52/90.74 elim (classic (gt zenon_TB_ec (succ (succ (n0))))); [ zenon_intro zenon_H237 | zenon_intro zenon_H234 ]. % 90.52/90.74 cut ((gt zenon_TB_ec (succ (succ (n0)))) = (gt zenon_TB_ec (n2))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H238. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_H237. % 90.52/90.74 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 90.52/90.74 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.74 congruence. % 90.52/90.74 apply zenon_Ha1. apply refl_equal. % 90.52/90.74 exact (zenon_H1ef successor_2). % 90.52/90.74 apply (zenon_L100_ zenon_TB_ec); trivial. % 90.52/90.74 (* end of lemma zenon_L101_ *) % 90.52/90.74 assert (zenon_L102_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (n3))) -> (~(gt zenon_TB_ec (n2))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ zenon_TB_ec))) -> False). % 90.52/90.74 do 1 intro. intros zenon_H73 zenon_H175 zenon_H238 zenon_H68 zenon_H97 zenon_Hb5 zenon_Hb6 zenon_Hce zenon_H1de. % 90.52/90.74 elim (classic ((tptp_minus_1) = (n3))); [ zenon_intro zenon_H106 | zenon_intro zenon_He8 ]. % 90.52/90.74 cut ((gt (n0) (tptp_minus_1)) = (gt (n0) (n3))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H175. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact gt_0_tptp_minus_1. % 90.52/90.74 cut (((tptp_minus_1) = (n3))); [idtac | apply NNPP; zenon_intro zenon_He8]. % 90.52/90.74 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.74 congruence. % 90.52/90.74 apply zenon_H67. apply refl_equal. % 90.52/90.74 exact (zenon_He8 zenon_H106). % 90.52/90.74 apply (zenon_L101_ zenon_TB_ec); trivial. % 90.52/90.74 (* end of lemma zenon_L102_ *) % 90.52/90.74 assert (zenon_L103_ : forall (zenon_TB_ec : zenon_U), (~(gt zenon_TB_ec (n2))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ zenon_TB_ec))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (n0))) -> False). % 90.52/90.74 do 1 intro. intros zenon_H238 zenon_H68 zenon_H97 zenon_Hb5 zenon_Hb6 zenon_Hce zenon_H1de zenon_H73 zenon_Hdf. % 90.52/90.74 elim (classic ((~((n0) = (n3)))/\(~(gt (n0) (n3))))); [ zenon_intro zenon_H239 | zenon_intro zenon_H23a ]. % 90.52/90.74 apply (zenon_and_s _ _ zenon_H239). zenon_intro zenon_H23b. zenon_intro zenon_H175. % 90.52/90.74 apply (zenon_L102_ zenon_TB_ec); trivial. % 90.52/90.74 cut ((gt (n3) (n0)) = (gt (n0) (n0))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_Hdf. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact gt_3_0. % 90.52/90.74 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.74 cut (((n3) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H23c]. % 90.52/90.74 congruence. % 90.52/90.74 apply (zenon_notand_s _ _ zenon_H23a); [ zenon_intro zenon_H23e | zenon_intro zenon_H23d ]. % 90.52/90.74 apply zenon_H23e. zenon_intro zenon_H23f. % 90.52/90.74 elim (classic ((n0) = (n0))); [ zenon_intro zenon_Hca | zenon_intro zenon_H67 ]. % 90.52/90.74 cut (((n0) = (n0)) = ((n3) = (n0))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H23c. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_Hca. % 90.52/90.74 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.74 cut (((n0) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H23b]. % 90.52/90.74 congruence. % 90.52/90.74 exact (zenon_H23b zenon_H23f). % 90.52/90.74 apply zenon_H67. apply refl_equal. % 90.52/90.74 apply zenon_H67. apply refl_equal. % 90.52/90.74 apply zenon_H23d. zenon_intro zenon_H177. % 90.52/90.74 generalize (zenon_H73 (n0)). zenon_intro zenon_H115. % 90.52/90.74 generalize (zenon_H115 (n3)). zenon_intro zenon_H240. % 90.52/90.74 generalize (zenon_H240 (n0)). zenon_intro zenon_H241. % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H241); [ zenon_intro zenon_H175 | zenon_intro zenon_H242 ]. % 90.52/90.74 exact (zenon_H175 zenon_H177). % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H242); [ zenon_intro zenon_H197 | zenon_intro zenon_H1b4 ]. % 90.52/90.74 exact (zenon_H197 gt_3_0). % 90.52/90.74 exact (zenon_Hdf zenon_H1b4). % 90.52/90.74 apply zenon_H67. apply refl_equal. % 90.52/90.74 (* end of lemma zenon_L103_ *) % 90.52/90.74 assert (zenon_L104_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (n3))) -> (~(gt (n0) (succ zenon_TB_ec))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (~(gt zenon_TB_ec (n2))) -> False). % 90.52/90.74 do 1 intro. intros zenon_H73 zenon_H176 zenon_H1de zenon_Hce zenon_Hb6 zenon_Hb5 zenon_H97 zenon_H68 zenon_H238. % 90.52/90.74 elim (classic (gt (n0) (n3))); [ zenon_intro zenon_H177 | zenon_intro zenon_H175 ]. % 90.52/90.74 generalize (zenon_H73 (n1)). zenon_intro zenon_H138. % 90.52/90.74 generalize (zenon_H138 (n0)). zenon_intro zenon_H139. % 90.52/90.74 generalize (zenon_H139 (n3)). zenon_intro zenon_H178. % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H178); [ zenon_intro zenon_H13c | zenon_intro zenon_H179 ]. % 90.52/90.74 exact (zenon_H13c gt_1_0). % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H179); [ zenon_intro zenon_H175 | zenon_intro zenon_H17a ]. % 90.52/90.74 exact (zenon_H175 zenon_H177). % 90.52/90.74 exact (zenon_H176 zenon_H17a). % 90.52/90.74 apply (zenon_L102_ zenon_TB_ec); trivial. % 90.52/90.74 (* end of lemma zenon_L104_ *) % 90.52/90.74 assert (zenon_L105_ : forall (zenon_TB_ec : zenon_U), (~(gt (n0) (succ zenon_TB_ec))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (~(gt zenon_TB_ec (n2))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (n1))) -> False). % 90.52/90.74 do 1 intro. intros zenon_H1de zenon_Hce zenon_Hb6 zenon_Hb5 zenon_H97 zenon_H68 zenon_H238 zenon_H73 zenon_H12d. % 90.52/90.74 elim (classic ((~((n1) = (n3)))/\(~(gt (n1) (n3))))); [ zenon_intro zenon_H17b | zenon_intro zenon_H17c ]. % 90.52/90.74 apply (zenon_and_s _ _ zenon_H17b). zenon_intro zenon_H17d. zenon_intro zenon_H176. % 90.52/90.74 apply (zenon_L104_ zenon_TB_ec); trivial. % 90.52/90.74 cut ((gt (n3) (n1)) = (gt (n1) (n1))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H12d. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact gt_3_1. % 90.52/90.74 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.74 cut (((n3) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 90.52/90.74 congruence. % 90.52/90.74 apply (zenon_notand_s _ _ zenon_H17c); [ zenon_intro zenon_H180 | zenon_intro zenon_H17f ]. % 90.52/90.74 apply zenon_H180. zenon_intro zenon_H181. % 90.52/90.74 elim (classic ((n1) = (n1))); [ zenon_intro zenon_H131 | zenon_intro zenon_H66 ]. % 90.52/90.74 cut (((n1) = (n1)) = ((n3) = (n1))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H17e. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_H131. % 90.52/90.74 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.74 cut (((n1) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H17d]. % 90.52/90.74 congruence. % 90.52/90.74 exact (zenon_H17d zenon_H181). % 90.52/90.74 apply zenon_H66. apply refl_equal. % 90.52/90.74 apply zenon_H66. apply refl_equal. % 90.52/90.74 apply zenon_H17f. zenon_intro zenon_H17a. % 90.52/90.74 generalize (zenon_H73 (n1)). zenon_intro zenon_H138. % 90.52/90.74 generalize (zenon_H138 (n3)). zenon_intro zenon_H182. % 90.52/90.74 generalize (zenon_H182 (n1)). zenon_intro zenon_H183. % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H183); [ zenon_intro zenon_H176 | zenon_intro zenon_H184 ]. % 90.52/90.74 exact (zenon_H176 zenon_H17a). % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H184); [ zenon_intro zenon_H185 | zenon_intro zenon_H13d ]. % 90.52/90.74 exact (zenon_H185 gt_3_1). % 90.52/90.74 exact (zenon_H12d zenon_H13d). % 90.52/90.74 apply zenon_H66. apply refl_equal. % 90.52/90.74 (* end of lemma zenon_L105_ *) % 90.52/90.74 assert (zenon_L106_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> (~(gt (tptp_minus_1) (succ (n0)))) -> (~(gt (n0) (succ (n0)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.74 do 1 intro. intros zenon_H68 zenon_H97 zenon_Hb5 zenon_Hb6 zenon_H10f zenon_H111 zenon_H73. % 90.52/90.74 apply (zenon_L59_ zenon_TB_ec); trivial. % 90.52/90.74 (* end of lemma zenon_L106_ *) % 90.52/90.74 assert (zenon_L107_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (succ (n0)))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> False). % 90.52/90.74 do 1 intro. intros zenon_H73 zenon_H111 zenon_H68 zenon_H97 zenon_Hb5 zenon_Hb6. % 90.52/90.74 elim (classic (gt (tptp_minus_1) (succ (n0)))); [ zenon_intro zenon_H114 | zenon_intro zenon_H10f ]. % 90.52/90.74 generalize (zenon_H73 (n0)). zenon_intro zenon_H115. % 90.52/90.74 generalize (zenon_H115 (tptp_minus_1)). zenon_intro zenon_H116. % 90.52/90.74 generalize (zenon_H116 (succ (n0))). zenon_intro zenon_H117. % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H117); [ zenon_intro zenon_H101 | zenon_intro zenon_H118 ]. % 90.52/90.74 exact (zenon_H101 gt_0_tptp_minus_1). % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H118); [ zenon_intro zenon_H10f | zenon_intro zenon_H110 ]. % 90.52/90.74 exact (zenon_H10f zenon_H114). % 90.52/90.74 exact (zenon_H111 zenon_H110). % 90.52/90.74 apply (zenon_L106_ zenon_TB_ec); trivial. % 90.52/90.74 (* end of lemma zenon_L107_ *) % 90.52/90.74 assert (zenon_L108_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (succ (n0)))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.74 do 1 intro. intros zenon_H73 zenon_H10a zenon_Hb6 zenon_Hb5 zenon_H97 zenon_H68. % 90.52/90.74 elim (classic (gt (n0) (succ (n0)))); [ zenon_intro zenon_H110 | zenon_intro zenon_H111 ]. % 90.52/90.74 cut ((gt (n0) (succ (n0))) = (gt (succ (tptp_minus_1)) (succ (n0)))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H10a. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_H110. % 90.52/90.74 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.74 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.74 congruence. % 90.52/90.74 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.74 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H72. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_Hc2. % 90.52/90.74 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.74 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.74 congruence. % 90.52/90.74 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.74 apply zenon_H8f. apply refl_equal. % 90.52/90.74 apply zenon_H8f. apply refl_equal. % 90.52/90.74 apply zenon_Hb2. apply refl_equal. % 90.52/90.74 apply (zenon_L107_ zenon_TB_ec); trivial. % 90.52/90.74 (* end of lemma zenon_L108_ *) % 90.52/90.74 assert (zenon_L109_ : forall (zenon_TB_ec : zenon_U), (~(zenon_TB_ec = (n3))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (~(gt (succ (tptp_minus_1)) (succ (n0)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt zenon_TB_ec (n1))) -> False). % 90.52/90.74 do 1 intro. intros zenon_Hb6 zenon_H97 zenon_H68 zenon_H10a zenon_H73 zenon_H148. % 90.52/90.74 elim (classic ((~(zenon_TB_ec = (n2)))/\(~(gt zenon_TB_ec (n2))))); [ zenon_intro zenon_H243 | zenon_intro zenon_H244 ]. % 90.52/90.74 apply (zenon_and_s _ _ zenon_H243). zenon_intro zenon_Hb5. zenon_intro zenon_H238. % 90.52/90.74 apply (zenon_L108_ zenon_TB_ec); trivial. % 90.52/90.74 cut ((gt (n2) (n1)) = (gt zenon_TB_ec (n1))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H148. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact gt_2_1. % 90.52/90.74 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.74 cut (((n2) = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_H245]. % 90.52/90.74 congruence. % 90.52/90.74 apply (zenon_notand_s _ _ zenon_H244); [ zenon_intro zenon_H247 | zenon_intro zenon_H246 ]. % 90.52/90.74 apply zenon_H247. zenon_intro zenon_Hbe. % 90.52/90.74 elim (classic (zenon_TB_ec = zenon_TB_ec)); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Ha1 ]. % 90.52/90.74 cut ((zenon_TB_ec = zenon_TB_ec) = ((n2) = zenon_TB_ec)). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H245. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_Hc9. % 90.52/90.74 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.74 cut ((zenon_TB_ec = (n2))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 90.52/90.74 congruence. % 90.52/90.74 exact (zenon_Hb5 zenon_Hbe). % 90.52/90.74 apply zenon_Ha1. apply refl_equal. % 90.52/90.74 apply zenon_Ha1. apply refl_equal. % 90.52/90.74 apply zenon_H246. zenon_intro zenon_H248. % 90.52/90.74 generalize (zenon_H73 zenon_TB_ec). zenon_intro zenon_H144. % 90.52/90.74 generalize (zenon_H144 (n2)). zenon_intro zenon_H249. % 90.52/90.74 generalize (zenon_H249 (n1)). zenon_intro zenon_H24a. % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H24a); [ zenon_intro zenon_H238 | zenon_intro zenon_H24b ]. % 90.52/90.74 exact (zenon_H238 zenon_H248). % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H24b); [ zenon_intro zenon_H7a | zenon_intro zenon_H164 ]. % 90.52/90.74 exact (zenon_H7a gt_2_1). % 90.52/90.74 exact (zenon_H148 zenon_H164). % 90.52/90.74 apply zenon_H66. apply refl_equal. % 90.52/90.74 (* end of lemma zenon_L109_ *) % 90.52/90.74 assert (zenon_L110_ : forall (zenon_TB_ec : zenon_U), (~(gt (succ (tptp_minus_1)) (succ (n0)))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n3))) -> (~(gt zenon_TB_ec (succ (n0)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.74 do 1 intro. intros zenon_H10a zenon_H68 zenon_H97 zenon_Hb6 zenon_H109 zenon_H73. % 90.52/90.74 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_H12e | zenon_intro zenon_Hb0 ]. % 90.52/90.74 elim (classic (gt zenon_TB_ec (n1))); [ zenon_intro zenon_H164 | zenon_intro zenon_H148 ]. % 90.52/90.74 cut ((gt zenon_TB_ec (n1)) = (gt zenon_TB_ec (succ (n0)))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H109. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_H164. % 90.52/90.74 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 90.52/90.74 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.74 congruence. % 90.52/90.74 apply zenon_Ha1. apply refl_equal. % 90.52/90.74 exact (zenon_Hb0 zenon_H12e). % 90.52/90.74 apply (zenon_L109_ zenon_TB_ec); trivial. % 90.52/90.74 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 90.52/90.74 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_Hb0. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_Hb1. % 90.52/90.74 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.74 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.74 congruence. % 90.52/90.74 exact (zenon_Hb3 successor_1). % 90.52/90.74 apply zenon_Hb2. apply refl_equal. % 90.52/90.74 apply zenon_Hb2. apply refl_equal. % 90.52/90.74 (* end of lemma zenon_L110_ *) % 90.52/90.74 assert (zenon_L111_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (succ (n0)))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n3))) -> False). % 90.52/90.74 do 1 intro. intros zenon_H73 zenon_H10a zenon_H68 zenon_H97 zenon_Hb6. % 90.52/90.74 elim (classic (gt zenon_TB_ec (succ (n0)))); [ zenon_intro zenon_H10b | zenon_intro zenon_H109 ]. % 90.52/90.74 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.74 generalize (zenon_Hd1 zenon_TB_ec). zenon_intro zenon_Hd2. % 90.52/90.74 generalize (zenon_Hd2 (succ (n0))). zenon_intro zenon_H10c. % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H10c); [ zenon_intro zenon_Hab | zenon_intro zenon_H10d ]. % 90.52/90.74 exact (zenon_Hab zenon_H97). % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H10d); [ zenon_intro zenon_H109 | zenon_intro zenon_H10e ]. % 90.52/90.74 exact (zenon_H109 zenon_H10b). % 90.52/90.74 exact (zenon_H10a zenon_H10e). % 90.52/90.74 apply (zenon_L110_ zenon_TB_ec); trivial. % 90.52/90.74 (* end of lemma zenon_L111_ *) % 90.52/90.74 assert (zenon_L112_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n3))) -> (~(gt (n0) (succ (n0)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.74 do 1 intro. intros zenon_H68 zenon_H97 zenon_Hb6 zenon_H111 zenon_H73. % 90.52/90.74 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 90.52/90.74 elim (classic (gt (succ (tptp_minus_1)) (succ (n0)))); [ zenon_intro zenon_H10e | zenon_intro zenon_H10a ]. % 90.52/90.74 cut ((gt (succ (tptp_minus_1)) (succ (n0))) = (gt (n0) (succ (n0)))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H111. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_H10e. % 90.52/90.74 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.74 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.74 congruence. % 90.52/90.74 elim (classic ((n0) = (n0))); [ zenon_intro zenon_Hca | zenon_intro zenon_H67 ]. % 90.52/90.74 cut (((n0) = (n0)) = ((succ (tptp_minus_1)) = (n0))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_Hc3. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_Hca. % 90.52/90.74 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.74 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.74 congruence. % 90.52/90.74 exact (zenon_H72 zenon_H71). % 90.52/90.74 apply zenon_H67. apply refl_equal. % 90.52/90.74 apply zenon_H67. apply refl_equal. % 90.52/90.74 apply zenon_Hb2. apply refl_equal. % 90.52/90.74 apply (zenon_L111_ zenon_TB_ec); trivial. % 90.52/90.74 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.74 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H72. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_Hc2. % 90.52/90.74 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.74 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.74 congruence. % 90.52/90.74 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.74 apply zenon_H8f. apply refl_equal. % 90.52/90.74 apply zenon_H8f. apply refl_equal. % 90.52/90.74 (* end of lemma zenon_L112_ *) % 90.52/90.74 assert (zenon_L113_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (succ (n0)))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False). % 90.52/90.74 do 1 intro. intros zenon_H73 zenon_H1a2 zenon_H68 zenon_H97 zenon_Hb6 zenon_Hce. % 90.52/90.74 elim (classic (gt (n0) (succ (n0)))); [ zenon_intro zenon_H110 | zenon_intro zenon_H111 ]. % 90.52/90.74 cut ((gt (n0) (succ (n0))) = (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (n0)))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H1a2. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_H110. % 90.52/90.74 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.74 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 90.52/90.74 congruence. % 90.52/90.74 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd9 | zenon_intro zenon_Hda ]. % 90.52/90.74 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_Hd7. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_Hd9. % 90.52/90.74 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.74 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 90.52/90.74 congruence. % 90.52/90.74 exact (zenon_Hdb zenon_Hce). % 90.52/90.74 apply zenon_Hda. apply refl_equal. % 90.52/90.74 apply zenon_Hda. apply refl_equal. % 90.52/90.74 apply zenon_Hb2. apply refl_equal. % 90.52/90.74 apply (zenon_L112_ zenon_TB_ec); trivial. % 90.52/90.74 (* end of lemma zenon_L113_ *) % 90.52/90.74 assert (zenon_L114_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (n1))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(zenon_TB_ec = (n3))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.74 do 1 intro. intros zenon_H73 zenon_H1a0 zenon_Hce zenon_Hb6 zenon_H97 zenon_H68. % 90.52/90.74 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (n0)))); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H1a2 ]. % 90.52/90.74 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (succ (n0))) = (gt (sum (n0) (tptp_minus_1) zenon_E) (n1))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H1a0. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_H1a1. % 90.52/90.74 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.74 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.74 congruence. % 90.52/90.74 apply zenon_Hda. apply refl_equal. % 90.52/90.74 exact (zenon_Hb3 successor_1). % 90.52/90.74 apply (zenon_L113_ zenon_TB_ec); trivial. % 90.52/90.74 (* end of lemma zenon_L114_ *) % 90.52/90.74 assert (zenon_L115_ : forall (zenon_TB_ec : zenon_U), ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(zenon_TB_ec = (n3))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (n0))) -> False). % 90.52/90.74 do 1 intro. intros zenon_Hce zenon_Hb6 zenon_H97 zenon_H68 zenon_H73 zenon_He1. % 90.52/90.74 elim (classic ((~((sum (n0) (tptp_minus_1) zenon_E) = (n1)))/\(~(gt (sum (n0) (tptp_minus_1) zenon_E) (n1))))); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H1a8 ]. % 90.52/90.74 apply (zenon_and_s _ _ zenon_H1a7). zenon_intro zenon_H1a9. zenon_intro zenon_H1a0. % 90.52/90.74 apply (zenon_L114_ zenon_TB_ec); trivial. % 90.52/90.74 cut ((gt (n1) (n0)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_He1. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact gt_1_0. % 90.52/90.74 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.74 cut (((n1) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1aa]. % 90.52/90.74 congruence. % 90.52/90.74 apply (zenon_notand_s _ _ zenon_H1a8); [ zenon_intro zenon_H1ac | zenon_intro zenon_H1ab ]. % 90.52/90.74 apply zenon_H1ac. zenon_intro zenon_H1ad. % 90.52/90.74 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd9 | zenon_intro zenon_Hda ]. % 90.52/90.74 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n1) = (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H1aa. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_Hd9. % 90.52/90.74 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.74 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 90.52/90.74 congruence. % 90.52/90.74 exact (zenon_H1a9 zenon_H1ad). % 90.52/90.74 apply zenon_Hda. apply refl_equal. % 90.52/90.74 apply zenon_Hda. apply refl_equal. % 90.52/90.74 apply zenon_H1ab. zenon_intro zenon_H1ae. % 90.52/90.74 generalize (zenon_H73 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H1a3. % 90.52/90.74 generalize (zenon_H1a3 (n1)). zenon_intro zenon_H1af. % 90.52/90.74 generalize (zenon_H1af (n0)). zenon_intro zenon_H1b0. % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H1b0); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H1b1 ]. % 90.52/90.74 exact (zenon_H1a0 zenon_H1ae). % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H1b1); [ zenon_intro zenon_H13c | zenon_intro zenon_He0 ]. % 90.52/90.74 exact (zenon_H13c gt_1_0). % 90.52/90.74 exact (zenon_He1 zenon_He0). % 90.52/90.74 apply zenon_H67. apply refl_equal. % 90.52/90.74 (* end of lemma zenon_L115_ *) % 90.52/90.74 assert (zenon_L116_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n3))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (n0))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False). % 90.52/90.74 do 1 intro. intros zenon_H68 zenon_H97 zenon_Hb6 zenon_H73 zenon_Hdf zenon_Hce. % 90.52/90.74 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 90.52/90.74 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))); [ zenon_intro zenon_He0 | zenon_intro zenon_He1 ]. % 90.52/90.74 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (n0)) = (gt (n0) (n0))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_Hdf. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_He0. % 90.52/90.74 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.74 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 90.52/90.74 congruence. % 90.52/90.74 elim (classic ((n0) = (n0))); [ zenon_intro zenon_Hca | zenon_intro zenon_H67 ]. % 90.52/90.74 cut (((n0) = (n0)) = ((sum (n0) (tptp_minus_1) zenon_E) = (n0))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_Hdb. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_Hca. % 90.52/90.74 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.74 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 90.52/90.74 congruence. % 90.52/90.74 exact (zenon_Hd7 zenon_Hd6). % 90.52/90.74 apply zenon_H67. apply refl_equal. % 90.52/90.74 apply zenon_H67. apply refl_equal. % 90.52/90.74 apply zenon_H67. apply refl_equal. % 90.52/90.74 apply (zenon_L115_ zenon_TB_ec); trivial. % 90.52/90.74 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd9 | zenon_intro zenon_Hda ]. % 90.52/90.74 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_Hd7. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_Hd9. % 90.52/90.74 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.74 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 90.52/90.74 congruence. % 90.52/90.74 exact (zenon_Hdb zenon_Hce). % 90.52/90.74 apply zenon_Hda. apply refl_equal. % 90.52/90.74 apply zenon_Hda. apply refl_equal. % 90.52/90.74 (* end of lemma zenon_L116_ *) % 90.52/90.74 assert (zenon_L117_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (n1))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(zenon_TB_ec = (n3))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.74 do 1 intro. intros zenon_H73 zenon_H12d zenon_Hce zenon_Hb6 zenon_H97 zenon_H68. % 90.52/90.74 elim (classic (gt (n0) (n1))); [ zenon_intro zenon_H137 | zenon_intro zenon_H133 ]. % 90.52/90.74 generalize (zenon_H73 (n1)). zenon_intro zenon_H138. % 90.52/90.74 generalize (zenon_H138 (n0)). zenon_intro zenon_H139. % 90.52/90.74 generalize (zenon_H139 (n1)). zenon_intro zenon_H13a. % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H13a); [ zenon_intro zenon_H13c | zenon_intro zenon_H13b ]. % 90.52/90.74 exact (zenon_H13c gt_1_0). % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H13b); [ zenon_intro zenon_H133 | zenon_intro zenon_H13d ]. % 90.52/90.74 exact (zenon_H133 zenon_H137). % 90.52/90.74 exact (zenon_H12d zenon_H13d). % 90.52/90.74 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 90.52/90.74 elim (classic (gt (n0) (n0))); [ zenon_intro zenon_H1b4 | zenon_intro zenon_Hdf ]. % 90.52/90.74 elim (classic (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hde ]. % 90.52/90.74 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (n1))); [ zenon_intro zenon_H1ae | zenon_intro zenon_H1a0 ]. % 90.52/90.74 generalize (zenon_H73 (n0)). zenon_intro zenon_H115. % 90.52/90.74 generalize (zenon_H115 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H1e1. % 90.52/90.74 generalize (zenon_H1e1 (n1)). zenon_intro zenon_H24c. % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H24c); [ zenon_intro zenon_Hde | zenon_intro zenon_H24d ]. % 90.52/90.74 exact (zenon_Hde zenon_Hdd). % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H24d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H137 ]. % 90.52/90.74 exact (zenon_H1a0 zenon_H1ae). % 90.52/90.74 exact (zenon_H133 zenon_H137). % 90.52/90.74 apply (zenon_L114_ zenon_TB_ec); trivial. % 90.52/90.74 cut ((gt (n0) (n0)) = (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_Hde. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_H1b4. % 90.52/90.74 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 90.52/90.74 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.74 congruence. % 90.52/90.74 apply zenon_H67. apply refl_equal. % 90.52/90.74 exact (zenon_Hd7 zenon_Hd6). % 90.52/90.74 apply (zenon_L116_ zenon_TB_ec); trivial. % 90.52/90.74 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd9 | zenon_intro zenon_Hda ]. % 90.52/90.74 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_Hd7. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_Hd9. % 90.52/90.74 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.74 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 90.52/90.74 congruence. % 90.52/90.74 exact (zenon_Hdb zenon_Hce). % 90.52/90.74 apply zenon_Hda. apply refl_equal. % 90.52/90.74 apply zenon_Hda. apply refl_equal. % 90.52/90.74 (* end of lemma zenon_L117_ *) % 90.52/90.74 assert (zenon_L118_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (n2))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~((tptp_minus_1) = (n3))) -> (~(gt (n0) (succ zenon_TB_ec))) -> False). % 90.52/90.74 do 1 intro. intros zenon_H73 zenon_H1da zenon_H68 zenon_H97 zenon_Hb6 zenon_Hce zenon_He8 zenon_H1de. % 90.52/90.74 elim (classic (zenon_TB_ec = (n2))); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hb5 ]. % 90.52/90.74 cut ((gt (succ (tptp_minus_1)) zenon_TB_ec) = (gt (succ (tptp_minus_1)) (n2))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H1da. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_H97. % 90.52/90.74 cut ((zenon_TB_ec = (n2))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 90.52/90.74 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.74 congruence. % 90.52/90.74 apply zenon_H8f. apply refl_equal. % 90.52/90.74 exact (zenon_Hb5 zenon_Hbe). % 90.52/90.74 elim (classic (gt zenon_TB_ec (n2))); [ zenon_intro zenon_H248 | zenon_intro zenon_H238 ]. % 90.52/90.74 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.74 generalize (zenon_Hd1 zenon_TB_ec). zenon_intro zenon_Hd2. % 90.52/90.74 generalize (zenon_Hd2 (n2)). zenon_intro zenon_H24e. % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H24e); [ zenon_intro zenon_Hab | zenon_intro zenon_H24f ]. % 90.52/90.74 exact (zenon_Hab zenon_H97). % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H24f); [ zenon_intro zenon_H238 | zenon_intro zenon_H1dd ]. % 90.52/90.74 exact (zenon_H238 zenon_H248). % 90.52/90.74 exact (zenon_H1da zenon_H1dd). % 90.52/90.74 apply (zenon_L101_ zenon_TB_ec); trivial. % 90.52/90.74 (* end of lemma zenon_L118_ *) % 90.52/90.74 assert (zenon_L119_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (succ zenon_TB_ec))) -> (~((tptp_minus_1) = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(zenon_TB_ec = (n3))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (~((n0) = zenon_TB_ec)) -> False). % 90.52/90.74 do 1 intro. intros zenon_H73 zenon_H1de zenon_He8 zenon_Hce zenon_Hb6 zenon_H97 zenon_H68 zenon_Hc8. % 90.52/90.74 generalize (finite_domain_0 (tptp_minus_1)). zenon_intro zenon_H1c8. % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H1c8); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H103 ]. % 90.52/90.74 apply (zenon_notand_s _ _ zenon_H1c9); [ zenon_intro zenon_Hed | zenon_intro zenon_H1b5 ]. % 90.52/90.74 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H6b. % 90.52/90.74 generalize (zenon_H6b (tptp_minus_1)). zenon_intro zenon_Hee. % 90.52/90.74 apply (zenon_equiv_s _ _ zenon_Hee); [ zenon_intro zenon_Hed; zenon_intro zenon_Hbf | zenon_intro zenon_Hef; zenon_intro zenon_Hc1 ]. % 90.52/90.74 elim (classic ((~((succ (tptp_minus_1)) = (n2)))/\(~(gt (succ (tptp_minus_1)) (n2))))); [ zenon_intro zenon_H250 | zenon_intro zenon_H251 ]. % 90.52/90.74 apply (zenon_and_s _ _ zenon_H250). zenon_intro zenon_H252. zenon_intro zenon_H1da. % 90.52/90.74 apply (zenon_L118_ zenon_TB_ec); trivial. % 90.52/90.74 cut ((gt (n2) (n0)) = (gt (succ (tptp_minus_1)) (n0))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_Hbf. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact gt_2_0. % 90.52/90.74 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.74 cut (((n2) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H253]. % 90.52/90.74 congruence. % 90.52/90.74 apply (zenon_notand_s _ _ zenon_H251); [ zenon_intro zenon_H255 | zenon_intro zenon_H254 ]. % 90.52/90.74 apply zenon_H255. zenon_intro zenon_H256. % 90.52/90.74 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.74 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n2) = (succ (tptp_minus_1)))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H253. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_Hc2. % 90.52/90.74 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.74 cut (((succ (tptp_minus_1)) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H252]. % 90.52/90.74 congruence. % 90.52/90.74 exact (zenon_H252 zenon_H256). % 90.52/90.74 apply zenon_H8f. apply refl_equal. % 90.52/90.74 apply zenon_H8f. apply refl_equal. % 90.52/90.74 apply zenon_H254. zenon_intro zenon_H1dd. % 90.52/90.74 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.74 generalize (zenon_Hd1 (n2)). zenon_intro zenon_H257. % 90.52/90.74 generalize (zenon_H257 (n0)). zenon_intro zenon_H258. % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H258); [ zenon_intro zenon_H1da | zenon_intro zenon_H259 ]. % 90.52/90.74 exact (zenon_H1da zenon_H1dd). % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H259); [ zenon_intro zenon_H194 | zenon_intro zenon_Hc1 ]. % 90.52/90.74 exact (zenon_H194 gt_2_0). % 90.52/90.74 exact (zenon_Hbf zenon_Hc1). % 90.52/90.74 apply zenon_H67. apply refl_equal. % 90.52/90.74 exact (zenon_Hed zenon_Hef). % 90.52/90.74 apply (zenon_L71_); trivial. % 90.52/90.74 apply (zenon_L74_ zenon_TB_ec); trivial. % 90.52/90.74 (* end of lemma zenon_L119_ *) % 90.52/90.74 assert (zenon_L120_ : forall (zenon_TB_ec : zenon_U), (~(gt (n0) (succ zenon_TB_ec))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(zenon_TB_ec = (n3))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (~(gt (n1) (succ zenon_TB_ec))) -> (~((tptp_minus_1) = (n3))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.74 do 1 intro. intros zenon_H1de zenon_Hce zenon_Hb6 zenon_H97 zenon_H68 zenon_H1d4 zenon_He8 zenon_H73. % 90.52/90.74 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_H12e | zenon_intro zenon_Hb0 ]. % 90.52/90.74 elim (classic (gt (n1) (n1))); [ zenon_intro zenon_H13d | zenon_intro zenon_H12d ]. % 90.52/90.74 elim (classic (gt (n1) (succ (n0)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 90.52/90.74 cut ((gt (n1) (succ (n0))) = (gt (n1) (succ zenon_TB_ec))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H1d4. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_H13e. % 90.52/90.74 cut (((succ (n0)) = (succ zenon_TB_ec))); [idtac | apply NNPP; zenon_intro zenon_He3]. % 90.52/90.74 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.74 congruence. % 90.52/90.74 apply zenon_H66. apply refl_equal. % 90.52/90.74 cut (((n0) = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Hc8]. % 90.52/90.74 congruence. % 90.52/90.74 apply (zenon_L119_ zenon_TB_ec); trivial. % 90.52/90.74 cut ((gt (n1) (n1)) = (gt (n1) (succ (n0)))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H13f. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_H13d. % 90.52/90.74 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 90.52/90.74 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.74 congruence. % 90.52/90.74 apply zenon_H66. apply refl_equal. % 90.52/90.74 exact (zenon_Hb0 zenon_H12e). % 90.52/90.74 apply (zenon_L117_ zenon_TB_ec); trivial. % 90.52/90.74 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 90.52/90.74 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_Hb0. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_Hb1. % 90.52/90.74 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.74 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.74 congruence. % 90.52/90.74 exact (zenon_Hb3 successor_1). % 90.52/90.74 apply zenon_Hb2. apply refl_equal. % 90.52/90.74 apply zenon_Hb2. apply refl_equal. % 90.52/90.74 (* end of lemma zenon_L120_ *) % 90.52/90.74 assert (zenon_L121_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~((tptp_minus_1) = (n3))) -> (~(gt (succ (tptp_minus_1)) (succ zenon_TB_ec))) -> (~(gt (n0) (succ zenon_TB_ec))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(zenon_TB_ec = (n3))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.74 do 1 intro. intros zenon_H73 zenon_He8 zenon_H1d5 zenon_H1de zenon_Hce zenon_Hb6 zenon_H97 zenon_H68. % 90.52/90.74 elim (classic (gt (succ (tptp_minus_1)) (succ (n0)))); [ zenon_intro zenon_H10e | zenon_intro zenon_H10a ]. % 90.52/90.74 elim (classic (gt (succ (tptp_minus_1)) (n1))); [ zenon_intro zenon_H167 | zenon_intro zenon_Hac ]. % 90.52/90.74 elim (classic (gt (n1) (succ zenon_TB_ec))); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H1d4 ]. % 90.52/90.74 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.74 generalize (zenon_Hd1 (n1)). zenon_intro zenon_H1d1. % 90.52/90.74 generalize (zenon_H1d1 (succ zenon_TB_ec)). zenon_intro zenon_H1d7. % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H1d7); [ zenon_intro zenon_Hac | zenon_intro zenon_H1d8 ]. % 90.52/90.74 exact (zenon_Hac zenon_H167). % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H1d8); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1d9 ]. % 90.52/90.74 exact (zenon_H1d4 zenon_H1d6). % 90.52/90.74 exact (zenon_H1d5 zenon_H1d9). % 90.52/90.74 apply (zenon_L120_ zenon_TB_ec); trivial. % 90.52/90.74 cut ((gt (succ (tptp_minus_1)) (succ (n0))) = (gt (succ (tptp_minus_1)) (n1))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_Hac. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_H10e. % 90.52/90.74 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.74 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.74 congruence. % 90.52/90.74 apply zenon_H8f. apply refl_equal. % 90.52/90.74 exact (zenon_Hb3 successor_1). % 90.52/90.74 apply (zenon_L111_ zenon_TB_ec); trivial. % 90.52/90.74 (* end of lemma zenon_L121_ *) % 90.52/90.74 assert (zenon_L122_ : forall (zenon_TB_ec : zenon_U), (~(gt (n0) (succ zenon_TB_ec))) -> (~(zenon_TB_ec = (n3))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (~((tptp_minus_1) = (n3))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False). % 90.52/90.74 do 1 intro. intros zenon_H1de zenon_Hb6 zenon_H97 zenon_H68 zenon_He8 zenon_H73 zenon_Hce. % 90.52/90.74 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 90.52/90.74 elim (classic (gt (n0) (n0))); [ zenon_intro zenon_H1b4 | zenon_intro zenon_Hdf ]. % 90.52/90.74 elim (classic (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hde ]. % 90.52/90.74 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (succ zenon_TB_ec))); [ zenon_intro zenon_H1df | zenon_intro zenon_H1e0 ]. % 90.52/90.74 generalize (zenon_H73 (n0)). zenon_intro zenon_H115. % 90.52/90.74 generalize (zenon_H115 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H1e1. % 90.52/90.74 generalize (zenon_H1e1 (succ zenon_TB_ec)). zenon_intro zenon_H1e2. % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H1e2); [ zenon_intro zenon_Hde | zenon_intro zenon_H1e3 ]. % 90.52/90.74 exact (zenon_Hde zenon_Hdd). % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H1e3); [ zenon_intro zenon_H1e0 | zenon_intro zenon_H1e4 ]. % 90.52/90.74 exact (zenon_H1e0 zenon_H1df). % 90.52/90.74 exact (zenon_H1de zenon_H1e4). % 90.52/90.74 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 90.52/90.74 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))); [ zenon_intro zenon_He0 | zenon_intro zenon_He1 ]. % 90.52/90.74 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (tptp_minus_1)))); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e6 ]. % 90.52/90.74 elim (classic (gt (succ (tptp_minus_1)) (succ zenon_TB_ec))); [ zenon_intro zenon_H1d9 | zenon_intro zenon_H1d5 ]. % 90.52/90.74 generalize (zenon_H73 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H1a3. % 90.52/90.74 generalize (zenon_H1a3 (succ (tptp_minus_1))). zenon_intro zenon_H1e7. % 90.52/90.74 generalize (zenon_H1e7 (succ zenon_TB_ec)). zenon_intro zenon_H1e8. % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H1e8); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H1e9 ]. % 90.52/90.74 exact (zenon_H1e6 zenon_H1e5). % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H1e9); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H1df ]. % 90.52/90.74 exact (zenon_H1d5 zenon_H1d9). % 90.52/90.74 exact (zenon_H1e0 zenon_H1df). % 90.52/90.74 apply (zenon_L121_ zenon_TB_ec); trivial. % 90.52/90.74 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (n0)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (tptp_minus_1)))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H1e6. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_He0. % 90.52/90.74 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.74 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.74 congruence. % 90.52/90.74 apply zenon_Hda. apply refl_equal. % 90.52/90.74 exact (zenon_H72 zenon_H71). % 90.52/90.74 apply (zenon_L115_ zenon_TB_ec); trivial. % 90.52/90.74 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.74 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H72. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_Hc2. % 90.52/90.74 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.74 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.74 congruence. % 90.52/90.74 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.74 apply zenon_H8f. apply refl_equal. % 90.52/90.74 apply zenon_H8f. apply refl_equal. % 90.52/90.74 cut ((gt (n0) (n0)) = (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_Hde. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_H1b4. % 90.52/90.74 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 90.52/90.74 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.74 congruence. % 90.52/90.74 apply zenon_H67. apply refl_equal. % 90.52/90.74 exact (zenon_Hd7 zenon_Hd6). % 90.52/90.74 apply (zenon_L116_ zenon_TB_ec); trivial. % 90.52/90.74 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd9 | zenon_intro zenon_Hda ]. % 90.52/90.74 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_Hd7. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_Hd9. % 90.52/90.74 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.74 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 90.52/90.74 congruence. % 90.52/90.74 exact (zenon_Hdb zenon_Hce). % 90.52/90.74 apply zenon_Hda. apply refl_equal. % 90.52/90.74 apply zenon_Hda. apply refl_equal. % 90.52/90.74 (* end of lemma zenon_L122_ *) % 90.52/90.74 assert (zenon_L123_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (n3))) -> (~(gt (n0) (succ zenon_TB_ec))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(zenon_TB_ec = (n3))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.74 do 1 intro. intros zenon_H73 zenon_H175 zenon_H1de zenon_Hce zenon_Hb6 zenon_H97 zenon_H68. % 90.52/90.74 elim (classic ((tptp_minus_1) = (n3))); [ zenon_intro zenon_H106 | zenon_intro zenon_He8 ]. % 90.52/90.74 cut ((gt (n0) (tptp_minus_1)) = (gt (n0) (n3))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H175. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact gt_0_tptp_minus_1. % 90.52/90.74 cut (((tptp_minus_1) = (n3))); [idtac | apply NNPP; zenon_intro zenon_He8]. % 90.52/90.74 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.74 congruence. % 90.52/90.74 apply zenon_H67. apply refl_equal. % 90.52/90.74 exact (zenon_He8 zenon_H106). % 90.52/90.74 apply (zenon_L122_ zenon_TB_ec); trivial. % 90.52/90.74 (* end of lemma zenon_L123_ *) % 90.52/90.74 assert (zenon_L124_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (n3))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ zenon_TB_ec))) -> False). % 90.52/90.74 do 1 intro. intros zenon_H73 zenon_H176 zenon_H68 zenon_H97 zenon_Hb6 zenon_Hce zenon_H1de. % 90.52/90.74 elim (classic (gt (n0) (n3))); [ zenon_intro zenon_H177 | zenon_intro zenon_H175 ]. % 90.52/90.74 generalize (zenon_H73 (n1)). zenon_intro zenon_H138. % 90.52/90.74 generalize (zenon_H138 (n0)). zenon_intro zenon_H139. % 90.52/90.74 generalize (zenon_H139 (n3)). zenon_intro zenon_H178. % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H178); [ zenon_intro zenon_H13c | zenon_intro zenon_H179 ]. % 90.52/90.74 exact (zenon_H13c gt_1_0). % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H179); [ zenon_intro zenon_H175 | zenon_intro zenon_H17a ]. % 90.52/90.74 exact (zenon_H175 zenon_H177). % 90.52/90.74 exact (zenon_H176 zenon_H17a). % 90.52/90.74 apply (zenon_L123_ zenon_TB_ec); trivial. % 90.52/90.74 (* end of lemma zenon_L124_ *) % 90.52/90.74 assert (zenon_L125_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n2) (n3))) -> (~(gt (n0) (succ zenon_TB_ec))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(zenon_TB_ec = (n3))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.74 do 1 intro. intros zenon_H73 zenon_H207 zenon_H1de zenon_Hce zenon_Hb6 zenon_H97 zenon_H68. % 90.52/90.74 elim (classic (gt (n1) (n3))); [ zenon_intro zenon_H17a | zenon_intro zenon_H176 ]. % 90.52/90.74 generalize (zenon_H73 (n2)). zenon_intro zenon_H76. % 90.52/90.74 generalize (zenon_H76 (n1)). zenon_intro zenon_H77. % 90.52/90.74 generalize (zenon_H77 (n3)). zenon_intro zenon_H208. % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H208); [ zenon_intro zenon_H7a | zenon_intro zenon_H209 ]. % 90.52/90.74 exact (zenon_H7a gt_2_1). % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H209); [ zenon_intro zenon_H176 | zenon_intro zenon_H20a ]. % 90.52/90.74 exact (zenon_H176 zenon_H17a). % 90.52/90.74 exact (zenon_H207 zenon_H20a). % 90.52/90.74 apply (zenon_L124_ zenon_TB_ec); trivial. % 90.52/90.74 (* end of lemma zenon_L125_ *) % 90.52/90.74 assert (zenon_L126_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n3) (n3))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ zenon_TB_ec))) -> False). % 90.52/90.74 do 1 intro. intros zenon_H73 zenon_H25a zenon_H68 zenon_H97 zenon_Hb6 zenon_Hce zenon_H1de. % 90.52/90.74 elim (classic (gt (n2) (n3))); [ zenon_intro zenon_H20a | zenon_intro zenon_H207 ]. % 90.52/90.74 generalize (zenon_H73 (n3)). zenon_intro zenon_H7d. % 90.52/90.74 generalize (zenon_H7d (n2)). zenon_intro zenon_H7e. % 90.52/90.74 generalize (zenon_H7e (n3)). zenon_intro zenon_H25b. % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H25b); [ zenon_intro zenon_H81 | zenon_intro zenon_H25c ]. % 90.52/90.74 exact (zenon_H81 gt_3_2). % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 90.52/90.74 exact (zenon_H207 zenon_H20a). % 90.52/90.74 exact (zenon_H25a zenon_H25d). % 90.52/90.74 apply (zenon_L125_ zenon_TB_ec); trivial. % 90.52/90.74 (* end of lemma zenon_L126_ *) % 90.52/90.74 assert (zenon_L127_ : forall (zenon_TB_ec : zenon_U), (~(gt (n0) (succ zenon_TB_ec))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(zenon_TB_ec = (n3))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (~(gt (n2) (succ (succ (succ (n0)))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.74 do 1 intro. intros zenon_H1de zenon_Hce zenon_Hb6 zenon_H97 zenon_H68 zenon_H20b zenon_H73. % 90.52/90.74 elim (classic ((n3) = (succ (succ (succ (n0)))))); [ zenon_intro zenon_H20c | zenon_intro zenon_H8b ]. % 90.52/90.74 elim (classic (gt (n2) (n3))); [ zenon_intro zenon_H20a | zenon_intro zenon_H207 ]. % 90.52/90.74 cut ((gt (n2) (n3)) = (gt (n2) (succ (succ (succ (n0)))))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H20b. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_H20a. % 90.52/90.74 cut (((n3) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 90.52/90.74 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 90.52/90.74 congruence. % 90.52/90.74 apply zenon_H65. apply refl_equal. % 90.52/90.74 exact (zenon_H8b zenon_H20c). % 90.52/90.74 apply (zenon_L125_ zenon_TB_ec); trivial. % 90.52/90.74 elim (classic ((succ (succ (succ (n0)))) = (succ (succ (succ (n0)))))); [ zenon_intro zenon_H20d | zenon_intro zenon_H20e ]. % 90.52/90.74 cut (((succ (succ (succ (n0)))) = (succ (succ (succ (n0))))) = ((n3) = (succ (succ (succ (n0)))))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H8b. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_H20d. % 90.52/90.74 cut (((succ (succ (succ (n0)))) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H20e]. % 90.52/90.74 cut (((succ (succ (succ (n0)))) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H20f]. % 90.52/90.74 congruence. % 90.52/90.74 exact (zenon_H20f successor_3). % 90.52/90.74 apply zenon_H20e. apply refl_equal. % 90.52/90.74 apply zenon_H20e. apply refl_equal. % 90.52/90.74 (* end of lemma zenon_L127_ *) % 90.52/90.74 assert (zenon_L128_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (succ (n0))) (succ (succ (succ (n0)))))) -> (~(gt (n0) (succ zenon_TB_ec))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(zenon_TB_ec = (n3))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.74 do 1 intro. intros zenon_H73 zenon_H210 zenon_H1de zenon_Hce zenon_Hb6 zenon_H97 zenon_H68. % 90.52/90.74 elim (classic (gt (n2) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H211 | zenon_intro zenon_H20b ]. % 90.52/90.74 cut ((gt (n2) (succ (succ (succ (n0))))) = (gt (succ (succ (n0))) (succ (succ (succ (n0)))))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H210. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_H211. % 90.52/90.74 cut (((succ (succ (succ (n0)))) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H20e]. % 90.52/90.74 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ec]. % 90.52/90.74 congruence. % 90.52/90.74 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1ee ]. % 90.52/90.74 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((n2) = (succ (succ (n0))))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H1ec. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_H1ed. % 90.52/90.74 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 90.52/90.74 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 90.52/90.74 congruence. % 90.52/90.74 exact (zenon_H1ef successor_2). % 90.52/90.74 apply zenon_H1ee. apply refl_equal. % 90.52/90.74 apply zenon_H1ee. apply refl_equal. % 90.52/90.74 apply zenon_H20e. apply refl_equal. % 90.52/90.74 apply (zenon_L127_ zenon_TB_ec); trivial. % 90.52/90.74 (* end of lemma zenon_L128_ *) % 90.52/90.74 assert (zenon_L129_ : forall (zenon_TB_ec : zenon_U), (~(gt (n0) (succ zenon_TB_ec))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(zenon_TB_ec = (n3))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (~(gt (n1) (succ (succ (succ (n0)))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.74 do 1 intro. intros zenon_H1de zenon_Hce zenon_Hb6 zenon_H97 zenon_H68 zenon_H25e zenon_H73. % 90.52/90.74 elim (classic ((n2) = (succ (succ (n0))))); [ zenon_intro zenon_H1eb | zenon_intro zenon_H1ec ]. % 90.52/90.74 elim (classic (gt (n1) (n2))); [ zenon_intro zenon_H14e | zenon_intro zenon_H14a ]. % 90.52/90.74 elim (classic (gt (n1) (succ (succ (n0))))); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H1f0 ]. % 90.52/90.74 elim (classic (gt (succ (succ (n0))) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H21e | zenon_intro zenon_H210 ]. % 90.52/90.74 generalize (zenon_H73 (n1)). zenon_intro zenon_H138. % 90.52/90.74 generalize (zenon_H138 (succ (succ (n0)))). zenon_intro zenon_H25f. % 90.52/90.74 generalize (zenon_H25f (succ (succ (succ (n0))))). zenon_intro zenon_H260. % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H260); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H261 ]. % 90.52/90.74 exact (zenon_H1f0 zenon_H1f5). % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H261); [ zenon_intro zenon_H210 | zenon_intro zenon_H262 ]. % 90.52/90.74 exact (zenon_H210 zenon_H21e). % 90.52/90.74 exact (zenon_H25e zenon_H262). % 90.52/90.74 apply (zenon_L128_ zenon_TB_ec); trivial. % 90.52/90.74 cut ((gt (n1) (n2)) = (gt (n1) (succ (succ (n0))))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H1f0. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_H14e. % 90.52/90.74 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ec]. % 90.52/90.74 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.74 congruence. % 90.52/90.74 apply zenon_H66. apply refl_equal. % 90.52/90.74 exact (zenon_H1ec zenon_H1eb). % 90.52/90.74 elim (classic ((~((n1) = (n3)))/\(~(gt (n1) (n3))))); [ zenon_intro zenon_H17b | zenon_intro zenon_H17c ]. % 90.52/90.74 apply (zenon_and_s _ _ zenon_H17b). zenon_intro zenon_H17d. zenon_intro zenon_H176. % 90.52/90.74 apply (zenon_L124_ zenon_TB_ec); trivial. % 90.52/90.74 cut ((gt (n3) (n2)) = (gt (n1) (n2))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H14a. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact gt_3_2. % 90.52/90.74 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 90.52/90.74 cut (((n3) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 90.52/90.74 congruence. % 90.52/90.74 apply (zenon_notand_s _ _ zenon_H17c); [ zenon_intro zenon_H180 | zenon_intro zenon_H17f ]. % 90.52/90.74 apply zenon_H180. zenon_intro zenon_H181. % 90.52/90.74 elim (classic ((n1) = (n1))); [ zenon_intro zenon_H131 | zenon_intro zenon_H66 ]. % 90.52/90.74 cut (((n1) = (n1)) = ((n3) = (n1))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H17e. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_H131. % 90.52/90.74 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.74 cut (((n1) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H17d]. % 90.52/90.74 congruence. % 90.52/90.74 exact (zenon_H17d zenon_H181). % 90.52/90.74 apply zenon_H66. apply refl_equal. % 90.52/90.74 apply zenon_H66. apply refl_equal. % 90.52/90.74 apply zenon_H17f. zenon_intro zenon_H17a. % 90.52/90.74 generalize (zenon_H73 (n1)). zenon_intro zenon_H138. % 90.52/90.74 generalize (zenon_H138 (n3)). zenon_intro zenon_H182. % 90.52/90.74 generalize (zenon_H182 (n2)). zenon_intro zenon_H263. % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H263); [ zenon_intro zenon_H176 | zenon_intro zenon_H264 ]. % 90.52/90.74 exact (zenon_H176 zenon_H17a). % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H264); [ zenon_intro zenon_H81 | zenon_intro zenon_H14e ]. % 90.52/90.74 exact (zenon_H81 gt_3_2). % 90.52/90.74 exact (zenon_H14a zenon_H14e). % 90.52/90.74 apply zenon_H65. apply refl_equal. % 90.52/90.74 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1ee ]. % 90.52/90.74 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((n2) = (succ (succ (n0))))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H1ec. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_H1ed. % 90.52/90.74 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 90.52/90.74 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 90.52/90.74 congruence. % 90.52/90.74 exact (zenon_H1ef successor_2). % 90.52/90.74 apply zenon_H1ee. apply refl_equal. % 90.52/90.74 apply zenon_H1ee. apply refl_equal. % 90.52/90.74 (* end of lemma zenon_L129_ *) % 90.52/90.74 assert (zenon_L130_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n0)) (succ (succ (succ (n0)))))) -> (~(gt (n0) (succ zenon_TB_ec))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(zenon_TB_ec = (n3))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.74 do 1 intro. intros zenon_H73 zenon_H265 zenon_H1de zenon_Hce zenon_Hb6 zenon_H97 zenon_H68. % 90.52/90.74 elim (classic (gt (n1) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H262 | zenon_intro zenon_H25e ]. % 90.52/90.74 cut ((gt (n1) (succ (succ (succ (n0))))) = (gt (succ (n0)) (succ (succ (succ (n0)))))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H265. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_H262. % 90.52/90.74 cut (((succ (succ (succ (n0)))) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H20e]. % 90.52/90.74 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 90.52/90.74 congruence. % 90.52/90.74 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 90.52/90.74 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_Hb0. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_Hb1. % 90.52/90.74 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.74 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.74 congruence. % 90.52/90.74 exact (zenon_Hb3 successor_1). % 90.52/90.74 apply zenon_Hb2. apply refl_equal. % 90.52/90.74 apply zenon_Hb2. apply refl_equal. % 90.52/90.74 apply zenon_H20e. apply refl_equal. % 90.52/90.74 apply (zenon_L129_ zenon_TB_ec); trivial. % 90.52/90.74 (* end of lemma zenon_L130_ *) % 90.52/90.74 assert (zenon_L131_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt zenon_TB_ec (n0))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> False). % 90.52/90.74 do 1 intro. intros zenon_H73 zenon_Hcb zenon_H68 zenon_H97 zenon_Hb5 zenon_Hb6. % 90.52/90.74 elim (classic ((~(zenon_TB_ec = (n1)))/\(~(gt zenon_TB_ec (n1))))); [ zenon_intro zenon_H198 | zenon_intro zenon_H199 ]. % 90.52/90.74 apply (zenon_and_s _ _ zenon_H198). zenon_intro zenon_Hae. zenon_intro zenon_H148. % 90.52/90.74 apply (zenon_L20_ zenon_TB_ec); trivial. % 90.52/90.74 cut ((gt (n1) (n0)) = (gt zenon_TB_ec (n0))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_Hcb. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact gt_1_0. % 90.52/90.74 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.74 cut (((n1) = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 90.52/90.74 congruence. % 90.52/90.74 apply (zenon_notand_s _ _ zenon_H199); [ zenon_intro zenon_H19c | zenon_intro zenon_H19b ]. % 90.52/90.74 apply zenon_H19c. zenon_intro zenon_Had. % 90.52/90.74 elim (classic (zenon_TB_ec = zenon_TB_ec)); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Ha1 ]. % 90.52/90.74 cut ((zenon_TB_ec = zenon_TB_ec) = ((n1) = zenon_TB_ec)). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H19a. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_Hc9. % 90.52/90.74 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.74 cut ((zenon_TB_ec = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hae]. % 90.52/90.74 congruence. % 90.52/90.74 exact (zenon_Hae zenon_Had). % 90.52/90.74 apply zenon_Ha1. apply refl_equal. % 90.52/90.74 apply zenon_Ha1. apply refl_equal. % 90.52/90.74 apply zenon_H19b. zenon_intro zenon_H164. % 90.52/90.74 generalize (zenon_H73 zenon_TB_ec). zenon_intro zenon_H144. % 90.52/90.74 generalize (zenon_H144 (n1)). zenon_intro zenon_H19d. % 90.52/90.74 generalize (zenon_H19d (n0)). zenon_intro zenon_H19e. % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H19e); [ zenon_intro zenon_H148 | zenon_intro zenon_H19f ]. % 90.52/90.74 exact (zenon_H148 zenon_H164). % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H19f); [ zenon_intro zenon_H13c | zenon_intro zenon_Hd8 ]. % 90.52/90.74 exact (zenon_H13c gt_1_0). % 90.52/90.74 exact (zenon_Hcb zenon_Hd8). % 90.52/90.74 apply zenon_H67. apply refl_equal. % 90.52/90.74 (* end of lemma zenon_L131_ *) % 90.52/90.74 assert (zenon_L132_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n3))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt zenon_TB_ec (n0))) -> False). % 90.52/90.74 do 1 intro. intros zenon_H68 zenon_H97 zenon_Hb6 zenon_H73 zenon_Hcb. % 90.52/90.74 elim (classic ((~(zenon_TB_ec = (n2)))/\(~(gt zenon_TB_ec (n2))))); [ zenon_intro zenon_H243 | zenon_intro zenon_H244 ]. % 90.52/90.74 apply (zenon_and_s _ _ zenon_H243). zenon_intro zenon_Hb5. zenon_intro zenon_H238. % 90.52/90.74 apply (zenon_L131_ zenon_TB_ec); trivial. % 90.52/90.74 cut ((gt (n2) (n0)) = (gt zenon_TB_ec (n0))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_Hcb. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact gt_2_0. % 90.52/90.74 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.74 cut (((n2) = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_H245]. % 90.52/90.74 congruence. % 90.52/90.74 apply (zenon_notand_s _ _ zenon_H244); [ zenon_intro zenon_H247 | zenon_intro zenon_H246 ]. % 90.52/90.74 apply zenon_H247. zenon_intro zenon_Hbe. % 90.52/90.74 elim (classic (zenon_TB_ec = zenon_TB_ec)); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Ha1 ]. % 90.52/90.74 cut ((zenon_TB_ec = zenon_TB_ec) = ((n2) = zenon_TB_ec)). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H245. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_Hc9. % 90.52/90.74 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.74 cut ((zenon_TB_ec = (n2))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 90.52/90.74 congruence. % 90.52/90.74 exact (zenon_Hb5 zenon_Hbe). % 90.52/90.74 apply zenon_Ha1. apply refl_equal. % 90.52/90.74 apply zenon_Ha1. apply refl_equal. % 90.52/90.74 apply zenon_H246. zenon_intro zenon_H248. % 90.52/90.74 generalize (zenon_H73 zenon_TB_ec). zenon_intro zenon_H144. % 90.52/90.74 generalize (zenon_H144 (n2)). zenon_intro zenon_H249. % 90.52/90.74 generalize (zenon_H249 (n0)). zenon_intro zenon_H266. % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H266); [ zenon_intro zenon_H238 | zenon_intro zenon_H267 ]. % 90.52/90.74 exact (zenon_H238 zenon_H248). % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H267); [ zenon_intro zenon_H194 | zenon_intro zenon_Hd8 ]. % 90.52/90.74 exact (zenon_H194 gt_2_0). % 90.52/90.74 exact (zenon_Hcb zenon_Hd8). % 90.52/90.74 apply zenon_H67. apply refl_equal. % 90.52/90.74 (* end of lemma zenon_L132_ *) % 90.52/90.74 assert (zenon_L133_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (succ (tptp_minus_1)))) -> (~(zenon_TB_ec = (n3))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.74 do 1 intro. intros zenon_H73 zenon_Hc0 zenon_Hb6 zenon_H97 zenon_H68. % 90.52/90.74 elim (classic (gt zenon_TB_ec (succ (tptp_minus_1)))); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hc4 ]. % 90.52/90.74 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.74 generalize (zenon_Hd1 zenon_TB_ec). zenon_intro zenon_Hd2. % 90.52/90.74 generalize (zenon_Hd2 (succ (tptp_minus_1))). zenon_intro zenon_H268. % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H268); [ zenon_intro zenon_Hab | zenon_intro zenon_H269 ]. % 90.52/90.74 exact (zenon_Hab zenon_H97). % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H269); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc5 ]. % 90.52/90.74 exact (zenon_Hc4 zenon_Hcc). % 90.52/90.74 exact (zenon_Hc0 zenon_Hc5). % 90.52/90.74 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 90.52/90.74 elim (classic (gt zenon_TB_ec (n0))); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hcb ]. % 90.52/90.74 cut ((gt zenon_TB_ec (n0)) = (gt zenon_TB_ec (succ (tptp_minus_1)))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_Hc4. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_Hd8. % 90.52/90.74 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.74 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.74 congruence. % 90.52/90.74 apply zenon_Ha1. apply refl_equal. % 90.52/90.74 exact (zenon_H72 zenon_H71). % 90.52/90.74 apply (zenon_L132_ zenon_TB_ec); trivial. % 90.52/90.74 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.74 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H72. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_Hc2. % 90.52/90.74 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.74 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.74 congruence. % 90.52/90.74 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.74 apply zenon_H8f. apply refl_equal. % 90.52/90.74 apply zenon_H8f. apply refl_equal. % 90.52/90.74 (* end of lemma zenon_L133_ *) % 90.52/90.74 assert (zenon_L134_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~((n0) = zenon_TB_ec)) -> (~(gt (succ (tptp_minus_1)) (succ (succ (succ (n0)))))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ zenon_TB_ec))) -> False). % 90.52/90.74 do 1 intro. intros zenon_H73 zenon_Hc8 zenon_H21d zenon_H68 zenon_H97 zenon_Hb6 zenon_Hce zenon_H1de. % 90.52/90.74 elim (classic (gt (succ (tptp_minus_1)) (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hc0 ]. % 90.52/90.74 elim (classic (gt (succ (tptp_minus_1)) (n0))); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hbf ]. % 90.52/90.74 elim (classic (gt (n0) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H26a | zenon_intro zenon_H26b ]. % 90.52/90.74 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.74 generalize (zenon_Hd1 (n0)). zenon_intro zenon_H141. % 90.52/90.74 generalize (zenon_H141 (succ (succ (succ (n0))))). zenon_intro zenon_H26c. % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H26c); [ zenon_intro zenon_Hbf | zenon_intro zenon_H26d ]. % 90.52/90.74 exact (zenon_Hbf zenon_Hc1). % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H26d); [ zenon_intro zenon_H26b | zenon_intro zenon_H222 ]. % 90.52/90.74 exact (zenon_H26b zenon_H26a). % 90.52/90.74 exact (zenon_H21d zenon_H222). % 90.52/90.74 elim (classic (gt (tptp_minus_1) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H26e | zenon_intro zenon_H26f ]. % 90.52/90.74 generalize (zenon_H73 (n0)). zenon_intro zenon_H115. % 90.52/90.74 generalize (zenon_H115 (tptp_minus_1)). zenon_intro zenon_H116. % 90.52/90.74 generalize (zenon_H116 (succ (succ (succ (n0))))). zenon_intro zenon_H270. % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H270); [ zenon_intro zenon_H101 | zenon_intro zenon_H271 ]. % 90.52/90.74 exact (zenon_H101 gt_0_tptp_minus_1). % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H271); [ zenon_intro zenon_H26f | zenon_intro zenon_H26a ]. % 90.52/90.74 exact (zenon_H26f zenon_H26e). % 90.52/90.74 exact (zenon_H26b zenon_H26a). % 90.52/90.74 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_H12e | zenon_intro zenon_Hb0 ]. % 90.52/90.74 elim (classic (gt (tptp_minus_1) (n1))); [ zenon_intro zenon_H134 | zenon_intro zenon_H132 ]. % 90.52/90.74 elim (classic (gt (tptp_minus_1) (succ (n0)))); [ zenon_intro zenon_H114 | zenon_intro zenon_H10f ]. % 90.52/90.74 elim (classic (gt (succ (n0)) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H272 | zenon_intro zenon_H265 ]. % 90.52/90.74 generalize (zenon_H73 (tptp_minus_1)). zenon_intro zenon_H171. % 90.52/90.74 generalize (zenon_H171 (succ (n0))). zenon_intro zenon_H273. % 90.52/90.74 generalize (zenon_H273 (succ (succ (succ (n0))))). zenon_intro zenon_H274. % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H274); [ zenon_intro zenon_H10f | zenon_intro zenon_H275 ]. % 90.52/90.74 exact (zenon_H10f zenon_H114). % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H275); [ zenon_intro zenon_H265 | zenon_intro zenon_H26e ]. % 90.52/90.74 exact (zenon_H265 zenon_H272). % 90.52/90.74 exact (zenon_H26f zenon_H26e). % 90.52/90.74 apply (zenon_L130_ zenon_TB_ec); trivial. % 90.52/90.74 cut ((gt (tptp_minus_1) (n1)) = (gt (tptp_minus_1) (succ (n0)))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H10f. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_H134. % 90.52/90.74 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 90.52/90.74 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_He4]. % 90.52/90.74 congruence. % 90.52/90.74 apply zenon_He4. apply refl_equal. % 90.52/90.74 exact (zenon_Hb0 zenon_H12e). % 90.52/90.74 elim (classic ((~((tptp_minus_1) = (n3)))/\(~(gt (tptp_minus_1) (n3))))); [ zenon_intro zenon_H186 | zenon_intro zenon_H187 ]. % 90.52/90.74 apply (zenon_and_s _ _ zenon_H186). zenon_intro zenon_He8. zenon_intro zenon_H188. % 90.52/90.74 apply (zenon_L119_ zenon_TB_ec); trivial. % 90.52/90.74 cut ((gt (n3) (n1)) = (gt (tptp_minus_1) (n1))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H132. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact gt_3_1. % 90.52/90.74 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.74 cut (((n3) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 90.52/90.74 congruence. % 90.52/90.74 apply (zenon_notand_s _ _ zenon_H187); [ zenon_intro zenon_H18b | zenon_intro zenon_H18a ]. % 90.52/90.74 apply zenon_H18b. zenon_intro zenon_H106. % 90.52/90.74 elim (classic ((tptp_minus_1) = (tptp_minus_1))); [ zenon_intro zenon_H113 | zenon_intro zenon_He4 ]. % 90.52/90.74 cut (((tptp_minus_1) = (tptp_minus_1)) = ((n3) = (tptp_minus_1))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_H189. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_H113. % 90.52/90.74 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_He4]. % 90.52/90.74 cut (((tptp_minus_1) = (n3))); [idtac | apply NNPP; zenon_intro zenon_He8]. % 90.52/90.74 congruence. % 90.52/90.74 exact (zenon_He8 zenon_H106). % 90.52/90.74 apply zenon_He4. apply refl_equal. % 90.52/90.74 apply zenon_He4. apply refl_equal. % 90.52/90.74 apply zenon_H18a. zenon_intro zenon_H18c. % 90.52/90.74 generalize (zenon_H73 (tptp_minus_1)). zenon_intro zenon_H171. % 90.52/90.74 generalize (zenon_H171 (n3)). zenon_intro zenon_H18d. % 90.52/90.74 generalize (zenon_H18d (n1)). zenon_intro zenon_H18e. % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H18e); [ zenon_intro zenon_H188 | zenon_intro zenon_H18f ]. % 90.52/90.74 exact (zenon_H188 zenon_H18c). % 90.52/90.74 apply (zenon_imply_s _ _ zenon_H18f); [ zenon_intro zenon_H185 | zenon_intro zenon_H134 ]. % 90.52/90.74 exact (zenon_H185 gt_3_1). % 90.52/90.74 exact (zenon_H132 zenon_H134). % 90.52/90.74 apply zenon_H66. apply refl_equal. % 90.52/90.74 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 90.52/90.74 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_Hb0. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_Hb1. % 90.52/90.74 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.74 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.74 congruence. % 90.52/90.74 exact (zenon_Hb3 successor_1). % 90.52/90.74 apply zenon_Hb2. apply refl_equal. % 90.52/90.74 apply zenon_Hb2. apply refl_equal. % 90.52/90.74 cut ((gt (succ (tptp_minus_1)) (succ (tptp_minus_1))) = (gt (succ (tptp_minus_1)) (n0))). % 90.52/90.74 intro zenon_D_pnotp. % 90.52/90.74 apply zenon_Hbf. % 90.52/90.74 rewrite <- zenon_D_pnotp. % 90.52/90.74 exact zenon_Hc5. % 90.52/90.74 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.74 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.74 congruence. % 90.52/90.74 apply zenon_H8f. apply refl_equal. % 90.52/90.74 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.74 apply (zenon_L133_ zenon_TB_ec); trivial. % 90.52/90.74 (* end of lemma zenon_L134_ *) % 90.52/90.74 assert (zenon_L135_ : forall (zenon_TB_ec : zenon_U), (~(gt (n0) (succ zenon_TB_ec))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(zenon_TB_ec = (n3))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (~(gt zenon_TB_ec (succ (succ (succ (n0)))))) -> (~((n0) = zenon_TB_ec)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.74 do 1 intro. intros zenon_H1de zenon_Hce zenon_Hb6 zenon_H97 zenon_H68 zenon_H276 zenon_Hc8 zenon_H73. % 90.52/90.74 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 90.52/90.74 elim (classic (gt zenon_TB_ec (n0))); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hcb ]. % 90.52/90.74 elim (classic (gt zenon_TB_ec (succ (tptp_minus_1)))); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hc4 ]. % 90.52/90.74 elim (classic (gt (succ (tptp_minus_1)) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H222 | zenon_intro zenon_H21d ]. % 90.52/90.74 generalize (zenon_H73 zenon_TB_ec). zenon_intro zenon_H144. % 90.52/90.74 generalize (zenon_H144 (succ (tptp_minus_1))). zenon_intro zenon_H145. % 90.52/90.74 generalize (zenon_H145 (succ (succ (succ (n0))))). zenon_intro zenon_H277. % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H277); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H278 ]. % 90.52/90.75 exact (zenon_Hc4 zenon_Hcc). % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H278); [ zenon_intro zenon_H21d | zenon_intro zenon_H279 ]. % 90.52/90.75 exact (zenon_H21d zenon_H222). % 90.52/90.75 exact (zenon_H276 zenon_H279). % 90.52/90.75 apply (zenon_L134_ zenon_TB_ec); trivial. % 90.52/90.75 cut ((gt zenon_TB_ec (n0)) = (gt zenon_TB_ec (succ (tptp_minus_1)))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_Hc4. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hd8. % 90.52/90.75 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.75 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.75 congruence. % 90.52/90.75 apply zenon_Ha1. apply refl_equal. % 90.52/90.75 exact (zenon_H72 zenon_H71). % 90.52/90.75 apply (zenon_L132_ zenon_TB_ec); trivial. % 90.52/90.75 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_H72. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hc2. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.75 congruence. % 90.52/90.75 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.75 apply zenon_H8f. apply refl_equal. % 90.52/90.75 apply zenon_H8f. apply refl_equal. % 90.52/90.75 (* end of lemma zenon_L135_ *) % 90.52/90.75 assert (zenon_L136_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt zenon_TB_ec (n3))) -> (~((n0) = zenon_TB_ec)) -> (~(gt (n0) (succ zenon_TB_ec))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(zenon_TB_ec = (n3))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.75 do 1 intro. intros zenon_H73 zenon_H27a zenon_Hc8 zenon_H1de zenon_Hce zenon_Hb6 zenon_H97 zenon_H68. % 90.52/90.75 elim (classic (gt zenon_TB_ec (succ (succ (succ (n0)))))); [ zenon_intro zenon_H279 | zenon_intro zenon_H276 ]. % 90.52/90.75 cut ((gt zenon_TB_ec (succ (succ (succ (n0))))) = (gt zenon_TB_ec (n3))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_H27a. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_H279. % 90.52/90.75 cut (((succ (succ (succ (n0)))) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H20f]. % 90.52/90.75 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.75 congruence. % 90.52/90.75 apply zenon_Ha1. apply refl_equal. % 90.52/90.75 exact (zenon_H20f successor_3). % 90.52/90.75 apply (zenon_L135_ zenon_TB_ec); trivial. % 90.52/90.75 (* end of lemma zenon_L136_ *) % 90.52/90.75 assert (zenon_L137_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (n3))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ zenon_TB_ec))) -> (~((n0) = zenon_TB_ec)) -> False). % 90.52/90.75 do 1 intro. intros zenon_H73 zenon_H225 zenon_H68 zenon_H97 zenon_Hce zenon_H1de zenon_Hc8. % 90.52/90.75 elim (classic (zenon_TB_ec = (n3))); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hb6 ]. % 90.52/90.75 cut ((gt (succ (tptp_minus_1)) zenon_TB_ec) = (gt (succ (tptp_minus_1)) (n3))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_H225. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_H97. % 90.52/90.75 cut ((zenon_TB_ec = (n3))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.75 congruence. % 90.52/90.75 apply zenon_H8f. apply refl_equal. % 90.52/90.75 exact (zenon_Hb6 zenon_Hbd). % 90.52/90.75 elim (classic (gt zenon_TB_ec (n3))); [ zenon_intro zenon_H27b | zenon_intro zenon_H27a ]. % 90.52/90.75 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.75 generalize (zenon_Hd1 zenon_TB_ec). zenon_intro zenon_Hd2. % 90.52/90.75 generalize (zenon_Hd2 (n3)). zenon_intro zenon_H27c. % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H27c); [ zenon_intro zenon_Hab | zenon_intro zenon_H27d ]. % 90.52/90.75 exact (zenon_Hab zenon_H97). % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H27d); [ zenon_intro zenon_H27a | zenon_intro zenon_H229 ]. % 90.52/90.75 exact (zenon_H27a zenon_H27b). % 90.52/90.75 exact (zenon_H225 zenon_H229). % 90.52/90.75 apply (zenon_L136_ zenon_TB_ec); trivial. % 90.52/90.75 (* end of lemma zenon_L137_ *) % 90.52/90.75 assert (zenon_L138_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (succ (succ (succ (n0)))))) -> (~(gt (n0) (succ zenon_TB_ec))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(zenon_TB_ec = (n3))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.75 do 1 intro. intros zenon_H73 zenon_H21d zenon_H1de zenon_Hce zenon_Hb6 zenon_H97 zenon_H68. % 90.52/90.75 elim (classic (gt (succ (tptp_minus_1)) (succ (n0)))); [ zenon_intro zenon_H10e | zenon_intro zenon_H10a ]. % 90.52/90.75 elim (classic (gt (succ (tptp_minus_1)) (n1))); [ zenon_intro zenon_H167 | zenon_intro zenon_Hac ]. % 90.52/90.75 elim (classic (gt (n1) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H262 | zenon_intro zenon_H25e ]. % 90.52/90.75 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.75 generalize (zenon_Hd1 (n1)). zenon_intro zenon_H1d1. % 90.52/90.75 generalize (zenon_H1d1 (succ (succ (succ (n0))))). zenon_intro zenon_H27e. % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H27e); [ zenon_intro zenon_Hac | zenon_intro zenon_H27f ]. % 90.52/90.75 exact (zenon_Hac zenon_H167). % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H27f); [ zenon_intro zenon_H25e | zenon_intro zenon_H222 ]. % 90.52/90.75 exact (zenon_H25e zenon_H262). % 90.52/90.75 exact (zenon_H21d zenon_H222). % 90.52/90.75 apply (zenon_L129_ zenon_TB_ec); trivial. % 90.52/90.75 cut ((gt (succ (tptp_minus_1)) (succ (n0))) = (gt (succ (tptp_minus_1)) (n1))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_Hac. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_H10e. % 90.52/90.75 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.75 congruence. % 90.52/90.75 apply zenon_H8f. apply refl_equal. % 90.52/90.75 exact (zenon_Hb3 successor_1). % 90.52/90.75 apply (zenon_L111_ zenon_TB_ec); trivial. % 90.52/90.75 (* end of lemma zenon_L138_ *) % 90.52/90.75 assert (zenon_L139_ : forall (zenon_TB_ec : zenon_U), (~(gt (n0) (succ zenon_TB_ec))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(zenon_TB_ec = (n3))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (~(gt zenon_TB_ec (succ (succ (succ (n0)))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.75 do 1 intro. intros zenon_H1de zenon_Hce zenon_Hb6 zenon_H97 zenon_H68 zenon_H276 zenon_H73. % 90.52/90.75 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 90.52/90.75 elim (classic (gt zenon_TB_ec (n0))); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hcb ]. % 90.52/90.75 elim (classic (gt zenon_TB_ec (succ (tptp_minus_1)))); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hc4 ]. % 90.52/90.75 elim (classic (gt (succ (tptp_minus_1)) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H222 | zenon_intro zenon_H21d ]. % 90.52/90.75 generalize (zenon_H73 zenon_TB_ec). zenon_intro zenon_H144. % 90.52/90.75 generalize (zenon_H144 (succ (tptp_minus_1))). zenon_intro zenon_H145. % 90.52/90.75 generalize (zenon_H145 (succ (succ (succ (n0))))). zenon_intro zenon_H277. % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H277); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H278 ]. % 90.52/90.75 exact (zenon_Hc4 zenon_Hcc). % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H278); [ zenon_intro zenon_H21d | zenon_intro zenon_H279 ]. % 90.52/90.75 exact (zenon_H21d zenon_H222). % 90.52/90.75 exact (zenon_H276 zenon_H279). % 90.52/90.75 apply (zenon_L138_ zenon_TB_ec); trivial. % 90.52/90.75 cut ((gt zenon_TB_ec (n0)) = (gt zenon_TB_ec (succ (tptp_minus_1)))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_Hc4. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hd8. % 90.52/90.75 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.75 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.75 congruence. % 90.52/90.75 apply zenon_Ha1. apply refl_equal. % 90.52/90.75 exact (zenon_H72 zenon_H71). % 90.52/90.75 apply (zenon_L132_ zenon_TB_ec); trivial. % 90.52/90.75 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_H72. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hc2. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.75 congruence. % 90.52/90.75 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.75 apply zenon_H8f. apply refl_equal. % 90.52/90.75 apply zenon_H8f. apply refl_equal. % 90.52/90.75 (* end of lemma zenon_L139_ *) % 90.52/90.75 assert (zenon_L140_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt zenon_TB_ec (n3))) -> (~(gt (n0) (succ zenon_TB_ec))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(zenon_TB_ec = (n3))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.75 do 1 intro. intros zenon_H73 zenon_H27a zenon_H1de zenon_Hce zenon_Hb6 zenon_H97 zenon_H68. % 90.52/90.75 elim (classic (gt zenon_TB_ec (succ (succ (succ (n0)))))); [ zenon_intro zenon_H279 | zenon_intro zenon_H276 ]. % 90.52/90.75 cut ((gt zenon_TB_ec (succ (succ (succ (n0))))) = (gt zenon_TB_ec (n3))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_H27a. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_H279. % 90.52/90.75 cut (((succ (succ (succ (n0)))) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H20f]. % 90.52/90.75 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.75 congruence. % 90.52/90.75 apply zenon_Ha1. apply refl_equal. % 90.52/90.75 exact (zenon_H20f successor_3). % 90.52/90.75 apply (zenon_L139_ zenon_TB_ec); trivial. % 90.52/90.75 (* end of lemma zenon_L140_ *) % 90.52/90.75 assert (zenon_L141_ : forall (zenon_TB_ec : zenon_U), (~(gt (n0) (succ zenon_TB_ec))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt zenon_TB_ec (n1))) -> False). % 90.52/90.75 do 1 intro. intros zenon_H1de zenon_Hce zenon_H97 zenon_H68 zenon_H73 zenon_H148. % 90.52/90.75 elim (classic ((~(zenon_TB_ec = (n3)))/\(~(gt zenon_TB_ec (n3))))); [ zenon_intro zenon_H280 | zenon_intro zenon_H281 ]. % 90.52/90.75 apply (zenon_and_s _ _ zenon_H280). zenon_intro zenon_Hb6. zenon_intro zenon_H27a. % 90.52/90.75 apply (zenon_L140_ zenon_TB_ec); trivial. % 90.52/90.75 cut ((gt (n3) (n1)) = (gt zenon_TB_ec (n1))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_H148. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact gt_3_1. % 90.52/90.75 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.75 cut (((n3) = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_H282]. % 90.52/90.75 congruence. % 90.52/90.75 apply (zenon_notand_s _ _ zenon_H281); [ zenon_intro zenon_H284 | zenon_intro zenon_H283 ]. % 90.52/90.75 apply zenon_H284. zenon_intro zenon_Hbd. % 90.52/90.75 elim (classic (zenon_TB_ec = zenon_TB_ec)); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Ha1 ]. % 90.52/90.75 cut ((zenon_TB_ec = zenon_TB_ec) = ((n3) = zenon_TB_ec)). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_H282. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hc9. % 90.52/90.75 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.75 cut ((zenon_TB_ec = (n3))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 90.52/90.75 congruence. % 90.52/90.75 exact (zenon_Hb6 zenon_Hbd). % 90.52/90.75 apply zenon_Ha1. apply refl_equal. % 90.52/90.75 apply zenon_Ha1. apply refl_equal. % 90.52/90.75 apply zenon_H283. zenon_intro zenon_H27b. % 90.52/90.75 generalize (zenon_H73 zenon_TB_ec). zenon_intro zenon_H144. % 90.52/90.75 generalize (zenon_H144 (n3)). zenon_intro zenon_H285. % 90.52/90.75 generalize (zenon_H285 (n1)). zenon_intro zenon_H286. % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H286); [ zenon_intro zenon_H27a | zenon_intro zenon_H287 ]. % 90.52/90.75 exact (zenon_H27a zenon_H27b). % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H287); [ zenon_intro zenon_H185 | zenon_intro zenon_H164 ]. % 90.52/90.75 exact (zenon_H185 gt_3_1). % 90.52/90.75 exact (zenon_H148 zenon_H164). % 90.52/90.75 apply zenon_H66. apply refl_equal. % 90.52/90.75 (* end of lemma zenon_L141_ *) % 90.52/90.75 assert (zenon_L142_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ zenon_TB_ec))) -> (~(gt zenon_TB_ec (succ (n0)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.75 do 1 intro. intros zenon_H68 zenon_H97 zenon_Hce zenon_H1de zenon_H109 zenon_H73. % 90.52/90.75 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_H12e | zenon_intro zenon_Hb0 ]. % 90.52/90.75 elim (classic (gt zenon_TB_ec (n1))); [ zenon_intro zenon_H164 | zenon_intro zenon_H148 ]. % 90.52/90.75 cut ((gt zenon_TB_ec (n1)) = (gt zenon_TB_ec (succ (n0)))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_H109. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_H164. % 90.52/90.75 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 90.52/90.75 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.75 congruence. % 90.52/90.75 apply zenon_Ha1. apply refl_equal. % 90.52/90.75 exact (zenon_Hb0 zenon_H12e). % 90.52/90.75 apply (zenon_L141_ zenon_TB_ec); trivial. % 90.52/90.75 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 90.52/90.75 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_Hb0. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hb1. % 90.52/90.75 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.75 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.75 congruence. % 90.52/90.75 exact (zenon_Hb3 successor_1). % 90.52/90.75 apply zenon_Hb2. apply refl_equal. % 90.52/90.75 apply zenon_Hb2. apply refl_equal. % 90.52/90.75 (* end of lemma zenon_L142_ *) % 90.52/90.75 assert (zenon_L143_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (succ (n0)))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ zenon_TB_ec))) -> False). % 90.52/90.75 do 1 intro. intros zenon_H73 zenon_H10a zenon_H68 zenon_H97 zenon_Hce zenon_H1de. % 90.52/90.75 elim (classic (gt zenon_TB_ec (succ (n0)))); [ zenon_intro zenon_H10b | zenon_intro zenon_H109 ]. % 90.52/90.75 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.75 generalize (zenon_Hd1 zenon_TB_ec). zenon_intro zenon_Hd2. % 90.52/90.75 generalize (zenon_Hd2 (succ (n0))). zenon_intro zenon_H10c. % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H10c); [ zenon_intro zenon_Hab | zenon_intro zenon_H10d ]. % 90.52/90.75 exact (zenon_Hab zenon_H97). % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H10d); [ zenon_intro zenon_H109 | zenon_intro zenon_H10e ]. % 90.52/90.75 exact (zenon_H109 zenon_H10b). % 90.52/90.75 exact (zenon_H10a zenon_H10e). % 90.52/90.75 apply (zenon_L142_ zenon_TB_ec); trivial. % 90.52/90.75 (* end of lemma zenon_L143_ *) % 90.52/90.75 assert (zenon_L144_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ zenon_TB_ec))) -> (~(gt (n0) (succ (n0)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.75 do 1 intro. intros zenon_H68 zenon_H97 zenon_Hce zenon_H1de zenon_H111 zenon_H73. % 90.52/90.75 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 90.52/90.75 elim (classic (gt (succ (tptp_minus_1)) (succ (n0)))); [ zenon_intro zenon_H10e | zenon_intro zenon_H10a ]. % 90.52/90.75 cut ((gt (succ (tptp_minus_1)) (succ (n0))) = (gt (n0) (succ (n0)))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_H111. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_H10e. % 90.52/90.75 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.75 congruence. % 90.52/90.75 elim (classic ((n0) = (n0))); [ zenon_intro zenon_Hca | zenon_intro zenon_H67 ]. % 90.52/90.75 cut (((n0) = (n0)) = ((succ (tptp_minus_1)) = (n0))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_Hc3. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hca. % 90.52/90.75 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.75 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.75 congruence. % 90.52/90.75 exact (zenon_H72 zenon_H71). % 90.52/90.75 apply zenon_H67. apply refl_equal. % 90.52/90.75 apply zenon_H67. apply refl_equal. % 90.52/90.75 apply zenon_Hb2. apply refl_equal. % 90.52/90.75 apply (zenon_L143_ zenon_TB_ec); trivial. % 90.52/90.75 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_H72. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hc2. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.75 congruence. % 90.52/90.75 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.75 apply zenon_H8f. apply refl_equal. % 90.52/90.75 apply zenon_H8f. apply refl_equal. % 90.52/90.75 (* end of lemma zenon_L144_ *) % 90.52/90.75 assert (zenon_L145_ : forall (zenon_TB_ec : zenon_U), (~(gt (n0) (succ zenon_TB_ec))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt zenon_TB_ec (n0))) -> False). % 90.52/90.75 do 1 intro. intros zenon_H1de zenon_Hce zenon_H97 zenon_H68 zenon_H73 zenon_Hcb. % 90.52/90.75 elim (classic ((~(zenon_TB_ec = (n3)))/\(~(gt zenon_TB_ec (n3))))); [ zenon_intro zenon_H280 | zenon_intro zenon_H281 ]. % 90.52/90.75 apply (zenon_and_s _ _ zenon_H280). zenon_intro zenon_Hb6. zenon_intro zenon_H27a. % 90.52/90.75 apply (zenon_L140_ zenon_TB_ec); trivial. % 90.52/90.75 cut ((gt (n3) (n0)) = (gt zenon_TB_ec (n0))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_Hcb. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact gt_3_0. % 90.52/90.75 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.75 cut (((n3) = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_H282]. % 90.52/90.75 congruence. % 90.52/90.75 apply (zenon_notand_s _ _ zenon_H281); [ zenon_intro zenon_H284 | zenon_intro zenon_H283 ]. % 90.52/90.75 apply zenon_H284. zenon_intro zenon_Hbd. % 90.52/90.75 elim (classic (zenon_TB_ec = zenon_TB_ec)); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Ha1 ]. % 90.52/90.75 cut ((zenon_TB_ec = zenon_TB_ec) = ((n3) = zenon_TB_ec)). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_H282. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hc9. % 90.52/90.75 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.75 cut ((zenon_TB_ec = (n3))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 90.52/90.75 congruence. % 90.52/90.75 exact (zenon_Hb6 zenon_Hbd). % 90.52/90.75 apply zenon_Ha1. apply refl_equal. % 90.52/90.75 apply zenon_Ha1. apply refl_equal. % 90.52/90.75 apply zenon_H283. zenon_intro zenon_H27b. % 90.52/90.75 generalize (zenon_H73 zenon_TB_ec). zenon_intro zenon_H144. % 90.52/90.75 generalize (zenon_H144 (n3)). zenon_intro zenon_H285. % 90.52/90.75 generalize (zenon_H285 (n0)). zenon_intro zenon_H288. % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H288); [ zenon_intro zenon_H27a | zenon_intro zenon_H289 ]. % 90.52/90.75 exact (zenon_H27a zenon_H27b). % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H289); [ zenon_intro zenon_H197 | zenon_intro zenon_Hd8 ]. % 90.52/90.75 exact (zenon_H197 gt_3_0). % 90.52/90.75 exact (zenon_Hcb zenon_Hd8). % 90.52/90.75 apply zenon_H67. apply refl_equal. % 90.52/90.75 (* end of lemma zenon_L145_ *) % 90.52/90.75 assert (zenon_L146_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (sum (n0) (tptp_minus_1) zenon_E))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ zenon_TB_ec))) -> False). % 90.52/90.75 do 1 intro. intros zenon_H73 zenon_Hcd zenon_H68 zenon_H97 zenon_Hce zenon_H1de. % 90.52/90.75 elim (classic (gt zenon_TB_ec (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd0 ]. % 90.52/90.75 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.75 generalize (zenon_Hd1 zenon_TB_ec). zenon_intro zenon_Hd2. % 90.52/90.75 generalize (zenon_Hd2 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_Hd3. % 90.52/90.75 apply (zenon_imply_s _ _ zenon_Hd3); [ zenon_intro zenon_Hab | zenon_intro zenon_Hd4 ]. % 90.52/90.75 exact (zenon_Hab zenon_H97). % 90.52/90.75 apply (zenon_imply_s _ _ zenon_Hd4); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hd5 ]. % 90.52/90.75 exact (zenon_Hd0 zenon_Hcf). % 90.52/90.75 exact (zenon_Hcd zenon_Hd5). % 90.52/90.75 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 90.52/90.75 elim (classic (gt zenon_TB_ec (n0))); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hcb ]. % 90.52/90.75 cut ((gt zenon_TB_ec (n0)) = (gt zenon_TB_ec (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_Hd0. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hd8. % 90.52/90.75 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 90.52/90.75 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.75 congruence. % 90.52/90.75 apply zenon_Ha1. apply refl_equal. % 90.52/90.75 exact (zenon_Hd7 zenon_Hd6). % 90.52/90.75 apply (zenon_L145_ zenon_TB_ec); trivial. % 90.52/90.75 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd9 | zenon_intro zenon_Hda ]. % 90.52/90.75 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_Hd7. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hd9. % 90.52/90.75 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.75 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 90.52/90.75 congruence. % 90.52/90.75 exact (zenon_Hdb zenon_Hce). % 90.52/90.75 apply zenon_Hda. apply refl_equal. % 90.52/90.75 apply zenon_Hda. apply refl_equal. % 90.52/90.75 (* end of lemma zenon_L146_ *) % 90.52/90.75 assert (zenon_L147_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ zenon_TB_ec))) -> False). % 90.52/90.75 do 1 intro. intros zenon_H73 zenon_Hdc zenon_H68 zenon_H97 zenon_Hce zenon_H1de. % 90.52/90.75 elim (classic (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hde ]. % 90.52/90.75 cut ((gt (n0) (sum (n0) (tptp_minus_1) zenon_E)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_Hdc. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hdd. % 90.52/90.75 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.75 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 90.52/90.75 congruence. % 90.52/90.75 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd9 | zenon_intro zenon_Hda ]. % 90.52/90.75 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_Hd7. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hd9. % 90.52/90.75 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.75 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 90.52/90.75 congruence. % 90.52/90.75 exact (zenon_Hdb zenon_Hce). % 90.52/90.75 apply zenon_Hda. apply refl_equal. % 90.52/90.75 apply zenon_Hda. apply refl_equal. % 90.52/90.75 apply zenon_Hda. apply refl_equal. % 90.52/90.75 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 90.52/90.75 elim (classic (gt (succ (tptp_minus_1)) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd5 | zenon_intro zenon_Hcd ]. % 90.52/90.75 cut ((gt (succ (tptp_minus_1)) (sum (n0) (tptp_minus_1) zenon_E)) = (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_Hde. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hd5. % 90.52/90.75 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.75 congruence. % 90.52/90.75 elim (classic ((n0) = (n0))); [ zenon_intro zenon_Hca | zenon_intro zenon_H67 ]. % 90.52/90.75 cut (((n0) = (n0)) = ((succ (tptp_minus_1)) = (n0))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_Hc3. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hca. % 90.52/90.75 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.75 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.75 congruence. % 90.52/90.75 exact (zenon_H72 zenon_H71). % 90.52/90.75 apply zenon_H67. apply refl_equal. % 90.52/90.75 apply zenon_H67. apply refl_equal. % 90.52/90.75 apply zenon_Hda. apply refl_equal. % 90.52/90.75 apply (zenon_L146_ zenon_TB_ec); trivial. % 90.52/90.75 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_H72. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hc2. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.75 congruence. % 90.52/90.75 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.75 apply zenon_H8f. apply refl_equal. % 90.52/90.75 apply zenon_H8f. apply refl_equal. % 90.52/90.75 (* end of lemma zenon_L147_ *) % 90.52/90.75 assert (zenon_L148_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (succ (n0)))) -> (~(gt (n0) (succ zenon_TB_ec))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.75 do 1 intro. intros zenon_H73 zenon_H1a2 zenon_H1de zenon_Hce zenon_H97 zenon_H68. % 90.52/90.75 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_He2 | zenon_intro zenon_Hdc ]. % 90.52/90.75 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))); [ zenon_intro zenon_He0 | zenon_intro zenon_He1 ]. % 90.52/90.75 elim (classic (gt (n0) (succ (n0)))); [ zenon_intro zenon_H110 | zenon_intro zenon_H111 ]. % 90.52/90.75 generalize (zenon_H73 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H1a3. % 90.52/90.75 generalize (zenon_H1a3 (n0)). zenon_intro zenon_H1a4. % 90.52/90.75 generalize (zenon_H1a4 (succ (n0))). zenon_intro zenon_H1a5. % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H1a5); [ zenon_intro zenon_He1 | zenon_intro zenon_H1a6 ]. % 90.52/90.75 exact (zenon_He1 zenon_He0). % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H1a6); [ zenon_intro zenon_H111 | zenon_intro zenon_H1a1 ]. % 90.52/90.75 exact (zenon_H111 zenon_H110). % 90.52/90.75 exact (zenon_H1a2 zenon_H1a1). % 90.52/90.75 apply (zenon_L144_ zenon_TB_ec); trivial. % 90.52/90.75 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (sum (n0) (tptp_minus_1) zenon_E)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_He1. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_He2. % 90.52/90.75 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 90.52/90.75 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.75 congruence. % 90.52/90.75 apply zenon_Hda. apply refl_equal. % 90.52/90.75 exact (zenon_Hdb zenon_Hce). % 90.52/90.75 apply (zenon_L147_ zenon_TB_ec); trivial. % 90.52/90.75 (* end of lemma zenon_L148_ *) % 90.52/90.75 assert (zenon_L149_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (n1))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ zenon_TB_ec))) -> False). % 90.52/90.75 do 1 intro. intros zenon_H73 zenon_H1a0 zenon_H68 zenon_H97 zenon_Hce zenon_H1de. % 90.52/90.75 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (n0)))); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H1a2 ]. % 90.52/90.75 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (succ (n0))) = (gt (sum (n0) (tptp_minus_1) zenon_E) (n1))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_H1a0. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_H1a1. % 90.52/90.75 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.75 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.75 congruence. % 90.52/90.75 apply zenon_Hda. apply refl_equal. % 90.52/90.75 exact (zenon_Hb3 successor_1). % 90.52/90.75 apply (zenon_L148_ zenon_TB_ec); trivial. % 90.52/90.75 (* end of lemma zenon_L149_ *) % 90.52/90.75 assert (zenon_L150_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ zenon_TB_ec))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (n0))) -> False). % 90.52/90.75 do 1 intro. intros zenon_H68 zenon_H97 zenon_Hce zenon_H1de zenon_H73 zenon_He1. % 90.52/90.75 elim (classic ((~((sum (n0) (tptp_minus_1) zenon_E) = (n1)))/\(~(gt (sum (n0) (tptp_minus_1) zenon_E) (n1))))); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H1a8 ]. % 90.52/90.75 apply (zenon_and_s _ _ zenon_H1a7). zenon_intro zenon_H1a9. zenon_intro zenon_H1a0. % 90.52/90.75 apply (zenon_L149_ zenon_TB_ec); trivial. % 90.52/90.75 cut ((gt (n1) (n0)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_He1. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact gt_1_0. % 90.52/90.75 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.75 cut (((n1) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1aa]. % 90.52/90.75 congruence. % 90.52/90.75 apply (zenon_notand_s _ _ zenon_H1a8); [ zenon_intro zenon_H1ac | zenon_intro zenon_H1ab ]. % 90.52/90.75 apply zenon_H1ac. zenon_intro zenon_H1ad. % 90.52/90.75 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd9 | zenon_intro zenon_Hda ]. % 90.52/90.75 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n1) = (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_H1aa. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hd9. % 90.52/90.75 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.75 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 90.52/90.75 congruence. % 90.52/90.75 exact (zenon_H1a9 zenon_H1ad). % 90.52/90.75 apply zenon_Hda. apply refl_equal. % 90.52/90.75 apply zenon_Hda. apply refl_equal. % 90.52/90.75 apply zenon_H1ab. zenon_intro zenon_H1ae. % 90.52/90.75 generalize (zenon_H73 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H1a3. % 90.52/90.75 generalize (zenon_H1a3 (n1)). zenon_intro zenon_H1af. % 90.52/90.75 generalize (zenon_H1af (n0)). zenon_intro zenon_H1b0. % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H1b0); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H1b1 ]. % 90.52/90.75 exact (zenon_H1a0 zenon_H1ae). % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H1b1); [ zenon_intro zenon_H13c | zenon_intro zenon_He0 ]. % 90.52/90.75 exact (zenon_H13c gt_1_0). % 90.52/90.75 exact (zenon_He1 zenon_He0). % 90.52/90.75 apply zenon_H67. apply refl_equal. % 90.52/90.75 (* end of lemma zenon_L150_ *) % 90.52/90.75 assert (zenon_L151_ : forall (zenon_TB_ec : zenon_U), (~(gt (n0) (succ zenon_TB_ec))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (n0))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False). % 90.52/90.75 do 1 intro. intros zenon_H1de zenon_H97 zenon_H68 zenon_H73 zenon_Hdf zenon_Hce. % 90.52/90.75 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 90.52/90.75 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))); [ zenon_intro zenon_He0 | zenon_intro zenon_He1 ]. % 90.52/90.75 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (n0)) = (gt (n0) (n0))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_Hdf. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_He0. % 90.52/90.75 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.75 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 90.52/90.75 congruence. % 90.52/90.75 elim (classic ((n0) = (n0))); [ zenon_intro zenon_Hca | zenon_intro zenon_H67 ]. % 90.52/90.75 cut (((n0) = (n0)) = ((sum (n0) (tptp_minus_1) zenon_E) = (n0))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_Hdb. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hca. % 90.52/90.75 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.75 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 90.52/90.75 congruence. % 90.52/90.75 exact (zenon_Hd7 zenon_Hd6). % 90.52/90.75 apply zenon_H67. apply refl_equal. % 90.52/90.75 apply zenon_H67. apply refl_equal. % 90.52/90.75 apply zenon_H67. apply refl_equal. % 90.52/90.75 apply (zenon_L150_ zenon_TB_ec); trivial. % 90.52/90.75 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd9 | zenon_intro zenon_Hda ]. % 90.52/90.75 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_Hd7. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hd9. % 90.52/90.75 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.75 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 90.52/90.75 congruence. % 90.52/90.75 exact (zenon_Hdb zenon_Hce). % 90.52/90.75 apply zenon_Hda. apply refl_equal. % 90.52/90.75 apply zenon_Hda. apply refl_equal. % 90.52/90.75 (* end of lemma zenon_L151_ *) % 90.52/90.75 assert (zenon_L152_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(gt (n0) (succ zenon_TB_ec))) -> (~(gt (n0) (n1))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False). % 90.52/90.75 do 1 intro. intros zenon_H68 zenon_H97 zenon_H1de zenon_H133 zenon_H73 zenon_Hce. % 90.52/90.75 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 90.52/90.75 elim (classic (gt (n0) (n0))); [ zenon_intro zenon_H1b4 | zenon_intro zenon_Hdf ]. % 90.52/90.75 elim (classic (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hde ]. % 90.52/90.75 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (n1))); [ zenon_intro zenon_H1ae | zenon_intro zenon_H1a0 ]. % 90.52/90.75 generalize (zenon_H73 (n0)). zenon_intro zenon_H115. % 90.52/90.75 generalize (zenon_H115 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H1e1. % 90.52/90.75 generalize (zenon_H1e1 (n1)). zenon_intro zenon_H24c. % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H24c); [ zenon_intro zenon_Hde | zenon_intro zenon_H24d ]. % 90.52/90.75 exact (zenon_Hde zenon_Hdd). % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H24d); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H137 ]. % 90.52/90.75 exact (zenon_H1a0 zenon_H1ae). % 90.52/90.75 exact (zenon_H133 zenon_H137). % 90.52/90.75 apply (zenon_L149_ zenon_TB_ec); trivial. % 90.52/90.75 cut ((gt (n0) (n0)) = (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_Hde. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_H1b4. % 90.52/90.75 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 90.52/90.75 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.75 congruence. % 90.52/90.75 apply zenon_H67. apply refl_equal. % 90.52/90.75 exact (zenon_Hd7 zenon_Hd6). % 90.52/90.75 apply (zenon_L151_ zenon_TB_ec); trivial. % 90.52/90.75 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd9 | zenon_intro zenon_Hda ]. % 90.52/90.75 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_Hd7. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hd9. % 90.52/90.75 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.75 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 90.52/90.75 congruence. % 90.52/90.75 exact (zenon_Hdb zenon_Hce). % 90.52/90.75 apply zenon_Hda. apply refl_equal. % 90.52/90.75 apply zenon_Hda. apply refl_equal. % 90.52/90.75 (* end of lemma zenon_L152_ *) % 90.52/90.75 assert (zenon_L153_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n1) (n1))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ zenon_TB_ec))) -> False). % 90.52/90.75 do 1 intro. intros zenon_H73 zenon_H12d zenon_H68 zenon_H97 zenon_Hce zenon_H1de. % 90.52/90.75 elim (classic (gt (n0) (n1))); [ zenon_intro zenon_H137 | zenon_intro zenon_H133 ]. % 90.52/90.75 generalize (zenon_H73 (n1)). zenon_intro zenon_H138. % 90.52/90.75 generalize (zenon_H138 (n0)). zenon_intro zenon_H139. % 90.52/90.75 generalize (zenon_H139 (n1)). zenon_intro zenon_H13a. % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H13a); [ zenon_intro zenon_H13c | zenon_intro zenon_H13b ]. % 90.52/90.75 exact (zenon_H13c gt_1_0). % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H13b); [ zenon_intro zenon_H133 | zenon_intro zenon_H13d ]. % 90.52/90.75 exact (zenon_H133 zenon_H137). % 90.52/90.75 exact (zenon_H12d zenon_H13d). % 90.52/90.75 apply (zenon_L152_ zenon_TB_ec); trivial. % 90.52/90.75 (* end of lemma zenon_L153_ *) % 90.52/90.75 assert (zenon_L154_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ zenon_TB_ec))) -> (~(gt (n1) (succ zenon_TB_ec))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.75 do 1 intro. intros zenon_H68 zenon_H97 zenon_Hce zenon_H1de zenon_H1d4 zenon_H73. % 90.52/90.75 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_H12e | zenon_intro zenon_Hb0 ]. % 90.52/90.75 elim (classic (gt (n1) (n1))); [ zenon_intro zenon_H13d | zenon_intro zenon_H12d ]. % 90.52/90.75 elim (classic (gt (n1) (succ (n0)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 90.52/90.75 cut ((gt (n1) (succ (n0))) = (gt (n1) (succ zenon_TB_ec))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_H1d4. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_H13e. % 90.52/90.75 cut (((succ (n0)) = (succ zenon_TB_ec))); [idtac | apply NNPP; zenon_intro zenon_He3]. % 90.52/90.75 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.75 congruence. % 90.52/90.75 apply zenon_H66. apply refl_equal. % 90.52/90.75 cut (((n0) = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Hc8]. % 90.52/90.75 congruence. % 90.52/90.75 generalize (finite_domain_0 (tptp_minus_1)). zenon_intro zenon_H1c8. % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H1c8); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H103 ]. % 90.52/90.75 apply (zenon_notand_s _ _ zenon_H1c9); [ zenon_intro zenon_Hed | zenon_intro zenon_H1b5 ]. % 90.52/90.75 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H6b. % 90.52/90.75 generalize (zenon_H6b (tptp_minus_1)). zenon_intro zenon_Hee. % 90.52/90.75 apply (zenon_equiv_s _ _ zenon_Hee); [ zenon_intro zenon_Hed; zenon_intro zenon_Hbf | zenon_intro zenon_Hef; zenon_intro zenon_Hc1 ]. % 90.52/90.75 elim (classic ((~((succ (tptp_minus_1)) = (n3)))/\(~(gt (succ (tptp_minus_1)) (n3))))); [ zenon_intro zenon_H223 | zenon_intro zenon_H224 ]. % 90.52/90.75 apply (zenon_and_s _ _ zenon_H223). zenon_intro zenon_H226. zenon_intro zenon_H225. % 90.52/90.75 apply (zenon_L137_ zenon_TB_ec); trivial. % 90.52/90.75 cut ((gt (n3) (n0)) = (gt (succ (tptp_minus_1)) (n0))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_Hbf. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact gt_3_0. % 90.52/90.75 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.75 cut (((n3) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H22a]. % 90.52/90.75 congruence. % 90.52/90.75 apply (zenon_notand_s _ _ zenon_H224); [ zenon_intro zenon_H22c | zenon_intro zenon_H22b ]. % 90.52/90.75 apply zenon_H22c. zenon_intro zenon_H22d. % 90.52/90.75 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n3) = (succ (tptp_minus_1)))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_H22a. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hc2. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H226]. % 90.52/90.75 congruence. % 90.52/90.75 exact (zenon_H226 zenon_H22d). % 90.52/90.75 apply zenon_H8f. apply refl_equal. % 90.52/90.75 apply zenon_H8f. apply refl_equal. % 90.52/90.75 apply zenon_H22b. zenon_intro zenon_H229. % 90.52/90.75 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.75 generalize (zenon_Hd1 (n3)). zenon_intro zenon_H22e. % 90.52/90.75 generalize (zenon_H22e (n0)). zenon_intro zenon_H28a. % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H28a); [ zenon_intro zenon_H225 | zenon_intro zenon_H28b ]. % 90.52/90.75 exact (zenon_H225 zenon_H229). % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H28b); [ zenon_intro zenon_H197 | zenon_intro zenon_Hc1 ]. % 90.52/90.75 exact (zenon_H197 gt_3_0). % 90.52/90.75 exact (zenon_Hbf zenon_Hc1). % 90.52/90.75 apply zenon_H67. apply refl_equal. % 90.52/90.75 exact (zenon_Hed zenon_Hef). % 90.52/90.75 apply (zenon_L71_); trivial. % 90.52/90.75 apply (zenon_L74_ zenon_TB_ec); trivial. % 90.52/90.75 cut ((gt (n1) (n1)) = (gt (n1) (succ (n0)))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_H13f. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_H13d. % 90.52/90.75 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 90.52/90.75 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.75 congruence. % 90.52/90.75 apply zenon_H66. apply refl_equal. % 90.52/90.75 exact (zenon_Hb0 zenon_H12e). % 90.52/90.75 apply (zenon_L153_ zenon_TB_ec); trivial. % 90.52/90.75 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 90.52/90.75 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_Hb0. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hb1. % 90.52/90.75 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.75 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.75 congruence. % 90.52/90.75 exact (zenon_Hb3 successor_1). % 90.52/90.75 apply zenon_Hb2. apply refl_equal. % 90.52/90.75 apply zenon_Hb2. apply refl_equal. % 90.52/90.75 (* end of lemma zenon_L154_ *) % 90.52/90.75 assert (zenon_L155_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (succ zenon_TB_ec))) -> (~(gt (n0) (succ zenon_TB_ec))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.75 do 1 intro. intros zenon_H73 zenon_H1d5 zenon_H1de zenon_Hce zenon_H97 zenon_H68. % 90.52/90.75 elim (classic (gt (succ (tptp_minus_1)) (succ (n0)))); [ zenon_intro zenon_H10e | zenon_intro zenon_H10a ]. % 90.52/90.75 elim (classic (gt (succ (tptp_minus_1)) (n1))); [ zenon_intro zenon_H167 | zenon_intro zenon_Hac ]. % 90.52/90.75 elim (classic (gt (n1) (succ zenon_TB_ec))); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H1d4 ]. % 90.52/90.75 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.75 generalize (zenon_Hd1 (n1)). zenon_intro zenon_H1d1. % 90.52/90.75 generalize (zenon_H1d1 (succ zenon_TB_ec)). zenon_intro zenon_H1d7. % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H1d7); [ zenon_intro zenon_Hac | zenon_intro zenon_H1d8 ]. % 90.52/90.75 exact (zenon_Hac zenon_H167). % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H1d8); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1d9 ]. % 90.52/90.75 exact (zenon_H1d4 zenon_H1d6). % 90.52/90.75 exact (zenon_H1d5 zenon_H1d9). % 90.52/90.75 apply (zenon_L154_ zenon_TB_ec); trivial. % 90.52/90.75 cut ((gt (succ (tptp_minus_1)) (succ (n0))) = (gt (succ (tptp_minus_1)) (n1))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_Hac. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_H10e. % 90.52/90.75 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.75 congruence. % 90.52/90.75 apply zenon_H8f. apply refl_equal. % 90.52/90.75 exact (zenon_Hb3 successor_1). % 90.52/90.75 apply (zenon_L143_ zenon_TB_ec); trivial. % 90.52/90.75 (* end of lemma zenon_L155_ *) % 90.52/90.75 assert (zenon_L156_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(gt (n0) (succ zenon_TB_ec))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False). % 90.52/90.75 do 1 intro. intros zenon_H68 zenon_H97 zenon_H1de zenon_H73 zenon_Hce. % 90.52/90.75 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 90.52/90.75 elim (classic (gt (n0) (n0))); [ zenon_intro zenon_H1b4 | zenon_intro zenon_Hdf ]. % 90.52/90.75 elim (classic (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hde ]. % 90.52/90.75 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (succ zenon_TB_ec))); [ zenon_intro zenon_H1df | zenon_intro zenon_H1e0 ]. % 90.52/90.75 generalize (zenon_H73 (n0)). zenon_intro zenon_H115. % 90.52/90.75 generalize (zenon_H115 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H1e1. % 90.52/90.75 generalize (zenon_H1e1 (succ zenon_TB_ec)). zenon_intro zenon_H1e2. % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H1e2); [ zenon_intro zenon_Hde | zenon_intro zenon_H1e3 ]. % 90.52/90.75 exact (zenon_Hde zenon_Hdd). % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H1e3); [ zenon_intro zenon_H1e0 | zenon_intro zenon_H1e4 ]. % 90.52/90.75 exact (zenon_H1e0 zenon_H1df). % 90.52/90.75 exact (zenon_H1de zenon_H1e4). % 90.52/90.75 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 90.52/90.75 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (n0))); [ zenon_intro zenon_He0 | zenon_intro zenon_He1 ]. % 90.52/90.75 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (tptp_minus_1)))); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H1e6 ]. % 90.52/90.75 elim (classic (gt (succ (tptp_minus_1)) (succ zenon_TB_ec))); [ zenon_intro zenon_H1d9 | zenon_intro zenon_H1d5 ]. % 90.52/90.75 generalize (zenon_H73 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H1a3. % 90.52/90.75 generalize (zenon_H1a3 (succ (tptp_minus_1))). zenon_intro zenon_H1e7. % 90.52/90.75 generalize (zenon_H1e7 (succ zenon_TB_ec)). zenon_intro zenon_H1e8. % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H1e8); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H1e9 ]. % 90.52/90.75 exact (zenon_H1e6 zenon_H1e5). % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H1e9); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H1df ]. % 90.52/90.75 exact (zenon_H1d5 zenon_H1d9). % 90.52/90.75 exact (zenon_H1e0 zenon_H1df). % 90.52/90.75 apply (zenon_L155_ zenon_TB_ec); trivial. % 90.52/90.75 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (n0)) = (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (tptp_minus_1)))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_H1e6. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_He0. % 90.52/90.75 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.75 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.75 congruence. % 90.52/90.75 apply zenon_Hda. apply refl_equal. % 90.52/90.75 exact (zenon_H72 zenon_H71). % 90.52/90.75 apply (zenon_L150_ zenon_TB_ec); trivial. % 90.52/90.75 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_H72. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hc2. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.75 congruence. % 90.52/90.75 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.75 apply zenon_H8f. apply refl_equal. % 90.52/90.75 apply zenon_H8f. apply refl_equal. % 90.52/90.75 cut ((gt (n0) (n0)) = (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_Hde. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_H1b4. % 90.52/90.75 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 90.52/90.75 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.75 congruence. % 90.52/90.75 apply zenon_H67. apply refl_equal. % 90.52/90.75 exact (zenon_Hd7 zenon_Hd6). % 90.52/90.75 apply (zenon_L151_ zenon_TB_ec); trivial. % 90.52/90.75 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd9 | zenon_intro zenon_Hda ]. % 90.52/90.75 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_Hd7. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hd9. % 90.52/90.75 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.75 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 90.52/90.75 congruence. % 90.52/90.75 exact (zenon_Hdb zenon_Hce). % 90.52/90.75 apply zenon_Hda. apply refl_equal. % 90.52/90.75 apply zenon_Hda. apply refl_equal. % 90.52/90.75 (* end of lemma zenon_L156_ *) % 90.52/90.75 assert (zenon_L157_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (succ (tptp_minus_1)))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(gt (n0) (succ zenon_TB_ec))) -> False). % 90.52/90.75 do 1 intro. intros zenon_H73 zenon_Hc0 zenon_H68 zenon_H97 zenon_Hce zenon_H1de. % 90.52/90.75 elim (classic (gt zenon_TB_ec (succ (tptp_minus_1)))); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hc4 ]. % 90.52/90.75 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.75 generalize (zenon_Hd1 zenon_TB_ec). zenon_intro zenon_Hd2. % 90.52/90.75 generalize (zenon_Hd2 (succ (tptp_minus_1))). zenon_intro zenon_H268. % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H268); [ zenon_intro zenon_Hab | zenon_intro zenon_H269 ]. % 90.52/90.75 exact (zenon_Hab zenon_H97). % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H269); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc5 ]. % 90.52/90.75 exact (zenon_Hc4 zenon_Hcc). % 90.52/90.75 exact (zenon_Hc0 zenon_Hc5). % 90.52/90.75 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 90.52/90.75 elim (classic (gt zenon_TB_ec (n0))); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hcb ]. % 90.52/90.75 cut ((gt zenon_TB_ec (n0)) = (gt zenon_TB_ec (succ (tptp_minus_1)))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_Hc4. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hd8. % 90.52/90.75 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.75 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.75 congruence. % 90.52/90.75 apply zenon_Ha1. apply refl_equal. % 90.52/90.75 exact (zenon_H72 zenon_H71). % 90.52/90.75 apply (zenon_L145_ zenon_TB_ec); trivial. % 90.52/90.75 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_H72. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hc2. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.75 congruence. % 90.52/90.75 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.75 apply zenon_H8f. apply refl_equal. % 90.52/90.75 apply zenon_H8f. apply refl_equal. % 90.52/90.75 (* end of lemma zenon_L157_ *) % 90.52/90.75 assert (zenon_L158_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (succ zenon_TB_ec))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.75 do 1 intro. intros zenon_H73 zenon_H1d5 zenon_Hce zenon_H97 zenon_H68. % 90.52/90.75 elim (classic (gt (succ (tptp_minus_1)) (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hc0 ]. % 90.52/90.75 elim (classic (gt (succ (tptp_minus_1)) (n0))); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hbf ]. % 90.52/90.75 elim (classic (gt (n0) (succ zenon_TB_ec))); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H1de ]. % 90.52/90.75 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.75 generalize (zenon_Hd1 (n0)). zenon_intro zenon_H141. % 90.52/90.75 generalize (zenon_H141 (succ zenon_TB_ec)). zenon_intro zenon_H28c. % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H28c); [ zenon_intro zenon_Hbf | zenon_intro zenon_H28d ]. % 90.52/90.75 exact (zenon_Hbf zenon_Hc1). % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H28d); [ zenon_intro zenon_H1de | zenon_intro zenon_H1d9 ]. % 90.52/90.75 exact (zenon_H1de zenon_H1e4). % 90.52/90.75 exact (zenon_H1d5 zenon_H1d9). % 90.52/90.75 apply (zenon_L156_ zenon_TB_ec); trivial. % 90.52/90.75 cut ((gt (succ (tptp_minus_1)) (succ (tptp_minus_1))) = (gt (succ (tptp_minus_1)) (n0))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_Hbf. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hc5. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.75 congruence. % 90.52/90.75 apply zenon_H8f. apply refl_equal. % 90.52/90.75 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.75 elim (classic (gt (n0) (succ zenon_TB_ec))); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H1de ]. % 90.52/90.75 cut ((gt (n0) (succ zenon_TB_ec)) = (gt (succ (tptp_minus_1)) (succ zenon_TB_ec))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_H1d5. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_H1e4. % 90.52/90.75 cut (((succ zenon_TB_ec) = (succ zenon_TB_ec))); [idtac | apply NNPP; zenon_intro zenon_H28e]. % 90.52/90.75 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.75 congruence. % 90.52/90.75 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_H72. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hc2. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.75 congruence. % 90.52/90.75 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.75 apply zenon_H8f. apply refl_equal. % 90.52/90.75 apply zenon_H8f. apply refl_equal. % 90.52/90.75 apply zenon_H28e. apply refl_equal. % 90.52/90.75 apply (zenon_L157_ zenon_TB_ec); trivial. % 90.52/90.75 (* end of lemma zenon_L158_ *) % 90.52/90.75 assert (zenon_L159_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (succ (n0))) (succ (tptp_minus_1)))) -> False). % 90.52/90.75 do 0 intro. intros zenon_H73 zenon_H28f. % 90.52/90.75 elim (classic (gt (succ (succ (n0))) (succ (n0)))); [ zenon_intro zenon_H1ff | zenon_intro zenon_H1f7 ]. % 90.52/90.75 elim (classic (gt (succ (succ (n0))) (n1))); [ zenon_intro zenon_H200 | zenon_intro zenon_H201 ]. % 90.52/90.75 elim (classic (gt (n1) (succ (tptp_minus_1)))); [ zenon_intro zenon_H75 | zenon_intro zenon_H70 ]. % 90.52/90.75 generalize (zenon_H73 (succ (succ (n0)))). zenon_intro zenon_H202. % 90.52/90.75 generalize (zenon_H202 (n1)). zenon_intro zenon_H203. % 90.52/90.75 generalize (zenon_H203 (succ (tptp_minus_1))). zenon_intro zenon_H290. % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H290); [ zenon_intro zenon_H201 | zenon_intro zenon_H291 ]. % 90.52/90.75 exact (zenon_H201 zenon_H200). % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H291); [ zenon_intro zenon_H70 | zenon_intro zenon_H292 ]. % 90.52/90.75 exact (zenon_H70 zenon_H75). % 90.52/90.75 exact (zenon_H28f zenon_H292). % 90.52/90.75 apply (zenon_L7_); trivial. % 90.52/90.75 cut ((gt (succ (succ (n0))) (succ (n0))) = (gt (succ (succ (n0))) (n1))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_H201. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_H1ff. % 90.52/90.75 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.75 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 90.52/90.75 congruence. % 90.52/90.75 apply zenon_H1ee. apply refl_equal. % 90.52/90.75 exact (zenon_Hb3 successor_1). % 90.52/90.75 apply (zenon_L89_); trivial. % 90.52/90.75 (* end of lemma zenon_L159_ *) % 90.52/90.75 assert (zenon_L160_ : forall (zenon_TB_ec : zenon_U), (~(gt (succ (tptp_minus_1)) (n2))) -> (~((tptp_minus_1) = (n3))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (~(gt zenon_TB_ec (succ (tptp_minus_1)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.75 do 1 intro. intros zenon_H1da zenon_He8 zenon_Hb6 zenon_Hb5 zenon_H97 zenon_H68 zenon_Hc4 zenon_H73. % 90.52/90.75 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 90.52/90.75 elim (classic (gt zenon_TB_ec (n0))); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hcb ]. % 90.52/90.75 cut ((gt zenon_TB_ec (n0)) = (gt zenon_TB_ec (succ (tptp_minus_1)))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_Hc4. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hd8. % 90.52/90.75 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.75 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.75 congruence. % 90.52/90.75 apply zenon_Ha1. apply refl_equal. % 90.52/90.75 exact (zenon_H72 zenon_H71). % 90.52/90.75 apply (zenon_L81_ zenon_TB_ec); trivial. % 90.52/90.75 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_H72. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hc2. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.75 congruence. % 90.52/90.75 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.75 apply zenon_H8f. apply refl_equal. % 90.52/90.75 apply zenon_H8f. apply refl_equal. % 90.52/90.75 (* end of lemma zenon_L160_ *) % 90.52/90.75 assert (zenon_L161_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (n2))) -> (~((tptp_minus_1) = (n3))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.75 do 1 intro. intros zenon_H73 zenon_H1da zenon_He8 zenon_Hb6 zenon_Hb5 zenon_H97 zenon_H68. % 90.52/90.75 generalize (irreflexivity_gt zenon_TB_ec). zenon_intro zenon_H293. % 90.52/90.75 elim (classic ((~(zenon_TB_ec = (succ (tptp_minus_1))))/\(~(gt zenon_TB_ec (succ (tptp_minus_1)))))); [ zenon_intro zenon_H294 | zenon_intro zenon_H295 ]. % 90.52/90.75 apply (zenon_and_s _ _ zenon_H294). zenon_intro zenon_H296. zenon_intro zenon_Hc4. % 90.52/90.75 apply (zenon_L160_ zenon_TB_ec); trivial. % 90.52/90.75 cut ((gt (succ (tptp_minus_1)) zenon_TB_ec) = (gt zenon_TB_ec zenon_TB_ec)). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_H293. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_H97. % 90.52/90.75 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.75 cut (((succ (tptp_minus_1)) = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_H297]. % 90.52/90.75 congruence. % 90.52/90.75 apply (zenon_notand_s _ _ zenon_H295); [ zenon_intro zenon_H299 | zenon_intro zenon_H298 ]. % 90.52/90.75 apply zenon_H299. zenon_intro zenon_H29a. % 90.52/90.75 elim (classic (zenon_TB_ec = zenon_TB_ec)); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Ha1 ]. % 90.52/90.75 cut ((zenon_TB_ec = zenon_TB_ec) = ((succ (tptp_minus_1)) = zenon_TB_ec)). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_H297. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hc9. % 90.52/90.75 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.75 cut ((zenon_TB_ec = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H296]. % 90.52/90.75 congruence. % 90.52/90.75 exact (zenon_H296 zenon_H29a). % 90.52/90.75 apply zenon_Ha1. apply refl_equal. % 90.52/90.75 apply zenon_Ha1. apply refl_equal. % 90.52/90.75 apply zenon_H298. zenon_intro zenon_Hcc. % 90.52/90.75 generalize (zenon_H73 zenon_TB_ec). zenon_intro zenon_H144. % 90.52/90.75 generalize (zenon_H144 (succ (tptp_minus_1))). zenon_intro zenon_H145. % 90.52/90.75 generalize (zenon_H145 zenon_TB_ec). zenon_intro zenon_H29b. % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H29b); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H29c ]. % 90.52/90.75 exact (zenon_Hc4 zenon_Hcc). % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H29c); [ zenon_intro zenon_Hab | zenon_intro zenon_H29d ]. % 90.52/90.75 exact (zenon_Hab zenon_H97). % 90.52/90.75 exact (zenon_H293 zenon_H29d). % 90.52/90.75 apply zenon_Ha1. apply refl_equal. % 90.52/90.75 (* end of lemma zenon_L161_ *) % 90.52/90.75 assert (zenon_L162_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> (~((tptp_minus_1) = (n3))) -> (~(gt (succ (tptp_minus_1)) (succ (succ (n0))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.75 do 1 intro. intros zenon_H68 zenon_H97 zenon_Hb5 zenon_Hb6 zenon_He8 zenon_H1ea zenon_H73. % 90.52/90.75 elim (classic ((n2) = (succ (succ (n0))))); [ zenon_intro zenon_H1eb | zenon_intro zenon_H1ec ]. % 90.52/90.75 elim (classic (gt (succ (tptp_minus_1)) (n2))); [ zenon_intro zenon_H1dd | zenon_intro zenon_H1da ]. % 90.52/90.75 cut ((gt (succ (tptp_minus_1)) (n2)) = (gt (succ (tptp_minus_1)) (succ (succ (n0))))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_H1ea. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_H1dd. % 90.52/90.75 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ec]. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.75 congruence. % 90.52/90.75 apply zenon_H8f. apply refl_equal. % 90.52/90.75 exact (zenon_H1ec zenon_H1eb). % 90.52/90.75 apply (zenon_L161_ zenon_TB_ec); trivial. % 90.52/90.75 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1ee ]. % 90.52/90.75 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((n2) = (succ (succ (n0))))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_H1ec. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_H1ed. % 90.52/90.75 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 90.52/90.75 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 90.52/90.75 congruence. % 90.52/90.75 exact (zenon_H1ef successor_2). % 90.52/90.75 apply zenon_H1ee. apply refl_equal. % 90.52/90.75 apply zenon_H1ee. apply refl_equal. % 90.52/90.75 (* end of lemma zenon_L162_ *) % 90.52/90.75 assert (zenon_L163_ : forall (zenon_TB_ec : zenon_U), (~(gt (n1) (succ (succ (n0))))) -> (~((tptp_minus_1) = (n3))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.75 do 1 intro. intros zenon_H1f0 zenon_He8 zenon_Hb6 zenon_Hb5 zenon_H97 zenon_H68 zenon_H73. % 90.52/90.75 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 90.52/90.75 elim (classic (gt (n1) (succ (tptp_minus_1)))); [ zenon_intro zenon_H75 | zenon_intro zenon_H70 ]. % 90.52/90.75 elim (classic (gt (succ (tptp_minus_1)) (succ (succ (n0))))); [ zenon_intro zenon_H1f1 | zenon_intro zenon_H1ea ]. % 90.52/90.75 generalize (zenon_H73 (n1)). zenon_intro zenon_H138. % 90.52/90.75 generalize (zenon_H138 (succ (tptp_minus_1))). zenon_intro zenon_H1f2. % 90.52/90.75 generalize (zenon_H1f2 (succ (succ (n0)))). zenon_intro zenon_H1f3. % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H1f3); [ zenon_intro zenon_H70 | zenon_intro zenon_H1f4 ]. % 90.52/90.75 exact (zenon_H70 zenon_H75). % 90.52/90.75 apply (zenon_imply_s _ _ zenon_H1f4); [ zenon_intro zenon_H1ea | zenon_intro zenon_H1f5 ]. % 90.52/90.75 exact (zenon_H1ea zenon_H1f1). % 90.52/90.75 exact (zenon_H1f0 zenon_H1f5). % 90.52/90.75 apply (zenon_L162_ zenon_TB_ec); trivial. % 90.52/90.75 cut ((gt (n1) (n0)) = (gt (n1) (succ (tptp_minus_1)))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_H70. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact gt_1_0. % 90.52/90.75 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.75 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.75 congruence. % 90.52/90.75 apply zenon_H66. apply refl_equal. % 90.52/90.75 exact (zenon_H72 zenon_H71). % 90.52/90.75 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))). % 90.52/90.75 intro zenon_D_pnotp. % 90.52/90.75 apply zenon_H72. % 90.52/90.75 rewrite <- zenon_D_pnotp. % 90.52/90.75 exact zenon_Hc2. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.75 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.75 congruence. % 90.52/90.75 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.75 apply zenon_H8f. apply refl_equal. % 90.52/90.75 apply zenon_H8f. apply refl_equal. % 90.52/90.75 (* end of lemma zenon_L163_ *) % 90.52/90.75 assert (zenon_L164_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> (~((tptp_minus_1) = (n3))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n2) (n2))) -> False). % 90.52/90.75 do 1 intro. intros zenon_H68 zenon_H97 zenon_Hb5 zenon_Hb6 zenon_He8 zenon_H73 zenon_H1f9. % 90.52/90.75 elim (classic ((n2) = (succ (succ (n0))))); [ zenon_intro zenon_H1eb | zenon_intro zenon_H1ec ]. % 90.52/90.76 elim (classic (gt (succ (succ (n0))) (n2))); [ zenon_intro zenon_H1fa | zenon_intro zenon_H1fb ]. % 90.52/90.76 cut ((gt (succ (succ (n0))) (n2)) = (gt (n2) (n2))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H1f9. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H1fa. % 90.52/90.76 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 90.52/90.76 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 90.52/90.76 congruence. % 90.52/90.76 elim (classic ((n2) = (n2))); [ zenon_intro zenon_H1fc | zenon_intro zenon_H65 ]. % 90.52/90.76 cut (((n2) = (n2)) = ((succ (succ (n0))) = (n2))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H1ef. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H1fc. % 90.52/90.76 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 90.52/90.76 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ec]. % 90.52/90.76 congruence. % 90.52/90.76 exact (zenon_H1ec zenon_H1eb). % 90.52/90.76 apply zenon_H65. apply refl_equal. % 90.52/90.76 apply zenon_H65. apply refl_equal. % 90.52/90.76 apply zenon_H65. apply refl_equal. % 90.52/90.76 elim (classic (gt (succ (succ (n0))) (succ (succ (n0))))); [ zenon_intro zenon_H1fd | zenon_intro zenon_H1fe ]. % 90.52/90.76 cut ((gt (succ (succ (n0))) (succ (succ (n0)))) = (gt (succ (succ (n0))) (n2))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H1fb. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H1fd. % 90.52/90.76 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 90.52/90.76 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 90.52/90.76 congruence. % 90.52/90.76 apply zenon_H1ee. apply refl_equal. % 90.52/90.76 exact (zenon_H1ef successor_2). % 90.52/90.76 elim (classic (gt (succ (succ (n0))) (succ (n0)))); [ zenon_intro zenon_H1ff | zenon_intro zenon_H1f7 ]. % 90.52/90.76 elim (classic (gt (succ (succ (n0))) (n1))); [ zenon_intro zenon_H200 | zenon_intro zenon_H201 ]. % 90.52/90.76 elim (classic (gt (n1) (succ (succ (n0))))); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H1f0 ]. % 90.52/90.76 generalize (zenon_H73 (succ (succ (n0)))). zenon_intro zenon_H202. % 90.52/90.76 generalize (zenon_H202 (n1)). zenon_intro zenon_H203. % 90.52/90.76 generalize (zenon_H203 (succ (succ (n0)))). zenon_intro zenon_H204. % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H204); [ zenon_intro zenon_H201 | zenon_intro zenon_H205 ]. % 90.52/90.76 exact (zenon_H201 zenon_H200). % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H205); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H1fd ]. % 90.52/90.76 exact (zenon_H1f0 zenon_H1f5). % 90.52/90.76 exact (zenon_H1fe zenon_H1fd). % 90.52/90.76 apply (zenon_L163_ zenon_TB_ec); trivial. % 90.52/90.76 cut ((gt (succ (succ (n0))) (succ (n0))) = (gt (succ (succ (n0))) (n1))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H201. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H1ff. % 90.52/90.76 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.76 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 90.52/90.76 congruence. % 90.52/90.76 apply zenon_H1ee. apply refl_equal. % 90.52/90.76 exact (zenon_Hb3 successor_1). % 90.52/90.76 apply (zenon_L89_); trivial. % 90.52/90.76 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1ee ]. % 90.52/90.76 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((n2) = (succ (succ (n0))))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H1ec. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H1ed. % 90.52/90.76 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 90.52/90.76 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 90.52/90.76 congruence. % 90.52/90.76 exact (zenon_H1ef successor_2). % 90.52/90.76 apply zenon_H1ee. apply refl_equal. % 90.52/90.76 apply zenon_H1ee. apply refl_equal. % 90.52/90.76 (* end of lemma zenon_L164_ *) % 90.52/90.76 assert (zenon_L165_ : forall (zenon_TB_ec : zenon_U), (~(gt zenon_TB_ec (succ (succ (n0))))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (~((tptp_minus_1) = (n3))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.76 do 1 intro. intros zenon_H234 zenon_Hb6 zenon_Hb5 zenon_H97 zenon_H68 zenon_He8 zenon_H73. % 90.52/90.76 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 90.52/90.76 elim (classic (gt zenon_TB_ec (n0))); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hcb ]. % 90.52/90.76 elim (classic (gt zenon_TB_ec (succ (tptp_minus_1)))); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hc4 ]. % 90.52/90.76 elim (classic (gt (succ (tptp_minus_1)) (succ (succ (n0))))); [ zenon_intro zenon_H1f1 | zenon_intro zenon_H1ea ]. % 90.52/90.76 generalize (zenon_H73 zenon_TB_ec). zenon_intro zenon_H144. % 90.52/90.76 generalize (zenon_H144 (succ (tptp_minus_1))). zenon_intro zenon_H145. % 90.52/90.76 generalize (zenon_H145 (succ (succ (n0)))). zenon_intro zenon_H235. % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H235); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H236 ]. % 90.52/90.76 exact (zenon_Hc4 zenon_Hcc). % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H236); [ zenon_intro zenon_H1ea | zenon_intro zenon_H237 ]. % 90.52/90.76 exact (zenon_H1ea zenon_H1f1). % 90.52/90.76 exact (zenon_H234 zenon_H237). % 90.52/90.76 apply (zenon_L162_ zenon_TB_ec); trivial. % 90.52/90.76 cut ((gt zenon_TB_ec (n0)) = (gt zenon_TB_ec (succ (tptp_minus_1)))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_Hc4. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_Hd8. % 90.52/90.76 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.76 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.76 congruence. % 90.52/90.76 apply zenon_Ha1. apply refl_equal. % 90.52/90.76 exact (zenon_H72 zenon_H71). % 90.52/90.76 apply (zenon_L99_ zenon_TB_ec); trivial. % 90.52/90.76 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.76 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H72. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_Hc2. % 90.52/90.76 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.76 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.76 congruence. % 90.52/90.76 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.76 apply zenon_H8f. apply refl_equal. % 90.52/90.76 apply zenon_H8f. apply refl_equal. % 90.52/90.76 (* end of lemma zenon_L165_ *) % 90.52/90.76 assert (zenon_L166_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt zenon_TB_ec (n2))) -> (~((tptp_minus_1) = (n3))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.76 do 1 intro. intros zenon_H73 zenon_H238 zenon_He8 zenon_Hb6 zenon_Hb5 zenon_H97 zenon_H68. % 90.52/90.76 elim (classic (gt zenon_TB_ec (succ (succ (n0))))); [ zenon_intro zenon_H237 | zenon_intro zenon_H234 ]. % 90.52/90.76 cut ((gt zenon_TB_ec (succ (succ (n0)))) = (gt zenon_TB_ec (n2))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H238. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H237. % 90.52/90.76 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 90.52/90.76 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.76 congruence. % 90.52/90.76 apply zenon_Ha1. apply refl_equal. % 90.52/90.76 exact (zenon_H1ef successor_2). % 90.52/90.76 apply (zenon_L165_ zenon_TB_ec); trivial. % 90.52/90.76 (* end of lemma zenon_L166_ *) % 90.52/90.76 assert (zenon_L167_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n3))) -> (~((tptp_minus_1) = (n3))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n2) (n2))) -> False). % 90.52/90.76 do 1 intro. intros zenon_H68 zenon_H97 zenon_Hb6 zenon_He8 zenon_H73 zenon_H1f9. % 90.52/90.76 elim (classic ((n2) = (succ (succ (n0))))); [ zenon_intro zenon_H1eb | zenon_intro zenon_H1ec ]. % 90.52/90.76 elim (classic (gt (succ (succ (n0))) (n2))); [ zenon_intro zenon_H1fa | zenon_intro zenon_H1fb ]. % 90.52/90.76 cut ((gt (succ (succ (n0))) (n2)) = (gt (n2) (n2))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H1f9. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H1fa. % 90.52/90.76 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 90.52/90.76 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 90.52/90.76 congruence. % 90.52/90.76 elim (classic ((n2) = (n2))); [ zenon_intro zenon_H1fc | zenon_intro zenon_H65 ]. % 90.52/90.76 cut (((n2) = (n2)) = ((succ (succ (n0))) = (n2))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H1ef. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H1fc. % 90.52/90.76 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 90.52/90.76 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ec]. % 90.52/90.76 congruence. % 90.52/90.76 exact (zenon_H1ec zenon_H1eb). % 90.52/90.76 apply zenon_H65. apply refl_equal. % 90.52/90.76 apply zenon_H65. apply refl_equal. % 90.52/90.76 apply zenon_H65. apply refl_equal. % 90.52/90.76 elim (classic ((~((succ (succ (n0))) = (succ (tptp_minus_1))))/\(~(gt (succ (succ (n0))) (succ (tptp_minus_1)))))); [ zenon_intro zenon_H29e | zenon_intro zenon_H29f ]. % 90.52/90.76 apply (zenon_and_s _ _ zenon_H29e). zenon_intro zenon_H2a0. zenon_intro zenon_H28f. % 90.52/90.76 apply (zenon_L159_); trivial. % 90.52/90.76 elim (classic (zenon_TB_ec = (n2))); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hb5 ]. % 90.52/90.76 cut ((gt (succ (tptp_minus_1)) zenon_TB_ec) = (gt (succ (succ (n0))) (n2))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H1fb. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H97. % 90.52/90.76 cut ((zenon_TB_ec = (n2))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 90.52/90.76 cut (((succ (tptp_minus_1)) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H2a1]. % 90.52/90.76 congruence. % 90.52/90.76 apply (zenon_notand_s _ _ zenon_H29f); [ zenon_intro zenon_H2a3 | zenon_intro zenon_H2a2 ]. % 90.52/90.76 apply zenon_H2a3. zenon_intro zenon_H2a4. % 90.52/90.76 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1ee ]. % 90.52/90.76 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((succ (tptp_minus_1)) = (succ (succ (n0))))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H2a1. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H1ed. % 90.52/90.76 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 90.52/90.76 cut (((succ (succ (n0))) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H2a0]. % 90.52/90.76 congruence. % 90.52/90.76 exact (zenon_H2a0 zenon_H2a4). % 90.52/90.76 apply zenon_H1ee. apply refl_equal. % 90.52/90.76 apply zenon_H1ee. apply refl_equal. % 90.52/90.76 apply zenon_H2a2. zenon_intro zenon_H292. % 90.52/90.76 generalize (zenon_H73 (succ (succ (n0)))). zenon_intro zenon_H202. % 90.52/90.76 generalize (zenon_H202 (succ (tptp_minus_1))). zenon_intro zenon_H2a5. % 90.52/90.76 generalize (zenon_H2a5 zenon_TB_ec). zenon_intro zenon_H2a6. % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H2a6); [ zenon_intro zenon_H28f | zenon_intro zenon_H2a7 ]. % 90.52/90.76 exact (zenon_H28f zenon_H292). % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H2a7); [ zenon_intro zenon_Hab | zenon_intro zenon_H2a8 ]. % 90.52/90.76 exact (zenon_Hab zenon_H97). % 90.52/90.76 cut ((gt (succ (succ (n0))) zenon_TB_ec) = (gt (succ (succ (n0))) (n2))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H1fb. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H2a8. % 90.52/90.76 cut ((zenon_TB_ec = (n2))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 90.52/90.76 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 90.52/90.76 congruence. % 90.52/90.76 apply zenon_H1ee. apply refl_equal. % 90.52/90.76 exact (zenon_Hb5 zenon_Hbe). % 90.52/90.76 exact (zenon_Hb5 zenon_Hbe). % 90.52/90.76 elim (classic (gt zenon_TB_ec (n2))); [ zenon_intro zenon_H248 | zenon_intro zenon_H238 ]. % 90.52/90.76 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.76 generalize (zenon_Hd1 zenon_TB_ec). zenon_intro zenon_Hd2. % 90.52/90.76 generalize (zenon_Hd2 (n2)). zenon_intro zenon_H24e. % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H24e); [ zenon_intro zenon_Hab | zenon_intro zenon_H24f ]. % 90.52/90.76 exact (zenon_Hab zenon_H97). % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H24f); [ zenon_intro zenon_H238 | zenon_intro zenon_H1dd ]. % 90.52/90.76 exact (zenon_H238 zenon_H248). % 90.52/90.76 cut ((gt (succ (tptp_minus_1)) (n2)) = (gt (succ (succ (n0))) (n2))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H1fb. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H1dd. % 90.52/90.76 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 90.52/90.76 cut (((succ (tptp_minus_1)) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H2a1]. % 90.52/90.76 congruence. % 90.52/90.76 apply (zenon_notand_s _ _ zenon_H29f); [ zenon_intro zenon_H2a3 | zenon_intro zenon_H2a2 ]. % 90.52/90.76 apply zenon_H2a3. zenon_intro zenon_H2a4. % 90.52/90.76 apply zenon_H2a1. apply sym_equal. exact zenon_H2a4. % 90.52/90.76 apply zenon_H2a2. zenon_intro zenon_H292. % 90.52/90.76 generalize (zenon_H73 (succ (succ (n0)))). zenon_intro zenon_H202. % 90.52/90.76 generalize (zenon_H202 (succ (tptp_minus_1))). zenon_intro zenon_H2a5. % 90.52/90.76 generalize (zenon_H2a5 (n2)). zenon_intro zenon_H2a9. % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H2a9); [ zenon_intro zenon_H28f | zenon_intro zenon_H2aa ]. % 90.52/90.76 exact (zenon_H28f zenon_H292). % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H2aa); [ zenon_intro zenon_H1da | zenon_intro zenon_H1fa ]. % 90.52/90.76 exact (zenon_H1da zenon_H1dd). % 90.52/90.76 exact (zenon_H1fb zenon_H1fa). % 90.52/90.76 apply zenon_H65. apply refl_equal. % 90.52/90.76 apply (zenon_L166_ zenon_TB_ec); trivial. % 90.52/90.76 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1ee ]. % 90.52/90.76 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((n2) = (succ (succ (n0))))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H1ec. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H1ed. % 90.52/90.76 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 90.52/90.76 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 90.52/90.76 congruence. % 90.52/90.76 exact (zenon_H1ef successor_2). % 90.52/90.76 apply zenon_H1ee. apply refl_equal. % 90.52/90.76 apply zenon_H1ee. apply refl_equal. % 90.52/90.76 (* end of lemma zenon_L167_ *) % 90.52/90.76 assert (zenon_L168_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n0)) (succ (succ (n0))))) -> (~((tptp_minus_1) = (n3))) -> (~(zenon_TB_ec = (n3))) -> (~(zenon_TB_ec = (n2))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.76 do 1 intro. intros zenon_H73 zenon_H2ab zenon_He8 zenon_Hb6 zenon_Hb5 zenon_H97 zenon_H68. % 90.52/90.76 elim (classic ((~((succ (n0)) = (succ (tptp_minus_1))))/\(~(gt (succ (n0)) (succ (tptp_minus_1)))))); [ zenon_intro zenon_H159 | zenon_intro zenon_H15a ]. % 90.52/90.76 apply (zenon_and_s _ _ zenon_H159). zenon_intro zenon_H15b. zenon_intro zenon_Haf. % 90.52/90.76 apply (zenon_L15_); trivial. % 90.52/90.76 elim (classic (gt zenon_TB_ec (succ (succ (n0))))); [ zenon_intro zenon_H237 | zenon_intro zenon_H234 ]. % 90.52/90.76 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.76 generalize (zenon_Hd1 zenon_TB_ec). zenon_intro zenon_Hd2. % 90.52/90.76 generalize (zenon_Hd2 (succ (succ (n0)))). zenon_intro zenon_H2ac. % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H2ac); [ zenon_intro zenon_Hab | zenon_intro zenon_H2ad ]. % 90.52/90.76 exact (zenon_Hab zenon_H97). % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H2ad); [ zenon_intro zenon_H234 | zenon_intro zenon_H1f1 ]. % 90.52/90.76 exact (zenon_H234 zenon_H237). % 90.52/90.76 cut ((gt (succ (tptp_minus_1)) (succ (succ (n0)))) = (gt (succ (n0)) (succ (succ (n0))))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H2ab. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H1f1. % 90.52/90.76 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 90.52/90.76 cut (((succ (tptp_minus_1)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 90.52/90.76 congruence. % 90.52/90.76 apply (zenon_notand_s _ _ zenon_H15a); [ zenon_intro zenon_H15d | zenon_intro zenon_H15c ]. % 90.52/90.76 apply zenon_H15d. zenon_intro zenon_H15e. % 90.52/90.76 apply zenon_H108. apply sym_equal. exact zenon_H15e. % 90.52/90.76 apply zenon_H15c. zenon_intro zenon_H15f. % 90.52/90.76 generalize (zenon_H73 (succ (n0))). zenon_intro zenon_H127. % 90.52/90.76 generalize (zenon_H127 (succ (tptp_minus_1))). zenon_intro zenon_H160. % 90.52/90.76 generalize (zenon_H160 (succ (succ (n0)))). zenon_intro zenon_H2ae. % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H2ae); [ zenon_intro zenon_Haf | zenon_intro zenon_H2af ]. % 90.52/90.76 exact (zenon_Haf zenon_H15f). % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H2af); [ zenon_intro zenon_H1ea | zenon_intro zenon_H2b0 ]. % 90.52/90.76 exact (zenon_H1ea zenon_H1f1). % 90.52/90.76 exact (zenon_H2ab zenon_H2b0). % 90.52/90.76 apply zenon_H1ee. apply refl_equal. % 90.52/90.76 apply (zenon_L165_ zenon_TB_ec); trivial. % 90.52/90.76 (* end of lemma zenon_L168_ *) % 90.52/90.76 assert (zenon_L169_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n0)) (n2))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n2))) -> (~(zenon_TB_ec = (n3))) -> (~((tptp_minus_1) = (n3))) -> False). % 90.52/90.76 do 1 intro. intros zenon_H73 zenon_H2b1 zenon_H68 zenon_H97 zenon_Hb5 zenon_Hb6 zenon_He8. % 90.52/90.76 elim (classic (gt (succ (n0)) (succ (succ (n0))))); [ zenon_intro zenon_H2b0 | zenon_intro zenon_H2ab ]. % 90.52/90.76 cut ((gt (succ (n0)) (succ (succ (n0)))) = (gt (succ (n0)) (n2))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H2b1. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H2b0. % 90.52/90.76 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 90.52/90.76 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.76 congruence. % 90.52/90.76 apply zenon_Hb2. apply refl_equal. % 90.52/90.76 exact (zenon_H1ef successor_2). % 90.52/90.76 apply (zenon_L168_ zenon_TB_ec); trivial. % 90.52/90.76 (* end of lemma zenon_L169_ *) % 90.52/90.76 assert (zenon_L170_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n0)) (n2))) -> (~((tptp_minus_1) = (n3))) -> (~(zenon_TB_ec = (n3))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.76 do 1 intro. intros zenon_H73 zenon_H2b1 zenon_He8 zenon_Hb6 zenon_H97 zenon_H68. % 90.52/90.76 elim (classic ((~((succ (n0)) = (succ (tptp_minus_1))))/\(~(gt (succ (n0)) (succ (tptp_minus_1)))))); [ zenon_intro zenon_H159 | zenon_intro zenon_H15a ]. % 90.52/90.76 apply (zenon_and_s _ _ zenon_H159). zenon_intro zenon_H15b. zenon_intro zenon_Haf. % 90.52/90.76 apply (zenon_L15_); trivial. % 90.52/90.76 elim (classic (zenon_TB_ec = (n2))); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hb5 ]. % 90.52/90.76 cut ((gt (succ (tptp_minus_1)) zenon_TB_ec) = (gt (succ (n0)) (n2))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H2b1. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H97. % 90.52/90.76 cut ((zenon_TB_ec = (n2))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 90.52/90.76 cut (((succ (tptp_minus_1)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 90.52/90.76 congruence. % 90.52/90.76 apply (zenon_notand_s _ _ zenon_H15a); [ zenon_intro zenon_H15d | zenon_intro zenon_H15c ]. % 90.52/90.76 apply zenon_H15d. zenon_intro zenon_H15e. % 90.52/90.76 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 90.52/90.76 cut (((succ (n0)) = (succ (n0))) = ((succ (tptp_minus_1)) = (succ (n0)))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H108. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_Hb1. % 90.52/90.76 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.76 cut (((succ (n0)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H15b]. % 90.52/90.76 congruence. % 90.52/90.76 exact (zenon_H15b zenon_H15e). % 90.52/90.76 apply zenon_Hb2. apply refl_equal. % 90.52/90.76 apply zenon_Hb2. apply refl_equal. % 90.52/90.76 apply zenon_H15c. zenon_intro zenon_H15f. % 90.52/90.76 generalize (zenon_H73 (succ (n0))). zenon_intro zenon_H127. % 90.52/90.76 generalize (zenon_H127 (succ (tptp_minus_1))). zenon_intro zenon_H160. % 90.52/90.76 generalize (zenon_H160 zenon_TB_ec). zenon_intro zenon_H161. % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H161); [ zenon_intro zenon_Haf | zenon_intro zenon_H162 ]. % 90.52/90.76 exact (zenon_Haf zenon_H15f). % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H162); [ zenon_intro zenon_Hab | zenon_intro zenon_H163 ]. % 90.52/90.76 exact (zenon_Hab zenon_H97). % 90.52/90.76 cut ((gt (succ (n0)) zenon_TB_ec) = (gt (succ (n0)) (n2))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H2b1. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H163. % 90.52/90.76 cut ((zenon_TB_ec = (n2))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 90.52/90.76 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.76 congruence. % 90.52/90.76 apply zenon_Hb2. apply refl_equal. % 90.52/90.76 exact (zenon_Hb5 zenon_Hbe). % 90.52/90.76 exact (zenon_Hb5 zenon_Hbe). % 90.52/90.76 apply (zenon_L169_ zenon_TB_ec); trivial. % 90.52/90.76 (* end of lemma zenon_L170_ *) % 90.52/90.76 assert (zenon_L171_ : forall (zenon_TB_ec : zenon_U), (~((tptp_minus_1) = (n3))) -> (~(zenon_TB_ec = (n3))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (~(gt (succ (n0)) (succ (succ (n0))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.76 do 1 intro. intros zenon_He8 zenon_Hb6 zenon_H97 zenon_H68 zenon_H2ab zenon_H73. % 90.52/90.76 elim (classic ((n2) = (succ (succ (n0))))); [ zenon_intro zenon_H1eb | zenon_intro zenon_H1ec ]. % 90.52/90.76 elim (classic (gt (succ (n0)) (n2))); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H2b1 ]. % 90.52/90.76 cut ((gt (succ (n0)) (n2)) = (gt (succ (n0)) (succ (succ (n0))))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H2ab. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H2b2. % 90.52/90.76 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ec]. % 90.52/90.76 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.76 congruence. % 90.52/90.76 apply zenon_Hb2. apply refl_equal. % 90.52/90.76 exact (zenon_H1ec zenon_H1eb). % 90.52/90.76 apply (zenon_L170_ zenon_TB_ec); trivial. % 90.52/90.76 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1ee ]. % 90.52/90.76 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((n2) = (succ (succ (n0))))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H1ec. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H1ed. % 90.52/90.76 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 90.52/90.76 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 90.52/90.76 congruence. % 90.52/90.76 exact (zenon_H1ef successor_2). % 90.52/90.76 apply zenon_H1ee. apply refl_equal. % 90.52/90.76 apply zenon_H1ee. apply refl_equal. % 90.52/90.76 (* end of lemma zenon_L171_ *) % 90.52/90.76 assert (zenon_L172_ : forall (zenon_TB_ec : zenon_U), (~((tptp_minus_1) = (n3))) -> (~(zenon_TB_ec = (n3))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt zenon_TB_ec (n1))) -> False). % 90.52/90.76 do 1 intro. intros zenon_He8 zenon_Hb6 zenon_H97 zenon_H68 zenon_H73 zenon_H148. % 90.52/90.76 elim (classic ((~(zenon_TB_ec = (n2)))/\(~(gt zenon_TB_ec (n2))))); [ zenon_intro zenon_H243 | zenon_intro zenon_H244 ]. % 90.52/90.76 apply (zenon_and_s _ _ zenon_H243). zenon_intro zenon_Hb5. zenon_intro zenon_H238. % 90.52/90.76 apply (zenon_L166_ zenon_TB_ec); trivial. % 90.52/90.76 cut ((gt (n2) (n1)) = (gt zenon_TB_ec (n1))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H148. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact gt_2_1. % 90.52/90.76 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.76 cut (((n2) = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_H245]. % 90.52/90.76 congruence. % 90.52/90.76 apply (zenon_notand_s _ _ zenon_H244); [ zenon_intro zenon_H247 | zenon_intro zenon_H246 ]. % 90.52/90.76 apply zenon_H247. zenon_intro zenon_Hbe. % 90.52/90.76 elim (classic (zenon_TB_ec = zenon_TB_ec)); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Ha1 ]. % 90.52/90.76 cut ((zenon_TB_ec = zenon_TB_ec) = ((n2) = zenon_TB_ec)). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H245. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_Hc9. % 90.52/90.76 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.76 cut ((zenon_TB_ec = (n2))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 90.52/90.76 congruence. % 90.52/90.76 exact (zenon_Hb5 zenon_Hbe). % 90.52/90.76 apply zenon_Ha1. apply refl_equal. % 90.52/90.76 apply zenon_Ha1. apply refl_equal. % 90.52/90.76 apply zenon_H246. zenon_intro zenon_H248. % 90.52/90.76 generalize (zenon_H73 zenon_TB_ec). zenon_intro zenon_H144. % 90.52/90.76 generalize (zenon_H144 (n2)). zenon_intro zenon_H249. % 90.52/90.76 generalize (zenon_H249 (n1)). zenon_intro zenon_H24a. % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H24a); [ zenon_intro zenon_H238 | zenon_intro zenon_H24b ]. % 90.52/90.76 exact (zenon_H238 zenon_H248). % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H24b); [ zenon_intro zenon_H7a | zenon_intro zenon_H164 ]. % 90.52/90.76 exact (zenon_H7a gt_2_1). % 90.52/90.76 exact (zenon_H148 zenon_H164). % 90.52/90.76 apply zenon_H66. apply refl_equal. % 90.52/90.76 (* end of lemma zenon_L172_ *) % 90.52/90.76 assert (zenon_L173_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n3))) -> (~((tptp_minus_1) = (n3))) -> (~(gt zenon_TB_ec (succ (n0)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.76 do 1 intro. intros zenon_H68 zenon_H97 zenon_Hb6 zenon_He8 zenon_H109 zenon_H73. % 90.52/90.76 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_H12e | zenon_intro zenon_Hb0 ]. % 90.52/90.76 elim (classic (gt zenon_TB_ec (n1))); [ zenon_intro zenon_H164 | zenon_intro zenon_H148 ]. % 90.52/90.76 cut ((gt zenon_TB_ec (n1)) = (gt zenon_TB_ec (succ (n0)))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H109. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H164. % 90.52/90.76 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 90.52/90.76 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.76 congruence. % 90.52/90.76 apply zenon_Ha1. apply refl_equal. % 90.52/90.76 exact (zenon_Hb0 zenon_H12e). % 90.52/90.76 apply (zenon_L172_ zenon_TB_ec); trivial. % 90.52/90.76 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 90.52/90.76 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_Hb0. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_Hb1. % 90.52/90.76 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.76 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.76 congruence. % 90.52/90.76 exact (zenon_Hb3 successor_1). % 90.52/90.76 apply zenon_Hb2. apply refl_equal. % 90.52/90.76 apply zenon_Hb2. apply refl_equal. % 90.52/90.76 (* end of lemma zenon_L173_ *) % 90.52/90.76 assert (zenon_L174_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (succ (n0)))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n3))) -> (~((tptp_minus_1) = (n3))) -> False). % 90.52/90.76 do 1 intro. intros zenon_H73 zenon_H10a zenon_H68 zenon_H97 zenon_Hb6 zenon_He8. % 90.52/90.76 elim (classic (gt zenon_TB_ec (succ (n0)))); [ zenon_intro zenon_H10b | zenon_intro zenon_H109 ]. % 90.52/90.76 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.76 generalize (zenon_Hd1 zenon_TB_ec). zenon_intro zenon_Hd2. % 90.52/90.76 generalize (zenon_Hd2 (succ (n0))). zenon_intro zenon_H10c. % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H10c); [ zenon_intro zenon_Hab | zenon_intro zenon_H10d ]. % 90.52/90.76 exact (zenon_Hab zenon_H97). % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H10d); [ zenon_intro zenon_H109 | zenon_intro zenon_H10e ]. % 90.52/90.76 exact (zenon_H109 zenon_H10b). % 90.52/90.76 exact (zenon_H10a zenon_H10e). % 90.52/90.76 apply (zenon_L173_ zenon_TB_ec); trivial. % 90.52/90.76 (* end of lemma zenon_L174_ *) % 90.52/90.76 assert (zenon_L175_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (succ (succ (n0))))) -> (~((tptp_minus_1) = (n3))) -> (~(zenon_TB_ec = (n3))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.76 do 1 intro. intros zenon_H73 zenon_H1ea zenon_He8 zenon_Hb6 zenon_H97 zenon_H68. % 90.52/90.76 elim (classic (gt (succ (tptp_minus_1)) (succ (n0)))); [ zenon_intro zenon_H10e | zenon_intro zenon_H10a ]. % 90.52/90.76 elim (classic (gt (succ (tptp_minus_1)) (n1))); [ zenon_intro zenon_H167 | zenon_intro zenon_Hac ]. % 90.52/90.76 elim (classic (gt (n1) (succ (succ (n0))))); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H1f0 ]. % 90.52/90.76 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.76 generalize (zenon_Hd1 (n1)). zenon_intro zenon_H1d1. % 90.52/90.76 generalize (zenon_H1d1 (succ (succ (n0)))). zenon_intro zenon_H2b3. % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H2b3); [ zenon_intro zenon_Hac | zenon_intro zenon_H2b4 ]. % 90.52/90.76 exact (zenon_Hac zenon_H167). % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H2b4); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H1f1 ]. % 90.52/90.76 exact (zenon_H1f0 zenon_H1f5). % 90.52/90.76 exact (zenon_H1ea zenon_H1f1). % 90.52/90.76 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_H12e | zenon_intro zenon_Hb0 ]. % 90.52/90.76 elim (classic (gt (succ (n0)) (succ (succ (n0))))); [ zenon_intro zenon_H2b0 | zenon_intro zenon_H2ab ]. % 90.52/90.76 cut ((gt (succ (n0)) (succ (succ (n0)))) = (gt (n1) (succ (succ (n0))))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H1f0. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H2b0. % 90.52/90.76 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 90.52/90.76 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.76 congruence. % 90.52/90.76 elim (classic ((n1) = (n1))); [ zenon_intro zenon_H131 | zenon_intro zenon_H66 ]. % 90.52/90.76 cut (((n1) = (n1)) = ((succ (n0)) = (n1))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_Hb3. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H131. % 90.52/90.76 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.76 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 90.52/90.76 congruence. % 90.52/90.76 exact (zenon_Hb0 zenon_H12e). % 90.52/90.76 apply zenon_H66. apply refl_equal. % 90.52/90.76 apply zenon_H66. apply refl_equal. % 90.52/90.76 apply zenon_H1ee. apply refl_equal. % 90.52/90.76 apply (zenon_L171_ zenon_TB_ec); trivial. % 90.52/90.76 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 90.52/90.76 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_Hb0. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_Hb1. % 90.52/90.76 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.76 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.76 congruence. % 90.52/90.76 exact (zenon_Hb3 successor_1). % 90.52/90.76 apply zenon_Hb2. apply refl_equal. % 90.52/90.76 apply zenon_Hb2. apply refl_equal. % 90.52/90.76 cut ((gt (succ (tptp_minus_1)) (succ (n0))) = (gt (succ (tptp_minus_1)) (n1))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_Hac. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H10e. % 90.52/90.76 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.76 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.76 congruence. % 90.52/90.76 apply zenon_H8f. apply refl_equal. % 90.52/90.76 exact (zenon_Hb3 successor_1). % 90.52/90.76 apply (zenon_L174_ zenon_TB_ec); trivial. % 90.52/90.76 (* end of lemma zenon_L175_ *) % 90.52/90.76 assert (zenon_L176_ : forall (zenon_TB_ec : zenon_U), (~((tptp_minus_1) = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~(zenon_TB_ec = (n3))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (succ (succ (n0))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.76 do 1 intro. intros zenon_He8 zenon_Hce zenon_Hb6 zenon_H97 zenon_H68 zenon_H2b5 zenon_H73. % 90.52/90.76 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 90.52/90.76 elim (classic (gt (succ (tptp_minus_1)) (succ (succ (n0))))); [ zenon_intro zenon_H1f1 | zenon_intro zenon_H1ea ]. % 90.52/90.76 elim (classic (gt (n0) (succ (succ (n0))))); [ zenon_intro zenon_H2b6 | zenon_intro zenon_H2b7 ]. % 90.52/90.76 cut ((gt (n0) (succ (succ (n0)))) = (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (succ (n0))))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H2b5. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H2b6. % 90.52/90.76 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 90.52/90.76 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 90.52/90.76 congruence. % 90.52/90.76 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd9 | zenon_intro zenon_Hda ]. % 90.52/90.76 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_Hd7. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_Hd9. % 90.52/90.76 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.76 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 90.52/90.76 congruence. % 90.52/90.76 exact (zenon_Hdb zenon_Hce). % 90.52/90.76 apply zenon_Hda. apply refl_equal. % 90.52/90.76 apply zenon_Hda. apply refl_equal. % 90.52/90.76 apply zenon_H1ee. apply refl_equal. % 90.52/90.76 cut ((gt (succ (tptp_minus_1)) (succ (succ (n0)))) = (gt (n0) (succ (succ (n0))))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H2b7. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H1f1. % 90.52/90.76 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 90.52/90.76 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.76 congruence. % 90.52/90.76 elim (classic ((n0) = (n0))); [ zenon_intro zenon_Hca | zenon_intro zenon_H67 ]. % 90.52/90.76 cut (((n0) = (n0)) = ((succ (tptp_minus_1)) = (n0))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_Hc3. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_Hca. % 90.52/90.76 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.76 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.76 congruence. % 90.52/90.76 exact (zenon_H72 zenon_H71). % 90.52/90.76 apply zenon_H67. apply refl_equal. % 90.52/90.76 apply zenon_H67. apply refl_equal. % 90.52/90.76 apply zenon_H1ee. apply refl_equal. % 90.52/90.76 apply (zenon_L175_ zenon_TB_ec); trivial. % 90.52/90.76 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.76 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H72. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_Hc2. % 90.52/90.76 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.76 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.76 congruence. % 90.52/90.76 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.76 apply zenon_H8f. apply refl_equal. % 90.52/90.76 apply zenon_H8f. apply refl_equal. % 90.52/90.76 (* end of lemma zenon_L176_ *) % 90.52/90.76 assert (zenon_L177_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (n2))) -> (~((tptp_minus_1) = (n3))) -> (~(zenon_TB_ec = (n3))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False). % 90.52/90.76 do 1 intro. intros zenon_H73 zenon_H2b8 zenon_He8 zenon_Hb6 zenon_H97 zenon_H68 zenon_Hce. % 90.52/90.76 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (succ (n0))))); [ zenon_intro zenon_H2b9 | zenon_intro zenon_H2b5 ]. % 90.52/90.76 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (succ (succ (n0)))) = (gt (sum (n0) (tptp_minus_1) zenon_E) (n2))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H2b8. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H2b9. % 90.52/90.76 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 90.52/90.76 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.76 congruence. % 90.52/90.76 apply zenon_Hda. apply refl_equal. % 90.52/90.76 exact (zenon_H1ef successor_2). % 90.52/90.76 apply (zenon_L176_ zenon_TB_ec); trivial. % 90.52/90.76 (* end of lemma zenon_L177_ *) % 90.52/90.76 assert (zenon_L178_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n3))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (n0))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False). % 90.52/90.76 do 1 intro. intros zenon_H68 zenon_H97 zenon_Hb6 zenon_H73 zenon_Hdf zenon_Hce. % 90.52/90.76 apply (zenon_L116_ zenon_TB_ec); trivial. % 90.52/90.76 (* end of lemma zenon_L178_ *) % 90.52/90.76 assert (zenon_L179_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~(zenon_TB_ec = (n3))) -> (~(gt (n0) (n2))) -> (~((tptp_minus_1) = (n3))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False). % 90.52/90.76 do 1 intro. intros zenon_H68 zenon_H97 zenon_Hb6 zenon_H149 zenon_He8 zenon_H73 zenon_Hce. % 90.52/90.76 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 90.52/90.76 elim (classic (gt (n0) (n0))); [ zenon_intro zenon_H1b4 | zenon_intro zenon_Hdf ]. % 90.52/90.76 elim (classic (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hde ]. % 90.52/90.76 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (n2))); [ zenon_intro zenon_H2ba | zenon_intro zenon_H2b8 ]. % 90.52/90.76 generalize (zenon_H73 (n0)). zenon_intro zenon_H115. % 90.52/90.76 generalize (zenon_H115 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H1e1. % 90.52/90.76 generalize (zenon_H1e1 (n2)). zenon_intro zenon_H2bb. % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H2bb); [ zenon_intro zenon_Hde | zenon_intro zenon_H2bc ]. % 90.52/90.76 exact (zenon_Hde zenon_Hdd). % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H2bc); [ zenon_intro zenon_H2b8 | zenon_intro zenon_H14b ]. % 90.52/90.76 exact (zenon_H2b8 zenon_H2ba). % 90.52/90.76 exact (zenon_H149 zenon_H14b). % 90.52/90.76 apply (zenon_L177_ zenon_TB_ec); trivial. % 90.52/90.76 cut ((gt (n0) (n0)) = (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_Hde. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H1b4. % 90.52/90.76 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 90.52/90.76 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.76 congruence. % 90.52/90.76 apply zenon_H67. apply refl_equal. % 90.52/90.76 exact (zenon_Hd7 zenon_Hd6). % 90.52/90.76 apply (zenon_L178_ zenon_TB_ec); trivial. % 90.52/90.76 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd9 | zenon_intro zenon_Hda ]. % 90.52/90.76 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_Hd7. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_Hd9. % 90.52/90.76 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.76 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 90.52/90.76 congruence. % 90.52/90.76 exact (zenon_Hdb zenon_Hce). % 90.52/90.76 apply zenon_Hda. apply refl_equal. % 90.52/90.76 apply zenon_Hda. apply refl_equal. % 90.52/90.76 (* end of lemma zenon_L179_ *) % 90.52/90.76 assert (zenon_L180_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(zenon_TB_ec = (n3))) -> (~((tptp_minus_1) = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (~(leq (n0) (tptp_minus_1))) -> False). % 90.52/90.76 do 1 intro. intros zenon_H73 zenon_Hb6 zenon_He8 zenon_Hce zenon_H97 zenon_H68 zenon_Hed. % 90.52/90.76 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H6b. % 90.52/90.76 generalize (zenon_H6b (tptp_minus_1)). zenon_intro zenon_Hee. % 90.52/90.76 apply (zenon_equiv_s _ _ zenon_Hee); [ zenon_intro zenon_Hed; zenon_intro zenon_Hbf | zenon_intro zenon_Hef; zenon_intro zenon_Hc1 ]. % 90.52/90.76 elim (classic ((~((succ (tptp_minus_1)) = (n2)))/\(~(gt (succ (tptp_minus_1)) (n2))))); [ zenon_intro zenon_H250 | zenon_intro zenon_H251 ]. % 90.52/90.76 apply (zenon_and_s _ _ zenon_H250). zenon_intro zenon_H252. zenon_intro zenon_H1da. % 90.52/90.76 elim (classic ((~((succ (tptp_minus_1)) = (succ zenon_TB_ec)))/\(~(gt (succ (tptp_minus_1)) (succ zenon_TB_ec))))); [ zenon_intro zenon_H2bd | zenon_intro zenon_H2be ]. % 90.52/90.76 apply (zenon_and_s _ _ zenon_H2bd). zenon_intro zenon_H2bf. zenon_intro zenon_H1d5. % 90.52/90.76 apply (zenon_L158_ zenon_TB_ec); trivial. % 90.52/90.76 elim (classic (gt (n0) (n2))); [ zenon_intro zenon_H14b | zenon_intro zenon_H149 ]. % 90.52/90.76 generalize (zenon_H73 (succ zenon_TB_ec)). zenon_intro zenon_H11d. % 90.52/90.76 generalize (zenon_H11d (n0)). zenon_intro zenon_H11e. % 90.52/90.76 generalize (zenon_H11e (n2)). zenon_intro zenon_H2c0. % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H2c0); [ zenon_intro zenon_H6e | zenon_intro zenon_H2c1 ]. % 90.52/90.76 exact (zenon_H6e zenon_H68). % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H2c1); [ zenon_intro zenon_H149 | zenon_intro zenon_H2c2 ]. % 90.52/90.76 exact (zenon_H149 zenon_H14b). % 90.52/90.76 cut ((gt (succ zenon_TB_ec) (n2)) = (gt (succ (tptp_minus_1)) (n2))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H1da. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H2c2. % 90.52/90.76 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 90.52/90.76 cut (((succ zenon_TB_ec) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H2c3]. % 90.52/90.76 congruence. % 90.52/90.76 apply (zenon_notand_s _ _ zenon_H2be); [ zenon_intro zenon_H2c5 | zenon_intro zenon_H2c4 ]. % 90.52/90.76 apply zenon_H2c5. zenon_intro zenon_H2c6. % 90.52/90.76 apply zenon_H2c3. apply sym_equal. exact zenon_H2c6. % 90.52/90.76 apply zenon_H2c4. zenon_intro zenon_H1d9. % 90.52/90.76 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.76 generalize (zenon_Hd1 (succ zenon_TB_ec)). zenon_intro zenon_H2c7. % 90.52/90.76 generalize (zenon_H2c7 (n2)). zenon_intro zenon_H2c8. % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H2c8); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H2c9 ]. % 90.52/90.76 exact (zenon_H1d5 zenon_H1d9). % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H2c9); [ zenon_intro zenon_H2ca | zenon_intro zenon_H1dd ]. % 90.52/90.76 exact (zenon_H2ca zenon_H2c2). % 90.52/90.76 exact (zenon_H1da zenon_H1dd). % 90.52/90.76 apply zenon_H65. apply refl_equal. % 90.52/90.76 apply (zenon_L179_ zenon_TB_ec); trivial. % 90.52/90.76 cut ((gt (n2) (n0)) = (gt (succ (tptp_minus_1)) (n0))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_Hbf. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact gt_2_0. % 90.52/90.76 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.76 cut (((n2) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H253]. % 90.52/90.76 congruence. % 90.52/90.76 apply (zenon_notand_s _ _ zenon_H251); [ zenon_intro zenon_H255 | zenon_intro zenon_H254 ]. % 90.52/90.76 apply zenon_H255. zenon_intro zenon_H256. % 90.52/90.76 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.76 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n2) = (succ (tptp_minus_1)))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H253. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_Hc2. % 90.52/90.76 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.76 cut (((succ (tptp_minus_1)) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H252]. % 90.52/90.76 congruence. % 90.52/90.76 exact (zenon_H252 zenon_H256). % 90.52/90.76 apply zenon_H8f. apply refl_equal. % 90.52/90.76 apply zenon_H8f. apply refl_equal. % 90.52/90.76 apply zenon_H254. zenon_intro zenon_H1dd. % 90.52/90.76 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.76 generalize (zenon_Hd1 (n2)). zenon_intro zenon_H257. % 90.52/90.76 generalize (zenon_H257 (n0)). zenon_intro zenon_H258. % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H258); [ zenon_intro zenon_H1da | zenon_intro zenon_H259 ]. % 90.52/90.76 exact (zenon_H1da zenon_H1dd). % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H259); [ zenon_intro zenon_H194 | zenon_intro zenon_Hc1 ]. % 90.52/90.76 exact (zenon_H194 gt_2_0). % 90.52/90.76 exact (zenon_Hbf zenon_Hc1). % 90.52/90.76 apply zenon_H67. apply refl_equal. % 90.52/90.76 exact (zenon_Hed zenon_Hef). % 90.52/90.76 (* end of lemma zenon_L180_ *) % 90.52/90.76 assert (zenon_L181_ : forall (zenon_TB_ec : zenon_U), (gt (succ (tptp_minus_1)) zenon_TB_ec) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (n0))) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.76 do 1 intro. intros zenon_H97 zenon_Hce zenon_H73 zenon_Hdf zenon_H68. % 90.52/90.76 elim (classic ((~((n0) = (succ zenon_TB_ec)))/\(~(gt (n0) (succ zenon_TB_ec))))); [ zenon_intro zenon_H2cb | zenon_intro zenon_H2cc ]. % 90.52/90.76 apply (zenon_and_s _ _ zenon_H2cb). zenon_intro zenon_H2cd. zenon_intro zenon_H1de. % 90.52/90.76 apply (zenon_L151_ zenon_TB_ec); trivial. % 90.52/90.76 cut ((gt (succ zenon_TB_ec) (n0)) = (gt (n0) (n0))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_Hdf. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H68. % 90.52/90.76 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.76 cut (((succ zenon_TB_ec) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H2ce]. % 90.52/90.76 congruence. % 90.52/90.76 apply (zenon_notand_s _ _ zenon_H2cc); [ zenon_intro zenon_H2d0 | zenon_intro zenon_H2cf ]. % 90.52/90.76 apply zenon_H2d0. zenon_intro zenon_H2d1. % 90.52/90.76 elim (classic ((n0) = (n0))); [ zenon_intro zenon_Hca | zenon_intro zenon_H67 ]. % 90.52/90.76 cut (((n0) = (n0)) = ((succ zenon_TB_ec) = (n0))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H2ce. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_Hca. % 90.52/90.76 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.76 cut (((n0) = (succ zenon_TB_ec))); [idtac | apply NNPP; zenon_intro zenon_H2cd]. % 90.52/90.76 congruence. % 90.52/90.76 exact (zenon_H2cd zenon_H2d1). % 90.52/90.76 apply zenon_H67. apply refl_equal. % 90.52/90.76 apply zenon_H67. apply refl_equal. % 90.52/90.76 apply zenon_H2cf. zenon_intro zenon_H1e4. % 90.52/90.76 generalize (zenon_H73 (n0)). zenon_intro zenon_H115. % 90.52/90.76 generalize (zenon_H115 (succ zenon_TB_ec)). zenon_intro zenon_H2d2. % 90.52/90.76 generalize (zenon_H2d2 (n0)). zenon_intro zenon_H2d3. % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H2d3); [ zenon_intro zenon_H1de | zenon_intro zenon_H2d4 ]. % 90.52/90.76 exact (zenon_H1de zenon_H1e4). % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H2d4); [ zenon_intro zenon_H6e | zenon_intro zenon_H1b4 ]. % 90.52/90.76 exact (zenon_H6e zenon_H68). % 90.52/90.76 exact (zenon_Hdf zenon_H1b4). % 90.52/90.76 apply zenon_H67. apply refl_equal. % 90.52/90.76 (* end of lemma zenon_L181_ *) % 90.52/90.76 assert (zenon_L182_ : ((tptp_minus_1) = (n0)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (tptp_minus_1) (tptp_minus_1))) -> False). % 90.52/90.76 do 0 intro. intros zenon_H103 zenon_H73 zenon_H2d5. % 90.52/90.76 elim (classic ((~((tptp_minus_1) = (n0)))/\(~(gt (tptp_minus_1) (n0))))); [ zenon_intro zenon_H2d6 | zenon_intro zenon_H2d7 ]. % 90.52/90.76 apply (zenon_and_s _ _ zenon_H2d6). zenon_intro zenon_He5. zenon_intro zenon_H190. % 90.52/90.76 exact (zenon_He5 zenon_H103). % 90.52/90.76 cut ((gt (n0) (tptp_minus_1)) = (gt (tptp_minus_1) (tptp_minus_1))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H2d5. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact gt_0_tptp_minus_1. % 90.52/90.76 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_He4]. % 90.52/90.76 cut (((n0) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_H112]. % 90.52/90.76 congruence. % 90.52/90.76 apply (zenon_notand_s _ _ zenon_H2d7); [ zenon_intro zenon_H2d9 | zenon_intro zenon_H2d8 ]. % 90.52/90.76 apply zenon_H2d9. zenon_intro zenon_H103. % 90.52/90.76 elim (classic ((tptp_minus_1) = (tptp_minus_1))); [ zenon_intro zenon_H113 | zenon_intro zenon_He4 ]. % 90.52/90.76 cut (((tptp_minus_1) = (tptp_minus_1)) = ((n0) = (tptp_minus_1))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H112. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H113. % 90.52/90.76 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_He4]. % 90.52/90.76 cut (((tptp_minus_1) = (n0))); [idtac | apply NNPP; zenon_intro zenon_He5]. % 90.52/90.76 congruence. % 90.52/90.76 exact (zenon_He5 zenon_H103). % 90.52/90.76 apply zenon_He4. apply refl_equal. % 90.52/90.76 apply zenon_He4. apply refl_equal. % 90.52/90.76 apply zenon_H2d8. zenon_intro zenon_H193. % 90.52/90.76 generalize (zenon_H73 (tptp_minus_1)). zenon_intro zenon_H171. % 90.52/90.76 generalize (zenon_H171 (n0)). zenon_intro zenon_H2da. % 90.52/90.76 generalize (zenon_H2da (tptp_minus_1)). zenon_intro zenon_H2db. % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H2db); [ zenon_intro zenon_H190 | zenon_intro zenon_H2dc ]. % 90.52/90.76 exact (zenon_H190 zenon_H193). % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H2dc); [ zenon_intro zenon_H101 | zenon_intro zenon_H2dd ]. % 90.52/90.76 exact (zenon_H101 gt_0_tptp_minus_1). % 90.52/90.76 exact (zenon_H2d5 zenon_H2dd). % 90.52/90.76 apply zenon_He4. apply refl_equal. % 90.52/90.76 (* end of lemma zenon_L182_ *) % 90.52/90.76 assert (zenon_L183_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (tptp_minus_1) (succ (tptp_minus_1)))) -> ((tptp_minus_1) = (n0)) -> False). % 90.52/90.76 do 0 intro. intros zenon_H73 zenon_H2de zenon_H103. % 90.52/90.76 elim (classic (gt (tptp_minus_1) (tptp_minus_1))); [ zenon_intro zenon_H2dd | zenon_intro zenon_H2d5 ]. % 90.52/90.76 elim (classic (gt (tptp_minus_1) (n0))); [ zenon_intro zenon_H193 | zenon_intro zenon_H190 ]. % 90.52/90.76 cut ((gt (tptp_minus_1) (n0)) = (gt (tptp_minus_1) (succ (tptp_minus_1)))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H2de. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H193. % 90.52/90.76 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.76 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_He4]. % 90.52/90.76 congruence. % 90.52/90.76 apply zenon_He4. apply refl_equal. % 90.52/90.76 apply zenon_H72. apply sym_equal. exact succ_tptp_minus_1. % 90.52/90.76 cut ((gt (tptp_minus_1) (tptp_minus_1)) = (gt (tptp_minus_1) (n0))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H190. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H2dd. % 90.52/90.76 cut (((tptp_minus_1) = (n0))); [idtac | apply NNPP; zenon_intro zenon_He5]. % 90.52/90.76 cut (((tptp_minus_1) = (tptp_minus_1))); [idtac | apply NNPP; zenon_intro zenon_He4]. % 90.52/90.76 congruence. % 90.52/90.76 apply zenon_He4. apply refl_equal. % 90.52/90.76 exact (zenon_He5 zenon_H103). % 90.52/90.76 apply (zenon_L182_); trivial. % 90.52/90.76 (* end of lemma zenon_L183_ *) % 90.52/90.76 assert (zenon_L184_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (gt (succ zenon_TB_ec) (n0)) -> ((tptp_minus_1) = (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> False). % 90.52/90.76 do 1 intro. intros zenon_H73 zenon_H68 zenon_H103 zenon_H97. % 90.52/90.76 generalize (finite_domain_0 zenon_TB_ec). zenon_intro zenon_H1c6. % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H1c6); [ zenon_intro zenon_H1c7 | zenon_intro zenon_Hbb ]. % 90.52/90.76 apply (zenon_notand_s _ _ zenon_H1c7); [ zenon_intro zenon_H69 | zenon_intro zenon_H1c2 ]. % 90.52/90.76 apply (zenon_L5_ zenon_TB_ec); trivial. % 90.52/90.76 apply (zenon_L73_ zenon_TB_ec); trivial. % 90.52/90.76 generalize (irreflexivity_gt zenon_TB_ec). zenon_intro zenon_H293. % 90.52/90.76 elim (classic ((~(zenon_TB_ec = (succ (tptp_minus_1))))/\(~(gt zenon_TB_ec (succ (tptp_minus_1)))))); [ zenon_intro zenon_H294 | zenon_intro zenon_H295 ]. % 90.52/90.76 apply (zenon_and_s _ _ zenon_H294). zenon_intro zenon_H296. zenon_intro zenon_Hc4. % 90.52/90.76 elim (classic (gt (n0) (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hc7 ]. % 90.52/90.76 cut ((gt (n0) (succ (tptp_minus_1))) = (gt zenon_TB_ec (succ (tptp_minus_1)))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_Hc4. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_Hc6. % 90.52/90.76 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.76 cut (((n0) = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Hc8]. % 90.52/90.76 congruence. % 90.52/90.76 elim (classic (zenon_TB_ec = zenon_TB_ec)); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Ha1 ]. % 90.52/90.76 cut ((zenon_TB_ec = zenon_TB_ec) = ((n0) = zenon_TB_ec)). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_Hc8. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_Hc9. % 90.52/90.76 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.76 cut ((zenon_TB_ec = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hb4]. % 90.52/90.76 congruence. % 90.52/90.76 exact (zenon_Hb4 zenon_Hbb). % 90.52/90.76 apply zenon_Ha1. apply refl_equal. % 90.52/90.76 apply zenon_Ha1. apply refl_equal. % 90.52/90.76 apply zenon_H8f. apply refl_equal. % 90.52/90.76 elim (classic (gt (tptp_minus_1) (succ (tptp_minus_1)))); [ zenon_intro zenon_H2df | zenon_intro zenon_H2de ]. % 90.52/90.76 generalize (zenon_H73 (n0)). zenon_intro zenon_H115. % 90.52/90.76 generalize (zenon_H115 (tptp_minus_1)). zenon_intro zenon_H116. % 90.52/90.76 generalize (zenon_H116 (succ (tptp_minus_1))). zenon_intro zenon_H2e0. % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H2e0); [ zenon_intro zenon_H101 | zenon_intro zenon_H2e1 ]. % 90.52/90.76 exact (zenon_H101 gt_0_tptp_minus_1). % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H2e1); [ zenon_intro zenon_H2de | zenon_intro zenon_Hc6 ]. % 90.52/90.76 exact (zenon_H2de zenon_H2df). % 90.52/90.76 exact (zenon_Hc7 zenon_Hc6). % 90.52/90.76 apply (zenon_L183_); trivial. % 90.52/90.76 cut ((gt (succ (tptp_minus_1)) zenon_TB_ec) = (gt zenon_TB_ec zenon_TB_ec)). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H293. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H97. % 90.52/90.76 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.76 cut (((succ (tptp_minus_1)) = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_H297]. % 90.52/90.76 congruence. % 90.52/90.76 apply (zenon_notand_s _ _ zenon_H295); [ zenon_intro zenon_H299 | zenon_intro zenon_H298 ]. % 90.52/90.76 apply zenon_H299. zenon_intro zenon_H29a. % 90.52/90.76 elim (classic (zenon_TB_ec = zenon_TB_ec)); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Ha1 ]. % 90.52/90.76 cut ((zenon_TB_ec = zenon_TB_ec) = ((succ (tptp_minus_1)) = zenon_TB_ec)). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H297. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_Hc9. % 90.52/90.76 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.76 cut ((zenon_TB_ec = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H296]. % 90.52/90.76 congruence. % 90.52/90.76 exact (zenon_H296 zenon_H29a). % 90.52/90.76 apply zenon_Ha1. apply refl_equal. % 90.52/90.76 apply zenon_Ha1. apply refl_equal. % 90.52/90.76 apply zenon_H298. zenon_intro zenon_Hcc. % 90.52/90.76 generalize (zenon_H73 zenon_TB_ec). zenon_intro zenon_H144. % 90.52/90.76 generalize (zenon_H144 (succ (tptp_minus_1))). zenon_intro zenon_H145. % 90.52/90.76 generalize (zenon_H145 zenon_TB_ec). zenon_intro zenon_H29b. % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H29b); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H29c ]. % 90.52/90.76 exact (zenon_Hc4 zenon_Hcc). % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H29c); [ zenon_intro zenon_Hab | zenon_intro zenon_H29d ]. % 90.52/90.76 exact (zenon_Hab zenon_H97). % 90.52/90.76 exact (zenon_H293 zenon_H29d). % 90.52/90.76 apply zenon_Ha1. apply refl_equal. % 90.52/90.76 (* end of lemma zenon_L184_ *) % 90.52/90.76 assert (zenon_L185_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(zenon_TB_ec = (n3))) -> (~((tptp_minus_1) = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.76 do 1 intro. intros zenon_H73 zenon_Hb6 zenon_He8 zenon_Hce zenon_H97 zenon_H68. % 90.52/90.76 generalize (finite_domain_0 (tptp_minus_1)). zenon_intro zenon_H1c8. % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H1c8); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H103 ]. % 90.52/90.76 apply (zenon_notand_s _ _ zenon_H1c9); [ zenon_intro zenon_Hed | zenon_intro zenon_H1b5 ]. % 90.52/90.76 apply (zenon_L180_ zenon_TB_ec); trivial. % 90.52/90.76 apply (zenon_L71_); trivial. % 90.52/90.76 apply (zenon_L184_ zenon_TB_ec); trivial. % 90.52/90.76 (* end of lemma zenon_L185_ *) % 90.52/90.76 assert (zenon_L186_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (succ (n0))) (n3))) -> (~((tptp_minus_1) = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.76 do 1 intro. intros zenon_H73 zenon_H2e2 zenon_He8 zenon_Hce zenon_H97 zenon_H68. % 90.52/90.76 elim (classic ((~((succ (succ (n0))) = (succ (tptp_minus_1))))/\(~(gt (succ (succ (n0))) (succ (tptp_minus_1)))))); [ zenon_intro zenon_H29e | zenon_intro zenon_H29f ]. % 90.52/90.76 apply (zenon_and_s _ _ zenon_H29e). zenon_intro zenon_H2a0. zenon_intro zenon_H28f. % 90.52/90.76 apply (zenon_L159_); trivial. % 90.52/90.76 elim (classic (zenon_TB_ec = (n3))); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hb6 ]. % 90.52/90.76 cut ((gt (succ (tptp_minus_1)) zenon_TB_ec) = (gt (succ (succ (n0))) (n3))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H2e2. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H97. % 90.52/90.76 cut ((zenon_TB_ec = (n3))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 90.52/90.76 cut (((succ (tptp_minus_1)) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H2a1]. % 90.52/90.76 congruence. % 90.52/90.76 apply (zenon_notand_s _ _ zenon_H29f); [ zenon_intro zenon_H2a3 | zenon_intro zenon_H2a2 ]. % 90.52/90.76 apply zenon_H2a3. zenon_intro zenon_H2a4. % 90.52/90.76 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1ee ]. % 90.52/90.76 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((succ (tptp_minus_1)) = (succ (succ (n0))))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H2a1. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H1ed. % 90.52/90.76 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 90.52/90.76 cut (((succ (succ (n0))) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H2a0]. % 90.52/90.76 congruence. % 90.52/90.76 exact (zenon_H2a0 zenon_H2a4). % 90.52/90.76 apply zenon_H1ee. apply refl_equal. % 90.52/90.76 apply zenon_H1ee. apply refl_equal. % 90.52/90.76 apply zenon_H2a2. zenon_intro zenon_H292. % 90.52/90.76 generalize (zenon_H73 (succ (succ (n0)))). zenon_intro zenon_H202. % 90.52/90.76 generalize (zenon_H202 (succ (tptp_minus_1))). zenon_intro zenon_H2a5. % 90.52/90.76 generalize (zenon_H2a5 zenon_TB_ec). zenon_intro zenon_H2a6. % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H2a6); [ zenon_intro zenon_H28f | zenon_intro zenon_H2a7 ]. % 90.52/90.76 exact (zenon_H28f zenon_H292). % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H2a7); [ zenon_intro zenon_Hab | zenon_intro zenon_H2a8 ]. % 90.52/90.76 exact (zenon_Hab zenon_H97). % 90.52/90.76 cut ((gt (succ (succ (n0))) zenon_TB_ec) = (gt (succ (succ (n0))) (n3))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H2e2. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H2a8. % 90.52/90.76 cut ((zenon_TB_ec = (n3))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 90.52/90.76 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 90.52/90.76 congruence. % 90.52/90.76 apply zenon_H1ee. apply refl_equal. % 90.52/90.76 exact (zenon_Hb6 zenon_Hbd). % 90.52/90.76 exact (zenon_Hb6 zenon_Hbd). % 90.52/90.76 apply (zenon_L185_ zenon_TB_ec); trivial. % 90.52/90.76 (* end of lemma zenon_L186_ *) % 90.52/90.76 assert (zenon_L187_ : forall (zenon_TB_ec : zenon_U), (~((tptp_minus_1) = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (~(gt (n2) (n3))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.76 do 1 intro. intros zenon_He8 zenon_Hce zenon_H97 zenon_H68 zenon_H207 zenon_H73. % 90.52/90.76 elim (classic ((n2) = (succ (succ (n0))))); [ zenon_intro zenon_H1eb | zenon_intro zenon_H1ec ]. % 90.52/90.76 elim (classic (gt (succ (succ (n0))) (n3))); [ zenon_intro zenon_H2e3 | zenon_intro zenon_H2e2 ]. % 90.52/90.76 cut ((gt (succ (succ (n0))) (n3)) = (gt (n2) (n3))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H207. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H2e3. % 90.52/90.76 cut (((n3) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 90.52/90.76 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 90.52/90.76 congruence. % 90.52/90.76 elim (classic ((n2) = (n2))); [ zenon_intro zenon_H1fc | zenon_intro zenon_H65 ]. % 90.52/90.76 cut (((n2) = (n2)) = ((succ (succ (n0))) = (n2))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H1ef. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H1fc. % 90.52/90.76 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 90.52/90.76 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ec]. % 90.52/90.76 congruence. % 90.52/90.76 exact (zenon_H1ec zenon_H1eb). % 90.52/90.76 apply zenon_H65. apply refl_equal. % 90.52/90.76 apply zenon_H65. apply refl_equal. % 90.52/90.76 apply zenon_H64. apply refl_equal. % 90.52/90.76 apply (zenon_L186_ zenon_TB_ec); trivial. % 90.52/90.76 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1ee ]. % 90.52/90.76 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((n2) = (succ (succ (n0))))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H1ec. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H1ed. % 90.52/90.76 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 90.52/90.76 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 90.52/90.76 congruence. % 90.52/90.76 exact (zenon_H1ef successor_2). % 90.52/90.76 apply zenon_H1ee. apply refl_equal. % 90.52/90.76 apply zenon_H1ee. apply refl_equal. % 90.52/90.76 (* end of lemma zenon_L187_ *) % 90.52/90.76 assert (zenon_L188_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n3) (n3))) -> (~((tptp_minus_1) = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.76 do 1 intro. intros zenon_H73 zenon_H25a zenon_He8 zenon_Hce zenon_H97 zenon_H68. % 90.52/90.76 elim (classic (gt (n2) (n3))); [ zenon_intro zenon_H20a | zenon_intro zenon_H207 ]. % 90.52/90.76 generalize (zenon_H73 (n3)). zenon_intro zenon_H7d. % 90.52/90.76 generalize (zenon_H7d (n2)). zenon_intro zenon_H7e. % 90.52/90.76 generalize (zenon_H7e (n3)). zenon_intro zenon_H25b. % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H25b); [ zenon_intro zenon_H81 | zenon_intro zenon_H25c ]. % 90.52/90.76 exact (zenon_H81 gt_3_2). % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H25c); [ zenon_intro zenon_H207 | zenon_intro zenon_H25d ]. % 90.52/90.76 exact (zenon_H207 zenon_H20a). % 90.52/90.76 exact (zenon_H25a zenon_H25d). % 90.52/90.76 apply (zenon_L187_ zenon_TB_ec); trivial. % 90.52/90.76 (* end of lemma zenon_L188_ *) % 90.52/90.76 assert (zenon_L189_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~((tptp_minus_1) = (n3))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n2) (n2))) -> False). % 90.52/90.76 do 1 intro. intros zenon_H68 zenon_H97 zenon_Hce zenon_He8 zenon_H73 zenon_H1f9. % 90.52/90.76 elim (classic ((~((n2) = (n3)))/\(~(gt (n2) (n3))))); [ zenon_intro zenon_H212 | zenon_intro zenon_H213 ]. % 90.52/90.76 apply (zenon_and_s _ _ zenon_H212). zenon_intro zenon_H214. zenon_intro zenon_H207. % 90.52/90.76 apply (zenon_L187_ zenon_TB_ec); trivial. % 90.52/90.76 cut ((gt (n3) (n2)) = (gt (n2) (n2))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H1f9. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact gt_3_2. % 90.52/90.76 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 90.52/90.76 cut (((n3) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H215]. % 90.52/90.76 congruence. % 90.52/90.76 apply (zenon_notand_s _ _ zenon_H213); [ zenon_intro zenon_H217 | zenon_intro zenon_H216 ]. % 90.52/90.76 apply zenon_H217. zenon_intro zenon_H218. % 90.52/90.76 elim (classic ((n2) = (n2))); [ zenon_intro zenon_H1fc | zenon_intro zenon_H65 ]. % 90.52/90.76 cut (((n2) = (n2)) = ((n3) = (n2))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H215. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H1fc. % 90.52/90.76 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 90.52/90.76 cut (((n2) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H214]. % 90.52/90.76 congruence. % 90.52/90.76 exact (zenon_H214 zenon_H218). % 90.52/90.76 apply zenon_H65. apply refl_equal. % 90.52/90.76 apply zenon_H65. apply refl_equal. % 90.52/90.76 apply zenon_H216. zenon_intro zenon_H20a. % 90.52/90.76 generalize (zenon_H73 (n2)). zenon_intro zenon_H76. % 90.52/90.76 generalize (zenon_H76 (n3)). zenon_intro zenon_H219. % 90.52/90.76 generalize (zenon_H219 (n2)). zenon_intro zenon_H21a. % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H21a); [ zenon_intro zenon_H207 | zenon_intro zenon_H21b ]. % 90.52/90.76 exact (zenon_H207 zenon_H20a). % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H21b); [ zenon_intro zenon_H81 | zenon_intro zenon_H21c ]. % 90.52/90.76 exact (zenon_H81 gt_3_2). % 90.52/90.76 exact (zenon_H1f9 zenon_H21c). % 90.52/90.76 apply zenon_H65. apply refl_equal. % 90.52/90.76 (* end of lemma zenon_L189_ *) % 90.52/90.76 assert (zenon_L190_ : forall (zenon_TB_ec : zenon_U), (~((tptp_minus_1) = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (~(gt (n2) (succ (succ (succ (n0)))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.76 do 1 intro. intros zenon_He8 zenon_Hce zenon_H97 zenon_H68 zenon_H20b zenon_H73. % 90.52/90.76 elim (classic ((n2) = (succ (succ (n0))))); [ zenon_intro zenon_H1eb | zenon_intro zenon_H1ec ]. % 90.52/90.76 elim (classic (gt (n2) (n2))); [ zenon_intro zenon_H21c | zenon_intro zenon_H1f9 ]. % 90.52/90.76 elim (classic (gt (n2) (succ (succ (n0))))); [ zenon_intro zenon_H2e4 | zenon_intro zenon_H2e5 ]. % 90.52/90.76 elim (classic (gt (succ (succ (n0))) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H21e | zenon_intro zenon_H210 ]. % 90.52/90.76 generalize (zenon_H73 (n2)). zenon_intro zenon_H76. % 90.52/90.76 generalize (zenon_H76 (succ (succ (n0)))). zenon_intro zenon_H2e6. % 90.52/90.76 generalize (zenon_H2e6 (succ (succ (succ (n0))))). zenon_intro zenon_H2e7. % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H2e7); [ zenon_intro zenon_H2e5 | zenon_intro zenon_H2e8 ]. % 90.52/90.76 exact (zenon_H2e5 zenon_H2e4). % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H2e8); [ zenon_intro zenon_H210 | zenon_intro zenon_H211 ]. % 90.52/90.76 exact (zenon_H210 zenon_H21e). % 90.52/90.76 exact (zenon_H20b zenon_H211). % 90.52/90.76 elim (classic ((n3) = (succ (succ (succ (n0)))))); [ zenon_intro zenon_H20c | zenon_intro zenon_H8b ]. % 90.52/90.76 elim (classic (gt (succ (succ (n0))) (n3))); [ zenon_intro zenon_H2e3 | zenon_intro zenon_H2e2 ]. % 90.52/90.76 cut ((gt (succ (succ (n0))) (n3)) = (gt (succ (succ (n0))) (succ (succ (succ (n0)))))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H210. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H2e3. % 90.52/90.76 cut (((n3) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 90.52/90.76 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 90.52/90.76 congruence. % 90.52/90.76 apply zenon_H1ee. apply refl_equal. % 90.52/90.76 exact (zenon_H8b zenon_H20c). % 90.52/90.76 apply (zenon_L186_ zenon_TB_ec); trivial. % 90.52/90.76 elim (classic ((succ (succ (succ (n0)))) = (succ (succ (succ (n0)))))); [ zenon_intro zenon_H20d | zenon_intro zenon_H20e ]. % 90.52/90.76 cut (((succ (succ (succ (n0)))) = (succ (succ (succ (n0))))) = ((n3) = (succ (succ (succ (n0)))))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H8b. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H20d. % 90.52/90.76 cut (((succ (succ (succ (n0)))) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H20e]. % 90.52/90.76 cut (((succ (succ (succ (n0)))) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H20f]. % 90.52/90.76 congruence. % 90.52/90.76 exact (zenon_H20f successor_3). % 90.52/90.76 apply zenon_H20e. apply refl_equal. % 90.52/90.76 apply zenon_H20e. apply refl_equal. % 90.52/90.76 cut ((gt (n2) (n2)) = (gt (n2) (succ (succ (n0))))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H2e5. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H21c. % 90.52/90.76 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ec]. % 90.52/90.76 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 90.52/90.76 congruence. % 90.52/90.76 apply zenon_H65. apply refl_equal. % 90.52/90.76 exact (zenon_H1ec zenon_H1eb). % 90.52/90.76 apply (zenon_L189_ zenon_TB_ec); trivial. % 90.52/90.76 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1ee ]. % 90.52/90.76 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((n2) = (succ (succ (n0))))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H1ec. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H1ed. % 90.52/90.76 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 90.52/90.76 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 90.52/90.76 congruence. % 90.52/90.76 exact (zenon_H1ef successor_2). % 90.52/90.76 apply zenon_H1ee. apply refl_equal. % 90.52/90.76 apply zenon_H1ee. apply refl_equal. % 90.52/90.76 (* end of lemma zenon_L190_ *) % 90.52/90.76 assert (zenon_L191_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (succ (n0))) (n3))) -> (~(gt (succ (n0)) (succ (succ (n0))))) -> (~((tptp_minus_1) = (n3))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.76 do 1 intro. intros zenon_H73 zenon_H2e2 zenon_H2ab zenon_He8 zenon_H97 zenon_H68. % 90.52/90.76 elim (classic ((~((succ (succ (n0))) = (succ (tptp_minus_1))))/\(~(gt (succ (succ (n0))) (succ (tptp_minus_1)))))); [ zenon_intro zenon_H29e | zenon_intro zenon_H29f ]. % 90.52/90.76 apply (zenon_and_s _ _ zenon_H29e). zenon_intro zenon_H2a0. zenon_intro zenon_H28f. % 90.52/90.76 apply (zenon_L159_); trivial. % 90.52/90.76 elim (classic (zenon_TB_ec = (n3))); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hb6 ]. % 90.52/90.76 cut ((gt (succ (tptp_minus_1)) zenon_TB_ec) = (gt (succ (succ (n0))) (n3))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H2e2. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H97. % 90.52/90.76 cut ((zenon_TB_ec = (n3))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 90.52/90.76 cut (((succ (tptp_minus_1)) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H2a1]. % 90.52/90.76 congruence. % 90.52/90.76 apply (zenon_notand_s _ _ zenon_H29f); [ zenon_intro zenon_H2a3 | zenon_intro zenon_H2a2 ]. % 90.52/90.76 apply zenon_H2a3. zenon_intro zenon_H2a4. % 90.52/90.76 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1ee ]. % 90.52/90.76 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((succ (tptp_minus_1)) = (succ (succ (n0))))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H2a1. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H1ed. % 90.52/90.76 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 90.52/90.76 cut (((succ (succ (n0))) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H2a0]. % 90.52/90.76 congruence. % 90.52/90.76 exact (zenon_H2a0 zenon_H2a4). % 90.52/90.76 apply zenon_H1ee. apply refl_equal. % 90.52/90.76 apply zenon_H1ee. apply refl_equal. % 90.52/90.76 apply zenon_H2a2. zenon_intro zenon_H292. % 90.52/90.76 generalize (zenon_H73 (succ (succ (n0)))). zenon_intro zenon_H202. % 90.52/90.76 generalize (zenon_H202 (succ (tptp_minus_1))). zenon_intro zenon_H2a5. % 90.52/90.76 generalize (zenon_H2a5 zenon_TB_ec). zenon_intro zenon_H2a6. % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H2a6); [ zenon_intro zenon_H28f | zenon_intro zenon_H2a7 ]. % 90.52/90.76 exact (zenon_H28f zenon_H292). % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H2a7); [ zenon_intro zenon_Hab | zenon_intro zenon_H2a8 ]. % 90.52/90.76 exact (zenon_Hab zenon_H97). % 90.52/90.76 cut ((gt (succ (succ (n0))) zenon_TB_ec) = (gt (succ (succ (n0))) (n3))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H2e2. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H2a8. % 90.52/90.76 cut ((zenon_TB_ec = (n3))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 90.52/90.76 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 90.52/90.76 congruence. % 90.52/90.76 apply zenon_H1ee. apply refl_equal. % 90.52/90.76 exact (zenon_Hb6 zenon_Hbd). % 90.52/90.76 exact (zenon_Hb6 zenon_Hbd). % 90.52/90.76 apply (zenon_L171_ zenon_TB_ec); trivial. % 90.52/90.76 (* end of lemma zenon_L191_ *) % 90.52/90.76 assert (zenon_L192_ : forall (zenon_TB_ec : zenon_U), (~(gt (succ (n0)) (succ (succ (n0))))) -> (~((tptp_minus_1) = (n3))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (~(gt (n2) (n3))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.76 do 1 intro. intros zenon_H2ab zenon_He8 zenon_H97 zenon_H68 zenon_H207 zenon_H73. % 90.52/90.76 elim (classic ((n2) = (succ (succ (n0))))); [ zenon_intro zenon_H1eb | zenon_intro zenon_H1ec ]. % 90.52/90.76 elim (classic (gt (succ (succ (n0))) (n3))); [ zenon_intro zenon_H2e3 | zenon_intro zenon_H2e2 ]. % 90.52/90.76 cut ((gt (succ (succ (n0))) (n3)) = (gt (n2) (n3))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H207. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H2e3. % 90.52/90.76 cut (((n3) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 90.52/90.76 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 90.52/90.76 congruence. % 90.52/90.76 elim (classic ((n2) = (n2))); [ zenon_intro zenon_H1fc | zenon_intro zenon_H65 ]. % 90.52/90.76 cut (((n2) = (n2)) = ((succ (succ (n0))) = (n2))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H1ef. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H1fc. % 90.52/90.76 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 90.52/90.76 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ec]. % 90.52/90.76 congruence. % 90.52/90.76 exact (zenon_H1ec zenon_H1eb). % 90.52/90.76 apply zenon_H65. apply refl_equal. % 90.52/90.76 apply zenon_H65. apply refl_equal. % 90.52/90.76 apply zenon_H64. apply refl_equal. % 90.52/90.76 apply (zenon_L191_ zenon_TB_ec); trivial. % 90.52/90.76 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1ee ]. % 90.52/90.76 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((n2) = (succ (succ (n0))))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H1ec. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H1ed. % 90.52/90.76 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 90.52/90.76 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 90.52/90.76 congruence. % 90.52/90.76 exact (zenon_H1ef successor_2). % 90.52/90.76 apply zenon_H1ee. apply refl_equal. % 90.52/90.76 apply zenon_H1ee. apply refl_equal. % 90.52/90.76 (* end of lemma zenon_L192_ *) % 90.52/90.76 assert (zenon_L193_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~((tptp_minus_1) = (n3))) -> (~(gt (succ (n0)) (succ (succ (n0))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n2) (n2))) -> False). % 90.52/90.76 do 1 intro. intros zenon_H68 zenon_H97 zenon_He8 zenon_H2ab zenon_H73 zenon_H1f9. % 90.52/90.76 elim (classic ((~((n2) = (n3)))/\(~(gt (n2) (n3))))); [ zenon_intro zenon_H212 | zenon_intro zenon_H213 ]. % 90.52/90.76 apply (zenon_and_s _ _ zenon_H212). zenon_intro zenon_H214. zenon_intro zenon_H207. % 90.52/90.76 apply (zenon_L192_ zenon_TB_ec); trivial. % 90.52/90.76 cut ((gt (n3) (n2)) = (gt (n2) (n2))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H1f9. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact gt_3_2. % 90.52/90.76 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 90.52/90.76 cut (((n3) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H215]. % 90.52/90.76 congruence. % 90.52/90.76 apply (zenon_notand_s _ _ zenon_H213); [ zenon_intro zenon_H217 | zenon_intro zenon_H216 ]. % 90.52/90.76 apply zenon_H217. zenon_intro zenon_H218. % 90.52/90.76 elim (classic ((n2) = (n2))); [ zenon_intro zenon_H1fc | zenon_intro zenon_H65 ]. % 90.52/90.76 cut (((n2) = (n2)) = ((n3) = (n2))). % 90.52/90.76 intro zenon_D_pnotp. % 90.52/90.76 apply zenon_H215. % 90.52/90.76 rewrite <- zenon_D_pnotp. % 90.52/90.76 exact zenon_H1fc. % 90.52/90.76 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 90.52/90.76 cut (((n2) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H214]. % 90.52/90.76 congruence. % 90.52/90.76 exact (zenon_H214 zenon_H218). % 90.52/90.76 apply zenon_H65. apply refl_equal. % 90.52/90.76 apply zenon_H65. apply refl_equal. % 90.52/90.76 apply zenon_H216. zenon_intro zenon_H20a. % 90.52/90.76 generalize (zenon_H73 (n2)). zenon_intro zenon_H76. % 90.52/90.76 generalize (zenon_H76 (n3)). zenon_intro zenon_H219. % 90.52/90.76 generalize (zenon_H219 (n2)). zenon_intro zenon_H21a. % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H21a); [ zenon_intro zenon_H207 | zenon_intro zenon_H21b ]. % 90.52/90.76 exact (zenon_H207 zenon_H20a). % 90.52/90.76 apply (zenon_imply_s _ _ zenon_H21b); [ zenon_intro zenon_H81 | zenon_intro zenon_H21c ]. % 90.52/90.76 exact (zenon_H81 gt_3_2). % 90.52/90.76 exact (zenon_H1f9 zenon_H21c). % 90.52/90.76 apply zenon_H65. apply refl_equal. % 90.52/90.76 (* end of lemma zenon_L193_ *) % 90.52/90.76 assert (zenon_L194_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n0)) (n2))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~((tptp_minus_1) = (n3))) -> False). % 90.52/90.77 do 1 intro. intros zenon_H73 zenon_H2b1 zenon_H68 zenon_H97 zenon_He8. % 90.52/90.77 elim (classic ((~((succ (n0)) = (n3)))/\(~(gt (succ (n0)) (n3))))); [ zenon_intro zenon_H2e9 | zenon_intro zenon_H2ea ]. % 90.52/90.77 apply (zenon_and_s _ _ zenon_H2e9). zenon_intro zenon_H2ec. zenon_intro zenon_H2eb. % 90.52/90.77 elim (classic ((~((succ (n0)) = (succ (tptp_minus_1))))/\(~(gt (succ (n0)) (succ (tptp_minus_1)))))); [ zenon_intro zenon_H159 | zenon_intro zenon_H15a ]. % 90.52/90.77 apply (zenon_and_s _ _ zenon_H159). zenon_intro zenon_H15b. zenon_intro zenon_Haf. % 90.52/90.77 apply (zenon_L15_); trivial. % 90.52/90.77 elim (classic (zenon_TB_ec = (n3))); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hb6 ]. % 90.52/90.77 cut ((gt (succ (tptp_minus_1)) zenon_TB_ec) = (gt (succ (n0)) (n3))). % 90.52/90.77 intro zenon_D_pnotp. % 90.52/90.77 apply zenon_H2eb. % 90.52/90.77 rewrite <- zenon_D_pnotp. % 90.52/90.77 exact zenon_H97. % 90.52/90.77 cut ((zenon_TB_ec = (n3))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 90.52/90.77 cut (((succ (tptp_minus_1)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 90.52/90.77 congruence. % 90.52/90.77 apply (zenon_notand_s _ _ zenon_H15a); [ zenon_intro zenon_H15d | zenon_intro zenon_H15c ]. % 90.52/90.77 apply zenon_H15d. zenon_intro zenon_H15e. % 90.52/90.77 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 90.52/90.77 cut (((succ (n0)) = (succ (n0))) = ((succ (tptp_minus_1)) = (succ (n0)))). % 90.52/90.77 intro zenon_D_pnotp. % 90.52/90.77 apply zenon_H108. % 90.52/90.77 rewrite <- zenon_D_pnotp. % 90.52/90.77 exact zenon_Hb1. % 90.52/90.77 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.77 cut (((succ (n0)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H15b]. % 90.52/90.77 congruence. % 90.52/90.77 exact (zenon_H15b zenon_H15e). % 90.52/90.77 apply zenon_Hb2. apply refl_equal. % 90.52/90.77 apply zenon_Hb2. apply refl_equal. % 90.52/90.77 apply zenon_H15c. zenon_intro zenon_H15f. % 90.52/90.77 generalize (zenon_H73 (succ (n0))). zenon_intro zenon_H127. % 90.52/90.77 generalize (zenon_H127 (succ (tptp_minus_1))). zenon_intro zenon_H160. % 90.52/90.77 generalize (zenon_H160 zenon_TB_ec). zenon_intro zenon_H161. % 90.52/90.77 apply (zenon_imply_s _ _ zenon_H161); [ zenon_intro zenon_Haf | zenon_intro zenon_H162 ]. % 90.52/90.77 exact (zenon_Haf zenon_H15f). % 90.52/90.77 apply (zenon_imply_s _ _ zenon_H162); [ zenon_intro zenon_Hab | zenon_intro zenon_H163 ]. % 90.52/90.77 exact (zenon_Hab zenon_H97). % 90.52/90.77 cut ((gt (succ (n0)) zenon_TB_ec) = (gt (succ (n0)) (n3))). % 90.52/90.77 intro zenon_D_pnotp. % 90.52/90.77 apply zenon_H2eb. % 90.52/90.77 rewrite <- zenon_D_pnotp. % 90.52/90.77 exact zenon_H163. % 90.52/90.77 cut ((zenon_TB_ec = (n3))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 90.52/90.77 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.77 congruence. % 90.52/90.77 apply zenon_Hb2. apply refl_equal. % 90.52/90.77 exact (zenon_Hb6 zenon_Hbd). % 90.52/90.77 exact (zenon_Hb6 zenon_Hbd). % 90.52/90.77 apply (zenon_L170_ zenon_TB_ec); trivial. % 90.52/90.77 cut ((gt (n3) (n2)) = (gt (succ (n0)) (n2))). % 90.52/90.77 intro zenon_D_pnotp. % 90.52/90.77 apply zenon_H2b1. % 90.52/90.77 rewrite <- zenon_D_pnotp. % 90.52/90.77 exact gt_3_2. % 90.52/90.77 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 90.52/90.77 cut (((n3) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_H2ed]. % 90.52/90.77 congruence. % 90.52/90.77 apply (zenon_notand_s _ _ zenon_H2ea); [ zenon_intro zenon_H2ef | zenon_intro zenon_H2ee ]. % 90.52/90.77 apply zenon_H2ef. zenon_intro zenon_H2f0. % 90.52/90.77 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 90.52/90.77 cut (((succ (n0)) = (succ (n0))) = ((n3) = (succ (n0)))). % 90.52/90.77 intro zenon_D_pnotp. % 90.52/90.77 apply zenon_H2ed. % 90.52/90.77 rewrite <- zenon_D_pnotp. % 90.52/90.77 exact zenon_Hb1. % 90.52/90.77 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.77 cut (((succ (n0)) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H2ec]. % 90.52/90.77 congruence. % 90.52/90.77 exact (zenon_H2ec zenon_H2f0). % 90.52/90.77 apply zenon_Hb2. apply refl_equal. % 90.52/90.77 apply zenon_Hb2. apply refl_equal. % 90.52/90.77 apply zenon_H2ee. zenon_intro zenon_H2f1. % 90.52/90.77 generalize (zenon_H73 (succ (n0))). zenon_intro zenon_H127. % 90.52/90.77 generalize (zenon_H127 (n3)). zenon_intro zenon_H2f2. % 90.52/90.77 generalize (zenon_H2f2 (n2)). zenon_intro zenon_H2f3. % 90.52/90.77 apply (zenon_imply_s _ _ zenon_H2f3); [ zenon_intro zenon_H2eb | zenon_intro zenon_H2f4 ]. % 90.52/90.77 exact (zenon_H2eb zenon_H2f1). % 90.52/90.77 apply (zenon_imply_s _ _ zenon_H2f4); [ zenon_intro zenon_H81 | zenon_intro zenon_H2b2 ]. % 90.52/90.77 exact (zenon_H81 gt_3_2). % 90.52/90.77 exact (zenon_H2b1 zenon_H2b2). % 90.52/90.77 apply zenon_H65. apply refl_equal. % 90.52/90.77 (* end of lemma zenon_L194_ *) % 90.52/90.77 assert (zenon_L195_ : forall (zenon_TB_ec : zenon_U), (~((tptp_minus_1) = (n3))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (~(gt (succ (n0)) (succ (succ (n0))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.77 do 1 intro. intros zenon_He8 zenon_H97 zenon_H68 zenon_H2ab zenon_H73. % 90.52/90.77 elim (classic ((n2) = (succ (succ (n0))))); [ zenon_intro zenon_H1eb | zenon_intro zenon_H1ec ]. % 90.52/90.77 elim (classic (gt (succ (n0)) (n2))); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H2b1 ]. % 90.52/90.77 cut ((gt (succ (n0)) (n2)) = (gt (succ (n0)) (succ (succ (n0))))). % 90.52/90.77 intro zenon_D_pnotp. % 90.52/90.77 apply zenon_H2ab. % 90.52/90.77 rewrite <- zenon_D_pnotp. % 90.52/90.77 exact zenon_H2b2. % 90.52/90.77 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ec]. % 90.52/90.77 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.77 congruence. % 90.52/90.77 apply zenon_Hb2. apply refl_equal. % 90.52/90.77 exact (zenon_H1ec zenon_H1eb). % 90.52/90.77 apply (zenon_L194_ zenon_TB_ec); trivial. % 90.52/90.77 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_H1ed | zenon_intro zenon_H1ee ]. % 90.52/90.77 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((n2) = (succ (succ (n0))))). % 90.52/90.77 intro zenon_D_pnotp. % 90.52/90.77 apply zenon_H1ec. % 90.52/90.77 rewrite <- zenon_D_pnotp. % 90.52/90.77 exact zenon_H1ed. % 90.52/90.77 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 90.52/90.77 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 90.52/90.77 congruence. % 90.52/90.77 exact (zenon_H1ef successor_2). % 90.52/90.77 apply zenon_H1ee. apply refl_equal. % 90.52/90.77 apply zenon_H1ee. apply refl_equal. % 90.52/90.77 (* end of lemma zenon_L195_ *) % 90.52/90.77 assert (zenon_L196_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (n0)) (succ (succ (succ (n0)))))) -> (~((tptp_minus_1) = (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.77 do 1 intro. intros zenon_H73 zenon_H265 zenon_He8 zenon_Hce zenon_H97 zenon_H68. % 90.52/90.77 elim (classic (gt (succ (n0)) (succ (succ (n0))))); [ zenon_intro zenon_H2b0 | zenon_intro zenon_H2ab ]. % 90.52/90.77 elim (classic (gt (succ (n0)) (n2))); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H2b1 ]. % 90.52/90.77 elim (classic (gt (n2) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H211 | zenon_intro zenon_H20b ]. % 90.52/90.77 generalize (zenon_H73 (succ (n0))). zenon_intro zenon_H127. % 90.52/90.77 generalize (zenon_H127 (n2)). zenon_intro zenon_H2f5. % 90.52/90.77 generalize (zenon_H2f5 (succ (succ (succ (n0))))). zenon_intro zenon_H2f6. % 90.52/90.77 apply (zenon_imply_s _ _ zenon_H2f6); [ zenon_intro zenon_H2b1 | zenon_intro zenon_H2f7 ]. % 90.52/90.77 exact (zenon_H2b1 zenon_H2b2). % 90.52/90.77 apply (zenon_imply_s _ _ zenon_H2f7); [ zenon_intro zenon_H20b | zenon_intro zenon_H272 ]. % 90.52/90.77 exact (zenon_H20b zenon_H211). % 90.52/90.77 exact (zenon_H265 zenon_H272). % 90.52/90.77 apply (zenon_L190_ zenon_TB_ec); trivial. % 90.52/90.77 cut ((gt (succ (n0)) (succ (succ (n0)))) = (gt (succ (n0)) (n2))). % 90.52/90.77 intro zenon_D_pnotp. % 90.52/90.77 apply zenon_H2b1. % 90.52/90.77 rewrite <- zenon_D_pnotp. % 90.52/90.77 exact zenon_H2b0. % 90.52/90.77 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 90.52/90.77 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.77 congruence. % 90.52/90.77 apply zenon_Hb2. apply refl_equal. % 90.52/90.77 exact (zenon_H1ef successor_2). % 90.52/90.77 apply (zenon_L195_ zenon_TB_ec); trivial. % 90.52/90.77 (* end of lemma zenon_L196_ *) % 90.52/90.77 assert (zenon_L197_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (~((tptp_minus_1) = (n3))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt zenon_TB_ec (n1))) -> False). % 90.52/90.77 do 1 intro. intros zenon_H68 zenon_H97 zenon_He8 zenon_H73 zenon_H148. % 90.52/90.77 elim (classic ((~(zenon_TB_ec = (n3)))/\(~(gt zenon_TB_ec (n3))))); [ zenon_intro zenon_H280 | zenon_intro zenon_H281 ]. % 90.52/90.77 apply (zenon_and_s _ _ zenon_H280). zenon_intro zenon_Hb6. zenon_intro zenon_H27a. % 90.52/90.77 apply (zenon_L172_ zenon_TB_ec); trivial. % 90.52/90.77 cut ((gt (n3) (n1)) = (gt zenon_TB_ec (n1))). % 90.52/90.77 intro zenon_D_pnotp. % 90.52/90.77 apply zenon_H148. % 90.52/90.77 rewrite <- zenon_D_pnotp. % 90.52/90.77 exact gt_3_1. % 90.52/90.77 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.77 cut (((n3) = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_H282]. % 90.52/90.77 congruence. % 90.52/90.77 apply (zenon_notand_s _ _ zenon_H281); [ zenon_intro zenon_H284 | zenon_intro zenon_H283 ]. % 90.52/90.77 apply zenon_H284. zenon_intro zenon_Hbd. % 90.52/90.77 elim (classic (zenon_TB_ec = zenon_TB_ec)); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Ha1 ]. % 90.52/90.77 cut ((zenon_TB_ec = zenon_TB_ec) = ((n3) = zenon_TB_ec)). % 90.52/90.77 intro zenon_D_pnotp. % 90.52/90.77 apply zenon_H282. % 90.52/90.77 rewrite <- zenon_D_pnotp. % 90.52/90.77 exact zenon_Hc9. % 90.52/90.77 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.77 cut ((zenon_TB_ec = (n3))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 90.52/90.77 congruence. % 90.52/90.77 exact (zenon_Hb6 zenon_Hbd). % 90.52/90.77 apply zenon_Ha1. apply refl_equal. % 90.52/90.77 apply zenon_Ha1. apply refl_equal. % 90.52/90.77 apply zenon_H283. zenon_intro zenon_H27b. % 90.52/90.77 generalize (zenon_H73 zenon_TB_ec). zenon_intro zenon_H144. % 90.52/90.77 generalize (zenon_H144 (n3)). zenon_intro zenon_H285. % 90.52/90.77 generalize (zenon_H285 (n1)). zenon_intro zenon_H286. % 90.52/90.77 apply (zenon_imply_s _ _ zenon_H286); [ zenon_intro zenon_H27a | zenon_intro zenon_H287 ]. % 90.52/90.77 exact (zenon_H27a zenon_H27b). % 90.52/90.77 apply (zenon_imply_s _ _ zenon_H287); [ zenon_intro zenon_H185 | zenon_intro zenon_H164 ]. % 90.52/90.77 exact (zenon_H185 gt_3_1). % 90.52/90.77 exact (zenon_H148 zenon_H164). % 90.52/90.77 apply zenon_H66. apply refl_equal. % 90.52/90.77 (* end of lemma zenon_L197_ *) % 90.52/90.77 assert (zenon_L198_ : forall (zenon_TB_ec : zenon_U), (~((tptp_minus_1) = (n3))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> (~(gt zenon_TB_ec (succ (n0)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.77 do 1 intro. intros zenon_He8 zenon_H97 zenon_H68 zenon_H109 zenon_H73. % 90.52/90.77 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_H12e | zenon_intro zenon_Hb0 ]. % 90.52/90.77 elim (classic (gt zenon_TB_ec (n1))); [ zenon_intro zenon_H164 | zenon_intro zenon_H148 ]. % 90.52/90.77 cut ((gt zenon_TB_ec (n1)) = (gt zenon_TB_ec (succ (n0)))). % 90.52/90.77 intro zenon_D_pnotp. % 90.52/90.77 apply zenon_H109. % 90.52/90.77 rewrite <- zenon_D_pnotp. % 90.52/90.77 exact zenon_H164. % 90.52/90.77 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 90.52/90.77 cut ((zenon_TB_ec = zenon_TB_ec)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 90.52/90.77 congruence. % 90.52/90.77 apply zenon_Ha1. apply refl_equal. % 90.52/90.77 exact (zenon_Hb0 zenon_H12e). % 90.52/90.77 apply (zenon_L197_ zenon_TB_ec); trivial. % 90.52/90.77 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 90.52/90.77 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))). % 90.52/90.77 intro zenon_D_pnotp. % 90.52/90.77 apply zenon_Hb0. % 90.52/90.77 rewrite <- zenon_D_pnotp. % 90.52/90.77 exact zenon_Hb1. % 90.52/90.77 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.77 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.77 congruence. % 90.52/90.77 exact (zenon_Hb3 successor_1). % 90.52/90.77 apply zenon_Hb2. apply refl_equal. % 90.52/90.77 apply zenon_Hb2. apply refl_equal. % 90.52/90.77 (* end of lemma zenon_L198_ *) % 90.52/90.77 assert (zenon_L199_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (succ (n0)))) -> (~((tptp_minus_1) = (n3))) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.77 do 1 intro. intros zenon_H73 zenon_H10a zenon_He8 zenon_H97 zenon_H68. % 90.52/90.77 elim (classic (gt zenon_TB_ec (succ (n0)))); [ zenon_intro zenon_H10b | zenon_intro zenon_H109 ]. % 90.52/90.77 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.77 generalize (zenon_Hd1 zenon_TB_ec). zenon_intro zenon_Hd2. % 90.52/90.77 generalize (zenon_Hd2 (succ (n0))). zenon_intro zenon_H10c. % 90.52/90.77 apply (zenon_imply_s _ _ zenon_H10c); [ zenon_intro zenon_Hab | zenon_intro zenon_H10d ]. % 90.52/90.77 exact (zenon_Hab zenon_H97). % 90.52/90.77 apply (zenon_imply_s _ _ zenon_H10d); [ zenon_intro zenon_H109 | zenon_intro zenon_H10e ]. % 90.52/90.77 exact (zenon_H109 zenon_H10b). % 90.52/90.77 exact (zenon_H10a zenon_H10e). % 90.52/90.77 apply (zenon_L198_ zenon_TB_ec); trivial. % 90.52/90.77 (* end of lemma zenon_L199_ *) % 90.52/90.77 assert (zenon_L200_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (succ (succ (succ (n0)))))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~((tptp_minus_1) = (n3))) -> False). % 90.52/90.77 do 1 intro. intros zenon_H73 zenon_H21d zenon_H68 zenon_H97 zenon_Hce zenon_He8. % 90.52/90.77 elim (classic (gt (succ (tptp_minus_1)) (succ (n0)))); [ zenon_intro zenon_H10e | zenon_intro zenon_H10a ]. % 90.52/90.77 elim (classic (gt (succ (tptp_minus_1)) (n1))); [ zenon_intro zenon_H167 | zenon_intro zenon_Hac ]. % 90.52/90.77 elim (classic (gt (n1) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H262 | zenon_intro zenon_H25e ]. % 90.52/90.77 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.77 generalize (zenon_Hd1 (n1)). zenon_intro zenon_H1d1. % 90.52/90.77 generalize (zenon_H1d1 (succ (succ (succ (n0))))). zenon_intro zenon_H27e. % 90.52/90.77 apply (zenon_imply_s _ _ zenon_H27e); [ zenon_intro zenon_Hac | zenon_intro zenon_H27f ]. % 90.52/90.77 exact (zenon_Hac zenon_H167). % 90.52/90.77 apply (zenon_imply_s _ _ zenon_H27f); [ zenon_intro zenon_H25e | zenon_intro zenon_H222 ]. % 90.52/90.77 exact (zenon_H25e zenon_H262). % 90.52/90.77 exact (zenon_H21d zenon_H222). % 90.52/90.77 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_H12e | zenon_intro zenon_Hb0 ]. % 90.52/90.77 elim (classic (gt (succ (n0)) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H272 | zenon_intro zenon_H265 ]. % 90.52/90.77 cut ((gt (succ (n0)) (succ (succ (succ (n0))))) = (gt (n1) (succ (succ (succ (n0)))))). % 90.52/90.77 intro zenon_D_pnotp. % 90.52/90.77 apply zenon_H25e. % 90.52/90.77 rewrite <- zenon_D_pnotp. % 90.52/90.77 exact zenon_H272. % 90.52/90.77 cut (((succ (succ (succ (n0)))) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H20e]. % 90.52/90.77 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.77 congruence. % 90.52/90.77 elim (classic ((n1) = (n1))); [ zenon_intro zenon_H131 | zenon_intro zenon_H66 ]. % 90.52/90.77 cut (((n1) = (n1)) = ((succ (n0)) = (n1))). % 90.52/90.77 intro zenon_D_pnotp. % 90.52/90.77 apply zenon_Hb3. % 90.52/90.77 rewrite <- zenon_D_pnotp. % 90.52/90.77 exact zenon_H131. % 90.52/90.77 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 90.52/90.77 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 90.52/90.77 congruence. % 90.52/90.77 exact (zenon_Hb0 zenon_H12e). % 90.52/90.77 apply zenon_H66. apply refl_equal. % 90.52/90.77 apply zenon_H66. apply refl_equal. % 90.52/90.77 apply zenon_H20e. apply refl_equal. % 90.52/90.77 apply (zenon_L196_ zenon_TB_ec); trivial. % 90.52/90.77 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb2 ]. % 90.52/90.77 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))). % 90.52/90.77 intro zenon_D_pnotp. % 90.52/90.77 apply zenon_Hb0. % 90.52/90.77 rewrite <- zenon_D_pnotp. % 90.52/90.77 exact zenon_Hb1. % 90.52/90.77 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 90.52/90.77 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.77 congruence. % 90.52/90.77 exact (zenon_Hb3 successor_1). % 90.52/90.77 apply zenon_Hb2. apply refl_equal. % 90.52/90.77 apply zenon_Hb2. apply refl_equal. % 90.52/90.77 cut ((gt (succ (tptp_minus_1)) (succ (n0))) = (gt (succ (tptp_minus_1)) (n1))). % 90.52/90.77 intro zenon_D_pnotp. % 90.52/90.77 apply zenon_Hac. % 90.52/90.77 rewrite <- zenon_D_pnotp. % 90.52/90.77 exact zenon_H10e. % 90.52/90.77 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 90.52/90.77 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.77 congruence. % 90.52/90.77 apply zenon_H8f. apply refl_equal. % 90.52/90.77 exact (zenon_Hb3 successor_1). % 90.52/90.77 apply (zenon_L199_ zenon_TB_ec); trivial. % 90.52/90.77 (* end of lemma zenon_L200_ *) % 90.52/90.77 assert (zenon_L201_ : forall (zenon_TB_ec : zenon_U), (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (~((tptp_minus_1) = (n3))) -> (~(gt (sum (n0) (tptp_minus_1) zenon_E) (succ (succ (succ (n0)))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 90.52/90.77 do 1 intro. intros zenon_H68 zenon_H97 zenon_Hce zenon_He8 zenon_H2f8 zenon_H73. % 90.52/90.77 elim (classic ((n0) = (succ (tptp_minus_1)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 90.52/90.77 elim (classic (gt (succ (tptp_minus_1)) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H222 | zenon_intro zenon_H21d ]. % 90.52/90.77 elim (classic (gt (n0) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H26a | zenon_intro zenon_H26b ]. % 90.52/90.77 cut ((gt (n0) (succ (succ (succ (n0))))) = (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (succ (succ (n0)))))). % 90.52/90.77 intro zenon_D_pnotp. % 90.52/90.77 apply zenon_H2f8. % 90.52/90.77 rewrite <- zenon_D_pnotp. % 90.52/90.77 exact zenon_H26a. % 90.52/90.77 cut (((succ (succ (succ (n0)))) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H20e]. % 90.52/90.77 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 90.52/90.77 congruence. % 90.52/90.77 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd9 | zenon_intro zenon_Hda ]. % 90.52/90.77 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.77 intro zenon_D_pnotp. % 90.52/90.77 apply zenon_Hd7. % 90.52/90.77 rewrite <- zenon_D_pnotp. % 90.52/90.77 exact zenon_Hd9. % 90.52/90.77 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.77 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 90.52/90.77 congruence. % 90.52/90.77 exact (zenon_Hdb zenon_Hce). % 90.52/90.77 apply zenon_Hda. apply refl_equal. % 90.52/90.77 apply zenon_Hda. apply refl_equal. % 90.52/90.77 apply zenon_H20e. apply refl_equal. % 90.52/90.77 cut ((gt (succ (tptp_minus_1)) (succ (succ (succ (n0))))) = (gt (n0) (succ (succ (succ (n0)))))). % 90.52/90.77 intro zenon_D_pnotp. % 90.52/90.77 apply zenon_H26b. % 90.52/90.77 rewrite <- zenon_D_pnotp. % 90.52/90.77 exact zenon_H222. % 90.52/90.77 cut (((succ (succ (succ (n0)))) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H20e]. % 90.52/90.77 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.77 congruence. % 90.52/90.77 elim (classic ((n0) = (n0))); [ zenon_intro zenon_Hca | zenon_intro zenon_H67 ]. % 90.52/90.77 cut (((n0) = (n0)) = ((succ (tptp_minus_1)) = (n0))). % 90.52/90.77 intro zenon_D_pnotp. % 90.52/90.77 apply zenon_Hc3. % 90.52/90.77 rewrite <- zenon_D_pnotp. % 90.52/90.77 exact zenon_Hca. % 90.52/90.77 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.77 cut (((n0) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 90.52/90.77 congruence. % 90.52/90.77 exact (zenon_H72 zenon_H71). % 90.52/90.77 apply zenon_H67. apply refl_equal. % 90.52/90.77 apply zenon_H67. apply refl_equal. % 90.52/90.77 apply zenon_H20e. apply refl_equal. % 90.52/90.77 apply (zenon_L200_ zenon_TB_ec); trivial. % 90.52/90.77 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.77 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n0) = (succ (tptp_minus_1)))). % 90.52/90.77 intro zenon_D_pnotp. % 90.52/90.77 apply zenon_H72. % 90.52/90.77 rewrite <- zenon_D_pnotp. % 90.52/90.77 exact zenon_Hc2. % 90.52/90.77 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.77 cut (((succ (tptp_minus_1)) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 90.52/90.77 congruence. % 90.52/90.77 exact (zenon_Hc3 succ_tptp_minus_1). % 90.52/90.77 apply zenon_H8f. apply refl_equal. % 90.52/90.77 apply zenon_H8f. apply refl_equal. % 90.52/90.77 (* end of lemma zenon_L201_ *) % 90.52/90.77 assert (zenon_L202_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n0) (n3))) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> (gt (succ zenon_TB_ec) (n0)) -> False). % 90.52/90.77 do 1 intro. intros zenon_H73 zenon_H175 zenon_Hce zenon_H97 zenon_H68. % 90.52/90.77 elim (classic ((tptp_minus_1) = (n3))); [ zenon_intro zenon_H106 | zenon_intro zenon_He8 ]. % 90.52/90.77 cut ((gt (n0) (tptp_minus_1)) = (gt (n0) (n3))). % 90.52/90.77 intro zenon_D_pnotp. % 90.52/90.77 apply zenon_H175. % 90.52/90.77 rewrite <- zenon_D_pnotp. % 90.52/90.77 exact gt_0_tptp_minus_1. % 90.52/90.77 cut (((tptp_minus_1) = (n3))); [idtac | apply NNPP; zenon_intro zenon_He8]. % 90.52/90.77 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.77 congruence. % 90.52/90.77 apply zenon_H67. apply refl_equal. % 90.52/90.77 exact (zenon_He8 zenon_H106). % 90.52/90.77 elim (classic ((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 90.52/90.77 elim (classic (gt (n0) (n0))); [ zenon_intro zenon_H1b4 | zenon_intro zenon_Hdf ]. % 90.52/90.77 elim (classic (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hde ]. % 90.52/90.77 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (n3))); [ zenon_intro zenon_H2f9 | zenon_intro zenon_H2fa ]. % 90.52/90.77 generalize (zenon_H73 (n0)). zenon_intro zenon_H115. % 90.52/90.77 generalize (zenon_H115 (sum (n0) (tptp_minus_1) zenon_E)). zenon_intro zenon_H1e1. % 90.52/90.77 generalize (zenon_H1e1 (n3)). zenon_intro zenon_H2fb. % 90.52/90.77 apply (zenon_imply_s _ _ zenon_H2fb); [ zenon_intro zenon_Hde | zenon_intro zenon_H2fc ]. % 90.52/90.77 exact (zenon_Hde zenon_Hdd). % 90.52/90.77 apply (zenon_imply_s _ _ zenon_H2fc); [ zenon_intro zenon_H2fa | zenon_intro zenon_H177 ]. % 90.52/90.77 exact (zenon_H2fa zenon_H2f9). % 90.52/90.77 exact (zenon_H175 zenon_H177). % 90.52/90.77 elim (classic (gt (sum (n0) (tptp_minus_1) zenon_E) (succ (succ (succ (n0)))))); [ zenon_intro zenon_H2fd | zenon_intro zenon_H2f8 ]. % 90.52/90.77 cut ((gt (sum (n0) (tptp_minus_1) zenon_E) (succ (succ (succ (n0))))) = (gt (sum (n0) (tptp_minus_1) zenon_E) (n3))). % 90.52/90.77 intro zenon_D_pnotp. % 90.52/90.77 apply zenon_H2fa. % 90.52/90.77 rewrite <- zenon_D_pnotp. % 90.52/90.77 exact zenon_H2fd. % 90.52/90.77 cut (((succ (succ (succ (n0)))) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H20f]. % 90.52/90.77 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.77 congruence. % 90.52/90.77 apply zenon_Hda. apply refl_equal. % 90.52/90.77 exact (zenon_H20f successor_3). % 90.52/90.77 apply (zenon_L201_ zenon_TB_ec); trivial. % 90.52/90.77 cut ((gt (n0) (n0)) = (gt (n0) (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.77 intro zenon_D_pnotp. % 90.52/90.77 apply zenon_Hde. % 90.52/90.77 rewrite <- zenon_D_pnotp. % 90.52/90.77 exact zenon_H1b4. % 90.52/90.77 cut (((n0) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 90.52/90.77 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.77 congruence. % 90.52/90.77 apply zenon_H67. apply refl_equal. % 90.52/90.77 exact (zenon_Hd7 zenon_Hd6). % 90.52/90.77 apply (zenon_L181_ zenon_TB_ec); trivial. % 90.52/90.77 elim (classic ((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [ zenon_intro zenon_Hd9 | zenon_intro zenon_Hda ]. % 90.52/90.77 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E)) = ((n0) = (sum (n0) (tptp_minus_1) zenon_E))). % 90.52/90.77 intro zenon_D_pnotp. % 90.52/90.77 apply zenon_Hd7. % 90.52/90.77 rewrite <- zenon_D_pnotp. % 90.52/90.77 exact zenon_Hd9. % 90.52/90.77 cut (((sum (n0) (tptp_minus_1) zenon_E) = (sum (n0) (tptp_minus_1) zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 90.52/90.77 cut (((sum (n0) (tptp_minus_1) zenon_E) = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 90.52/90.77 congruence. % 90.52/90.77 exact (zenon_Hdb zenon_Hce). % 90.52/90.77 apply zenon_Hda. apply refl_equal. % 90.52/90.77 apply zenon_Hda. apply refl_equal. % 90.52/90.77 (* end of lemma zenon_L202_ *) % 90.52/90.77 assert (zenon_L203_ : forall (zenon_TB_ec : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (succ (tptp_minus_1)) (n3))) -> (gt (succ zenon_TB_ec) (n0)) -> (gt (succ (tptp_minus_1)) zenon_TB_ec) -> ((sum (n0) (tptp_minus_1) zenon_E) = (n0)) -> False). % 90.52/90.77 do 1 intro. intros zenon_H73 zenon_H225 zenon_H68 zenon_H97 zenon_Hce. % 90.52/90.77 elim (classic ((~((succ (tptp_minus_1)) = (succ zenon_TB_ec)))/\(~(gt (succ (tptp_minus_1)) (succ zenon_TB_ec))))); [ zenon_intro zenon_H2bd | zenon_intro zenon_H2be ]. % 90.52/90.77 apply (zenon_and_s _ _ zenon_H2bd). zenon_intro zenon_H2bf. zenon_intro zenon_H1d5. % 90.52/90.77 apply (zenon_L158_ zenon_TB_ec); trivial. % 90.52/90.77 elim (classic (gt (n0) (n3))); [ zenon_intro zenon_H177 | zenon_intro zenon_H175 ]. % 90.52/90.77 generalize (zenon_H73 (succ zenon_TB_ec)). zenon_intro zenon_H11d. % 90.52/90.77 generalize (zenon_H11d (n0)). zenon_intro zenon_H11e. % 90.52/90.77 generalize (zenon_H11e (n3)). zenon_intro zenon_H2fe. % 90.52/90.77 apply (zenon_imply_s _ _ zenon_H2fe); [ zenon_intro zenon_H6e | zenon_intro zenon_H2ff ]. % 90.52/90.77 exact (zenon_H6e zenon_H68). % 90.52/90.77 apply (zenon_imply_s _ _ zenon_H2ff); [ zenon_intro zenon_H175 | zenon_intro zenon_H300 ]. % 90.52/90.77 exact (zenon_H175 zenon_H177). % 90.52/90.77 cut ((gt (succ zenon_TB_ec) (n3)) = (gt (succ (tptp_minus_1)) (n3))). % 90.52/90.77 intro zenon_D_pnotp. % 90.52/90.77 apply zenon_H225. % 90.52/90.77 rewrite <- zenon_D_pnotp. % 90.52/90.77 exact zenon_H300. % 90.52/90.77 cut (((n3) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 90.52/90.77 cut (((succ zenon_TB_ec) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H2c3]. % 90.52/90.77 congruence. % 90.52/90.77 apply (zenon_notand_s _ _ zenon_H2be); [ zenon_intro zenon_H2c5 | zenon_intro zenon_H2c4 ]. % 90.52/90.77 apply zenon_H2c5. zenon_intro zenon_H2c6. % 90.52/90.77 apply zenon_H2c3. apply sym_equal. exact zenon_H2c6. % 90.52/90.77 apply zenon_H2c4. zenon_intro zenon_H1d9. % 90.52/90.77 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.77 generalize (zenon_Hd1 (succ zenon_TB_ec)). zenon_intro zenon_H2c7. % 90.52/90.77 generalize (zenon_H2c7 (n3)). zenon_intro zenon_H301. % 90.52/90.77 apply (zenon_imply_s _ _ zenon_H301); [ zenon_intro zenon_H1d5 | zenon_intro zenon_H302 ]. % 90.52/90.77 exact (zenon_H1d5 zenon_H1d9). % 90.52/90.77 apply (zenon_imply_s _ _ zenon_H302); [ zenon_intro zenon_H303 | zenon_intro zenon_H229 ]. % 90.52/90.77 exact (zenon_H303 zenon_H300). % 90.52/90.77 exact (zenon_H225 zenon_H229). % 90.52/90.77 apply zenon_H64. apply refl_equal. % 90.52/90.77 apply (zenon_L202_ zenon_TB_ec); trivial. % 90.52/90.77 (* end of lemma zenon_L203_ *) % 90.52/90.77 apply NNPP. intro zenon_G. % 90.52/90.77 elim (classic (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z))))))); [ zenon_intro zenon_H73 | zenon_intro zenon_H304 ]. % 90.52/90.77 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H306. zenon_intro zenon_H305. % 90.52/90.77 apply (zenon_notallex_s (fun B : zenon_U => (((leq (n0) B)/\(leq B (tptp_minus_1)))->((a_select3 (q) (pv10) B) = (divide (divide (times (exp (divide (divide (times (minus (a_select2 (x) (pv10)) (a_select2 (mu) B)) (minus (a_select2 (x) (pv10)) (a_select2 (mu) B))) (tptp_minus_2)) (times (a_select2 (sigma) B) (a_select2 (sigma) B)))) (a_select2 (rho) B)) (times (sqrt (times (n2) (tptp_pi))) (a_select2 (sigma) B))) (sum (n0) (n4) (divide (times (exp (divide (divide (times (minus (a_select2 (x) (pv10)) (a_select2 (mu) (tptp_sum_index))) (minus (a_select2 (x) (pv10)) (a_select2 (mu) (tptp_sum_index)))) (tptp_minus_2)) (times (a_select2 (sigma) (tptp_sum_index)) (a_select2 (sigma) (tptp_sum_index))))) (a_select2 (rho) (tptp_sum_index))) (times (sqrt (times (n2) (tptp_pi))) (a_select2 (sigma) (tptp_sum_index))))))))) zenon_H305); [ zenon_intro zenon_H307; idtac ]. % 90.52/90.77 elim zenon_H307. zenon_intro zenon_TB_ec. zenon_intro zenon_H308. % 90.52/90.77 apply (zenon_notimply_s _ _ zenon_H308). zenon_intro zenon_H30a. zenon_intro zenon_H309. % 90.52/90.77 apply (zenon_and_s _ _ zenon_H30a). zenon_intro zenon_H6d. zenon_intro zenon_H30b. % 90.52/90.77 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H6b. % 90.52/90.77 generalize (zenon_H6b zenon_TB_ec). zenon_intro zenon_H6c. % 90.52/90.77 apply (zenon_equiv_s _ _ zenon_H6c); [ zenon_intro zenon_H69; zenon_intro zenon_H6e | zenon_intro zenon_H6d; zenon_intro zenon_H68 ]. % 90.52/90.77 exact (zenon_H69 zenon_H6d). % 90.52/90.77 generalize (leq_succ_gt_equiv zenon_TB_ec). zenon_intro zenon_H99. % 90.52/90.77 generalize (zenon_H99 (tptp_minus_1)). zenon_intro zenon_H30c. % 90.52/90.77 apply (zenon_equiv_s _ _ zenon_H30c); [ zenon_intro zenon_H30d; zenon_intro zenon_Hab | zenon_intro zenon_H30b; zenon_intro zenon_H97 ]. % 90.52/90.77 exact (zenon_H30d zenon_H30b). % 90.52/90.77 generalize (sum_plus_base zenon_E). zenon_intro zenon_Hce. % 90.52/90.77 generalize (finite_domain_0 (tptp_minus_1)). zenon_intro zenon_H1c8. % 90.52/90.77 apply (zenon_imply_s _ _ zenon_H1c8); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H103 ]. % 90.52/90.77 apply (zenon_notand_s _ _ zenon_H1c9); [ zenon_intro zenon_Hed | zenon_intro zenon_H1b5 ]. % 90.52/90.77 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H6b. % 90.52/90.77 generalize (zenon_H6b (tptp_minus_1)). zenon_intro zenon_Hee. % 90.52/90.77 apply (zenon_equiv_s _ _ zenon_Hee); [ zenon_intro zenon_Hed; zenon_intro zenon_Hbf | zenon_intro zenon_Hef; zenon_intro zenon_Hc1 ]. % 90.52/90.77 elim (classic ((~((succ (tptp_minus_1)) = (n3)))/\(~(gt (succ (tptp_minus_1)) (n3))))); [ zenon_intro zenon_H223 | zenon_intro zenon_H224 ]. % 90.52/90.77 apply (zenon_and_s _ _ zenon_H223). zenon_intro zenon_H226. zenon_intro zenon_H225. % 90.52/90.77 apply (zenon_L203_ zenon_TB_ec); trivial. % 90.52/90.77 cut ((gt (n3) (n0)) = (gt (succ (tptp_minus_1)) (n0))). % 90.52/90.77 intro zenon_D_pnotp. % 90.52/90.77 apply zenon_Hbf. % 90.52/90.77 rewrite <- zenon_D_pnotp. % 90.52/90.77 exact gt_3_0. % 90.52/90.77 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 90.52/90.77 cut (((n3) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H22a]. % 90.52/90.77 congruence. % 90.52/90.77 apply (zenon_notand_s _ _ zenon_H224); [ zenon_intro zenon_H22c | zenon_intro zenon_H22b ]. % 90.52/90.77 apply zenon_H22c. zenon_intro zenon_H22d. % 90.52/90.77 elim (classic ((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H8f ]. % 90.52/90.77 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1))) = ((n3) = (succ (tptp_minus_1)))). % 90.52/90.77 intro zenon_D_pnotp. % 90.52/90.77 apply zenon_H22a. % 90.52/90.77 rewrite <- zenon_D_pnotp. % 90.52/90.77 exact zenon_Hc2. % 90.52/90.77 cut (((succ (tptp_minus_1)) = (succ (tptp_minus_1)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 90.52/90.77 cut (((succ (tptp_minus_1)) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H226]. % 90.52/90.77 congruence. % 90.52/90.77 exact (zenon_H226 zenon_H22d). % 90.52/90.77 apply zenon_H8f. apply refl_equal. % 90.52/90.77 apply zenon_H8f. apply refl_equal. % 90.52/90.77 apply zenon_H22b. zenon_intro zenon_H229. % 90.52/90.77 generalize (zenon_H73 (succ (tptp_minus_1))). zenon_intro zenon_Hd1. % 90.52/90.77 generalize (zenon_Hd1 (n3)). zenon_intro zenon_H22e. % 90.52/90.77 generalize (zenon_H22e (n0)). zenon_intro zenon_H28a. % 90.52/90.77 apply (zenon_imply_s _ _ zenon_H28a); [ zenon_intro zenon_H225 | zenon_intro zenon_H28b ]. % 90.52/90.77 exact (zenon_H225 zenon_H229). % 90.52/90.77 apply (zenon_imply_s _ _ zenon_H28b); [ zenon_intro zenon_H197 | zenon_intro zenon_Hc1 ]. % 90.52/90.77 exact (zenon_H197 gt_3_0). % 90.52/90.77 exact (zenon_Hbf zenon_Hc1). % 90.52/90.77 apply zenon_H67. apply refl_equal. % 90.52/90.77 exact (zenon_Hed zenon_Hef). % 90.52/90.77 apply (zenon_L71_); trivial. % 90.52/90.77 apply (zenon_L184_ zenon_TB_ec); trivial. % 90.52/90.77 apply zenon_H304. zenon_intro zenon_Tx_bec. apply NNPP. zenon_intro zenon_H30f. % 90.52/90.77 apply zenon_H30f. zenon_intro zenon_Ty_bee. apply NNPP. zenon_intro zenon_H311. % 90.52/90.77 apply zenon_H311. zenon_intro zenon_Tz_beg. apply NNPP. zenon_intro zenon_H313. % 90.52/90.77 apply (zenon_notimply_s _ _ zenon_H313). zenon_intro zenon_H315. zenon_intro zenon_H314. % 90.52/90.77 apply (zenon_notimply_s _ _ zenon_H314). zenon_intro zenon_H317. zenon_intro zenon_H316. % 90.52/90.77 generalize (transitivity_gt zenon_Tx_bec). zenon_intro zenon_H318. % 90.52/90.77 generalize (zenon_H318 zenon_Ty_bee). zenon_intro zenon_H319. % 90.52/90.77 generalize (zenon_H319 zenon_Tz_beg). zenon_intro zenon_H31a. % 90.52/90.77 apply (zenon_imply_s _ _ zenon_H31a); [ zenon_intro zenon_H31c | zenon_intro zenon_H31b ]. % 90.52/90.77 apply (zenon_notand_s _ _ zenon_H31c); [ zenon_intro zenon_H31e | zenon_intro zenon_H31d ]. % 90.52/90.77 exact (zenon_H31e zenon_H315). % 90.52/90.77 exact (zenon_H31d zenon_H317). % 90.52/90.77 exact (zenon_H316 zenon_H31b). % 90.52/90.77 Qed. % 90.52/90.77 % SZS output end Proof % 90.52/90.77 (* END-PROOF *) % 90.52/90.77 nodes searched: 6890034 % 90.52/90.77 max branch formulas: 13547 % 90.52/90.77 proof nodes created: 11517 % 90.52/90.77 formulas created: 2186525 % 90.52/90.77 %------------------------------------------------------------------------------