%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWV209+1 : TPTP v8.1.0. Bugfixed v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n011.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 23:03:19 EDT 2022 % Result : Theorem 8.47s 8.69s % Output : Proof 8.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SWV209+1 : TPTP v8.1.0. Bugfixed v3.3.0. % 0.07/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n011.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Tue Jun 14 18:18:34 EDT 2022 % 0.12/0.34 % CPUTime : % 8.47/8.69 (* PROOF-FOUND *) % 8.47/8.69 % SZS status Theorem % 8.47/8.69 (* BEGIN-PROOF *) % 8.47/8.69 % SZS output start Proof % 8.47/8.69 Theorem quaternion_ds1_inuse_0020 : ((((a_select2 (rho_defuse) (n0)) = (use))/\(((a_select2 (rho_defuse) (n1)) = (use))/\(((a_select2 (rho_defuse) (n2)) = (use))/\(((a_select2 (sigma_defuse) (n0)) = (use))/\(((a_select2 (sigma_defuse) (n1)) = (use))/\(((a_select2 (sigma_defuse) (n2)) = (use))/\(((a_select2 (sigma_defuse) (n3)) = (use))/\(((a_select2 (sigma_defuse) (n4)) = (use))/\(((a_select2 (sigma_defuse) (n5)) = (use))/\(((a_select3 (u_defuse) (n0) (n0)) = (use))/\(((a_select3 (u_defuse) (n1) (n0)) = (use))/\(((a_select3 (u_defuse) (n2) (n0)) = (use))/\(((a_select2 (xinit_defuse) (n3)) = (use))/\(((a_select2 (xinit_defuse) (n4)) = (use))/\(((a_select2 (xinit_defuse) (n5)) = (use))/\(((a_select2 (xinit_mean_defuse) (n0)) = (use))/\(((a_select2 (xinit_mean_defuse) (n1)) = (use))/\(((a_select2 (xinit_mean_defuse) (n2)) = (use))/\(((a_select2 (xinit_mean_defuse) (n3)) = (use))/\(((a_select2 (xinit_mean_defuse) (n4)) = (use))/\(((a_select2 (xinit_mean_defuse) (n5)) = (use))/\(((a_select2 (xinit_noise_defuse) (n0)) = (use))/\(((a_select2 (xinit_noise_defuse) (n1)) = (use))/\(((a_select2 (xinit_noise_defuse) (n2)) = (use))/\(((a_select2 (xinit_noise_defuse) (n3)) = (use))/\(((a_select2 (xinit_noise_defuse) (n4)) = (use))/\(((a_select2 (xinit_noise_defuse) (n5)) = (use))/\((forall A : zenon_U, (forall B : zenon_U, (((leq (n0) A)/\((leq (n0) B)/\((leq A (n2))/\(leq B (n998)))))->((a_select3 (u_defuse) A B) = (use)))))/\(forall C : zenon_U, (forall D : zenon_U, (((leq (n0) C)/\((leq (n0) D)/\((leq C (n2))/\(leq D (n998)))))->((a_select3 (z_defuse) C D) = (use)))))))))))))))))))))))))))))))))->(forall E : zenon_U, (((leq (n0) E)/\(leq E (n5)))->((a_select2 (xinit_noise_defuse) E) = (use))))). % 8.47/8.69 Proof. % 8.47/8.69 assert (zenon_L1_ : (~((xinit_noise_defuse) = (xinit_noise_defuse))) -> False). % 8.47/8.69 do 0 intro. intros zenon_H5c. % 8.47/8.69 apply zenon_H5c. apply refl_equal. % 8.47/8.69 (* end of lemma zenon_L1_ *) % 8.47/8.69 assert (zenon_L2_ : forall (zenon_TE_dr : zenon_U), (gt (succ zenon_TE_dr) (n0)) -> (~(leq (n0) zenon_TE_dr)) -> False). % 8.47/8.69 do 1 intro. intros zenon_H5d zenon_H5e. % 8.47/8.69 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H60. % 8.47/8.69 generalize (zenon_H60 zenon_TE_dr). zenon_intro zenon_H61. % 8.47/8.69 apply (zenon_equiv_s _ _ zenon_H61); [ zenon_intro zenon_H5e; zenon_intro zenon_H63 | zenon_intro zenon_H62; zenon_intro zenon_H5d ]. % 8.47/8.69 exact (zenon_H63 zenon_H5d). % 8.47/8.69 exact (zenon_H5e zenon_H62). % 8.47/8.69 (* end of lemma zenon_L2_ *) % 8.47/8.69 assert (zenon_L3_ : (~((n4) = (n4))) -> False). % 8.47/8.69 do 0 intro. intros zenon_H64. % 8.47/8.69 apply zenon_H64. apply refl_equal. % 8.47/8.69 (* end of lemma zenon_L3_ *) % 8.47/8.69 assert (zenon_L4_ : (~((n3) = (n3))) -> False). % 8.47/8.69 do 0 intro. intros zenon_H65. % 8.47/8.69 apply zenon_H65. apply refl_equal. % 8.47/8.69 (* end of lemma zenon_L4_ *) % 8.47/8.69 assert (zenon_L5_ : (~((n2) = (n2))) -> False). % 8.47/8.69 do 0 intro. intros zenon_H66. % 8.47/8.69 apply zenon_H66. apply refl_equal. % 8.47/8.69 (* end of lemma zenon_L5_ *) % 8.47/8.69 assert (zenon_L6_ : forall (zenon_TE_dr : zenon_U), (gt (succ (n5)) zenon_TE_dr) -> (~(leq zenon_TE_dr (n5))) -> False). % 8.47/8.69 do 1 intro. intros zenon_H67 zenon_H68. % 8.47/8.69 generalize (leq_succ_gt_equiv zenon_TE_dr). zenon_intro zenon_H69. % 8.47/8.69 generalize (zenon_H69 (n5)). zenon_intro zenon_H6a. % 8.47/8.69 apply (zenon_equiv_s _ _ zenon_H6a); [ zenon_intro zenon_H68; zenon_intro zenon_H6c | zenon_intro zenon_H6b; zenon_intro zenon_H67 ]. % 8.47/8.69 exact (zenon_H6c zenon_H67). % 8.47/8.69 exact (zenon_H68 zenon_H6b). % 8.47/8.69 (* end of lemma zenon_L6_ *) % 8.47/8.69 assert (zenon_L7_ : forall (zenon_TE_dr : zenon_U), (gt (succ zenon_TE_dr) (n0)) -> (gt (succ (n5)) zenon_TE_dr) -> (~((n0) = zenon_TE_dr)) -> (~((n1) = zenon_TE_dr)) -> (~((n2) = zenon_TE_dr)) -> (~((n3) = zenon_TE_dr)) -> (~(zenon_TE_dr = (n4))) -> (~(zenon_TE_dr = (n5))) -> False). % 8.47/8.69 do 1 intro. intros zenon_H5d zenon_H67 zenon_H6d zenon_H6e zenon_H6f zenon_H70 zenon_H71 zenon_H72. % 8.47/8.69 generalize (finite_domain_5 zenon_TE_dr). zenon_intro zenon_H73. % 8.47/8.69 apply (zenon_imply_s _ _ zenon_H73); [ zenon_intro zenon_H75 | zenon_intro zenon_H74 ]. % 8.47/8.69 apply (zenon_notand_s _ _ zenon_H75); [ zenon_intro zenon_H5e | zenon_intro zenon_H68 ]. % 8.47/8.69 apply (zenon_L2_ zenon_TE_dr); trivial. % 8.47/8.69 apply (zenon_L6_ zenon_TE_dr); trivial. % 8.47/8.69 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H77 | zenon_intro zenon_H76 ]. % 8.47/8.69 apply zenon_H6d. apply sym_equal. exact zenon_H77. % 8.47/8.69 apply (zenon_or_s _ _ zenon_H76); [ zenon_intro zenon_H79 | zenon_intro zenon_H78 ]. % 8.47/8.69 apply zenon_H6e. apply sym_equal. exact zenon_H79. % 8.47/8.69 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H7b | zenon_intro zenon_H7a ]. % 8.47/8.69 apply zenon_H6f. apply sym_equal. exact zenon_H7b. % 8.47/8.69 apply (zenon_or_s _ _ zenon_H7a); [ zenon_intro zenon_H7d | zenon_intro zenon_H7c ]. % 8.47/8.69 apply zenon_H70. apply sym_equal. exact zenon_H7d. % 8.47/8.69 apply (zenon_or_s _ _ zenon_H7c); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ]. % 8.47/8.69 exact (zenon_H71 zenon_H7f). % 8.47/8.69 exact (zenon_H72 zenon_H7e). % 8.47/8.69 (* end of lemma zenon_L7_ *) % 8.47/8.69 assert (zenon_L8_ : forall (zenon_TE_dr : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n4) zenon_TE_dr)) -> (gt (succ zenon_TE_dr) (n0)) -> (gt (succ (n5)) zenon_TE_dr) -> (~((n0) = zenon_TE_dr)) -> (~(zenon_TE_dr = (n4))) -> (~(zenon_TE_dr = (n5))) -> False). % 8.47/8.69 do 1 intro. intros zenon_H80 zenon_H81 zenon_H5d zenon_H67 zenon_H6d zenon_H71 zenon_H72. % 8.47/8.69 elim (classic ((n3) = zenon_TE_dr)); [ zenon_intro zenon_H82 | zenon_intro zenon_H70 ]. % 8.47/8.69 cut ((gt (n4) (n3)) = (gt (n4) zenon_TE_dr)). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_H81. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact gt_4_3. % 8.47/8.69 cut (((n3) = zenon_TE_dr)); [idtac | apply NNPP; zenon_intro zenon_H70]. % 8.47/8.69 cut (((n4) = (n4))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 8.47/8.69 congruence. % 8.47/8.69 apply zenon_H64. apply refl_equal. % 8.47/8.69 exact (zenon_H70 zenon_H82). % 8.47/8.69 elim (classic (gt (n3) zenon_TE_dr)); [ zenon_intro zenon_H83 | zenon_intro zenon_H84 ]. % 8.47/8.69 generalize (zenon_H80 (n4)). zenon_intro zenon_H85. % 8.47/8.69 generalize (zenon_H85 (n3)). zenon_intro zenon_H86. % 8.47/8.69 generalize (zenon_H86 zenon_TE_dr). zenon_intro zenon_H87. % 8.47/8.69 apply (zenon_imply_s _ _ zenon_H87); [ zenon_intro zenon_H89 | zenon_intro zenon_H88 ]. % 8.47/8.69 exact (zenon_H89 gt_4_3). % 8.47/8.69 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H84 | zenon_intro zenon_H8a ]. % 8.47/8.69 exact (zenon_H84 zenon_H83). % 8.47/8.69 exact (zenon_H81 zenon_H8a). % 8.47/8.69 elim (classic ((n2) = zenon_TE_dr)); [ zenon_intro zenon_H8b | zenon_intro zenon_H6f ]. % 8.47/8.69 cut ((gt (n3) (n2)) = (gt (n3) zenon_TE_dr)). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_H84. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact gt_3_2. % 8.47/8.69 cut (((n2) = zenon_TE_dr)); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 8.47/8.69 cut (((n3) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 8.47/8.69 congruence. % 8.47/8.69 apply zenon_H65. apply refl_equal. % 8.47/8.69 exact (zenon_H6f zenon_H8b). % 8.47/8.69 elim (classic (gt (n2) zenon_TE_dr)); [ zenon_intro zenon_H8c | zenon_intro zenon_H8d ]. % 8.47/8.69 generalize (zenon_H80 (n3)). zenon_intro zenon_H8e. % 8.47/8.69 generalize (zenon_H8e (n2)). zenon_intro zenon_H8f. % 8.47/8.69 generalize (zenon_H8f zenon_TE_dr). zenon_intro zenon_H90. % 8.47/8.69 apply (zenon_imply_s _ _ zenon_H90); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 8.47/8.69 exact (zenon_H92 gt_3_2). % 8.47/8.69 apply (zenon_imply_s _ _ zenon_H91); [ zenon_intro zenon_H8d | zenon_intro zenon_H83 ]. % 8.47/8.69 exact (zenon_H8d zenon_H8c). % 8.47/8.69 exact (zenon_H84 zenon_H83). % 8.47/8.69 elim (classic ((n1) = zenon_TE_dr)); [ zenon_intro zenon_H93 | zenon_intro zenon_H6e ]. % 8.47/8.69 cut ((gt (n2) (n1)) = (gt (n2) zenon_TE_dr)). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_H8d. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact gt_2_1. % 8.47/8.69 cut (((n1) = zenon_TE_dr)); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 8.47/8.69 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 8.47/8.69 congruence. % 8.47/8.69 apply zenon_H66. apply refl_equal. % 8.47/8.69 exact (zenon_H6e zenon_H93). % 8.47/8.69 apply (zenon_L7_ zenon_TE_dr); trivial. % 8.47/8.69 (* end of lemma zenon_L8_ *) % 8.47/8.69 assert (zenon_L9_ : (~((succ (n3)) = (succ (succ (succ (succ (n0))))))) -> False). % 8.47/8.69 do 0 intro. intros zenon_H94. % 8.47/8.69 cut (((n3) = (succ (succ (succ (n0)))))); [idtac | apply NNPP; zenon_intro zenon_H95]. % 8.47/8.69 congruence. % 8.47/8.69 apply zenon_H95. apply sym_equal. exact successor_3. % 8.47/8.69 (* end of lemma zenon_L9_ *) % 8.47/8.69 assert (zenon_L10_ : forall (zenon_TE_dr : 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 (n3)) zenon_TE_dr)) -> (~(zenon_TE_dr = (n5))) -> (~(zenon_TE_dr = (n4))) -> (~((n0) = zenon_TE_dr)) -> (gt (succ (n5)) zenon_TE_dr) -> (gt (succ zenon_TE_dr) (n0)) -> False). % 8.47/8.69 do 1 intro. intros zenon_H80 zenon_H96 zenon_H72 zenon_H71 zenon_H6d zenon_H67 zenon_H5d. % 8.47/8.69 elim (classic (gt (n4) zenon_TE_dr)); [ zenon_intro zenon_H8a | zenon_intro zenon_H81 ]. % 8.47/8.69 elim (classic (gt (succ (succ (succ (succ (n0))))) zenon_TE_dr)); [ zenon_intro zenon_H97 | zenon_intro zenon_H98 ]. % 8.47/8.69 cut ((gt (succ (succ (succ (succ (n0))))) zenon_TE_dr) = (gt (succ (n3)) zenon_TE_dr)). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_H96. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_H97. % 8.47/8.69 cut ((zenon_TE_dr = zenon_TE_dr)); [idtac | apply NNPP; zenon_intro zenon_H99]. % 8.47/8.69 cut (((succ (succ (succ (succ (n0))))) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 8.47/8.69 congruence. % 8.47/8.69 elim (classic ((succ (n3)) = (succ (n3)))); [ zenon_intro zenon_H9b | zenon_intro zenon_H9c ]. % 8.47/8.69 cut (((succ (n3)) = (succ (n3))) = ((succ (succ (succ (succ (n0))))) = (succ (n3)))). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_H9a. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_H9b. % 8.47/8.69 cut (((succ (n3)) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 8.47/8.69 cut (((succ (n3)) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 8.47/8.69 congruence. % 8.47/8.69 apply (zenon_L9_); trivial. % 8.47/8.69 apply zenon_H9c. apply refl_equal. % 8.47/8.69 apply zenon_H9c. apply refl_equal. % 8.47/8.69 apply zenon_H99. apply refl_equal. % 8.47/8.69 cut ((gt (n4) zenon_TE_dr) = (gt (succ (succ (succ (succ (n0))))) zenon_TE_dr)). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_H98. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_H8a. % 8.47/8.69 cut ((zenon_TE_dr = zenon_TE_dr)); [idtac | apply NNPP; zenon_intro zenon_H99]. % 8.47/8.69 cut (((n4) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_H9d]. % 8.47/8.69 congruence. % 8.47/8.69 elim (classic ((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0))))))); [ zenon_intro zenon_H9e | zenon_intro zenon_H9f ]. % 8.47/8.69 cut (((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0)))))) = ((n4) = (succ (succ (succ (succ (n0))))))). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_H9d. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_H9e. % 8.47/8.69 cut (((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_H9f]. % 8.47/8.69 cut (((succ (succ (succ (succ (n0))))) = (n4))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 8.47/8.69 congruence. % 8.47/8.69 exact (zenon_Ha0 successor_4). % 8.47/8.69 apply zenon_H9f. apply refl_equal. % 8.47/8.69 apply zenon_H9f. apply refl_equal. % 8.47/8.69 apply zenon_H99. apply refl_equal. % 8.47/8.69 apply (zenon_L8_ zenon_TE_dr); trivial. % 8.47/8.69 (* end of lemma zenon_L10_ *) % 8.47/8.69 assert (zenon_L11_ : (~((use) = (use))) -> False). % 8.47/8.69 do 0 intro. intros zenon_Ha1. % 8.47/8.69 apply zenon_Ha1. apply refl_equal. % 8.47/8.69 (* end of lemma zenon_L11_ *) % 8.47/8.69 assert (zenon_L12_ : forall (zenon_TE_dr : zenon_U), (~((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (use))) -> ((a_select2 (xinit_noise_defuse) (n1)) = (use)) -> (zenon_TE_dr = (n1)) -> False). % 8.47/8.69 do 1 intro. intros zenon_Ha2 zenon_Ha3 zenon_H79. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) (n1)) = (use)) = ((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (use))). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_Ha2. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_Ha3. % 8.47/8.69 cut (((use) = (use))); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) (n1)) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 8.47/8.69 congruence. % 8.47/8.69 elim (classic ((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ]. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) zenon_TE_dr)) = ((a_select2 (xinit_noise_defuse) (n1)) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_Ha4. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_Ha5. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) (n1)))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 8.47/8.69 congruence. % 8.47/8.69 cut ((zenon_TE_dr = (n1))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 8.47/8.69 cut (((xinit_noise_defuse) = (xinit_noise_defuse))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 8.47/8.69 congruence. % 8.47/8.69 apply zenon_H5c. apply refl_equal. % 8.47/8.69 exact (zenon_Ha8 zenon_H79). % 8.47/8.69 apply zenon_Ha6. apply refl_equal. % 8.47/8.69 apply zenon_Ha6. apply refl_equal. % 8.47/8.69 apply zenon_Ha1. apply refl_equal. % 8.47/8.69 (* end of lemma zenon_L12_ *) % 8.47/8.69 assert (zenon_L13_ : forall (zenon_TE_dr : zenon_U), (~((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (use))) -> ((a_select2 (xinit_noise_defuse) (n2)) = (use)) -> (zenon_TE_dr = (n2)) -> False). % 8.47/8.69 do 1 intro. intros zenon_Ha2 zenon_Ha9 zenon_H7b. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) (n2)) = (use)) = ((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (use))). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_Ha2. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_Ha9. % 8.47/8.69 cut (((use) = (use))); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) (n2)) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 8.47/8.69 congruence. % 8.47/8.69 elim (classic ((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ]. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) zenon_TE_dr)) = ((a_select2 (xinit_noise_defuse) (n2)) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_Haa. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_Ha5. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) (n2)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 8.47/8.69 congruence. % 8.47/8.69 cut ((zenon_TE_dr = (n2))); [idtac | apply NNPP; zenon_intro zenon_Hac]. % 8.47/8.69 cut (((xinit_noise_defuse) = (xinit_noise_defuse))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 8.47/8.69 congruence. % 8.47/8.69 apply zenon_H5c. apply refl_equal. % 8.47/8.69 exact (zenon_Hac zenon_H7b). % 8.47/8.69 apply zenon_Ha6. apply refl_equal. % 8.47/8.69 apply zenon_Ha6. apply refl_equal. % 8.47/8.69 apply zenon_Ha1. apply refl_equal. % 8.47/8.69 (* end of lemma zenon_L13_ *) % 8.47/8.69 assert (zenon_L14_ : forall (zenon_TE_dr : zenon_U), (~((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (use))) -> ((a_select2 (xinit_noise_defuse) (n3)) = (use)) -> (zenon_TE_dr = (n3)) -> False). % 8.47/8.69 do 1 intro. intros zenon_Ha2 zenon_Had zenon_H7d. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) (n3)) = (use)) = ((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (use))). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_Ha2. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_Had. % 8.47/8.69 cut (((use) = (use))); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) (n3)) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))); [idtac | apply NNPP; zenon_intro zenon_Hae]. % 8.47/8.69 congruence. % 8.47/8.69 elim (classic ((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ]. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) zenon_TE_dr)) = ((a_select2 (xinit_noise_defuse) (n3)) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_Hae. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_Ha5. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) (n3)))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 8.47/8.69 congruence. % 8.47/8.69 cut ((zenon_TE_dr = (n3))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 8.47/8.69 cut (((xinit_noise_defuse) = (xinit_noise_defuse))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 8.47/8.69 congruence. % 8.47/8.69 apply zenon_H5c. apply refl_equal. % 8.47/8.69 exact (zenon_Hb0 zenon_H7d). % 8.47/8.69 apply zenon_Ha6. apply refl_equal. % 8.47/8.69 apply zenon_Ha6. apply refl_equal. % 8.47/8.69 apply zenon_Ha1. apply refl_equal. % 8.47/8.69 (* end of lemma zenon_L14_ *) % 8.47/8.69 assert (zenon_L15_ : forall (zenon_TE_dr : 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_TE_dr) (n0)) -> (~(zenon_TE_dr = (n5))) -> (~(zenon_TE_dr = (n4))) -> (~((n0) = zenon_TE_dr)) -> (gt (succ (n5)) zenon_TE_dr) -> (~((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (use))) -> ((a_select2 (xinit_noise_defuse) (n1)) = (use)) -> ((a_select2 (xinit_noise_defuse) (n2)) = (use)) -> ((a_select2 (xinit_noise_defuse) (n3)) = (use)) -> False). % 8.47/8.69 do 1 intro. intros zenon_H80 zenon_H5d zenon_H72 zenon_H71 zenon_H6d zenon_H67 zenon_Ha2 zenon_Ha3 zenon_Ha9 zenon_Had. % 8.47/8.69 generalize (finite_domain_3 zenon_TE_dr). zenon_intro zenon_Hb1. % 8.47/8.69 apply (zenon_imply_s _ _ zenon_Hb1); [ zenon_intro zenon_Hb3 | zenon_intro zenon_Hb2 ]. % 8.47/8.69 apply (zenon_notand_s _ _ zenon_Hb3); [ zenon_intro zenon_H5e | zenon_intro zenon_Hb4 ]. % 8.47/8.69 apply (zenon_L2_ zenon_TE_dr); trivial. % 8.47/8.69 generalize (leq_succ_gt_equiv zenon_TE_dr). zenon_intro zenon_H69. % 8.47/8.69 generalize (zenon_H69 (n3)). zenon_intro zenon_Hb5. % 8.47/8.69 apply (zenon_equiv_s _ _ zenon_Hb5); [ zenon_intro zenon_Hb4; zenon_intro zenon_H96 | zenon_intro zenon_Hb7; zenon_intro zenon_Hb6 ]. % 8.47/8.69 apply (zenon_L10_ zenon_TE_dr); trivial. % 8.47/8.69 exact (zenon_Hb4 zenon_Hb7). % 8.47/8.69 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H77 | zenon_intro zenon_Hb8 ]. % 8.47/8.69 apply zenon_H6d. apply sym_equal. exact zenon_H77. % 8.47/8.69 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H79 | zenon_intro zenon_Hb9 ]. % 8.47/8.69 apply (zenon_L12_ zenon_TE_dr); trivial. % 8.47/8.69 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H7b | zenon_intro zenon_H7d ]. % 8.47/8.69 apply (zenon_L13_ zenon_TE_dr); trivial. % 8.47/8.69 apply (zenon_L14_ zenon_TE_dr); trivial. % 8.47/8.69 (* end of lemma zenon_L15_ *) % 8.47/8.69 assert (zenon_L16_ : forall (zenon_TE_dr : 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_TE_dr))) -> ((a_select2 (xinit_noise_defuse) (n3)) = (use)) -> ((a_select2 (xinit_noise_defuse) (n2)) = (use)) -> ((a_select2 (xinit_noise_defuse) (n1)) = (use)) -> (~((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (use))) -> (gt (succ (n5)) zenon_TE_dr) -> (~(zenon_TE_dr = (n4))) -> (~(zenon_TE_dr = (n5))) -> (gt (succ zenon_TE_dr) (n0)) -> False). % 8.47/8.69 do 1 intro. intros zenon_H80 zenon_Hba zenon_Had zenon_Ha9 zenon_Ha3 zenon_Ha2 zenon_H67 zenon_H71 zenon_H72 zenon_H5d. % 8.47/8.69 cut (((n0) = zenon_TE_dr)); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 8.47/8.69 congruence. % 8.47/8.69 apply (zenon_L15_ zenon_TE_dr); trivial. % 8.47/8.69 (* end of lemma zenon_L16_ *) % 8.47/8.69 assert (zenon_L17_ : (~((n1) = (n1))) -> False). % 8.47/8.69 do 0 intro. intros zenon_Hbb. % 8.47/8.69 apply zenon_Hbb. apply refl_equal. % 8.47/8.69 (* end of lemma zenon_L17_ *) % 8.47/8.69 assert (zenon_L18_ : (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))) (n1))) -> False). % 8.47/8.69 do 0 intro. intros zenon_H80 zenon_Hbc. % 8.47/8.69 elim (classic ((~((succ (succ (n0))) = (n2)))/\(~(gt (succ (succ (n0))) (n2))))); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hbe ]. % 8.47/8.69 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hc0. zenon_intro zenon_Hbf. % 8.47/8.69 exact (zenon_Hc0 successor_2). % 8.47/8.69 cut ((gt (n2) (n1)) = (gt (succ (succ (n0))) (n1))). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_Hbc. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact gt_2_1. % 8.47/8.69 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hbb]. % 8.47/8.69 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_Hc1]. % 8.47/8.69 congruence. % 8.47/8.69 apply (zenon_notand_s _ _ zenon_Hbe); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc2 ]. % 8.47/8.69 apply zenon_Hc3. zenon_intro successor_2. % 8.47/8.69 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc5 ]. % 8.47/8.69 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((n2) = (succ (succ (n0))))). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_Hc1. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_Hc4. % 8.47/8.69 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 8.47/8.69 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_Hc0]. % 8.47/8.69 congruence. % 8.47/8.69 exact (zenon_Hc0 successor_2). % 8.47/8.69 apply zenon_Hc5. apply refl_equal. % 8.47/8.69 apply zenon_Hc5. apply refl_equal. % 8.47/8.69 apply zenon_Hc2. zenon_intro zenon_Hc6. % 8.47/8.69 generalize (zenon_H80 (succ (succ (n0)))). zenon_intro zenon_Hc7. % 8.47/8.69 generalize (zenon_Hc7 (n2)). zenon_intro zenon_Hc8. % 8.47/8.69 generalize (zenon_Hc8 (n1)). zenon_intro zenon_Hc9. % 8.47/8.69 apply (zenon_imply_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hca ]. % 8.47/8.69 exact (zenon_Hbf zenon_Hc6). % 8.47/8.69 apply (zenon_imply_s _ _ zenon_Hca); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hcb ]. % 8.47/8.69 exact (zenon_Hcc gt_2_1). % 8.47/8.69 exact (zenon_Hbc zenon_Hcb). % 8.47/8.69 apply zenon_Hbb. apply refl_equal. % 8.47/8.69 (* end of lemma zenon_L18_ *) % 8.47/8.69 assert (zenon_L19_ : forall (zenon_TE_dr : zenon_U), (~(gt (succ (succ (n0))) (succ zenon_TE_dr))) -> (gt (succ zenon_TE_dr) (n0)) -> (~(zenon_TE_dr = (n5))) -> (~(zenon_TE_dr = (n4))) -> (gt (succ (n5)) zenon_TE_dr) -> (~((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (use))) -> ((a_select2 (xinit_noise_defuse) (n1)) = (use)) -> ((a_select2 (xinit_noise_defuse) (n2)) = (use)) -> ((a_select2 (xinit_noise_defuse) (n3)) = (use)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 8.47/8.69 do 1 intro. intros zenon_Hcd zenon_H5d zenon_H72 zenon_H71 zenon_H67 zenon_Ha2 zenon_Ha3 zenon_Ha9 zenon_Had zenon_H80. % 8.47/8.69 elim (classic ((n1) = (succ (n0)))); [ zenon_intro zenon_Hce | zenon_intro zenon_Hcf ]. % 8.47/8.69 elim (classic (gt (succ (succ (n0))) (n1))); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hbc ]. % 8.47/8.69 elim (classic (gt (succ (succ (n0))) (succ (n0)))); [ zenon_intro zenon_Hd0 | zenon_intro zenon_Hd1 ]. % 8.47/8.69 cut ((gt (succ (succ (n0))) (succ (n0))) = (gt (succ (succ (n0))) (succ zenon_TE_dr))). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_Hcd. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_Hd0. % 8.47/8.69 cut (((succ (n0)) = (succ zenon_TE_dr))); [idtac | apply NNPP; zenon_intro zenon_Hba]. % 8.47/8.69 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 8.47/8.69 congruence. % 8.47/8.69 apply zenon_Hc5. apply refl_equal. % 8.47/8.69 apply (zenon_L16_ zenon_TE_dr); trivial. % 8.47/8.69 cut ((gt (succ (succ (n0))) (n1)) = (gt (succ (succ (n0))) (succ (n0)))). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_Hd1. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_Hcb. % 8.47/8.69 cut (((n1) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hcf]. % 8.47/8.69 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 8.47/8.69 congruence. % 8.47/8.69 apply zenon_Hc5. apply refl_equal. % 8.47/8.69 exact (zenon_Hcf zenon_Hce). % 8.47/8.69 apply (zenon_L18_); trivial. % 8.47/8.69 elim (classic ((succ (n0)) = (succ (n0)))); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd3 ]. % 8.47/8.69 cut (((succ (n0)) = (succ (n0))) = ((n1) = (succ (n0)))). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_Hcf. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_Hd2. % 8.47/8.69 cut (((succ (n0)) = (succ (n0)))); [idtac | apply NNPP; zenon_intro zenon_Hd3]. % 8.47/8.69 cut (((succ (n0)) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Hd4]. % 8.47/8.69 congruence. % 8.47/8.69 exact (zenon_Hd4 successor_1). % 8.47/8.69 apply zenon_Hd3. apply refl_equal. % 8.47/8.69 apply zenon_Hd3. apply refl_equal. % 8.47/8.69 (* end of lemma zenon_L19_ *) % 8.47/8.69 assert (zenon_L20_ : forall (zenon_TE_dr : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) (n4)))) -> ((a_select2 (xinit_noise_defuse) (n3)) = (use)) -> ((a_select2 (xinit_noise_defuse) (n2)) = (use)) -> ((a_select2 (xinit_noise_defuse) (n1)) = (use)) -> (~((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (use))) -> (gt (succ (n5)) zenon_TE_dr) -> (~(zenon_TE_dr = (n5))) -> (gt (succ zenon_TE_dr) (n0)) -> (~(gt (succ (succ (n0))) (succ zenon_TE_dr))) -> False). % 8.47/8.69 do 1 intro. intros zenon_H80 zenon_Hd5 zenon_Had zenon_Ha9 zenon_Ha3 zenon_Ha2 zenon_H67 zenon_H72 zenon_H5d zenon_Hcd. % 8.47/8.69 cut ((zenon_TE_dr = (n4))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 8.47/8.69 cut (((xinit_noise_defuse) = (xinit_noise_defuse))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 8.47/8.69 congruence. % 8.47/8.69 apply zenon_H5c. apply refl_equal. % 8.47/8.69 apply (zenon_L19_ zenon_TE_dr); trivial. % 8.47/8.69 (* end of lemma zenon_L20_ *) % 8.47/8.69 assert (zenon_L21_ : forall (zenon_TE_dr : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> ((a_select2 (xinit_noise_defuse) (n4)) = (use)) -> (~(gt (succ (succ (n0))) (succ zenon_TE_dr))) -> (gt (succ zenon_TE_dr) (n0)) -> (gt (succ (n5)) zenon_TE_dr) -> (~((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (use))) -> ((a_select2 (xinit_noise_defuse) (n1)) = (use)) -> ((a_select2 (xinit_noise_defuse) (n2)) = (use)) -> ((a_select2 (xinit_noise_defuse) (n3)) = (use)) -> ((a_select2 (xinit_noise_defuse) (n5)) = (use)) -> False). % 8.47/8.69 do 1 intro. intros zenon_H80 zenon_Hd6 zenon_Hcd zenon_H5d zenon_H67 zenon_Ha2 zenon_Ha3 zenon_Ha9 zenon_Had zenon_Hd7. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) (n4)) = (use)) = ((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (use))). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_Ha2. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_Hd6. % 8.47/8.69 cut (((use) = (use))); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) (n4)) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))); [idtac | apply NNPP; zenon_intro zenon_Hd8]. % 8.47/8.69 congruence. % 8.47/8.69 elim (classic ((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ]. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) zenon_TE_dr)) = ((a_select2 (xinit_noise_defuse) (n4)) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_Hd8. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_Ha5. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) (n4)))); [idtac | apply NNPP; zenon_intro zenon_Hd5]. % 8.47/8.69 congruence. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) (n5)) = (use)) = ((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (use))). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_Ha2. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_Hd7. % 8.47/8.69 cut (((use) = (use))); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) (n5)) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 8.47/8.69 congruence. % 8.47/8.69 elim (classic ((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ]. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) zenon_TE_dr)) = ((a_select2 (xinit_noise_defuse) (n5)) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_Hd9. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_Ha5. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) (n5)))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 8.47/8.69 congruence. % 8.47/8.69 cut ((zenon_TE_dr = (n5))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 8.47/8.69 cut (((xinit_noise_defuse) = (xinit_noise_defuse))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 8.47/8.69 congruence. % 8.47/8.69 apply zenon_H5c. apply refl_equal. % 8.47/8.69 apply (zenon_L20_ zenon_TE_dr); trivial. % 8.47/8.69 apply zenon_Ha6. apply refl_equal. % 8.47/8.69 apply zenon_Ha6. apply refl_equal. % 8.47/8.69 apply zenon_Ha1. apply refl_equal. % 8.47/8.69 apply zenon_Ha6. apply refl_equal. % 8.47/8.69 apply zenon_Ha6. apply refl_equal. % 8.47/8.69 apply zenon_Ha1. apply refl_equal. % 8.47/8.69 (* end of lemma zenon_L21_ *) % 8.47/8.69 assert (zenon_L22_ : forall (zenon_TE_dr : zenon_U), ((a_select2 (xinit_noise_defuse) (n5)) = (use)) -> ((a_select2 (xinit_noise_defuse) (n3)) = (use)) -> ((a_select2 (xinit_noise_defuse) (n2)) = (use)) -> ((a_select2 (xinit_noise_defuse) (n1)) = (use)) -> (~((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (use))) -> (gt (succ (n5)) zenon_TE_dr) -> (gt (succ zenon_TE_dr) (n0)) -> ((a_select2 (xinit_noise_defuse) (n4)) = (use)) -> (~(gt (n2) (succ zenon_TE_dr))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> False). % 8.47/8.69 do 1 intro. intros zenon_Hd7 zenon_Had zenon_Ha9 zenon_Ha3 zenon_Ha2 zenon_H67 zenon_H5d zenon_Hd6 zenon_Hdb zenon_H80. % 8.47/8.69 elim (classic ((n2) = (succ (succ (n0))))); [ zenon_intro zenon_Hdc | zenon_intro zenon_Hc1 ]. % 8.47/8.69 elim (classic (gt (succ (succ (n0))) (succ zenon_TE_dr))); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hcd ]. % 8.47/8.69 cut ((gt (succ (succ (n0))) (succ zenon_TE_dr)) = (gt (n2) (succ zenon_TE_dr))). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_Hdb. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_Hdd. % 8.47/8.69 cut (((succ zenon_TE_dr) = (succ zenon_TE_dr))); [idtac | apply NNPP; zenon_intro zenon_Hde]. % 8.47/8.69 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_Hc0]. % 8.47/8.69 congruence. % 8.47/8.69 elim (classic ((n2) = (n2))); [ zenon_intro zenon_Hdf | zenon_intro zenon_H66 ]. % 8.47/8.69 cut (((n2) = (n2)) = ((succ (succ (n0))) = (n2))). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_Hc0. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_Hdf. % 8.47/8.69 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 8.47/8.69 cut (((n2) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_Hc1]. % 8.47/8.69 congruence. % 8.47/8.69 exact (zenon_Hc1 zenon_Hdc). % 8.47/8.69 apply zenon_H66. apply refl_equal. % 8.47/8.69 apply zenon_H66. apply refl_equal. % 8.47/8.69 apply zenon_Hde. apply refl_equal. % 8.47/8.69 apply (zenon_L21_ zenon_TE_dr); trivial. % 8.47/8.69 elim (classic ((succ (succ (n0))) = (succ (succ (n0))))); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc5 ]. % 8.47/8.69 cut (((succ (succ (n0))) = (succ (succ (n0)))) = ((n2) = (succ (succ (n0))))). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_Hc1. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_Hc4. % 8.47/8.69 cut (((succ (succ (n0))) = (succ (succ (n0))))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 8.47/8.69 cut (((succ (succ (n0))) = (n2))); [idtac | apply NNPP; zenon_intro zenon_Hc0]. % 8.47/8.69 congruence. % 8.47/8.69 exact (zenon_Hc0 successor_2). % 8.47/8.69 apply zenon_Hc5. apply refl_equal. % 8.47/8.69 apply zenon_Hc5. apply refl_equal. % 8.47/8.69 (* end of lemma zenon_L22_ *) % 8.47/8.69 assert (zenon_L23_ : forall (zenon_TE_dr : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~(gt (n4) (succ zenon_TE_dr))) -> ((a_select2 (xinit_noise_defuse) (n4)) = (use)) -> (gt (succ zenon_TE_dr) (n0)) -> (gt (succ (n5)) zenon_TE_dr) -> (~((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (use))) -> ((a_select2 (xinit_noise_defuse) (n1)) = (use)) -> ((a_select2 (xinit_noise_defuse) (n2)) = (use)) -> ((a_select2 (xinit_noise_defuse) (n3)) = (use)) -> ((a_select2 (xinit_noise_defuse) (n5)) = (use)) -> False). % 8.47/8.69 do 1 intro. intros zenon_H80 zenon_He0 zenon_Hd6 zenon_H5d zenon_H67 zenon_Ha2 zenon_Ha3 zenon_Ha9 zenon_Had zenon_Hd7. % 8.47/8.69 elim (classic (gt (n3) (succ zenon_TE_dr))); [ zenon_intro zenon_He1 | zenon_intro zenon_He2 ]. % 8.47/8.69 generalize (zenon_H80 (n4)). zenon_intro zenon_H85. % 8.47/8.69 generalize (zenon_H85 (n3)). zenon_intro zenon_H86. % 8.47/8.69 generalize (zenon_H86 (succ zenon_TE_dr)). zenon_intro zenon_He3. % 8.47/8.69 apply (zenon_imply_s _ _ zenon_He3); [ zenon_intro zenon_H89 | zenon_intro zenon_He4 ]. % 8.47/8.69 exact (zenon_H89 gt_4_3). % 8.47/8.69 apply (zenon_imply_s _ _ zenon_He4); [ zenon_intro zenon_He2 | zenon_intro zenon_He5 ]. % 8.47/8.69 exact (zenon_He2 zenon_He1). % 8.47/8.69 exact (zenon_He0 zenon_He5). % 8.47/8.69 elim (classic (gt (n2) (succ zenon_TE_dr))); [ zenon_intro zenon_He6 | zenon_intro zenon_Hdb ]. % 8.47/8.69 generalize (zenon_H80 (n3)). zenon_intro zenon_H8e. % 8.47/8.69 generalize (zenon_H8e (n2)). zenon_intro zenon_H8f. % 8.47/8.69 generalize (zenon_H8f (succ zenon_TE_dr)). zenon_intro zenon_He7. % 8.47/8.69 apply (zenon_imply_s _ _ zenon_He7); [ zenon_intro zenon_H92 | zenon_intro zenon_He8 ]. % 8.47/8.69 exact (zenon_H92 gt_3_2). % 8.47/8.69 apply (zenon_imply_s _ _ zenon_He8); [ zenon_intro zenon_Hdb | zenon_intro zenon_He1 ]. % 8.47/8.69 exact (zenon_Hdb zenon_He6). % 8.47/8.69 exact (zenon_He2 zenon_He1). % 8.47/8.69 apply (zenon_L22_ zenon_TE_dr); trivial. % 8.47/8.69 (* end of lemma zenon_L23_ *) % 8.47/8.69 assert (zenon_L24_ : forall (zenon_TE_dr : zenon_U), (~((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (use))) -> ((a_select2 (xinit_noise_defuse) (n0)) = (use)) -> (zenon_TE_dr = (n0)) -> False). % 8.47/8.69 do 1 intro. intros zenon_Ha2 zenon_He9 zenon_H77. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) (n0)) = (use)) = ((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (use))). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_Ha2. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_He9. % 8.47/8.69 cut (((use) = (use))); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) (n0)) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))); [idtac | apply NNPP; zenon_intro zenon_Hea]. % 8.47/8.69 congruence. % 8.47/8.69 elim (classic ((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ]. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) zenon_TE_dr)) = ((a_select2 (xinit_noise_defuse) (n0)) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_Hea. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_Ha5. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) (n0)))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 8.47/8.69 congruence. % 8.47/8.69 cut ((zenon_TE_dr = (n0))); [idtac | apply NNPP; zenon_intro zenon_Hec]. % 8.47/8.69 cut (((xinit_noise_defuse) = (xinit_noise_defuse))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 8.47/8.69 congruence. % 8.47/8.69 apply zenon_H5c. apply refl_equal. % 8.47/8.69 exact (zenon_Hec zenon_H77). % 8.47/8.69 apply zenon_Ha6. apply refl_equal. % 8.47/8.69 apply zenon_Ha6. apply refl_equal. % 8.47/8.69 apply zenon_Ha1. apply refl_equal. % 8.47/8.69 (* end of lemma zenon_L24_ *) % 8.47/8.69 assert (zenon_L25_ : forall (zenon_TE_dr : 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_TE_dr) (n0)) -> ((a_select2 (xinit_noise_defuse) (n4)) = (use)) -> (gt (succ (n5)) zenon_TE_dr) -> (~((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (use))) -> ((a_select2 (xinit_noise_defuse) (n1)) = (use)) -> ((a_select2 (xinit_noise_defuse) (n2)) = (use)) -> ((a_select2 (xinit_noise_defuse) (n3)) = (use)) -> ((a_select2 (xinit_noise_defuse) (n5)) = (use)) -> (~(zenon_TE_dr = (n4))) -> (~(zenon_TE_dr = (n5))) -> ((a_select2 (xinit_noise_defuse) (n0)) = (use)) -> False). % 8.47/8.69 do 1 intro. intros zenon_H80 zenon_H5d zenon_Hd6 zenon_H67 zenon_Ha2 zenon_Ha3 zenon_Ha9 zenon_Had zenon_Hd7 zenon_H71 zenon_H72 zenon_He9. % 8.47/8.69 generalize (finite_domain_3 zenon_TE_dr). zenon_intro zenon_Hb1. % 8.47/8.69 apply (zenon_imply_s _ _ zenon_Hb1); [ zenon_intro zenon_Hb3 | zenon_intro zenon_Hb2 ]. % 8.47/8.69 apply (zenon_notand_s _ _ zenon_Hb3); [ zenon_intro zenon_H5e | zenon_intro zenon_Hb4 ]. % 8.47/8.69 apply (zenon_L2_ zenon_TE_dr); trivial. % 8.47/8.69 generalize (leq_succ_gt_equiv zenon_TE_dr). zenon_intro zenon_H69. % 8.47/8.69 generalize (zenon_H69 (n3)). zenon_intro zenon_Hb5. % 8.47/8.69 apply (zenon_equiv_s _ _ zenon_Hb5); [ zenon_intro zenon_Hb4; zenon_intro zenon_H96 | zenon_intro zenon_Hb7; zenon_intro zenon_Hb6 ]. % 8.47/8.69 elim (classic ((~((succ (n3)) = (succ zenon_TE_dr)))/\(~(gt (succ (n3)) (succ zenon_TE_dr))))); [ zenon_intro zenon_Hed | zenon_intro zenon_Hee ]. % 8.47/8.69 apply (zenon_and_s _ _ zenon_Hed). zenon_intro zenon_Hf0. zenon_intro zenon_Hef. % 8.47/8.69 elim (classic (gt (n4) (succ zenon_TE_dr))); [ zenon_intro zenon_He5 | zenon_intro zenon_He0 ]. % 8.47/8.69 elim (classic (gt (succ (succ (succ (succ (n0))))) (succ zenon_TE_dr))); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf2 ]. % 8.47/8.69 cut ((gt (succ (succ (succ (succ (n0))))) (succ zenon_TE_dr)) = (gt (succ (n3)) (succ zenon_TE_dr))). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_Hef. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_Hf1. % 8.47/8.69 cut (((succ zenon_TE_dr) = (succ zenon_TE_dr))); [idtac | apply NNPP; zenon_intro zenon_Hde]. % 8.47/8.69 cut (((succ (succ (succ (succ (n0))))) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 8.47/8.69 congruence. % 8.47/8.69 elim (classic ((succ (n3)) = (succ (n3)))); [ zenon_intro zenon_H9b | zenon_intro zenon_H9c ]. % 8.47/8.69 cut (((succ (n3)) = (succ (n3))) = ((succ (succ (succ (succ (n0))))) = (succ (n3)))). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_H9a. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_H9b. % 8.47/8.69 cut (((succ (n3)) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 8.47/8.69 cut (((succ (n3)) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 8.47/8.69 congruence. % 8.47/8.69 apply (zenon_L9_); trivial. % 8.47/8.69 apply zenon_H9c. apply refl_equal. % 8.47/8.69 apply zenon_H9c. apply refl_equal. % 8.47/8.69 apply zenon_Hde. apply refl_equal. % 8.47/8.69 cut ((gt (n4) (succ zenon_TE_dr)) = (gt (succ (succ (succ (succ (n0))))) (succ zenon_TE_dr))). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_Hf2. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_He5. % 8.47/8.69 cut (((succ zenon_TE_dr) = (succ zenon_TE_dr))); [idtac | apply NNPP; zenon_intro zenon_Hde]. % 8.47/8.69 cut (((n4) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_H9d]. % 8.47/8.69 congruence. % 8.47/8.69 elim (classic ((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0))))))); [ zenon_intro zenon_H9e | zenon_intro zenon_H9f ]. % 8.47/8.69 cut (((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0)))))) = ((n4) = (succ (succ (succ (succ (n0))))))). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_H9d. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_H9e. % 8.47/8.69 cut (((succ (succ (succ (succ (n0))))) = (succ (succ (succ (succ (n0))))))); [idtac | apply NNPP; zenon_intro zenon_H9f]. % 8.47/8.69 cut (((succ (succ (succ (succ (n0))))) = (n4))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 8.47/8.69 congruence. % 8.47/8.69 exact (zenon_Ha0 successor_4). % 8.47/8.69 apply zenon_H9f. apply refl_equal. % 8.47/8.69 apply zenon_H9f. apply refl_equal. % 8.47/8.69 apply zenon_Hde. apply refl_equal. % 8.47/8.69 apply (zenon_L23_ zenon_TE_dr); trivial. % 8.47/8.69 elim (classic ((n0) = zenon_TE_dr)); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H6d ]. % 8.47/8.69 cut ((gt (succ zenon_TE_dr) (n0)) = (gt (succ (n3)) zenon_TE_dr)). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_H96. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_H5d. % 8.47/8.69 cut (((n0) = zenon_TE_dr)); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 8.47/8.69 cut (((succ zenon_TE_dr) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_Hf4]. % 8.47/8.69 congruence. % 8.47/8.69 apply (zenon_notand_s _ _ zenon_Hee); [ zenon_intro zenon_Hf6 | zenon_intro zenon_Hf5 ]. % 8.47/8.69 apply zenon_Hf6. zenon_intro zenon_Hf7. % 8.47/8.69 elim (classic ((succ (n3)) = (succ (n3)))); [ zenon_intro zenon_H9b | zenon_intro zenon_H9c ]. % 8.47/8.69 cut (((succ (n3)) = (succ (n3))) = ((succ zenon_TE_dr) = (succ (n3)))). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_Hf4. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_H9b. % 8.47/8.69 cut (((succ (n3)) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 8.47/8.69 cut (((succ (n3)) = (succ zenon_TE_dr))); [idtac | apply NNPP; zenon_intro zenon_Hf0]. % 8.47/8.69 congruence. % 8.47/8.69 exact (zenon_Hf0 zenon_Hf7). % 8.47/8.69 apply zenon_H9c. apply refl_equal. % 8.47/8.69 apply zenon_H9c. apply refl_equal. % 8.47/8.69 apply zenon_Hf5. zenon_intro zenon_Hf8. % 8.47/8.69 generalize (zenon_H80 (succ (n3))). zenon_intro zenon_Hf9. % 8.47/8.69 generalize (zenon_Hf9 (succ zenon_TE_dr)). zenon_intro zenon_Hfa. % 8.47/8.69 generalize (zenon_Hfa (n0)). zenon_intro zenon_Hfb. % 8.47/8.69 apply (zenon_imply_s _ _ zenon_Hfb); [ zenon_intro zenon_Hef | zenon_intro zenon_Hfc ]. % 8.47/8.69 exact (zenon_Hef zenon_Hf8). % 8.47/8.69 apply (zenon_imply_s _ _ zenon_Hfc); [ zenon_intro zenon_H63 | zenon_intro zenon_Hfd ]. % 8.47/8.69 exact (zenon_H63 zenon_H5d). % 8.47/8.69 cut ((gt (succ (n3)) (n0)) = (gt (succ (n3)) zenon_TE_dr)). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_H96. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_Hfd. % 8.47/8.69 cut (((n0) = zenon_TE_dr)); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 8.47/8.69 cut (((succ (n3)) = (succ (n3)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 8.47/8.69 congruence. % 8.47/8.69 apply zenon_H9c. apply refl_equal. % 8.47/8.69 exact (zenon_H6d zenon_Hf3). % 8.47/8.69 exact (zenon_H6d zenon_Hf3). % 8.47/8.69 apply (zenon_L10_ zenon_TE_dr); trivial. % 8.47/8.69 exact (zenon_Hb4 zenon_Hb7). % 8.47/8.69 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H77 | zenon_intro zenon_Hb8 ]. % 8.47/8.69 apply (zenon_L24_ zenon_TE_dr); trivial. % 8.47/8.69 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H79 | zenon_intro zenon_Hb9 ]. % 8.47/8.69 apply (zenon_L12_ zenon_TE_dr); trivial. % 8.47/8.69 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H7b | zenon_intro zenon_H7d ]. % 8.47/8.69 apply (zenon_L13_ zenon_TE_dr); trivial. % 8.47/8.69 apply (zenon_L14_ zenon_TE_dr); trivial. % 8.47/8.69 (* end of lemma zenon_L25_ *) % 8.47/8.69 assert (zenon_L26_ : forall (zenon_TE_dr : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((gt x y)->((gt y z)->(gt x z)))))) -> (~((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) (n4)))) -> ((a_select2 (xinit_noise_defuse) (n0)) = (use)) -> (~(zenon_TE_dr = (n5))) -> ((a_select2 (xinit_noise_defuse) (n5)) = (use)) -> ((a_select2 (xinit_noise_defuse) (n3)) = (use)) -> ((a_select2 (xinit_noise_defuse) (n2)) = (use)) -> ((a_select2 (xinit_noise_defuse) (n1)) = (use)) -> (~((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (use))) -> (gt (succ (n5)) zenon_TE_dr) -> ((a_select2 (xinit_noise_defuse) (n4)) = (use)) -> (gt (succ zenon_TE_dr) (n0)) -> False). % 8.47/8.69 do 1 intro. intros zenon_H80 zenon_Hd5 zenon_He9 zenon_H72 zenon_Hd7 zenon_Had zenon_Ha9 zenon_Ha3 zenon_Ha2 zenon_H67 zenon_Hd6 zenon_H5d. % 8.47/8.69 cut ((zenon_TE_dr = (n4))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 8.47/8.69 cut (((xinit_noise_defuse) = (xinit_noise_defuse))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 8.47/8.69 congruence. % 8.47/8.69 apply zenon_H5c. apply refl_equal. % 8.47/8.69 apply (zenon_L25_ zenon_TE_dr); trivial. % 8.47/8.69 (* end of lemma zenon_L26_ *) % 8.47/8.69 apply NNPP. intro zenon_G. % 8.47/8.69 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_H80 | zenon_intro zenon_Hfe ]. % 8.47/8.69 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H100. zenon_intro zenon_Hff. % 8.47/8.69 apply (zenon_and_s _ _ zenon_H100). zenon_intro zenon_H102. zenon_intro zenon_H101. % 8.47/8.69 apply (zenon_and_s _ _ zenon_H101). zenon_intro zenon_H104. zenon_intro zenon_H103. % 8.47/8.69 apply (zenon_and_s _ _ zenon_H103). zenon_intro zenon_H106. zenon_intro zenon_H105. % 8.47/8.69 apply (zenon_and_s _ _ zenon_H105). zenon_intro zenon_H108. zenon_intro zenon_H107. % 8.47/8.69 apply (zenon_and_s _ _ zenon_H107). zenon_intro zenon_H10a. zenon_intro zenon_H109. % 8.47/8.69 apply (zenon_and_s _ _ zenon_H109). zenon_intro zenon_H10c. zenon_intro zenon_H10b. % 8.47/8.69 apply (zenon_and_s _ _ zenon_H10b). zenon_intro zenon_H10e. zenon_intro zenon_H10d. % 8.47/8.69 apply (zenon_and_s _ _ zenon_H10d). zenon_intro zenon_H110. zenon_intro zenon_H10f. % 8.47/8.69 apply (zenon_and_s _ _ zenon_H10f). zenon_intro zenon_H112. zenon_intro zenon_H111. % 8.47/8.69 apply (zenon_and_s _ _ zenon_H111). zenon_intro zenon_H114. zenon_intro zenon_H113. % 8.47/8.69 apply (zenon_and_s _ _ zenon_H113). zenon_intro zenon_H116. zenon_intro zenon_H115. % 8.47/8.69 apply (zenon_and_s _ _ zenon_H115). zenon_intro zenon_H118. zenon_intro zenon_H117. % 8.47/8.69 apply (zenon_and_s _ _ zenon_H117). zenon_intro zenon_H11a. zenon_intro zenon_H119. % 8.47/8.69 apply (zenon_and_s _ _ zenon_H119). zenon_intro zenon_H11c. zenon_intro zenon_H11b. % 8.47/8.69 apply (zenon_and_s _ _ zenon_H11b). zenon_intro zenon_H11e. zenon_intro zenon_H11d. % 8.47/8.69 apply (zenon_and_s _ _ zenon_H11d). zenon_intro zenon_H120. zenon_intro zenon_H11f. % 8.47/8.69 apply (zenon_and_s _ _ zenon_H11f). zenon_intro zenon_H122. zenon_intro zenon_H121. % 8.47/8.69 apply (zenon_and_s _ _ zenon_H121). zenon_intro zenon_H124. zenon_intro zenon_H123. % 8.47/8.69 apply (zenon_and_s _ _ zenon_H123). zenon_intro zenon_H126. zenon_intro zenon_H125. % 8.47/8.69 apply (zenon_and_s _ _ zenon_H125). zenon_intro zenon_H128. zenon_intro zenon_H127. % 8.47/8.69 apply (zenon_and_s _ _ zenon_H127). zenon_intro zenon_H12a. zenon_intro zenon_H129. % 8.47/8.69 apply (zenon_and_s _ _ zenon_H129). zenon_intro zenon_He9. zenon_intro zenon_H12b. % 8.47/8.69 apply (zenon_and_s _ _ zenon_H12b). zenon_intro zenon_Ha3. zenon_intro zenon_H12c. % 8.47/8.69 apply (zenon_and_s _ _ zenon_H12c). zenon_intro zenon_Ha9. zenon_intro zenon_H12d. % 8.47/8.69 apply (zenon_and_s _ _ zenon_H12d). zenon_intro zenon_Had. zenon_intro zenon_H12e. % 8.47/8.69 apply (zenon_and_s _ _ zenon_H12e). zenon_intro zenon_Hd6. zenon_intro zenon_H12f. % 8.47/8.69 apply (zenon_and_s _ _ zenon_H12f). zenon_intro zenon_Hd7. zenon_intro zenon_H130. % 8.47/8.69 apply (zenon_notallex_s (fun E : zenon_U => (((leq (n0) E)/\(leq E (n5)))->((a_select2 (xinit_noise_defuse) E) = (use)))) zenon_Hff); [ zenon_intro zenon_H131; idtac ]. % 8.47/8.69 elim zenon_H131. zenon_intro zenon_TE_dr. zenon_intro zenon_H132. % 8.47/8.69 apply (zenon_notimply_s _ _ zenon_H132). zenon_intro zenon_H133. zenon_intro zenon_Ha2. % 8.47/8.69 apply (zenon_and_s _ _ zenon_H133). zenon_intro zenon_H62. zenon_intro zenon_H6b. % 8.47/8.69 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H60. % 8.47/8.69 generalize (zenon_H60 zenon_TE_dr). zenon_intro zenon_H61. % 8.47/8.69 apply (zenon_equiv_s _ _ zenon_H61); [ zenon_intro zenon_H5e; zenon_intro zenon_H63 | zenon_intro zenon_H62; zenon_intro zenon_H5d ]. % 8.47/8.69 exact (zenon_H5e zenon_H62). % 8.47/8.69 generalize (leq_succ_gt_equiv zenon_TE_dr). zenon_intro zenon_H69. % 8.47/8.69 generalize (zenon_H69 (n5)). zenon_intro zenon_H6a. % 8.47/8.69 apply (zenon_equiv_s _ _ zenon_H6a); [ zenon_intro zenon_H68; zenon_intro zenon_H6c | zenon_intro zenon_H6b; zenon_intro zenon_H67 ]. % 8.47/8.69 exact (zenon_H68 zenon_H6b). % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) (n4)) = (use)) = ((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (use))). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_Ha2. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_Hd6. % 8.47/8.69 cut (((use) = (use))); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) (n4)) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))); [idtac | apply NNPP; zenon_intro zenon_Hd8]. % 8.47/8.69 congruence. % 8.47/8.69 elim (classic ((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ]. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) zenon_TE_dr)) = ((a_select2 (xinit_noise_defuse) (n4)) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_Hd8. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_Ha5. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) (n4)))); [idtac | apply NNPP; zenon_intro zenon_Hd5]. % 8.47/8.69 congruence. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) (n5)) = (use)) = ((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (use))). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_Ha2. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_Hd7. % 8.47/8.69 cut (((use) = (use))); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) (n5)) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 8.47/8.69 congruence. % 8.47/8.69 elim (classic ((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha6 ]. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) zenon_TE_dr)) = ((a_select2 (xinit_noise_defuse) (n5)) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))). % 8.47/8.69 intro zenon_D_pnotp. % 8.47/8.69 apply zenon_Hd9. % 8.47/8.69 rewrite <- zenon_D_pnotp. % 8.47/8.69 exact zenon_Ha5. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) zenon_TE_dr))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 8.47/8.69 cut (((a_select2 (xinit_noise_defuse) zenon_TE_dr) = (a_select2 (xinit_noise_defuse) (n5)))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 8.47/8.69 congruence. % 8.47/8.69 cut ((zenon_TE_dr = (n5))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 8.47/8.69 cut (((xinit_noise_defuse) = (xinit_noise_defuse))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 8.47/8.69 congruence. % 8.47/8.69 apply zenon_H5c. apply refl_equal. % 8.47/8.69 apply (zenon_L26_ zenon_TE_dr); trivial. % 8.47/8.69 apply zenon_Ha6. apply refl_equal. % 8.47/8.69 apply zenon_Ha6. apply refl_equal. % 8.47/8.69 apply zenon_Ha1. apply refl_equal. % 8.47/8.69 apply zenon_Ha6. apply refl_equal. % 8.47/8.69 apply zenon_Ha6. apply refl_equal. % 8.47/8.69 apply zenon_Ha1. apply refl_equal. % 8.47/8.69 apply zenon_Hfe. zenon_intro zenon_Tx_lw. apply NNPP. zenon_intro zenon_H135. % 8.47/8.69 apply zenon_H135. zenon_intro zenon_Ty_ly. apply NNPP. zenon_intro zenon_H137. % 8.47/8.69 apply zenon_H137. zenon_intro zenon_Tz_ma. apply NNPP. zenon_intro zenon_H139. % 8.47/8.69 apply (zenon_notimply_s _ _ zenon_H139). zenon_intro zenon_H13b. zenon_intro zenon_H13a. % 8.47/8.69 apply (zenon_notimply_s _ _ zenon_H13a). zenon_intro zenon_H13d. zenon_intro zenon_H13c. % 8.47/8.69 generalize (transitivity_gt zenon_Tx_lw). zenon_intro zenon_H13e. % 8.47/8.69 generalize (zenon_H13e zenon_Ty_ly). zenon_intro zenon_H13f. % 8.47/8.69 generalize (zenon_H13f zenon_Tz_ma). zenon_intro zenon_H140. % 8.47/8.69 apply (zenon_imply_s _ _ zenon_H140); [ zenon_intro zenon_H142 | zenon_intro zenon_H141 ]. % 8.47/8.69 apply (zenon_notand_s _ _ zenon_H142); [ zenon_intro zenon_H144 | zenon_intro zenon_H143 ]. % 8.47/8.69 exact (zenon_H144 zenon_H13b). % 8.47/8.69 exact (zenon_H143 zenon_H13d). % 8.47/8.69 exact (zenon_H13c zenon_H141). % 8.47/8.69 Qed. % 8.47/8.69 % SZS output end Proof % 8.47/8.69 (* END-PROOF *) % 8.47/8.69 nodes searched: 612029 % 8.47/8.69 max branch formulas: 3213 % 8.47/8.69 proof nodes created: 1403 % 8.47/8.69 formulas created: 364751 % 8.47/8.69 %------------------------------------------------------------------------------