%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : MGT063+1 : TPTP v9.3.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n031.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Tue Sep 8 06:24:25 AM UTC 2026 % Result : Theorem 112.02s 112.35s % Output : Proof 0.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT063+1 : TPTP v9.3.0. Released v2.4.0. % 0.00/0.03 % Command : run_zenon %s %d % 0.08/0.35 % Computer : n031.cluster.edu % 0.08/0.35 % Model : x86_64 x86_64 % 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.35 % Memory : 8046.5625MB % 0.08/0.35 % OS : Linux 6.8.0-71-generic % 0.08/0.35 % CPULimit : 300 % 0.08/0.35 % WCLimit : 300 % 0.08/0.35 % DateTime : Mon Sep 7 13:43:26 UTC 2026 % 0.08/0.36 % CPUTime : % 112.02/112.35 (* PROOF-FOUND *) % 112.02/112.35 % SZS status Theorem % 112.02/112.35 (* BEGIN-PROOF *) % 112.02/112.35 % SZS output start Proof % 112.02/112.35 Theorem theorem_9 : (forall X : zenon_U, (forall T0 : zenon_U, (forall T1 : zenon_U, (forall T2 : zenon_U, (forall T3 : zenon_U, (((organization X)/\((robust_position X)/\((~(has_endowment X))/\(((age X T0) = (zero))/\((greater (sigma) (zero))/\((greater (tau) (zero))/\((smaller (sigma) (tau))/\((smaller_or_equal (age X T1) (sigma))/\((greater (age X T2) (sigma))/\((smaller_or_equal (age X T2) (tau))/\(greater (age X T3) (tau))))))))))))->((smaller (hazard_of_mortality X T3) (hazard_of_mortality X T1))/\((smaller (hazard_of_mortality X T1) (hazard_of_mortality X T2))/\((hazard_of_mortality X T1) = (hazard_of_mortality X T0)))))))))). % 112.02/112.35 Proof. % 112.02/112.35 assert (zenon_L1_ : forall (zenon_TT3_x : zenon_U) (zenon_TX_y : zenon_U), (~(~(has_immunity zenon_TX_y zenon_TT3_x))) -> (~(has_immunity zenon_TX_y zenon_TT3_x)) -> False). % 112.02/112.35 do 2 intro. intros zenon_H15 zenon_H16. % 112.02/112.35 exact (zenon_H15 zenon_H16). % 112.02/112.35 (* end of lemma zenon_L1_ *) % 112.02/112.35 assert (zenon_L2_ : forall (zenon_TX_y : zenon_U), (has_endowment zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> False). % 112.02/112.35 do 1 intro. intros zenon_H19 zenon_H1a. % 112.02/112.35 generalize (definition_1 zenon_TX_y). zenon_intro zenon_H1b. % 112.02/112.35 apply (zenon_equiv_s _ _ zenon_H1b); [ zenon_intro zenon_H1d; zenon_intro zenon_H1a | zenon_intro zenon_H19; zenon_intro zenon_H1c ]. % 112.02/112.35 exact (zenon_H1d zenon_H19). % 112.02/112.35 exact (zenon_H1a zenon_H1c). % 112.02/112.35 (* end of lemma zenon_L2_ *) % 112.02/112.35 assert (zenon_L3_ : forall (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (~(~(has_immunity zenon_TX_y zenon_TT1_bg))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> False). % 112.02/112.35 do 2 intro. intros zenon_H1e zenon_H1f zenon_H1a. % 112.02/112.35 apply zenon_H1e. zenon_intro zenon_H21. % 112.02/112.35 generalize (assumption_1 zenon_TX_y). zenon_intro zenon_H22. % 112.02/112.35 generalize (zenon_H22 zenon_TT1_bg). zenon_intro zenon_H23. % 112.02/112.35 apply (zenon_imply_s _ _ zenon_H23); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 112.02/112.35 apply (zenon_notand_s _ _ zenon_H25); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 112.02/112.35 exact (zenon_H27 zenon_H1f). % 112.02/112.35 apply zenon_H26. zenon_intro zenon_H19. % 112.02/112.35 apply (zenon_L2_ zenon_TX_y); trivial. % 112.02/112.35 exact (zenon_H24 zenon_H21). % 112.02/112.35 (* end of lemma zenon_L3_ *) % 112.02/112.35 assert (zenon_L4_ : forall (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (((~(is_aligned zenon_TX_y zenon_TT1_bg))/\(~(positional_advantage zenon_TX_y zenon_TT1_bg)))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))) -> (~(positional_advantage zenon_TX_y zenon_TT1_bg)) -> (~(is_aligned zenon_TX_y zenon_TT1_bg)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))) -> False). % 112.02/112.35 do 2 intro. intros zenon_H28 zenon_H29 zenon_H2a zenon_H2b. % 112.02/112.35 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ]. % 112.02/112.35 apply (zenon_notand_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ]. % 112.02/112.35 exact (zenon_H2f zenon_H2a). % 112.02/112.35 exact (zenon_H2e zenon_H29). % 112.02/112.35 exact (zenon_H2b zenon_H2c). % 112.02/112.35 (* end of lemma zenon_L4_ *) % 112.02/112.35 assert (zenon_L5_ : forall (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (((is_aligned zenon_TX_y zenon_TT1_bg)/\(~(positional_advantage zenon_TX_y zenon_TT1_bg)))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))) -> (~(positional_advantage zenon_TX_y zenon_TT1_bg)) -> (((~(is_aligned zenon_TX_y zenon_TT1_bg))/\(~(positional_advantage zenon_TX_y zenon_TT1_bg)))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))) -> False). % 112.02/112.35 do 2 intro. intros zenon_H30 zenon_H29 zenon_H28 zenon_H2b zenon_H31. % 112.02/112.35 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 112.02/112.35 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ]. % 112.02/112.35 apply (zenon_L4_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.35 exact (zenon_H2e zenon_H29). % 112.02/112.35 exact (zenon_H31 zenon_H32). % 112.02/112.35 (* end of lemma zenon_L5_ *) % 112.02/112.35 assert (zenon_L6_ : forall (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (positional_advantage zenon_TX_y zenon_TT1_bg) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (greater (tau) (sigma)) -> False). % 112.02/112.35 do 2 intro. intros zenon_H34 zenon_H35 zenon_H36 zenon_H37 zenon_H38. % 112.02/112.35 generalize (zenon_H35 zenon_TT1_bg). zenon_intro zenon_H39. % 112.02/112.35 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_H3b. zenon_intro zenon_H3a. % 112.02/112.35 apply (zenon_imply_s _ _ zenon_H3b); [ zenon_intro zenon_H3c | zenon_intro zenon_H29 ]. % 112.02/112.35 generalize (definition_smaller_or_equal (age zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H3d. % 112.02/112.35 generalize (zenon_H3d (tau)). zenon_intro zenon_H3e. % 112.02/112.35 apply (zenon_equiv_s _ _ zenon_H3e); [ zenon_intro zenon_H3c; zenon_intro zenon_H41 | zenon_intro zenon_H40; zenon_intro zenon_H3f ]. % 112.02/112.35 apply (zenon_notor_s _ _ zenon_H41). zenon_intro zenon_H43. zenon_intro zenon_H42. % 112.02/112.35 generalize (definition_smaller (age zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H44. % 112.02/112.35 generalize (zenon_H44 (tau)). zenon_intro zenon_H45. % 112.02/112.35 apply (zenon_equiv_s _ _ zenon_H45); [ zenon_intro zenon_H43; zenon_intro zenon_H48 | zenon_intro zenon_H47; zenon_intro zenon_H46 ]. % 112.02/112.35 elim (classic ((~((tau) = (sigma)))/\(~(greater (tau) (sigma))))); [ zenon_intro zenon_H49 | zenon_intro zenon_H4a ]. % 112.02/112.35 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 112.02/112.35 exact (zenon_H4b zenon_H38). % 112.02/112.35 cut ((greater (sigma) (age zenon_TX_y zenon_TT1_bg)) = (greater (tau) (age zenon_TX_y zenon_TT1_bg))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_H48. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact zenon_H37. % 112.02/112.35 cut (((age zenon_TX_y zenon_TT1_bg) = (age zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 112.02/112.35 cut (((sigma) = (tau))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 112.02/112.35 congruence. % 112.02/112.35 apply (zenon_notand_s _ _ zenon_H4a); [ zenon_intro zenon_H50 | zenon_intro zenon_H4f ]. % 112.02/112.35 apply zenon_H50. zenon_intro zenon_H51. % 112.02/112.35 elim (classic ((tau) = (tau))); [ zenon_intro zenon_H52 | zenon_intro zenon_H53 ]. % 112.02/112.35 cut (((tau) = (tau)) = ((sigma) = (tau))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_H4e. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact zenon_H52. % 112.02/112.35 cut (((tau) = (tau))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 112.02/112.35 cut (((tau) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 112.02/112.35 congruence. % 112.02/112.35 exact (zenon_H4c zenon_H51). % 112.02/112.35 apply zenon_H53. apply refl_equal. % 112.02/112.35 apply zenon_H53. apply refl_equal. % 112.02/112.35 apply zenon_H4f. zenon_intro zenon_H38. % 112.02/112.35 generalize (zenon_H34 (tau)). zenon_intro zenon_H54. % 112.02/112.35 generalize (zenon_H54 (sigma)). zenon_intro zenon_H55. % 112.02/112.35 generalize (zenon_H55 (age zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H56. % 112.02/112.35 apply (zenon_imply_s _ _ zenon_H56); [ zenon_intro zenon_H4b | zenon_intro zenon_H57 ]. % 112.02/112.35 exact (zenon_H4b zenon_H38). % 112.02/112.35 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H58 | zenon_intro zenon_H46 ]. % 112.02/112.35 exact (zenon_H58 zenon_H37). % 112.02/112.35 exact (zenon_H48 zenon_H46). % 112.02/112.35 apply zenon_H4d. apply refl_equal. % 112.02/112.35 exact (zenon_H43 zenon_H47). % 112.02/112.35 exact (zenon_H3c zenon_H40). % 112.02/112.35 exact (zenon_H29 zenon_H36). % 112.02/112.35 (* end of lemma zenon_L6_ *) % 112.02/112.35 assert (zenon_L7_ : (~((mod1) = (mod1))) -> False). % 112.02/112.35 do 0 intro. intros zenon_H59. % 112.02/112.35 apply zenon_H59. apply refl_equal. % 112.02/112.35 (* end of lemma zenon_L7_ *) % 112.02/112.35 assert (zenon_L8_ : forall (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1))) -> False). % 112.02/112.35 do 2 intro. intros zenon_H32 zenon_H34 zenon_H5a. % 112.02/112.35 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod2))))); [ zenon_intro zenon_H5b | zenon_intro zenon_H5c ]. % 112.02/112.35 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H31. zenon_intro zenon_H5d. % 112.02/112.35 exact (zenon_H31 zenon_H32). % 112.02/112.35 cut ((greater (mod2) (mod1)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_H5a. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact assumption_19. % 112.02/112.35 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 112.02/112.35 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 112.02/112.35 congruence. % 112.02/112.35 apply (zenon_notand_s _ _ zenon_H5c); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ]. % 112.02/112.35 apply zenon_H60. zenon_intro zenon_H32. % 112.02/112.35 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_H5e. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact zenon_H61. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31]. % 112.02/112.35 congruence. % 112.02/112.35 exact (zenon_H31 zenon_H32). % 112.02/112.35 apply zenon_H62. apply refl_equal. % 112.02/112.35 apply zenon_H62. apply refl_equal. % 112.02/112.35 apply zenon_H5f. zenon_intro zenon_H63. % 112.02/112.35 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64. % 112.02/112.35 generalize (zenon_H64 (mod2)). zenon_intro zenon_H65. % 112.02/112.35 generalize (zenon_H65 (mod1)). zenon_intro zenon_H66. % 112.02/112.35 apply (zenon_imply_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H67 ]. % 112.02/112.35 exact (zenon_H5d zenon_H63). % 112.02/112.35 apply (zenon_imply_s _ _ zenon_H67); [ zenon_intro zenon_H69 | zenon_intro zenon_H68 ]. % 112.02/112.35 exact (zenon_H69 assumption_19). % 112.02/112.35 exact (zenon_H5a zenon_H68). % 112.02/112.35 apply zenon_H59. apply refl_equal. % 112.02/112.35 (* end of lemma zenon_L8_ *) % 112.02/112.35 assert (zenon_L9_ : (~((low) = (low))) -> False). % 112.02/112.35 do 0 intro. intros zenon_H6a. % 112.02/112.35 apply zenon_H6a. apply refl_equal. % 112.02/112.35 (* end of lemma zenon_L9_ *) % 112.02/112.35 assert (zenon_L10_ : forall (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2)) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (low) (low))) -> False). % 112.02/112.35 do 2 intro. intros zenon_H32 zenon_H6b zenon_H34 zenon_H6c. % 112.02/112.35 elim (classic ((~((low) = (mod1)))/\(~(greater (low) (mod1))))); [ zenon_intro zenon_H6d | zenon_intro zenon_H6e ]. % 112.02/112.35 apply (zenon_and_s _ _ zenon_H6d). zenon_intro zenon_H70. zenon_intro zenon_H6f. % 112.02/112.35 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 112.02/112.35 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1))); [ zenon_intro zenon_H68 | zenon_intro zenon_H5a ]. % 112.02/112.35 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1)) = (greater (low) (mod1))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_H6f. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact zenon_H68. % 112.02/112.35 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 112.02/112.35 congruence. % 112.02/112.35 elim (classic ((low) = (low))); [ zenon_intro zenon_H74 | zenon_intro zenon_H6a ]. % 112.02/112.35 cut (((low) = (low)) = ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_H73. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact zenon_H74. % 112.02/112.35 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.02/112.35 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 112.02/112.35 congruence. % 112.02/112.35 exact (zenon_H72 zenon_H71). % 112.02/112.35 apply zenon_H6a. apply refl_equal. % 112.02/112.35 apply zenon_H6a. apply refl_equal. % 112.02/112.35 apply zenon_H59. apply refl_equal. % 112.02/112.35 apply (zenon_L8_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.35 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_H72. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact zenon_H61. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 112.02/112.35 congruence. % 112.02/112.35 exact (zenon_H73 zenon_H6b). % 112.02/112.35 apply zenon_H62. apply refl_equal. % 112.02/112.35 apply zenon_H62. apply refl_equal. % 112.02/112.35 cut ((greater (mod1) (low)) = (greater (low) (low))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_H6c. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact assumption_18b. % 112.02/112.35 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.02/112.35 cut (((mod1) = (low))); [idtac | apply NNPP; zenon_intro zenon_H75]. % 112.02/112.35 congruence. % 112.02/112.35 apply (zenon_notand_s _ _ zenon_H6e); [ zenon_intro zenon_H77 | zenon_intro zenon_H76 ]. % 112.02/112.35 apply zenon_H77. zenon_intro zenon_H78. % 112.02/112.35 elim (classic ((low) = (low))); [ zenon_intro zenon_H74 | zenon_intro zenon_H6a ]. % 112.02/112.35 cut (((low) = (low)) = ((mod1) = (low))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_H75. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact zenon_H74. % 112.02/112.35 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.02/112.35 cut (((low) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 112.02/112.35 congruence. % 112.02/112.35 exact (zenon_H70 zenon_H78). % 112.02/112.35 apply zenon_H6a. apply refl_equal. % 112.02/112.35 apply zenon_H6a. apply refl_equal. % 112.02/112.35 apply zenon_H76. zenon_intro zenon_H79. % 112.02/112.35 generalize (zenon_H34 (low)). zenon_intro zenon_H7a. % 112.02/112.35 generalize (zenon_H7a (mod1)). zenon_intro zenon_H7b. % 112.02/112.35 generalize (zenon_H7b (low)). zenon_intro zenon_H7c. % 112.02/112.35 apply (zenon_imply_s _ _ zenon_H7c); [ zenon_intro zenon_H6f | zenon_intro zenon_H7d ]. % 112.02/112.35 exact (zenon_H6f zenon_H79). % 112.02/112.35 apply (zenon_imply_s _ _ zenon_H7d); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ]. % 112.02/112.35 exact (zenon_H7f assumption_18b). % 112.02/112.35 exact (zenon_H6c zenon_H7e). % 112.02/112.35 apply zenon_H6a. apply refl_equal. % 112.02/112.35 (* end of lemma zenon_L10_ *) % 112.02/112.35 assert (zenon_L11_ : forall (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low)) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2)) -> False). % 112.02/112.35 do 2 intro. intros zenon_H34 zenon_H6b zenon_H32. % 112.02/112.35 generalize (meaning_postulate_greater_strict (low)). zenon_intro zenon_H80. % 112.02/112.35 generalize (zenon_H80 (low)). zenon_intro zenon_H81. % 112.02/112.35 apply (zenon_notand_s _ _ zenon_H81); [ zenon_intro zenon_H6c | zenon_intro zenon_H6c ]. % 112.02/112.35 apply (zenon_L10_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.35 apply (zenon_L10_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.35 (* end of lemma zenon_L11_ *) % 112.02/112.35 assert (zenon_L12_ : forall (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (((is_aligned zenon_TX_y zenon_TT1_bg)/\(~(positional_advantage zenon_TX_y zenon_TT1_bg)))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))) -> (greater (tau) (sigma)) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (is_aligned zenon_TX_y zenon_TT1_bg) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low)) -> False). % 112.02/112.35 do 2 intro. intros zenon_H30 zenon_H38 zenon_H37 zenon_H35 zenon_H82 zenon_H34 zenon_H6b. % 112.02/112.35 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 112.02/112.35 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ]. % 112.02/112.35 exact (zenon_H2a zenon_H82). % 112.02/112.35 apply zenon_H2e. zenon_intro zenon_H36. % 112.02/112.35 apply (zenon_L6_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.35 apply (zenon_L11_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.35 (* end of lemma zenon_L12_ *) % 112.02/112.35 assert (zenon_L13_ : (~((mod2) = (mod2))) -> False). % 112.02/112.35 do 0 intro. intros zenon_H83. % 112.02/112.35 apply zenon_H83. apply refl_equal. % 112.02/112.35 (* end of lemma zenon_L13_ *) % 112.02/112.35 assert (zenon_L14_ : forall (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (greater (tau) (sigma)) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod1))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (organization zenon_TX_y) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod2))) -> False). % 112.02/112.35 do 2 intro. intros zenon_H38 zenon_H37 zenon_H35 zenon_H31 zenon_H84 zenon_H1a zenon_H1f zenon_H0 zenon_H34 zenon_H5d. % 112.02/112.35 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (high))))); [ zenon_intro zenon_H85 | zenon_intro zenon_H86 ]. % 112.02/112.35 apply (zenon_and_s _ _ zenon_H85). zenon_intro zenon_H2b. zenon_intro zenon_H87. % 112.02/112.35 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88. % 112.02/112.35 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ]. % 112.02/112.35 exact (zenon_H27 zenon_H1f). % 112.02/112.35 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a. % 112.02/112.35 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ]. % 112.02/112.35 apply (zenon_L3_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.35 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d. % 112.02/112.35 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f. % 112.02/112.35 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H30. zenon_intro zenon_H28. % 112.02/112.35 apply (zenon_imply_s _ _ zenon_H8e); [ zenon_intro zenon_H91 | zenon_intro zenon_H6b ]. % 112.02/112.35 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 112.02/112.35 apply (zenon_imply_s _ _ zenon_H90); [ zenon_intro zenon_H93 | zenon_intro zenon_H92 ]. % 112.02/112.35 apply (zenon_notand_s _ _ zenon_H93); [ zenon_intro zenon_H2f | zenon_intro zenon_H29 ]. % 112.02/112.35 exact (zenon_H2f zenon_H2a). % 112.02/112.35 apply (zenon_L5_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.35 exact (zenon_H84 zenon_H92). % 112.02/112.35 apply (zenon_L5_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.35 apply (zenon_imply_s _ _ zenon_H90); [ zenon_intro zenon_H93 | zenon_intro zenon_H92 ]. % 112.02/112.35 apply (zenon_notand_s _ _ zenon_H93); [ zenon_intro zenon_H2f | zenon_intro zenon_H29 ]. % 112.02/112.35 apply zenon_H2f. zenon_intro zenon_H82. % 112.02/112.35 apply (zenon_L12_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.35 apply (zenon_L5_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.35 exact (zenon_H84 zenon_H92). % 112.02/112.35 cut ((greater (high) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod2))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_H5d. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact assumption_18d. % 112.02/112.35 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 112.02/112.35 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 112.02/112.35 congruence. % 112.02/112.35 apply (zenon_notand_s _ _ zenon_H86); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 112.02/112.35 apply zenon_H96. zenon_intro zenon_H2c. % 112.02/112.35 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_H94. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact zenon_H61. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 112.02/112.35 congruence. % 112.02/112.35 exact (zenon_H2b zenon_H2c). % 112.02/112.35 apply zenon_H62. apply refl_equal. % 112.02/112.35 apply zenon_H62. apply refl_equal. % 112.02/112.35 apply zenon_H95. zenon_intro zenon_H97. % 112.02/112.35 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64. % 112.02/112.35 generalize (zenon_H64 (high)). zenon_intro zenon_H98. % 112.02/112.35 generalize (zenon_H98 (mod2)). zenon_intro zenon_H99. % 112.02/112.35 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H87 | zenon_intro zenon_H9a ]. % 112.02/112.35 exact (zenon_H87 zenon_H97). % 112.02/112.35 apply (zenon_imply_s _ _ zenon_H9a); [ zenon_intro zenon_H9b | zenon_intro zenon_H63 ]. % 112.02/112.35 exact (zenon_H9b assumption_18d). % 112.02/112.35 exact (zenon_H5d zenon_H63). % 112.02/112.35 apply zenon_H83. apply refl_equal. % 112.02/112.35 (* end of lemma zenon_L14_ *) % 112.02/112.35 assert (zenon_L15_ : forall (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod1))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (greater (tau) (sigma)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1))) -> False). % 112.02/112.35 do 2 intro. intros zenon_H0 zenon_H1f zenon_H1a zenon_H84 zenon_H35 zenon_H37 zenon_H38 zenon_H34 zenon_H5a. % 112.02/112.35 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod2))))); [ zenon_intro zenon_H5b | zenon_intro zenon_H5c ]. % 112.02/112.35 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H31. zenon_intro zenon_H5d. % 112.02/112.35 apply (zenon_L14_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.35 cut ((greater (mod2) (mod1)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_H5a. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact assumption_19. % 112.02/112.35 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 112.02/112.35 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 112.02/112.35 congruence. % 112.02/112.35 apply (zenon_notand_s _ _ zenon_H5c); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ]. % 112.02/112.35 apply zenon_H60. zenon_intro zenon_H32. % 112.02/112.35 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_H5e. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact zenon_H61. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31]. % 112.02/112.35 congruence. % 112.02/112.35 exact (zenon_H31 zenon_H32). % 112.02/112.35 apply zenon_H62. apply refl_equal. % 112.02/112.35 apply zenon_H62. apply refl_equal. % 112.02/112.35 apply zenon_H5f. zenon_intro zenon_H63. % 112.02/112.35 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64. % 112.02/112.35 generalize (zenon_H64 (mod2)). zenon_intro zenon_H65. % 112.02/112.35 generalize (zenon_H65 (mod1)). zenon_intro zenon_H66. % 112.02/112.35 apply (zenon_imply_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H67 ]. % 112.02/112.35 exact (zenon_H5d zenon_H63). % 112.02/112.35 apply (zenon_imply_s _ _ zenon_H67); [ zenon_intro zenon_H69 | zenon_intro zenon_H68 ]. % 112.02/112.35 exact (zenon_H69 assumption_19). % 112.02/112.35 exact (zenon_H5a zenon_H68). % 112.02/112.35 apply zenon_H59. apply refl_equal. % 112.02/112.35 (* end of lemma zenon_L15_ *) % 112.02/112.35 assert (zenon_L16_ : forall (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (((~(is_aligned zenon_TX_y zenon_TT1_bg))/\(~(positional_advantage zenon_TX_y zenon_TT1_bg)))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))) -> (greater (tau) (sigma)) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(is_aligned zenon_TX_y zenon_TT1_bg)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))) -> False). % 112.02/112.35 do 2 intro. intros zenon_H28 zenon_H38 zenon_H37 zenon_H35 zenon_H34 zenon_H2a zenon_H2b. % 112.02/112.35 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ]. % 112.02/112.35 apply (zenon_notand_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ]. % 112.02/112.35 exact (zenon_H2f zenon_H2a). % 112.02/112.35 apply zenon_H2e. zenon_intro zenon_H36. % 112.02/112.35 apply (zenon_L6_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.35 exact (zenon_H2b zenon_H2c). % 112.02/112.35 (* end of lemma zenon_L16_ *) % 112.02/112.35 assert (zenon_L17_ : forall (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod1)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (low) (low))) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low)) -> False). % 112.02/112.35 do 2 intro. intros zenon_H92 zenon_H34 zenon_H6c zenon_H6b. % 112.02/112.35 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 112.02/112.35 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low))); [ zenon_intro zenon_H9c | zenon_intro zenon_H9d ]. % 112.02/112.35 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low)) = (greater (low) (low))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_H6c. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact zenon_H9c. % 112.02/112.35 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 112.02/112.35 congruence. % 112.02/112.35 elim (classic ((low) = (low))); [ zenon_intro zenon_H74 | zenon_intro zenon_H6a ]. % 112.02/112.35 cut (((low) = (low)) = ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_H73. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact zenon_H74. % 112.02/112.35 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.02/112.35 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 112.02/112.35 congruence. % 112.02/112.35 exact (zenon_H72 zenon_H71). % 112.02/112.35 apply zenon_H6a. apply refl_equal. % 112.02/112.35 apply zenon_H6a. apply refl_equal. % 112.02/112.35 apply zenon_H6a. apply refl_equal. % 112.02/112.35 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod1)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1))))); [ zenon_intro zenon_H9e | zenon_intro zenon_H9f ]. % 112.02/112.35 apply (zenon_and_s _ _ zenon_H9e). zenon_intro zenon_H84. zenon_intro zenon_H5a. % 112.02/112.35 exact (zenon_H84 zenon_H92). % 112.02/112.35 cut ((greater (mod1) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_H9d. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact assumption_18b. % 112.02/112.35 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.02/112.35 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 112.02/112.35 congruence. % 112.02/112.35 apply (zenon_notand_s _ _ zenon_H9f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Ha1 ]. % 112.02/112.35 apply zenon_Ha2. zenon_intro zenon_H92. % 112.02/112.35 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_Ha0. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact zenon_H61. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 112.02/112.35 congruence. % 112.02/112.35 exact (zenon_H84 zenon_H92). % 112.02/112.35 apply zenon_H62. apply refl_equal. % 112.02/112.35 apply zenon_H62. apply refl_equal. % 112.02/112.35 apply zenon_Ha1. zenon_intro zenon_H68. % 112.02/112.35 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64. % 112.02/112.35 generalize (zenon_H64 (mod1)). zenon_intro zenon_Ha3. % 112.02/112.35 generalize (zenon_Ha3 (low)). zenon_intro zenon_Ha4. % 112.02/112.35 apply (zenon_imply_s _ _ zenon_Ha4); [ zenon_intro zenon_H5a | zenon_intro zenon_Ha5 ]. % 112.02/112.35 exact (zenon_H5a zenon_H68). % 112.02/112.35 apply (zenon_imply_s _ _ zenon_Ha5); [ zenon_intro zenon_H7f | zenon_intro zenon_H9c ]. % 112.02/112.35 exact (zenon_H7f assumption_18b). % 112.02/112.35 exact (zenon_H9d zenon_H9c). % 112.02/112.35 apply zenon_H6a. apply refl_equal. % 112.02/112.35 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_H72. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact zenon_H61. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 112.02/112.35 congruence. % 112.02/112.35 exact (zenon_H73 zenon_H6b). % 112.02/112.35 apply zenon_H62. apply refl_equal. % 112.02/112.35 apply zenon_H62. apply refl_equal. % 112.02/112.35 (* end of lemma zenon_L17_ *) % 112.02/112.35 assert (zenon_L18_ : forall (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (mod1) (mod1))) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod1)) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low)) -> False). % 112.02/112.35 do 2 intro. intros zenon_H34 zenon_Ha6 zenon_H92 zenon_H6b. % 112.02/112.35 elim (classic (greater (low) (mod1))); [ zenon_intro zenon_H79 | zenon_intro zenon_H6f ]. % 112.02/112.35 generalize (zenon_H34 (mod1)). zenon_intro zenon_Ha7. % 112.02/112.35 generalize (zenon_Ha7 (low)). zenon_intro zenon_Ha8. % 112.02/112.35 generalize (zenon_Ha8 (mod1)). zenon_intro zenon_Ha9. % 112.02/112.35 apply (zenon_imply_s _ _ zenon_Ha9); [ zenon_intro zenon_H7f | zenon_intro zenon_Haa ]. % 112.02/112.35 exact (zenon_H7f assumption_18b). % 112.02/112.35 apply (zenon_imply_s _ _ zenon_Haa); [ zenon_intro zenon_H6f | zenon_intro zenon_Hab ]. % 112.02/112.35 exact (zenon_H6f zenon_H79). % 112.02/112.35 exact (zenon_Ha6 zenon_Hab). % 112.02/112.35 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 112.02/112.35 elim (classic (greater (low) (low))); [ zenon_intro zenon_H7e | zenon_intro zenon_H6c ]. % 112.02/112.35 elim (classic (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_Hac | zenon_intro zenon_Had ]. % 112.02/112.35 cut ((greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (low) (mod1))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_H6f. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact zenon_Hac. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 112.02/112.35 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.02/112.35 congruence. % 112.02/112.35 apply zenon_H6a. apply refl_equal. % 112.02/112.35 exact (zenon_H84 zenon_H92). % 112.02/112.35 cut ((greater (low) (low)) = (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_Had. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact zenon_H7e. % 112.02/112.35 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 112.02/112.35 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.02/112.35 congruence. % 112.02/112.35 apply zenon_H6a. apply refl_equal. % 112.02/112.35 exact (zenon_H72 zenon_H71). % 112.02/112.35 apply (zenon_L17_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.35 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_H72. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact zenon_H61. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 112.02/112.35 congruence. % 112.02/112.35 exact (zenon_H73 zenon_H6b). % 112.02/112.35 apply zenon_H62. apply refl_equal. % 112.02/112.35 apply zenon_H62. apply refl_equal. % 112.02/112.35 (* end of lemma zenon_L18_ *) % 112.02/112.35 assert (zenon_L19_ : forall (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))) -> (greater (tau) (sigma)) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))) -> (~(greater (mod1) (mod1))) -> False). % 112.02/112.35 do 2 intro. intros zenon_H34 zenon_H0 zenon_H1f zenon_H1a zenon_H2b zenon_H38 zenon_H37 zenon_H35 zenon_H31 zenon_Ha6. % 112.02/112.35 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88. % 112.02/112.35 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ]. % 112.02/112.35 exact (zenon_H27 zenon_H1f). % 112.02/112.35 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a. % 112.02/112.35 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ]. % 112.02/112.35 apply (zenon_L3_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.35 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d. % 112.02/112.35 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f. % 112.02/112.35 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H30. zenon_intro zenon_H28. % 112.02/112.35 apply (zenon_imply_s _ _ zenon_H8e); [ zenon_intro zenon_H91 | zenon_intro zenon_H6b ]. % 112.02/112.35 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 112.02/112.35 apply (zenon_L16_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.35 apply (zenon_L5_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.35 apply (zenon_imply_s _ _ zenon_H90); [ zenon_intro zenon_H93 | zenon_intro zenon_H92 ]. % 112.02/112.35 apply (zenon_notand_s _ _ zenon_H93); [ zenon_intro zenon_H2f | zenon_intro zenon_H29 ]. % 112.02/112.35 apply zenon_H2f. zenon_intro zenon_H82. % 112.02/112.35 apply (zenon_L12_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.35 apply (zenon_L5_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.35 apply (zenon_L18_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.35 (* end of lemma zenon_L19_ *) % 112.02/112.35 assert (zenon_L20_ : forall (zenon_TT3_x : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (greater (tau) (sigma)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (organization zenon_TX_y) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (mod1)) -> False). % 112.02/112.35 do 3 intro. intros zenon_H35 zenon_H37 zenon_H38 zenon_H1a zenon_H1f zenon_H0 zenon_Hae zenon_H34 zenon_Haf. % 112.02/112.35 elim (classic ((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hb1 ]. % 112.02/112.35 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1))); [ zenon_intro zenon_H68 | zenon_intro zenon_H5a ]. % 112.02/112.35 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_Hae. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact zenon_H68. % 112.02/112.35 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hb1]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.02/112.35 congruence. % 112.02/112.35 apply zenon_H62. apply refl_equal. % 112.02/112.35 exact (zenon_Hb1 zenon_Hb0). % 112.02/112.35 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT3_x) (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb3 ]. % 112.02/112.35 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb5 ]. % 112.02/112.35 cut ((greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT3_x)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_Hae. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact zenon_Hb4. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 112.02/112.35 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 112.02/112.35 congruence. % 112.02/112.35 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_Ha0. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact zenon_H61. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 112.02/112.35 congruence. % 112.02/112.35 apply (zenon_L15_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.35 apply zenon_H62. apply refl_equal. % 112.02/112.35 apply zenon_H62. apply refl_equal. % 112.02/112.35 apply zenon_Hb6. apply refl_equal. % 112.02/112.35 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT3_x) (hazard_of_mortality zenon_TX_y zenon_TT3_x)) = (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT3_x))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_Hb5. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact zenon_Hb2. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 112.02/112.35 congruence. % 112.02/112.35 elim (classic ((mod1) = (mod1))); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H59 ]. % 112.02/112.35 cut (((mod1) = (mod1)) = ((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (mod1))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_Hb7. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact zenon_Hb8. % 112.02/112.35 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 112.02/112.35 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hb1]. % 112.02/112.35 congruence. % 112.02/112.35 exact (zenon_Hb1 zenon_Hb0). % 112.02/112.35 apply zenon_H59. apply refl_equal. % 112.02/112.35 apply zenon_H59. apply refl_equal. % 112.02/112.35 apply zenon_Hb6. apply refl_equal. % 112.02/112.35 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod2))))); [ zenon_intro zenon_H5b | zenon_intro zenon_H5c ]. % 112.02/112.35 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H31. zenon_intro zenon_H5d. % 112.02/112.35 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (high))))); [ zenon_intro zenon_H85 | zenon_intro zenon_H86 ]. % 112.02/112.35 apply (zenon_and_s _ _ zenon_H85). zenon_intro zenon_H2b. zenon_intro zenon_H87. % 112.02/112.35 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb5 ]. % 112.02/112.35 cut ((greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT3_x)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT3_x) (hazard_of_mortality zenon_TX_y zenon_TT3_x))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_Hb3. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact zenon_Hb4. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 112.02/112.35 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hb1]. % 112.02/112.35 congruence. % 112.02/112.35 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb6 ]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x)) = ((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_Hb1. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact zenon_Hb9. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 112.02/112.35 congruence. % 112.02/112.35 exact (zenon_Hb7 zenon_Haf). % 112.02/112.35 apply zenon_Hb6. apply refl_equal. % 112.02/112.35 apply zenon_Hb6. apply refl_equal. % 112.02/112.35 apply zenon_Hb6. apply refl_equal. % 112.02/112.35 elim (classic ((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hb1 ]. % 112.02/112.35 elim (classic (greater (mod1) (mod1))); [ zenon_intro zenon_Hab | zenon_intro zenon_Ha6 ]. % 112.02/112.35 cut ((greater (mod1) (mod1)) = (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT3_x))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_Hb5. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact zenon_Hab. % 112.02/112.35 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hb1]. % 112.02/112.35 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 112.02/112.35 congruence. % 112.02/112.35 apply zenon_H59. apply refl_equal. % 112.02/112.35 exact (zenon_Hb1 zenon_Hb0). % 112.02/112.35 apply (zenon_L19_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.35 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb6 ]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x)) = ((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_Hb1. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact zenon_Hb9. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 112.02/112.35 congruence. % 112.02/112.35 exact (zenon_Hb7 zenon_Haf). % 112.02/112.35 apply zenon_Hb6. apply refl_equal. % 112.02/112.35 apply zenon_Hb6. apply refl_equal. % 112.02/112.35 cut ((greater (high) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod2))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_H5d. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact assumption_18d. % 112.02/112.35 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 112.02/112.35 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 112.02/112.35 congruence. % 112.02/112.35 apply (zenon_notand_s _ _ zenon_H86); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 112.02/112.35 apply zenon_H96. zenon_intro zenon_H2c. % 112.02/112.35 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_H94. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact zenon_H61. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 112.02/112.35 congruence. % 112.02/112.35 exact (zenon_H2b zenon_H2c). % 112.02/112.35 apply zenon_H62. apply refl_equal. % 112.02/112.35 apply zenon_H62. apply refl_equal. % 112.02/112.35 apply zenon_H95. zenon_intro zenon_H97. % 112.02/112.35 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64. % 112.02/112.35 generalize (zenon_H64 (high)). zenon_intro zenon_H98. % 112.02/112.35 generalize (zenon_H98 (mod2)). zenon_intro zenon_H99. % 112.02/112.35 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H87 | zenon_intro zenon_H9a ]. % 112.02/112.35 exact (zenon_H87 zenon_H97). % 112.02/112.35 apply (zenon_imply_s _ _ zenon_H9a); [ zenon_intro zenon_H9b | zenon_intro zenon_H63 ]. % 112.02/112.35 exact (zenon_H9b assumption_18d). % 112.02/112.35 exact (zenon_H5d zenon_H63). % 112.02/112.35 apply zenon_H83. apply refl_equal. % 112.02/112.35 cut ((greater (mod2) (mod1)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_H5a. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact assumption_19. % 112.02/112.35 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 112.02/112.35 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 112.02/112.35 congruence. % 112.02/112.35 apply (zenon_notand_s _ _ zenon_H5c); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ]. % 112.02/112.35 apply zenon_H60. zenon_intro zenon_H32. % 112.02/112.35 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_H5e. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact zenon_H61. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31]. % 112.02/112.35 congruence. % 112.02/112.35 exact (zenon_H31 zenon_H32). % 112.02/112.35 apply zenon_H62. apply refl_equal. % 112.02/112.35 apply zenon_H62. apply refl_equal. % 112.02/112.35 apply zenon_H5f. zenon_intro zenon_H63. % 112.02/112.35 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64. % 112.02/112.35 generalize (zenon_H64 (mod2)). zenon_intro zenon_H65. % 112.02/112.35 generalize (zenon_H65 (mod1)). zenon_intro zenon_H66. % 112.02/112.35 apply (zenon_imply_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H67 ]. % 112.02/112.35 exact (zenon_H5d zenon_H63). % 112.02/112.35 apply (zenon_imply_s _ _ zenon_H67); [ zenon_intro zenon_H69 | zenon_intro zenon_H68 ]. % 112.02/112.35 exact (zenon_H69 assumption_19). % 112.02/112.35 exact (zenon_H5a zenon_H68). % 112.02/112.35 apply zenon_H59. apply refl_equal. % 112.02/112.35 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb6 ]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x)) = ((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_Hb1. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact zenon_Hb9. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 112.02/112.35 congruence. % 112.02/112.35 exact (zenon_Hb7 zenon_Haf). % 112.02/112.35 apply zenon_Hb6. apply refl_equal. % 112.02/112.35 apply zenon_Hb6. apply refl_equal. % 112.02/112.35 (* end of lemma zenon_L20_ *) % 112.02/112.35 assert (zenon_L21_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT3_x : zenon_U) (zenon_TX_y : zenon_U), (((~(is_aligned zenon_TX_y zenon_TT3_x))/\(positional_advantage zenon_TX_y zenon_TT3_x))->((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (mod1))) -> (positional_advantage zenon_TX_y zenon_TT3_x) -> (~(is_aligned zenon_TX_y zenon_TT3_x)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (greater (tau) (sigma)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (organization zenon_TX_y) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> False). % 112.02/112.35 do 3 intro. intros zenon_Hba zenon_Hbb zenon_Hbc zenon_H35 zenon_H37 zenon_H38 zenon_H1a zenon_H1f zenon_H0 zenon_Hae zenon_H34. % 112.02/112.35 apply (zenon_imply_s _ _ zenon_Hba); [ zenon_intro zenon_Hbd | zenon_intro zenon_Haf ]. % 112.02/112.35 apply (zenon_notand_s _ _ zenon_Hbd); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hbe ]. % 112.02/112.35 exact (zenon_Hbf zenon_Hbc). % 112.02/112.35 exact (zenon_Hbe zenon_Hbb). % 112.02/112.35 apply (zenon_L20_ zenon_TT3_x zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.35 (* end of lemma zenon_L21_ *) % 112.02/112.35 assert (zenon_L22_ : forall (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (greater (tau) (sigma)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod2))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low))) -> False). % 112.02/112.35 do 2 intro. intros zenon_H0 zenon_H1f zenon_H1a zenon_H31 zenon_H35 zenon_H37 zenon_H38 zenon_H5d zenon_H34 zenon_H9d. % 112.02/112.35 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod1)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1))))); [ zenon_intro zenon_H9e | zenon_intro zenon_H9f ]. % 112.02/112.35 apply (zenon_and_s _ _ zenon_H9e). zenon_intro zenon_H84. zenon_intro zenon_H5a. % 112.02/112.35 apply (zenon_L14_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.35 cut ((greater (mod1) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_H9d. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact assumption_18b. % 112.02/112.35 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.02/112.35 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 112.02/112.35 congruence. % 112.02/112.35 apply (zenon_notand_s _ _ zenon_H9f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Ha1 ]. % 112.02/112.35 apply zenon_Ha2. zenon_intro zenon_H92. % 112.02/112.35 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_Ha0. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact zenon_H61. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 112.02/112.35 congruence. % 112.02/112.35 exact (zenon_H84 zenon_H92). % 112.02/112.35 apply zenon_H62. apply refl_equal. % 112.02/112.35 apply zenon_H62. apply refl_equal. % 112.02/112.35 apply zenon_Ha1. zenon_intro zenon_H68. % 112.02/112.35 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64. % 112.02/112.35 generalize (zenon_H64 (mod1)). zenon_intro zenon_Ha3. % 112.02/112.35 generalize (zenon_Ha3 (low)). zenon_intro zenon_Ha4. % 112.02/112.35 apply (zenon_imply_s _ _ zenon_Ha4); [ zenon_intro zenon_H5a | zenon_intro zenon_Ha5 ]. % 112.02/112.35 exact (zenon_H5a zenon_H68). % 112.02/112.35 apply (zenon_imply_s _ _ zenon_Ha5); [ zenon_intro zenon_H7f | zenon_intro zenon_H9c ]. % 112.02/112.35 exact (zenon_H7f assumption_18b). % 112.02/112.35 exact (zenon_H9d zenon_H9c). % 112.02/112.35 apply zenon_H6a. apply refl_equal. % 112.02/112.35 (* end of lemma zenon_L22_ *) % 112.02/112.35 assert (zenon_L23_ : forall (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (greater (tau) (sigma)) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (organization zenon_TX_y) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low))) -> False). % 112.02/112.35 do 2 intro. intros zenon_H38 zenon_H37 zenon_H35 zenon_H1a zenon_H1f zenon_H0 zenon_H34 zenon_H9d. % 112.02/112.35 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod2))))); [ zenon_intro zenon_H5b | zenon_intro zenon_H5c ]. % 112.02/112.35 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H31. zenon_intro zenon_H5d. % 112.02/112.35 apply (zenon_L22_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.35 cut ((greater (mod2) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_H9d. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact assumption_18e. % 112.02/112.35 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.02/112.35 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 112.02/112.35 congruence. % 112.02/112.35 apply (zenon_notand_s _ _ zenon_H5c); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ]. % 112.02/112.35 apply zenon_H60. zenon_intro zenon_H32. % 112.02/112.35 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.02/112.35 intro zenon_D_pnotp. % 112.02/112.35 apply zenon_H5e. % 112.02/112.35 rewrite <- zenon_D_pnotp. % 112.02/112.35 exact zenon_H61. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.02/112.35 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31]. % 112.02/112.35 congruence. % 112.02/112.35 exact (zenon_H31 zenon_H32). % 112.02/112.35 apply zenon_H62. apply refl_equal. % 112.02/112.35 apply zenon_H62. apply refl_equal. % 112.02/112.35 apply zenon_H5f. zenon_intro zenon_H63. % 112.02/112.35 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64. % 112.02/112.35 generalize (zenon_H64 (mod2)). zenon_intro zenon_H65. % 112.02/112.35 generalize (zenon_H65 (low)). zenon_intro zenon_Hc0. % 112.02/112.35 apply (zenon_imply_s _ _ zenon_Hc0); [ zenon_intro zenon_H5d | zenon_intro zenon_Hc1 ]. % 112.02/112.35 exact (zenon_H5d zenon_H63). % 112.02/112.35 apply (zenon_imply_s _ _ zenon_Hc1); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H9c ]. % 112.02/112.35 exact (zenon_Hc2 assumption_18e). % 112.02/112.35 exact (zenon_H9d zenon_H9c). % 112.02/112.35 apply zenon_H6a. apply refl_equal. % 112.02/112.35 (* end of lemma zenon_L23_ *) % 112.02/112.35 assert (zenon_L24_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT3_x : zenon_U) (zenon_TX_y : zenon_U), ((((is_aligned zenon_TX_y zenon_TT3_x)/\(positional_advantage zenon_TX_y zenon_TT3_x))->((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (low)))/\((((~(is_aligned zenon_TX_y zenon_TT3_x))/\(positional_advantage zenon_TX_y zenon_TT3_x))->((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (mod1)))/\((((is_aligned zenon_TX_y zenon_TT3_x)/\(~(positional_advantage zenon_TX_y zenon_TT3_x)))->((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (mod2)))/\(((~(is_aligned zenon_TX_y zenon_TT3_x))/\(~(positional_advantage zenon_TX_y zenon_TT3_x)))->((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (high)))))) -> (positional_advantage zenon_TX_y zenon_TT3_x) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (greater (tau) (sigma)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> False). % 112.02/112.36 do 3 intro. intros zenon_Hc3 zenon_Hbb zenon_H0 zenon_H1f zenon_H1a zenon_H35 zenon_H37 zenon_H38 zenon_Hae zenon_H34. % 112.02/112.36 apply (zenon_and_s _ _ zenon_Hc3). zenon_intro zenon_Hc5. zenon_intro zenon_Hc4. % 112.02/112.36 apply (zenon_and_s _ _ zenon_Hc4). zenon_intro zenon_Hba. zenon_intro zenon_Hc6. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_Hc5); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hc7 ]. % 112.02/112.36 apply (zenon_notand_s _ _ zenon_Hc8); [ zenon_intro zenon_Hbc | zenon_intro zenon_Hbe ]. % 112.02/112.36 apply (zenon_L21_ zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial. % 112.02/112.36 exact (zenon_Hbe zenon_Hbb). % 112.02/112.36 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hca ]. % 112.02/112.36 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low))); [ zenon_intro zenon_H9c | zenon_intro zenon_H9d ]. % 112.02/112.36 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))). % 112.02/112.36 intro zenon_D_pnotp. % 112.02/112.36 apply zenon_Hae. % 112.02/112.36 rewrite <- zenon_D_pnotp. % 112.02/112.36 exact zenon_H9c. % 112.02/112.36 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 112.02/112.36 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.02/112.36 congruence. % 112.02/112.36 apply zenon_H62. apply refl_equal. % 112.02/112.36 exact (zenon_Hca zenon_Hc9). % 112.02/112.36 apply (zenon_L23_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.36 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb6 ]. % 112.02/112.36 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x)) = ((low) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))). % 112.02/112.36 intro zenon_D_pnotp. % 112.02/112.36 apply zenon_Hca. % 112.02/112.36 rewrite <- zenon_D_pnotp. % 112.02/112.36 exact zenon_Hb9. % 112.02/112.36 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 112.02/112.36 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (low))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 112.02/112.36 congruence. % 112.02/112.36 exact (zenon_Hcb zenon_Hc7). % 112.02/112.36 apply zenon_Hb6. apply refl_equal. % 112.02/112.36 apply zenon_Hb6. apply refl_equal. % 112.02/112.36 (* end of lemma zenon_L24_ *) % 112.02/112.36 assert (zenon_L25_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT3_x : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((~(has_immunity zenon_TX_y zenon_TT3_x))->((((is_aligned zenon_TX_y zenon_TT3_x)/\(positional_advantage zenon_TX_y zenon_TT3_x))->((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (low)))/\((((~(is_aligned zenon_TX_y zenon_TT3_x))/\(positional_advantage zenon_TX_y zenon_TT3_x))->((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (mod1)))/\((((is_aligned zenon_TX_y zenon_TT3_x)/\(~(positional_advantage zenon_TX_y zenon_TT3_x)))->((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (mod2)))/\(((~(is_aligned zenon_TX_y zenon_TT3_x))/\(~(positional_advantage zenon_TX_y zenon_TT3_x)))->((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (high))))))) -> (positional_advantage zenon_TX_y zenon_TT3_x) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> (greater (tau) (sigma)) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (organization zenon_TX_y) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (~(has_immunity zenon_TX_y zenon_TT3_x)) -> False). % 112.02/112.36 do 3 intro. intros zenon_H34 zenon_Hcc zenon_Hbb zenon_Hae zenon_H38 zenon_H37 zenon_H35 zenon_H1a zenon_H1f zenon_H0 zenon_H16. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_Hcc); [ zenon_intro zenon_H15 | zenon_intro zenon_Hc3 ]. % 112.02/112.36 exact (zenon_H15 zenon_H16). % 112.02/112.36 apply (zenon_L24_ zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial. % 112.02/112.36 (* end of lemma zenon_L25_ *) % 112.02/112.36 assert (zenon_L26_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (organization zenon_TX_y) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> (~(is_aligned zenon_TX_y zenon_TT1_bg)) -> (~(dissimilar zenon_TX_y zenon_TT0_hz zenon_TT1_bg)) -> False). % 112.02/112.36 do 3 intro. intros zenon_H1f zenon_Hcd zenon_H2a zenon_Hce. % 112.02/112.36 generalize (definition_2 zenon_TX_y). zenon_intro zenon_Hd0. % 112.02/112.36 generalize (zenon_Hd0 zenon_TT0_hz). zenon_intro zenon_Hd1. % 112.02/112.36 generalize (zenon_Hd1 zenon_TT1_bg). zenon_intro zenon_Hd2. % 112.02/112.36 apply (zenon_equiv_s _ _ zenon_Hd2); [ zenon_intro zenon_Hce; zenon_intro zenon_Hd5 | zenon_intro zenon_Hd4; zenon_intro zenon_Hd3 ]. % 112.02/112.36 apply (zenon_notand_s _ _ zenon_Hd5); [ zenon_intro zenon_H27 | zenon_intro zenon_Hd6 ]. % 112.02/112.36 exact (zenon_H27 zenon_H1f). % 112.02/112.36 apply zenon_Hd6. zenon_intro zenon_Hd7. % 112.02/112.36 apply (zenon_equiv_s _ _ zenon_Hd7); [ zenon_intro zenon_Hd8; zenon_intro zenon_H2a | zenon_intro zenon_Hcd; zenon_intro zenon_H82 ]. % 112.02/112.36 exact (zenon_Hd8 zenon_Hcd). % 112.02/112.36 exact (zenon_H2a zenon_H82). % 112.02/112.36 exact (zenon_Hce zenon_Hd4). % 112.02/112.36 (* end of lemma zenon_L26_ *) % 112.02/112.36 assert (zenon_L27_ : (~((sigma) = (sigma))) -> False). % 112.02/112.36 do 0 intro. intros zenon_Hd9. % 112.02/112.36 apply zenon_Hd9. apply refl_equal. % 112.02/112.36 (* end of lemma zenon_L27_ *) % 112.02/112.36 assert (zenon_L28_ : forall (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (sigma) (sigma))) -> (greater (age zenon_TX_y zenon_TT1_bg) (sigma)) -> False). % 112.02/112.36 do 2 intro. intros zenon_H37 zenon_H34 zenon_Hda zenon_Hdb. % 112.02/112.36 elim (classic ((~((sigma) = (age zenon_TX_y zenon_TT1_bg)))/\(~(greater (sigma) (age zenon_TX_y zenon_TT1_bg))))); [ zenon_intro zenon_Hdc | zenon_intro zenon_Hdd ]. % 112.02/112.36 apply (zenon_and_s _ _ zenon_Hdc). zenon_intro zenon_Hde. zenon_intro zenon_H58. % 112.02/112.36 exact (zenon_H58 zenon_H37). % 112.02/112.36 cut ((greater (age zenon_TX_y zenon_TT1_bg) (sigma)) = (greater (sigma) (sigma))). % 112.02/112.36 intro zenon_D_pnotp. % 112.02/112.36 apply zenon_Hda. % 112.02/112.36 rewrite <- zenon_D_pnotp. % 112.02/112.36 exact zenon_Hdb. % 112.02/112.36 cut (((sigma) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 112.02/112.36 cut (((age zenon_TX_y zenon_TT1_bg) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hdf]. % 112.02/112.36 congruence. % 112.02/112.36 apply (zenon_notand_s _ _ zenon_Hdd); [ zenon_intro zenon_He1 | zenon_intro zenon_He0 ]. % 112.02/112.36 apply zenon_He1. zenon_intro zenon_He2. % 112.02/112.36 elim (classic ((sigma) = (sigma))); [ zenon_intro zenon_He3 | zenon_intro zenon_Hd9 ]. % 112.02/112.36 cut (((sigma) = (sigma)) = ((age zenon_TX_y zenon_TT1_bg) = (sigma))). % 112.02/112.36 intro zenon_D_pnotp. % 112.02/112.36 apply zenon_Hdf. % 112.02/112.36 rewrite <- zenon_D_pnotp. % 112.02/112.36 exact zenon_He3. % 112.02/112.36 cut (((sigma) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 112.02/112.36 cut (((sigma) = (age zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_Hde]. % 112.02/112.36 congruence. % 112.02/112.36 exact (zenon_Hde zenon_He2). % 112.02/112.36 apply zenon_Hd9. apply refl_equal. % 112.02/112.36 apply zenon_Hd9. apply refl_equal. % 112.02/112.36 apply zenon_He0. zenon_intro zenon_H37. % 112.02/112.36 generalize (zenon_H34 (sigma)). zenon_intro zenon_He4. % 112.02/112.36 generalize (zenon_He4 (age zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_He5. % 112.02/112.36 generalize (zenon_He5 (sigma)). zenon_intro zenon_He6. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_He6); [ zenon_intro zenon_H58 | zenon_intro zenon_He7 ]. % 112.02/112.36 exact (zenon_H58 zenon_H37). % 112.02/112.36 apply (zenon_imply_s _ _ zenon_He7); [ zenon_intro zenon_He9 | zenon_intro zenon_He8 ]. % 112.02/112.36 exact (zenon_He9 zenon_Hdb). % 112.02/112.36 exact (zenon_Hda zenon_He8). % 112.02/112.36 apply zenon_Hd9. apply refl_equal. % 112.02/112.36 (* end of lemma zenon_L28_ *) % 112.02/112.36 assert (zenon_L29_ : forall (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (forall Y : zenon_U, (~((greater (sigma) Y)/\(greater Y (sigma))))) -> (greater (age zenon_TX_y zenon_TT1_bg) (sigma)) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> False). % 112.02/112.36 do 2 intro. intros zenon_H34 zenon_Hea zenon_Hdb zenon_H37. % 112.02/112.36 generalize (zenon_Hea (sigma)). zenon_intro zenon_Heb. % 112.02/112.36 apply (zenon_notand_s _ _ zenon_Heb); [ zenon_intro zenon_Hda | zenon_intro zenon_Hda ]. % 112.02/112.36 apply (zenon_L28_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.36 apply (zenon_L28_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.36 (* end of lemma zenon_L29_ *) % 112.02/112.36 assert (zenon_L30_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (~(is_aligned zenon_TX_y zenon_TT1_bg)) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T0) = (zero)))->((greater (age zenon_TX_y T) (sigma))<->(dissimilar zenon_TX_y T0 T))))) -> False). % 112.02/112.36 do 3 intro. intros zenon_H34 zenon_H1f zenon_Hec zenon_H37 zenon_H2a zenon_Hcd zenon_Hed. % 112.02/112.36 generalize (meaning_postulate_greater_strict (sigma)). zenon_intro zenon_Hea. % 112.02/112.36 generalize (zenon_Hed zenon_TT0_hz). zenon_intro zenon_Hee. % 112.02/112.36 generalize (zenon_Hee zenon_TT1_bg). zenon_intro zenon_Hef. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_Hef); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf0 ]. % 112.02/112.36 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ]. % 112.02/112.36 exact (zenon_H27 zenon_H1f). % 112.02/112.36 exact (zenon_Hf2 zenon_Hec). % 112.02/112.36 apply (zenon_equiv_s _ _ zenon_Hf0); [ zenon_intro zenon_He9; zenon_intro zenon_Hce | zenon_intro zenon_Hdb; zenon_intro zenon_Hd4 ]. % 112.02/112.36 apply (zenon_L26_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.02/112.36 apply (zenon_L29_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.36 (* end of lemma zenon_L30_ *) % 112.02/112.36 assert (zenon_L31_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> (~(is_aligned zenon_TX_y zenon_TT1_bg)) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> False). % 112.02/112.36 do 3 intro. intros zenon_H34 zenon_Hcd zenon_H2a zenon_H37 zenon_Hec zenon_H1f. % 112.02/112.36 generalize (assumption_15 zenon_TX_y). zenon_intro zenon_Hed. % 112.02/112.36 apply (zenon_L30_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.02/112.36 (* end of lemma zenon_L31_ *) % 112.02/112.36 assert (zenon_L32_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low))) -> False). % 112.02/112.36 do 3 intro. intros zenon_H34 zenon_H0 zenon_H1f zenon_H1a zenon_Hcd zenon_H37 zenon_Hec zenon_H31 zenon_H2b zenon_H73. % 112.02/112.36 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ]. % 112.02/112.36 exact (zenon_H27 zenon_H1f). % 112.02/112.36 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ]. % 112.02/112.36 apply (zenon_L3_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.36 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d. % 112.02/112.36 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f. % 112.02/112.36 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H30. zenon_intro zenon_H28. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_H8e); [ zenon_intro zenon_H91 | zenon_intro zenon_H6b ]. % 112.02/112.36 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 112.02/112.36 apply (zenon_L31_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.02/112.36 apply (zenon_L5_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.36 exact (zenon_H73 zenon_H6b). % 112.02/112.36 (* end of lemma zenon_L32_ *) % 112.02/112.36 assert (zenon_L33_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low))) -> False). % 112.02/112.36 do 3 intro. intros zenon_H34 zenon_Hf3 zenon_H1f zenon_Hec zenon_H0 zenon_H1a zenon_H37 zenon_H31 zenon_H2b zenon_H73. % 112.02/112.36 generalize (zenon_Hf3 zenon_TT0_hz). zenon_intro zenon_Hf4. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcd ]. % 112.02/112.36 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ]. % 112.02/112.36 exact (zenon_H27 zenon_H1f). % 112.02/112.36 exact (zenon_Hf2 zenon_Hec). % 112.02/112.36 apply (zenon_L32_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.02/112.36 (* end of lemma zenon_L33_ *) % 112.02/112.36 assert (zenon_L34_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> False). % 112.02/112.36 do 3 intro. intros zenon_H34 zenon_H73 zenon_H2b zenon_H31 zenon_H37 zenon_H1a zenon_Hec zenon_H1f zenon_Hf3. % 112.02/112.36 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0. % 112.02/112.36 apply (zenon_L33_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.02/112.36 (* end of lemma zenon_L34_ *) % 112.02/112.36 assert (zenon_L35_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low))) -> False). % 112.02/112.36 do 3 intro. intros zenon_H34 zenon_H1f zenon_Hec zenon_H1a zenon_H37 zenon_H31 zenon_H2b zenon_H73. % 112.02/112.36 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3. % 112.02/112.36 apply (zenon_L34_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.36 (* end of lemma zenon_L35_ *) % 112.02/112.36 assert (zenon_L36_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod2))) -> False). % 112.02/112.36 do 3 intro. intros zenon_H73 zenon_H31 zenon_H37 zenon_H1a zenon_Hec zenon_H1f zenon_H34 zenon_H5d. % 112.02/112.36 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (high))))); [ zenon_intro zenon_H85 | zenon_intro zenon_H86 ]. % 112.02/112.36 apply (zenon_and_s _ _ zenon_H85). zenon_intro zenon_H2b. zenon_intro zenon_H87. % 112.02/112.36 apply (zenon_L35_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.02/112.36 cut ((greater (high) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod2))). % 112.02/112.36 intro zenon_D_pnotp. % 112.02/112.36 apply zenon_H5d. % 112.02/112.36 rewrite <- zenon_D_pnotp. % 112.02/112.36 exact assumption_18d. % 112.02/112.36 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 112.02/112.36 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 112.02/112.36 congruence. % 112.02/112.36 apply (zenon_notand_s _ _ zenon_H86); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 112.02/112.36 apply zenon_H96. zenon_intro zenon_H2c. % 112.02/112.36 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.02/112.36 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.02/112.36 intro zenon_D_pnotp. % 112.02/112.36 apply zenon_H94. % 112.02/112.36 rewrite <- zenon_D_pnotp. % 112.02/112.36 exact zenon_H61. % 112.02/112.36 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.02/112.36 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 112.02/112.36 congruence. % 112.02/112.36 exact (zenon_H2b zenon_H2c). % 112.02/112.36 apply zenon_H62. apply refl_equal. % 112.02/112.36 apply zenon_H62. apply refl_equal. % 112.02/112.36 apply zenon_H95. zenon_intro zenon_H97. % 112.02/112.36 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64. % 112.02/112.36 generalize (zenon_H64 (high)). zenon_intro zenon_H98. % 112.02/112.36 generalize (zenon_H98 (mod2)). zenon_intro zenon_H99. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H87 | zenon_intro zenon_H9a ]. % 112.02/112.36 exact (zenon_H87 zenon_H97). % 112.02/112.36 apply (zenon_imply_s _ _ zenon_H9a); [ zenon_intro zenon_H9b | zenon_intro zenon_H63 ]. % 112.02/112.36 exact (zenon_H9b assumption_18d). % 112.02/112.36 exact (zenon_H5d zenon_H63). % 112.02/112.36 apply zenon_H83. apply refl_equal. % 112.02/112.36 (* end of lemma zenon_L36_ *) % 112.02/112.36 assert (zenon_L37_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low))) -> False). % 112.02/112.36 do 3 intro. intros zenon_H1f zenon_Hec zenon_H1a zenon_H37 zenon_H73 zenon_H34 zenon_H9d. % 112.02/112.36 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod2))))); [ zenon_intro zenon_H5b | zenon_intro zenon_H5c ]. % 112.02/112.36 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H31. zenon_intro zenon_H5d. % 112.02/112.36 apply (zenon_L36_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.36 cut ((greater (mod2) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low))). % 112.02/112.36 intro zenon_D_pnotp. % 112.02/112.36 apply zenon_H9d. % 112.02/112.36 rewrite <- zenon_D_pnotp. % 112.02/112.36 exact assumption_18e. % 112.02/112.36 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.02/112.36 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 112.02/112.36 congruence. % 112.02/112.36 apply (zenon_notand_s _ _ zenon_H5c); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ]. % 112.02/112.36 apply zenon_H60. zenon_intro zenon_H32. % 112.02/112.36 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.02/112.36 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.02/112.36 intro zenon_D_pnotp. % 112.02/112.36 apply zenon_H5e. % 112.02/112.36 rewrite <- zenon_D_pnotp. % 112.02/112.36 exact zenon_H61. % 112.02/112.36 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.02/112.36 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31]. % 112.02/112.36 congruence. % 112.02/112.36 exact (zenon_H31 zenon_H32). % 112.02/112.36 apply zenon_H62. apply refl_equal. % 112.02/112.36 apply zenon_H62. apply refl_equal. % 112.02/112.36 apply zenon_H5f. zenon_intro zenon_H63. % 112.02/112.36 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64. % 112.02/112.36 generalize (zenon_H64 (mod2)). zenon_intro zenon_H65. % 112.02/112.36 generalize (zenon_H65 (low)). zenon_intro zenon_Hc0. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_Hc0); [ zenon_intro zenon_H5d | zenon_intro zenon_Hc1 ]. % 112.02/112.36 exact (zenon_H5d zenon_H63). % 112.02/112.36 apply (zenon_imply_s _ _ zenon_Hc1); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H9c ]. % 112.02/112.36 exact (zenon_Hc2 assumption_18e). % 112.02/112.36 exact (zenon_H9d zenon_H9c). % 112.02/112.36 apply zenon_H6a. apply refl_equal. % 112.02/112.36 (* end of lemma zenon_L37_ *) % 112.02/112.36 assert (zenon_L38_ : (~((very_low) = (very_low))) -> False). % 112.02/112.36 do 0 intro. intros zenon_Hf5. % 112.02/112.36 apply zenon_Hf5. apply refl_equal. % 112.02/112.36 (* end of lemma zenon_L38_ *) % 112.02/112.36 assert (zenon_L39_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (very_low))) -> False). % 112.02/112.36 do 3 intro. intros zenon_H37 zenon_H1a zenon_Hec zenon_H1f zenon_H34 zenon_Hf6. % 112.02/112.36 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low))))); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hf8 ]. % 112.02/112.36 apply (zenon_and_s _ _ zenon_Hf7). zenon_intro zenon_H73. zenon_intro zenon_H9d. % 112.02/112.36 apply (zenon_L37_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.02/112.36 cut ((greater (low) (very_low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (very_low))). % 112.02/112.36 intro zenon_D_pnotp. % 112.02/112.36 apply zenon_Hf6. % 112.02/112.36 rewrite <- zenon_D_pnotp. % 112.02/112.36 exact assumption_18c. % 112.02/112.36 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 112.02/112.36 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 112.02/112.36 congruence. % 112.02/112.36 apply (zenon_notand_s _ _ zenon_Hf8); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hf9 ]. % 112.02/112.36 apply zenon_Hfa. zenon_intro zenon_H6b. % 112.02/112.36 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.02/112.36 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.02/112.36 intro zenon_D_pnotp. % 112.02/112.36 apply zenon_H72. % 112.02/112.36 rewrite <- zenon_D_pnotp. % 112.02/112.36 exact zenon_H61. % 112.02/112.36 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.02/112.36 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 112.02/112.36 congruence. % 112.02/112.36 exact (zenon_H73 zenon_H6b). % 112.02/112.36 apply zenon_H62. apply refl_equal. % 112.02/112.36 apply zenon_H62. apply refl_equal. % 112.02/112.36 apply zenon_Hf9. zenon_intro zenon_H9c. % 112.02/112.36 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64. % 112.02/112.36 generalize (zenon_H64 (low)). zenon_intro zenon_Hfb. % 112.02/112.36 generalize (zenon_Hfb (very_low)). zenon_intro zenon_Hfc. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_Hfc); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfd ]. % 112.02/112.36 exact (zenon_H9d zenon_H9c). % 112.02/112.36 apply (zenon_imply_s _ _ zenon_Hfd); [ zenon_intro zenon_Hff | zenon_intro zenon_Hfe ]. % 112.02/112.36 exact (zenon_Hff assumption_18c). % 112.02/112.36 exact (zenon_Hf6 zenon_Hfe). % 112.02/112.36 apply zenon_Hf5. apply refl_equal. % 112.02/112.36 (* end of lemma zenon_L39_ *) % 112.02/112.36 assert (zenon_L40_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TT3_x : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (greater (age zenon_TX_y zenon_TT3_x) (tau)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (greater (tau) (sigma)) -> (organization zenon_TX_y) -> (~(smaller (hazard_of_mortality zenon_TX_y zenon_TT3_x) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> False). % 112.02/112.36 do 4 intro. intros zenon_H34 zenon_H100 zenon_Hec zenon_H1a zenon_H35 zenon_H37 zenon_H38 zenon_H1f zenon_H101. % 112.02/112.36 generalize (definition_smaller (hazard_of_mortality zenon_TX_y zenon_TT3_x)). zenon_intro zenon_H102. % 112.02/112.36 generalize (zenon_H102 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H103. % 112.02/112.36 apply (zenon_equiv_s _ _ zenon_H103); [ zenon_intro zenon_H101; zenon_intro zenon_Hae | zenon_intro zenon_H105; zenon_intro zenon_H104 ]. % 112.02/112.36 generalize (zenon_H35 zenon_TT3_x). zenon_intro zenon_H106. % 112.02/112.36 apply (zenon_and_s _ _ zenon_H106). zenon_intro zenon_H108. zenon_intro zenon_H107. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_H107); [ zenon_intro zenon_H109 | zenon_intro zenon_Hbb ]. % 112.02/112.36 exact (zenon_H109 zenon_H100). % 112.02/112.36 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0. % 112.02/112.36 generalize (zenon_H0 zenon_TT3_x). zenon_intro zenon_H10a. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_H10a); [ zenon_intro zenon_H27 | zenon_intro zenon_H10b ]. % 112.02/112.36 exact (zenon_H27 zenon_H1f). % 112.02/112.36 apply (zenon_and_s _ _ zenon_H10b). zenon_intro zenon_H10c. zenon_intro zenon_Hcc. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_H10c); [ zenon_intro zenon_H16 | zenon_intro zenon_H10d ]. % 112.02/112.36 apply (zenon_L25_ zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial. % 112.02/112.36 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_H10e | zenon_intro zenon_H10f ]. % 112.02/112.36 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (very_low))); [ zenon_intro zenon_Hfe | zenon_intro zenon_Hf6 ]. % 112.02/112.36 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (very_low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))). % 112.02/112.36 intro zenon_D_pnotp. % 112.02/112.36 apply zenon_Hae. % 112.02/112.36 rewrite <- zenon_D_pnotp. % 112.02/112.36 exact zenon_Hfe. % 112.02/112.36 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 112.02/112.36 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.02/112.36 congruence. % 112.02/112.36 apply zenon_H62. apply refl_equal. % 112.02/112.36 exact (zenon_H10f zenon_H10e). % 112.02/112.36 apply (zenon_L39_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.36 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb6 ]. % 112.02/112.36 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x)) = ((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))). % 112.02/112.36 intro zenon_D_pnotp. % 112.02/112.36 apply zenon_H10f. % 112.02/112.36 rewrite <- zenon_D_pnotp. % 112.02/112.36 exact zenon_Hb9. % 112.02/112.36 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 112.02/112.36 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H110]. % 112.02/112.36 congruence. % 112.02/112.36 exact (zenon_H110 zenon_H10d). % 112.02/112.36 apply zenon_Hb6. apply refl_equal. % 112.02/112.36 apply zenon_Hb6. apply refl_equal. % 112.02/112.36 exact (zenon_H101 zenon_H105). % 112.02/112.36 (* end of lemma zenon_L40_ *) % 112.02/112.36 assert (zenon_L41_ : forall (zenon_TX_y : zenon_U), (~(~(has_immunity zenon_TX_y zenon_E))) -> (~(has_immunity zenon_TX_y zenon_E)) -> False). % 112.02/112.36 do 1 intro. intros zenon_H111 zenon_H112. % 112.02/112.36 exact (zenon_H111 zenon_H112). % 112.02/112.36 (* end of lemma zenon_L41_ *) % 112.02/112.36 assert (zenon_L42_ : (~((high) = (high))) -> False). % 112.02/112.36 do 0 intro. intros zenon_H113. % 112.02/112.36 apply zenon_H113. apply refl_equal. % 112.02/112.36 (* end of lemma zenon_L42_ *) % 112.02/112.36 assert (zenon_L43_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), ((((is_aligned zenon_TX_y zenon_TT1_bg)/\(positional_advantage zenon_TX_y zenon_TT1_bg))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low)))/\((((~(is_aligned zenon_TX_y zenon_TT1_bg))/\(positional_advantage zenon_TX_y zenon_TT1_bg))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod1)))/\((((is_aligned zenon_TX_y zenon_TT1_bg)/\(~(positional_advantage zenon_TX_y zenon_TT1_bg)))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2)))/\(((~(is_aligned zenon_TX_y zenon_TT1_bg))/\(~(positional_advantage zenon_TX_y zenon_TT1_bg)))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high)))))) -> (greater (tau) (sigma)) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T0) = (zero)))->((greater (age zenon_TX_y T) (sigma))<->(dissimilar zenon_TX_y T0 T))))) -> (~((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> False). % 112.02/112.36 do 3 intro. intros zenon_H8c zenon_H38 zenon_H37 zenon_H35 zenon_H34 zenon_H1f zenon_Hec zenon_Hcd zenon_Hed zenon_H5e. % 112.02/112.36 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d. % 112.02/112.36 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f. % 112.02/112.36 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H30. zenon_intro zenon_H28. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 112.02/112.36 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ]. % 112.02/112.36 apply (zenon_L30_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.02/112.36 apply zenon_H2e. zenon_intro zenon_H36. % 112.02/112.36 apply (zenon_L6_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.36 apply zenon_H5e. apply sym_equal. exact zenon_H32. % 112.02/112.36 (* end of lemma zenon_L43_ *) % 112.02/112.36 assert (zenon_L44_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (greater (tau) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (organization zenon_TX_y) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> False). % 112.02/112.36 do 3 intro. intros zenon_H34 zenon_H5e zenon_H38 zenon_H35 zenon_Hcd zenon_H37 zenon_Hec zenon_H1a zenon_H1f zenon_H0. % 112.02/112.36 generalize (assumption_15 zenon_TX_y). zenon_intro zenon_Hed. % 112.02/112.36 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ]. % 112.02/112.36 exact (zenon_H27 zenon_H1f). % 112.02/112.36 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ]. % 112.02/112.36 apply (zenon_L3_ zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.36 apply (zenon_L43_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.36 (* end of lemma zenon_L44_ *) % 112.02/112.36 assert (zenon_L45_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (greater (tau) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> False). % 112.02/112.36 do 3 intro. intros zenon_H34 zenon_Hf3 zenon_H1f zenon_Hec zenon_H5e zenon_H38 zenon_H35 zenon_H37 zenon_H1a zenon_H0. % 112.02/112.36 generalize (zenon_Hf3 zenon_TT0_hz). zenon_intro zenon_Hf4. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcd ]. % 112.02/112.36 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ]. % 112.02/112.36 exact (zenon_H27 zenon_H1f). % 112.02/112.36 exact (zenon_Hf2 zenon_Hec). % 112.02/112.36 apply (zenon_L44_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.36 (* end of lemma zenon_L45_ *) % 112.02/112.36 assert (zenon_L46_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> (~((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> False). % 112.02/112.36 do 3 intro. intros zenon_H34 zenon_H1a zenon_H37 zenon_H35 zenon_H38 zenon_H5e zenon_Hec zenon_H1f zenon_Hf3. % 112.02/112.36 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0. % 112.02/112.36 apply (zenon_L45_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.02/112.36 (* end of lemma zenon_L46_ *) % 112.02/112.36 assert (zenon_L47_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (greater (tau) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> False). % 112.02/112.36 do 3 intro. intros zenon_H34 zenon_H1f zenon_Hec zenon_H5e zenon_H38 zenon_H35 zenon_H37 zenon_H1a. % 112.02/112.36 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3. % 112.02/112.36 apply (zenon_L46_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.36 (* end of lemma zenon_L47_ *) % 112.02/112.36 assert (zenon_L48_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (greater (tau) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> False). % 112.02/112.36 do 3 intro. intros zenon_H34 zenon_H114 zenon_H1f zenon_Hec zenon_H38 zenon_H35 zenon_H37 zenon_H1a. % 112.02/112.36 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H115 | zenon_intro zenon_H5e ]. % 112.02/112.36 cut ((greater (high) (mod2)) = (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.02/112.36 intro zenon_D_pnotp. % 112.02/112.36 apply zenon_H114. % 112.02/112.36 rewrite <- zenon_D_pnotp. % 112.02/112.36 exact assumption_18d. % 112.02/112.36 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 112.02/112.36 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113]. % 112.02/112.36 congruence. % 112.02/112.36 apply zenon_H113. apply refl_equal. % 112.02/112.36 exact (zenon_H5e zenon_H115). % 112.02/112.36 apply (zenon_L47_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.02/112.36 (* end of lemma zenon_L48_ *) % 112.02/112.36 assert (zenon_L49_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (high)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> False). % 112.02/112.36 do 3 intro. intros zenon_H34 zenon_H116 zenon_H117 zenon_H1a zenon_H37 zenon_H35 zenon_H38 zenon_Hec zenon_H1f. % 112.02/112.36 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H118 | zenon_intro zenon_H114 ]. % 112.02/112.36 cut ((greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.02/112.36 intro zenon_D_pnotp. % 112.02/112.36 apply zenon_H117. % 112.02/112.36 rewrite <- zenon_D_pnotp. % 112.02/112.36 exact zenon_H118. % 112.02/112.36 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.02/112.36 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H119]. % 112.02/112.36 congruence. % 112.02/112.36 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.02/112.36 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.02/112.36 intro zenon_D_pnotp. % 112.02/112.36 apply zenon_H119. % 112.02/112.36 rewrite <- zenon_D_pnotp. % 112.02/112.36 exact zenon_H11a. % 112.02/112.36 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.02/112.36 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 112.02/112.36 congruence. % 112.02/112.36 exact (zenon_H11c zenon_H116). % 112.02/112.36 apply zenon_H11b. apply refl_equal. % 112.02/112.36 apply zenon_H11b. apply refl_equal. % 112.02/112.36 apply zenon_H62. apply refl_equal. % 112.02/112.36 apply (zenon_L48_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.36 (* end of lemma zenon_L49_ *) % 112.02/112.36 assert (zenon_L50_ : forall (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (~(~(has_immunity zenon_TX_y zenon_TT2_la))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> False). % 112.02/112.36 do 2 intro. intros zenon_H11d zenon_H1f zenon_H1a. % 112.02/112.36 apply zenon_H11d. zenon_intro zenon_H11f. % 112.02/112.36 generalize (assumption_1 zenon_TX_y). zenon_intro zenon_H22. % 112.02/112.36 generalize (zenon_H22 zenon_TT2_la). zenon_intro zenon_H120. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_H120); [ zenon_intro zenon_H25 | zenon_intro zenon_H121 ]. % 112.02/112.36 apply (zenon_notand_s _ _ zenon_H25); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 112.02/112.36 exact (zenon_H27 zenon_H1f). % 112.02/112.36 apply zenon_H26. zenon_intro zenon_H19. % 112.02/112.36 apply (zenon_L2_ zenon_TX_y); trivial. % 112.02/112.36 exact (zenon_H121 zenon_H11f). % 112.02/112.36 (* end of lemma zenon_L50_ *) % 112.02/112.36 assert (zenon_L51_ : forall (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (positional_advantage zenon_TX_y zenon_TT2_la) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> False). % 112.02/112.36 do 2 intro. intros zenon_H35 zenon_H122 zenon_H123. % 112.02/112.36 generalize (zenon_H35 zenon_TT2_la). zenon_intro zenon_H124. % 112.02/112.36 apply (zenon_and_s _ _ zenon_H124). zenon_intro zenon_H126. zenon_intro zenon_H125. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_H126); [ zenon_intro zenon_H128 | zenon_intro zenon_H127 ]. % 112.02/112.36 generalize (definition_smaller_or_equal (age zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H129. % 112.02/112.36 generalize (zenon_H129 (tau)). zenon_intro zenon_H12a. % 112.02/112.36 apply (zenon_equiv_s _ _ zenon_H12a); [ zenon_intro zenon_H128; zenon_intro zenon_H12d | zenon_intro zenon_H12c; zenon_intro zenon_H12b ]. % 112.02/112.36 apply (zenon_notor_s _ _ zenon_H12d). zenon_intro zenon_H12f. zenon_intro zenon_H12e. % 112.02/112.36 generalize (definition_smaller (age zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H130. % 112.02/112.36 generalize (zenon_H130 (tau)). zenon_intro zenon_H131. % 112.02/112.36 apply (zenon_equiv_s _ _ zenon_H131); [ zenon_intro zenon_H12f; zenon_intro zenon_H133 | zenon_intro zenon_H132; zenon_intro zenon_H123 ]. % 112.02/112.36 exact (zenon_H133 zenon_H123). % 112.02/112.36 exact (zenon_H12f zenon_H132). % 112.02/112.36 exact (zenon_H128 zenon_H12c). % 112.02/112.36 exact (zenon_H127 zenon_H122). % 112.02/112.36 (* end of lemma zenon_L51_ *) % 112.02/112.36 assert (zenon_L52_ : forall (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (((~(is_aligned zenon_TX_y zenon_TT2_la))/\(~(positional_advantage zenon_TX_y zenon_TT2_la)))->((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (~(is_aligned zenon_TX_y zenon_TT2_la)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> False). % 112.02/112.36 do 2 intro. intros zenon_H134 zenon_H123 zenon_H35 zenon_H135 zenon_H136. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_H134); [ zenon_intro zenon_H138 | zenon_intro zenon_H137 ]. % 112.02/112.36 apply (zenon_notand_s _ _ zenon_H138); [ zenon_intro zenon_H13a | zenon_intro zenon_H139 ]. % 112.02/112.36 exact (zenon_H13a zenon_H135). % 112.02/112.36 apply zenon_H139. zenon_intro zenon_H122. % 112.02/112.36 apply (zenon_L51_ zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.36 exact (zenon_H136 zenon_H137). % 112.02/112.36 (* end of lemma zenon_L52_ *) % 112.02/112.36 assert (zenon_L53_ : forall (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))) -> False). % 112.02/112.36 do 2 intro. intros zenon_H0 zenon_H1f zenon_H1a zenon_H136 zenon_H123 zenon_H35 zenon_H13b. % 112.02/112.36 generalize (zenon_H0 zenon_TT2_la). zenon_intro zenon_H13c. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_H13c); [ zenon_intro zenon_H27 | zenon_intro zenon_H13d ]. % 112.02/112.36 exact (zenon_H27 zenon_H1f). % 112.02/112.36 apply (zenon_and_s _ _ zenon_H13d). zenon_intro zenon_H13f. zenon_intro zenon_H13e. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_H13e); [ zenon_intro zenon_H11d | zenon_intro zenon_H140 ]. % 112.02/112.36 apply (zenon_L50_ zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.36 apply (zenon_and_s _ _ zenon_H140). zenon_intro zenon_H142. zenon_intro zenon_H141. % 112.02/112.36 apply (zenon_and_s _ _ zenon_H141). zenon_intro zenon_H144. zenon_intro zenon_H143. % 112.02/112.36 apply (zenon_and_s _ _ zenon_H143). zenon_intro zenon_H145. zenon_intro zenon_H134. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_H145); [ zenon_intro zenon_H147 | zenon_intro zenon_H146 ]. % 112.02/112.36 apply (zenon_notand_s _ _ zenon_H147); [ zenon_intro zenon_H135 | zenon_intro zenon_H139 ]. % 112.02/112.36 apply (zenon_L52_ zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.36 apply zenon_H139. zenon_intro zenon_H122. % 112.02/112.36 apply (zenon_L51_ zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.36 exact (zenon_H13b zenon_H146). % 112.02/112.36 (* end of lemma zenon_L53_ *) % 112.02/112.36 assert (zenon_L54_ : forall (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (~(~(has_immunity zenon_TX_y zenon_TT2_la))) -> (~(has_immunity zenon_TX_y zenon_TT2_la)) -> False). % 112.02/112.36 do 2 intro. intros zenon_H11d zenon_H121. % 112.02/112.36 exact (zenon_H11d zenon_H121). % 112.02/112.36 (* end of lemma zenon_L54_ *) % 112.02/112.36 assert (zenon_L55_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T0) = (zero)))->((greater (age zenon_TX_y T) (sigma))<->(dissimilar zenon_TX_y T0 T))))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (is_aligned zenon_TX_y zenon_TT2_la) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> False). % 112.02/112.36 do 3 intro. intros zenon_Hed zenon_H148 zenon_H149 zenon_Hcd zenon_Hec zenon_H1f. % 112.02/112.36 generalize (zenon_Hed zenon_TT0_hz). zenon_intro zenon_Hee. % 112.02/112.36 generalize (zenon_Hee zenon_TT2_la). zenon_intro zenon_H14a. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_H14a); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H14b ]. % 112.02/112.36 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ]. % 112.02/112.36 exact (zenon_H27 zenon_H1f). % 112.02/112.36 exact (zenon_Hf2 zenon_Hec). % 112.02/112.36 apply (zenon_equiv_s _ _ zenon_H14b); [ zenon_intro zenon_H14e; zenon_intro zenon_H14d | zenon_intro zenon_H148; zenon_intro zenon_H14c ]. % 112.02/112.36 exact (zenon_H14e zenon_H148). % 112.02/112.36 generalize (definition_2 zenon_TX_y). zenon_intro zenon_Hd0. % 112.02/112.36 generalize (zenon_Hd0 zenon_TT0_hz). zenon_intro zenon_Hd1. % 112.02/112.36 generalize (zenon_Hd1 zenon_TT2_la). zenon_intro zenon_H14f. % 112.02/112.36 apply (zenon_equiv_s _ _ zenon_H14f); [ zenon_intro zenon_H14d; zenon_intro zenon_H151 | zenon_intro zenon_H14c; zenon_intro zenon_H150 ]. % 112.02/112.36 exact (zenon_H14d zenon_H14c). % 112.02/112.36 apply (zenon_and_s _ _ zenon_H150). zenon_intro zenon_H1f. zenon_intro zenon_H152. % 112.02/112.36 apply (zenon_notequiv_s _ _ zenon_H152); [ zenon_intro zenon_Hd8; zenon_intro zenon_H149 | zenon_intro zenon_Hcd; zenon_intro zenon_H135 ]. % 112.02/112.36 exact (zenon_Hd8 zenon_Hcd). % 112.02/112.36 exact (zenon_H135 zenon_H149). % 112.02/112.36 (* end of lemma zenon_L55_ *) % 112.02/112.36 assert (zenon_L56_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (((~(is_aligned zenon_TX_y zenon_TT2_la))/\(~(positional_advantage zenon_TX_y zenon_TT2_la)))->((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (~(positional_advantage zenon_TX_y zenon_TT2_la)) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T0) = (zero)))->((greater (age zenon_TX_y T) (sigma))<->(dissimilar zenon_TX_y T0 T))))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> False). % 112.02/112.36 do 3 intro. intros zenon_H134 zenon_H127 zenon_Hed zenon_H148 zenon_Hcd zenon_Hec zenon_H1f zenon_H136. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_H134); [ zenon_intro zenon_H138 | zenon_intro zenon_H137 ]. % 112.02/112.36 apply (zenon_notand_s _ _ zenon_H138); [ zenon_intro zenon_H13a | zenon_intro zenon_H139 ]. % 112.02/112.36 apply zenon_H13a. zenon_intro zenon_H149. % 112.02/112.36 apply (zenon_L55_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.36 exact (zenon_H139 zenon_H127). % 112.02/112.36 exact (zenon_H136 zenon_H137). % 112.02/112.36 (* end of lemma zenon_L56_ *) % 112.02/112.36 assert (zenon_L57_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2)) -> (~(greater (mod2) (mod2))) -> (~((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T0) = (zero)))->((greater (age zenon_TX_y T) (sigma))<->(dissimilar zenon_TX_y T0 T))))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (~((low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))) -> (organization zenon_TX_y) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> False). % 112.02/112.36 do 3 intro. intros zenon_H146 zenon_H153 zenon_H154 zenon_Hed zenon_H148 zenon_Hcd zenon_Hec zenon_H136 zenon_H155 zenon_H1f zenon_H0. % 112.02/112.36 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H156 | zenon_intro zenon_H157 ]. % 112.02/112.36 cut ((greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = (greater (mod2) (mod2))). % 112.02/112.36 intro zenon_D_pnotp. % 112.02/112.36 apply zenon_H153. % 112.02/112.36 rewrite <- zenon_D_pnotp. % 112.02/112.36 exact zenon_H156. % 112.02/112.36 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 112.02/112.36 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 112.02/112.36 congruence. % 112.02/112.36 apply zenon_H83. apply refl_equal. % 112.02/112.36 exact (zenon_H13b zenon_H146). % 112.02/112.36 elim (classic ((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H158 | zenon_intro zenon_H159 ]. % 112.02/112.36 cut ((greater (mod2) (mod1)) = (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.02/112.36 intro zenon_D_pnotp. % 112.02/112.36 apply zenon_H157. % 112.02/112.36 rewrite <- zenon_D_pnotp. % 112.02/112.36 exact assumption_19. % 112.02/112.36 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H159]. % 112.02/112.36 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 112.02/112.36 congruence. % 112.02/112.36 apply zenon_H83. apply refl_equal. % 112.02/112.36 exact (zenon_H159 zenon_H158). % 112.02/112.36 generalize (zenon_H0 zenon_TT2_la). zenon_intro zenon_H13c. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_H13c); [ zenon_intro zenon_H27 | zenon_intro zenon_H13d ]. % 112.02/112.36 exact (zenon_H27 zenon_H1f). % 112.02/112.36 apply (zenon_and_s _ _ zenon_H13d). zenon_intro zenon_H13f. zenon_intro zenon_H13e. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_H13f); [ zenon_intro zenon_H121 | zenon_intro zenon_H15a ]. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_H13e); [ zenon_intro zenon_H11d | zenon_intro zenon_H140 ]. % 112.02/112.36 exact (zenon_H11d zenon_H121). % 112.02/112.36 apply (zenon_and_s _ _ zenon_H140). zenon_intro zenon_H142. zenon_intro zenon_H141. % 112.02/112.36 apply (zenon_and_s _ _ zenon_H141). zenon_intro zenon_H144. zenon_intro zenon_H143. % 112.02/112.36 apply (zenon_and_s _ _ zenon_H143). zenon_intro zenon_H145. zenon_intro zenon_H134. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_H142); [ zenon_intro zenon_H15c | zenon_intro zenon_H15b ]. % 112.02/112.36 apply (zenon_notand_s _ _ zenon_H15c); [ zenon_intro zenon_H135 | zenon_intro zenon_H127 ]. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_H144); [ zenon_intro zenon_H15e | zenon_intro zenon_H15d ]. % 112.02/112.36 apply (zenon_notand_s _ _ zenon_H15e); [ zenon_intro zenon_H13a | zenon_intro zenon_H127 ]. % 112.02/112.36 exact (zenon_H13a zenon_H135). % 112.02/112.36 apply (zenon_L56_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.36 apply zenon_H159. apply sym_equal. exact zenon_H15d. % 112.02/112.36 apply (zenon_L56_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.36 apply zenon_H155. apply sym_equal. exact zenon_H15b. % 112.02/112.36 apply zenon_H154. apply sym_equal. exact zenon_H15a. % 112.02/112.36 (* end of lemma zenon_L57_ *) % 112.02/112.36 assert (zenon_L58_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT2_la))) -> ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2)) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T0) = (zero)))->((greater (age zenon_TX_y T) (sigma))<->(dissimilar zenon_TX_y T0 T))))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (organization zenon_TX_y) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (~(greater (mod2) (mod2))) -> False). % 112.02/112.36 do 3 intro. intros zenon_H34 zenon_H15f zenon_H146 zenon_Hed zenon_H148 zenon_Hcd zenon_Hec zenon_H136 zenon_H1f zenon_H0 zenon_H153. % 112.02/112.36 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H160 | zenon_intro zenon_H155 ]. % 112.02/112.36 cut ((greater (mod1) (low)) = (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.02/112.36 intro zenon_D_pnotp. % 112.02/112.36 apply zenon_H15f. % 112.02/112.36 rewrite <- zenon_D_pnotp. % 112.02/112.36 exact assumption_18b. % 112.02/112.36 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H155]. % 112.02/112.36 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 112.02/112.36 congruence. % 112.02/112.36 apply zenon_H59. apply refl_equal. % 112.02/112.36 exact (zenon_H155 zenon_H160). % 112.02/112.36 elim (classic (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H161 | zenon_intro zenon_H162 ]. % 112.02/112.36 generalize (zenon_H34 (mod1)). zenon_intro zenon_Ha7. % 112.02/112.36 generalize (zenon_Ha7 (low)). zenon_intro zenon_Ha8. % 112.02/112.36 generalize (zenon_Ha8 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H163. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_H163); [ zenon_intro zenon_H7f | zenon_intro zenon_H164 ]. % 112.02/112.36 exact (zenon_H7f assumption_18b). % 112.02/112.36 apply (zenon_imply_s _ _ zenon_H164); [ zenon_intro zenon_H162 | zenon_intro zenon_H165 ]. % 112.02/112.36 exact (zenon_H162 zenon_H161). % 112.02/112.36 exact (zenon_H15f zenon_H165). % 112.02/112.36 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H166 | zenon_intro zenon_H154 ]. % 112.02/112.36 cut ((greater (low) (very_low)) = (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.02/112.36 intro zenon_D_pnotp. % 112.02/112.36 apply zenon_H162. % 112.02/112.36 rewrite <- zenon_D_pnotp. % 112.02/112.36 exact assumption_18c. % 112.02/112.36 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H154]. % 112.02/112.36 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.02/112.36 congruence. % 112.02/112.36 apply zenon_H6a. apply refl_equal. % 112.02/112.36 exact (zenon_H154 zenon_H166). % 112.02/112.36 apply (zenon_L57_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.36 (* end of lemma zenon_L58_ *) % 112.02/112.36 assert (zenon_L59_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (organization zenon_TX_y) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T0) = (zero)))->((greater (age zenon_TX_y T) (sigma))<->(dissimilar zenon_TX_y T0 T))))) -> ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2)) -> False). % 112.02/112.36 do 3 intro. intros zenon_H34 zenon_H167 zenon_H0 zenon_H1f zenon_H136 zenon_Hec zenon_Hcd zenon_H148 zenon_Hed zenon_H146. % 112.02/112.36 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H168 | zenon_intro zenon_H169 ]. % 112.02/112.36 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))). % 112.02/112.36 intro zenon_D_pnotp. % 112.02/112.36 apply zenon_H167. % 112.02/112.36 rewrite <- zenon_D_pnotp. % 112.02/112.36 exact zenon_H168. % 112.02/112.36 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 112.02/112.36 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.36 congruence. % 112.02/112.36 apply zenon_H16a. apply refl_equal. % 112.02/112.36 exact (zenon_H13b zenon_H146). % 112.02/112.36 elim (classic (greater (mod2) (mod2))); [ zenon_intro zenon_H16b | zenon_intro zenon_H153 ]. % 112.02/112.36 cut ((greater (mod2) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))). % 112.02/112.36 intro zenon_D_pnotp. % 112.02/112.36 apply zenon_H167. % 112.02/112.36 rewrite <- zenon_D_pnotp. % 112.02/112.36 exact zenon_H16b. % 112.02/112.36 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 112.02/112.36 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 112.02/112.36 congruence. % 112.02/112.36 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.02/112.36 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.02/112.36 intro zenon_D_pnotp. % 112.02/112.36 apply zenon_H16c. % 112.02/112.36 rewrite <- zenon_D_pnotp. % 112.02/112.36 exact zenon_H16d. % 112.02/112.36 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.36 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 112.02/112.36 congruence. % 112.02/112.36 exact (zenon_H13b zenon_H146). % 112.02/112.36 apply zenon_H16a. apply refl_equal. % 112.02/112.36 apply zenon_H16a. apply refl_equal. % 112.02/112.36 apply zenon_H83. apply refl_equal. % 112.02/112.36 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H156 | zenon_intro zenon_H157 ]. % 112.02/112.36 cut ((greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.02/112.36 intro zenon_D_pnotp. % 112.02/112.36 apply zenon_H169. % 112.02/112.36 rewrite <- zenon_D_pnotp. % 112.02/112.36 exact zenon_H156. % 112.02/112.36 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.36 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 112.02/112.36 congruence. % 112.02/112.36 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.02/112.36 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.02/112.36 intro zenon_D_pnotp. % 112.02/112.36 apply zenon_H16c. % 112.02/112.36 rewrite <- zenon_D_pnotp. % 112.02/112.36 exact zenon_H16d. % 112.02/112.36 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.36 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 112.02/112.36 congruence. % 112.02/112.36 exact (zenon_H13b zenon_H146). % 112.02/112.36 apply zenon_H16a. apply refl_equal. % 112.02/112.36 apply zenon_H16a. apply refl_equal. % 112.02/112.36 apply zenon_H16a. apply refl_equal. % 112.02/112.36 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H165 | zenon_intro zenon_H15f ]. % 112.02/112.36 generalize (zenon_H34 (mod2)). zenon_intro zenon_H16e. % 112.02/112.36 generalize (zenon_H16e (mod1)). zenon_intro zenon_H16f. % 112.02/112.36 generalize (zenon_H16f (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H170. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_H170); [ zenon_intro zenon_H69 | zenon_intro zenon_H171 ]. % 112.02/112.36 exact (zenon_H69 assumption_19). % 112.02/112.36 apply (zenon_imply_s _ _ zenon_H171); [ zenon_intro zenon_H15f | zenon_intro zenon_H156 ]. % 112.02/112.36 exact (zenon_H15f zenon_H165). % 112.02/112.36 exact (zenon_H157 zenon_H156). % 112.02/112.36 apply (zenon_L58_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.36 (* end of lemma zenon_L59_ *) % 112.02/112.36 assert (zenon_L60_ : forall (zenon_TT2_la : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (~(greater (mod2) (mod2))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> False). % 112.02/112.36 do 3 intro. intros zenon_H34 zenon_Hf3 zenon_H1f zenon_Hec zenon_H0 zenon_H1a zenon_H136 zenon_H123 zenon_H35 zenon_H153 zenon_H167 zenon_H148. % 112.02/112.36 generalize (zenon_Hf3 zenon_TT0_hz). zenon_intro zenon_Hf4. % 112.02/112.36 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcd ]. % 112.02/112.36 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ]. % 112.02/112.36 exact (zenon_H27 zenon_H1f). % 112.02/112.36 exact (zenon_Hf2 zenon_Hec). % 112.02/112.36 generalize (assumption_15 zenon_TX_y). zenon_intro zenon_Hed. % 112.02/112.36 generalize (meaning_postulate_greater_comparable (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H172. % 112.02/112.36 generalize (zenon_H172 (mod2)). zenon_intro zenon_H173. % 112.02/112.36 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H175 | zenon_intro zenon_H174 ]. % 112.02/112.37 generalize (definition_smaller (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H176. % 112.02/112.37 generalize (zenon_H176 (mod2)). zenon_intro zenon_H177. % 112.02/112.37 apply (zenon_equiv_s _ _ zenon_H177); [ zenon_intro zenon_H178; zenon_intro zenon_H157 | zenon_intro zenon_H175; zenon_intro zenon_H156 ]. % 112.02/112.37 exact (zenon_H178 zenon_H175). % 112.02/112.37 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [ zenon_intro zenon_H146 | zenon_intro zenon_H13b ]. % 112.02/112.37 cut ((greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = (greater (mod2) (mod2))). % 112.02/112.37 intro zenon_D_pnotp. % 112.02/112.37 apply zenon_H153. % 112.02/112.37 rewrite <- zenon_D_pnotp. % 112.02/112.37 exact zenon_H156. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 112.02/112.37 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 112.02/112.37 congruence. % 112.02/112.37 apply zenon_H83. apply refl_equal. % 112.02/112.37 exact (zenon_H13b zenon_H146). % 112.02/112.37 apply (zenon_L53_ zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.37 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H146 | zenon_intro zenon_H179 ]. % 112.02/112.37 apply (zenon_L59_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.37 exact (zenon_H167 zenon_H179). % 112.02/112.37 (* end of lemma zenon_L60_ *) % 112.02/112.37 assert (zenon_L61_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (mod2) (mod2))) -> ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2)) -> False). % 112.02/112.37 do 3 intro. intros zenon_H148 zenon_H35 zenon_H123 zenon_H136 zenon_H1a zenon_H0 zenon_Hec zenon_H1f zenon_Hf3 zenon_H34 zenon_H153 zenon_H146. % 112.02/112.37 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H17a | zenon_intro zenon_H16c ]. % 112.02/112.37 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ]. % 112.02/112.37 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2)) = (greater (mod2) (mod2))). % 112.02/112.37 intro zenon_D_pnotp. % 112.02/112.37 apply zenon_H153. % 112.02/112.37 rewrite <- zenon_D_pnotp. % 112.02/112.37 exact zenon_H179. % 112.02/112.37 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 112.02/112.37 congruence. % 112.02/112.37 elim (classic ((mod2) = (mod2))); [ zenon_intro zenon_H17b | zenon_intro zenon_H83 ]. % 112.02/112.37 cut (((mod2) = (mod2)) = ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))). % 112.02/112.37 intro zenon_D_pnotp. % 112.02/112.37 apply zenon_H13b. % 112.02/112.37 rewrite <- zenon_D_pnotp. % 112.02/112.37 exact zenon_H17b. % 112.02/112.37 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 112.02/112.37 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 112.02/112.37 congruence. % 112.02/112.37 exact (zenon_H16c zenon_H17a). % 112.02/112.37 apply zenon_H83. apply refl_equal. % 112.02/112.37 apply zenon_H83. apply refl_equal. % 112.02/112.37 apply zenon_H83. apply refl_equal. % 112.02/112.37 apply (zenon_L60_ zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial. % 112.02/112.37 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.02/112.37 intro zenon_D_pnotp. % 112.02/112.37 apply zenon_H16c. % 112.02/112.37 rewrite <- zenon_D_pnotp. % 112.02/112.37 exact zenon_H16d. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 112.02/112.37 congruence. % 112.02/112.37 exact (zenon_H13b zenon_H146). % 112.02/112.37 apply zenon_H16a. apply refl_equal. % 112.02/112.37 apply zenon_H16a. apply refl_equal. % 112.02/112.37 (* end of lemma zenon_L61_ *) % 112.02/112.37 assert (zenon_L62_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT2_la))) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2)) -> False). % 112.02/112.37 do 3 intro. intros zenon_H34 zenon_H169 zenon_Hf3 zenon_H1f zenon_Hec zenon_H0 zenon_H1a zenon_H136 zenon_H123 zenon_H35 zenon_H148 zenon_H146. % 112.02/112.37 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H156 | zenon_intro zenon_H157 ]. % 112.02/112.37 cut ((greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.02/112.37 intro zenon_D_pnotp. % 112.02/112.37 apply zenon_H169. % 112.02/112.37 rewrite <- zenon_D_pnotp. % 112.02/112.37 exact zenon_H156. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.37 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 112.02/112.37 congruence. % 112.02/112.37 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.02/112.37 intro zenon_D_pnotp. % 112.02/112.37 apply zenon_H16c. % 112.02/112.37 rewrite <- zenon_D_pnotp. % 112.02/112.37 exact zenon_H16d. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 112.02/112.37 congruence. % 112.02/112.37 exact (zenon_H13b zenon_H146). % 112.02/112.37 apply zenon_H16a. apply refl_equal. % 112.02/112.37 apply zenon_H16a. apply refl_equal. % 112.02/112.37 apply zenon_H16a. apply refl_equal. % 112.02/112.37 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H17a | zenon_intro zenon_H16c ]. % 112.02/112.37 elim (classic (greater (mod2) (mod2))); [ zenon_intro zenon_H16b | zenon_intro zenon_H153 ]. % 112.02/112.37 cut ((greater (mod2) (mod2)) = (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.02/112.37 intro zenon_D_pnotp. % 112.02/112.37 apply zenon_H157. % 112.02/112.37 rewrite <- zenon_D_pnotp. % 112.02/112.37 exact zenon_H16b. % 112.02/112.37 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 112.02/112.37 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 112.02/112.37 congruence. % 112.02/112.37 apply zenon_H83. apply refl_equal. % 112.02/112.37 exact (zenon_H16c zenon_H17a). % 112.02/112.37 apply (zenon_L61_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.37 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.02/112.37 intro zenon_D_pnotp. % 112.02/112.37 apply zenon_H16c. % 112.02/112.37 rewrite <- zenon_D_pnotp. % 112.02/112.37 exact zenon_H16d. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 112.02/112.37 congruence. % 112.02/112.37 exact (zenon_H13b zenon_H146). % 112.02/112.37 apply zenon_H16a. apply refl_equal. % 112.02/112.37 apply zenon_H16a. apply refl_equal. % 112.02/112.37 (* end of lemma zenon_L62_ *) % 112.02/112.37 assert (zenon_L63_ : forall (zenon_TT2_la : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (greater (tau) (sigma)) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2)) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> False). % 112.02/112.37 do 4 intro. intros zenon_H34 zenon_H38 zenon_Hcd zenon_H37 zenon_H17c zenon_H146 zenon_H148 zenon_H35 zenon_H123 zenon_H136 zenon_H1a zenon_H0 zenon_Hec zenon_H1f zenon_Hf3. % 112.02/112.37 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H168 | zenon_intro zenon_H169 ]. % 112.02/112.37 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ]. % 112.02/112.37 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.02/112.37 intro zenon_D_pnotp. % 112.02/112.37 apply zenon_H17c. % 112.02/112.37 rewrite <- zenon_D_pnotp. % 112.02/112.37 exact zenon_H179. % 112.02/112.37 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.37 congruence. % 112.02/112.37 apply zenon_H16a. apply refl_equal. % 112.02/112.37 apply (zenon_L44_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.37 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))). % 112.02/112.37 intro zenon_D_pnotp. % 112.02/112.37 apply zenon_H167. % 112.02/112.37 rewrite <- zenon_D_pnotp. % 112.02/112.37 exact zenon_H168. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.37 congruence. % 112.02/112.37 apply zenon_H16a. apply refl_equal. % 112.02/112.37 exact (zenon_H13b zenon_H146). % 112.02/112.37 apply (zenon_L62_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.37 (* end of lemma zenon_L63_ *) % 112.02/112.37 assert (zenon_L64_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (greater (tau) (sigma)) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> False). % 112.02/112.37 do 4 intro. intros zenon_H34 zenon_H148 zenon_Hf3 zenon_H38 zenon_H37 zenon_H17c zenon_H35 zenon_H123 zenon_H136 zenon_H1a zenon_Hec zenon_H1f. % 112.02/112.37 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0. % 112.02/112.37 generalize (zenon_Hf3 zenon_TT0_hz). zenon_intro zenon_Hf4. % 112.02/112.37 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcd ]. % 112.02/112.37 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ]. % 112.02/112.37 exact (zenon_H27 zenon_H1f). % 112.02/112.37 exact (zenon_Hf2 zenon_Hec). % 112.02/112.37 generalize (zenon_H0 zenon_TT2_la). zenon_intro zenon_H13c. % 112.02/112.37 apply (zenon_imply_s _ _ zenon_H13c); [ zenon_intro zenon_H27 | zenon_intro zenon_H13d ]. % 112.02/112.37 exact (zenon_H27 zenon_H1f). % 112.02/112.37 apply (zenon_and_s _ _ zenon_H13d). zenon_intro zenon_H13f. zenon_intro zenon_H13e. % 112.02/112.37 apply (zenon_imply_s _ _ zenon_H13e); [ zenon_intro zenon_H11d | zenon_intro zenon_H140 ]. % 112.02/112.37 apply (zenon_L50_ zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.37 apply (zenon_and_s _ _ zenon_H140). zenon_intro zenon_H142. zenon_intro zenon_H141. % 112.02/112.37 apply (zenon_and_s _ _ zenon_H141). zenon_intro zenon_H144. zenon_intro zenon_H143. % 112.02/112.37 apply (zenon_and_s _ _ zenon_H143). zenon_intro zenon_H145. zenon_intro zenon_H134. % 112.02/112.37 apply (zenon_imply_s _ _ zenon_H145); [ zenon_intro zenon_H147 | zenon_intro zenon_H146 ]. % 112.02/112.37 apply (zenon_notand_s _ _ zenon_H147); [ zenon_intro zenon_H135 | zenon_intro zenon_H139 ]. % 112.02/112.37 apply (zenon_L52_ zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.37 apply zenon_H139. zenon_intro zenon_H122. % 112.02/112.37 apply (zenon_L51_ zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.37 apply (zenon_L63_ zenon_TT2_la zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.02/112.37 (* end of lemma zenon_L64_ *) % 112.02/112.37 assert (zenon_L65_ : forall (zenon_TT2_la : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (high)) -> False). % 112.02/112.37 do 4 intro. intros zenon_H1a zenon_H37 zenon_H35 zenon_H38 zenon_Hec zenon_H1f zenon_H148 zenon_Hf3 zenon_H17c zenon_H123 zenon_H34 zenon_H116. % 112.02/112.37 elim (classic ((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H17d | zenon_intro zenon_H119 ]. % 112.02/112.37 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H17e | zenon_intro zenon_H117 ]. % 112.02/112.37 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H118 | zenon_intro zenon_H114 ]. % 112.02/112.37 cut ((greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.02/112.37 intro zenon_D_pnotp. % 112.02/112.37 apply zenon_H17c. % 112.02/112.37 rewrite <- zenon_D_pnotp. % 112.02/112.37 exact zenon_H118. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.02/112.37 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 112.02/112.37 congruence. % 112.02/112.37 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.02/112.37 intro zenon_D_pnotp. % 112.02/112.37 apply zenon_H17f. % 112.02/112.37 rewrite <- zenon_D_pnotp. % 112.02/112.37 exact zenon_H16d. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 112.02/112.37 congruence. % 112.02/112.37 apply (zenon_L64_ zenon_TT0_hz zenon_TT1_bg zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.37 apply zenon_H16a. apply refl_equal. % 112.02/112.37 apply zenon_H16a. apply refl_equal. % 112.02/112.37 apply zenon_H62. apply refl_equal. % 112.02/112.37 cut ((greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.02/112.37 intro zenon_D_pnotp. % 112.02/112.37 apply zenon_H114. % 112.02/112.37 rewrite <- zenon_D_pnotp. % 112.02/112.37 exact zenon_H17e. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 112.02/112.37 congruence. % 112.02/112.37 elim (classic ((high) = (high))); [ zenon_intro zenon_H180 | zenon_intro zenon_H113 ]. % 112.02/112.37 cut (((high) = (high)) = ((hazard_of_mortality zenon_TX_y zenon_E) = (high))). % 112.02/112.37 intro zenon_D_pnotp. % 112.02/112.37 apply zenon_H11c. % 112.02/112.37 rewrite <- zenon_D_pnotp. % 112.02/112.37 exact zenon_H180. % 112.02/112.37 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113]. % 112.02/112.37 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H119]. % 112.02/112.37 congruence. % 112.02/112.37 exact (zenon_H119 zenon_H17d). % 112.02/112.37 apply zenon_H113. apply refl_equal. % 112.02/112.37 apply zenon_H113. apply refl_equal. % 112.02/112.37 apply zenon_H62. apply refl_equal. % 112.02/112.37 apply (zenon_L49_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.37 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.02/112.37 intro zenon_D_pnotp. % 112.02/112.37 apply zenon_H119. % 112.02/112.37 rewrite <- zenon_D_pnotp. % 112.02/112.37 exact zenon_H11a. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 112.02/112.37 congruence. % 112.02/112.37 exact (zenon_H11c zenon_H116). % 112.02/112.37 apply zenon_H11b. apply refl_equal. % 112.02/112.37 apply zenon_H11b. apply refl_equal. % 112.02/112.37 (* end of lemma zenon_L65_ *) % 112.02/112.37 assert (zenon_L66_ : forall (zenon_TT2_la : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (((~(is_aligned zenon_TX_y zenon_E))/\(~(positional_advantage zenon_TX_y zenon_E)))->((hazard_of_mortality zenon_TX_y zenon_E) = (high))) -> (~(positional_advantage zenon_TX_y zenon_E)) -> (~(is_aligned zenon_TX_y zenon_E)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> False). % 112.02/112.37 do 4 intro. intros zenon_H181 zenon_H182 zenon_H183 zenon_H1a zenon_H37 zenon_H35 zenon_H38 zenon_Hec zenon_H1f zenon_H148 zenon_Hf3 zenon_H17c zenon_H123 zenon_H34. % 112.02/112.37 apply (zenon_imply_s _ _ zenon_H181); [ zenon_intro zenon_H184 | zenon_intro zenon_H116 ]. % 112.02/112.37 apply (zenon_notand_s _ _ zenon_H184); [ zenon_intro zenon_H186 | zenon_intro zenon_H185 ]. % 112.02/112.37 exact (zenon_H186 zenon_H183). % 112.02/112.37 exact (zenon_H185 zenon_H182). % 112.02/112.37 apply (zenon_L65_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.37 (* end of lemma zenon_L66_ *) % 112.02/112.37 assert (zenon_L67_ : forall (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (((~(is_aligned zenon_TX_y zenon_TT2_la))/\(~(positional_advantage zenon_TX_y zenon_TT2_la)))->((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (~(positional_advantage zenon_TX_y zenon_TT2_la)) -> (~(is_aligned zenon_TX_y zenon_TT2_la)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> False). % 112.02/112.37 do 2 intro. intros zenon_H134 zenon_H127 zenon_H135 zenon_H136. % 112.02/112.37 apply (zenon_imply_s _ _ zenon_H134); [ zenon_intro zenon_H138 | zenon_intro zenon_H137 ]. % 112.02/112.37 apply (zenon_notand_s _ _ zenon_H138); [ zenon_intro zenon_H13a | zenon_intro zenon_H139 ]. % 112.02/112.37 exact (zenon_H13a zenon_H135). % 112.02/112.37 exact (zenon_H139 zenon_H127). % 112.02/112.37 exact (zenon_H136 zenon_H137). % 112.02/112.37 (* end of lemma zenon_L67_ *) % 112.02/112.37 assert (zenon_L68_ : forall (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (~(~(has_immunity zenon_TX_y zenon_TT1_bg))) -> (~(has_immunity zenon_TX_y zenon_TT1_bg)) -> False). % 112.02/112.37 do 2 intro. intros zenon_H1e zenon_H24. % 112.02/112.37 exact (zenon_H1e zenon_H24). % 112.02/112.37 (* end of lemma zenon_L68_ *) % 112.02/112.37 assert (zenon_L69_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> (~((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (organization zenon_TX_y) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> False). % 112.02/112.37 do 3 intro. intros zenon_H34 zenon_H187 zenon_Hec zenon_H37 zenon_Hcd zenon_H35 zenon_H38 zenon_H5e zenon_H1f zenon_H0. % 112.02/112.37 generalize (assumption_15 zenon_TX_y). zenon_intro zenon_Hed. % 112.02/112.37 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88. % 112.02/112.37 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ]. % 112.02/112.37 exact (zenon_H27 zenon_H1f). % 112.02/112.37 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a. % 112.02/112.37 apply (zenon_imply_s _ _ zenon_H8b); [ zenon_intro zenon_H24 | zenon_intro zenon_H188 ]. % 112.02/112.37 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ]. % 112.02/112.37 exact (zenon_H1e zenon_H24). % 112.02/112.37 apply (zenon_L43_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.37 apply zenon_H187. apply sym_equal. exact zenon_H188. % 112.02/112.37 (* end of lemma zenon_L69_ *) % 112.02/112.37 assert (zenon_L70_ : forall (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT2_la))) -> ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (low)) -> False). % 112.02/112.37 do 2 intro. intros zenon_H34 zenon_H146 zenon_H169 zenon_H15b. % 112.02/112.37 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H156 | zenon_intro zenon_H157 ]. % 112.02/112.37 cut ((greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.02/112.37 intro zenon_D_pnotp. % 112.02/112.37 apply zenon_H169. % 112.02/112.37 rewrite <- zenon_D_pnotp. % 112.02/112.37 exact zenon_H156. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.37 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 112.02/112.37 congruence. % 112.02/112.37 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.02/112.37 intro zenon_D_pnotp. % 112.02/112.37 apply zenon_H16c. % 112.02/112.37 rewrite <- zenon_D_pnotp. % 112.02/112.37 exact zenon_H16d. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 112.02/112.37 congruence. % 112.02/112.37 exact (zenon_H13b zenon_H146). % 112.02/112.37 apply zenon_H16a. apply refl_equal. % 112.02/112.37 apply zenon_H16a. apply refl_equal. % 112.02/112.37 apply zenon_H16a. apply refl_equal. % 112.02/112.37 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H165 | zenon_intro zenon_H15f ]. % 112.02/112.37 generalize (zenon_H34 (mod2)). zenon_intro zenon_H16e. % 112.02/112.37 generalize (zenon_H16e (mod1)). zenon_intro zenon_H16f. % 112.02/112.37 generalize (zenon_H16f (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H170. % 112.02/112.37 apply (zenon_imply_s _ _ zenon_H170); [ zenon_intro zenon_H69 | zenon_intro zenon_H171 ]. % 112.02/112.37 exact (zenon_H69 assumption_19). % 112.02/112.37 apply (zenon_imply_s _ _ zenon_H171); [ zenon_intro zenon_H15f | zenon_intro zenon_H156 ]. % 112.02/112.37 exact (zenon_H15f zenon_H165). % 112.02/112.37 exact (zenon_H157 zenon_H156). % 112.02/112.37 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H160 | zenon_intro zenon_H155 ]. % 112.02/112.37 cut ((greater (mod1) (low)) = (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.02/112.37 intro zenon_D_pnotp. % 112.02/112.37 apply zenon_H15f. % 112.02/112.37 rewrite <- zenon_D_pnotp. % 112.02/112.37 exact assumption_18b. % 112.02/112.37 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H155]. % 112.02/112.37 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 112.02/112.37 congruence. % 112.02/112.37 apply zenon_H59. apply refl_equal. % 112.02/112.37 exact (zenon_H155 zenon_H160). % 112.02/112.37 apply zenon_H155. apply sym_equal. exact zenon_H15b. % 112.02/112.37 (* end of lemma zenon_L70_ *) % 112.02/112.37 assert (zenon_L71_ : forall (zenon_TT2_la : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> (organization zenon_TX_y) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2)) -> ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (low)) -> False). % 112.02/112.37 do 4 intro. intros zenon_H34 zenon_H187 zenon_Hec zenon_H37 zenon_Hcd zenon_H35 zenon_H38 zenon_H1f zenon_H0 zenon_H17c zenon_H146 zenon_H15b. % 112.02/112.37 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H168 | zenon_intro zenon_H169 ]. % 112.02/112.37 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ]. % 112.02/112.37 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.02/112.37 intro zenon_D_pnotp. % 112.02/112.37 apply zenon_H17c. % 112.02/112.37 rewrite <- zenon_D_pnotp. % 112.02/112.37 exact zenon_H179. % 112.02/112.37 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.37 congruence. % 112.02/112.37 apply zenon_H16a. apply refl_equal. % 112.02/112.37 apply (zenon_L69_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.37 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))). % 112.02/112.37 intro zenon_D_pnotp. % 112.02/112.37 apply zenon_H167. % 112.02/112.37 rewrite <- zenon_D_pnotp. % 112.02/112.37 exact zenon_H168. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.37 congruence. % 112.02/112.37 apply zenon_H16a. apply refl_equal. % 112.02/112.37 exact (zenon_H13b zenon_H146). % 112.02/112.37 apply (zenon_L70_ zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.37 (* end of lemma zenon_L71_ *) % 112.02/112.37 assert (zenon_L72_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (((is_aligned zenon_TX_y zenon_TT2_la)/\(~(positional_advantage zenon_TX_y zenon_TT2_la)))->((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (((~(is_aligned zenon_TX_y zenon_TT2_la))/\(~(positional_advantage zenon_TX_y zenon_TT2_la)))->((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> (organization zenon_TX_y) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (low)) -> False). % 112.02/112.37 do 4 intro. intros zenon_H145 zenon_H123 zenon_H134 zenon_H136 zenon_H34 zenon_H187 zenon_Hec zenon_H37 zenon_Hcd zenon_H35 zenon_H38 zenon_H1f zenon_H0 zenon_H17c zenon_H15b. % 112.02/112.37 apply (zenon_imply_s _ _ zenon_H145); [ zenon_intro zenon_H147 | zenon_intro zenon_H146 ]. % 112.02/112.37 apply (zenon_notand_s _ _ zenon_H147); [ zenon_intro zenon_H135 | zenon_intro zenon_H139 ]. % 112.02/112.37 apply (zenon_L52_ zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.37 apply zenon_H139. zenon_intro zenon_H122. % 112.02/112.37 apply (zenon_L51_ zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.37 apply (zenon_L71_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.37 (* end of lemma zenon_L72_ *) % 112.02/112.37 assert (zenon_L73_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (greater (tau) (sigma)) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> False). % 112.02/112.37 do 4 intro. intros zenon_H34 zenon_H1f zenon_H1a zenon_H136 zenon_H123 zenon_H35 zenon_H148 zenon_H0 zenon_Hec zenon_Hf3 zenon_H38 zenon_Hcd zenon_H37 zenon_H17c zenon_H187. % 112.02/112.37 generalize (zenon_H0 zenon_TT2_la). zenon_intro zenon_H13c. % 112.02/112.37 apply (zenon_imply_s _ _ zenon_H13c); [ zenon_intro zenon_H27 | zenon_intro zenon_H13d ]. % 112.02/112.37 exact (zenon_H27 zenon_H1f). % 112.02/112.37 apply (zenon_and_s _ _ zenon_H13d). zenon_intro zenon_H13f. zenon_intro zenon_H13e. % 112.02/112.37 apply (zenon_imply_s _ _ zenon_H13e); [ zenon_intro zenon_H11d | zenon_intro zenon_H140 ]. % 112.02/112.37 apply (zenon_L50_ zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.37 apply (zenon_and_s _ _ zenon_H140). zenon_intro zenon_H142. zenon_intro zenon_H141. % 112.02/112.37 apply (zenon_and_s _ _ zenon_H141). zenon_intro zenon_H144. zenon_intro zenon_H143. % 112.02/112.37 apply (zenon_and_s _ _ zenon_H143). zenon_intro zenon_H145. zenon_intro zenon_H134. % 112.02/112.37 apply (zenon_imply_s _ _ zenon_H142); [ zenon_intro zenon_H15c | zenon_intro zenon_H15b ]. % 112.02/112.37 apply (zenon_notand_s _ _ zenon_H15c); [ zenon_intro zenon_H135 | zenon_intro zenon_H127 ]. % 112.02/112.37 apply (zenon_L52_ zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.37 apply (zenon_imply_s _ _ zenon_H145); [ zenon_intro zenon_H147 | zenon_intro zenon_H146 ]. % 112.02/112.37 apply (zenon_notand_s _ _ zenon_H147); [ zenon_intro zenon_H135 | zenon_intro zenon_H139 ]. % 112.02/112.37 apply (zenon_L67_ zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.37 exact (zenon_H139 zenon_H127). % 112.02/112.37 apply (zenon_L63_ zenon_TT2_la zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.02/112.37 apply (zenon_L72_ zenon_TT0_hz zenon_TT1_bg zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.37 (* end of lemma zenon_L73_ *) % 112.02/112.37 assert (zenon_L74_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (greater (tau) (sigma)) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> False). % 112.02/112.37 do 4 intro. intros zenon_H34 zenon_H1f zenon_Hec zenon_H1a zenon_H136 zenon_H123 zenon_H35 zenon_H148 zenon_H0 zenon_Hf3 zenon_H38 zenon_H37 zenon_H17c zenon_H187. % 112.02/112.37 generalize (zenon_Hf3 zenon_TT0_hz). zenon_intro zenon_Hf4. % 112.02/112.37 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcd ]. % 112.02/112.37 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ]. % 112.02/112.37 exact (zenon_H27 zenon_H1f). % 112.02/112.37 exact (zenon_Hf2 zenon_Hec). % 112.02/112.37 apply (zenon_L73_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.37 (* end of lemma zenon_L74_ *) % 112.02/112.37 assert (zenon_L75_ : forall (zenon_TT2_la : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (high)) -> False). % 112.02/112.37 do 4 intro. intros zenon_H1a zenon_H37 zenon_H35 zenon_H38 zenon_Hec zenon_H1f zenon_H123 zenon_H148 zenon_H0 zenon_Hf3 zenon_H17c zenon_H187 zenon_H34 zenon_H116. % 112.02/112.37 elim (classic ((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H17d | zenon_intro zenon_H119 ]. % 112.02/112.37 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H17e | zenon_intro zenon_H117 ]. % 112.02/112.37 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H118 | zenon_intro zenon_H114 ]. % 112.02/112.37 cut ((greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.02/112.37 intro zenon_D_pnotp. % 112.02/112.37 apply zenon_H17c. % 112.02/112.37 rewrite <- zenon_D_pnotp. % 112.02/112.37 exact zenon_H118. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.02/112.37 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 112.02/112.37 congruence. % 112.02/112.37 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.02/112.37 intro zenon_D_pnotp. % 112.02/112.37 apply zenon_H17f. % 112.02/112.37 rewrite <- zenon_D_pnotp. % 112.02/112.37 exact zenon_H16d. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 112.02/112.37 congruence. % 112.02/112.37 apply (zenon_L74_ zenon_TT1_bg zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial. % 112.02/112.37 apply zenon_H16a. apply refl_equal. % 112.02/112.37 apply zenon_H16a. apply refl_equal. % 112.02/112.37 apply zenon_H62. apply refl_equal. % 112.02/112.37 cut ((greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.02/112.37 intro zenon_D_pnotp. % 112.02/112.37 apply zenon_H114. % 112.02/112.37 rewrite <- zenon_D_pnotp. % 112.02/112.37 exact zenon_H17e. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 112.02/112.37 congruence. % 112.02/112.37 elim (classic ((high) = (high))); [ zenon_intro zenon_H180 | zenon_intro zenon_H113 ]. % 112.02/112.37 cut (((high) = (high)) = ((hazard_of_mortality zenon_TX_y zenon_E) = (high))). % 112.02/112.37 intro zenon_D_pnotp. % 112.02/112.37 apply zenon_H11c. % 112.02/112.37 rewrite <- zenon_D_pnotp. % 112.02/112.37 exact zenon_H180. % 112.02/112.37 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113]. % 112.02/112.37 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H119]. % 112.02/112.37 congruence. % 112.02/112.37 exact (zenon_H119 zenon_H17d). % 112.02/112.37 apply zenon_H113. apply refl_equal. % 112.02/112.37 apply zenon_H113. apply refl_equal. % 112.02/112.37 apply zenon_H62. apply refl_equal. % 112.02/112.37 apply (zenon_L49_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.37 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.02/112.37 intro zenon_D_pnotp. % 112.02/112.37 apply zenon_H119. % 112.02/112.37 rewrite <- zenon_D_pnotp. % 112.02/112.37 exact zenon_H11a. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 112.02/112.37 congruence. % 112.02/112.37 exact (zenon_H11c zenon_H116). % 112.02/112.37 apply zenon_H11b. apply refl_equal. % 112.02/112.37 apply zenon_H11b. apply refl_equal. % 112.02/112.37 (* end of lemma zenon_L75_ *) % 112.02/112.37 assert (zenon_L76_ : forall (zenon_TT2_la : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (((~(is_aligned zenon_TX_y zenon_E))/\(~(positional_advantage zenon_TX_y zenon_E)))->((hazard_of_mortality zenon_TX_y zenon_E) = (high))) -> (~(positional_advantage zenon_TX_y zenon_E)) -> (~(is_aligned zenon_TX_y zenon_E)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> False). % 112.02/112.37 do 4 intro. intros zenon_H181 zenon_H182 zenon_H183 zenon_H1a zenon_H37 zenon_H35 zenon_H38 zenon_Hec zenon_H1f zenon_H123 zenon_H148 zenon_H0 zenon_Hf3 zenon_H17c zenon_H187 zenon_H34. % 112.02/112.37 apply (zenon_imply_s _ _ zenon_H181); [ zenon_intro zenon_H184 | zenon_intro zenon_H116 ]. % 112.02/112.37 apply (zenon_notand_s _ _ zenon_H184); [ zenon_intro zenon_H186 | zenon_intro zenon_H185 ]. % 112.02/112.37 exact (zenon_H186 zenon_H183). % 112.02/112.37 exact (zenon_H185 zenon_H182). % 112.02/112.37 apply (zenon_L75_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.02/112.37 (* end of lemma zenon_L76_ *) % 112.02/112.37 assert (zenon_L77_ : forall (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (organization zenon_TX_y) -> False). % 112.02/112.37 do 2 intro. intros zenon_H13b zenon_H35 zenon_H123 zenon_H136 zenon_H1a zenon_H1f. % 112.02/112.37 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0. % 112.02/112.37 apply (zenon_L53_ zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.37 (* end of lemma zenon_L77_ *) % 112.02/112.37 assert (zenon_L78_ : forall (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))) -> False). % 112.02/112.37 do 2 intro. intros zenon_H1f zenon_H1a zenon_H123 zenon_H35 zenon_H13b zenon_H34 zenon_H167. % 112.02/112.37 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (high))))); [ zenon_intro zenon_H189 | zenon_intro zenon_H18a ]. % 112.02/112.37 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H136. zenon_intro zenon_H18b. % 112.02/112.37 apply (zenon_L77_ zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.37 cut ((greater (high) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))). % 112.02/112.37 intro zenon_D_pnotp. % 112.02/112.37 apply zenon_H167. % 112.02/112.37 rewrite <- zenon_D_pnotp. % 112.02/112.37 exact assumption_18d. % 112.02/112.37 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 112.02/112.37 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 112.02/112.37 congruence. % 112.02/112.37 apply (zenon_notand_s _ _ zenon_H18a); [ zenon_intro zenon_H18d | zenon_intro zenon_H18c ]. % 112.02/112.37 apply zenon_H18d. zenon_intro zenon_H137. % 112.02/112.37 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.02/112.37 intro zenon_D_pnotp. % 112.02/112.37 apply zenon_H17f. % 112.02/112.37 rewrite <- zenon_D_pnotp. % 112.02/112.37 exact zenon_H16d. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.37 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 112.02/112.37 congruence. % 112.02/112.37 exact (zenon_H136 zenon_H137). % 112.02/112.37 apply zenon_H16a. apply refl_equal. % 112.02/112.37 apply zenon_H16a. apply refl_equal. % 112.02/112.37 apply zenon_H18c. zenon_intro zenon_H18e. % 112.02/112.37 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.02/112.37 generalize (zenon_H18f (high)). zenon_intro zenon_H190. % 112.02/112.37 generalize (zenon_H190 (mod2)). zenon_intro zenon_H191. % 112.02/112.37 apply (zenon_imply_s _ _ zenon_H191); [ zenon_intro zenon_H18b | zenon_intro zenon_H192 ]. % 112.02/112.37 exact (zenon_H18b zenon_H18e). % 112.02/112.37 apply (zenon_imply_s _ _ zenon_H192); [ zenon_intro zenon_H9b | zenon_intro zenon_H179 ]. % 112.02/112.37 exact (zenon_H9b assumption_18d). % 112.02/112.37 exact (zenon_H167 zenon_H179). % 112.02/112.37 apply zenon_H83. apply refl_equal. % 112.02/112.37 (* end of lemma zenon_L78_ *) % 112.02/112.37 assert (zenon_L79_ : forall (zenon_TT2_la : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (greater (tau) (sigma)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> False). % 112.02/112.38 do 4 intro. intros zenon_H34 zenon_H193 zenon_H1f zenon_Hec zenon_H148 zenon_H0 zenon_Hf3 zenon_H38 zenon_H17c zenon_H187 zenon_H35 zenon_H123 zenon_H1a zenon_H37. % 112.02/112.38 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 112.02/112.38 cut ((greater (mod1) (low)) = (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.02/112.38 intro zenon_D_pnotp. % 112.02/112.38 apply zenon_H193. % 112.02/112.38 rewrite <- zenon_D_pnotp. % 112.02/112.38 exact assumption_18b. % 112.02/112.38 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 112.02/112.38 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 112.02/112.38 congruence. % 112.02/112.38 apply zenon_H59. apply refl_equal. % 112.02/112.38 exact (zenon_H72 zenon_H71). % 112.02/112.38 generalize (zenon_Hf3 zenon_TT0_hz). zenon_intro zenon_Hf4. % 112.02/112.38 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcd ]. % 112.02/112.38 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ]. % 112.02/112.38 exact (zenon_H27 zenon_H1f). % 112.02/112.38 exact (zenon_Hf2 zenon_Hec). % 112.02/112.38 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88. % 112.02/112.38 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ]. % 112.02/112.38 exact (zenon_H27 zenon_H1f). % 112.02/112.38 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a. % 112.02/112.38 apply (zenon_imply_s _ _ zenon_H8b); [ zenon_intro zenon_H24 | zenon_intro zenon_H188 ]. % 112.02/112.38 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ]. % 112.02/112.38 exact (zenon_H1e zenon_H24). % 112.02/112.38 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d. % 112.02/112.38 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f. % 112.02/112.38 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H30. zenon_intro zenon_H28. % 112.02/112.38 apply (zenon_imply_s _ _ zenon_H8e); [ zenon_intro zenon_H91 | zenon_intro zenon_H6b ]. % 112.02/112.38 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 112.02/112.38 apply (zenon_L31_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.02/112.38 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 112.02/112.38 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ]. % 112.02/112.38 apply (zenon_L31_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.02/112.38 exact (zenon_H2e zenon_H29). % 112.02/112.38 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H115 | zenon_intro zenon_H5e ]. % 112.02/112.38 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ]. % 112.02/112.38 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.02/112.38 intro zenon_D_pnotp. % 112.02/112.38 apply zenon_H17c. % 112.02/112.38 rewrite <- zenon_D_pnotp. % 112.02/112.38 exact zenon_H179. % 112.02/112.38 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 112.02/112.38 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.38 congruence. % 112.02/112.38 apply zenon_H16a. apply refl_equal. % 112.02/112.38 exact (zenon_H5e zenon_H115). % 112.02/112.38 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (high))))); [ zenon_intro zenon_H189 | zenon_intro zenon_H18a ]. % 112.02/112.38 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H136. zenon_intro zenon_H18b. % 112.02/112.38 apply (zenon_L73_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.38 cut ((greater (high) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))). % 112.02/112.38 intro zenon_D_pnotp. % 112.02/112.38 apply zenon_H167. % 112.02/112.38 rewrite <- zenon_D_pnotp. % 112.02/112.38 exact assumption_18d. % 112.02/112.38 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 112.02/112.38 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 112.02/112.38 congruence. % 112.02/112.38 apply (zenon_notand_s _ _ zenon_H18a); [ zenon_intro zenon_H18d | zenon_intro zenon_H18c ]. % 112.02/112.38 apply zenon_H18d. zenon_intro zenon_H137. % 112.02/112.38 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.02/112.38 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.02/112.38 intro zenon_D_pnotp. % 112.02/112.38 apply zenon_H17f. % 112.02/112.38 rewrite <- zenon_D_pnotp. % 112.02/112.38 exact zenon_H16d. % 112.02/112.38 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.38 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 112.02/112.38 congruence. % 112.02/112.38 exact (zenon_H136 zenon_H137). % 112.02/112.38 apply zenon_H16a. apply refl_equal. % 112.02/112.38 apply zenon_H16a. apply refl_equal. % 112.02/112.38 apply zenon_H18c. zenon_intro zenon_H18e. % 112.02/112.38 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.02/112.38 generalize (zenon_H18f (high)). zenon_intro zenon_H190. % 112.02/112.38 generalize (zenon_H190 (mod2)). zenon_intro zenon_H191. % 112.02/112.38 apply (zenon_imply_s _ _ zenon_H191); [ zenon_intro zenon_H18b | zenon_intro zenon_H192 ]. % 112.02/112.38 exact (zenon_H18b zenon_H18e). % 112.02/112.38 apply (zenon_imply_s _ _ zenon_H192); [ zenon_intro zenon_H9b | zenon_intro zenon_H179 ]. % 112.02/112.38 exact (zenon_H9b assumption_18d). % 112.02/112.38 exact (zenon_H167 zenon_H179). % 112.02/112.38 apply zenon_H83. apply refl_equal. % 112.02/112.38 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H5e. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H61. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31]. % 112.02/112.39 congruence. % 112.02/112.39 exact (zenon_H31 zenon_H32). % 112.02/112.39 apply zenon_H62. apply refl_equal. % 112.02/112.39 apply zenon_H62. apply refl_equal. % 112.02/112.39 apply zenon_H72. apply sym_equal. exact zenon_H6b. % 112.02/112.39 apply zenon_H187. apply sym_equal. exact zenon_H188. % 112.02/112.39 (* end of lemma zenon_L79_ *) % 112.02/112.39 assert (zenon_L80_ : forall (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (organization zenon_TX_y) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))) -> False). % 112.02/112.39 do 2 intro. intros zenon_H35 zenon_H123 zenon_H1a zenon_H1f zenon_H34 zenon_H194. % 112.02/112.39 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))))); [ zenon_intro zenon_H195 | zenon_intro zenon_H196 ]. % 112.02/112.39 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H13b. zenon_intro zenon_H167. % 112.02/112.39 apply (zenon_L78_ zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.39 cut ((greater (mod2) (mod1)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H194. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact assumption_19. % 112.02/112.39 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 112.02/112.39 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 112.02/112.39 congruence. % 112.02/112.39 apply (zenon_notand_s _ _ zenon_H196); [ zenon_intro zenon_H198 | zenon_intro zenon_H197 ]. % 112.02/112.39 apply zenon_H198. zenon_intro zenon_H146. % 112.02/112.39 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H16c. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H16d. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 112.02/112.39 congruence. % 112.02/112.39 exact (zenon_H13b zenon_H146). % 112.02/112.39 apply zenon_H16a. apply refl_equal. % 112.02/112.39 apply zenon_H16a. apply refl_equal. % 112.02/112.39 apply zenon_H197. zenon_intro zenon_H179. % 112.02/112.39 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.02/112.39 generalize (zenon_H18f (mod2)). zenon_intro zenon_H199. % 112.02/112.39 generalize (zenon_H199 (mod1)). zenon_intro zenon_H19a. % 112.02/112.39 apply (zenon_imply_s _ _ zenon_H19a); [ zenon_intro zenon_H167 | zenon_intro zenon_H19b ]. % 112.02/112.39 exact (zenon_H167 zenon_H179). % 112.02/112.39 apply (zenon_imply_s _ _ zenon_H19b); [ zenon_intro zenon_H69 | zenon_intro zenon_H19c ]. % 112.02/112.39 exact (zenon_H69 assumption_19). % 112.02/112.39 exact (zenon_H194 zenon_H19c). % 112.02/112.39 apply zenon_H59. apply refl_equal. % 112.02/112.39 (* end of lemma zenon_L80_ *) % 112.02/112.39 assert (zenon_L81_ : forall (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (organization zenon_TX_y) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))) -> False). % 112.02/112.39 do 2 intro. intros zenon_H13b zenon_H35 zenon_H123 zenon_H1a zenon_H1f zenon_H0 zenon_H34 zenon_H167. % 112.02/112.39 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (high))))); [ zenon_intro zenon_H189 | zenon_intro zenon_H18a ]. % 112.02/112.39 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H136. zenon_intro zenon_H18b. % 112.02/112.39 apply (zenon_L53_ zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.39 cut ((greater (high) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H167. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact assumption_18d. % 112.02/112.39 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 112.02/112.39 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 112.02/112.39 congruence. % 112.02/112.39 apply (zenon_notand_s _ _ zenon_H18a); [ zenon_intro zenon_H18d | zenon_intro zenon_H18c ]. % 112.02/112.39 apply zenon_H18d. zenon_intro zenon_H137. % 112.02/112.39 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H17f. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H16d. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 112.02/112.39 congruence. % 112.02/112.39 exact (zenon_H136 zenon_H137). % 112.02/112.39 apply zenon_H16a. apply refl_equal. % 112.02/112.39 apply zenon_H16a. apply refl_equal. % 112.02/112.39 apply zenon_H18c. zenon_intro zenon_H18e. % 112.02/112.39 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.02/112.39 generalize (zenon_H18f (high)). zenon_intro zenon_H190. % 112.02/112.39 generalize (zenon_H190 (mod2)). zenon_intro zenon_H191. % 112.02/112.39 apply (zenon_imply_s _ _ zenon_H191); [ zenon_intro zenon_H18b | zenon_intro zenon_H192 ]. % 112.02/112.39 exact (zenon_H18b zenon_H18e). % 112.02/112.39 apply (zenon_imply_s _ _ zenon_H192); [ zenon_intro zenon_H9b | zenon_intro zenon_H179 ]. % 112.02/112.39 exact (zenon_H9b assumption_18d). % 112.02/112.39 exact (zenon_H167 zenon_H179). % 112.02/112.39 apply zenon_H83. apply refl_equal. % 112.02/112.39 (* end of lemma zenon_L81_ *) % 112.02/112.39 assert (zenon_L82_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_E))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (mod2)) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> False). % 112.02/112.39 do 3 intro. intros zenon_H34 zenon_H19d zenon_H19e zenon_H148 zenon_H167 zenon_H35 zenon_H123 zenon_H136 zenon_H1a zenon_H0 zenon_Hec zenon_H1f zenon_Hf3. % 112.02/112.39 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H19f | zenon_intro zenon_H1a0 ]. % 112.02/112.39 cut ((greater (mod2) (hazard_of_mortality zenon_TX_y zenon_E)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H19d. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H19f. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.02/112.39 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 112.02/112.39 congruence. % 112.02/112.39 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H1a1. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H11a. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 112.02/112.39 congruence. % 112.02/112.39 exact (zenon_H1a2 zenon_H19e). % 112.02/112.39 apply zenon_H11b. apply refl_equal. % 112.02/112.39 apply zenon_H11b. apply refl_equal. % 112.02/112.39 apply zenon_H11b. apply refl_equal. % 112.02/112.39 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H1a1 ]. % 112.02/112.39 elim (classic (greater (mod2) (mod2))); [ zenon_intro zenon_H16b | zenon_intro zenon_H153 ]. % 112.02/112.39 cut ((greater (mod2) (mod2)) = (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H1a0. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H16b. % 112.02/112.39 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 112.02/112.39 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 112.02/112.39 congruence. % 112.02/112.39 apply zenon_H83. apply refl_equal. % 112.02/112.39 exact (zenon_H1a1 zenon_H1a3). % 112.02/112.39 apply (zenon_L60_ zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial. % 112.02/112.39 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H1a1. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H11a. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 112.02/112.39 congruence. % 112.02/112.39 exact (zenon_H1a2 zenon_H19e). % 112.02/112.39 apply zenon_H11b. apply refl_equal. % 112.02/112.39 apply zenon_H11b. apply refl_equal. % 112.02/112.39 (* end of lemma zenon_L82_ *) % 112.02/112.39 assert (zenon_L83_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), ((hazard_of_mortality zenon_TX_y zenon_E) = (mod2)) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (organization zenon_TX_y) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))) -> False). % 112.02/112.39 do 3 intro. intros zenon_H19e zenon_H148 zenon_Hec zenon_Hf3 zenon_H35 zenon_H123 zenon_H1a zenon_H1f zenon_H0 zenon_H34 zenon_H167. % 112.02/112.39 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (high))))); [ zenon_intro zenon_H189 | zenon_intro zenon_H18a ]. % 112.02/112.39 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H136. zenon_intro zenon_H18b. % 112.02/112.39 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1a5 ]. % 112.02/112.39 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H167. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H1a4. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.39 congruence. % 112.02/112.39 apply zenon_H16a. apply refl_equal. % 112.02/112.39 exact (zenon_H1a2 zenon_H19e). % 112.02/112.39 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H1a1 ]. % 112.02/112.39 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ]. % 112.02/112.39 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H1a5. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H179. % 112.02/112.39 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.39 congruence. % 112.02/112.39 apply zenon_H16a. apply refl_equal. % 112.02/112.39 exact (zenon_H1a1 zenon_H1a3). % 112.02/112.39 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H19d ]. % 112.02/112.39 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H19f | zenon_intro zenon_H1a0 ]. % 112.02/112.39 cut ((greater (mod2) (hazard_of_mortality zenon_TX_y zenon_E)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H1a5. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H19f. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.02/112.39 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 112.02/112.39 congruence. % 112.02/112.39 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H16c. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H16d. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 112.02/112.39 congruence. % 112.02/112.39 apply (zenon_L53_ zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.39 apply zenon_H16a. apply refl_equal. % 112.02/112.39 apply zenon_H16a. apply refl_equal. % 112.02/112.39 apply zenon_H11b. apply refl_equal. % 112.02/112.39 cut ((greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_E)) = (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H1a0. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H1a6. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 112.02/112.39 congruence. % 112.02/112.39 elim (classic ((mod2) = (mod2))); [ zenon_intro zenon_H17b | zenon_intro zenon_H83 ]. % 112.02/112.39 cut (((mod2) = (mod2)) = ((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H1a2. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H17b. % 112.02/112.39 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 112.02/112.39 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 112.02/112.39 congruence. % 112.02/112.39 exact (zenon_H1a1 zenon_H1a3). % 112.02/112.39 apply zenon_H83. apply refl_equal. % 112.02/112.39 apply zenon_H83. apply refl_equal. % 112.02/112.39 apply zenon_H11b. apply refl_equal. % 112.02/112.39 apply (zenon_L82_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.39 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H1a1. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H11a. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 112.02/112.39 congruence. % 112.02/112.39 exact (zenon_H1a2 zenon_H19e). % 112.02/112.39 apply zenon_H11b. apply refl_equal. % 112.02/112.39 apply zenon_H11b. apply refl_equal. % 112.02/112.39 cut ((greater (high) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H167. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact assumption_18d. % 112.02/112.39 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 112.02/112.39 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 112.02/112.39 congruence. % 112.02/112.39 apply (zenon_notand_s _ _ zenon_H18a); [ zenon_intro zenon_H18d | zenon_intro zenon_H18c ]. % 112.02/112.39 apply zenon_H18d. zenon_intro zenon_H137. % 112.02/112.39 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H17f. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H16d. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 112.02/112.39 congruence. % 112.02/112.39 exact (zenon_H136 zenon_H137). % 112.02/112.39 apply zenon_H16a. apply refl_equal. % 112.02/112.39 apply zenon_H16a. apply refl_equal. % 112.02/112.39 apply zenon_H18c. zenon_intro zenon_H18e. % 112.02/112.39 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.02/112.39 generalize (zenon_H18f (high)). zenon_intro zenon_H190. % 112.02/112.39 generalize (zenon_H190 (mod2)). zenon_intro zenon_H191. % 112.02/112.39 apply (zenon_imply_s _ _ zenon_H191); [ zenon_intro zenon_H18b | zenon_intro zenon_H192 ]. % 112.02/112.39 exact (zenon_H18b zenon_H18e). % 112.02/112.39 apply (zenon_imply_s _ _ zenon_H192); [ zenon_intro zenon_H9b | zenon_intro zenon_H179 ]. % 112.02/112.39 exact (zenon_H9b assumption_18d). % 112.02/112.39 exact (zenon_H167 zenon_H179). % 112.02/112.39 apply zenon_H83. apply refl_equal. % 112.02/112.39 (* end of lemma zenon_L83_ *) % 112.02/112.39 assert (zenon_L84_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (mod2)) -> False). % 112.02/112.39 do 3 intro. intros zenon_H0 zenon_H1f zenon_H1a zenon_H123 zenon_H35 zenon_Hf3 zenon_Hec zenon_H148 zenon_H1a5 zenon_H34 zenon_H19e. % 112.02/112.39 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H1a1 ]. % 112.02/112.39 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ]. % 112.02/112.39 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H1a5. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H179. % 112.02/112.39 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.39 congruence. % 112.02/112.39 apply zenon_H16a. apply refl_equal. % 112.02/112.39 exact (zenon_H1a1 zenon_H1a3). % 112.02/112.39 apply (zenon_L83_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.39 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H1a1. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H11a. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 112.02/112.39 congruence. % 112.02/112.39 exact (zenon_H1a2 zenon_H19e). % 112.02/112.39 apply zenon_H11b. apply refl_equal. % 112.02/112.39 apply zenon_H11b. apply refl_equal. % 112.02/112.39 (* end of lemma zenon_L84_ *) % 112.02/112.39 assert (zenon_L85_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (greater (tau) (sigma)) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (mod2)) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> False). % 112.02/112.39 do 4 intro. intros zenon_H34 zenon_H38 zenon_H37 zenon_H17c zenon_Hf3 zenon_Hec zenon_H148 zenon_H19e zenon_H0 zenon_H1f zenon_H1a zenon_H123 zenon_H35. % 112.02/112.39 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1a5 ]. % 112.02/112.39 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ]. % 112.02/112.39 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H17c. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H179. % 112.02/112.39 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.39 congruence. % 112.02/112.39 apply zenon_H16a. apply refl_equal. % 112.02/112.39 apply (zenon_L45_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.02/112.39 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H167. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H1a4. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.39 congruence. % 112.02/112.39 apply zenon_H16a. apply refl_equal. % 112.02/112.39 exact (zenon_H1a2 zenon_H19e). % 112.02/112.39 apply (zenon_L84_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.39 (* end of lemma zenon_L85_ *) % 112.02/112.39 assert (zenon_L86_ : forall (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (((is_aligned zenon_TX_y zenon_TT2_la)/\(~(positional_advantage zenon_TX_y zenon_TT2_la)))->((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))) -> (~(positional_advantage zenon_TX_y zenon_TT2_la)) -> (((~(is_aligned zenon_TX_y zenon_TT2_la))/\(~(positional_advantage zenon_TX_y zenon_TT2_la)))->((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))) -> False). % 112.02/112.39 do 2 intro. intros zenon_H145 zenon_H127 zenon_H134 zenon_H136 zenon_H13b. % 112.02/112.39 apply (zenon_imply_s _ _ zenon_H145); [ zenon_intro zenon_H147 | zenon_intro zenon_H146 ]. % 112.02/112.39 apply (zenon_notand_s _ _ zenon_H147); [ zenon_intro zenon_H135 | zenon_intro zenon_H139 ]. % 112.02/112.39 apply (zenon_L67_ zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.39 exact (zenon_H139 zenon_H127). % 112.02/112.39 exact (zenon_H13b zenon_H146). % 112.02/112.39 (* end of lemma zenon_L86_ *) % 112.02/112.39 assert (zenon_L87_ : forall (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod1))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (low))) -> False). % 112.02/112.39 do 2 intro. intros zenon_H0 zenon_H1f zenon_H1a zenon_H1a7 zenon_H136 zenon_H13b zenon_H1a8. % 112.02/112.39 generalize (zenon_H0 zenon_TT2_la). zenon_intro zenon_H13c. % 112.02/112.39 apply (zenon_imply_s _ _ zenon_H13c); [ zenon_intro zenon_H27 | zenon_intro zenon_H13d ]. % 112.02/112.39 exact (zenon_H27 zenon_H1f). % 112.02/112.39 apply (zenon_and_s _ _ zenon_H13d). zenon_intro zenon_H13f. zenon_intro zenon_H13e. % 112.02/112.39 apply (zenon_imply_s _ _ zenon_H13e); [ zenon_intro zenon_H11d | zenon_intro zenon_H140 ]. % 112.02/112.39 apply (zenon_L50_ zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.39 apply (zenon_and_s _ _ zenon_H140). zenon_intro zenon_H142. zenon_intro zenon_H141. % 112.02/112.39 apply (zenon_and_s _ _ zenon_H141). zenon_intro zenon_H144. zenon_intro zenon_H143. % 112.02/112.39 apply (zenon_and_s _ _ zenon_H143). zenon_intro zenon_H145. zenon_intro zenon_H134. % 112.02/112.39 apply (zenon_imply_s _ _ zenon_H142); [ zenon_intro zenon_H15c | zenon_intro zenon_H15b ]. % 112.02/112.39 apply (zenon_notand_s _ _ zenon_H15c); [ zenon_intro zenon_H135 | zenon_intro zenon_H127 ]. % 112.02/112.39 apply (zenon_imply_s _ _ zenon_H144); [ zenon_intro zenon_H15e | zenon_intro zenon_H15d ]. % 112.02/112.39 apply (zenon_notand_s _ _ zenon_H15e); [ zenon_intro zenon_H13a | zenon_intro zenon_H127 ]. % 112.02/112.39 exact (zenon_H13a zenon_H135). % 112.02/112.39 apply (zenon_L67_ zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.39 exact (zenon_H1a7 zenon_H15d). % 112.02/112.39 apply (zenon_L86_ zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.39 exact (zenon_H1a8 zenon_H15b). % 112.02/112.39 (* end of lemma zenon_L87_ *) % 112.02/112.39 assert (zenon_L88_ : forall (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (low))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (organization zenon_TX_y) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))) -> False). % 112.02/112.39 do 2 intro. intros zenon_H1a8 zenon_H13b zenon_H136 zenon_H1a zenon_H1f zenon_H0 zenon_H34 zenon_H1a9. % 112.02/112.39 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod1)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))))); [ zenon_intro zenon_H1aa | zenon_intro zenon_H1ab ]. % 112.02/112.39 apply (zenon_and_s _ _ zenon_H1aa). zenon_intro zenon_H1a7. zenon_intro zenon_H194. % 112.02/112.39 apply (zenon_L87_ zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.39 cut ((greater (mod1) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H1a9. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact assumption_18b. % 112.02/112.39 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.02/112.39 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H159]. % 112.02/112.39 congruence. % 112.02/112.39 apply (zenon_notand_s _ _ zenon_H1ab); [ zenon_intro zenon_H1ad | zenon_intro zenon_H1ac ]. % 112.02/112.39 apply zenon_H1ad. zenon_intro zenon_H15d. % 112.02/112.39 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H159. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H16d. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H1a7]. % 112.02/112.39 congruence. % 112.02/112.39 exact (zenon_H1a7 zenon_H15d). % 112.02/112.39 apply zenon_H16a. apply refl_equal. % 112.02/112.39 apply zenon_H16a. apply refl_equal. % 112.02/112.39 apply zenon_H1ac. zenon_intro zenon_H19c. % 112.02/112.39 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.02/112.39 generalize (zenon_H18f (mod1)). zenon_intro zenon_H1ae. % 112.02/112.39 generalize (zenon_H1ae (low)). zenon_intro zenon_H1af. % 112.02/112.39 apply (zenon_imply_s _ _ zenon_H1af); [ zenon_intro zenon_H194 | zenon_intro zenon_H1b0 ]. % 112.02/112.39 exact (zenon_H194 zenon_H19c). % 112.02/112.39 apply (zenon_imply_s _ _ zenon_H1b0); [ zenon_intro zenon_H7f | zenon_intro zenon_H1b1 ]. % 112.02/112.39 exact (zenon_H7f assumption_18b). % 112.02/112.39 exact (zenon_H1a9 zenon_H1b1). % 112.02/112.39 apply zenon_H6a. apply refl_equal. % 112.02/112.39 (* end of lemma zenon_L88_ *) % 112.02/112.39 assert (zenon_L89_ : forall (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (smaller (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low)) -> (~(greater (low) (low))) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))) -> False). % 112.02/112.39 do 2 intro. intros zenon_H34 zenon_H1b2 zenon_H6c zenon_H0 zenon_H1f zenon_H1a zenon_H136 zenon_H13b. % 112.02/112.39 generalize (definition_smaller (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H176. % 112.02/112.39 generalize (zenon_H176 (low)). zenon_intro zenon_H1b3. % 112.02/112.39 apply (zenon_equiv_s _ _ zenon_H1b3); [ zenon_intro zenon_H1b4; zenon_intro zenon_H162 | zenon_intro zenon_H1b2; zenon_intro zenon_H161 ]. % 112.02/112.39 exact (zenon_H1b4 zenon_H1b2). % 112.02/112.39 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (low))); [ zenon_intro zenon_H15b | zenon_intro zenon_H1a8 ]. % 112.02/112.39 cut ((greater (low) (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = (greater (low) (low))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H6c. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H161. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1a8]. % 112.02/112.39 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.02/112.39 congruence. % 112.02/112.39 apply zenon_H6a. apply refl_equal. % 112.02/112.39 exact (zenon_H1a8 zenon_H15b). % 112.02/112.39 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1a9 ]. % 112.02/112.39 generalize (zenon_H34 (low)). zenon_intro zenon_H7a. % 112.02/112.39 generalize (zenon_H7a (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H1b5. % 112.02/112.39 generalize (zenon_H1b5 (low)). zenon_intro zenon_H1b6. % 112.02/112.39 apply (zenon_imply_s _ _ zenon_H1b6); [ zenon_intro zenon_H162 | zenon_intro zenon_H1b7 ]. % 112.02/112.39 exact (zenon_H162 zenon_H161). % 112.02/112.39 apply (zenon_imply_s _ _ zenon_H1b7); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H7e ]. % 112.02/112.39 exact (zenon_H1a9 zenon_H1b1). % 112.02/112.39 exact (zenon_H6c zenon_H7e). % 112.02/112.39 apply (zenon_L88_ zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.39 (* end of lemma zenon_L89_ *) % 112.02/112.39 assert (zenon_L90_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (organization zenon_TX_y) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod1))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T0) = (zero)))->((greater (age zenon_TX_y T) (sigma))<->(dissimilar zenon_TX_y T0 T))))) -> (~((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))) -> False). % 112.02/112.39 do 3 intro. intros zenon_H0 zenon_H1f zenon_H1a7 zenon_H136 zenon_Hec zenon_Hcd zenon_H148 zenon_Hed zenon_H154. % 112.02/112.39 generalize (zenon_H0 zenon_TT2_la). zenon_intro zenon_H13c. % 112.02/112.39 apply (zenon_imply_s _ _ zenon_H13c); [ zenon_intro zenon_H27 | zenon_intro zenon_H13d ]. % 112.02/112.39 exact (zenon_H27 zenon_H1f). % 112.02/112.39 apply (zenon_and_s _ _ zenon_H13d). zenon_intro zenon_H13f. zenon_intro zenon_H13e. % 112.02/112.39 apply (zenon_imply_s _ _ zenon_H13f); [ zenon_intro zenon_H121 | zenon_intro zenon_H15a ]. % 112.02/112.39 apply (zenon_imply_s _ _ zenon_H13e); [ zenon_intro zenon_H11d | zenon_intro zenon_H140 ]. % 112.02/112.39 exact (zenon_H11d zenon_H121). % 112.02/112.39 apply (zenon_and_s _ _ zenon_H140). zenon_intro zenon_H142. zenon_intro zenon_H141. % 112.02/112.39 apply (zenon_and_s _ _ zenon_H141). zenon_intro zenon_H144. zenon_intro zenon_H143. % 112.02/112.39 apply (zenon_and_s _ _ zenon_H143). zenon_intro zenon_H145. zenon_intro zenon_H134. % 112.02/112.39 apply (zenon_imply_s _ _ zenon_H144); [ zenon_intro zenon_H15e | zenon_intro zenon_H15d ]. % 112.02/112.39 apply (zenon_notand_s _ _ zenon_H15e); [ zenon_intro zenon_H13a | zenon_intro zenon_H127 ]. % 112.02/112.39 apply zenon_H13a. zenon_intro zenon_H149. % 112.02/112.39 apply (zenon_L55_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.39 apply (zenon_L56_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.39 exact (zenon_H1a7 zenon_H15d). % 112.02/112.39 apply zenon_H154. apply sym_equal. exact zenon_H15a. % 112.02/112.39 (* end of lemma zenon_L90_ *) % 112.02/112.39 assert (zenon_L91_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (organization zenon_TX_y) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T0) = (zero)))->((greater (age zenon_TX_y T) (sigma))<->(dissimilar zenon_TX_y T0 T))))) -> (~((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (low)) -> False). % 112.02/112.39 do 3 intro. intros zenon_H0 zenon_H1f zenon_H136 zenon_Hec zenon_Hcd zenon_H148 zenon_Hed zenon_H154 zenon_H1a5 zenon_H34 zenon_H1b8. % 112.02/112.39 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1ba ]. % 112.02/112.39 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1a9 ]. % 112.02/112.39 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H1a5. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H1b1. % 112.02/112.39 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.39 congruence. % 112.02/112.39 apply zenon_H16a. apply refl_equal. % 112.02/112.39 exact (zenon_H1ba zenon_H1b9). % 112.02/112.39 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod1)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))))); [ zenon_intro zenon_H1aa | zenon_intro zenon_H1ab ]. % 112.02/112.39 apply (zenon_and_s _ _ zenon_H1aa). zenon_intro zenon_H1a7. zenon_intro zenon_H194. % 112.02/112.39 apply (zenon_L90_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.39 cut ((greater (mod1) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H1a9. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact assumption_18b. % 112.02/112.39 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.02/112.39 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H159]. % 112.02/112.39 congruence. % 112.02/112.39 apply (zenon_notand_s _ _ zenon_H1ab); [ zenon_intro zenon_H1ad | zenon_intro zenon_H1ac ]. % 112.02/112.39 apply zenon_H1ad. zenon_intro zenon_H15d. % 112.02/112.39 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H159. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H16d. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H1a7]. % 112.02/112.39 congruence. % 112.02/112.39 exact (zenon_H1a7 zenon_H15d). % 112.02/112.39 apply zenon_H16a. apply refl_equal. % 112.02/112.39 apply zenon_H16a. apply refl_equal. % 112.02/112.39 apply zenon_H1ac. zenon_intro zenon_H19c. % 112.02/112.39 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.02/112.39 generalize (zenon_H18f (mod1)). zenon_intro zenon_H1ae. % 112.02/112.39 generalize (zenon_H1ae (low)). zenon_intro zenon_H1af. % 112.02/112.39 apply (zenon_imply_s _ _ zenon_H1af); [ zenon_intro zenon_H194 | zenon_intro zenon_H1b0 ]. % 112.02/112.39 exact (zenon_H194 zenon_H19c). % 112.02/112.39 apply (zenon_imply_s _ _ zenon_H1b0); [ zenon_intro zenon_H7f | zenon_intro zenon_H1b1 ]. % 112.02/112.39 exact (zenon_H7f assumption_18b). % 112.02/112.39 exact (zenon_H1a9 zenon_H1b1). % 112.02/112.39 apply zenon_H6a. apply refl_equal. % 112.02/112.39 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((low) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H1ba. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H11a. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 112.02/112.39 congruence. % 112.02/112.39 exact (zenon_H1bb zenon_H1b8). % 112.02/112.39 apply zenon_H11b. apply refl_equal. % 112.02/112.39 apply zenon_H11b. apply refl_equal. % 112.02/112.39 (* end of lemma zenon_L91_ *) % 112.02/112.39 assert (zenon_L92_ : forall (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (~(greater (low) (hazard_of_mortality zenon_TX_y zenon_TT2_la))) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (organization zenon_TX_y) -> (~((low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> False). % 112.02/112.39 do 2 intro. intros zenon_H162 zenon_H0 zenon_H1f zenon_H155 zenon_H13b zenon_H35 zenon_H123 zenon_H136. % 112.02/112.39 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H166 | zenon_intro zenon_H154 ]. % 112.02/112.39 cut ((greater (low) (very_low)) = (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H162. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact assumption_18c. % 112.02/112.39 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H154]. % 112.02/112.39 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.02/112.39 congruence. % 112.02/112.39 apply zenon_H6a. apply refl_equal. % 112.02/112.39 exact (zenon_H154 zenon_H166). % 112.02/112.39 generalize (zenon_H0 zenon_TT2_la). zenon_intro zenon_H13c. % 112.02/112.39 apply (zenon_imply_s _ _ zenon_H13c); [ zenon_intro zenon_H27 | zenon_intro zenon_H13d ]. % 112.02/112.39 exact (zenon_H27 zenon_H1f). % 112.02/112.39 apply (zenon_and_s _ _ zenon_H13d). zenon_intro zenon_H13f. zenon_intro zenon_H13e. % 112.02/112.39 apply (zenon_imply_s _ _ zenon_H13f); [ zenon_intro zenon_H121 | zenon_intro zenon_H15a ]. % 112.02/112.39 apply (zenon_imply_s _ _ zenon_H13e); [ zenon_intro zenon_H11d | zenon_intro zenon_H140 ]. % 112.02/112.39 exact (zenon_H11d zenon_H121). % 112.02/112.39 apply (zenon_and_s _ _ zenon_H140). zenon_intro zenon_H142. zenon_intro zenon_H141. % 112.02/112.39 apply (zenon_and_s _ _ zenon_H141). zenon_intro zenon_H144. zenon_intro zenon_H143. % 112.02/112.39 apply (zenon_and_s _ _ zenon_H143). zenon_intro zenon_H145. zenon_intro zenon_H134. % 112.02/112.39 apply (zenon_imply_s _ _ zenon_H142); [ zenon_intro zenon_H15c | zenon_intro zenon_H15b ]. % 112.02/112.39 apply (zenon_notand_s _ _ zenon_H15c); [ zenon_intro zenon_H135 | zenon_intro zenon_H127 ]. % 112.02/112.39 apply (zenon_L52_ zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.39 apply (zenon_L86_ zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.39 apply zenon_H155. apply sym_equal. exact zenon_H15b. % 112.02/112.39 apply zenon_H154. apply sym_equal. exact zenon_H15a. % 112.02/112.39 (* end of lemma zenon_L92_ *) % 112.02/112.39 assert (zenon_L93_ : forall (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (organization zenon_TX_y) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (low) (low))) -> (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low)) -> False). % 112.02/112.39 do 2 intro. intros zenon_H0 zenon_H1f zenon_H13b zenon_H35 zenon_H123 zenon_H136 zenon_H34 zenon_H6c zenon_H1b1. % 112.02/112.39 elim (classic ((~((low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)))/\(~(greater (low) (hazard_of_mortality zenon_TX_y zenon_TT2_la))))); [ zenon_intro zenon_H1bc | zenon_intro zenon_H1bd ]. % 112.02/112.39 apply (zenon_and_s _ _ zenon_H1bc). zenon_intro zenon_H155. zenon_intro zenon_H162. % 112.02/112.39 apply (zenon_L92_ zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.39 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low)) = (greater (low) (low))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H6c. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H1b1. % 112.02/112.39 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1a8]. % 112.02/112.39 congruence. % 112.02/112.39 apply (zenon_notand_s _ _ zenon_H1bd); [ zenon_intro zenon_H1bf | zenon_intro zenon_H1be ]. % 112.02/112.39 apply zenon_H1bf. zenon_intro zenon_H160. % 112.02/112.39 elim (classic ((low) = (low))); [ zenon_intro zenon_H74 | zenon_intro zenon_H6a ]. % 112.02/112.39 cut (((low) = (low)) = ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (low))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H1a8. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H74. % 112.02/112.39 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.02/112.39 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H155]. % 112.02/112.39 congruence. % 112.02/112.39 exact (zenon_H155 zenon_H160). % 112.02/112.39 apply zenon_H6a. apply refl_equal. % 112.02/112.39 apply zenon_H6a. apply refl_equal. % 112.02/112.39 apply zenon_H1be. zenon_intro zenon_H161. % 112.02/112.39 generalize (zenon_H34 (low)). zenon_intro zenon_H7a. % 112.02/112.39 generalize (zenon_H7a (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H1b5. % 112.02/112.39 generalize (zenon_H1b5 (low)). zenon_intro zenon_H1b6. % 112.02/112.39 apply (zenon_imply_s _ _ zenon_H1b6); [ zenon_intro zenon_H162 | zenon_intro zenon_H1b7 ]. % 112.02/112.39 exact (zenon_H162 zenon_H161). % 112.02/112.39 apply (zenon_imply_s _ _ zenon_H1b7); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H7e ]. % 112.02/112.39 exact (zenon_H1a9 zenon_H1b1). % 112.02/112.39 exact (zenon_H6c zenon_H7e). % 112.02/112.39 apply zenon_H6a. apply refl_equal. % 112.02/112.39 (* end of lemma zenon_L93_ *) % 112.02/112.39 assert (zenon_L94_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (forall Y : zenon_U, ((smaller (hazard_of_mortality zenon_TX_y zenon_TT2_la) Y)\/(((hazard_of_mortality zenon_TX_y zenon_TT2_la) = Y)\/(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) Y)))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (organization zenon_TX_y) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (~(greater (low) (low))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (low)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T0) = (zero)))->((greater (age zenon_TX_y T) (sigma))<->(dissimilar zenon_TX_y T0 T))))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> False). % 112.02/112.39 do 3 intro. intros zenon_H34 zenon_H172 zenon_H13b zenon_H136 zenon_H1a zenon_H1f zenon_H0 zenon_H6c zenon_H1b8 zenon_Hec zenon_Hcd zenon_H148 zenon_Hed zenon_H35 zenon_H123. % 112.02/112.39 generalize (zenon_H172 (low)). zenon_intro zenon_H1c0. % 112.02/112.39 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H1c1 ]. % 112.02/112.39 apply (zenon_L89_ zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.39 apply (zenon_or_s _ _ zenon_H1c1); [ zenon_intro zenon_H15b | zenon_intro zenon_H1b1 ]. % 112.02/112.39 elim (classic (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H161 | zenon_intro zenon_H162 ]. % 112.02/112.39 cut ((greater (low) (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = (greater (low) (low))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H6c. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H161. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1a8]. % 112.02/112.39 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.02/112.39 congruence. % 112.02/112.39 apply zenon_H6a. apply refl_equal. % 112.02/112.39 exact (zenon_H1a8 zenon_H15b). % 112.02/112.39 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H166 | zenon_intro zenon_H154 ]. % 112.02/112.39 cut ((greater (low) (very_low)) = (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H162. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact assumption_18c. % 112.02/112.39 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H154]. % 112.02/112.39 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.02/112.39 congruence. % 112.02/112.39 apply zenon_H6a. apply refl_equal. % 112.02/112.39 exact (zenon_H154 zenon_H166). % 112.02/112.39 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H160 | zenon_intro zenon_H155 ]. % 112.02/112.39 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H168 | zenon_intro zenon_H169 ]. % 112.02/112.39 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H162. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H168. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1a8]. % 112.02/112.39 congruence. % 112.02/112.39 elim (classic ((low) = (low))); [ zenon_intro zenon_H74 | zenon_intro zenon_H6a ]. % 112.02/112.39 cut (((low) = (low)) = ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (low))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H1a8. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H74. % 112.02/112.39 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.02/112.39 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H155]. % 112.02/112.39 congruence. % 112.02/112.39 exact (zenon_H155 zenon_H160). % 112.02/112.39 apply zenon_H6a. apply refl_equal. % 112.02/112.39 apply zenon_H6a. apply refl_equal. % 112.02/112.39 apply zenon_H16a. apply refl_equal. % 112.02/112.39 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1a5 ]. % 112.02/112.39 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1a9 ]. % 112.02/112.39 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H169. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H1b1. % 112.02/112.39 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H155]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.39 congruence. % 112.02/112.39 apply zenon_H16a. apply refl_equal. % 112.02/112.39 apply zenon_H155. apply sym_equal. exact zenon_H15b. % 112.02/112.39 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H1a9. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H1a4. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.39 congruence. % 112.02/112.39 apply zenon_H16a. apply refl_equal. % 112.02/112.39 exact (zenon_H1bb zenon_H1b8). % 112.02/112.39 apply (zenon_L91_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.39 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H155. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H16d. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1a8]. % 112.02/112.39 congruence. % 112.02/112.39 exact (zenon_H1a8 zenon_H15b). % 112.02/112.39 apply zenon_H16a. apply refl_equal. % 112.02/112.39 apply zenon_H16a. apply refl_equal. % 112.02/112.39 apply (zenon_L93_ zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.39 (* end of lemma zenon_L94_ *) % 112.02/112.39 assert (zenon_L95_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))) -> (~(greater (mod2) (mod2))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T0) = (zero)))->((greater (age zenon_TX_y T) (sigma))<->(dissimilar zenon_TX_y T0 T))))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (low)) -> (~(greater (low) (low))) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> False). % 112.02/112.39 do 3 intro. intros zenon_H34 zenon_H167 zenon_H153 zenon_H123 zenon_H35 zenon_Hed zenon_H148 zenon_Hcd zenon_Hec zenon_H1b8 zenon_H6c zenon_H0 zenon_H1f zenon_H1a zenon_H136. % 112.02/112.39 generalize (meaning_postulate_greater_comparable (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H172. % 112.02/112.39 generalize (zenon_H172 (mod2)). zenon_intro zenon_H173. % 112.02/112.39 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H175 | zenon_intro zenon_H174 ]. % 112.02/112.39 generalize (definition_smaller (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H176. % 112.02/112.39 generalize (zenon_H176 (mod2)). zenon_intro zenon_H177. % 112.02/112.39 apply (zenon_equiv_s _ _ zenon_H177); [ zenon_intro zenon_H178; zenon_intro zenon_H157 | zenon_intro zenon_H175; zenon_intro zenon_H156 ]. % 112.02/112.39 exact (zenon_H178 zenon_H175). % 112.02/112.39 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [ zenon_intro zenon_H146 | zenon_intro zenon_H13b ]. % 112.02/112.39 cut ((greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = (greater (mod2) (mod2))). % 112.02/112.39 intro zenon_D_pnotp. % 112.02/112.39 apply zenon_H153. % 112.02/112.39 rewrite <- zenon_D_pnotp. % 112.02/112.39 exact zenon_H156. % 112.02/112.39 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 112.02/112.39 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 112.02/112.39 congruence. % 112.02/112.39 apply zenon_H83. apply refl_equal. % 112.02/112.39 exact (zenon_H13b zenon_H146). % 112.02/112.39 apply (zenon_L94_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.39 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H146 | zenon_intro zenon_H179 ]. % 112.02/112.39 apply (zenon_L59_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.02/112.39 exact (zenon_H167 zenon_H179). % 112.02/112.39 (* end of lemma zenon_L95_ *) % 112.02/112.39 assert (zenon_L96_ : forall (zenon_TT2_la : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))) -> (~(greater (mod2) (mod2))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (low)) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> False). % 112.12/112.40 do 3 intro. intros zenon_H34 zenon_Hf3 zenon_H1f zenon_Hec zenon_H167 zenon_H153 zenon_H123 zenon_H35 zenon_H148 zenon_H1b8 zenon_H0 zenon_H1a zenon_H136. % 112.12/112.40 generalize (zenon_Hf3 zenon_TT0_hz). zenon_intro zenon_Hf4. % 112.12/112.40 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcd ]. % 112.12/112.40 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ]. % 112.12/112.40 exact (zenon_H27 zenon_H1f). % 112.12/112.40 exact (zenon_Hf2 zenon_Hec). % 112.12/112.40 generalize (assumption_15 zenon_TX_y). zenon_intro zenon_Hed. % 112.12/112.40 generalize (meaning_postulate_greater_strict (low)). zenon_intro zenon_H80. % 112.12/112.40 generalize (zenon_H80 (low)). zenon_intro zenon_H81. % 112.12/112.40 apply (zenon_notand_s _ _ zenon_H81); [ zenon_intro zenon_H6c | zenon_intro zenon_H6c ]. % 112.12/112.40 apply (zenon_L95_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.40 apply (zenon_L95_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.40 (* end of lemma zenon_L96_ *) % 112.12/112.40 assert (zenon_L97_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (low)) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> False). % 112.12/112.40 do 4 intro. intros zenon_H34 zenon_H1c2 zenon_H32 zenon_H136 zenon_H1a zenon_H0 zenon_H1b8 zenon_H148 zenon_H35 zenon_H123 zenon_H167 zenon_Hec zenon_H1f zenon_Hf3. % 112.12/112.40 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1c4 ]. % 112.12/112.40 cut ((greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H1c2. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H1c3. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.40 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 112.12/112.40 congruence. % 112.12/112.40 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H5e. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H61. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31]. % 112.12/112.40 congruence. % 112.12/112.40 exact (zenon_H31 zenon_H32). % 112.12/112.40 apply zenon_H62. apply refl_equal. % 112.12/112.40 apply zenon_H62. apply refl_equal. % 112.12/112.40 apply zenon_H62. apply refl_equal. % 112.12/112.40 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H115 | zenon_intro zenon_H5e ]. % 112.12/112.40 elim (classic (greater (mod2) (mod2))); [ zenon_intro zenon_H16b | zenon_intro zenon_H153 ]. % 112.12/112.40 cut ((greater (mod2) (mod2)) = (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H1c4. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H16b. % 112.12/112.40 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 112.12/112.40 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 112.12/112.40 congruence. % 112.12/112.40 apply zenon_H83. apply refl_equal. % 112.12/112.40 exact (zenon_H5e zenon_H115). % 112.12/112.40 apply (zenon_L96_ zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.40 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H5e. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H61. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31]. % 112.12/112.40 congruence. % 112.12/112.40 exact (zenon_H31 zenon_H32). % 112.12/112.40 apply zenon_H62. apply refl_equal. % 112.12/112.40 apply zenon_H62. apply refl_equal. % 112.12/112.40 (* end of lemma zenon_L97_ *) % 112.12/112.40 assert (zenon_L98_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (low)) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2)) -> False). % 112.12/112.40 do 4 intro. intros zenon_Hf3 zenon_H1f zenon_Hec zenon_H123 zenon_H35 zenon_H148 zenon_H1b8 zenon_H0 zenon_H1a zenon_H17c zenon_H34 zenon_H32. % 112.12/112.40 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H115 | zenon_intro zenon_H5e ]. % 112.12/112.40 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ]. % 112.12/112.40 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H17c. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H179. % 112.12/112.40 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.40 congruence. % 112.12/112.40 apply zenon_H16a. apply refl_equal. % 112.12/112.40 exact (zenon_H5e zenon_H115). % 112.12/112.40 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H1c2 ]. % 112.12/112.40 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1c4 ]. % 112.12/112.40 cut ((greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H17c. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H1c3. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.40 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 112.12/112.40 congruence. % 112.12/112.40 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H16c. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H16d. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 112.12/112.40 congruence. % 112.12/112.40 apply (zenon_L81_ zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.40 apply zenon_H16a. apply refl_equal. % 112.12/112.40 apply zenon_H16a. apply refl_equal. % 112.12/112.40 apply zenon_H62. apply refl_equal. % 112.12/112.40 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H1c4. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H1c5. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31]. % 112.12/112.40 congruence. % 112.12/112.40 elim (classic ((mod2) = (mod2))); [ zenon_intro zenon_H17b | zenon_intro zenon_H83 ]. % 112.12/112.40 cut (((mod2) = (mod2)) = ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H31. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H17b. % 112.12/112.40 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 112.12/112.40 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 112.12/112.40 congruence. % 112.12/112.40 exact (zenon_H5e zenon_H115). % 112.12/112.40 apply zenon_H83. apply refl_equal. % 112.12/112.40 apply zenon_H83. apply refl_equal. % 112.12/112.40 apply zenon_H62. apply refl_equal. % 112.12/112.40 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (high))))); [ zenon_intro zenon_H189 | zenon_intro zenon_H18a ]. % 112.12/112.40 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H136. zenon_intro zenon_H18b. % 112.12/112.40 apply (zenon_L97_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.40 cut ((greater (high) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H167. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact assumption_18d. % 112.12/112.40 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 112.12/112.40 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 112.12/112.40 congruence. % 112.12/112.40 apply (zenon_notand_s _ _ zenon_H18a); [ zenon_intro zenon_H18d | zenon_intro zenon_H18c ]. % 112.12/112.40 apply zenon_H18d. zenon_intro zenon_H137. % 112.12/112.40 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H17f. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H16d. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 112.12/112.40 congruence. % 112.12/112.40 exact (zenon_H136 zenon_H137). % 112.12/112.40 apply zenon_H16a. apply refl_equal. % 112.12/112.40 apply zenon_H16a. apply refl_equal. % 112.12/112.40 apply zenon_H18c. zenon_intro zenon_H18e. % 112.12/112.40 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.12/112.40 generalize (zenon_H18f (high)). zenon_intro zenon_H190. % 112.12/112.40 generalize (zenon_H190 (mod2)). zenon_intro zenon_H191. % 112.12/112.40 apply (zenon_imply_s _ _ zenon_H191); [ zenon_intro zenon_H18b | zenon_intro zenon_H192 ]. % 112.12/112.40 exact (zenon_H18b zenon_H18e). % 112.12/112.40 apply (zenon_imply_s _ _ zenon_H192); [ zenon_intro zenon_H9b | zenon_intro zenon_H179 ]. % 112.12/112.40 exact (zenon_H9b assumption_18d). % 112.12/112.40 exact (zenon_H167 zenon_H179). % 112.12/112.40 apply zenon_H83. apply refl_equal. % 112.12/112.40 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H5e. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H61. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31]. % 112.12/112.40 congruence. % 112.12/112.40 exact (zenon_H31 zenon_H32). % 112.12/112.40 apply zenon_H62. apply refl_equal. % 112.12/112.40 apply zenon_H62. apply refl_equal. % 112.12/112.40 (* end of lemma zenon_L98_ *) % 112.12/112.40 assert (zenon_L99_ : forall (zenon_TT2_la : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (low)) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (~((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> False). % 112.12/112.40 do 4 intro. intros zenon_H34 zenon_H1f zenon_Hec zenon_H72 zenon_H17c zenon_Hf3 zenon_H148 zenon_H1b8 zenon_H0 zenon_H1a zenon_H123 zenon_H35 zenon_H37 zenon_H187. % 112.12/112.40 generalize (zenon_Hf3 zenon_TT0_hz). zenon_intro zenon_Hf4. % 112.12/112.40 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcd ]. % 112.12/112.40 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ]. % 112.12/112.40 exact (zenon_H27 zenon_H1f). % 112.12/112.40 exact (zenon_Hf2 zenon_Hec). % 112.12/112.40 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88. % 112.12/112.40 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ]. % 112.12/112.40 exact (zenon_H27 zenon_H1f). % 112.12/112.40 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a. % 112.12/112.40 apply (zenon_imply_s _ _ zenon_H8b); [ zenon_intro zenon_H24 | zenon_intro zenon_H188 ]. % 112.12/112.40 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ]. % 112.12/112.40 exact (zenon_H1e zenon_H24). % 112.12/112.40 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d. % 112.12/112.40 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f. % 112.12/112.40 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H30. zenon_intro zenon_H28. % 112.12/112.40 apply (zenon_imply_s _ _ zenon_H8e); [ zenon_intro zenon_H91 | zenon_intro zenon_H6b ]. % 112.12/112.40 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 112.12/112.40 apply (zenon_L31_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.40 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 112.12/112.40 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ]. % 112.12/112.40 apply (zenon_L31_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.40 exact (zenon_H2e zenon_H29). % 112.12/112.40 apply (zenon_L98_ zenon_TT1_bg zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.40 apply zenon_H72. apply sym_equal. exact zenon_H6b. % 112.12/112.40 apply zenon_H187. apply sym_equal. exact zenon_H188. % 112.12/112.40 (* end of lemma zenon_L99_ *) % 112.12/112.40 assert (zenon_L100_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T0) = (zero)))->((greater (age zenon_TX_y T) (sigma))<->(dissimilar zenon_TX_y T0 T))))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (low)) -> (~(greater (low) (low))) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))) -> False). % 112.12/112.40 do 3 intro. intros zenon_H34 zenon_H123 zenon_H35 zenon_Hed zenon_H148 zenon_Hcd zenon_Hec zenon_H1b8 zenon_H6c zenon_H0 zenon_H1f zenon_H1a zenon_H136 zenon_H13b. % 112.12/112.40 generalize (meaning_postulate_greater_comparable (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H172. % 112.12/112.40 apply (zenon_L94_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.40 (* end of lemma zenon_L100_ *) % 112.12/112.40 assert (zenon_L101_ : forall (zenon_TT2_la : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (low)) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))) -> False). % 112.12/112.40 do 3 intro. intros zenon_H34 zenon_Hf3 zenon_H1f zenon_Hec zenon_H123 zenon_H35 zenon_H148 zenon_H1b8 zenon_H0 zenon_H1a zenon_H136 zenon_H13b. % 112.12/112.40 generalize (zenon_Hf3 zenon_TT0_hz). zenon_intro zenon_Hf4. % 112.12/112.40 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcd ]. % 112.12/112.40 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ]. % 112.12/112.40 exact (zenon_H27 zenon_H1f). % 112.12/112.40 exact (zenon_Hf2 zenon_Hec). % 112.12/112.40 generalize (assumption_15 zenon_TX_y). zenon_intro zenon_Hed. % 112.12/112.40 generalize (meaning_postulate_greater_strict (low)). zenon_intro zenon_H80. % 112.12/112.40 generalize (zenon_H80 (low)). zenon_intro zenon_H81. % 112.12/112.40 apply (zenon_notand_s _ _ zenon_H81); [ zenon_intro zenon_H6c | zenon_intro zenon_H6c ]. % 112.12/112.40 apply (zenon_L100_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.40 apply (zenon_L100_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.40 (* end of lemma zenon_L101_ *) % 112.12/112.40 assert (zenon_L102_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (low)) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))) -> False). % 112.12/112.40 do 3 intro. intros zenon_H13b zenon_H1a zenon_H0 zenon_H1b8 zenon_H148 zenon_H35 zenon_H123 zenon_Hec zenon_H1f zenon_Hf3 zenon_H34 zenon_H167. % 112.12/112.40 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (high))))); [ zenon_intro zenon_H189 | zenon_intro zenon_H18a ]. % 112.12/112.40 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H136. zenon_intro zenon_H18b. % 112.12/112.40 apply (zenon_L101_ zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.40 cut ((greater (high) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H167. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact assumption_18d. % 112.12/112.40 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 112.12/112.40 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 112.12/112.40 congruence. % 112.12/112.40 apply (zenon_notand_s _ _ zenon_H18a); [ zenon_intro zenon_H18d | zenon_intro zenon_H18c ]. % 112.12/112.40 apply zenon_H18d. zenon_intro zenon_H137. % 112.12/112.40 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H17f. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H16d. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 112.12/112.40 congruence. % 112.12/112.40 exact (zenon_H136 zenon_H137). % 112.12/112.40 apply zenon_H16a. apply refl_equal. % 112.12/112.40 apply zenon_H16a. apply refl_equal. % 112.12/112.40 apply zenon_H18c. zenon_intro zenon_H18e. % 112.12/112.40 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.12/112.40 generalize (zenon_H18f (high)). zenon_intro zenon_H190. % 112.12/112.40 generalize (zenon_H190 (mod2)). zenon_intro zenon_H191. % 112.12/112.40 apply (zenon_imply_s _ _ zenon_H191); [ zenon_intro zenon_H18b | zenon_intro zenon_H192 ]. % 112.12/112.40 exact (zenon_H18b zenon_H18e). % 112.12/112.40 apply (zenon_imply_s _ _ zenon_H192); [ zenon_intro zenon_H9b | zenon_intro zenon_H179 ]. % 112.12/112.40 exact (zenon_H9b assumption_18d). % 112.12/112.40 exact (zenon_H167 zenon_H179). % 112.12/112.40 apply zenon_H83. apply refl_equal. % 112.12/112.40 (* end of lemma zenon_L102_ *) % 112.12/112.40 assert (zenon_L103_ : forall (zenon_TT2_la : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (low)) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))) -> False). % 112.12/112.40 do 3 intro. intros zenon_Hf3 zenon_H1f zenon_Hec zenon_H123 zenon_H35 zenon_H148 zenon_H1b8 zenon_H0 zenon_H1a zenon_H34 zenon_H1a9. % 112.12/112.40 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))))); [ zenon_intro zenon_H195 | zenon_intro zenon_H196 ]. % 112.12/112.40 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H13b. zenon_intro zenon_H167. % 112.12/112.40 apply (zenon_L102_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.40 cut ((greater (mod2) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H1a9. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact assumption_18e. % 112.12/112.40 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.12/112.40 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 112.12/112.40 congruence. % 112.12/112.40 apply (zenon_notand_s _ _ zenon_H196); [ zenon_intro zenon_H198 | zenon_intro zenon_H197 ]. % 112.12/112.40 apply zenon_H198. zenon_intro zenon_H146. % 112.12/112.40 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H16c. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H16d. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 112.12/112.40 congruence. % 112.12/112.40 exact (zenon_H13b zenon_H146). % 112.12/112.40 apply zenon_H16a. apply refl_equal. % 112.12/112.40 apply zenon_H16a. apply refl_equal. % 112.12/112.40 apply zenon_H197. zenon_intro zenon_H179. % 112.12/112.40 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.12/112.40 generalize (zenon_H18f (mod2)). zenon_intro zenon_H199. % 112.12/112.40 generalize (zenon_H199 (low)). zenon_intro zenon_H1c6. % 112.12/112.40 apply (zenon_imply_s _ _ zenon_H1c6); [ zenon_intro zenon_H167 | zenon_intro zenon_H1c7 ]. % 112.12/112.40 exact (zenon_H167 zenon_H179). % 112.12/112.40 apply (zenon_imply_s _ _ zenon_H1c7); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H1b1 ]. % 112.12/112.40 exact (zenon_Hc2 assumption_18e). % 112.12/112.40 exact (zenon_H1a9 zenon_H1b1). % 112.12/112.40 apply zenon_H6a. apply refl_equal. % 112.12/112.40 (* end of lemma zenon_L103_ *) % 112.12/112.40 assert (zenon_L104_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (low)) -> False). % 112.12/112.40 do 3 intro. intros zenon_H1a zenon_H0 zenon_H148 zenon_H35 zenon_H123 zenon_Hec zenon_H1f zenon_Hf3 zenon_H1a5 zenon_H34 zenon_H1b8. % 112.12/112.40 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1ba ]. % 112.12/112.40 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1a9 ]. % 112.12/112.40 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H1a5. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H1b1. % 112.12/112.40 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.40 congruence. % 112.12/112.40 apply zenon_H16a. apply refl_equal. % 112.12/112.40 exact (zenon_H1ba zenon_H1b9). % 112.12/112.40 apply (zenon_L103_ zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.40 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((low) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H1ba. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H11a. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 112.12/112.40 congruence. % 112.12/112.40 exact (zenon_H1bb zenon_H1b8). % 112.12/112.40 apply zenon_H11b. apply refl_equal. % 112.12/112.40 apply zenon_H11b. apply refl_equal. % 112.12/112.40 (* end of lemma zenon_L104_ *) % 112.12/112.40 assert (zenon_L105_ : forall (zenon_TX_y : zenon_U), (~(~(has_immunity zenon_TX_y zenon_E))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> False). % 112.12/112.40 do 1 intro. intros zenon_H111 zenon_H1f zenon_H1a. % 112.12/112.40 apply zenon_H111. zenon_intro zenon_H1c8. % 112.12/112.40 generalize (assumption_1 zenon_TX_y). zenon_intro zenon_H22. % 112.12/112.40 generalize (zenon_H22 zenon_E). zenon_intro zenon_H1c9. % 112.12/112.40 apply (zenon_imply_s _ _ zenon_H1c9); [ zenon_intro zenon_H25 | zenon_intro zenon_H112 ]. % 112.12/112.40 apply (zenon_notand_s _ _ zenon_H25); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 112.12/112.40 exact (zenon_H27 zenon_H1f). % 112.12/112.40 apply zenon_H26. zenon_intro zenon_H19. % 112.12/112.40 apply (zenon_L2_ zenon_TX_y); trivial. % 112.12/112.40 exact (zenon_H112 zenon_H1c8). % 112.12/112.40 (* end of lemma zenon_L105_ *) % 112.12/112.40 assert (zenon_L106_ : forall (zenon_TX_y : zenon_U), ((hazard_of_mortality zenon_TX_y zenon_E) = (high)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_E) (mod2))) -> False). % 112.12/112.40 do 1 intro. intros zenon_H116 zenon_H34 zenon_H1ca. % 112.12/112.40 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_E) = (high)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_E) (high))))); [ zenon_intro zenon_H1cb | zenon_intro zenon_H1cc ]. % 112.12/112.40 apply (zenon_and_s _ _ zenon_H1cb). zenon_intro zenon_H11c. zenon_intro zenon_H1cd. % 112.12/112.40 exact (zenon_H11c zenon_H116). % 112.12/112.40 cut ((greater (high) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (mod2))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H1ca. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact assumption_18d. % 112.12/112.40 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 112.12/112.40 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H119]. % 112.12/112.40 congruence. % 112.12/112.40 apply (zenon_notand_s _ _ zenon_H1cc); [ zenon_intro zenon_H1cf | zenon_intro zenon_H1ce ]. % 112.12/112.40 apply zenon_H1cf. zenon_intro zenon_H116. % 112.12/112.40 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H119. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H11a. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 112.12/112.40 congruence. % 112.12/112.40 exact (zenon_H11c zenon_H116). % 112.12/112.40 apply zenon_H11b. apply refl_equal. % 112.12/112.40 apply zenon_H11b. apply refl_equal. % 112.12/112.40 apply zenon_H1ce. zenon_intro zenon_H1d0. % 112.12/112.40 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H1d1. % 112.12/112.40 generalize (zenon_H1d1 (high)). zenon_intro zenon_H1d2. % 112.12/112.40 generalize (zenon_H1d2 (mod2)). zenon_intro zenon_H1d3. % 112.12/112.40 apply (zenon_imply_s _ _ zenon_H1d3); [ zenon_intro zenon_H1cd | zenon_intro zenon_H1d4 ]. % 112.12/112.40 exact (zenon_H1cd zenon_H1d0). % 112.12/112.40 apply (zenon_imply_s _ _ zenon_H1d4); [ zenon_intro zenon_H9b | zenon_intro zenon_H1d5 ]. % 112.12/112.40 exact (zenon_H9b assumption_18d). % 112.12/112.40 exact (zenon_H1ca zenon_H1d5). % 112.12/112.40 apply zenon_H83. apply refl_equal. % 112.12/112.40 (* end of lemma zenon_L106_ *) % 112.12/112.40 assert (zenon_L107_ : forall (zenon_TX_y : zenon_U), ((hazard_of_mortality zenon_TX_y zenon_E) = (high)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_E) (low))) -> False). % 112.12/112.40 do 1 intro. intros zenon_H116 zenon_H34 zenon_H1d6. % 112.12/112.40 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_E) = (mod2)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_E) (mod2))))); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H1d8 ]. % 112.12/112.40 apply (zenon_and_s _ _ zenon_H1d7). zenon_intro zenon_H1a2. zenon_intro zenon_H1ca. % 112.12/112.40 apply (zenon_L106_ zenon_TX_y); trivial. % 112.12/112.40 cut ((greater (mod2) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (low))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H1d6. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact assumption_18e. % 112.12/112.40 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.12/112.40 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 112.12/112.40 congruence. % 112.12/112.40 apply (zenon_notand_s _ _ zenon_H1d8); [ zenon_intro zenon_H1da | zenon_intro zenon_H1d9 ]. % 112.12/112.40 apply zenon_H1da. zenon_intro zenon_H19e. % 112.12/112.40 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H1a1. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H11a. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 112.12/112.40 congruence. % 112.12/112.40 exact (zenon_H1a2 zenon_H19e). % 112.12/112.40 apply zenon_H11b. apply refl_equal. % 112.12/112.40 apply zenon_H11b. apply refl_equal. % 112.12/112.40 apply zenon_H1d9. zenon_intro zenon_H1d5. % 112.12/112.40 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H1d1. % 112.12/112.40 generalize (zenon_H1d1 (mod2)). zenon_intro zenon_H1db. % 112.12/112.40 generalize (zenon_H1db (low)). zenon_intro zenon_H1dc. % 112.12/112.40 apply (zenon_imply_s _ _ zenon_H1dc); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1dd ]. % 112.12/112.40 exact (zenon_H1ca zenon_H1d5). % 112.12/112.40 apply (zenon_imply_s _ _ zenon_H1dd); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H1de ]. % 112.12/112.40 exact (zenon_Hc2 assumption_18e). % 112.12/112.40 exact (zenon_H1d6 zenon_H1de). % 112.12/112.40 apply zenon_H6a. apply refl_equal. % 112.12/112.40 (* end of lemma zenon_L107_ *) % 112.12/112.40 assert (zenon_L108_ : forall (zenon_TX_y : zenon_U), ((hazard_of_mortality zenon_TX_y zenon_E) = (high)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (very_low) (very_low))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (very_low)) -> False). % 112.12/112.40 do 1 intro. intros zenon_H116 zenon_H34 zenon_H1df zenon_H1e0. % 112.12/112.40 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e2 ]. % 112.12/112.40 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (very_low))); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H1e4 ]. % 112.12/112.40 cut ((greater (hazard_of_mortality zenon_TX_y zenon_E) (very_low)) = (greater (very_low) (very_low))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H1df. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H1e3. % 112.12/112.40 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 112.12/112.40 congruence. % 112.12/112.40 elim (classic ((very_low) = (very_low))); [ zenon_intro zenon_H1e6 | zenon_intro zenon_Hf5 ]. % 112.12/112.40 cut (((very_low) = (very_low)) = ((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H1e5. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H1e6. % 112.12/112.40 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 112.12/112.40 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1e2]. % 112.12/112.40 congruence. % 112.12/112.40 exact (zenon_H1e2 zenon_H1e1). % 112.12/112.40 apply zenon_Hf5. apply refl_equal. % 112.12/112.40 apply zenon_Hf5. apply refl_equal. % 112.12/112.40 apply zenon_Hf5. apply refl_equal. % 112.12/112.40 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_E) = (low)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_E) (low))))); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H1e8 ]. % 112.12/112.40 apply (zenon_and_s _ _ zenon_H1e7). zenon_intro zenon_H1bb. zenon_intro zenon_H1d6. % 112.12/112.40 apply (zenon_L107_ zenon_TX_y); trivial. % 112.12/112.40 cut ((greater (low) (very_low)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (very_low))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H1e4. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact assumption_18c. % 112.12/112.40 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 112.12/112.40 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba]. % 112.12/112.40 congruence. % 112.12/112.40 apply (zenon_notand_s _ _ zenon_H1e8); [ zenon_intro zenon_H1ea | zenon_intro zenon_H1e9 ]. % 112.12/112.40 apply zenon_H1ea. zenon_intro zenon_H1b8. % 112.12/112.40 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((low) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H1ba. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H11a. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 112.12/112.40 congruence. % 112.12/112.40 exact (zenon_H1bb zenon_H1b8). % 112.12/112.40 apply zenon_H11b. apply refl_equal. % 112.12/112.40 apply zenon_H11b. apply refl_equal. % 112.12/112.40 apply zenon_H1e9. zenon_intro zenon_H1de. % 112.12/112.40 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H1d1. % 112.12/112.40 generalize (zenon_H1d1 (low)). zenon_intro zenon_H1eb. % 112.12/112.40 generalize (zenon_H1eb (very_low)). zenon_intro zenon_H1ec. % 112.12/112.40 apply (zenon_imply_s _ _ zenon_H1ec); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H1ed ]. % 112.12/112.40 exact (zenon_H1d6 zenon_H1de). % 112.12/112.40 apply (zenon_imply_s _ _ zenon_H1ed); [ zenon_intro zenon_Hff | zenon_intro zenon_H1e3 ]. % 112.12/112.40 exact (zenon_Hff assumption_18c). % 112.12/112.40 exact (zenon_H1e4 zenon_H1e3). % 112.12/112.40 apply zenon_Hf5. apply refl_equal. % 112.12/112.40 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H1e2. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H11a. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 112.12/112.40 congruence. % 112.12/112.40 exact (zenon_H1e5 zenon_H1e0). % 112.12/112.40 apply zenon_H11b. apply refl_equal. % 112.12/112.40 apply zenon_H11b. apply refl_equal. % 112.12/112.40 (* end of lemma zenon_L108_ *) % 112.12/112.40 assert (zenon_L109_ : forall (zenon_TX_y : zenon_U), ((hazard_of_mortality zenon_TX_y zenon_E) = (high)) -> (~(greater (very_low) (high))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (very_low)) -> False). % 112.12/112.40 do 1 intro. intros zenon_H116 zenon_H1ee zenon_H34 zenon_H1e0. % 112.12/112.40 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e2 ]. % 112.12/112.40 elim (classic (greater (very_low) (very_low))); [ zenon_intro zenon_H1ef | zenon_intro zenon_H1df ]. % 112.12/112.40 elim (classic (greater (very_low) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H1f1 ]. % 112.12/112.40 cut ((greater (very_low) (hazard_of_mortality zenon_TX_y zenon_E)) = (greater (very_low) (high))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H1ee. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H1f0. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 112.12/112.40 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 112.12/112.40 congruence. % 112.12/112.40 apply zenon_Hf5. apply refl_equal. % 112.12/112.40 exact (zenon_H11c zenon_H116). % 112.12/112.40 cut ((greater (very_low) (very_low)) = (greater (very_low) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H1f1. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H1ef. % 112.12/112.40 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1e2]. % 112.12/112.40 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 112.12/112.40 congruence. % 112.12/112.40 apply zenon_Hf5. apply refl_equal. % 112.12/112.40 exact (zenon_H1e2 zenon_H1e1). % 112.12/112.40 apply (zenon_L108_ zenon_TX_y); trivial. % 112.12/112.40 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H1e2. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H11a. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 112.12/112.40 congruence. % 112.12/112.40 exact (zenon_H1e5 zenon_H1e0). % 112.12/112.40 apply zenon_H11b. apply refl_equal. % 112.12/112.40 apply zenon_H11b. apply refl_equal. % 112.12/112.40 (* end of lemma zenon_L109_ *) % 112.12/112.40 assert (zenon_L110_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (high) (low))) -> False). % 112.12/112.40 do 0 intro. intros zenon_H34 zenon_H1f2. % 112.12/112.40 elim (classic ((~((high) = (mod2)))/\(~(greater (high) (mod2))))); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H1f4 ]. % 112.12/112.40 apply (zenon_and_s _ _ zenon_H1f3). zenon_intro zenon_H1f5. zenon_intro zenon_H9b. % 112.12/112.40 exact (zenon_H9b assumption_18d). % 112.12/112.40 cut ((greater (mod2) (low)) = (greater (high) (low))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H1f2. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact assumption_18e. % 112.12/112.40 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.12/112.40 cut (((mod2) = (high))); [idtac | apply NNPP; zenon_intro zenon_H1f6]. % 112.12/112.40 congruence. % 112.12/112.40 apply (zenon_notand_s _ _ zenon_H1f4); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H1f7 ]. % 112.12/112.40 apply zenon_H1f8. zenon_intro zenon_H1f9. % 112.12/112.40 elim (classic ((high) = (high))); [ zenon_intro zenon_H180 | zenon_intro zenon_H113 ]. % 112.12/112.40 cut (((high) = (high)) = ((mod2) = (high))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H1f6. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H180. % 112.12/112.40 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113]. % 112.12/112.40 cut (((high) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1f5]. % 112.12/112.40 congruence. % 112.12/112.40 exact (zenon_H1f5 zenon_H1f9). % 112.12/112.40 apply zenon_H113. apply refl_equal. % 112.12/112.40 apply zenon_H113. apply refl_equal. % 112.12/112.40 apply zenon_H1f7. zenon_intro assumption_18d. % 112.12/112.40 generalize (zenon_H34 (high)). zenon_intro zenon_H1fa. % 112.12/112.40 generalize (zenon_H1fa (mod2)). zenon_intro zenon_H1fb. % 112.12/112.40 generalize (zenon_H1fb (low)). zenon_intro zenon_H1fc. % 112.12/112.40 apply (zenon_imply_s _ _ zenon_H1fc); [ zenon_intro zenon_H9b | zenon_intro zenon_H1fd ]. % 112.12/112.40 exact (zenon_H9b assumption_18d). % 112.12/112.40 apply (zenon_imply_s _ _ zenon_H1fd); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H1fe ]. % 112.12/112.40 exact (zenon_Hc2 assumption_18e). % 112.12/112.40 exact (zenon_H1f2 zenon_H1fe). % 112.12/112.40 apply zenon_H6a. apply refl_equal. % 112.12/112.40 (* end of lemma zenon_L110_ *) % 112.12/112.40 assert (zenon_L111_ : (~(greater (low) (high))) -> ((very_low) = (high)) -> False). % 112.12/112.40 do 0 intro. intros zenon_H1ff zenon_H200. % 112.12/112.40 cut ((greater (low) (very_low)) = (greater (low) (high))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H1ff. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact assumption_18c. % 112.12/112.40 cut (((very_low) = (high))); [idtac | apply NNPP; zenon_intro zenon_H201]. % 112.12/112.40 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.12/112.40 congruence. % 112.12/112.40 apply zenon_H6a. apply refl_equal. % 112.12/112.40 exact (zenon_H201 zenon_H200). % 112.12/112.40 (* end of lemma zenon_L111_ *) % 112.12/112.40 assert (zenon_L112_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (forall Y : zenon_U, (~((greater (high) Y)/\(greater Y (high))))) -> ((very_low) = (high)) -> False). % 112.12/112.40 do 0 intro. intros zenon_H34 zenon_H202 zenon_H200. % 112.12/112.40 generalize (zenon_H202 (low)). zenon_intro zenon_H203. % 112.12/112.40 apply (zenon_notand_s _ _ zenon_H203); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H1ff ]. % 112.12/112.40 apply (zenon_L110_); trivial. % 112.12/112.40 apply (zenon_L111_); trivial. % 112.12/112.40 (* end of lemma zenon_L112_ *) % 112.12/112.40 assert (zenon_L113_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((very_low) = (high)) -> False). % 112.12/112.40 do 0 intro. intros zenon_H34 zenon_H200. % 112.12/112.40 generalize (meaning_postulate_greater_strict (high)). zenon_intro zenon_H202. % 112.12/112.40 apply (zenon_L112_); trivial. % 112.12/112.40 (* end of lemma zenon_L113_ *) % 112.12/112.40 assert (zenon_L114_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (low) (high))) -> (greater (very_low) (high)) -> False). % 112.12/112.40 do 0 intro. intros zenon_H34 zenon_H1ff zenon_H204. % 112.12/112.40 elim (classic ((~((low) = (very_low)))/\(~(greater (low) (very_low))))); [ zenon_intro zenon_H205 | zenon_intro zenon_H206 ]. % 112.12/112.40 apply (zenon_and_s _ _ zenon_H205). zenon_intro zenon_H207. zenon_intro zenon_Hff. % 112.12/112.40 exact (zenon_Hff assumption_18c). % 112.12/112.40 cut ((greater (very_low) (high)) = (greater (low) (high))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H1ff. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H204. % 112.12/112.40 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113]. % 112.12/112.40 cut (((very_low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H208]. % 112.12/112.40 congruence. % 112.12/112.40 apply (zenon_notand_s _ _ zenon_H206); [ zenon_intro zenon_H20a | zenon_intro zenon_H209 ]. % 112.12/112.40 apply zenon_H20a. zenon_intro zenon_H20b. % 112.12/112.40 elim (classic ((low) = (low))); [ zenon_intro zenon_H74 | zenon_intro zenon_H6a ]. % 112.12/112.40 cut (((low) = (low)) = ((very_low) = (low))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H208. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H74. % 112.12/112.40 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.12/112.40 cut (((low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H207]. % 112.12/112.40 congruence. % 112.12/112.40 exact (zenon_H207 zenon_H20b). % 112.12/112.40 apply zenon_H6a. apply refl_equal. % 112.12/112.40 apply zenon_H6a. apply refl_equal. % 112.12/112.40 apply zenon_H209. zenon_intro assumption_18c. % 112.12/112.40 generalize (zenon_H34 (low)). zenon_intro zenon_H7a. % 112.12/112.40 generalize (zenon_H7a (very_low)). zenon_intro zenon_H20c. % 112.12/112.40 generalize (zenon_H20c (high)). zenon_intro zenon_H20d. % 112.12/112.40 apply (zenon_imply_s _ _ zenon_H20d); [ zenon_intro zenon_Hff | zenon_intro zenon_H20e ]. % 112.12/112.40 exact (zenon_Hff assumption_18c). % 112.12/112.40 apply (zenon_imply_s _ _ zenon_H20e); [ zenon_intro zenon_H1ee | zenon_intro zenon_H20f ]. % 112.12/112.40 exact (zenon_H1ee zenon_H204). % 112.12/112.40 exact (zenon_H1ff zenon_H20f). % 112.12/112.40 apply zenon_H113. apply refl_equal. % 112.12/112.40 (* end of lemma zenon_L114_ *) % 112.12/112.40 assert (zenon_L115_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (forall Y : zenon_U, (~((greater (high) Y)/\(greater Y (high))))) -> (greater (very_low) (high)) -> False). % 112.12/112.40 do 0 intro. intros zenon_H34 zenon_H202 zenon_H204. % 112.12/112.40 generalize (zenon_H202 (low)). zenon_intro zenon_H203. % 112.12/112.40 apply (zenon_notand_s _ _ zenon_H203); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H1ff ]. % 112.12/112.40 apply (zenon_L110_); trivial. % 112.12/112.40 apply (zenon_L114_); trivial. % 112.12/112.40 (* end of lemma zenon_L115_ *) % 112.12/112.40 assert (zenon_L116_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (greater (very_low) (high)) -> False). % 112.12/112.40 do 0 intro. intros zenon_H34 zenon_H204. % 112.12/112.40 generalize (meaning_postulate_greater_strict (high)). zenon_intro zenon_H202. % 112.12/112.40 apply (zenon_L115_); trivial. % 112.12/112.40 (* end of lemma zenon_L116_ *) % 112.12/112.40 assert (zenon_L117_ : forall (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (forall Y : zenon_U, ((smaller (very_low) Y)\/(((very_low) = Y)\/(greater (very_low) Y)))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (high)) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (very_low)) -> False). % 112.12/112.40 do 1 intro. intros zenon_H34 zenon_H210 zenon_H116 zenon_H1e0. % 112.12/112.40 generalize (zenon_H210 (high)). zenon_intro zenon_H211. % 112.12/112.40 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H213 | zenon_intro zenon_H212 ]. % 112.12/112.40 generalize (definition_smaller (very_low)). zenon_intro zenon_H214. % 112.12/112.40 generalize (zenon_H214 (high)). zenon_intro zenon_H215. % 112.12/112.40 apply (zenon_equiv_s _ _ zenon_H215); [ zenon_intro zenon_H218; zenon_intro zenon_H217 | zenon_intro zenon_H213; zenon_intro zenon_H216 ]. % 112.12/112.40 exact (zenon_H218 zenon_H213). % 112.12/112.40 generalize (meaning_postulate_greater_strict (high)). zenon_intro zenon_H202. % 112.12/112.40 generalize (zenon_H202 (very_low)). zenon_intro zenon_H219. % 112.12/112.40 apply (zenon_notand_s _ _ zenon_H219); [ zenon_intro zenon_H217 | zenon_intro zenon_H1ee ]. % 112.12/112.40 exact (zenon_H217 zenon_H216). % 112.12/112.40 apply (zenon_L109_ zenon_TX_y); trivial. % 112.12/112.40 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H200 | zenon_intro zenon_H204 ]. % 112.12/112.40 apply (zenon_L113_); trivial. % 112.12/112.40 apply (zenon_L116_); trivial. % 112.12/112.40 (* end of lemma zenon_L117_ *) % 112.12/112.40 assert (zenon_L118_ : forall (zenon_TX_y : zenon_U), (((~(is_aligned zenon_TX_y zenon_E))/\(~(positional_advantage zenon_TX_y zenon_E)))->((hazard_of_mortality zenon_TX_y zenon_E) = (high))) -> (~(positional_advantage zenon_TX_y zenon_E)) -> (~(is_aligned zenon_TX_y zenon_E)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (very_low)) -> False). % 112.12/112.40 do 1 intro. intros zenon_H181 zenon_H182 zenon_H183 zenon_H34 zenon_H1e0. % 112.12/112.40 apply (zenon_imply_s _ _ zenon_H181); [ zenon_intro zenon_H184 | zenon_intro zenon_H116 ]. % 112.12/112.40 apply (zenon_notand_s _ _ zenon_H184); [ zenon_intro zenon_H186 | zenon_intro zenon_H185 ]. % 112.12/112.40 exact (zenon_H186 zenon_H183). % 112.12/112.40 exact (zenon_H185 zenon_H182). % 112.12/112.40 generalize (meaning_postulate_greater_comparable (very_low)). zenon_intro zenon_H210. % 112.12/112.40 apply (zenon_L117_ zenon_TX_y); trivial. % 112.12/112.40 (* end of lemma zenon_L118_ *) % 112.12/112.40 assert (zenon_L119_ : forall (zenon_TX_y : zenon_U), ((hazard_of_mortality zenon_TX_y zenon_E) = (mod1)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_E) (low))) -> False). % 112.12/112.40 do 1 intro. intros zenon_H21a zenon_H34 zenon_H1d6. % 112.12/112.40 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_E) = (mod1)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_E) (mod1))))); [ zenon_intro zenon_H21b | zenon_intro zenon_H21c ]. % 112.12/112.40 apply (zenon_and_s _ _ zenon_H21b). zenon_intro zenon_H21e. zenon_intro zenon_H21d. % 112.12/112.40 exact (zenon_H21e zenon_H21a). % 112.12/112.40 cut ((greater (mod1) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (low))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H1d6. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact assumption_18b. % 112.12/112.40 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.12/112.40 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 112.12/112.40 congruence. % 112.12/112.40 apply (zenon_notand_s _ _ zenon_H21c); [ zenon_intro zenon_H221 | zenon_intro zenon_H220 ]. % 112.12/112.40 apply zenon_H221. zenon_intro zenon_H21a. % 112.12/112.40 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H21f. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H11a. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 112.12/112.40 congruence. % 112.12/112.40 exact (zenon_H21e zenon_H21a). % 112.12/112.40 apply zenon_H11b. apply refl_equal. % 112.12/112.40 apply zenon_H11b. apply refl_equal. % 112.12/112.40 apply zenon_H220. zenon_intro zenon_H222. % 112.12/112.40 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H1d1. % 112.12/112.40 generalize (zenon_H1d1 (mod1)). zenon_intro zenon_H223. % 112.12/112.40 generalize (zenon_H223 (low)). zenon_intro zenon_H224. % 112.12/112.40 apply (zenon_imply_s _ _ zenon_H224); [ zenon_intro zenon_H21d | zenon_intro zenon_H225 ]. % 112.12/112.40 exact (zenon_H21d zenon_H222). % 112.12/112.40 apply (zenon_imply_s _ _ zenon_H225); [ zenon_intro zenon_H7f | zenon_intro zenon_H1de ]. % 112.12/112.40 exact (zenon_H7f assumption_18b). % 112.12/112.40 exact (zenon_H1d6 zenon_H1de). % 112.12/112.40 apply zenon_H6a. apply refl_equal. % 112.12/112.40 (* end of lemma zenon_L119_ *) % 112.12/112.40 assert (zenon_L120_ : forall (zenon_TX_y : zenon_U), ((hazard_of_mortality zenon_TX_y zenon_E) = (mod1)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (very_low) (very_low))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (very_low)) -> False). % 112.12/112.40 do 1 intro. intros zenon_H21a zenon_H34 zenon_H1df zenon_H1e0. % 112.12/112.40 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e2 ]. % 112.12/112.40 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (very_low))); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H1e4 ]. % 112.12/112.40 cut ((greater (hazard_of_mortality zenon_TX_y zenon_E) (very_low)) = (greater (very_low) (very_low))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H1df. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H1e3. % 112.12/112.40 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 112.12/112.40 congruence. % 112.12/112.40 elim (classic ((very_low) = (very_low))); [ zenon_intro zenon_H1e6 | zenon_intro zenon_Hf5 ]. % 112.12/112.40 cut (((very_low) = (very_low)) = ((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H1e5. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H1e6. % 112.12/112.40 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 112.12/112.40 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1e2]. % 112.12/112.40 congruence. % 112.12/112.40 exact (zenon_H1e2 zenon_H1e1). % 112.12/112.40 apply zenon_Hf5. apply refl_equal. % 112.12/112.40 apply zenon_Hf5. apply refl_equal. % 112.12/112.40 apply zenon_Hf5. apply refl_equal. % 112.12/112.40 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_E) = (low)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_E) (low))))); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H1e8 ]. % 112.12/112.40 apply (zenon_and_s _ _ zenon_H1e7). zenon_intro zenon_H1bb. zenon_intro zenon_H1d6. % 112.12/112.40 apply (zenon_L119_ zenon_TX_y); trivial. % 112.12/112.40 cut ((greater (low) (very_low)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (very_low))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H1e4. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact assumption_18c. % 112.12/112.40 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 112.12/112.40 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba]. % 112.12/112.40 congruence. % 112.12/112.40 apply (zenon_notand_s _ _ zenon_H1e8); [ zenon_intro zenon_H1ea | zenon_intro zenon_H1e9 ]. % 112.12/112.40 apply zenon_H1ea. zenon_intro zenon_H1b8. % 112.12/112.40 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((low) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H1ba. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H11a. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 112.12/112.40 congruence. % 112.12/112.40 exact (zenon_H1bb zenon_H1b8). % 112.12/112.40 apply zenon_H11b. apply refl_equal. % 112.12/112.40 apply zenon_H11b. apply refl_equal. % 112.12/112.40 apply zenon_H1e9. zenon_intro zenon_H1de. % 112.12/112.40 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H1d1. % 112.12/112.40 generalize (zenon_H1d1 (low)). zenon_intro zenon_H1eb. % 112.12/112.40 generalize (zenon_H1eb (very_low)). zenon_intro zenon_H1ec. % 112.12/112.40 apply (zenon_imply_s _ _ zenon_H1ec); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H1ed ]. % 112.12/112.40 exact (zenon_H1d6 zenon_H1de). % 112.12/112.40 apply (zenon_imply_s _ _ zenon_H1ed); [ zenon_intro zenon_Hff | zenon_intro zenon_H1e3 ]. % 112.12/112.40 exact (zenon_Hff assumption_18c). % 112.12/112.40 exact (zenon_H1e4 zenon_H1e3). % 112.12/112.40 apply zenon_Hf5. apply refl_equal. % 112.12/112.40 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H1e2. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H11a. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 112.12/112.40 congruence. % 112.12/112.40 exact (zenon_H1e5 zenon_H1e0). % 112.12/112.40 apply zenon_H11b. apply refl_equal. % 112.12/112.40 apply zenon_H11b. apply refl_equal. % 112.12/112.40 (* end of lemma zenon_L120_ *) % 112.12/112.40 assert (zenon_L121_ : forall (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (low) (low))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (mod1)) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (very_low)) -> False). % 112.12/112.40 do 1 intro. intros zenon_H34 zenon_H6c zenon_H21a zenon_H1e0. % 112.12/112.40 elim (classic (greater (very_low) (low))); [ zenon_intro zenon_H226 | zenon_intro zenon_H227 ]. % 112.12/112.40 generalize (zenon_H34 (low)). zenon_intro zenon_H7a. % 112.12/112.40 generalize (zenon_H7a (very_low)). zenon_intro zenon_H20c. % 112.12/112.40 generalize (zenon_H20c (low)). zenon_intro zenon_H228. % 112.12/112.40 apply (zenon_imply_s _ _ zenon_H228); [ zenon_intro zenon_Hff | zenon_intro zenon_H229 ]. % 112.12/112.40 exact (zenon_Hff assumption_18c). % 112.12/112.40 apply (zenon_imply_s _ _ zenon_H229); [ zenon_intro zenon_H227 | zenon_intro zenon_H7e ]. % 112.12/112.40 exact (zenon_H227 zenon_H226). % 112.12/112.40 exact (zenon_H6c zenon_H7e). % 112.12/112.40 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e2 ]. % 112.12/112.40 elim (classic (greater (very_low) (very_low))); [ zenon_intro zenon_H1ef | zenon_intro zenon_H1df ]. % 112.12/112.40 elim (classic (greater (very_low) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H1f1 ]. % 112.12/112.40 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (low))); [ zenon_intro zenon_H1de | zenon_intro zenon_H1d6 ]. % 112.12/112.40 generalize (zenon_H34 (very_low)). zenon_intro zenon_H22a. % 112.12/112.40 generalize (zenon_H22a (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H22b. % 112.12/112.40 generalize (zenon_H22b (low)). zenon_intro zenon_H22c. % 112.12/112.40 apply (zenon_imply_s _ _ zenon_H22c); [ zenon_intro zenon_H1f1 | zenon_intro zenon_H22d ]. % 112.12/112.40 exact (zenon_H1f1 zenon_H1f0). % 112.12/112.40 apply (zenon_imply_s _ _ zenon_H22d); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H226 ]. % 112.12/112.40 exact (zenon_H1d6 zenon_H1de). % 112.12/112.40 exact (zenon_H227 zenon_H226). % 112.12/112.40 apply (zenon_L119_ zenon_TX_y); trivial. % 112.12/112.40 cut ((greater (very_low) (very_low)) = (greater (very_low) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H1f1. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H1ef. % 112.12/112.40 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1e2]. % 112.12/112.40 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 112.12/112.40 congruence. % 112.12/112.40 apply zenon_Hf5. apply refl_equal. % 112.12/112.40 exact (zenon_H1e2 zenon_H1e1). % 112.12/112.40 apply (zenon_L120_ zenon_TX_y); trivial. % 112.12/112.40 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H1e2. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H11a. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 112.12/112.40 congruence. % 112.12/112.40 exact (zenon_H1e5 zenon_H1e0). % 112.12/112.40 apply zenon_H11b. apply refl_equal. % 112.12/112.40 apply zenon_H11b. apply refl_equal. % 112.12/112.40 (* end of lemma zenon_L121_ *) % 112.12/112.40 assert (zenon_L122_ : forall (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (mod1)) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (very_low)) -> False). % 112.12/112.40 do 1 intro. intros zenon_H34 zenon_H21a zenon_H1e0. % 112.12/112.40 generalize (meaning_postulate_greater_strict (low)). zenon_intro zenon_H80. % 112.12/112.40 generalize (zenon_H80 (low)). zenon_intro zenon_H81. % 112.12/112.40 apply (zenon_notand_s _ _ zenon_H81); [ zenon_intro zenon_H6c | zenon_intro zenon_H6c ]. % 112.12/112.40 apply (zenon_L121_ zenon_TX_y); trivial. % 112.12/112.40 apply (zenon_L121_ zenon_TX_y); trivial. % 112.12/112.40 (* end of lemma zenon_L122_ *) % 112.12/112.40 assert (zenon_L123_ : forall (zenon_TX_y : zenon_U), ((hazard_of_mortality zenon_TX_y zenon_E) = (mod2)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_E) (low))) -> False). % 112.12/112.40 do 1 intro. intros zenon_H19e zenon_H34 zenon_H1d6. % 112.12/112.40 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_E) = (mod2)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_E) (mod2))))); [ zenon_intro zenon_H1d7 | zenon_intro zenon_H1d8 ]. % 112.12/112.40 apply (zenon_and_s _ _ zenon_H1d7). zenon_intro zenon_H1a2. zenon_intro zenon_H1ca. % 112.12/112.40 exact (zenon_H1a2 zenon_H19e). % 112.12/112.40 cut ((greater (mod2) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (low))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H1d6. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact assumption_18e. % 112.12/112.40 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.12/112.40 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 112.12/112.40 congruence. % 112.12/112.40 apply (zenon_notand_s _ _ zenon_H1d8); [ zenon_intro zenon_H1da | zenon_intro zenon_H1d9 ]. % 112.12/112.40 apply zenon_H1da. zenon_intro zenon_H19e. % 112.12/112.40 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.40 intro zenon_D_pnotp. % 112.12/112.40 apply zenon_H1a1. % 112.12/112.40 rewrite <- zenon_D_pnotp. % 112.12/112.40 exact zenon_H11a. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.40 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 112.12/112.40 congruence. % 112.12/112.40 exact (zenon_H1a2 zenon_H19e). % 112.12/112.41 apply zenon_H11b. apply refl_equal. % 112.12/112.41 apply zenon_H11b. apply refl_equal. % 112.12/112.41 apply zenon_H1d9. zenon_intro zenon_H1d5. % 112.12/112.41 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H1d1. % 112.12/112.41 generalize (zenon_H1d1 (mod2)). zenon_intro zenon_H1db. % 112.12/112.41 generalize (zenon_H1db (low)). zenon_intro zenon_H1dc. % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H1dc); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1dd ]. % 112.12/112.41 exact (zenon_H1ca zenon_H1d5). % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H1dd); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H1de ]. % 112.12/112.41 exact (zenon_Hc2 assumption_18e). % 112.12/112.41 exact (zenon_H1d6 zenon_H1de). % 112.12/112.41 apply zenon_H6a. apply refl_equal. % 112.12/112.41 (* end of lemma zenon_L123_ *) % 112.12/112.41 assert (zenon_L124_ : forall (zenon_TX_y : zenon_U), ((hazard_of_mortality zenon_TX_y zenon_E) = (mod2)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (very_low) (very_low))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (very_low)) -> False). % 112.12/112.41 do 1 intro. intros zenon_H19e zenon_H34 zenon_H1df zenon_H1e0. % 112.12/112.41 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e2 ]. % 112.12/112.41 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (very_low))); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H1e4 ]. % 112.12/112.41 cut ((greater (hazard_of_mortality zenon_TX_y zenon_E) (very_low)) = (greater (very_low) (very_low))). % 112.12/112.41 intro zenon_D_pnotp. % 112.12/112.41 apply zenon_H1df. % 112.12/112.41 rewrite <- zenon_D_pnotp. % 112.12/112.41 exact zenon_H1e3. % 112.12/112.41 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 112.12/112.41 congruence. % 112.12/112.41 elim (classic ((very_low) = (very_low))); [ zenon_intro zenon_H1e6 | zenon_intro zenon_Hf5 ]. % 112.12/112.41 cut (((very_low) = (very_low)) = ((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))). % 112.12/112.41 intro zenon_D_pnotp. % 112.12/112.41 apply zenon_H1e5. % 112.12/112.41 rewrite <- zenon_D_pnotp. % 112.12/112.41 exact zenon_H1e6. % 112.12/112.41 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 112.12/112.41 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1e2]. % 112.12/112.41 congruence. % 112.12/112.41 exact (zenon_H1e2 zenon_H1e1). % 112.12/112.41 apply zenon_Hf5. apply refl_equal. % 112.12/112.41 apply zenon_Hf5. apply refl_equal. % 112.12/112.41 apply zenon_Hf5. apply refl_equal. % 112.12/112.41 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_E) = (low)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_E) (low))))); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H1e8 ]. % 112.12/112.41 apply (zenon_and_s _ _ zenon_H1e7). zenon_intro zenon_H1bb. zenon_intro zenon_H1d6. % 112.12/112.41 apply (zenon_L123_ zenon_TX_y); trivial. % 112.12/112.41 cut ((greater (low) (very_low)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (very_low))). % 112.12/112.41 intro zenon_D_pnotp. % 112.12/112.41 apply zenon_H1e4. % 112.12/112.41 rewrite <- zenon_D_pnotp. % 112.12/112.41 exact assumption_18c. % 112.12/112.41 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 112.12/112.41 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba]. % 112.12/112.41 congruence. % 112.12/112.41 apply (zenon_notand_s _ _ zenon_H1e8); [ zenon_intro zenon_H1ea | zenon_intro zenon_H1e9 ]. % 112.12/112.41 apply zenon_H1ea. zenon_intro zenon_H1b8. % 112.12/112.41 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((low) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.41 intro zenon_D_pnotp. % 112.12/112.41 apply zenon_H1ba. % 112.12/112.41 rewrite <- zenon_D_pnotp. % 112.12/112.41 exact zenon_H11a. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 112.12/112.41 congruence. % 112.12/112.41 exact (zenon_H1bb zenon_H1b8). % 112.12/112.41 apply zenon_H11b. apply refl_equal. % 112.12/112.41 apply zenon_H11b. apply refl_equal. % 112.12/112.41 apply zenon_H1e9. zenon_intro zenon_H1de. % 112.12/112.41 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H1d1. % 112.12/112.41 generalize (zenon_H1d1 (low)). zenon_intro zenon_H1eb. % 112.12/112.41 generalize (zenon_H1eb (very_low)). zenon_intro zenon_H1ec. % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H1ec); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H1ed ]. % 112.12/112.41 exact (zenon_H1d6 zenon_H1de). % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H1ed); [ zenon_intro zenon_Hff | zenon_intro zenon_H1e3 ]. % 112.12/112.41 exact (zenon_Hff assumption_18c). % 112.12/112.41 exact (zenon_H1e4 zenon_H1e3). % 112.12/112.41 apply zenon_Hf5. apply refl_equal. % 112.12/112.41 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.41 intro zenon_D_pnotp. % 112.12/112.41 apply zenon_H1e2. % 112.12/112.41 rewrite <- zenon_D_pnotp. % 112.12/112.41 exact zenon_H11a. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 112.12/112.41 congruence. % 112.12/112.41 exact (zenon_H1e5 zenon_H1e0). % 112.12/112.41 apply zenon_H11b. apply refl_equal. % 112.12/112.41 apply zenon_H11b. apply refl_equal. % 112.12/112.41 (* end of lemma zenon_L124_ *) % 112.12/112.41 assert (zenon_L125_ : forall (zenon_TX_y : zenon_U), ((hazard_of_mortality zenon_TX_y zenon_E) = (mod2)) -> (~(greater (very_low) (low))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (very_low)) -> False). % 112.12/112.41 do 1 intro. intros zenon_H19e zenon_H227 zenon_H34 zenon_H1e0. % 112.12/112.41 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e2 ]. % 112.12/112.41 elim (classic (greater (very_low) (very_low))); [ zenon_intro zenon_H1ef | zenon_intro zenon_H1df ]. % 112.12/112.41 elim (classic (greater (very_low) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H1f1 ]. % 112.12/112.41 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (low))); [ zenon_intro zenon_H1de | zenon_intro zenon_H1d6 ]. % 112.12/112.41 generalize (zenon_H34 (very_low)). zenon_intro zenon_H22a. % 112.12/112.41 generalize (zenon_H22a (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H22b. % 112.12/112.41 generalize (zenon_H22b (low)). zenon_intro zenon_H22c. % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H22c); [ zenon_intro zenon_H1f1 | zenon_intro zenon_H22d ]. % 112.12/112.41 exact (zenon_H1f1 zenon_H1f0). % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H22d); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H226 ]. % 112.12/112.41 exact (zenon_H1d6 zenon_H1de). % 112.12/112.41 exact (zenon_H227 zenon_H226). % 112.12/112.41 apply (zenon_L123_ zenon_TX_y); trivial. % 112.12/112.41 cut ((greater (very_low) (very_low)) = (greater (very_low) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.41 intro zenon_D_pnotp. % 112.12/112.41 apply zenon_H1f1. % 112.12/112.41 rewrite <- zenon_D_pnotp. % 112.12/112.41 exact zenon_H1ef. % 112.12/112.41 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1e2]. % 112.12/112.41 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 112.12/112.41 congruence. % 112.12/112.41 apply zenon_Hf5. apply refl_equal. % 112.12/112.41 exact (zenon_H1e2 zenon_H1e1). % 112.12/112.41 apply (zenon_L124_ zenon_TX_y); trivial. % 112.12/112.41 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.41 intro zenon_D_pnotp. % 112.12/112.41 apply zenon_H1e2. % 112.12/112.41 rewrite <- zenon_D_pnotp. % 112.12/112.41 exact zenon_H11a. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 112.12/112.41 congruence. % 112.12/112.41 exact (zenon_H1e5 zenon_H1e0). % 112.12/112.41 apply zenon_H11b. apply refl_equal. % 112.12/112.41 apply zenon_H11b. apply refl_equal. % 112.12/112.41 (* end of lemma zenon_L125_ *) % 112.12/112.41 assert (zenon_L126_ : forall (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (very_low)) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (mod2)) -> False). % 112.12/112.41 do 1 intro. intros zenon_H34 zenon_H1e0 zenon_H19e. % 112.12/112.41 generalize (meaning_postulate_greater_strict (low)). zenon_intro zenon_H80. % 112.12/112.41 generalize (zenon_H80 (very_low)). zenon_intro zenon_H22e. % 112.12/112.41 apply (zenon_notand_s _ _ zenon_H22e); [ zenon_intro zenon_Hff | zenon_intro zenon_H227 ]. % 112.12/112.41 exact (zenon_Hff assumption_18c). % 112.12/112.41 apply (zenon_L125_ zenon_TX_y); trivial. % 112.12/112.41 (* end of lemma zenon_L126_ *) % 112.12/112.41 assert (zenon_L127_ : forall (zenon_TX_y : zenon_U), ((hazard_of_mortality zenon_TX_y zenon_E) = (low)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (very_low) (very_low))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (very_low)) -> False). % 112.12/112.41 do 1 intro. intros zenon_H1b8 zenon_H34 zenon_H1df zenon_H1e0. % 112.12/112.41 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e2 ]. % 112.12/112.41 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (very_low))); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H1e4 ]. % 112.12/112.41 cut ((greater (hazard_of_mortality zenon_TX_y zenon_E) (very_low)) = (greater (very_low) (very_low))). % 112.12/112.41 intro zenon_D_pnotp. % 112.12/112.41 apply zenon_H1df. % 112.12/112.41 rewrite <- zenon_D_pnotp. % 112.12/112.41 exact zenon_H1e3. % 112.12/112.41 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 112.12/112.41 congruence. % 112.12/112.41 elim (classic ((very_low) = (very_low))); [ zenon_intro zenon_H1e6 | zenon_intro zenon_Hf5 ]. % 112.12/112.41 cut (((very_low) = (very_low)) = ((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))). % 112.12/112.41 intro zenon_D_pnotp. % 112.12/112.41 apply zenon_H1e5. % 112.12/112.41 rewrite <- zenon_D_pnotp. % 112.12/112.41 exact zenon_H1e6. % 112.12/112.41 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 112.12/112.41 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1e2]. % 112.12/112.41 congruence. % 112.12/112.41 exact (zenon_H1e2 zenon_H1e1). % 112.12/112.41 apply zenon_Hf5. apply refl_equal. % 112.12/112.41 apply zenon_Hf5. apply refl_equal. % 112.12/112.41 apply zenon_Hf5. apply refl_equal. % 112.12/112.41 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_E) = (low)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_E) (low))))); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H1e8 ]. % 112.12/112.41 apply (zenon_and_s _ _ zenon_H1e7). zenon_intro zenon_H1bb. zenon_intro zenon_H1d6. % 112.12/112.41 exact (zenon_H1bb zenon_H1b8). % 112.12/112.41 cut ((greater (low) (very_low)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (very_low))). % 112.12/112.41 intro zenon_D_pnotp. % 112.12/112.41 apply zenon_H1e4. % 112.12/112.41 rewrite <- zenon_D_pnotp. % 112.12/112.41 exact assumption_18c. % 112.12/112.41 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 112.12/112.41 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba]. % 112.12/112.41 congruence. % 112.12/112.41 apply (zenon_notand_s _ _ zenon_H1e8); [ zenon_intro zenon_H1ea | zenon_intro zenon_H1e9 ]. % 112.12/112.41 apply zenon_H1ea. zenon_intro zenon_H1b8. % 112.12/112.41 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((low) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.41 intro zenon_D_pnotp. % 112.12/112.41 apply zenon_H1ba. % 112.12/112.41 rewrite <- zenon_D_pnotp. % 112.12/112.41 exact zenon_H11a. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 112.12/112.41 congruence. % 112.12/112.41 exact (zenon_H1bb zenon_H1b8). % 112.12/112.41 apply zenon_H11b. apply refl_equal. % 112.12/112.41 apply zenon_H11b. apply refl_equal. % 112.12/112.41 apply zenon_H1e9. zenon_intro zenon_H1de. % 112.12/112.41 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H1d1. % 112.12/112.41 generalize (zenon_H1d1 (low)). zenon_intro zenon_H1eb. % 112.12/112.41 generalize (zenon_H1eb (very_low)). zenon_intro zenon_H1ec. % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H1ec); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H1ed ]. % 112.12/112.41 exact (zenon_H1d6 zenon_H1de). % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H1ed); [ zenon_intro zenon_Hff | zenon_intro zenon_H1e3 ]. % 112.12/112.41 exact (zenon_Hff assumption_18c). % 112.12/112.41 exact (zenon_H1e4 zenon_H1e3). % 112.12/112.41 apply zenon_Hf5. apply refl_equal. % 112.12/112.41 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.41 intro zenon_D_pnotp. % 112.12/112.41 apply zenon_H1e2. % 112.12/112.41 rewrite <- zenon_D_pnotp. % 112.12/112.41 exact zenon_H11a. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 112.12/112.41 congruence. % 112.12/112.41 exact (zenon_H1e5 zenon_H1e0). % 112.12/112.41 apply zenon_H11b. apply refl_equal. % 112.12/112.41 apply zenon_H11b. apply refl_equal. % 112.12/112.41 (* end of lemma zenon_L127_ *) % 112.12/112.41 assert (zenon_L128_ : forall (zenon_TX_y : zenon_U), ((hazard_of_mortality zenon_TX_y zenon_E) = (low)) -> (~(greater (very_low) (low))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (very_low)) -> False). % 112.12/112.41 do 1 intro. intros zenon_H1b8 zenon_H227 zenon_H34 zenon_H1e0. % 112.12/112.41 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e2 ]. % 112.12/112.41 elim (classic (greater (very_low) (very_low))); [ zenon_intro zenon_H1ef | zenon_intro zenon_H1df ]. % 112.12/112.41 elim (classic (greater (very_low) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H1f1 ]. % 112.12/112.41 cut ((greater (very_low) (hazard_of_mortality zenon_TX_y zenon_E)) = (greater (very_low) (low))). % 112.12/112.41 intro zenon_D_pnotp. % 112.12/112.41 apply zenon_H227. % 112.12/112.41 rewrite <- zenon_D_pnotp. % 112.12/112.41 exact zenon_H1f0. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 112.12/112.41 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 112.12/112.41 congruence. % 112.12/112.41 apply zenon_Hf5. apply refl_equal. % 112.12/112.41 exact (zenon_H1bb zenon_H1b8). % 112.12/112.41 cut ((greater (very_low) (very_low)) = (greater (very_low) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.41 intro zenon_D_pnotp. % 112.12/112.41 apply zenon_H1f1. % 112.12/112.41 rewrite <- zenon_D_pnotp. % 112.12/112.41 exact zenon_H1ef. % 112.12/112.41 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1e2]. % 112.12/112.41 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 112.12/112.41 congruence. % 112.12/112.41 apply zenon_Hf5. apply refl_equal. % 112.12/112.41 exact (zenon_H1e2 zenon_H1e1). % 112.12/112.41 apply (zenon_L127_ zenon_TX_y); trivial. % 112.12/112.41 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.41 intro zenon_D_pnotp. % 112.12/112.41 apply zenon_H1e2. % 112.12/112.41 rewrite <- zenon_D_pnotp. % 112.12/112.41 exact zenon_H11a. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 112.12/112.41 congruence. % 112.12/112.41 exact (zenon_H1e5 zenon_H1e0). % 112.12/112.41 apply zenon_H11b. apply refl_equal. % 112.12/112.41 apply zenon_H11b. apply refl_equal. % 112.12/112.41 (* end of lemma zenon_L128_ *) % 112.12/112.41 assert (zenon_L129_ : forall (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (very_low)) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (low)) -> False). % 112.12/112.41 do 1 intro. intros zenon_H34 zenon_H1e0 zenon_H1b8. % 112.12/112.41 generalize (meaning_postulate_greater_strict (low)). zenon_intro zenon_H80. % 112.12/112.41 generalize (zenon_H80 (very_low)). zenon_intro zenon_H22e. % 112.12/112.41 apply (zenon_notand_s _ _ zenon_H22e); [ zenon_intro zenon_Hff | zenon_intro zenon_H227 ]. % 112.12/112.41 exact (zenon_Hff assumption_18c). % 112.12/112.41 apply (zenon_L128_ zenon_TX_y); trivial. % 112.12/112.41 (* end of lemma zenon_L129_ *) % 112.12/112.41 assert (zenon_L130_ : forall (zenon_TX_y : zenon_U), ((((is_aligned zenon_TX_y zenon_E)/\(positional_advantage zenon_TX_y zenon_E))->((hazard_of_mortality zenon_TX_y zenon_E) = (low)))/\((((~(is_aligned zenon_TX_y zenon_E))/\(positional_advantage zenon_TX_y zenon_E))->((hazard_of_mortality zenon_TX_y zenon_E) = (mod1)))/\((((is_aligned zenon_TX_y zenon_E)/\(~(positional_advantage zenon_TX_y zenon_E)))->((hazard_of_mortality zenon_TX_y zenon_E) = (mod2)))/\(((~(is_aligned zenon_TX_y zenon_E))/\(~(positional_advantage zenon_TX_y zenon_E)))->((hazard_of_mortality zenon_TX_y zenon_E) = (high)))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (very_low)) -> False). % 112.12/112.41 do 1 intro. intros zenon_H22f zenon_H34 zenon_H1e0. % 112.12/112.41 apply (zenon_and_s _ _ zenon_H22f). zenon_intro zenon_H231. zenon_intro zenon_H230. % 112.12/112.41 apply (zenon_and_s _ _ zenon_H230). zenon_intro zenon_H233. zenon_intro zenon_H232. % 112.12/112.41 apply (zenon_and_s _ _ zenon_H232). zenon_intro zenon_H234. zenon_intro zenon_H181. % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H231); [ zenon_intro zenon_H235 | zenon_intro zenon_H1b8 ]. % 112.12/112.41 apply (zenon_notand_s _ _ zenon_H235); [ zenon_intro zenon_H183 | zenon_intro zenon_H182 ]. % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H233); [ zenon_intro zenon_H236 | zenon_intro zenon_H21a ]. % 112.12/112.41 apply (zenon_notand_s _ _ zenon_H236); [ zenon_intro zenon_H186 | zenon_intro zenon_H182 ]. % 112.12/112.41 exact (zenon_H186 zenon_H183). % 112.12/112.41 apply (zenon_L118_ zenon_TX_y); trivial. % 112.12/112.41 apply (zenon_L122_ zenon_TX_y); trivial. % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H234); [ zenon_intro zenon_H237 | zenon_intro zenon_H19e ]. % 112.12/112.41 apply (zenon_notand_s _ _ zenon_H237); [ zenon_intro zenon_H183 | zenon_intro zenon_H185 ]. % 112.12/112.41 apply (zenon_L118_ zenon_TX_y); trivial. % 112.12/112.41 exact (zenon_H185 zenon_H182). % 112.12/112.41 apply (zenon_L126_ zenon_TX_y); trivial. % 112.12/112.41 apply (zenon_L129_ zenon_TX_y); trivial. % 112.12/112.41 (* end of lemma zenon_L130_ *) % 112.12/112.41 assert (zenon_L131_ : forall (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((~(has_immunity zenon_TX_y zenon_E))->((((is_aligned zenon_TX_y zenon_E)/\(positional_advantage zenon_TX_y zenon_E))->((hazard_of_mortality zenon_TX_y zenon_E) = (low)))/\((((~(is_aligned zenon_TX_y zenon_E))/\(positional_advantage zenon_TX_y zenon_E))->((hazard_of_mortality zenon_TX_y zenon_E) = (mod1)))/\((((is_aligned zenon_TX_y zenon_E)/\(~(positional_advantage zenon_TX_y zenon_E)))->((hazard_of_mortality zenon_TX_y zenon_E) = (mod2)))/\(((~(is_aligned zenon_TX_y zenon_E))/\(~(positional_advantage zenon_TX_y zenon_E)))->((hazard_of_mortality zenon_TX_y zenon_E) = (high))))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (very_low)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (organization zenon_TX_y) -> False). % 112.12/112.41 do 1 intro. intros zenon_H34 zenon_H238 zenon_H1e0 zenon_H1a zenon_H1f. % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H238); [ zenon_intro zenon_H111 | zenon_intro zenon_H22f ]. % 112.12/112.41 apply (zenon_L105_ zenon_TX_y); trivial. % 112.12/112.41 apply (zenon_L130_ zenon_TX_y); trivial. % 112.12/112.41 (* end of lemma zenon_L131_ *) % 112.12/112.41 assert (zenon_L132_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (greater (tau) (sigma)) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> False). % 112.12/112.41 do 4 intro. intros zenon_H34 zenon_H187 zenon_H17c zenon_H37 zenon_H38 zenon_Hf3 zenon_H148 zenon_H35 zenon_H123 zenon_H1a zenon_Hec zenon_H1f. % 112.12/112.41 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0. % 112.12/112.41 generalize (zenon_H0 zenon_E). zenon_intro zenon_H239. % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H239); [ zenon_intro zenon_H27 | zenon_intro zenon_H23a ]. % 112.12/112.41 exact (zenon_H27 zenon_H1f). % 112.12/112.41 apply (zenon_and_s _ _ zenon_H23a). zenon_intro zenon_H23b. zenon_intro zenon_H238. % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H23b); [ zenon_intro zenon_H112 | zenon_intro zenon_H1e0 ]. % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H238); [ zenon_intro zenon_H111 | zenon_intro zenon_H22f ]. % 112.12/112.41 exact (zenon_H111 zenon_H112). % 112.12/112.41 apply (zenon_and_s _ _ zenon_H22f). zenon_intro zenon_H231. zenon_intro zenon_H230. % 112.12/112.41 apply (zenon_and_s _ _ zenon_H230). zenon_intro zenon_H233. zenon_intro zenon_H232. % 112.12/112.41 apply (zenon_and_s _ _ zenon_H232). zenon_intro zenon_H234. zenon_intro zenon_H181. % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H231); [ zenon_intro zenon_H235 | zenon_intro zenon_H1b8 ]. % 112.12/112.41 apply (zenon_notand_s _ _ zenon_H235); [ zenon_intro zenon_H183 | zenon_intro zenon_H182 ]. % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H233); [ zenon_intro zenon_H236 | zenon_intro zenon_H21a ]. % 112.12/112.41 apply (zenon_notand_s _ _ zenon_H236); [ zenon_intro zenon_H186 | zenon_intro zenon_H182 ]. % 112.12/112.41 exact (zenon_H186 zenon_H183). % 112.12/112.41 apply (zenon_L76_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.41 elim (classic ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H23c | zenon_intro zenon_H21f ]. % 112.12/112.41 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))); [ zenon_intro zenon_H19c | zenon_intro zenon_H194 ]. % 112.12/112.41 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1a5 ]. % 112.12/112.41 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H17e | zenon_intro zenon_H117 ]. % 112.12/112.41 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.12/112.41 generalize (zenon_H18f (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H23d. % 112.12/112.41 generalize (zenon_H23d (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H23e. % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H23f ]. % 112.12/112.41 exact (zenon_H1a5 zenon_H1a4). % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H23f); [ zenon_intro zenon_H117 | zenon_intro zenon_H240 ]. % 112.12/112.41 exact (zenon_H117 zenon_H17e). % 112.12/112.41 exact (zenon_H17c zenon_H240). % 112.12/112.41 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H241 | zenon_intro zenon_H193 ]. % 112.12/112.41 cut ((greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.41 intro zenon_D_pnotp. % 112.12/112.41 apply zenon_H117. % 112.12/112.41 rewrite <- zenon_D_pnotp. % 112.12/112.41 exact zenon_H241. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.41 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 112.12/112.41 congruence. % 112.12/112.41 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.41 intro zenon_D_pnotp. % 112.12/112.41 apply zenon_H21f. % 112.12/112.41 rewrite <- zenon_D_pnotp. % 112.12/112.41 exact zenon_H11a. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 112.12/112.41 congruence. % 112.12/112.41 exact (zenon_H21e zenon_H21a). % 112.12/112.41 apply zenon_H11b. apply refl_equal. % 112.12/112.41 apply zenon_H11b. apply refl_equal. % 112.12/112.41 apply zenon_H62. apply refl_equal. % 112.12/112.41 apply (zenon_L79_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.41 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.41 intro zenon_D_pnotp. % 112.12/112.41 apply zenon_H1a5. % 112.12/112.41 rewrite <- zenon_D_pnotp. % 112.12/112.41 exact zenon_H19c. % 112.12/112.41 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.41 congruence. % 112.12/112.41 apply zenon_H16a. apply refl_equal. % 112.12/112.41 exact (zenon_H21f zenon_H23c). % 112.12/112.41 apply (zenon_L80_ zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.41 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.41 intro zenon_D_pnotp. % 112.12/112.41 apply zenon_H21f. % 112.12/112.41 rewrite <- zenon_D_pnotp. % 112.12/112.41 exact zenon_H11a. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 112.12/112.41 congruence. % 112.12/112.41 exact (zenon_H21e zenon_H21a). % 112.12/112.41 apply zenon_H11b. apply refl_equal. % 112.12/112.41 apply zenon_H11b. apply refl_equal. % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H234); [ zenon_intro zenon_H237 | zenon_intro zenon_H19e ]. % 112.12/112.41 apply (zenon_notand_s _ _ zenon_H237); [ zenon_intro zenon_H183 | zenon_intro zenon_H185 ]. % 112.12/112.41 apply (zenon_L76_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.41 exact (zenon_H185 zenon_H182). % 112.12/112.41 apply (zenon_L85_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.41 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1a5 ]. % 112.12/112.41 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1a9 ]. % 112.12/112.41 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.41 intro zenon_D_pnotp. % 112.12/112.41 apply zenon_H17c. % 112.12/112.41 rewrite <- zenon_D_pnotp. % 112.12/112.41 exact zenon_H1b1. % 112.12/112.41 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.41 congruence. % 112.12/112.41 apply zenon_H16a. apply refl_equal. % 112.12/112.41 apply (zenon_L99_ zenon_TT2_la zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.41 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))). % 112.12/112.41 intro zenon_D_pnotp. % 112.12/112.41 apply zenon_H1a9. % 112.12/112.41 rewrite <- zenon_D_pnotp. % 112.12/112.41 exact zenon_H1a4. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.41 congruence. % 112.12/112.41 apply zenon_H16a. apply refl_equal. % 112.12/112.41 exact (zenon_H1bb zenon_H1b8). % 112.12/112.41 apply (zenon_L104_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.41 apply (zenon_L131_ zenon_TX_y); trivial. % 112.12/112.41 (* end of lemma zenon_L132_ *) % 112.12/112.41 assert (zenon_L133_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (greater (tau) (sigma)) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> False). % 112.12/112.41 do 4 intro. intros zenon_H34 zenon_H1f zenon_Hec zenon_H1a zenon_H123 zenon_H35 zenon_H148 zenon_H38 zenon_H37 zenon_H17c zenon_H187. % 112.12/112.41 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3. % 112.12/112.41 apply (zenon_L132_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.41 (* end of lemma zenon_L133_ *) % 112.12/112.41 assert (zenon_L134_ : forall (zenon_TT2_la : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (greater (tau) (sigma)) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> False). % 112.12/112.41 do 4 intro. intros zenon_H34 zenon_Had zenon_H1f zenon_Hec zenon_H1a zenon_H123 zenon_H35 zenon_H148 zenon_H38 zenon_H37 zenon_H17c. % 112.12/112.41 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H242 | zenon_intro zenon_H187 ]. % 112.12/112.41 cut ((greater (low) (very_low)) = (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.41 intro zenon_D_pnotp. % 112.12/112.41 apply zenon_Had. % 112.12/112.41 rewrite <- zenon_D_pnotp. % 112.12/112.41 exact assumption_18c. % 112.12/112.41 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H187]. % 112.12/112.41 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.12/112.41 congruence. % 112.12/112.41 apply zenon_H6a. apply refl_equal. % 112.12/112.41 exact (zenon_H187 zenon_H242). % 112.12/112.41 apply (zenon_L133_ zenon_TT1_bg zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.41 (* end of lemma zenon_L134_ *) % 112.12/112.41 assert (zenon_L135_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (greater (tau) (sigma)) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> False). % 112.12/112.41 do 4 intro. intros zenon_H34 zenon_H193 zenon_H17c zenon_H37 zenon_H38 zenon_H148 zenon_H35 zenon_H123 zenon_H1a zenon_Hec zenon_H1f. % 112.12/112.41 elim (classic (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_Hac | zenon_intro zenon_Had ]. % 112.12/112.41 generalize (zenon_H34 (mod1)). zenon_intro zenon_Ha7. % 112.12/112.41 generalize (zenon_Ha7 (low)). zenon_intro zenon_Ha8. % 112.12/112.41 generalize (zenon_Ha8 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H243. % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H243); [ zenon_intro zenon_H7f | zenon_intro zenon_H244 ]. % 112.12/112.41 exact (zenon_H7f assumption_18b). % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H244); [ zenon_intro zenon_Had | zenon_intro zenon_H241 ]. % 112.12/112.41 exact (zenon_Had zenon_Hac). % 112.12/112.41 exact (zenon_H193 zenon_H241). % 112.12/112.41 apply (zenon_L134_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.41 (* end of lemma zenon_L135_ *) % 112.12/112.41 assert (zenon_L136_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (low)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (greater (tau) (sigma)) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> False). % 112.12/112.41 do 4 intro. intros zenon_H34 zenon_H1b8 zenon_H117 zenon_H17c zenon_H37 zenon_H38 zenon_H148 zenon_H35 zenon_H123 zenon_H1a zenon_Hec zenon_H1f. % 112.12/112.41 elim (classic (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_Hac | zenon_intro zenon_Had ]. % 112.12/112.41 cut ((greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.41 intro zenon_D_pnotp. % 112.12/112.41 apply zenon_H117. % 112.12/112.41 rewrite <- zenon_D_pnotp. % 112.12/112.41 exact zenon_Hac. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.41 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba]. % 112.12/112.41 congruence. % 112.12/112.41 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((low) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.41 intro zenon_D_pnotp. % 112.12/112.41 apply zenon_H1ba. % 112.12/112.41 rewrite <- zenon_D_pnotp. % 112.12/112.41 exact zenon_H11a. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 112.12/112.41 congruence. % 112.12/112.41 exact (zenon_H1bb zenon_H1b8). % 112.12/112.41 apply zenon_H11b. apply refl_equal. % 112.12/112.41 apply zenon_H11b. apply refl_equal. % 112.12/112.41 apply zenon_H62. apply refl_equal. % 112.12/112.41 apply (zenon_L134_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.41 (* end of lemma zenon_L136_ *) % 112.12/112.41 assert (zenon_L137_ : forall (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (~(~(has_immunity zenon_TX_y zenon_TT0_hz))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> False). % 112.12/112.41 do 2 intro. intros zenon_H245 zenon_H1f zenon_H1a. % 112.12/112.41 apply zenon_H245. zenon_intro zenon_H246. % 112.12/112.41 generalize (assumption_1 zenon_TX_y). zenon_intro zenon_H22. % 112.12/112.41 generalize (zenon_H22 zenon_TT0_hz). zenon_intro zenon_H247. % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H247); [ zenon_intro zenon_H25 | zenon_intro zenon_H248 ]. % 112.12/112.41 apply (zenon_notand_s _ _ zenon_H25); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 112.12/112.41 exact (zenon_H27 zenon_H1f). % 112.12/112.41 apply zenon_H26. zenon_intro zenon_H19. % 112.12/112.41 apply (zenon_L2_ zenon_TX_y); trivial. % 112.12/112.41 exact (zenon_H248 zenon_H246). % 112.12/112.41 (* end of lemma zenon_L137_ *) % 112.12/112.41 assert (zenon_L138_ : (~((tau) = (tau))) -> False). % 112.12/112.41 do 0 intro. intros zenon_H53. % 112.12/112.41 apply zenon_H53. apply refl_equal. % 112.12/112.41 (* end of lemma zenon_L138_ *) % 112.12/112.41 assert (zenon_L139_ : forall (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (~(greater (tau) (age zenon_TX_y zenon_TT0_hz))) -> (greater (tau) (zero)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> False). % 112.12/112.41 do 2 intro. intros zenon_H249 zenon_H24a zenon_Hec. % 112.12/112.41 elim (classic ((zero) = (age zenon_TX_y zenon_TT0_hz))); [ zenon_intro zenon_H24b | zenon_intro zenon_H24c ]. % 112.12/112.41 cut ((greater (tau) (zero)) = (greater (tau) (age zenon_TX_y zenon_TT0_hz))). % 112.12/112.41 intro zenon_D_pnotp. % 112.12/112.41 apply zenon_H249. % 112.12/112.41 rewrite <- zenon_D_pnotp. % 112.12/112.41 exact zenon_H24a. % 112.12/112.41 cut (((zero) = (age zenon_TX_y zenon_TT0_hz))); [idtac | apply NNPP; zenon_intro zenon_H24c]. % 112.12/112.41 cut (((tau) = (tau))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 112.12/112.41 congruence. % 112.12/112.41 apply zenon_H53. apply refl_equal. % 112.12/112.41 exact (zenon_H24c zenon_H24b). % 112.12/112.41 apply zenon_H24c. apply sym_equal. exact zenon_Hec. % 112.12/112.41 (* end of lemma zenon_L139_ *) % 112.12/112.41 assert (zenon_L140_ : forall (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (positional_advantage zenon_TX_y zenon_TT0_hz) -> (greater (tau) (zero)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> False). % 112.12/112.41 do 2 intro. intros zenon_H35 zenon_H24d zenon_H24a zenon_Hec. % 112.12/112.41 generalize (zenon_H35 zenon_TT0_hz). zenon_intro zenon_H24e. % 112.12/112.41 apply (zenon_and_s _ _ zenon_H24e). zenon_intro zenon_H250. zenon_intro zenon_H24f. % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H250); [ zenon_intro zenon_H252 | zenon_intro zenon_H251 ]. % 112.12/112.41 generalize (definition_smaller_or_equal (age zenon_TX_y zenon_TT0_hz)). zenon_intro zenon_H253. % 112.12/112.41 generalize (zenon_H253 (tau)). zenon_intro zenon_H254. % 112.12/112.41 apply (zenon_equiv_s _ _ zenon_H254); [ zenon_intro zenon_H252; zenon_intro zenon_H257 | zenon_intro zenon_H256; zenon_intro zenon_H255 ]. % 112.12/112.41 apply (zenon_notor_s _ _ zenon_H257). zenon_intro zenon_H259. zenon_intro zenon_H258. % 112.12/112.41 generalize (definition_smaller (age zenon_TX_y zenon_TT0_hz)). zenon_intro zenon_H25a. % 112.12/112.41 generalize (zenon_H25a (tau)). zenon_intro zenon_H25b. % 112.12/112.41 apply (zenon_equiv_s _ _ zenon_H25b); [ zenon_intro zenon_H259; zenon_intro zenon_H249 | zenon_intro zenon_H25d; zenon_intro zenon_H25c ]. % 112.12/112.41 apply (zenon_L139_ zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.41 exact (zenon_H259 zenon_H25d). % 112.12/112.41 exact (zenon_H252 zenon_H256). % 112.12/112.41 exact (zenon_H251 zenon_H24d). % 112.12/112.41 (* end of lemma zenon_L140_ *) % 112.12/112.41 assert (zenon_L141_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT0_hz))) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2)) -> ((hazard_of_mortality zenon_TX_y zenon_TT0_hz) = (mod2)) -> False). % 112.12/112.41 do 3 intro. intros zenon_H25e zenon_H32 zenon_H25f. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2)) = ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT0_hz))). % 112.12/112.41 intro zenon_D_pnotp. % 112.12/112.41 apply zenon_H25e. % 112.12/112.41 rewrite <- zenon_D_pnotp. % 112.12/112.41 exact zenon_H32. % 112.12/112.41 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT0_hz))); [idtac | apply NNPP; zenon_intro zenon_H260]. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.41 congruence. % 112.12/112.41 apply zenon_H62. apply refl_equal. % 112.12/112.41 apply zenon_H260. apply sym_equal. exact zenon_H25f. % 112.12/112.41 (* end of lemma zenon_L141_ *) % 112.12/112.41 assert (zenon_L142_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), ((((is_aligned zenon_TX_y zenon_TT0_hz)/\(positional_advantage zenon_TX_y zenon_TT0_hz))->((hazard_of_mortality zenon_TX_y zenon_TT0_hz) = (low)))/\((((~(is_aligned zenon_TX_y zenon_TT0_hz))/\(positional_advantage zenon_TX_y zenon_TT0_hz))->((hazard_of_mortality zenon_TX_y zenon_TT0_hz) = (mod1)))/\((((is_aligned zenon_TX_y zenon_TT0_hz)/\(~(positional_advantage zenon_TX_y zenon_TT0_hz)))->((hazard_of_mortality zenon_TX_y zenon_TT0_hz) = (mod2)))/\(((~(is_aligned zenon_TX_y zenon_TT0_hz))/\(~(positional_advantage zenon_TX_y zenon_TT0_hz)))->((hazard_of_mortality zenon_TX_y zenon_TT0_hz) = (high)))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (greater (tau) (zero)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT0_hz))) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2)) -> False). % 112.12/112.41 do 3 intro. intros zenon_H261 zenon_Hec zenon_H24a zenon_H35 zenon_Hcd zenon_H25e zenon_H32. % 112.12/112.41 apply (zenon_and_s _ _ zenon_H261). zenon_intro zenon_H263. zenon_intro zenon_H262. % 112.12/112.41 apply (zenon_and_s _ _ zenon_H262). zenon_intro zenon_H265. zenon_intro zenon_H264. % 112.12/112.41 apply (zenon_and_s _ _ zenon_H264). zenon_intro zenon_H267. zenon_intro zenon_H266. % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H267); [ zenon_intro zenon_H268 | zenon_intro zenon_H25f ]. % 112.12/112.41 apply (zenon_notand_s _ _ zenon_H268); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H269 ]. % 112.12/112.41 exact (zenon_Hd8 zenon_Hcd). % 112.12/112.41 apply zenon_H269. zenon_intro zenon_H24d. % 112.12/112.41 apply (zenon_L140_ zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.41 apply (zenon_L141_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.41 (* end of lemma zenon_L142_ *) % 112.12/112.41 assert (zenon_L143_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (zero)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT0_hz))) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2)) -> False). % 112.12/112.41 do 3 intro. intros zenon_H0 zenon_H1f zenon_H1a zenon_Hcd zenon_H35 zenon_H24a zenon_Hec zenon_H25e zenon_H32. % 112.12/112.41 generalize (zenon_H0 zenon_TT0_hz). zenon_intro zenon_H26a. % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H26a); [ zenon_intro zenon_H27 | zenon_intro zenon_H26b ]. % 112.12/112.41 exact (zenon_H27 zenon_H1f). % 112.12/112.41 apply (zenon_and_s _ _ zenon_H26b). zenon_intro zenon_H26d. zenon_intro zenon_H26c. % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H26c); [ zenon_intro zenon_H245 | zenon_intro zenon_H261 ]. % 112.12/112.41 apply (zenon_L137_ zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.41 apply (zenon_L142_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.41 (* end of lemma zenon_L143_ *) % 112.12/112.41 assert (zenon_L144_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (((is_aligned zenon_TX_y zenon_TT1_bg)/\(~(positional_advantage zenon_TX_y zenon_TT1_bg)))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))) -> (~(positional_advantage zenon_TX_y zenon_TT1_bg)) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (zero)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT0_hz))) -> False). % 112.12/112.41 do 3 intro. intros zenon_H30 zenon_H29 zenon_H37 zenon_H34 zenon_H0 zenon_H1f zenon_H1a zenon_Hcd zenon_H35 zenon_H24a zenon_Hec zenon_H25e. % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 112.12/112.41 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ]. % 112.12/112.41 apply (zenon_L31_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.41 exact (zenon_H2e zenon_H29). % 112.12/112.41 apply (zenon_L143_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.41 (* end of lemma zenon_L144_ *) % 112.12/112.41 assert (zenon_L145_ : forall (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2)) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (low) (low))) -> False). % 112.12/112.41 do 2 intro. intros zenon_H32 zenon_H6b zenon_H34 zenon_H6c. % 112.12/112.41 elim (classic ((~((low) = (mod1)))/\(~(greater (low) (mod1))))); [ zenon_intro zenon_H6d | zenon_intro zenon_H6e ]. % 112.12/112.41 apply (zenon_and_s _ _ zenon_H6d). zenon_intro zenon_H70. zenon_intro zenon_H6f. % 112.12/112.41 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 112.12/112.41 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1))); [ zenon_intro zenon_H68 | zenon_intro zenon_H5a ]. % 112.12/112.41 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1)) = (greater (low) (mod1))). % 112.12/112.41 intro zenon_D_pnotp. % 112.12/112.41 apply zenon_H6f. % 112.12/112.41 rewrite <- zenon_D_pnotp. % 112.12/112.41 exact zenon_H68. % 112.12/112.41 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 112.12/112.41 congruence. % 112.12/112.41 elim (classic ((low) = (low))); [ zenon_intro zenon_H74 | zenon_intro zenon_H6a ]. % 112.12/112.41 cut (((low) = (low)) = ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low))). % 112.12/112.41 intro zenon_D_pnotp. % 112.12/112.41 apply zenon_H73. % 112.12/112.41 rewrite <- zenon_D_pnotp. % 112.12/112.41 exact zenon_H74. % 112.12/112.41 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.12/112.41 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 112.12/112.41 congruence. % 112.12/112.41 exact (zenon_H72 zenon_H71). % 112.12/112.41 apply zenon_H6a. apply refl_equal. % 112.12/112.41 apply zenon_H6a. apply refl_equal. % 112.12/112.41 apply zenon_H59. apply refl_equal. % 112.12/112.41 apply (zenon_L8_ zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.41 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.41 intro zenon_D_pnotp. % 112.12/112.41 apply zenon_H72. % 112.12/112.41 rewrite <- zenon_D_pnotp. % 112.12/112.41 exact zenon_H61. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.41 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 112.12/112.41 congruence. % 112.12/112.41 exact (zenon_H73 zenon_H6b). % 112.12/112.41 apply zenon_H62. apply refl_equal. % 112.12/112.41 apply zenon_H62. apply refl_equal. % 112.12/112.41 cut ((greater (mod1) (low)) = (greater (low) (low))). % 112.12/112.41 intro zenon_D_pnotp. % 112.12/112.41 apply zenon_H6c. % 112.12/112.41 rewrite <- zenon_D_pnotp. % 112.12/112.41 exact assumption_18b. % 112.12/112.41 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.12/112.41 cut (((mod1) = (low))); [idtac | apply NNPP; zenon_intro zenon_H75]. % 112.12/112.41 congruence. % 112.12/112.41 apply (zenon_notand_s _ _ zenon_H6e); [ zenon_intro zenon_H77 | zenon_intro zenon_H76 ]. % 112.12/112.41 apply zenon_H77. zenon_intro zenon_H78. % 112.12/112.41 elim (classic ((low) = (low))); [ zenon_intro zenon_H74 | zenon_intro zenon_H6a ]. % 112.12/112.41 cut (((low) = (low)) = ((mod1) = (low))). % 112.12/112.41 intro zenon_D_pnotp. % 112.12/112.41 apply zenon_H75. % 112.12/112.41 rewrite <- zenon_D_pnotp. % 112.12/112.41 exact zenon_H74. % 112.12/112.41 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.12/112.41 cut (((low) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 112.12/112.41 congruence. % 112.12/112.41 exact (zenon_H70 zenon_H78). % 112.12/112.41 apply zenon_H6a. apply refl_equal. % 112.12/112.41 apply zenon_H6a. apply refl_equal. % 112.12/112.41 apply zenon_H76. zenon_intro zenon_H79. % 112.12/112.41 generalize (zenon_H34 (low)). zenon_intro zenon_H7a. % 112.12/112.41 generalize (zenon_H7a (mod1)). zenon_intro zenon_H7b. % 112.12/112.41 generalize (zenon_H7b (low)). zenon_intro zenon_H7c. % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H7c); [ zenon_intro zenon_H6f | zenon_intro zenon_H7d ]. % 112.12/112.41 exact (zenon_H6f zenon_H79). % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H7d); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ]. % 112.12/112.41 exact (zenon_H7f assumption_18b). % 112.12/112.41 exact (zenon_H6c zenon_H7e). % 112.12/112.41 apply zenon_H6a. apply refl_equal. % 112.12/112.41 (* end of lemma zenon_L145_ *) % 112.12/112.41 assert (zenon_L146_ : forall (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low)) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2)) -> False). % 112.12/112.41 do 2 intro. intros zenon_H34 zenon_H6b zenon_H32. % 112.12/112.41 generalize (meaning_postulate_greater_strict (low)). zenon_intro zenon_H80. % 112.12/112.41 generalize (zenon_H80 (low)). zenon_intro zenon_H81. % 112.12/112.41 apply (zenon_notand_s _ _ zenon_H81); [ zenon_intro zenon_H6c | zenon_intro zenon_H6c ]. % 112.12/112.41 apply (zenon_L145_ zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.41 apply (zenon_L145_ zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.41 (* end of lemma zenon_L146_ *) % 112.12/112.41 assert (zenon_L147_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (((is_aligned zenon_TX_y zenon_TT1_bg)/\(~(positional_advantage zenon_TX_y zenon_TT1_bg)))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))) -> (greater (tau) (sigma)) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T0) = (zero)))->((greater (age zenon_TX_y T) (sigma))<->(dissimilar zenon_TX_y T0 T))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low)) -> False). % 112.12/112.41 do 3 intro. intros zenon_H30 zenon_H38 zenon_H37 zenon_H35 zenon_H1f zenon_Hec zenon_Hcd zenon_Hed zenon_H34 zenon_H6b. % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 112.12/112.41 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ]. % 112.12/112.41 apply (zenon_L30_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.41 apply zenon_H2e. zenon_intro zenon_H36. % 112.12/112.41 apply (zenon_L6_ zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.41 apply (zenon_L146_ zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.41 (* end of lemma zenon_L147_ *) % 112.12/112.41 assert (zenon_L148_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), ((((is_aligned zenon_TX_y zenon_TT1_bg)/\(positional_advantage zenon_TX_y zenon_TT1_bg))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low)))/\((((~(is_aligned zenon_TX_y zenon_TT1_bg))/\(positional_advantage zenon_TX_y zenon_TT1_bg))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod1)))/\((((is_aligned zenon_TX_y zenon_TT1_bg)/\(~(positional_advantage zenon_TX_y zenon_TT1_bg)))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2)))/\(((~(is_aligned zenon_TX_y zenon_TT1_bg))/\(~(positional_advantage zenon_TX_y zenon_TT1_bg)))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high)))))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT0_hz))) -> (greater (tau) (zero)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (greater (tau) (sigma)) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T0) = (zero)))->((greater (age zenon_TX_y T) (sigma))<->(dissimilar zenon_TX_y T0 T))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> False). % 112.12/112.41 do 3 intro. intros zenon_H8c zenon_H25e zenon_H24a zenon_H1a zenon_H0 zenon_H38 zenon_H37 zenon_H35 zenon_H1f zenon_Hec zenon_Hcd zenon_Hed zenon_H34. % 112.12/112.41 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d. % 112.12/112.41 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f. % 112.12/112.41 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H30. zenon_intro zenon_H28. % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H8e); [ zenon_intro zenon_H91 | zenon_intro zenon_H6b ]. % 112.12/112.41 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 112.12/112.41 apply (zenon_L30_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.41 apply (zenon_L144_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.41 apply (zenon_L147_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.41 (* end of lemma zenon_L148_ *) % 112.12/112.41 assert (zenon_L149_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (greater (tau) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (zero)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT0_hz))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> False). % 112.12/112.41 do 3 intro. intros zenon_H34 zenon_H1f zenon_Hec zenon_H38 zenon_H35 zenon_H24a zenon_H25e zenon_H37 zenon_H1a. % 112.12/112.41 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3. % 112.12/112.41 generalize (assumption_15 zenon_TX_y). zenon_intro zenon_Hed. % 112.12/112.41 generalize (zenon_Hf3 zenon_TT0_hz). zenon_intro zenon_Hf4. % 112.12/112.41 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcd ]. % 112.12/112.41 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ]. % 112.12/112.41 exact (zenon_H27 zenon_H1f). % 112.12/112.41 exact (zenon_Hf2 zenon_Hec). % 112.12/112.41 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0. % 112.12/112.41 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88. % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ]. % 112.12/112.41 exact (zenon_H27 zenon_H1f). % 112.12/112.41 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a. % 112.12/112.41 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ]. % 112.12/112.41 apply (zenon_L3_ zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.41 apply (zenon_L148_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.41 (* end of lemma zenon_L149_ *) % 112.12/112.41 assert (zenon_L150_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T0) = (zero)))->((greater (age zenon_TX_y T) (sigma))<->(dissimilar zenon_TX_y T0 T))))) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> (~(is_aligned zenon_TX_y zenon_TT1_bg)) -> (~(greater (age zenon_TX_y zenon_TT1_bg) (sigma))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> False). % 112.12/112.41 do 3 intro. intros zenon_Hed zenon_Hcd zenon_H2a zenon_He9 zenon_Hec zenon_H1f. % 112.12/112.41 generalize (zenon_Hed zenon_TT0_hz). zenon_intro zenon_Hee. % 112.12/112.41 generalize (zenon_Hee zenon_TT1_bg). zenon_intro zenon_Hef. % 112.12/112.41 apply (zenon_imply_s _ _ zenon_Hef); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf0 ]. % 112.12/112.41 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ]. % 112.12/112.41 exact (zenon_H27 zenon_H1f). % 112.12/112.41 exact (zenon_Hf2 zenon_Hec). % 112.12/112.41 apply (zenon_equiv_s _ _ zenon_Hf0); [ zenon_intro zenon_He9; zenon_intro zenon_Hce | zenon_intro zenon_Hdb; zenon_intro zenon_Hd4 ]. % 112.12/112.41 apply (zenon_L26_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.41 exact (zenon_He9 zenon_Hdb). % 112.12/112.41 (* end of lemma zenon_L150_ *) % 112.12/112.41 assert (zenon_L151_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (((organization zenon_TX_y)/\((age zenon_TX_y zenon_TT0_hz) = (zero)))->(is_aligned zenon_TX_y zenon_TT0_hz)) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T0) = (zero)))->((greater (age zenon_TX_y T) (sigma))<->(dissimilar zenon_TX_y T0 T))))) -> (~(is_aligned zenon_TX_y zenon_TT1_bg)) -> (~(greater (age zenon_TX_y zenon_TT1_bg) (sigma))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> False). % 112.12/112.41 do 3 intro. intros zenon_Hf4 zenon_Hed zenon_H2a zenon_He9 zenon_Hec zenon_H1f. % 112.12/112.41 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcd ]. % 112.12/112.41 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ]. % 112.12/112.41 exact (zenon_H27 zenon_H1f). % 112.12/112.41 exact (zenon_Hf2 zenon_Hec). % 112.12/112.41 apply (zenon_L150_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.41 (* end of lemma zenon_L151_ *) % 112.12/112.41 assert (zenon_L152_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T0) = (zero)))->((greater (age zenon_TX_y T) (sigma))<->(dissimilar zenon_TX_y T0 T))))) -> (~(is_aligned zenon_TX_y zenon_TT1_bg)) -> (~(greater (age zenon_TX_y zenon_TT1_bg) (sigma))) -> False). % 112.12/112.41 do 3 intro. intros zenon_Hf3 zenon_H1f zenon_Hec zenon_Hed zenon_H2a zenon_He9. % 112.12/112.41 generalize (zenon_Hf3 zenon_TT0_hz). zenon_intro zenon_Hf4. % 112.12/112.41 apply (zenon_L151_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.41 (* end of lemma zenon_L152_ *) % 112.12/112.41 assert (zenon_L153_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (~(greater (age zenon_TX_y zenon_TT1_bg) (sigma))) -> (~(is_aligned zenon_TX_y zenon_TT1_bg)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> False). % 112.12/112.42 do 3 intro. intros zenon_He9 zenon_H2a zenon_Hec zenon_H1f zenon_Hf3. % 112.12/112.42 generalize (assumption_15 zenon_TX_y). zenon_intro zenon_Hed. % 112.12/112.42 apply (zenon_L152_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.42 (* end of lemma zenon_L153_ *) % 112.12/112.42 assert (zenon_L154_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (((is_aligned zenon_TX_y zenon_TT1_bg)/\(~(positional_advantage zenon_TX_y zenon_TT1_bg)))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))) -> (~(positional_advantage zenon_TX_y zenon_TT1_bg)) -> (~(greater (age zenon_TX_y zenon_TT1_bg) (sigma))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))) -> False). % 112.12/112.42 do 3 intro. intros zenon_H30 zenon_H29 zenon_He9 zenon_Hec zenon_H1f zenon_Hf3 zenon_H31. % 112.12/112.42 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 112.12/112.42 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ]. % 112.12/112.42 apply (zenon_L153_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.42 exact (zenon_H2e zenon_H29). % 112.12/112.42 exact (zenon_H31 zenon_H32). % 112.12/112.42 (* end of lemma zenon_L154_ *) % 112.12/112.42 assert (zenon_L155_ : forall (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (positional_advantage zenon_TX_y zenon_TT1_bg) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> False). % 112.12/112.42 do 2 intro. intros zenon_H35 zenon_H36 zenon_H38 zenon_H26e. % 112.12/112.42 generalize (zenon_H35 zenon_TT1_bg). zenon_intro zenon_H39. % 112.12/112.42 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_H3b. zenon_intro zenon_H3a. % 112.12/112.42 apply (zenon_imply_s _ _ zenon_H3b); [ zenon_intro zenon_H3c | zenon_intro zenon_H29 ]. % 112.12/112.42 generalize (definition_smaller_or_equal (age zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H3d. % 112.12/112.42 generalize (zenon_H3d (tau)). zenon_intro zenon_H3e. % 112.12/112.42 apply (zenon_equiv_s _ _ zenon_H3e); [ zenon_intro zenon_H3c; zenon_intro zenon_H41 | zenon_intro zenon_H40; zenon_intro zenon_H3f ]. % 112.12/112.42 apply (zenon_notor_s _ _ zenon_H41). zenon_intro zenon_H43. zenon_intro zenon_H42. % 112.12/112.42 generalize (definition_smaller (age zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H44. % 112.12/112.42 generalize (zenon_H44 (tau)). zenon_intro zenon_H45. % 112.12/112.42 apply (zenon_equiv_s _ _ zenon_H45); [ zenon_intro zenon_H43; zenon_intro zenon_H48 | zenon_intro zenon_H47; zenon_intro zenon_H46 ]. % 112.12/112.42 elim (classic ((sigma) = (age zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_He2 | zenon_intro zenon_Hde ]. % 112.12/112.42 cut ((greater (tau) (sigma)) = (greater (tau) (age zenon_TX_y zenon_TT1_bg))). % 112.12/112.42 intro zenon_D_pnotp. % 112.12/112.42 apply zenon_H48. % 112.12/112.42 rewrite <- zenon_D_pnotp. % 112.12/112.42 exact zenon_H38. % 112.12/112.42 cut (((sigma) = (age zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_Hde]. % 112.12/112.42 cut (((tau) = (tau))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 112.12/112.42 congruence. % 112.12/112.42 apply zenon_H53. apply refl_equal. % 112.12/112.42 exact (zenon_Hde zenon_He2). % 112.12/112.42 apply zenon_Hde. apply sym_equal. exact zenon_H26e. % 112.12/112.42 exact (zenon_H43 zenon_H47). % 112.12/112.42 exact (zenon_H3c zenon_H40). % 112.12/112.42 exact (zenon_H29 zenon_H36). % 112.12/112.42 (* end of lemma zenon_L155_ *) % 112.12/112.42 assert (zenon_L156_ : forall (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (((is_aligned zenon_TX_y zenon_TT1_bg)/\(~(positional_advantage zenon_TX_y zenon_TT1_bg)))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (greater (tau) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (is_aligned zenon_TX_y zenon_TT1_bg) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low)) -> False). % 112.12/112.42 do 2 intro. intros zenon_H30 zenon_H26e zenon_H38 zenon_H35 zenon_H82 zenon_H34 zenon_H6b. % 112.12/112.42 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 112.12/112.42 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ]. % 112.12/112.42 exact (zenon_H2a zenon_H82). % 112.12/112.42 apply zenon_H2e. zenon_intro zenon_H36. % 112.12/112.42 apply (zenon_L155_ zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.42 apply (zenon_L11_ zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.42 (* end of lemma zenon_L156_ *) % 112.12/112.42 assert (zenon_L157_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (((is_aligned zenon_TX_y zenon_TT1_bg)/\(~(positional_advantage zenon_TX_y zenon_TT1_bg)))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))) -> (~(positional_advantage zenon_TX_y zenon_TT1_bg)) -> (~(greater (age zenon_TX_y zenon_TT1_bg) (sigma))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low)) -> False). % 112.12/112.42 do 3 intro. intros zenon_H30 zenon_H29 zenon_He9 zenon_Hec zenon_H1f zenon_Hf3 zenon_H34 zenon_H6b. % 112.12/112.42 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 112.12/112.42 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ]. % 112.12/112.42 apply (zenon_L153_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.42 exact (zenon_H2e zenon_H29). % 112.12/112.42 apply (zenon_L11_ zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.42 (* end of lemma zenon_L157_ *) % 112.12/112.42 assert (zenon_L158_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (((is_aligned zenon_TX_y zenon_TT1_bg)/\(~(positional_advantage zenon_TX_y zenon_TT1_bg)))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (greater (tau) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (~(greater (age zenon_TX_y zenon_TT1_bg) (sigma))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low)) -> False). % 112.12/112.42 do 3 intro. intros zenon_H30 zenon_H26e zenon_H38 zenon_H35 zenon_He9 zenon_Hec zenon_H1f zenon_Hf3 zenon_H34 zenon_H6b. % 112.12/112.42 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 112.12/112.42 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ]. % 112.12/112.42 apply (zenon_L153_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.42 apply zenon_H2e. zenon_intro zenon_H36. % 112.12/112.42 apply (zenon_L155_ zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.42 apply (zenon_L146_ zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.42 (* end of lemma zenon_L158_ *) % 112.12/112.42 assert (zenon_L159_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~(greater (age zenon_TX_y zenon_TT1_bg) (sigma))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> False). % 112.12/112.42 do 3 intro. intros zenon_H34 zenon_H0 zenon_H1f zenon_H1a zenon_He9 zenon_Hec zenon_Hf3 zenon_H31 zenon_H35 zenon_H38 zenon_H26e. % 112.12/112.42 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88. % 112.12/112.42 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ]. % 112.12/112.42 exact (zenon_H27 zenon_H1f). % 112.12/112.42 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a. % 112.12/112.42 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ]. % 112.12/112.42 apply (zenon_L3_ zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.42 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d. % 112.12/112.42 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f. % 112.12/112.42 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H30. zenon_intro zenon_H28. % 112.12/112.42 apply (zenon_imply_s _ _ zenon_H8e); [ zenon_intro zenon_H91 | zenon_intro zenon_H6b ]. % 112.12/112.42 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 112.12/112.42 apply (zenon_L153_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.42 apply (zenon_L154_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.42 apply (zenon_L158_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.42 (* end of lemma zenon_L159_ *) % 112.12/112.42 assert (zenon_L160_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (greater (tau) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(greater (age zenon_TX_y zenon_TT1_bg) (sigma))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (organization zenon_TX_y) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1))) -> False). % 112.12/112.42 do 3 intro. intros zenon_H26e zenon_H38 zenon_H35 zenon_Hf3 zenon_Hec zenon_He9 zenon_H1a zenon_H1f zenon_H0 zenon_H34 zenon_H5a. % 112.12/112.42 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod2))))); [ zenon_intro zenon_H5b | zenon_intro zenon_H5c ]. % 112.12/112.42 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H31. zenon_intro zenon_H5d. % 112.12/112.42 apply (zenon_L159_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.42 cut ((greater (mod2) (mod1)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1))). % 112.12/112.42 intro zenon_D_pnotp. % 112.12/112.42 apply zenon_H5a. % 112.12/112.42 rewrite <- zenon_D_pnotp. % 112.12/112.42 exact assumption_19. % 112.12/112.42 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 112.12/112.42 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 112.12/112.42 congruence. % 112.12/112.42 apply (zenon_notand_s _ _ zenon_H5c); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ]. % 112.12/112.42 apply zenon_H60. zenon_intro zenon_H32. % 112.12/112.42 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.12/112.42 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.42 intro zenon_D_pnotp. % 112.12/112.42 apply zenon_H5e. % 112.12/112.42 rewrite <- zenon_D_pnotp. % 112.12/112.42 exact zenon_H61. % 112.12/112.42 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.42 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31]. % 112.12/112.42 congruence. % 112.12/112.42 exact (zenon_H31 zenon_H32). % 112.12/112.42 apply zenon_H62. apply refl_equal. % 112.12/112.42 apply zenon_H62. apply refl_equal. % 112.12/112.42 apply zenon_H5f. zenon_intro zenon_H63. % 112.12/112.42 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64. % 112.12/112.42 generalize (zenon_H64 (mod2)). zenon_intro zenon_H65. % 112.12/112.42 generalize (zenon_H65 (mod1)). zenon_intro zenon_H66. % 112.12/112.42 apply (zenon_imply_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H67 ]. % 112.12/112.42 exact (zenon_H5d zenon_H63). % 112.12/112.42 apply (zenon_imply_s _ _ zenon_H67); [ zenon_intro zenon_H69 | zenon_intro zenon_H68 ]. % 112.12/112.42 exact (zenon_H69 assumption_19). % 112.12/112.42 exact (zenon_H5a zenon_H68). % 112.12/112.42 apply zenon_H59. apply refl_equal. % 112.12/112.42 (* end of lemma zenon_L160_ *) % 112.12/112.42 assert (zenon_L161_ : forall (zenon_TT3_x : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~(greater (age zenon_TX_y zenon_TT1_bg) (sigma))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (mod1)) -> False). % 112.12/112.42 do 4 intro. intros zenon_H0 zenon_H1f zenon_H1a zenon_He9 zenon_Hec zenon_Hf3 zenon_H35 zenon_H38 zenon_H26e zenon_Hae zenon_H34 zenon_Haf. % 112.12/112.42 elim (classic ((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hb1 ]. % 112.12/112.42 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1))); [ zenon_intro zenon_H68 | zenon_intro zenon_H5a ]. % 112.12/112.42 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))). % 112.12/112.42 intro zenon_D_pnotp. % 112.12/112.42 apply zenon_Hae. % 112.12/112.42 rewrite <- zenon_D_pnotp. % 112.12/112.42 exact zenon_H68. % 112.12/112.42 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hb1]. % 112.12/112.42 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.42 congruence. % 112.12/112.42 apply zenon_H62. apply refl_equal. % 112.12/112.42 exact (zenon_Hb1 zenon_Hb0). % 112.12/112.42 apply (zenon_L160_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.42 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb6 ]. % 112.12/112.42 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x)) = ((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))). % 112.12/112.42 intro zenon_D_pnotp. % 112.12/112.42 apply zenon_Hb1. % 112.12/112.42 rewrite <- zenon_D_pnotp. % 112.12/112.42 exact zenon_Hb9. % 112.12/112.42 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 112.12/112.42 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 112.12/112.42 congruence. % 112.12/112.42 exact (zenon_Hb7 zenon_Haf). % 112.12/112.42 apply zenon_Hb6. apply refl_equal. % 112.12/112.42 apply zenon_Hb6. apply refl_equal. % 112.12/112.42 (* end of lemma zenon_L161_ *) % 112.12/112.42 assert (zenon_L162_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TT3_x : zenon_U) (zenon_TX_y : zenon_U), (((~(is_aligned zenon_TX_y zenon_TT3_x))/\(positional_advantage zenon_TX_y zenon_TT3_x))->((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (mod1))) -> (positional_advantage zenon_TX_y zenon_TT3_x) -> (~(is_aligned zenon_TX_y zenon_TT3_x)) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~(greater (age zenon_TX_y zenon_TT1_bg) (sigma))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> False). % 112.12/112.42 do 4 intro. intros zenon_Hba zenon_Hbb zenon_Hbc zenon_H0 zenon_H1f zenon_H1a zenon_He9 zenon_Hec zenon_Hf3 zenon_H35 zenon_H38 zenon_H26e zenon_Hae zenon_H34. % 112.12/112.42 apply (zenon_imply_s _ _ zenon_Hba); [ zenon_intro zenon_Hbd | zenon_intro zenon_Haf ]. % 112.12/112.42 apply (zenon_notand_s _ _ zenon_Hbd); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hbe ]. % 112.12/112.42 exact (zenon_Hbf zenon_Hbc). % 112.12/112.42 exact (zenon_Hbe zenon_Hbb). % 112.12/112.42 apply (zenon_L161_ zenon_TT3_x zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.42 (* end of lemma zenon_L162_ *) % 112.12/112.42 assert (zenon_L163_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (greater (tau) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(greater (age zenon_TX_y zenon_TT1_bg) (sigma))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (organization zenon_TX_y) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low))) -> False). % 112.12/112.42 do 3 intro. intros zenon_H26e zenon_H38 zenon_H35 zenon_Hf3 zenon_Hec zenon_He9 zenon_H1a zenon_H1f zenon_H0 zenon_H34 zenon_H9d. % 112.12/112.42 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod2))))); [ zenon_intro zenon_H5b | zenon_intro zenon_H5c ]. % 112.12/112.42 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H31. zenon_intro zenon_H5d. % 112.12/112.42 apply (zenon_L159_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.42 cut ((greater (mod2) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low))). % 112.12/112.42 intro zenon_D_pnotp. % 112.12/112.42 apply zenon_H9d. % 112.12/112.42 rewrite <- zenon_D_pnotp. % 112.12/112.42 exact assumption_18e. % 112.12/112.42 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.12/112.42 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 112.12/112.42 congruence. % 112.12/112.42 apply (zenon_notand_s _ _ zenon_H5c); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ]. % 112.12/112.42 apply zenon_H60. zenon_intro zenon_H32. % 112.12/112.42 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.12/112.42 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.42 intro zenon_D_pnotp. % 112.12/112.42 apply zenon_H5e. % 112.12/112.42 rewrite <- zenon_D_pnotp. % 112.12/112.42 exact zenon_H61. % 112.12/112.42 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.42 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31]. % 112.12/112.42 congruence. % 112.12/112.42 exact (zenon_H31 zenon_H32). % 112.12/112.42 apply zenon_H62. apply refl_equal. % 112.12/112.42 apply zenon_H62. apply refl_equal. % 112.12/112.42 apply zenon_H5f. zenon_intro zenon_H63. % 112.12/112.42 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64. % 112.12/112.42 generalize (zenon_H64 (mod2)). zenon_intro zenon_H65. % 112.12/112.42 generalize (zenon_H65 (low)). zenon_intro zenon_Hc0. % 112.12/112.42 apply (zenon_imply_s _ _ zenon_Hc0); [ zenon_intro zenon_H5d | zenon_intro zenon_Hc1 ]. % 112.12/112.42 exact (zenon_H5d zenon_H63). % 112.12/112.42 apply (zenon_imply_s _ _ zenon_Hc1); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H9c ]. % 112.12/112.42 exact (zenon_Hc2 assumption_18e). % 112.12/112.42 exact (zenon_H9d zenon_H9c). % 112.12/112.42 apply zenon_H6a. apply refl_equal. % 112.12/112.42 (* end of lemma zenon_L163_ *) % 112.12/112.42 assert (zenon_L164_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TT3_x : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (organization zenon_TX_y) -> (positional_advantage zenon_TX_y zenon_TT3_x) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~(greater (age zenon_TX_y zenon_TT1_bg) (sigma))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> False). % 112.12/112.42 do 4 intro. intros zenon_H34 zenon_H1f zenon_Hbb zenon_Hae zenon_H0 zenon_H1a zenon_He9 zenon_Hec zenon_Hf3 zenon_H35 zenon_H38 zenon_H26e zenon_H10f. % 112.12/112.42 generalize (zenon_H0 zenon_TT3_x). zenon_intro zenon_H10a. % 112.12/112.42 apply (zenon_imply_s _ _ zenon_H10a); [ zenon_intro zenon_H27 | zenon_intro zenon_H10b ]. % 112.12/112.42 exact (zenon_H27 zenon_H1f). % 112.12/112.42 apply (zenon_and_s _ _ zenon_H10b). zenon_intro zenon_H10c. zenon_intro zenon_Hcc. % 112.12/112.42 apply (zenon_imply_s _ _ zenon_H10c); [ zenon_intro zenon_H16 | zenon_intro zenon_H10d ]. % 112.12/112.42 apply (zenon_imply_s _ _ zenon_Hcc); [ zenon_intro zenon_H15 | zenon_intro zenon_Hc3 ]. % 112.12/112.42 exact (zenon_H15 zenon_H16). % 112.12/112.42 apply (zenon_and_s _ _ zenon_Hc3). zenon_intro zenon_Hc5. zenon_intro zenon_Hc4. % 112.12/112.42 apply (zenon_and_s _ _ zenon_Hc4). zenon_intro zenon_Hba. zenon_intro zenon_Hc6. % 112.12/112.42 apply (zenon_imply_s _ _ zenon_Hc5); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hc7 ]. % 112.12/112.42 apply (zenon_notand_s _ _ zenon_Hc8); [ zenon_intro zenon_Hbc | zenon_intro zenon_Hbe ]. % 112.12/112.42 apply (zenon_L162_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial. % 112.12/112.42 exact (zenon_Hbe zenon_Hbb). % 112.12/112.42 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hca ]. % 112.12/112.42 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low))); [ zenon_intro zenon_H9c | zenon_intro zenon_H9d ]. % 112.12/112.42 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))). % 112.12/112.42 intro zenon_D_pnotp. % 112.12/112.42 apply zenon_Hae. % 112.12/112.42 rewrite <- zenon_D_pnotp. % 112.12/112.42 exact zenon_H9c. % 112.12/112.42 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 112.12/112.42 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.42 congruence. % 112.12/112.42 apply zenon_H62. apply refl_equal. % 112.12/112.42 exact (zenon_Hca zenon_Hc9). % 112.12/112.42 apply (zenon_L163_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.42 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb6 ]. % 112.12/112.42 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x)) = ((low) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))). % 112.12/112.42 intro zenon_D_pnotp. % 112.12/112.42 apply zenon_Hca. % 112.12/112.42 rewrite <- zenon_D_pnotp. % 112.12/112.42 exact zenon_Hb9. % 112.12/112.42 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 112.12/112.42 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (low))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 112.12/112.42 congruence. % 112.12/112.42 exact (zenon_Hcb zenon_Hc7). % 112.12/112.42 apply zenon_Hb6. apply refl_equal. % 112.12/112.42 apply zenon_Hb6. apply refl_equal. % 112.12/112.42 apply zenon_H10f. apply sym_equal. exact zenon_H10d. % 112.12/112.42 (* end of lemma zenon_L164_ *) % 112.12/112.42 assert (zenon_L165_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TT3_x : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (greater (tau) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(greater (age zenon_TX_y zenon_TT1_bg) (sigma))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> (positional_advantage zenon_TX_y zenon_TT3_x) -> (organization zenon_TX_y) -> False). % 112.12/112.42 do 4 intro. intros zenon_H34 zenon_H10f zenon_H26e zenon_H38 zenon_H35 zenon_Hf3 zenon_Hec zenon_He9 zenon_H1a zenon_Hae zenon_Hbb zenon_H1f. % 112.12/112.42 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0. % 112.12/112.42 apply (zenon_L164_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial. % 112.12/112.42 (* end of lemma zenon_L165_ *) % 112.12/112.42 assert (zenon_L166_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TT3_x : zenon_U) (zenon_TX_y : zenon_U), (organization zenon_TX_y) -> (positional_advantage zenon_TX_y zenon_TT3_x) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> (~((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (sigma) (sigma))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> False). % 112.12/112.42 do 4 intro. intros zenon_H1f zenon_Hbb zenon_Hae zenon_H1a zenon_Hec zenon_Hf3 zenon_H35 zenon_H38 zenon_H10f zenon_H34 zenon_Hda zenon_H26e. % 112.12/112.42 elim (classic ((sigma) = (age zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_He2 | zenon_intro zenon_Hde ]. % 112.12/112.42 elim (classic (greater (age zenon_TX_y zenon_TT1_bg) (sigma))); [ zenon_intro zenon_Hdb | zenon_intro zenon_He9 ]. % 112.12/112.42 cut ((greater (age zenon_TX_y zenon_TT1_bg) (sigma)) = (greater (sigma) (sigma))). % 112.12/112.42 intro zenon_D_pnotp. % 112.12/112.42 apply zenon_Hda. % 112.12/112.42 rewrite <- zenon_D_pnotp. % 112.12/112.42 exact zenon_Hdb. % 112.12/112.42 cut (((sigma) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 112.12/112.42 cut (((age zenon_TX_y zenon_TT1_bg) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hdf]. % 112.12/112.42 congruence. % 112.12/112.42 elim (classic ((sigma) = (sigma))); [ zenon_intro zenon_He3 | zenon_intro zenon_Hd9 ]. % 112.12/112.42 cut (((sigma) = (sigma)) = ((age zenon_TX_y zenon_TT1_bg) = (sigma))). % 112.12/112.42 intro zenon_D_pnotp. % 112.12/112.42 apply zenon_Hdf. % 112.12/112.42 rewrite <- zenon_D_pnotp. % 112.12/112.42 exact zenon_He3. % 112.12/112.42 cut (((sigma) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 112.12/112.42 cut (((sigma) = (age zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_Hde]. % 112.12/112.42 congruence. % 112.12/112.42 exact (zenon_Hde zenon_He2). % 112.12/112.42 apply zenon_Hd9. apply refl_equal. % 112.12/112.42 apply zenon_Hd9. apply refl_equal. % 112.12/112.42 apply zenon_Hd9. apply refl_equal. % 112.12/112.42 apply (zenon_L165_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial. % 112.12/112.42 elim (classic ((age zenon_TX_y zenon_TT1_bg) = (age zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H26f | zenon_intro zenon_H4d ]. % 112.12/112.42 cut (((age zenon_TX_y zenon_TT1_bg) = (age zenon_TX_y zenon_TT1_bg)) = ((sigma) = (age zenon_TX_y zenon_TT1_bg))). % 112.12/112.42 intro zenon_D_pnotp. % 112.12/112.42 apply zenon_Hde. % 112.12/112.42 rewrite <- zenon_D_pnotp. % 112.12/112.42 exact zenon_H26f. % 112.12/112.42 cut (((age zenon_TX_y zenon_TT1_bg) = (age zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 112.12/112.42 cut (((age zenon_TX_y zenon_TT1_bg) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hdf]. % 112.12/112.42 congruence. % 112.12/112.42 exact (zenon_Hdf zenon_H26e). % 112.12/112.42 apply zenon_H4d. apply refl_equal. % 112.12/112.42 apply zenon_H4d. apply refl_equal. % 112.12/112.42 (* end of lemma zenon_L166_ *) % 112.12/112.42 assert (zenon_L167_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TT3_x : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (greater (tau) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> (positional_advantage zenon_TX_y zenon_TT3_x) -> (organization zenon_TX_y) -> False). % 112.12/112.42 do 4 intro. intros zenon_H34 zenon_H10f zenon_H26e zenon_H38 zenon_H35 zenon_Hf3 zenon_Hec zenon_H1a zenon_Hae zenon_Hbb zenon_H1f. % 112.12/112.42 generalize (meaning_postulate_greater_strict (sigma)). zenon_intro zenon_Hea. % 112.12/112.42 generalize (zenon_Hea (sigma)). zenon_intro zenon_Heb. % 112.12/112.42 apply (zenon_notand_s _ _ zenon_Heb); [ zenon_intro zenon_Hda | zenon_intro zenon_Hda ]. % 112.12/112.42 apply (zenon_L166_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial. % 112.12/112.42 apply (zenon_L166_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial. % 112.12/112.42 (* end of lemma zenon_L167_ *) % 112.12/112.42 assert (zenon_L168_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT3_x : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (organization zenon_TX_y) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> (greater (age zenon_TX_y zenon_TT3_x) (tau)) -> False). % 112.12/112.42 do 4 intro. intros zenon_H34 zenon_H1f zenon_Hae zenon_H1a zenon_Hec zenon_Hf3 zenon_H35 zenon_H38 zenon_H26e zenon_H10f zenon_H100. % 112.12/112.42 generalize (zenon_H35 zenon_TT3_x). zenon_intro zenon_H106. % 112.12/112.42 apply (zenon_and_s _ _ zenon_H106). zenon_intro zenon_H108. zenon_intro zenon_H107. % 112.12/112.42 apply (zenon_imply_s _ _ zenon_H107); [ zenon_intro zenon_H109 | zenon_intro zenon_Hbb ]. % 112.12/112.42 exact (zenon_H109 zenon_H100). % 112.12/112.42 apply (zenon_L167_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial. % 112.12/112.42 (* end of lemma zenon_L168_ *) % 112.12/112.42 assert (zenon_L169_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TT3_x : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (greater (age zenon_TX_y zenon_TT3_x) (tau)) -> (~((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (greater (tau) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> (organization zenon_TX_y) -> False). % 112.12/112.42 do 4 intro. intros zenon_H34 zenon_H100 zenon_H10f zenon_H26e zenon_H38 zenon_H35 zenon_Hec zenon_H1a zenon_Hae zenon_H1f. % 112.12/112.42 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3. % 112.12/112.42 apply (zenon_L168_ zenon_TT0_hz zenon_TT3_x zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.42 (* end of lemma zenon_L169_ *) % 112.12/112.42 assert (zenon_L170_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TT3_x : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (low) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> (greater (age zenon_TX_y zenon_TT3_x) (tau)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (greater (tau) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> (organization zenon_TX_y) -> False). % 112.12/112.42 do 4 intro. intros zenon_H34 zenon_H270 zenon_H100 zenon_H26e zenon_H38 zenon_H35 zenon_Hec zenon_H1a zenon_Hae zenon_H1f. % 112.12/112.42 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_H10e | zenon_intro zenon_H10f ]. % 112.12/112.42 cut ((greater (low) (very_low)) = (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT3_x))). % 112.12/112.42 intro zenon_D_pnotp. % 112.12/112.42 apply zenon_H270. % 112.12/112.42 rewrite <- zenon_D_pnotp. % 112.12/112.42 exact assumption_18c. % 112.12/112.42 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 112.12/112.42 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.12/112.42 congruence. % 112.12/112.42 apply zenon_H6a. apply refl_equal. % 112.12/112.42 exact (zenon_H10f zenon_H10e). % 112.12/112.42 apply (zenon_L169_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial. % 112.12/112.42 (* end of lemma zenon_L170_ *) % 112.12/112.42 assert (zenon_L171_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TT3_x : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> (organization zenon_TX_y) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (greater (age zenon_TX_y zenon_TT3_x) (tau)) -> False). % 112.12/112.42 do 4 intro. intros zenon_H34 zenon_Hb5 zenon_H1f zenon_Hae zenon_H1a zenon_Hec zenon_H35 zenon_H38 zenon_H26e zenon_H100. % 112.12/112.42 elim (classic (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_H271 | zenon_intro zenon_H270 ]. % 112.12/112.42 generalize (zenon_H34 (mod1)). zenon_intro zenon_Ha7. % 112.12/112.42 generalize (zenon_Ha7 (low)). zenon_intro zenon_Ha8. % 112.12/112.42 generalize (zenon_Ha8 (hazard_of_mortality zenon_TX_y zenon_TT3_x)). zenon_intro zenon_H272. % 112.12/112.42 apply (zenon_imply_s _ _ zenon_H272); [ zenon_intro zenon_H7f | zenon_intro zenon_H273 ]. % 112.12/112.42 exact (zenon_H7f assumption_18b). % 112.12/112.42 apply (zenon_imply_s _ _ zenon_H273); [ zenon_intro zenon_H270 | zenon_intro zenon_Hb4 ]. % 112.12/112.42 exact (zenon_H270 zenon_H271). % 112.12/112.42 exact (zenon_Hb5 zenon_Hb4). % 112.12/112.42 apply (zenon_L170_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial. % 112.12/112.42 (* end of lemma zenon_L171_ *) % 112.12/112.42 assert (zenon_L172_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TT3_x : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> (greater (age zenon_TX_y zenon_TT3_x) (tau)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (greater (tau) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> (organization zenon_TX_y) -> False). % 112.12/112.42 do 4 intro. intros zenon_H34 zenon_H274 zenon_H100 zenon_H26e zenon_H38 zenon_H35 zenon_Hec zenon_H1a zenon_Hae zenon_H1f. % 112.12/112.42 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb5 ]. % 112.12/112.42 generalize (zenon_H34 (mod2)). zenon_intro zenon_H16e. % 112.12/112.42 generalize (zenon_H16e (mod1)). zenon_intro zenon_H16f. % 112.12/112.42 generalize (zenon_H16f (hazard_of_mortality zenon_TX_y zenon_TT3_x)). zenon_intro zenon_H275. % 112.12/112.42 apply (zenon_imply_s _ _ zenon_H275); [ zenon_intro zenon_H69 | zenon_intro zenon_H276 ]. % 112.12/112.42 exact (zenon_H69 assumption_19). % 112.12/112.42 apply (zenon_imply_s _ _ zenon_H276); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H277 ]. % 112.12/112.42 exact (zenon_Hb5 zenon_Hb4). % 112.12/112.42 exact (zenon_H274 zenon_H277). % 112.12/112.42 apply (zenon_L171_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial. % 112.12/112.42 (* end of lemma zenon_L172_ *) % 112.12/112.42 assert (zenon_L173_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TT3_x : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (high) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> (organization zenon_TX_y) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (greater (age zenon_TX_y zenon_TT3_x) (tau)) -> False). % 112.12/112.42 do 4 intro. intros zenon_H34 zenon_H278 zenon_H1f zenon_Hae zenon_H1a zenon_Hec zenon_H35 zenon_H38 zenon_H26e zenon_H100. % 112.12/112.42 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_H277 | zenon_intro zenon_H274 ]. % 112.12/112.42 generalize (zenon_H34 (high)). zenon_intro zenon_H1fa. % 112.12/112.42 generalize (zenon_H1fa (mod2)). zenon_intro zenon_H1fb. % 112.12/112.42 generalize (zenon_H1fb (hazard_of_mortality zenon_TX_y zenon_TT3_x)). zenon_intro zenon_H279. % 112.12/112.42 apply (zenon_imply_s _ _ zenon_H279); [ zenon_intro zenon_H9b | zenon_intro zenon_H27a ]. % 112.12/112.42 exact (zenon_H9b assumption_18d). % 112.12/112.42 apply (zenon_imply_s _ _ zenon_H27a); [ zenon_intro zenon_H274 | zenon_intro zenon_H27b ]. % 112.12/112.42 exact (zenon_H274 zenon_H277). % 112.12/112.42 exact (zenon_H278 zenon_H27b). % 112.12/112.42 apply (zenon_L172_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial. % 112.12/112.42 (* end of lemma zenon_L173_ *) % 112.12/112.42 assert (zenon_L174_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TT3_x : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (high)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> (greater (age zenon_TX_y zenon_TT3_x) (tau)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (greater (tau) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> (organization zenon_TX_y) -> False). % 112.12/112.42 do 4 intro. intros zenon_H34 zenon_H116 zenon_H27c zenon_H100 zenon_H26e zenon_H38 zenon_H35 zenon_Hec zenon_H1a zenon_Hae zenon_H1f. % 112.12/112.42 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_H27b | zenon_intro zenon_H278 ]. % 112.12/112.42 cut ((greater (high) (hazard_of_mortality zenon_TX_y zenon_TT3_x)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT3_x))). % 112.12/112.42 intro zenon_D_pnotp. % 112.12/112.42 apply zenon_H27c. % 112.12/112.42 rewrite <- zenon_D_pnotp. % 112.12/112.42 exact zenon_H27b. % 112.12/112.42 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 112.12/112.42 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H119]. % 112.12/112.42 congruence. % 112.12/112.42 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.42 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.42 intro zenon_D_pnotp. % 112.12/112.42 apply zenon_H119. % 112.12/112.42 rewrite <- zenon_D_pnotp. % 112.12/112.42 exact zenon_H11a. % 112.12/112.42 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.42 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 112.12/112.42 congruence. % 112.12/112.42 exact (zenon_H11c zenon_H116). % 112.12/112.42 apply zenon_H11b. apply refl_equal. % 112.12/112.42 apply zenon_H11b. apply refl_equal. % 112.12/112.42 apply zenon_Hb6. apply refl_equal. % 112.12/112.42 apply (zenon_L173_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial. % 112.12/112.42 (* end of lemma zenon_L174_ *) % 112.12/112.42 assert (zenon_L175_ : forall (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (~(greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod1)) -> False). % 112.12/112.42 do 2 intro. intros zenon_H1c4 zenon_H92. % 112.12/112.42 elim (classic ((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H27d | zenon_intro zenon_Ha0 ]. % 112.12/112.42 cut ((greater (mod2) (mod1)) = (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.42 intro zenon_D_pnotp. % 112.12/112.42 apply zenon_H1c4. % 112.12/112.42 rewrite <- zenon_D_pnotp. % 112.12/112.42 exact assumption_19. % 112.12/112.42 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 112.12/112.42 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 112.12/112.42 congruence. % 112.12/112.42 apply zenon_H83. apply refl_equal. % 112.12/112.42 exact (zenon_Ha0 zenon_H27d). % 112.12/112.42 apply zenon_Ha0. apply sym_equal. exact zenon_H92. % 112.12/112.42 (* end of lemma zenon_L175_ *) % 112.12/112.42 assert (zenon_L176_ : forall (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod1)) -> False). % 112.12/112.42 do 2 intro. intros zenon_H34 zenon_H2c zenon_H1c2 zenon_H92. % 112.12/112.42 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H118 | zenon_intro zenon_H114 ]. % 112.12/112.42 cut ((greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.42 intro zenon_D_pnotp. % 112.12/112.42 apply zenon_H1c2. % 112.12/112.42 rewrite <- zenon_D_pnotp. % 112.12/112.42 exact zenon_H118. % 112.12/112.42 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.42 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 112.12/112.42 congruence. % 112.12/112.42 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.12/112.42 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.42 intro zenon_D_pnotp. % 112.12/112.42 apply zenon_H94. % 112.12/112.42 rewrite <- zenon_D_pnotp. % 112.12/112.42 exact zenon_H61. % 112.12/112.42 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.42 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 112.12/112.42 congruence. % 112.12/112.42 exact (zenon_H2b zenon_H2c). % 112.12/112.42 apply zenon_H62. apply refl_equal. % 112.12/112.42 apply zenon_H62. apply refl_equal. % 112.12/112.42 apply zenon_H62. apply refl_equal. % 112.12/112.42 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1c4 ]. % 112.12/112.42 generalize (zenon_H34 (high)). zenon_intro zenon_H1fa. % 112.12/112.42 generalize (zenon_H1fa (mod2)). zenon_intro zenon_H1fb. % 112.12/112.42 generalize (zenon_H1fb (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H27e. % 112.12/112.42 apply (zenon_imply_s _ _ zenon_H27e); [ zenon_intro zenon_H9b | zenon_intro zenon_H27f ]. % 112.12/112.42 exact (zenon_H9b assumption_18d). % 112.12/112.42 apply (zenon_imply_s _ _ zenon_H27f); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H118 ]. % 112.12/112.42 exact (zenon_H1c4 zenon_H1c3). % 112.12/112.42 exact (zenon_H114 zenon_H118). % 112.12/112.42 apply (zenon_L175_ zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.42 (* end of lemma zenon_L176_ *) % 112.12/112.42 assert (zenon_L177_ : forall (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod1)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (high) (high))) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high)) -> False). % 112.12/112.42 do 2 intro. intros zenon_H92 zenon_H34 zenon_H280 zenon_H2c. % 112.12/112.42 elim (classic ((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H281 | zenon_intro zenon_H94 ]. % 112.12/112.42 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (high))); [ zenon_intro zenon_H97 | zenon_intro zenon_H87 ]. % 112.12/112.42 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (high)) = (greater (high) (high))). % 112.12/112.42 intro zenon_D_pnotp. % 112.12/112.42 apply zenon_H280. % 112.12/112.42 rewrite <- zenon_D_pnotp. % 112.12/112.42 exact zenon_H97. % 112.12/112.42 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113]. % 112.12/112.42 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 112.12/112.42 congruence. % 112.12/112.42 elim (classic ((high) = (high))); [ zenon_intro zenon_H180 | zenon_intro zenon_H113 ]. % 112.12/112.42 cut (((high) = (high)) = ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))). % 112.12/112.42 intro zenon_D_pnotp. % 112.12/112.42 apply zenon_H2b. % 112.12/112.42 rewrite <- zenon_D_pnotp. % 112.12/112.42 exact zenon_H180. % 112.12/112.42 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113]. % 112.12/112.42 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 112.12/112.42 congruence. % 112.12/112.42 exact (zenon_H94 zenon_H281). % 112.12/112.42 apply zenon_H113. apply refl_equal. % 112.12/112.42 apply zenon_H113. apply refl_equal. % 112.12/112.42 apply zenon_H113. apply refl_equal. % 112.12/112.42 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H1c2 ]. % 112.12/112.42 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (high))). % 112.12/112.42 intro zenon_D_pnotp. % 112.12/112.42 apply zenon_H87. % 112.12/112.42 rewrite <- zenon_D_pnotp. % 112.12/112.42 exact zenon_H1c5. % 112.12/112.42 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 112.12/112.42 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.42 congruence. % 112.12/112.42 apply zenon_H62. apply refl_equal. % 112.12/112.42 exact (zenon_H2b zenon_H2c). % 112.12/112.42 apply (zenon_L176_ zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.42 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.12/112.42 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.42 intro zenon_D_pnotp. % 112.12/112.42 apply zenon_H94. % 112.12/112.42 rewrite <- zenon_D_pnotp. % 112.12/112.42 exact zenon_H61. % 112.12/112.42 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.42 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 112.12/112.42 congruence. % 112.12/112.42 exact (zenon_H2b zenon_H2c). % 112.12/112.42 apply zenon_H62. apply refl_equal. % 112.12/112.42 apply zenon_H62. apply refl_equal. % 112.12/112.42 (* end of lemma zenon_L177_ *) % 112.12/112.42 assert (zenon_L178_ : forall (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (((~(is_aligned zenon_TX_y zenon_TT1_bg))/\(~(positional_advantage zenon_TX_y zenon_TT1_bg)))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (greater (tau) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (~(is_aligned zenon_TX_y zenon_TT1_bg)) -> (~(greater (mod2) (high))) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod1)) -> False). % 112.12/112.43 do 2 intro. intros zenon_H28 zenon_H26e zenon_H38 zenon_H35 zenon_H2a zenon_H282 zenon_H92. % 112.12/112.43 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ]. % 112.12/112.43 apply (zenon_notand_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ]. % 112.12/112.43 exact (zenon_H2f zenon_H2a). % 112.12/112.43 apply zenon_H2e. zenon_intro zenon_H36. % 112.12/112.43 apply (zenon_L155_ zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.43 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1c4 ]. % 112.12/112.43 cut ((greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (mod2) (high))). % 112.12/112.43 intro zenon_D_pnotp. % 112.12/112.43 apply zenon_H282. % 112.12/112.43 rewrite <- zenon_D_pnotp. % 112.12/112.43 exact zenon_H1c3. % 112.12/112.43 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 112.12/112.43 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 112.12/112.43 congruence. % 112.12/112.43 apply zenon_H83. apply refl_equal. % 112.12/112.43 exact (zenon_H2b zenon_H2c). % 112.12/112.43 apply (zenon_L175_ zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.43 (* end of lemma zenon_L178_ *) % 112.12/112.43 assert (zenon_L179_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT3_x : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~(greater (mod2) (high))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (greater (age zenon_TX_y zenon_TT3_x) (tau)) -> (~((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> False). % 112.12/112.43 do 4 intro. intros zenon_H34 zenon_H0 zenon_H1f zenon_H1a zenon_H35 zenon_H38 zenon_H26e zenon_H282 zenon_H2b zenon_Hae zenon_Hec zenon_H100 zenon_H72. % 112.12/112.43 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88. % 112.12/112.43 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ]. % 112.12/112.43 exact (zenon_H27 zenon_H1f). % 112.12/112.43 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a. % 112.12/112.43 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ]. % 112.12/112.43 apply (zenon_L3_ zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.43 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d. % 112.12/112.43 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f. % 112.12/112.43 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H30. zenon_intro zenon_H28. % 112.12/112.43 apply (zenon_imply_s _ _ zenon_H8e); [ zenon_intro zenon_H91 | zenon_intro zenon_H6b ]. % 112.12/112.43 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 112.12/112.43 apply (zenon_imply_s _ _ zenon_H90); [ zenon_intro zenon_H93 | zenon_intro zenon_H92 ]. % 112.12/112.43 apply (zenon_notand_s _ _ zenon_H93); [ zenon_intro zenon_H2f | zenon_intro zenon_H29 ]. % 112.12/112.43 exact (zenon_H2f zenon_H2a). % 112.12/112.43 apply (zenon_L4_ zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.43 apply (zenon_L178_ zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.43 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 112.12/112.43 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ]. % 112.12/112.43 apply (zenon_L4_ zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.43 exact (zenon_H2e zenon_H29). % 112.12/112.43 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_H277 | zenon_intro zenon_H274 ]. % 112.12/112.43 cut ((greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT3_x)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))). % 112.12/112.43 intro zenon_D_pnotp. % 112.12/112.43 apply zenon_Hae. % 112.12/112.43 rewrite <- zenon_D_pnotp. % 112.12/112.43 exact zenon_H277. % 112.12/112.43 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 112.12/112.43 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 112.12/112.43 congruence. % 112.12/112.43 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.12/112.43 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.43 intro zenon_D_pnotp. % 112.12/112.43 apply zenon_H5e. % 112.12/112.43 rewrite <- zenon_D_pnotp. % 112.12/112.43 exact zenon_H61. % 112.12/112.43 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.43 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31]. % 112.12/112.43 congruence. % 112.12/112.43 exact (zenon_H31 zenon_H32). % 112.12/112.43 apply zenon_H62. apply refl_equal. % 112.12/112.43 apply zenon_H62. apply refl_equal. % 112.12/112.43 apply zenon_Hb6. apply refl_equal. % 112.12/112.43 apply (zenon_L172_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial. % 112.12/112.43 apply zenon_H72. apply sym_equal. exact zenon_H6b. % 112.12/112.43 (* end of lemma zenon_L179_ *) % 112.12/112.43 assert (zenon_L180_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT3_x : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~(greater (mod2) (high))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (greater (age zenon_TX_y zenon_TT3_x) (tau)) -> False). % 112.12/112.43 do 4 intro. intros zenon_H34 zenon_H1f zenon_H1a zenon_H35 zenon_H38 zenon_H26e zenon_H282 zenon_H2b zenon_Hae zenon_Hec zenon_H100. % 112.12/112.43 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0. % 112.12/112.43 cut ((greater (low) (very_low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))). % 112.12/112.43 intro zenon_D_pnotp. % 112.12/112.43 apply zenon_Hae. % 112.12/112.43 rewrite <- zenon_D_pnotp. % 112.12/112.43 exact assumption_18c. % 112.12/112.43 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 112.12/112.43 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 112.12/112.43 congruence. % 112.12/112.43 apply (zenon_L179_ zenon_TT0_hz zenon_TT3_x zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.43 apply (zenon_L169_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial. % 112.12/112.43 (* end of lemma zenon_L180_ *) % 112.12/112.43 assert (zenon_L181_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT3_x : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (high) (high))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (greater (age zenon_TX_y zenon_TT3_x) (tau)) -> False). % 112.12/112.43 do 4 intro. intros zenon_H34 zenon_H280 zenon_H1f zenon_H1a zenon_H35 zenon_H38 zenon_H26e zenon_H2b zenon_Hae zenon_Hec zenon_H100. % 112.12/112.43 elim (classic (greater (mod2) (high))); [ zenon_intro zenon_H283 | zenon_intro zenon_H282 ]. % 112.12/112.43 generalize (zenon_H34 (high)). zenon_intro zenon_H1fa. % 112.12/112.43 generalize (zenon_H1fa (mod2)). zenon_intro zenon_H1fb. % 112.12/112.43 generalize (zenon_H1fb (high)). zenon_intro zenon_H284. % 112.12/112.43 apply (zenon_imply_s _ _ zenon_H284); [ zenon_intro zenon_H9b | zenon_intro zenon_H285 ]. % 112.12/112.43 exact (zenon_H9b assumption_18d). % 112.12/112.43 apply (zenon_imply_s _ _ zenon_H285); [ zenon_intro zenon_H282 | zenon_intro zenon_H286 ]. % 112.12/112.43 exact (zenon_H282 zenon_H283). % 112.12/112.43 exact (zenon_H280 zenon_H286). % 112.12/112.43 apply (zenon_L180_ zenon_TT0_hz zenon_TT3_x zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.43 (* end of lemma zenon_L181_ *) % 112.12/112.43 assert (zenon_L182_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT3_x : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (greater (age zenon_TX_y zenon_TT3_x) (tau)) -> False). % 112.12/112.44 do 4 intro. intros zenon_H34 zenon_H1f zenon_H1a zenon_H35 zenon_H38 zenon_H26e zenon_H2b zenon_Hae zenon_Hec zenon_H100. % 112.12/112.44 generalize (meaning_postulate_greater_strict (high)). zenon_intro zenon_H202. % 112.12/112.44 generalize (zenon_H202 (high)). zenon_intro zenon_H287. % 112.12/112.44 apply (zenon_notand_s _ _ zenon_H287); [ zenon_intro zenon_H280 | zenon_intro zenon_H280 ]. % 112.12/112.44 apply (zenon_L181_ zenon_TT0_hz zenon_TT3_x zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.44 apply (zenon_L181_ zenon_TT0_hz zenon_TT3_x zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.44 (* end of lemma zenon_L182_ *) % 112.12/112.44 assert (zenon_L183_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TT3_x : zenon_U) (zenon_TX_y : zenon_U), (greater (age zenon_TX_y zenon_TT3_x) (tau)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (greater (tau) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> (organization zenon_TX_y) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (high)) -> False). % 112.12/112.44 do 4 intro. intros zenon_H100 zenon_H26e zenon_H38 zenon_H35 zenon_Hec zenon_H1a zenon_Hae zenon_H1f zenon_H34 zenon_H116. % 112.12/112.44 elim (classic ((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H17d | zenon_intro zenon_H119 ]. % 112.12/112.44 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_H288 | zenon_intro zenon_H27c ]. % 112.12/112.44 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_H27b | zenon_intro zenon_H278 ]. % 112.12/112.44 cut ((greater (high) (hazard_of_mortality zenon_TX_y zenon_TT3_x)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_Hae. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_H27b. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 112.12/112.44 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 112.12/112.44 congruence. % 112.12/112.44 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_H94. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_H61. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 112.12/112.44 congruence. % 112.12/112.44 apply (zenon_L182_ zenon_TT0_hz zenon_TT3_x zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.44 apply zenon_H62. apply refl_equal. % 112.12/112.44 apply zenon_H62. apply refl_equal. % 112.12/112.44 apply zenon_Hb6. apply refl_equal. % 112.12/112.44 cut ((greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT3_x)) = (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT3_x))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_H278. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_H288. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 112.12/112.44 congruence. % 112.12/112.44 elim (classic ((high) = (high))); [ zenon_intro zenon_H180 | zenon_intro zenon_H113 ]. % 112.12/112.44 cut (((high) = (high)) = ((hazard_of_mortality zenon_TX_y zenon_E) = (high))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_H11c. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_H180. % 112.12/112.44 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113]. % 112.12/112.44 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H119]. % 112.12/112.44 congruence. % 112.12/112.44 exact (zenon_H119 zenon_H17d). % 112.12/112.44 apply zenon_H113. apply refl_equal. % 112.12/112.44 apply zenon_H113. apply refl_equal. % 112.12/112.44 apply zenon_Hb6. apply refl_equal. % 112.12/112.44 apply (zenon_L174_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial. % 112.12/112.44 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_H119. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_H11a. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 112.12/112.44 congruence. % 112.12/112.44 exact (zenon_H11c zenon_H116). % 112.12/112.44 apply zenon_H11b. apply refl_equal. % 112.12/112.44 apply zenon_H11b. apply refl_equal. % 112.12/112.44 (* end of lemma zenon_L183_ *) % 112.12/112.44 assert (zenon_L184_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TT3_x : zenon_U) (zenon_TX_y : zenon_U), (((~(is_aligned zenon_TX_y zenon_E))/\(~(positional_advantage zenon_TX_y zenon_E)))->((hazard_of_mortality zenon_TX_y zenon_E) = (high))) -> (~(positional_advantage zenon_TX_y zenon_E)) -> (~(is_aligned zenon_TX_y zenon_E)) -> (greater (age zenon_TX_y zenon_TT3_x) (tau)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (greater (tau) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> (organization zenon_TX_y) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> False). % 112.12/112.44 do 4 intro. intros zenon_H181 zenon_H182 zenon_H183 zenon_H100 zenon_H26e zenon_H38 zenon_H35 zenon_Hec zenon_H1a zenon_Hae zenon_H1f zenon_H34. % 112.12/112.44 apply (zenon_imply_s _ _ zenon_H181); [ zenon_intro zenon_H184 | zenon_intro zenon_H116 ]. % 112.12/112.44 apply (zenon_notand_s _ _ zenon_H184); [ zenon_intro zenon_H186 | zenon_intro zenon_H185 ]. % 112.12/112.44 exact (zenon_H186 zenon_H183). % 112.12/112.44 exact (zenon_H185 zenon_H182). % 112.12/112.44 apply (zenon_L183_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial. % 112.12/112.44 (* end of lemma zenon_L184_ *) % 112.12/112.44 assert (zenon_L185_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (sigma) (sigma))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> False). % 112.12/112.44 do 3 intro. intros zenon_H1f zenon_H1a zenon_Hec zenon_Hf3 zenon_H31 zenon_H35 zenon_H38 zenon_H34 zenon_Hda zenon_H26e. % 112.12/112.44 elim (classic ((sigma) = (age zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_He2 | zenon_intro zenon_Hde ]. % 112.12/112.44 elim (classic (greater (age zenon_TX_y zenon_TT1_bg) (sigma))); [ zenon_intro zenon_Hdb | zenon_intro zenon_He9 ]. % 112.12/112.44 cut ((greater (age zenon_TX_y zenon_TT1_bg) (sigma)) = (greater (sigma) (sigma))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_Hda. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_Hdb. % 112.12/112.44 cut (((sigma) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 112.12/112.44 cut (((age zenon_TX_y zenon_TT1_bg) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hdf]. % 112.12/112.44 congruence. % 112.12/112.44 elim (classic ((sigma) = (sigma))); [ zenon_intro zenon_He3 | zenon_intro zenon_Hd9 ]. % 112.12/112.44 cut (((sigma) = (sigma)) = ((age zenon_TX_y zenon_TT1_bg) = (sigma))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_Hdf. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_He3. % 112.12/112.44 cut (((sigma) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 112.12/112.44 cut (((sigma) = (age zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_Hde]. % 112.12/112.44 congruence. % 112.12/112.44 exact (zenon_Hde zenon_He2). % 112.12/112.44 apply zenon_Hd9. apply refl_equal. % 112.12/112.44 apply zenon_Hd9. apply refl_equal. % 112.12/112.44 apply zenon_Hd9. apply refl_equal. % 112.12/112.44 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0. % 112.12/112.44 apply (zenon_L159_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.44 elim (classic ((age zenon_TX_y zenon_TT1_bg) = (age zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H26f | zenon_intro zenon_H4d ]. % 112.12/112.44 cut (((age zenon_TX_y zenon_TT1_bg) = (age zenon_TX_y zenon_TT1_bg)) = ((sigma) = (age zenon_TX_y zenon_TT1_bg))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_Hde. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_H26f. % 112.12/112.44 cut (((age zenon_TX_y zenon_TT1_bg) = (age zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 112.12/112.44 cut (((age zenon_TX_y zenon_TT1_bg) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hdf]. % 112.12/112.44 congruence. % 112.12/112.44 exact (zenon_Hdf zenon_H26e). % 112.12/112.44 apply zenon_H4d. apply refl_equal. % 112.12/112.44 apply zenon_H4d. apply refl_equal. % 112.12/112.44 (* end of lemma zenon_L185_ *) % 112.12/112.44 assert (zenon_L186_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (greater (tau) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (organization zenon_TX_y) -> False). % 112.12/112.44 do 3 intro. intros zenon_H34 zenon_H26e zenon_H38 zenon_H35 zenon_H31 zenon_Hf3 zenon_Hec zenon_H1a zenon_H1f. % 112.12/112.44 generalize (meaning_postulate_greater_strict (sigma)). zenon_intro zenon_Hea. % 112.12/112.44 generalize (zenon_Hea (sigma)). zenon_intro zenon_Heb. % 112.12/112.44 apply (zenon_notand_s _ _ zenon_Heb); [ zenon_intro zenon_Hda | zenon_intro zenon_Hda ]. % 112.12/112.44 apply (zenon_L185_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.44 apply (zenon_L185_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.44 (* end of lemma zenon_L186_ *) % 112.12/112.44 assert (zenon_L187_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> False). % 112.12/112.44 do 3 intro. intros zenon_H34 zenon_H1f zenon_H1a zenon_Hec zenon_H31 zenon_H35 zenon_H38 zenon_H26e. % 112.12/112.44 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3. % 112.12/112.44 apply (zenon_L186_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.44 (* end of lemma zenon_L187_ *) % 112.12/112.44 assert (zenon_L188_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (greater (tau) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (organization zenon_TX_y) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1))) -> False). % 112.12/112.44 do 3 intro. intros zenon_H26e zenon_H38 zenon_H35 zenon_Hec zenon_H1a zenon_H1f zenon_H34 zenon_H5a. % 112.12/112.44 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod2))))); [ zenon_intro zenon_H5b | zenon_intro zenon_H5c ]. % 112.12/112.44 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H31. zenon_intro zenon_H5d. % 112.12/112.44 apply (zenon_L187_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.44 cut ((greater (mod2) (mod1)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_H5a. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact assumption_19. % 112.12/112.44 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 112.12/112.44 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 112.12/112.44 congruence. % 112.12/112.44 apply (zenon_notand_s _ _ zenon_H5c); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ]. % 112.12/112.44 apply zenon_H60. zenon_intro zenon_H32. % 112.12/112.44 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_H5e. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_H61. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31]. % 112.12/112.44 congruence. % 112.12/112.44 exact (zenon_H31 zenon_H32). % 112.12/112.44 apply zenon_H62. apply refl_equal. % 112.12/112.44 apply zenon_H62. apply refl_equal. % 112.12/112.44 apply zenon_H5f. zenon_intro zenon_H63. % 112.12/112.44 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64. % 112.12/112.44 generalize (zenon_H64 (mod2)). zenon_intro zenon_H65. % 112.12/112.44 generalize (zenon_H65 (mod1)). zenon_intro zenon_H66. % 112.12/112.44 apply (zenon_imply_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H67 ]. % 112.12/112.44 exact (zenon_H5d zenon_H63). % 112.12/112.44 apply (zenon_imply_s _ _ zenon_H67); [ zenon_intro zenon_H69 | zenon_intro zenon_H68 ]. % 112.12/112.44 exact (zenon_H69 assumption_19). % 112.12/112.44 exact (zenon_H5a zenon_H68). % 112.12/112.44 apply zenon_H59. apply refl_equal. % 112.12/112.44 (* end of lemma zenon_L188_ *) % 112.12/112.44 assert (zenon_L189_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TT3_x : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (mod2)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> (organization zenon_TX_y) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (greater (age zenon_TX_y zenon_TT3_x) (tau)) -> False). % 112.12/112.44 do 4 intro. intros zenon_H34 zenon_H19e zenon_H27c zenon_H1f zenon_Hae zenon_H1a zenon_Hec zenon_H35 zenon_H38 zenon_H26e zenon_H100. % 112.12/112.44 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_H277 | zenon_intro zenon_H274 ]. % 112.12/112.44 cut ((greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT3_x)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT3_x))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_H27c. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_H277. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 112.12/112.44 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 112.12/112.44 congruence. % 112.12/112.44 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_H1a1. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_H11a. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 112.12/112.44 congruence. % 112.12/112.44 exact (zenon_H1a2 zenon_H19e). % 112.12/112.44 apply zenon_H11b. apply refl_equal. % 112.12/112.44 apply zenon_H11b. apply refl_equal. % 112.12/112.44 apply zenon_Hb6. apply refl_equal. % 112.12/112.44 apply (zenon_L172_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial. % 112.12/112.44 (* end of lemma zenon_L189_ *) % 112.12/112.44 assert (zenon_L190_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT3_x : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (organization zenon_TX_y) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (greater (age zenon_TX_y zenon_TT3_x) (tau)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (mod2)) -> False). % 112.12/112.44 do 4 intro. intros zenon_H1f zenon_Hae zenon_H1a zenon_Hec zenon_H35 zenon_H38 zenon_H26e zenon_H100 zenon_H34 zenon_H19e. % 112.12/112.44 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H1a1 ]. % 112.12/112.44 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_H288 | zenon_intro zenon_H27c ]. % 112.12/112.44 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_H277 | zenon_intro zenon_H274 ]. % 112.12/112.44 cut ((greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT3_x)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_Hae. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_H277. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 112.12/112.44 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 112.12/112.44 congruence. % 112.12/112.44 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_H5e. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_H61. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31]. % 112.12/112.44 congruence. % 112.12/112.44 apply (zenon_L187_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.44 apply zenon_H62. apply refl_equal. % 112.12/112.44 apply zenon_H62. apply refl_equal. % 112.12/112.44 apply zenon_Hb6. apply refl_equal. % 112.12/112.44 cut ((greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT3_x)) = (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT3_x))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_H274. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_H288. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 112.12/112.44 congruence. % 112.12/112.44 elim (classic ((mod2) = (mod2))); [ zenon_intro zenon_H17b | zenon_intro zenon_H83 ]. % 112.12/112.44 cut (((mod2) = (mod2)) = ((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_H1a2. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_H17b. % 112.12/112.44 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 112.12/112.44 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 112.12/112.44 congruence. % 112.12/112.44 exact (zenon_H1a1 zenon_H1a3). % 112.12/112.44 apply zenon_H83. apply refl_equal. % 112.12/112.44 apply zenon_H83. apply refl_equal. % 112.12/112.44 apply zenon_Hb6. apply refl_equal. % 112.12/112.44 apply (zenon_L189_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial. % 112.12/112.44 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_H1a1. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_H11a. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 112.12/112.44 congruence. % 112.12/112.44 exact (zenon_H1a2 zenon_H19e). % 112.12/112.44 apply zenon_H11b. apply refl_equal. % 112.12/112.44 apply zenon_H11b. apply refl_equal. % 112.12/112.44 (* end of lemma zenon_L190_ *) % 112.12/112.44 assert (zenon_L191_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (greater (tau) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (organization zenon_TX_y) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low))) -> False). % 112.12/112.44 do 3 intro. intros zenon_H26e zenon_H38 zenon_H35 zenon_Hec zenon_H1a zenon_H1f zenon_H34 zenon_H9d. % 112.12/112.44 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod2))))); [ zenon_intro zenon_H5b | zenon_intro zenon_H5c ]. % 112.12/112.44 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H31. zenon_intro zenon_H5d. % 112.12/112.44 apply (zenon_L187_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.44 cut ((greater (mod2) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_H9d. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact assumption_18e. % 112.12/112.44 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.12/112.44 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 112.12/112.44 congruence. % 112.12/112.44 apply (zenon_notand_s _ _ zenon_H5c); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ]. % 112.12/112.44 apply zenon_H60. zenon_intro zenon_H32. % 112.12/112.44 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_H5e. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_H61. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31]. % 112.12/112.44 congruence. % 112.12/112.44 exact (zenon_H31 zenon_H32). % 112.12/112.44 apply zenon_H62. apply refl_equal. % 112.12/112.44 apply zenon_H62. apply refl_equal. % 112.12/112.44 apply zenon_H5f. zenon_intro zenon_H63. % 112.12/112.44 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64. % 112.12/112.44 generalize (zenon_H64 (mod2)). zenon_intro zenon_H65. % 112.12/112.44 generalize (zenon_H65 (low)). zenon_intro zenon_Hc0. % 112.12/112.44 apply (zenon_imply_s _ _ zenon_Hc0); [ zenon_intro zenon_H5d | zenon_intro zenon_Hc1 ]. % 112.12/112.44 exact (zenon_H5d zenon_H63). % 112.12/112.44 apply (zenon_imply_s _ _ zenon_Hc1); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H9c ]. % 112.12/112.44 exact (zenon_Hc2 assumption_18e). % 112.12/112.44 exact (zenon_H9d zenon_H9c). % 112.12/112.44 apply zenon_H6a. apply refl_equal. % 112.12/112.44 (* end of lemma zenon_L191_ *) % 112.12/112.44 assert (zenon_L192_ : forall (zenon_TT3_x : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))) -> (greater (age zenon_TX_y zenon_TT3_x) (tau)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (low)) -> False). % 112.12/112.44 do 4 intro. intros zenon_H1f zenon_H1a zenon_Hec zenon_H35 zenon_H38 zenon_H26e zenon_Hae zenon_H100 zenon_H34 zenon_H1b8. % 112.12/112.44 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1ba ]. % 112.12/112.44 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low))); [ zenon_intro zenon_H9c | zenon_intro zenon_H9d ]. % 112.12/112.44 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H289 | zenon_intro zenon_H28a ]. % 112.12/112.44 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_H288 | zenon_intro zenon_H27c ]. % 112.12/112.44 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64. % 112.12/112.44 generalize (zenon_H64 (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H28b. % 112.12/112.44 generalize (zenon_H28b (hazard_of_mortality zenon_TX_y zenon_TT3_x)). zenon_intro zenon_H28c. % 112.12/112.44 apply (zenon_imply_s _ _ zenon_H28c); [ zenon_intro zenon_H28a | zenon_intro zenon_H28d ]. % 112.12/112.44 exact (zenon_H28a zenon_H289). % 112.12/112.44 apply (zenon_imply_s _ _ zenon_H28d); [ zenon_intro zenon_H27c | zenon_intro zenon_H104 ]. % 112.12/112.44 exact (zenon_H27c zenon_H288). % 112.12/112.44 exact (zenon_Hae zenon_H104). % 112.12/112.44 elim (classic (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_H271 | zenon_intro zenon_H270 ]. % 112.12/112.44 cut ((greater (low) (hazard_of_mortality zenon_TX_y zenon_TT3_x)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT3_x))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_H27c. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_H271. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 112.12/112.44 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba]. % 112.12/112.44 congruence. % 112.12/112.44 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((low) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_H1ba. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_H11a. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 112.12/112.44 congruence. % 112.12/112.44 exact (zenon_H1bb zenon_H1b8). % 112.12/112.44 apply zenon_H11b. apply refl_equal. % 112.12/112.44 apply zenon_H11b. apply refl_equal. % 112.12/112.44 apply zenon_Hb6. apply refl_equal. % 112.12/112.44 apply (zenon_L170_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial. % 112.12/112.44 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_H28a. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_H9c. % 112.12/112.44 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.44 congruence. % 112.12/112.44 apply zenon_H62. apply refl_equal. % 112.12/112.44 exact (zenon_H1ba zenon_H1b9). % 112.12/112.44 apply (zenon_L191_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.44 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((low) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_H1ba. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_H11a. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 112.12/112.44 congruence. % 112.12/112.44 exact (zenon_H1bb zenon_H1b8). % 112.12/112.44 apply zenon_H11b. apply refl_equal. % 112.12/112.44 apply zenon_H11b. apply refl_equal. % 112.12/112.44 (* end of lemma zenon_L192_ *) % 112.12/112.44 assert (zenon_L193_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (very_low))) -> False). % 112.12/112.44 do 3 intro. intros zenon_H1f zenon_H1a zenon_Hec zenon_H35 zenon_H38 zenon_H26e zenon_H34 zenon_Hf6. % 112.12/112.44 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low))))); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hf8 ]. % 112.12/112.44 apply (zenon_and_s _ _ zenon_Hf7). zenon_intro zenon_H73. zenon_intro zenon_H9d. % 112.12/112.44 apply (zenon_L191_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.44 cut ((greater (low) (very_low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (very_low))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_Hf6. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact assumption_18c. % 112.12/112.44 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 112.12/112.44 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 112.12/112.44 congruence. % 112.12/112.44 apply (zenon_notand_s _ _ zenon_Hf8); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hf9 ]. % 112.12/112.44 apply zenon_Hfa. zenon_intro zenon_H6b. % 112.12/112.44 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_H72. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_H61. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 112.12/112.44 congruence. % 112.12/112.44 exact (zenon_H73 zenon_H6b). % 112.12/112.44 apply zenon_H62. apply refl_equal. % 112.12/112.44 apply zenon_H62. apply refl_equal. % 112.12/112.44 apply zenon_Hf9. zenon_intro zenon_H9c. % 112.12/112.44 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64. % 112.12/112.44 generalize (zenon_H64 (low)). zenon_intro zenon_Hfb. % 112.12/112.44 generalize (zenon_Hfb (very_low)). zenon_intro zenon_Hfc. % 112.12/112.44 apply (zenon_imply_s _ _ zenon_Hfc); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfd ]. % 112.12/112.44 exact (zenon_H9d zenon_H9c). % 112.12/112.44 apply (zenon_imply_s _ _ zenon_Hfd); [ zenon_intro zenon_Hff | zenon_intro zenon_Hfe ]. % 112.12/112.44 exact (zenon_Hff assumption_18c). % 112.12/112.44 exact (zenon_Hf6 zenon_Hfe). % 112.12/112.44 apply zenon_Hf5. apply refl_equal. % 112.12/112.44 (* end of lemma zenon_L193_ *) % 112.12/112.44 assert (zenon_L194_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (greater (tau) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (organization zenon_TX_y) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_E))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (very_low)) -> False). % 112.12/112.44 do 3 intro. intros zenon_H26e zenon_H38 zenon_H35 zenon_Hec zenon_H1a zenon_H1f zenon_H28a zenon_H34 zenon_H1e0. % 112.12/112.44 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e2 ]. % 112.12/112.44 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (very_low))); [ zenon_intro zenon_Hfe | zenon_intro zenon_Hf6 ]. % 112.12/112.44 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (very_low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_H28a. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_Hfe. % 112.12/112.44 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1e2]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.44 congruence. % 112.12/112.44 apply zenon_H62. apply refl_equal. % 112.12/112.44 exact (zenon_H1e2 zenon_H1e1). % 112.12/112.44 apply (zenon_L193_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.44 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_H1e2. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_H11a. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 112.12/112.44 congruence. % 112.12/112.44 exact (zenon_H1e5 zenon_H1e0). % 112.12/112.44 apply zenon_H11b. apply refl_equal. % 112.12/112.44 apply zenon_H11b. apply refl_equal. % 112.12/112.44 (* end of lemma zenon_L194_ *) % 112.12/112.44 assert (zenon_L195_ : forall (zenon_TT3_x : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (greater (age zenon_TX_y zenon_TT3_x) (tau)) -> (~(smaller (hazard_of_mortality zenon_TX_y zenon_TT3_x) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> False). % 112.12/112.44 do 4 intro. intros zenon_H34 zenon_H1f zenon_H1a zenon_H35 zenon_H38 zenon_H26e zenon_Hec zenon_H100 zenon_H101. % 112.12/112.44 generalize (definition_smaller (hazard_of_mortality zenon_TX_y zenon_TT3_x)). zenon_intro zenon_H102. % 112.12/112.44 generalize (zenon_H102 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H103. % 112.12/112.44 apply (zenon_equiv_s _ _ zenon_H103); [ zenon_intro zenon_H101; zenon_intro zenon_Hae | zenon_intro zenon_H105; zenon_intro zenon_H104 ]. % 112.12/112.44 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0. % 112.12/112.44 generalize (zenon_H0 zenon_E). zenon_intro zenon_H239. % 112.12/112.44 apply (zenon_imply_s _ _ zenon_H239); [ zenon_intro zenon_H27 | zenon_intro zenon_H23a ]. % 112.12/112.44 exact (zenon_H27 zenon_H1f). % 112.12/112.44 apply (zenon_and_s _ _ zenon_H23a). zenon_intro zenon_H23b. zenon_intro zenon_H238. % 112.12/112.44 apply (zenon_imply_s _ _ zenon_H23b); [ zenon_intro zenon_H112 | zenon_intro zenon_H1e0 ]. % 112.12/112.44 apply (zenon_imply_s _ _ zenon_H238); [ zenon_intro zenon_H111 | zenon_intro zenon_H22f ]. % 112.12/112.44 exact (zenon_H111 zenon_H112). % 112.12/112.44 apply (zenon_and_s _ _ zenon_H22f). zenon_intro zenon_H231. zenon_intro zenon_H230. % 112.12/112.44 apply (zenon_and_s _ _ zenon_H230). zenon_intro zenon_H233. zenon_intro zenon_H232. % 112.12/112.44 apply (zenon_and_s _ _ zenon_H232). zenon_intro zenon_H234. zenon_intro zenon_H181. % 112.12/112.44 apply (zenon_imply_s _ _ zenon_H231); [ zenon_intro zenon_H235 | zenon_intro zenon_H1b8 ]. % 112.12/112.44 apply (zenon_notand_s _ _ zenon_H235); [ zenon_intro zenon_H183 | zenon_intro zenon_H182 ]. % 112.12/112.44 apply (zenon_imply_s _ _ zenon_H233); [ zenon_intro zenon_H236 | zenon_intro zenon_H21a ]. % 112.12/112.44 apply (zenon_notand_s _ _ zenon_H236); [ zenon_intro zenon_H186 | zenon_intro zenon_H182 ]. % 112.12/112.44 exact (zenon_H186 zenon_H183). % 112.12/112.44 apply (zenon_L184_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial. % 112.12/112.44 elim (classic ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H23c | zenon_intro zenon_H21f ]. % 112.12/112.44 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1))); [ zenon_intro zenon_H68 | zenon_intro zenon_H5a ]. % 112.12/112.44 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H289 | zenon_intro zenon_H28a ]. % 112.12/112.44 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_H288 | zenon_intro zenon_H27c ]. % 112.12/112.44 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64. % 112.12/112.44 generalize (zenon_H64 (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H28b. % 112.12/112.44 generalize (zenon_H28b (hazard_of_mortality zenon_TX_y zenon_TT3_x)). zenon_intro zenon_H28c. % 112.12/112.44 apply (zenon_imply_s _ _ zenon_H28c); [ zenon_intro zenon_H28a | zenon_intro zenon_H28d ]. % 112.12/112.44 exact (zenon_H28a zenon_H289). % 112.12/112.44 apply (zenon_imply_s _ _ zenon_H28d); [ zenon_intro zenon_H27c | zenon_intro zenon_H104 ]. % 112.12/112.44 exact (zenon_H27c zenon_H288). % 112.12/112.44 exact (zenon_Hae zenon_H104). % 112.12/112.44 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb5 ]. % 112.12/112.44 cut ((greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT3_x)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT3_x))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_H27c. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_Hb4. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 112.12/112.44 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 112.12/112.44 congruence. % 112.12/112.44 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_H21f. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_H11a. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 112.12/112.44 congruence. % 112.12/112.44 exact (zenon_H21e zenon_H21a). % 112.12/112.44 apply zenon_H11b. apply refl_equal. % 112.12/112.44 apply zenon_H11b. apply refl_equal. % 112.12/112.44 apply zenon_Hb6. apply refl_equal. % 112.12/112.44 apply (zenon_L171_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial. % 112.12/112.44 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_H28a. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_H68. % 112.12/112.44 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.44 congruence. % 112.12/112.44 apply zenon_H62. apply refl_equal. % 112.12/112.44 exact (zenon_H21f zenon_H23c). % 112.12/112.44 apply (zenon_L188_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.44 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_H21f. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_H11a. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 112.12/112.44 congruence. % 112.12/112.44 exact (zenon_H21e zenon_H21a). % 112.12/112.44 apply zenon_H11b. apply refl_equal. % 112.12/112.44 apply zenon_H11b. apply refl_equal. % 112.12/112.44 apply (zenon_imply_s _ _ zenon_H234); [ zenon_intro zenon_H237 | zenon_intro zenon_H19e ]. % 112.12/112.44 apply (zenon_notand_s _ _ zenon_H237); [ zenon_intro zenon_H183 | zenon_intro zenon_H185 ]. % 112.12/112.44 apply (zenon_L184_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial. % 112.12/112.44 exact (zenon_H185 zenon_H182). % 112.12/112.44 apply (zenon_L190_ zenon_TT0_hz zenon_TT3_x zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.44 apply (zenon_L192_ zenon_TT3_x zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.44 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H289 | zenon_intro zenon_H28a ]. % 112.12/112.44 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (very_low))); [ zenon_intro zenon_Hfe | zenon_intro zenon_Hf6 ]. % 112.12/112.44 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (very_low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_Hae. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_Hfe. % 112.12/112.44 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.44 congruence. % 112.12/112.44 apply zenon_H62. apply refl_equal. % 112.12/112.44 apply (zenon_L169_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial. % 112.12/112.44 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_E)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (very_low))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_Hf6. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_H289. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.44 congruence. % 112.12/112.44 apply zenon_H62. apply refl_equal. % 112.12/112.44 exact (zenon_H1e5 zenon_H1e0). % 112.12/112.44 apply (zenon_L194_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.44 exact (zenon_H101 zenon_H105). % 112.12/112.44 (* end of lemma zenon_L195_ *) % 112.12/112.44 assert (zenon_L196_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (((is_aligned zenon_TX_y zenon_TT1_bg)/\(~(positional_advantage zenon_TX_y zenon_TT1_bg)))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))) -> (~(positional_advantage zenon_TX_y zenon_TT1_bg)) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T0) = (zero)))->((greater (age zenon_TX_y T) (sigma))<->(dissimilar zenon_TX_y T0 T))))) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> (~(greater (age zenon_TX_y zenon_TT1_bg) (sigma))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (~((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> False). % 112.12/112.44 do 3 intro. intros zenon_H30 zenon_H29 zenon_Hed zenon_Hcd zenon_He9 zenon_Hec zenon_H1f zenon_H5e. % 112.12/112.44 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 112.12/112.44 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ]. % 112.12/112.44 apply (zenon_L150_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.44 exact (zenon_H2e zenon_H29). % 112.12/112.44 apply zenon_H5e. apply sym_equal. exact zenon_H32. % 112.12/112.44 (* end of lemma zenon_L196_ *) % 112.12/112.44 assert (zenon_L197_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), ((((is_aligned zenon_TX_y zenon_TT1_bg)/\(positional_advantage zenon_TX_y zenon_TT1_bg))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low)))/\((((~(is_aligned zenon_TX_y zenon_TT1_bg))/\(positional_advantage zenon_TX_y zenon_TT1_bg))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod1)))/\((((is_aligned zenon_TX_y zenon_TT1_bg)/\(~(positional_advantage zenon_TX_y zenon_TT1_bg)))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2)))/\(((~(is_aligned zenon_TX_y zenon_TT1_bg))/\(~(positional_advantage zenon_TX_y zenon_TT1_bg)))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high)))))) -> (~((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(greater (age zenon_TX_y zenon_TT1_bg) (sigma))) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T0) = (zero)))->((greater (age zenon_TX_y T) (sigma))<->(dissimilar zenon_TX_y T0 T))))) -> (~((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> False). % 112.12/112.44 do 3 intro. intros zenon_H8c zenon_H5e zenon_H1f zenon_Hec zenon_He9 zenon_Hcd zenon_Hed zenon_H72. % 112.12/112.44 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d. % 112.12/112.44 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f. % 112.12/112.44 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H30. zenon_intro zenon_H28. % 112.12/112.44 apply (zenon_imply_s _ _ zenon_H8e); [ zenon_intro zenon_H91 | zenon_intro zenon_H6b ]. % 112.12/112.44 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 112.12/112.44 apply (zenon_L150_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.44 apply (zenon_L196_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.44 apply zenon_H72. apply sym_equal. exact zenon_H6b. % 112.12/112.44 (* end of lemma zenon_L197_ *) % 112.12/112.44 assert (zenon_L198_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T0) = (zero)))->((greater (age zenon_TX_y T) (sigma))<->(dissimilar zenon_TX_y T0 T))))) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> (~(greater (age zenon_TX_y zenon_TT1_bg) (sigma))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> False). % 112.12/112.44 do 3 intro. intros zenon_H0 zenon_H1f zenon_H1a zenon_Hed zenon_Hcd zenon_He9 zenon_Hec zenon_H5e zenon_H72. % 112.12/112.44 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88. % 112.12/112.44 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ]. % 112.12/112.44 exact (zenon_H27 zenon_H1f). % 112.12/112.44 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a. % 112.12/112.44 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ]. % 112.12/112.44 apply (zenon_L3_ zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.44 apply (zenon_L197_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.44 (* end of lemma zenon_L198_ *) % 112.12/112.44 assert (zenon_L199_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (((organization zenon_TX_y)/\((age zenon_TX_y zenon_TT0_hz) = (zero)))->(is_aligned zenon_TX_y zenon_TT0_hz)) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T0) = (zero)))->((greater (age zenon_TX_y T) (sigma))<->(dissimilar zenon_TX_y T0 T))))) -> (~(greater (age zenon_TX_y zenon_TT1_bg) (sigma))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> False). % 112.12/112.44 do 3 intro. intros zenon_Hf4 zenon_H0 zenon_H1f zenon_H1a zenon_Hed zenon_He9 zenon_Hec zenon_H5e zenon_H72. % 112.12/112.44 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcd ]. % 112.12/112.44 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ]. % 112.12/112.44 exact (zenon_H27 zenon_H1f). % 112.12/112.44 exact (zenon_Hf2 zenon_Hec). % 112.12/112.44 apply (zenon_L198_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.44 (* end of lemma zenon_L199_ *) % 112.12/112.44 assert (zenon_L200_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~(greater (age zenon_TX_y zenon_TT1_bg) (sigma))) -> (~((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> False). % 112.12/112.44 do 3 intro. intros zenon_Hf3 zenon_H1f zenon_Hec zenon_H1a zenon_He9 zenon_H5e zenon_H72. % 112.12/112.44 generalize (assumption_15 zenon_TX_y). zenon_intro zenon_Hed. % 112.12/112.44 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0. % 112.12/112.44 generalize (zenon_Hf3 zenon_TT0_hz). zenon_intro zenon_Hf4. % 112.12/112.44 apply (zenon_L199_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.44 (* end of lemma zenon_L200_ *) % 112.12/112.44 assert (zenon_L201_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (~((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (~(greater (sigma) (sigma))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> False). % 112.12/112.44 do 3 intro. intros zenon_H72 zenon_H5e zenon_H1a zenon_Hec zenon_H1f zenon_Hf3 zenon_Hda zenon_H26e. % 112.12/112.44 elim (classic ((sigma) = (age zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_He2 | zenon_intro zenon_Hde ]. % 112.12/112.44 elim (classic (greater (age zenon_TX_y zenon_TT1_bg) (sigma))); [ zenon_intro zenon_Hdb | zenon_intro zenon_He9 ]. % 112.12/112.44 cut ((greater (age zenon_TX_y zenon_TT1_bg) (sigma)) = (greater (sigma) (sigma))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_Hda. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_Hdb. % 112.12/112.44 cut (((sigma) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 112.12/112.44 cut (((age zenon_TX_y zenon_TT1_bg) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hdf]. % 112.12/112.44 congruence. % 112.12/112.44 elim (classic ((sigma) = (sigma))); [ zenon_intro zenon_He3 | zenon_intro zenon_Hd9 ]. % 112.12/112.44 cut (((sigma) = (sigma)) = ((age zenon_TX_y zenon_TT1_bg) = (sigma))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_Hdf. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_He3. % 112.12/112.44 cut (((sigma) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 112.12/112.44 cut (((sigma) = (age zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_Hde]. % 112.12/112.44 congruence. % 112.12/112.44 exact (zenon_Hde zenon_He2). % 112.12/112.44 apply zenon_Hd9. apply refl_equal. % 112.12/112.44 apply zenon_Hd9. apply refl_equal. % 112.12/112.44 apply zenon_Hd9. apply refl_equal. % 112.12/112.44 apply (zenon_L200_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.44 elim (classic ((age zenon_TX_y zenon_TT1_bg) = (age zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H26f | zenon_intro zenon_H4d ]. % 112.12/112.44 cut (((age zenon_TX_y zenon_TT1_bg) = (age zenon_TX_y zenon_TT1_bg)) = ((sigma) = (age zenon_TX_y zenon_TT1_bg))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_Hde. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_H26f. % 112.12/112.44 cut (((age zenon_TX_y zenon_TT1_bg) = (age zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 112.12/112.44 cut (((age zenon_TX_y zenon_TT1_bg) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hdf]. % 112.12/112.44 congruence. % 112.12/112.44 exact (zenon_Hdf zenon_H26e). % 112.12/112.44 apply zenon_H4d. apply refl_equal. % 112.12/112.44 apply zenon_H4d. apply refl_equal. % 112.12/112.44 (* end of lemma zenon_L201_ *) % 112.12/112.44 assert (zenon_L202_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall Y : zenon_U, (~((greater (sigma) Y)/\(greater Y (sigma))))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> False). % 112.12/112.44 do 3 intro. intros zenon_Hea zenon_H26e zenon_H72 zenon_H5e zenon_H1a zenon_Hec zenon_H1f zenon_Hf3. % 112.12/112.44 generalize (zenon_Hea (sigma)). zenon_intro zenon_Heb. % 112.12/112.44 apply (zenon_notand_s _ _ zenon_Heb); [ zenon_intro zenon_Hda | zenon_intro zenon_Hda ]. % 112.12/112.44 apply (zenon_L201_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.44 apply (zenon_L201_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.44 (* end of lemma zenon_L202_ *) % 112.12/112.44 assert (zenon_L203_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> False). % 112.12/112.44 do 3 intro. intros zenon_Hf3 zenon_H1f zenon_Hec zenon_H1a zenon_H5e zenon_H72 zenon_H26e. % 112.12/112.44 generalize (meaning_postulate_greater_strict (sigma)). zenon_intro zenon_Hea. % 112.12/112.44 apply (zenon_L202_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.44 (* end of lemma zenon_L203_ *) % 112.12/112.44 assert (zenon_L204_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> False). % 112.12/112.44 do 3 intro. intros zenon_H26e zenon_H72 zenon_H5e zenon_H1a zenon_Hec zenon_H1f. % 112.12/112.44 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3. % 112.12/112.44 apply (zenon_L203_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.44 (* end of lemma zenon_L204_ *) % 112.12/112.44 assert (zenon_L205_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> False). % 112.12/112.44 do 3 intro. intros zenon_H34 zenon_H1c4 zenon_H1f zenon_Hec zenon_H1a zenon_H5e zenon_H26e. % 112.12/112.44 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H241 | zenon_intro zenon_H193 ]. % 112.12/112.44 generalize (zenon_H34 (mod2)). zenon_intro zenon_H16e. % 112.12/112.44 generalize (zenon_H16e (mod1)). zenon_intro zenon_H16f. % 112.12/112.44 generalize (zenon_H16f (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H28e. % 112.12/112.44 apply (zenon_imply_s _ _ zenon_H28e); [ zenon_intro zenon_H69 | zenon_intro zenon_H28f ]. % 112.12/112.44 exact (zenon_H69 assumption_19). % 112.12/112.44 apply (zenon_imply_s _ _ zenon_H28f); [ zenon_intro zenon_H193 | zenon_intro zenon_H1c3 ]. % 112.12/112.44 exact (zenon_H193 zenon_H241). % 112.12/112.44 exact (zenon_H1c4 zenon_H1c3). % 112.12/112.44 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 112.12/112.44 cut ((greater (mod1) (low)) = (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_H193. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact assumption_18b. % 112.12/112.44 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 112.12/112.44 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 112.12/112.44 congruence. % 112.12/112.44 apply zenon_H59. apply refl_equal. % 112.12/112.44 exact (zenon_H72 zenon_H71). % 112.12/112.44 apply (zenon_L204_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.44 (* end of lemma zenon_L205_ *) % 112.12/112.44 assert (zenon_L206_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> False). % 112.12/112.44 do 3 intro. intros zenon_H34 zenon_H114 zenon_H26e zenon_H1a zenon_Hec zenon_H1f. % 112.12/112.44 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H115 | zenon_intro zenon_H5e ]. % 112.12/112.44 cut ((greater (high) (mod2)) = (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_H114. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact assumption_18d. % 112.12/112.44 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 112.12/112.44 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113]. % 112.12/112.44 congruence. % 112.12/112.44 apply zenon_H113. apply refl_equal. % 112.12/112.44 exact (zenon_H5e zenon_H115). % 112.12/112.44 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1c4 ]. % 112.12/112.44 generalize (zenon_H34 (high)). zenon_intro zenon_H1fa. % 112.12/112.44 generalize (zenon_H1fa (mod2)). zenon_intro zenon_H1fb. % 112.12/112.44 generalize (zenon_H1fb (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H27e. % 112.12/112.44 apply (zenon_imply_s _ _ zenon_H27e); [ zenon_intro zenon_H9b | zenon_intro zenon_H27f ]. % 112.12/112.44 exact (zenon_H9b assumption_18d). % 112.12/112.44 apply (zenon_imply_s _ _ zenon_H27f); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H118 ]. % 112.12/112.44 exact (zenon_H1c4 zenon_H1c3). % 112.12/112.44 exact (zenon_H114 zenon_H118). % 112.12/112.44 apply (zenon_L205_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.44 (* end of lemma zenon_L206_ *) % 112.12/112.44 assert (zenon_L207_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (high)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> False). % 112.12/112.44 do 3 intro. intros zenon_H34 zenon_H116 zenon_H117 zenon_H1f zenon_Hec zenon_H1a zenon_H26e. % 112.12/112.44 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H118 | zenon_intro zenon_H114 ]. % 112.12/112.44 cut ((greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_H117. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_H118. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.44 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H119]. % 112.12/112.44 congruence. % 112.12/112.44 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_H119. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact zenon_H11a. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.44 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 112.12/112.44 congruence. % 112.12/112.44 exact (zenon_H11c zenon_H116). % 112.12/112.44 apply zenon_H11b. apply refl_equal. % 112.12/112.44 apply zenon_H11b. apply refl_equal. % 112.12/112.44 apply zenon_H62. apply refl_equal. % 112.12/112.44 apply (zenon_L206_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.44 (* end of lemma zenon_L207_ *) % 112.12/112.44 assert (zenon_L208_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (~(greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> False). % 112.12/112.44 do 3 intro. intros zenon_H193 zenon_Hf3 zenon_H1f zenon_Hec zenon_H1a zenon_H5e zenon_H26e. % 112.12/112.44 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 112.12/112.44 cut ((greater (mod1) (low)) = (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.44 intro zenon_D_pnotp. % 112.12/112.44 apply zenon_H193. % 112.12/112.44 rewrite <- zenon_D_pnotp. % 112.12/112.44 exact assumption_18b. % 112.12/112.44 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 112.12/112.44 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 112.12/112.44 congruence. % 112.12/112.44 apply zenon_H59. apply refl_equal. % 112.12/112.44 exact (zenon_H72 zenon_H71). % 112.12/112.44 apply (zenon_L203_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.44 (* end of lemma zenon_L208_ *) % 112.12/112.44 assert (zenon_L209_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> False). % 112.12/112.44 do 3 intro. intros zenon_H34 zenon_H1c4 zenon_H26e zenon_H5e zenon_H1a zenon_Hec zenon_H1f zenon_Hf3. % 112.12/112.45 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H241 | zenon_intro zenon_H193 ]. % 112.12/112.45 generalize (zenon_H34 (mod2)). zenon_intro zenon_H16e. % 112.12/112.45 generalize (zenon_H16e (mod1)). zenon_intro zenon_H16f. % 112.12/112.45 generalize (zenon_H16f (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H28e. % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H28e); [ zenon_intro zenon_H69 | zenon_intro zenon_H28f ]. % 112.12/112.45 exact (zenon_H69 assumption_19). % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H28f); [ zenon_intro zenon_H193 | zenon_intro zenon_H1c3 ]. % 112.12/112.45 exact (zenon_H193 zenon_H241). % 112.12/112.45 exact (zenon_H1c4 zenon_H1c3). % 112.12/112.45 apply (zenon_L208_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.45 (* end of lemma zenon_L209_ *) % 112.12/112.45 assert (zenon_L210_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (((is_aligned zenon_TX_y zenon_TT2_la)/\(~(positional_advantage zenon_TX_y zenon_TT2_la)))->((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))) -> (~(positional_advantage zenon_TX_y zenon_TT2_la)) -> (((~(is_aligned zenon_TX_y zenon_TT2_la))/\(~(positional_advantage zenon_TX_y zenon_TT2_la)))->((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> False). % 112.12/112.45 do 4 intro. intros zenon_H145 zenon_H127 zenon_H134 zenon_H34 zenon_H26e zenon_H17c zenon_H148 zenon_H35 zenon_H123 zenon_H136 zenon_H1a zenon_H0 zenon_Hec zenon_H1f zenon_Hf3. % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H145); [ zenon_intro zenon_H147 | zenon_intro zenon_H146 ]. % 112.12/112.45 apply (zenon_notand_s _ _ zenon_H147); [ zenon_intro zenon_H135 | zenon_intro zenon_H139 ]. % 112.12/112.45 apply (zenon_L67_ zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.45 exact (zenon_H139 zenon_H127). % 112.12/112.45 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H168 | zenon_intro zenon_H169 ]. % 112.12/112.45 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ]. % 112.12/112.45 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.45 intro zenon_D_pnotp. % 112.12/112.45 apply zenon_H17c. % 112.12/112.45 rewrite <- zenon_D_pnotp. % 112.12/112.45 exact zenon_H179. % 112.12/112.45 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.45 congruence. % 112.12/112.45 apply zenon_H16a. apply refl_equal. % 112.12/112.45 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1c4 ]. % 112.12/112.45 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.12/112.45 generalize (zenon_H18f (mod2)). zenon_intro zenon_H199. % 112.12/112.45 generalize (zenon_H199 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H290. % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H290); [ zenon_intro zenon_H167 | zenon_intro zenon_H291 ]. % 112.12/112.45 exact (zenon_H167 zenon_H179). % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H291); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H240 ]. % 112.12/112.45 exact (zenon_H1c4 zenon_H1c3). % 112.12/112.45 exact (zenon_H17c zenon_H240). % 112.12/112.45 apply (zenon_L209_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.45 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))). % 112.12/112.45 intro zenon_D_pnotp. % 112.12/112.45 apply zenon_H167. % 112.12/112.45 rewrite <- zenon_D_pnotp. % 112.12/112.45 exact zenon_H168. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.45 congruence. % 112.12/112.45 apply zenon_H16a. apply refl_equal. % 112.12/112.45 exact (zenon_H13b zenon_H146). % 112.12/112.45 apply (zenon_L62_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.45 (* end of lemma zenon_L210_ *) % 112.12/112.45 assert (zenon_L211_ : forall (zenon_TT2_la : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2)) -> ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (low)) -> False). % 112.12/112.45 do 4 intro. intros zenon_H34 zenon_Hf3 zenon_H1f zenon_Hec zenon_H1a zenon_H26e zenon_H17c zenon_H146 zenon_H15b. % 112.12/112.45 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H168 | zenon_intro zenon_H169 ]. % 112.12/112.45 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ]. % 112.12/112.45 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.45 intro zenon_D_pnotp. % 112.12/112.45 apply zenon_H17c. % 112.12/112.45 rewrite <- zenon_D_pnotp. % 112.12/112.45 exact zenon_H179. % 112.12/112.45 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.45 congruence. % 112.12/112.45 apply zenon_H16a. apply refl_equal. % 112.12/112.45 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1c4 ]. % 112.12/112.45 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.12/112.45 generalize (zenon_H18f (mod2)). zenon_intro zenon_H199. % 112.12/112.45 generalize (zenon_H199 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H290. % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H290); [ zenon_intro zenon_H167 | zenon_intro zenon_H291 ]. % 112.12/112.45 exact (zenon_H167 zenon_H179). % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H291); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H240 ]. % 112.12/112.45 exact (zenon_H1c4 zenon_H1c3). % 112.12/112.45 exact (zenon_H17c zenon_H240). % 112.12/112.45 apply (zenon_L209_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.45 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))). % 112.12/112.45 intro zenon_D_pnotp. % 112.12/112.45 apply zenon_H167. % 112.12/112.45 rewrite <- zenon_D_pnotp. % 112.12/112.45 exact zenon_H168. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.45 congruence. % 112.12/112.45 apply zenon_H16a. apply refl_equal. % 112.12/112.45 exact (zenon_H13b zenon_H146). % 112.12/112.45 apply (zenon_L70_ zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.45 (* end of lemma zenon_L211_ *) % 112.12/112.45 assert (zenon_L212_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> False). % 112.12/112.45 do 4 intro. intros zenon_H34 zenon_H1f zenon_H1a zenon_H136 zenon_H123 zenon_H35 zenon_H148 zenon_H0 zenon_Hec zenon_Hf3 zenon_H26e zenon_H17c. % 112.12/112.45 generalize (zenon_H0 zenon_TT2_la). zenon_intro zenon_H13c. % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H13c); [ zenon_intro zenon_H27 | zenon_intro zenon_H13d ]. % 112.12/112.45 exact (zenon_H27 zenon_H1f). % 112.12/112.45 apply (zenon_and_s _ _ zenon_H13d). zenon_intro zenon_H13f. zenon_intro zenon_H13e. % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H13e); [ zenon_intro zenon_H11d | zenon_intro zenon_H140 ]. % 112.12/112.45 apply (zenon_L50_ zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.45 apply (zenon_and_s _ _ zenon_H140). zenon_intro zenon_H142. zenon_intro zenon_H141. % 112.12/112.45 apply (zenon_and_s _ _ zenon_H141). zenon_intro zenon_H144. zenon_intro zenon_H143. % 112.12/112.45 apply (zenon_and_s _ _ zenon_H143). zenon_intro zenon_H145. zenon_intro zenon_H134. % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H142); [ zenon_intro zenon_H15c | zenon_intro zenon_H15b ]. % 112.12/112.45 apply (zenon_notand_s _ _ zenon_H15c); [ zenon_intro zenon_H135 | zenon_intro zenon_H127 ]. % 112.12/112.45 apply (zenon_L52_ zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.45 apply (zenon_L210_ zenon_TT0_hz zenon_TT1_bg zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H145); [ zenon_intro zenon_H147 | zenon_intro zenon_H146 ]. % 112.12/112.45 apply (zenon_notand_s _ _ zenon_H147); [ zenon_intro zenon_H135 | zenon_intro zenon_H139 ]. % 112.12/112.45 apply (zenon_L52_ zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.45 apply zenon_H139. zenon_intro zenon_H122. % 112.12/112.45 apply (zenon_L51_ zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.45 apply (zenon_L211_ zenon_TT2_la zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.45 (* end of lemma zenon_L212_ *) % 112.12/112.45 assert (zenon_L213_ : forall (zenon_TT2_la : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (high)) -> False). % 112.12/112.45 do 4 intro. intros zenon_H1f zenon_Hec zenon_H1a zenon_H26e zenon_H123 zenon_H35 zenon_H148 zenon_H0 zenon_Hf3 zenon_H17c zenon_H34 zenon_H116. % 112.12/112.45 elim (classic ((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H17d | zenon_intro zenon_H119 ]. % 112.12/112.45 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H17e | zenon_intro zenon_H117 ]. % 112.12/112.45 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H118 | zenon_intro zenon_H114 ]. % 112.12/112.45 cut ((greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.45 intro zenon_D_pnotp. % 112.12/112.45 apply zenon_H17c. % 112.12/112.45 rewrite <- zenon_D_pnotp. % 112.12/112.45 exact zenon_H118. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.45 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 112.12/112.45 congruence. % 112.12/112.45 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.12/112.45 intro zenon_D_pnotp. % 112.12/112.45 apply zenon_H17f. % 112.12/112.45 rewrite <- zenon_D_pnotp. % 112.12/112.45 exact zenon_H16d. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 112.12/112.45 congruence. % 112.12/112.45 apply (zenon_L212_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.45 apply zenon_H16a. apply refl_equal. % 112.12/112.45 apply zenon_H16a. apply refl_equal. % 112.12/112.45 apply zenon_H62. apply refl_equal. % 112.12/112.45 cut ((greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.45 intro zenon_D_pnotp. % 112.12/112.45 apply zenon_H114. % 112.12/112.45 rewrite <- zenon_D_pnotp. % 112.12/112.45 exact zenon_H17e. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 112.12/112.45 congruence. % 112.12/112.45 elim (classic ((high) = (high))); [ zenon_intro zenon_H180 | zenon_intro zenon_H113 ]. % 112.12/112.45 cut (((high) = (high)) = ((hazard_of_mortality zenon_TX_y zenon_E) = (high))). % 112.12/112.45 intro zenon_D_pnotp. % 112.12/112.45 apply zenon_H11c. % 112.12/112.45 rewrite <- zenon_D_pnotp. % 112.12/112.45 exact zenon_H180. % 112.12/112.45 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113]. % 112.12/112.45 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H119]. % 112.12/112.45 congruence. % 112.12/112.45 exact (zenon_H119 zenon_H17d). % 112.12/112.45 apply zenon_H113. apply refl_equal. % 112.12/112.45 apply zenon_H113. apply refl_equal. % 112.12/112.45 apply zenon_H62. apply refl_equal. % 112.12/112.45 apply (zenon_L207_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.45 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.45 intro zenon_D_pnotp. % 112.12/112.45 apply zenon_H119. % 112.12/112.45 rewrite <- zenon_D_pnotp. % 112.12/112.45 exact zenon_H11a. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 112.12/112.45 congruence. % 112.12/112.45 exact (zenon_H11c zenon_H116). % 112.12/112.45 apply zenon_H11b. apply refl_equal. % 112.12/112.45 apply zenon_H11b. apply refl_equal. % 112.12/112.45 (* end of lemma zenon_L213_ *) % 112.12/112.45 assert (zenon_L214_ : forall (zenon_TT2_la : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (((~(is_aligned zenon_TX_y zenon_E))/\(~(positional_advantage zenon_TX_y zenon_E)))->((hazard_of_mortality zenon_TX_y zenon_E) = (high))) -> (~(positional_advantage zenon_TX_y zenon_E)) -> (~(is_aligned zenon_TX_y zenon_E)) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> False). % 112.12/112.45 do 4 intro. intros zenon_H181 zenon_H182 zenon_H183 zenon_H1f zenon_Hec zenon_H1a zenon_H26e zenon_H123 zenon_H35 zenon_H148 zenon_H0 zenon_Hf3 zenon_H17c zenon_H34. % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H181); [ zenon_intro zenon_H184 | zenon_intro zenon_H116 ]. % 112.12/112.45 apply (zenon_notand_s _ _ zenon_H184); [ zenon_intro zenon_H186 | zenon_intro zenon_H185 ]. % 112.12/112.45 exact (zenon_H186 zenon_H183). % 112.12/112.45 exact (zenon_H185 zenon_H182). % 112.12/112.45 apply (zenon_L213_ zenon_TT2_la zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.45 (* end of lemma zenon_L214_ *) % 112.12/112.45 assert (zenon_L215_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (organization zenon_TX_y) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (mod2)) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> False). % 112.12/112.45 do 4 intro. intros zenon_H34 zenon_H117 zenon_H17c zenon_H26e zenon_H35 zenon_H123 zenon_H1a zenon_H1f zenon_H0 zenon_H19e zenon_H148 zenon_Hec zenon_Hf3. % 112.12/112.45 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1c4 ]. % 112.12/112.45 cut ((greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.45 intro zenon_D_pnotp. % 112.12/112.45 apply zenon_H117. % 112.12/112.45 rewrite <- zenon_D_pnotp. % 112.12/112.45 exact zenon_H1c3. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.45 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 112.12/112.45 congruence. % 112.12/112.45 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.45 intro zenon_D_pnotp. % 112.12/112.45 apply zenon_H1a1. % 112.12/112.45 rewrite <- zenon_D_pnotp. % 112.12/112.45 exact zenon_H11a. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 112.12/112.45 congruence. % 112.12/112.45 exact (zenon_H1a2 zenon_H19e). % 112.12/112.45 apply zenon_H11b. apply refl_equal. % 112.12/112.45 apply zenon_H11b. apply refl_equal. % 112.12/112.45 apply zenon_H62. apply refl_equal. % 112.12/112.45 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H241 | zenon_intro zenon_H193 ]. % 112.12/112.45 generalize (zenon_H34 (mod2)). zenon_intro zenon_H16e. % 112.12/112.45 generalize (zenon_H16e (mod1)). zenon_intro zenon_H16f. % 112.12/112.45 generalize (zenon_H16f (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H28e. % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H28e); [ zenon_intro zenon_H69 | zenon_intro zenon_H28f ]. % 112.12/112.45 exact (zenon_H69 assumption_19). % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H28f); [ zenon_intro zenon_H193 | zenon_intro zenon_H1c3 ]. % 112.12/112.45 exact (zenon_H193 zenon_H241). % 112.12/112.45 exact (zenon_H1c4 zenon_H1c3). % 112.12/112.45 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 112.12/112.45 cut ((greater (mod1) (low)) = (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.45 intro zenon_D_pnotp. % 112.12/112.45 apply zenon_H193. % 112.12/112.45 rewrite <- zenon_D_pnotp. % 112.12/112.45 exact assumption_18b. % 112.12/112.45 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 112.12/112.45 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 112.12/112.45 congruence. % 112.12/112.45 apply zenon_H59. apply refl_equal. % 112.12/112.45 exact (zenon_H72 zenon_H71). % 112.12/112.45 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1a5 ]. % 112.12/112.45 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ]. % 112.12/112.45 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.45 intro zenon_D_pnotp. % 112.12/112.45 apply zenon_H17c. % 112.12/112.45 rewrite <- zenon_D_pnotp. % 112.12/112.45 exact zenon_H179. % 112.12/112.45 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.45 congruence. % 112.12/112.45 apply zenon_H16a. apply refl_equal. % 112.12/112.45 apply (zenon_L204_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.45 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))). % 112.12/112.45 intro zenon_D_pnotp. % 112.12/112.45 apply zenon_H167. % 112.12/112.45 rewrite <- zenon_D_pnotp. % 112.12/112.45 exact zenon_H1a4. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.45 congruence. % 112.12/112.45 apply zenon_H16a. apply refl_equal. % 112.12/112.45 exact (zenon_H1a2 zenon_H19e). % 112.12/112.45 apply (zenon_L84_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.45 (* end of lemma zenon_L215_ *) % 112.12/112.45 assert (zenon_L216_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (((is_aligned zenon_TX_y zenon_E)/\(~(positional_advantage zenon_TX_y zenon_E)))->((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))) -> (~(positional_advantage zenon_TX_y zenon_E)) -> (((~(is_aligned zenon_TX_y zenon_E))/\(~(positional_advantage zenon_TX_y zenon_E)))->((hazard_of_mortality zenon_TX_y zenon_E) = (high))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (organization zenon_TX_y) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> False). % 112.12/112.45 do 4 intro. intros zenon_H234 zenon_H182 zenon_H181 zenon_H17c zenon_H26e zenon_H35 zenon_H123 zenon_H1a zenon_H1f zenon_H0 zenon_H148 zenon_Hec zenon_Hf3 zenon_H34. % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H234); [ zenon_intro zenon_H237 | zenon_intro zenon_H19e ]. % 112.12/112.45 apply (zenon_notand_s _ _ zenon_H237); [ zenon_intro zenon_H183 | zenon_intro zenon_H185 ]. % 112.12/112.45 apply (zenon_L214_ zenon_TT2_la zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.45 exact (zenon_H185 zenon_H182). % 112.12/112.45 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H1a1 ]. % 112.12/112.45 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ]. % 112.12/112.45 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1a5 ]. % 112.12/112.45 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H17e | zenon_intro zenon_H117 ]. % 112.12/112.45 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.12/112.45 generalize (zenon_H18f (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H23d. % 112.12/112.45 generalize (zenon_H23d (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H23e. % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H23f ]. % 112.12/112.45 exact (zenon_H1a5 zenon_H1a4). % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H23f); [ zenon_intro zenon_H117 | zenon_intro zenon_H240 ]. % 112.12/112.45 exact (zenon_H117 zenon_H17e). % 112.12/112.45 exact (zenon_H17c zenon_H240). % 112.12/112.45 apply (zenon_L215_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.45 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.45 intro zenon_D_pnotp. % 112.12/112.45 apply zenon_H1a5. % 112.12/112.45 rewrite <- zenon_D_pnotp. % 112.12/112.45 exact zenon_H179. % 112.12/112.45 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.45 congruence. % 112.12/112.45 apply zenon_H16a. apply refl_equal. % 112.12/112.45 exact (zenon_H1a1 zenon_H1a3). % 112.12/112.45 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H17e | zenon_intro zenon_H117 ]. % 112.12/112.45 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1c4 ]. % 112.12/112.45 cut ((greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.45 intro zenon_D_pnotp. % 112.12/112.45 apply zenon_H17c. % 112.12/112.45 rewrite <- zenon_D_pnotp. % 112.12/112.45 exact zenon_H1c3. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.45 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 112.12/112.45 congruence. % 112.12/112.45 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.12/112.45 intro zenon_D_pnotp. % 112.12/112.45 apply zenon_H16c. % 112.12/112.45 rewrite <- zenon_D_pnotp. % 112.12/112.45 exact zenon_H16d. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 112.12/112.45 congruence. % 112.12/112.45 apply (zenon_L81_ zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.45 apply zenon_H16a. apply refl_equal. % 112.12/112.45 apply zenon_H16a. apply refl_equal. % 112.12/112.45 apply zenon_H62. apply refl_equal. % 112.12/112.45 cut ((greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.45 intro zenon_D_pnotp. % 112.12/112.45 apply zenon_H1c4. % 112.12/112.45 rewrite <- zenon_D_pnotp. % 112.12/112.45 exact zenon_H17e. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 112.12/112.45 congruence. % 112.12/112.45 elim (classic ((mod2) = (mod2))); [ zenon_intro zenon_H17b | zenon_intro zenon_H83 ]. % 112.12/112.45 cut (((mod2) = (mod2)) = ((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))). % 112.12/112.45 intro zenon_D_pnotp. % 112.12/112.45 apply zenon_H1a2. % 112.12/112.45 rewrite <- zenon_D_pnotp. % 112.12/112.45 exact zenon_H17b. % 112.12/112.45 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 112.12/112.45 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 112.12/112.45 congruence. % 112.12/112.45 exact (zenon_H1a1 zenon_H1a3). % 112.12/112.45 apply zenon_H83. apply refl_equal. % 112.12/112.45 apply zenon_H83. apply refl_equal. % 112.12/112.45 apply zenon_H62. apply refl_equal. % 112.12/112.45 apply (zenon_L215_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.45 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.45 intro zenon_D_pnotp. % 112.12/112.45 apply zenon_H1a1. % 112.12/112.45 rewrite <- zenon_D_pnotp. % 112.12/112.45 exact zenon_H11a. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 112.12/112.45 congruence. % 112.12/112.45 exact (zenon_H1a2 zenon_H19e). % 112.12/112.45 apply zenon_H11b. apply refl_equal. % 112.12/112.45 apply zenon_H11b. apply refl_equal. % 112.12/112.45 (* end of lemma zenon_L216_ *) % 112.12/112.45 assert (zenon_L217_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> False). % 112.12/112.45 do 3 intro. intros zenon_H34 zenon_H114 zenon_Hf3 zenon_H1f zenon_Hec zenon_H1a zenon_H26e. % 112.12/112.45 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H115 | zenon_intro zenon_H5e ]. % 112.12/112.45 cut ((greater (high) (mod2)) = (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.45 intro zenon_D_pnotp. % 112.12/112.45 apply zenon_H114. % 112.12/112.45 rewrite <- zenon_D_pnotp. % 112.12/112.45 exact assumption_18d. % 112.12/112.45 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 112.12/112.45 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113]. % 112.12/112.45 congruence. % 112.12/112.45 apply zenon_H113. apply refl_equal. % 112.12/112.45 exact (zenon_H5e zenon_H115). % 112.12/112.45 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1c4 ]. % 112.12/112.45 generalize (zenon_H34 (high)). zenon_intro zenon_H1fa. % 112.12/112.45 generalize (zenon_H1fa (mod2)). zenon_intro zenon_H1fb. % 112.12/112.45 generalize (zenon_H1fb (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H27e. % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H27e); [ zenon_intro zenon_H9b | zenon_intro zenon_H27f ]. % 112.12/112.45 exact (zenon_H9b assumption_18d). % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H27f); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H118 ]. % 112.12/112.45 exact (zenon_H1c4 zenon_H1c3). % 112.12/112.45 exact (zenon_H114 zenon_H118). % 112.12/112.45 apply (zenon_L209_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.45 (* end of lemma zenon_L217_ *) % 112.12/112.45 assert (zenon_L218_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high)) -> (~(greater (high) (high))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> False). % 112.12/112.45 do 3 intro. intros zenon_H34 zenon_H2c zenon_H280 zenon_H26e zenon_H1a zenon_Hec zenon_H1f zenon_Hf3. % 112.12/112.45 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H118 | zenon_intro zenon_H114 ]. % 112.12/112.45 cut ((greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (high) (high))). % 112.12/112.45 intro zenon_D_pnotp. % 112.12/112.45 apply zenon_H280. % 112.12/112.45 rewrite <- zenon_D_pnotp. % 112.12/112.45 exact zenon_H118. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 112.12/112.45 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113]. % 112.12/112.45 congruence. % 112.12/112.45 apply zenon_H113. apply refl_equal. % 112.12/112.45 exact (zenon_H2b zenon_H2c). % 112.12/112.45 apply (zenon_L217_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.45 (* end of lemma zenon_L218_ *) % 112.12/112.45 assert (zenon_L219_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high)) -> (~(greater (high) (high))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> False). % 112.12/112.45 do 3 intro. intros zenon_H34 zenon_H2c zenon_H280 zenon_H26e zenon_H1a zenon_Hec zenon_H1f zenon_Hf3. % 112.12/112.45 apply (zenon_L218_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.45 (* end of lemma zenon_L219_ *) % 112.12/112.45 assert (zenon_L220_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (high) (high))) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high)) -> False). % 112.12/112.45 do 3 intro. intros zenon_H34 zenon_H280 zenon_Hf3 zenon_H1f zenon_Hec zenon_H1a zenon_H26e zenon_H2c. % 112.12/112.45 apply (zenon_L219_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.45 (* end of lemma zenon_L220_ *) % 112.12/112.45 assert (zenon_L221_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> False). % 112.12/112.45 do 3 intro. intros zenon_H34 zenon_H2c zenon_H26e zenon_H1a zenon_Hec zenon_H1f zenon_Hf3. % 112.12/112.45 generalize (meaning_postulate_greater_strict (high)). zenon_intro zenon_H202. % 112.12/112.45 generalize (zenon_H202 (high)). zenon_intro zenon_H287. % 112.12/112.45 apply (zenon_notand_s _ _ zenon_H287); [ zenon_intro zenon_H280 | zenon_intro zenon_H280 ]. % 112.12/112.45 apply (zenon_L220_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.45 apply (zenon_L220_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.45 (* end of lemma zenon_L221_ *) % 112.12/112.45 assert (zenon_L222_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (((~(is_aligned zenon_TX_y zenon_TT1_bg))/\(~(positional_advantage zenon_TX_y zenon_TT1_bg)))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))) -> (greater (tau) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (~(is_aligned zenon_TX_y zenon_TT1_bg)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> False). % 112.12/112.45 do 3 intro. intros zenon_H28 zenon_H38 zenon_H35 zenon_H2a zenon_H34 zenon_H26e zenon_H1a zenon_Hec zenon_H1f zenon_Hf3. % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ]. % 112.12/112.45 apply (zenon_notand_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ]. % 112.12/112.45 exact (zenon_H2f zenon_H2a). % 112.12/112.45 apply zenon_H2e. zenon_intro zenon_H36. % 112.12/112.45 apply (zenon_L155_ zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.45 apply (zenon_L221_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.45 (* end of lemma zenon_L222_ *) % 112.12/112.45 assert (zenon_L223_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (((~(is_aligned zenon_TX_y zenon_TT1_bg))/\(~(positional_advantage zenon_TX_y zenon_TT1_bg)))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))) -> (~(positional_advantage zenon_TX_y zenon_TT1_bg)) -> (~(is_aligned zenon_TX_y zenon_TT1_bg)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> False). % 112.12/112.45 do 3 intro. intros zenon_H28 zenon_H29 zenon_H2a zenon_H34 zenon_H26e zenon_H1a zenon_Hec zenon_H1f zenon_Hf3. % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ]. % 112.12/112.45 apply (zenon_notand_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ]. % 112.12/112.45 exact (zenon_H2f zenon_H2a). % 112.12/112.45 exact (zenon_H2e zenon_H29). % 112.12/112.45 apply (zenon_L221_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.45 (* end of lemma zenon_L223_ *) % 112.12/112.45 assert (zenon_L224_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (organization zenon_TX_y) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))) -> False). % 112.12/112.45 do 4 intro. intros zenon_H17c zenon_H26e zenon_Hf3 zenon_Hec zenon_H0 zenon_H148 zenon_H35 zenon_H123 zenon_H1a zenon_H1f zenon_H34 zenon_H167. % 112.12/112.45 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (high))))); [ zenon_intro zenon_H189 | zenon_intro zenon_H18a ]. % 112.12/112.45 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H136. zenon_intro zenon_H18b. % 112.12/112.45 apply (zenon_L212_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.45 cut ((greater (high) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))). % 112.12/112.45 intro zenon_D_pnotp. % 112.12/112.45 apply zenon_H167. % 112.12/112.45 rewrite <- zenon_D_pnotp. % 112.12/112.45 exact assumption_18d. % 112.12/112.45 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 112.12/112.45 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 112.12/112.45 congruence. % 112.12/112.45 apply (zenon_notand_s _ _ zenon_H18a); [ zenon_intro zenon_H18d | zenon_intro zenon_H18c ]. % 112.12/112.45 apply zenon_H18d. zenon_intro zenon_H137. % 112.12/112.45 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.12/112.45 intro zenon_D_pnotp. % 112.12/112.45 apply zenon_H17f. % 112.12/112.45 rewrite <- zenon_D_pnotp. % 112.12/112.45 exact zenon_H16d. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 112.12/112.45 congruence. % 112.12/112.45 exact (zenon_H136 zenon_H137). % 112.12/112.45 apply zenon_H16a. apply refl_equal. % 112.12/112.45 apply zenon_H16a. apply refl_equal. % 112.12/112.45 apply zenon_H18c. zenon_intro zenon_H18e. % 112.12/112.45 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.12/112.45 generalize (zenon_H18f (high)). zenon_intro zenon_H190. % 112.12/112.45 generalize (zenon_H190 (mod2)). zenon_intro zenon_H191. % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H191); [ zenon_intro zenon_H18b | zenon_intro zenon_H192 ]. % 112.12/112.45 exact (zenon_H18b zenon_H18e). % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H192); [ zenon_intro zenon_H9b | zenon_intro zenon_H179 ]. % 112.12/112.45 exact (zenon_H9b assumption_18d). % 112.12/112.45 exact (zenon_H167 zenon_H179). % 112.12/112.45 apply zenon_H83. apply refl_equal. % 112.12/112.45 (* end of lemma zenon_L224_ *) % 112.12/112.45 assert (zenon_L225_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (organization zenon_TX_y) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (~((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> False). % 112.12/112.45 do 4 intro. intros zenon_H34 zenon_H193 zenon_H1f zenon_H148 zenon_H17c zenon_H0 zenon_H123 zenon_H35 zenon_H38 zenon_H26e zenon_H1a zenon_Hec zenon_Hf3 zenon_H187. % 112.12/112.45 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 112.12/112.45 cut ((greater (mod1) (low)) = (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.45 intro zenon_D_pnotp. % 112.12/112.45 apply zenon_H193. % 112.12/112.45 rewrite <- zenon_D_pnotp. % 112.12/112.45 exact assumption_18b. % 112.12/112.45 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 112.12/112.45 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 112.12/112.45 congruence. % 112.12/112.45 apply zenon_H59. apply refl_equal. % 112.12/112.45 exact (zenon_H72 zenon_H71). % 112.12/112.45 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88. % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ]. % 112.12/112.45 exact (zenon_H27 zenon_H1f). % 112.12/112.45 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a. % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H8b); [ zenon_intro zenon_H24 | zenon_intro zenon_H188 ]. % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ]. % 112.12/112.45 exact (zenon_H1e zenon_H24). % 112.12/112.45 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d. % 112.12/112.45 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f. % 112.12/112.45 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H30. zenon_intro zenon_H28. % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H8e); [ zenon_intro zenon_H91 | zenon_intro zenon_H6b ]. % 112.12/112.45 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 112.12/112.45 apply (zenon_L222_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 112.12/112.45 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ]. % 112.12/112.45 apply (zenon_L223_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.45 exact (zenon_H2e zenon_H29). % 112.12/112.45 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H115 | zenon_intro zenon_H5e ]. % 112.12/112.45 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ]. % 112.12/112.45 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.45 intro zenon_D_pnotp. % 112.12/112.45 apply zenon_H17c. % 112.12/112.45 rewrite <- zenon_D_pnotp. % 112.12/112.45 exact zenon_H179. % 112.12/112.45 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.45 congruence. % 112.12/112.45 apply zenon_H16a. apply refl_equal. % 112.12/112.45 exact (zenon_H5e zenon_H115). % 112.12/112.45 apply (zenon_L224_ zenon_TT0_hz zenon_TT1_bg zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.45 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.45 intro zenon_D_pnotp. % 112.12/112.45 apply zenon_H5e. % 112.12/112.45 rewrite <- zenon_D_pnotp. % 112.12/112.45 exact zenon_H61. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31]. % 112.12/112.45 congruence. % 112.12/112.45 exact (zenon_H31 zenon_H32). % 112.12/112.45 apply zenon_H62. apply refl_equal. % 112.12/112.45 apply zenon_H62. apply refl_equal. % 112.12/112.45 apply zenon_H72. apply sym_equal. exact zenon_H6b. % 112.12/112.45 apply zenon_H187. apply sym_equal. exact zenon_H188. % 112.12/112.45 (* end of lemma zenon_L225_ *) % 112.12/112.45 assert (zenon_L226_ : forall (zenon_TT2_la : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (mod1)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (greater (tau) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (organization zenon_TX_y) -> False). % 112.12/112.45 do 4 intro. intros zenon_H34 zenon_H21a zenon_H117 zenon_H187 zenon_Hf3 zenon_Hec zenon_H1a zenon_H26e zenon_H38 zenon_H35 zenon_H123 zenon_H0 zenon_H17c zenon_H148 zenon_H1f. % 112.12/112.45 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H241 | zenon_intro zenon_H193 ]. % 112.12/112.45 cut ((greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.45 intro zenon_D_pnotp. % 112.12/112.45 apply zenon_H117. % 112.12/112.45 rewrite <- zenon_D_pnotp. % 112.12/112.45 exact zenon_H241. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.45 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 112.12/112.45 congruence. % 112.12/112.45 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.45 intro zenon_D_pnotp. % 112.12/112.45 apply zenon_H21f. % 112.12/112.45 rewrite <- zenon_D_pnotp. % 112.12/112.45 exact zenon_H11a. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 112.12/112.45 congruence. % 112.12/112.45 exact (zenon_H21e zenon_H21a). % 112.12/112.45 apply zenon_H11b. apply refl_equal. % 112.12/112.45 apply zenon_H11b. apply refl_equal. % 112.12/112.45 apply zenon_H62. apply refl_equal. % 112.12/112.45 apply (zenon_L225_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.45 (* end of lemma zenon_L226_ *) % 112.12/112.45 assert (zenon_L227_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))) -> False). % 112.12/112.45 do 4 intro. intros zenon_H1f zenon_H1a zenon_H123 zenon_H35 zenon_H148 zenon_H0 zenon_Hec zenon_Hf3 zenon_H26e zenon_H17c zenon_H34 zenon_H194. % 112.12/112.45 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))))); [ zenon_intro zenon_H195 | zenon_intro zenon_H196 ]. % 112.12/112.45 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H13b. zenon_intro zenon_H167. % 112.12/112.45 apply (zenon_L224_ zenon_TT0_hz zenon_TT1_bg zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.45 cut ((greater (mod2) (mod1)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))). % 112.12/112.45 intro zenon_D_pnotp. % 112.12/112.45 apply zenon_H194. % 112.12/112.45 rewrite <- zenon_D_pnotp. % 112.12/112.45 exact assumption_19. % 112.12/112.45 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 112.12/112.45 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 112.12/112.45 congruence. % 112.12/112.45 apply (zenon_notand_s _ _ zenon_H196); [ zenon_intro zenon_H198 | zenon_intro zenon_H197 ]. % 112.12/112.45 apply zenon_H198. zenon_intro zenon_H146. % 112.12/112.45 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.12/112.45 intro zenon_D_pnotp. % 112.12/112.45 apply zenon_H16c. % 112.12/112.45 rewrite <- zenon_D_pnotp. % 112.12/112.45 exact zenon_H16d. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.45 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 112.12/112.45 congruence. % 112.12/112.45 exact (zenon_H13b zenon_H146). % 112.12/112.45 apply zenon_H16a. apply refl_equal. % 112.12/112.45 apply zenon_H16a. apply refl_equal. % 112.12/112.45 apply zenon_H197. zenon_intro zenon_H179. % 112.12/112.45 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.12/112.45 generalize (zenon_H18f (mod2)). zenon_intro zenon_H199. % 112.12/112.45 generalize (zenon_H199 (mod1)). zenon_intro zenon_H19a. % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H19a); [ zenon_intro zenon_H167 | zenon_intro zenon_H19b ]. % 112.12/112.45 exact (zenon_H167 zenon_H179). % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H19b); [ zenon_intro zenon_H69 | zenon_intro zenon_H19c ]. % 112.12/112.45 exact (zenon_H69 assumption_19). % 112.12/112.45 exact (zenon_H194 zenon_H19c). % 112.12/112.45 apply zenon_H59. apply refl_equal. % 112.12/112.45 (* end of lemma zenon_L227_ *) % 112.12/112.45 assert (zenon_L228_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (organization zenon_TX_y) -> (~((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (low)) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (~((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> False). % 112.12/112.45 do 4 intro. intros zenon_H34 zenon_H1f zenon_H72 zenon_H17c zenon_H148 zenon_H1b8 zenon_H0 zenon_H123 zenon_H35 zenon_H38 zenon_H26e zenon_H1a zenon_Hec zenon_Hf3 zenon_H187. % 112.12/112.45 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88. % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ]. % 112.12/112.45 exact (zenon_H27 zenon_H1f). % 112.12/112.45 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a. % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H8b); [ zenon_intro zenon_H24 | zenon_intro zenon_H188 ]. % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ]. % 112.12/112.45 exact (zenon_H1e zenon_H24). % 112.12/112.45 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d. % 112.12/112.45 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f. % 112.12/112.45 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H30. zenon_intro zenon_H28. % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H8e); [ zenon_intro zenon_H91 | zenon_intro zenon_H6b ]. % 112.12/112.45 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 112.12/112.45 apply (zenon_L222_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.45 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 112.12/112.45 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ]. % 112.12/112.45 apply (zenon_L223_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.45 exact (zenon_H2e zenon_H29). % 112.12/112.45 apply (zenon_L98_ zenon_TT1_bg zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.45 apply zenon_H72. apply sym_equal. exact zenon_H6b. % 112.12/112.45 apply zenon_H187. apply sym_equal. exact zenon_H188. % 112.12/112.46 (* end of lemma zenon_L228_ *) % 112.12/112.46 assert (zenon_L229_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (greater (tau) (sigma)) -> (~((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (organization zenon_TX_y) -> False). % 112.12/112.46 do 4 intro. intros zenon_H34 zenon_H38 zenon_H187 zenon_H17c zenon_H26e zenon_Hf3 zenon_Hec zenon_H148 zenon_H35 zenon_H123 zenon_H1a zenon_H1f. % 112.12/112.46 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0. % 112.12/112.46 generalize (zenon_H0 zenon_E). zenon_intro zenon_H239. % 112.12/112.46 apply (zenon_imply_s _ _ zenon_H239); [ zenon_intro zenon_H27 | zenon_intro zenon_H23a ]. % 112.12/112.46 exact (zenon_H27 zenon_H1f). % 112.12/112.46 apply (zenon_and_s _ _ zenon_H23a). zenon_intro zenon_H23b. zenon_intro zenon_H238. % 112.12/112.46 apply (zenon_imply_s _ _ zenon_H23b); [ zenon_intro zenon_H112 | zenon_intro zenon_H1e0 ]. % 112.12/112.46 apply (zenon_imply_s _ _ zenon_H238); [ zenon_intro zenon_H111 | zenon_intro zenon_H22f ]. % 112.12/112.46 exact (zenon_H111 zenon_H112). % 112.12/112.46 apply (zenon_and_s _ _ zenon_H22f). zenon_intro zenon_H231. zenon_intro zenon_H230. % 112.12/112.46 apply (zenon_and_s _ _ zenon_H230). zenon_intro zenon_H233. zenon_intro zenon_H232. % 112.12/112.46 apply (zenon_and_s _ _ zenon_H232). zenon_intro zenon_H234. zenon_intro zenon_H181. % 112.12/112.46 apply (zenon_imply_s _ _ zenon_H231); [ zenon_intro zenon_H235 | zenon_intro zenon_H1b8 ]. % 112.12/112.46 apply (zenon_notand_s _ _ zenon_H235); [ zenon_intro zenon_H183 | zenon_intro zenon_H182 ]. % 112.12/112.46 apply (zenon_imply_s _ _ zenon_H233); [ zenon_intro zenon_H236 | zenon_intro zenon_H21a ]. % 112.12/112.46 apply (zenon_notand_s _ _ zenon_H236); [ zenon_intro zenon_H186 | zenon_intro zenon_H182 ]. % 112.12/112.46 exact (zenon_H186 zenon_H183). % 112.12/112.46 apply (zenon_L214_ zenon_TT2_la zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.46 elim (classic ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H23c | zenon_intro zenon_H21f ]. % 112.12/112.46 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))); [ zenon_intro zenon_H19c | zenon_intro zenon_H194 ]. % 112.12/112.46 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1a5 ]. % 112.12/112.46 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H17e | zenon_intro zenon_H117 ]. % 112.12/112.46 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.12/112.46 generalize (zenon_H18f (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H23d. % 112.12/112.46 generalize (zenon_H23d (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H23e. % 112.12/112.46 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H23f ]. % 112.12/112.46 exact (zenon_H1a5 zenon_H1a4). % 112.12/112.46 apply (zenon_imply_s _ _ zenon_H23f); [ zenon_intro zenon_H117 | zenon_intro zenon_H240 ]. % 112.12/112.46 exact (zenon_H117 zenon_H17e). % 112.12/112.46 exact (zenon_H17c zenon_H240). % 112.12/112.46 apply (zenon_L226_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.46 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.46 intro zenon_D_pnotp. % 112.12/112.46 apply zenon_H1a5. % 112.12/112.46 rewrite <- zenon_D_pnotp. % 112.12/112.46 exact zenon_H19c. % 112.12/112.46 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 112.12/112.46 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.46 congruence. % 112.12/112.46 apply zenon_H16a. apply refl_equal. % 112.12/112.46 exact (zenon_H21f zenon_H23c). % 112.12/112.46 apply (zenon_L227_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.46 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.46 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.46 intro zenon_D_pnotp. % 112.12/112.46 apply zenon_H21f. % 112.12/112.46 rewrite <- zenon_D_pnotp. % 112.12/112.46 exact zenon_H11a. % 112.12/112.46 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.46 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 112.12/112.46 congruence. % 112.12/112.46 exact (zenon_H21e zenon_H21a). % 112.12/112.46 apply zenon_H11b. apply refl_equal. % 112.12/112.46 apply zenon_H11b. apply refl_equal. % 112.12/112.46 apply (zenon_L216_ zenon_TT0_hz zenon_TT1_bg zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.46 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1a5 ]. % 112.12/112.46 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1a9 ]. % 112.12/112.46 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.46 intro zenon_D_pnotp. % 112.12/112.46 apply zenon_H17c. % 112.12/112.46 rewrite <- zenon_D_pnotp. % 112.12/112.46 exact zenon_H1b1. % 112.12/112.46 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 112.12/112.46 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.46 congruence. % 112.12/112.46 apply zenon_H16a. apply refl_equal. % 112.12/112.46 apply (zenon_L228_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.46 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))). % 112.12/112.46 intro zenon_D_pnotp. % 112.12/112.46 apply zenon_H1a9. % 112.12/112.46 rewrite <- zenon_D_pnotp. % 112.12/112.46 exact zenon_H1a4. % 112.12/112.46 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 112.12/112.46 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.46 congruence. % 112.12/112.46 apply zenon_H16a. apply refl_equal. % 112.12/112.46 exact (zenon_H1bb zenon_H1b8). % 112.12/112.46 apply (zenon_L104_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.46 apply (zenon_L131_ zenon_TX_y); trivial. % 112.12/112.46 (* end of lemma zenon_L229_ *) % 112.12/112.46 assert (zenon_L230_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (greater (tau) (sigma)) -> False). % 112.12/112.46 do 4 intro. intros zenon_H34 zenon_H1f zenon_H1a zenon_H123 zenon_H35 zenon_H148 zenon_Hec zenon_H26e zenon_H17c zenon_H187 zenon_H38. % 112.12/112.46 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3. % 112.12/112.46 apply (zenon_L229_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.46 (* end of lemma zenon_L230_ *) % 112.12/112.46 assert (zenon_L231_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (greater (tau) (sigma)) -> False). % 112.12/112.46 do 4 intro. intros zenon_H34 zenon_Had zenon_H1f zenon_H1a zenon_H123 zenon_H35 zenon_H148 zenon_Hec zenon_H26e zenon_H17c zenon_H38. % 112.12/112.46 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H242 | zenon_intro zenon_H187 ]. % 112.12/112.46 cut ((greater (low) (very_low)) = (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.46 intro zenon_D_pnotp. % 112.12/112.46 apply zenon_Had. % 112.12/112.46 rewrite <- zenon_D_pnotp. % 112.12/112.46 exact assumption_18c. % 112.12/112.46 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H187]. % 112.12/112.46 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.12/112.46 congruence. % 112.12/112.46 apply zenon_H6a. apply refl_equal. % 112.12/112.46 exact (zenon_H187 zenon_H242). % 112.12/112.46 apply (zenon_L230_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.46 (* end of lemma zenon_L231_ *) % 112.12/112.46 assert (zenon_L232_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (greater (tau) (sigma)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (age zenon_TX_y zenon_TT2_la)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (organization zenon_TX_y) -> False). % 112.12/112.46 do 4 intro. intros zenon_H34 zenon_H193 zenon_H38 zenon_H17c zenon_H26e zenon_Hec zenon_H148 zenon_H35 zenon_H123 zenon_H1a zenon_H1f. % 112.12/112.46 elim (classic (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_Hac | zenon_intro zenon_Had ]. % 112.12/112.46 generalize (zenon_H34 (mod1)). zenon_intro zenon_Ha7. % 112.12/112.46 generalize (zenon_Ha7 (low)). zenon_intro zenon_Ha8. % 112.12/112.46 generalize (zenon_Ha8 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H243. % 112.12/112.46 apply (zenon_imply_s _ _ zenon_H243); [ zenon_intro zenon_H7f | zenon_intro zenon_H244 ]. % 112.12/112.46 exact (zenon_H7f assumption_18b). % 112.12/112.46 apply (zenon_imply_s _ _ zenon_H244); [ zenon_intro zenon_Had | zenon_intro zenon_H241 ]. % 112.12/112.46 exact (zenon_Had zenon_Hac). % 112.12/112.46 exact (zenon_H193 zenon_H241). % 112.12/112.46 apply (zenon_L231_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.46 (* end of lemma zenon_L232_ *) % 112.12/112.46 assert (zenon_L233_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), ((((is_aligned zenon_TX_y zenon_TT1_bg)/\(positional_advantage zenon_TX_y zenon_TT1_bg))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low)))/\((((~(is_aligned zenon_TX_y zenon_TT1_bg))/\(positional_advantage zenon_TX_y zenon_TT1_bg))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod1)))/\((((is_aligned zenon_TX_y zenon_TT1_bg)/\(~(positional_advantage zenon_TX_y zenon_TT1_bg)))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2)))/\(((~(is_aligned zenon_TX_y zenon_TT1_bg))/\(~(positional_advantage zenon_TX_y zenon_TT1_bg)))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high)))))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (greater (tau) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T0) = (zero)))->((greater (age zenon_TX_y T) (sigma))<->(dissimilar zenon_TX_y T0 T))))) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> (~(greater (age zenon_TX_y zenon_TT1_bg) (sigma))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT0_hz))) -> ((hazard_of_mortality zenon_TX_y zenon_TT0_hz) = (mod2)) -> False). % 112.12/112.46 do 3 intro. intros zenon_H8c zenon_H26e zenon_H38 zenon_H35 zenon_Hed zenon_Hcd zenon_He9 zenon_Hec zenon_H1f zenon_H25e zenon_H25f. % 112.12/112.46 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d. % 112.12/112.46 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f. % 112.12/112.46 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H30. zenon_intro zenon_H28. % 112.12/112.46 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 112.12/112.46 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ]. % 112.12/112.46 apply (zenon_L150_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.46 apply zenon_H2e. zenon_intro zenon_H36. % 112.12/112.46 apply (zenon_L155_ zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.46 apply (zenon_L141_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.46 (* end of lemma zenon_L233_ *) % 112.12/112.46 assert (zenon_L234_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (zero)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T0) = (zero)))->((greater (age zenon_TX_y T) (sigma))<->(dissimilar zenon_TX_y T0 T))))) -> (~(greater (age zenon_TX_y zenon_TT1_bg) (sigma))) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT0_hz))) -> False). % 112.12/112.46 do 3 intro. intros zenon_H1f zenon_H1a zenon_Hcd zenon_H35 zenon_H24a zenon_Hec zenon_H0 zenon_Hed zenon_He9 zenon_H38 zenon_H26e zenon_H25e. % 112.12/112.46 generalize (zenon_H0 zenon_TT0_hz). zenon_intro zenon_H26a. % 112.12/112.46 apply (zenon_imply_s _ _ zenon_H26a); [ zenon_intro zenon_H27 | zenon_intro zenon_H26b ]. % 112.12/112.46 exact (zenon_H27 zenon_H1f). % 112.12/112.46 apply (zenon_and_s _ _ zenon_H26b). zenon_intro zenon_H26d. zenon_intro zenon_H26c. % 112.12/112.46 apply (zenon_imply_s _ _ zenon_H26c); [ zenon_intro zenon_H245 | zenon_intro zenon_H261 ]. % 112.12/112.46 apply (zenon_L137_ zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.46 apply (zenon_and_s _ _ zenon_H261). zenon_intro zenon_H263. zenon_intro zenon_H262. % 112.12/112.46 apply (zenon_and_s _ _ zenon_H262). zenon_intro zenon_H265. zenon_intro zenon_H264. % 112.12/112.46 apply (zenon_and_s _ _ zenon_H264). zenon_intro zenon_H267. zenon_intro zenon_H266. % 112.12/112.46 apply (zenon_imply_s _ _ zenon_H267); [ zenon_intro zenon_H268 | zenon_intro zenon_H25f ]. % 112.12/112.46 apply (zenon_notand_s _ _ zenon_H268); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H269 ]. % 112.12/112.46 exact (zenon_Hd8 zenon_Hcd). % 112.12/112.46 apply zenon_H269. zenon_intro zenon_H24d. % 112.12/112.46 apply (zenon_L140_ zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.46 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88. % 112.12/112.46 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ]. % 112.12/112.46 exact (zenon_H27 zenon_H1f). % 112.12/112.46 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a. % 112.12/112.46 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ]. % 112.12/112.46 apply (zenon_L3_ zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.46 apply (zenon_L233_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.46 (* end of lemma zenon_L234_ *) % 112.12/112.46 assert (zenon_L235_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT0_hz))) -> (greater (tau) (sigma)) -> (greater (tau) (zero)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (~(greater (sigma) (sigma))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> False). % 112.12/112.46 do 3 intro. intros zenon_H25e zenon_H38 zenon_H24a zenon_H35 zenon_H1a zenon_Hec zenon_H1f zenon_Hf3 zenon_Hda zenon_H26e. % 112.12/112.46 elim (classic ((sigma) = (age zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_He2 | zenon_intro zenon_Hde ]. % 112.12/112.46 elim (classic (greater (age zenon_TX_y zenon_TT1_bg) (sigma))); [ zenon_intro zenon_Hdb | zenon_intro zenon_He9 ]. % 112.12/112.46 cut ((greater (age zenon_TX_y zenon_TT1_bg) (sigma)) = (greater (sigma) (sigma))). % 112.12/112.46 intro zenon_D_pnotp. % 112.12/112.46 apply zenon_Hda. % 112.12/112.46 rewrite <- zenon_D_pnotp. % 112.12/112.46 exact zenon_Hdb. % 112.12/112.46 cut (((sigma) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 112.12/112.46 cut (((age zenon_TX_y zenon_TT1_bg) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hdf]. % 112.12/112.46 congruence. % 112.12/112.46 elim (classic ((sigma) = (sigma))); [ zenon_intro zenon_He3 | zenon_intro zenon_Hd9 ]. % 112.12/112.46 cut (((sigma) = (sigma)) = ((age zenon_TX_y zenon_TT1_bg) = (sigma))). % 112.12/112.46 intro zenon_D_pnotp. % 112.12/112.46 apply zenon_Hdf. % 112.12/112.46 rewrite <- zenon_D_pnotp. % 112.12/112.46 exact zenon_He3. % 112.12/112.46 cut (((sigma) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 112.12/112.46 cut (((sigma) = (age zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_Hde]. % 112.12/112.46 congruence. % 112.12/112.46 exact (zenon_Hde zenon_He2). % 112.12/112.46 apply zenon_Hd9. apply refl_equal. % 112.12/112.46 apply zenon_Hd9. apply refl_equal. % 112.12/112.46 apply zenon_Hd9. apply refl_equal. % 112.12/112.46 generalize (assumption_15 zenon_TX_y). zenon_intro zenon_Hed. % 112.12/112.46 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0. % 112.12/112.46 generalize (zenon_Hf3 zenon_TT0_hz). zenon_intro zenon_Hf4. % 112.12/112.46 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcd ]. % 112.12/112.46 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ]. % 112.12/112.46 exact (zenon_H27 zenon_H1f). % 112.12/112.46 exact (zenon_Hf2 zenon_Hec). % 112.12/112.46 apply (zenon_L234_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.46 elim (classic ((age zenon_TX_y zenon_TT1_bg) = (age zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H26f | zenon_intro zenon_H4d ]. % 112.12/112.46 cut (((age zenon_TX_y zenon_TT1_bg) = (age zenon_TX_y zenon_TT1_bg)) = ((sigma) = (age zenon_TX_y zenon_TT1_bg))). % 112.12/112.46 intro zenon_D_pnotp. % 112.12/112.46 apply zenon_Hde. % 112.12/112.46 rewrite <- zenon_D_pnotp. % 112.12/112.46 exact zenon_H26f. % 112.12/112.46 cut (((age zenon_TX_y zenon_TT1_bg) = (age zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 112.12/112.46 cut (((age zenon_TX_y zenon_TT1_bg) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hdf]. % 112.12/112.46 congruence. % 112.12/112.46 exact (zenon_Hdf zenon_H26e). % 112.12/112.46 apply zenon_H4d. apply refl_equal. % 112.12/112.46 apply zenon_H4d. apply refl_equal. % 112.12/112.46 (* end of lemma zenon_L235_ *) % 112.12/112.46 assert (zenon_L236_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (~((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT0_hz))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (greater (tau) (sigma)) -> (greater (tau) (zero)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> False). % 112.12/112.46 do 3 intro. intros zenon_H25e zenon_H26e zenon_H38 zenon_H24a zenon_H35 zenon_H1a zenon_Hec zenon_H1f. % 112.12/112.46 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3. % 112.12/112.46 generalize (meaning_postulate_greater_strict (sigma)). zenon_intro zenon_Hea. % 112.12/112.46 generalize (zenon_Hea (sigma)). zenon_intro zenon_Heb. % 112.12/112.46 apply (zenon_notand_s _ _ zenon_Heb); [ zenon_intro zenon_Hda | zenon_intro zenon_Hda ]. % 112.12/112.46 apply (zenon_L235_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.46 apply (zenon_L235_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.46 (* end of lemma zenon_L236_ *) % 112.12/112.46 assert (zenon_L237_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (organization zenon_TX_y) -> (~((low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T0) = (zero)))->((greater (age zenon_TX_y T) (sigma))<->(dissimilar zenon_TX_y T0 T))))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (~((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))) -> False). % 112.12/112.46 do 3 intro. intros zenon_H0 zenon_H1f zenon_H155 zenon_Hed zenon_H148 zenon_Hcd zenon_Hec zenon_H35 zenon_H292 zenon_H136 zenon_H154. % 112.12/112.46 generalize (zenon_H0 zenon_TT2_la). zenon_intro zenon_H13c. % 112.12/112.46 apply (zenon_imply_s _ _ zenon_H13c); [ zenon_intro zenon_H27 | zenon_intro zenon_H13d ]. % 112.12/112.46 exact (zenon_H27 zenon_H1f). % 112.12/112.46 apply (zenon_and_s _ _ zenon_H13d). zenon_intro zenon_H13f. zenon_intro zenon_H13e. % 112.12/112.46 apply (zenon_imply_s _ _ zenon_H13f); [ zenon_intro zenon_H121 | zenon_intro zenon_H15a ]. % 112.12/112.46 apply (zenon_imply_s _ _ zenon_H13e); [ zenon_intro zenon_H11d | zenon_intro zenon_H140 ]. % 112.12/112.46 exact (zenon_H11d zenon_H121). % 112.12/112.46 apply (zenon_and_s _ _ zenon_H140). zenon_intro zenon_H142. zenon_intro zenon_H141. % 112.12/112.46 apply (zenon_and_s _ _ zenon_H141). zenon_intro zenon_H144. zenon_intro zenon_H143. % 112.12/112.46 apply (zenon_and_s _ _ zenon_H143). zenon_intro zenon_H145. zenon_intro zenon_H134. % 112.12/112.46 apply (zenon_imply_s _ _ zenon_H142); [ zenon_intro zenon_H15c | zenon_intro zenon_H15b ]. % 112.12/112.46 apply (zenon_notand_s _ _ zenon_H15c); [ zenon_intro zenon_H135 | zenon_intro zenon_H127 ]. % 112.12/112.46 apply (zenon_imply_s _ _ zenon_H134); [ zenon_intro zenon_H138 | zenon_intro zenon_H137 ]. % 112.12/112.46 apply (zenon_notand_s _ _ zenon_H138); [ zenon_intro zenon_H13a | zenon_intro zenon_H139 ]. % 112.12/112.46 exact (zenon_H13a zenon_H135). % 112.12/112.46 apply zenon_H139. zenon_intro zenon_H122. % 112.12/112.46 generalize (zenon_H35 zenon_TT2_la). zenon_intro zenon_H124. % 112.12/112.46 apply (zenon_and_s _ _ zenon_H124). zenon_intro zenon_H126. zenon_intro zenon_H125. % 112.12/112.46 apply (zenon_imply_s _ _ zenon_H126); [ zenon_intro zenon_H128 | zenon_intro zenon_H127 ]. % 112.12/112.46 generalize (definition_smaller_or_equal (age zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H129. % 112.12/112.46 generalize (zenon_H129 (tau)). zenon_intro zenon_H12a. % 112.12/112.46 apply (zenon_equiv_s _ _ zenon_H12a); [ zenon_intro zenon_H128; zenon_intro zenon_H12d | zenon_intro zenon_H12c; zenon_intro zenon_H12b ]. % 112.12/112.46 apply (zenon_notor_s _ _ zenon_H12d). zenon_intro zenon_H12f. zenon_intro zenon_H12e. % 112.12/112.46 exact (zenon_H12e zenon_H292). % 112.12/112.46 exact (zenon_H128 zenon_H12c). % 112.12/112.46 exact (zenon_H127 zenon_H122). % 112.12/112.46 exact (zenon_H136 zenon_H137). % 112.12/112.46 apply (zenon_L56_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.46 apply zenon_H155. apply sym_equal. exact zenon_H15b. % 112.12/112.46 apply zenon_H154. apply sym_equal. exact zenon_H15a. % 112.12/112.46 (* end of lemma zenon_L237_ *) % 112.12/112.46 assert (zenon_L238_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (~(greater (low) (hazard_of_mortality zenon_TX_y zenon_TT2_la))) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (organization zenon_TX_y) -> (~((low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T0) = (zero)))->((greater (age zenon_TX_y T) (sigma))<->(dissimilar zenon_TX_y T0 T))))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> False). % 112.12/112.46 do 3 intro. intros zenon_H162 zenon_H0 zenon_H1f zenon_H155 zenon_Hed zenon_H148 zenon_Hcd zenon_Hec zenon_H35 zenon_H292 zenon_H136. % 112.12/112.46 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H166 | zenon_intro zenon_H154 ]. % 112.12/112.46 cut ((greater (low) (very_low)) = (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.12/112.46 intro zenon_D_pnotp. % 112.12/112.46 apply zenon_H162. % 112.12/112.46 rewrite <- zenon_D_pnotp. % 112.12/112.46 exact assumption_18c. % 112.12/112.46 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H154]. % 112.12/112.46 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.12/112.46 congruence. % 112.12/112.46 apply zenon_H6a. apply refl_equal. % 112.12/112.46 exact (zenon_H154 zenon_H166). % 112.12/112.46 apply (zenon_L237_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.46 (* end of lemma zenon_L238_ *) % 112.12/112.46 assert (zenon_L239_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod1)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT2_la))) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (organization zenon_TX_y) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T0) = (zero)))->((greater (age zenon_TX_y T) (sigma))<->(dissimilar zenon_TX_y T0 T))))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> False). % 112.12/112.46 do 3 intro. intros zenon_H34 zenon_H15d zenon_H169 zenon_H0 zenon_H1f zenon_Hed zenon_H148 zenon_Hcd zenon_Hec zenon_H35 zenon_H292 zenon_H136. % 112.12/112.46 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H165 | zenon_intro zenon_H15f ]. % 112.12/112.46 cut ((greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.12/112.46 intro zenon_D_pnotp. % 112.12/112.46 apply zenon_H169. % 112.12/112.46 rewrite <- zenon_D_pnotp. % 112.12/112.46 exact zenon_H165. % 112.12/112.46 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.46 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H159]. % 112.12/112.46 congruence. % 112.12/112.46 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.12/112.46 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.12/112.46 intro zenon_D_pnotp. % 112.12/112.46 apply zenon_H159. % 112.12/112.46 rewrite <- zenon_D_pnotp. % 112.12/112.46 exact zenon_H16d. % 112.12/112.46 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.46 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H1a7]. % 112.12/112.46 congruence. % 112.12/112.46 exact (zenon_H1a7 zenon_H15d). % 112.12/112.46 apply zenon_H16a. apply refl_equal. % 112.12/112.46 apply zenon_H16a. apply refl_equal. % 112.12/112.46 apply zenon_H16a. apply refl_equal. % 112.12/112.46 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H160 | zenon_intro zenon_H155 ]. % 112.12/112.46 cut ((greater (mod1) (low)) = (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.12/112.46 intro zenon_D_pnotp. % 112.12/112.46 apply zenon_H15f. % 112.12/112.46 rewrite <- zenon_D_pnotp. % 112.12/112.46 exact assumption_18b. % 112.12/112.46 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H155]. % 112.12/112.46 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 112.12/112.46 congruence. % 112.12/112.46 apply zenon_H59. apply refl_equal. % 112.12/112.46 exact (zenon_H155 zenon_H160). % 112.12/112.46 elim (classic (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H161 | zenon_intro zenon_H162 ]. % 112.12/112.46 generalize (zenon_H34 (mod1)). zenon_intro zenon_Ha7. % 112.12/112.46 generalize (zenon_Ha7 (low)). zenon_intro zenon_Ha8. % 112.12/112.46 generalize (zenon_Ha8 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H163. % 112.12/112.46 apply (zenon_imply_s _ _ zenon_H163); [ zenon_intro zenon_H7f | zenon_intro zenon_H164 ]. % 112.12/112.46 exact (zenon_H7f assumption_18b). % 112.12/112.46 apply (zenon_imply_s _ _ zenon_H164); [ zenon_intro zenon_H162 | zenon_intro zenon_H165 ]. % 112.12/112.46 exact (zenon_H162 zenon_H161). % 112.12/112.46 exact (zenon_H15f zenon_H165). % 112.12/112.46 apply (zenon_L238_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.46 (* end of lemma zenon_L239_ *) % 112.12/112.46 assert (zenon_L240_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T0) = (zero)))->((greater (age zenon_TX_y T) (sigma))<->(dissimilar zenon_TX_y T0 T))))) -> (organization zenon_TX_y) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (mod1) (mod1))) -> ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod1)) -> False). % 112.12/112.46 do 3 intro. intros zenon_H136 zenon_H292 zenon_H35 zenon_Hec zenon_Hcd zenon_H148 zenon_Hed zenon_H1f zenon_H0 zenon_H34 zenon_Ha6 zenon_H15d. % 112.12/112.46 elim (classic ((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H158 | zenon_intro zenon_H159 ]. % 112.12/112.46 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))); [ zenon_intro zenon_H19c | zenon_intro zenon_H194 ]. % 112.12/112.46 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1)) = (greater (mod1) (mod1))). % 112.12/112.46 intro zenon_D_pnotp. % 112.12/112.46 apply zenon_Ha6. % 112.12/112.46 rewrite <- zenon_D_pnotp. % 112.12/112.46 exact zenon_H19c. % 112.12/112.46 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 112.12/112.46 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H1a7]. % 112.12/112.46 congruence. % 112.12/112.46 elim (classic ((mod1) = (mod1))); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H59 ]. % 112.12/112.46 cut (((mod1) = (mod1)) = ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod1))). % 112.12/112.46 intro zenon_D_pnotp. % 112.12/112.46 apply zenon_H1a7. % 112.12/112.46 rewrite <- zenon_D_pnotp. % 112.12/112.46 exact zenon_Hb8. % 112.12/112.46 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 112.12/112.46 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H159]. % 112.12/112.46 congruence. % 112.12/112.46 exact (zenon_H159 zenon_H158). % 112.12/112.46 apply zenon_H59. apply refl_equal. % 112.12/112.46 apply zenon_H59. apply refl_equal. % 112.12/112.46 apply zenon_H59. apply refl_equal. % 112.12/112.46 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H168 | zenon_intro zenon_H169 ]. % 112.12/112.46 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))). % 112.12/112.46 intro zenon_D_pnotp. % 112.12/112.46 apply zenon_H194. % 112.12/112.46 rewrite <- zenon_D_pnotp. % 112.12/112.46 exact zenon_H168. % 112.12/112.46 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H1a7]. % 112.12/112.46 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.46 congruence. % 112.12/112.46 apply zenon_H16a. apply refl_equal. % 112.12/112.46 exact (zenon_H1a7 zenon_H15d). % 112.12/112.46 apply (zenon_L239_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.46 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.12/112.46 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.12/112.46 intro zenon_D_pnotp. % 112.12/112.46 apply zenon_H159. % 112.12/112.46 rewrite <- zenon_D_pnotp. % 112.12/112.46 exact zenon_H16d. % 112.12/112.46 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.46 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H1a7]. % 112.12/112.46 congruence. % 112.12/112.46 exact (zenon_H1a7 zenon_H15d). % 112.12/112.46 apply zenon_H16a. apply refl_equal. % 112.12/112.46 apply zenon_H16a. apply refl_equal. % 112.12/112.46 (* end of lemma zenon_L240_ *) % 112.12/112.46 assert (zenon_L241_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (low) (mod1))) -> ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod1)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T0) = (zero)))->((greater (age zenon_TX_y T) (sigma))<->(dissimilar zenon_TX_y T0 T))))) -> (organization zenon_TX_y) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> False). % 112.12/112.46 do 3 intro. intros zenon_H34 zenon_H6f zenon_H15d zenon_H136 zenon_H292 zenon_H35 zenon_Hec zenon_Hcd zenon_H148 zenon_Hed zenon_H1f zenon_H0. % 112.12/112.46 elim (classic (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H161 | zenon_intro zenon_H162 ]. % 112.12/112.46 cut ((greater (low) (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = (greater (low) (mod1))). % 112.12/112.46 intro zenon_D_pnotp. % 112.12/112.46 apply zenon_H6f. % 112.12/112.46 rewrite <- zenon_D_pnotp. % 112.12/112.46 exact zenon_H161. % 112.12/112.46 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H1a7]. % 112.12/112.46 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.12/112.46 congruence. % 112.12/112.46 apply zenon_H6a. apply refl_equal. % 112.12/112.46 exact (zenon_H1a7 zenon_H15d). % 112.12/112.46 elim (classic (greater (mod1) (mod1))); [ zenon_intro zenon_Hab | zenon_intro zenon_Ha6 ]. % 112.12/112.46 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))); [ zenon_intro zenon_H19c | zenon_intro zenon_H194 ]. % 112.12/112.46 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1)) = (greater (low) (mod1))). % 112.12/112.46 intro zenon_D_pnotp. % 112.12/112.46 apply zenon_H6f. % 112.12/112.46 rewrite <- zenon_D_pnotp. % 112.12/112.46 exact zenon_H19c. % 112.12/112.46 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 112.12/112.46 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1a8]. % 112.12/112.46 congruence. % 112.12/112.46 elim (classic ((low) = (low))); [ zenon_intro zenon_H74 | zenon_intro zenon_H6a ]. % 112.12/112.46 cut (((low) = (low)) = ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (low))). % 112.12/112.46 intro zenon_D_pnotp. % 112.12/112.46 apply zenon_H1a8. % 112.12/112.46 rewrite <- zenon_D_pnotp. % 112.12/112.46 exact zenon_H74. % 112.12/112.46 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.12/112.46 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H155]. % 112.12/112.46 congruence. % 112.12/112.46 apply (zenon_L238_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.46 apply zenon_H6a. apply refl_equal. % 112.12/112.46 apply zenon_H6a. apply refl_equal. % 112.12/112.46 apply zenon_H59. apply refl_equal. % 112.12/112.46 cut ((greater (mod1) (mod1)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))). % 112.12/112.46 intro zenon_D_pnotp. % 112.12/112.46 apply zenon_H194. % 112.12/112.46 rewrite <- zenon_D_pnotp. % 112.12/112.46 exact zenon_Hab. % 112.12/112.46 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 112.12/112.46 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H159]. % 112.12/112.46 congruence. % 112.12/112.46 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.12/112.46 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.12/112.46 intro zenon_D_pnotp. % 112.12/112.46 apply zenon_H159. % 112.12/112.46 rewrite <- zenon_D_pnotp. % 112.12/112.46 exact zenon_H16d. % 112.12/112.46 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.46 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H1a7]. % 112.12/112.46 congruence. % 112.12/112.46 exact (zenon_H1a7 zenon_H15d). % 112.12/112.46 apply zenon_H16a. apply refl_equal. % 112.12/112.46 apply zenon_H16a. apply refl_equal. % 112.12/112.46 apply zenon_H59. apply refl_equal. % 112.12/112.46 apply (zenon_L240_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.46 (* end of lemma zenon_L241_ *) % 112.12/112.46 assert (zenon_L242_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), ((((is_aligned zenon_TX_y zenon_TT2_la)/\(positional_advantage zenon_TX_y zenon_TT2_la))->((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (low)))/\((((~(is_aligned zenon_TX_y zenon_TT2_la))/\(positional_advantage zenon_TX_y zenon_TT2_la))->((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod1)))/\((((is_aligned zenon_TX_y zenon_TT2_la)/\(~(positional_advantage zenon_TX_y zenon_TT2_la)))->((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2)))/\(((~(is_aligned zenon_TX_y zenon_TT2_la))/\(~(positional_advantage zenon_TX_y zenon_TT2_la)))->((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high)))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (low) (mod1))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (is_aligned zenon_TX_y zenon_TT0_hz) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T0) = (zero)))->((greater (age zenon_TX_y T) (sigma))<->(dissimilar zenon_TX_y T0 T))))) -> (organization zenon_TX_y) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> False). % 112.12/112.46 do 3 intro. intros zenon_H140 zenon_H34 zenon_H6f zenon_H136 zenon_H292 zenon_H35 zenon_Hec zenon_Hcd zenon_H148 zenon_Hed zenon_H1f zenon_H0. % 112.12/112.46 apply (zenon_and_s _ _ zenon_H140). zenon_intro zenon_H142. zenon_intro zenon_H141. % 112.12/112.46 apply (zenon_and_s _ _ zenon_H141). zenon_intro zenon_H144. zenon_intro zenon_H143. % 112.12/112.46 apply (zenon_and_s _ _ zenon_H143). zenon_intro zenon_H145. zenon_intro zenon_H134. % 112.12/112.46 apply (zenon_imply_s _ _ zenon_H144); [ zenon_intro zenon_H15e | zenon_intro zenon_H15d ]. % 112.12/112.46 apply (zenon_notand_s _ _ zenon_H15e); [ zenon_intro zenon_H13a | zenon_intro zenon_H127 ]. % 112.12/112.46 apply zenon_H13a. zenon_intro zenon_H149. % 112.12/112.46 apply (zenon_L55_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.46 apply (zenon_L56_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.46 apply (zenon_L241_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.46 (* end of lemma zenon_L242_ *) % 112.12/112.46 assert (zenon_L243_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> False). % 112.12/112.46 do 3 intro. intros zenon_H34 zenon_H1a zenon_H148 zenon_H136 zenon_H0 zenon_H35 zenon_H292 zenon_Hec zenon_H1f zenon_Hf3. % 112.12/112.46 generalize (assumption_15 zenon_TX_y). zenon_intro zenon_Hed. % 112.12/112.46 generalize (zenon_Hf3 zenon_TT0_hz). zenon_intro zenon_Hf4. % 112.12/112.46 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcd ]. % 112.12/112.46 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ]. % 112.12/112.46 exact (zenon_H27 zenon_H1f). % 112.12/112.46 exact (zenon_Hf2 zenon_Hec). % 112.12/112.46 generalize (meaning_postulate_greater_strict (low)). zenon_intro zenon_H80. % 112.12/112.46 generalize (zenon_H80 (mod1)). zenon_intro zenon_H293. % 112.12/112.46 apply (zenon_notand_s _ _ zenon_H293); [ zenon_intro zenon_H6f | zenon_intro zenon_H7f ]. % 112.12/112.46 generalize (zenon_H0 zenon_TT2_la). zenon_intro zenon_H13c. % 112.12/112.46 apply (zenon_imply_s _ _ zenon_H13c); [ zenon_intro zenon_H27 | zenon_intro zenon_H13d ]. % 112.12/112.46 exact (zenon_H27 zenon_H1f). % 112.12/112.46 apply (zenon_and_s _ _ zenon_H13d). zenon_intro zenon_H13f. zenon_intro zenon_H13e. % 112.12/112.46 apply (zenon_imply_s _ _ zenon_H13e); [ zenon_intro zenon_H11d | zenon_intro zenon_H140 ]. % 112.12/112.46 apply (zenon_L50_ zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.46 apply (zenon_L242_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.46 exact (zenon_H7f assumption_18b). % 112.12/112.46 (* end of lemma zenon_L243_ *) % 112.12/112.46 assert (zenon_L244_ : forall (zenon_TT2_la : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> False). % 112.12/112.46 do 3 intro. intros zenon_H34 zenon_Hf3 zenon_H1f zenon_Hec zenon_H292 zenon_H35 zenon_H136 zenon_H148 zenon_H1a. % 112.12/112.46 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0. % 112.12/112.46 apply (zenon_L243_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.46 (* end of lemma zenon_L244_ *) % 112.12/112.46 assert (zenon_L245_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> False). % 112.12/112.46 do 3 intro. intros zenon_H34 zenon_H1a zenon_H148 zenon_H136 zenon_H35 zenon_H292 zenon_Hec zenon_H1f. % 112.12/112.46 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3. % 112.12/112.46 apply (zenon_L244_ zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.46 (* end of lemma zenon_L245_ *) % 112.12/112.46 assert (zenon_L246_ : forall (zenon_TT2_la : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (high)) -> False). % 112.12/112.46 do 4 intro. intros zenon_H1a zenon_H37 zenon_H35 zenon_H38 zenon_Hec zenon_H1f zenon_H148 zenon_H292 zenon_H17c zenon_H34 zenon_H116. % 112.12/112.46 elim (classic ((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H17d | zenon_intro zenon_H119 ]. % 112.12/112.46 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H17e | zenon_intro zenon_H117 ]. % 112.12/112.46 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H118 | zenon_intro zenon_H114 ]. % 112.12/112.46 cut ((greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.46 intro zenon_D_pnotp. % 112.12/112.46 apply zenon_H17c. % 112.12/112.46 rewrite <- zenon_D_pnotp. % 112.12/112.46 exact zenon_H118. % 112.12/112.46 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.46 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 112.12/112.46 congruence. % 112.12/112.46 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.12/112.46 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.12/112.46 intro zenon_D_pnotp. % 112.12/112.46 apply zenon_H17f. % 112.12/112.46 rewrite <- zenon_D_pnotp. % 112.12/112.46 exact zenon_H16d. % 112.12/112.46 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.46 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 112.12/112.46 congruence. % 112.12/112.46 apply (zenon_L245_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.46 apply zenon_H16a. apply refl_equal. % 112.12/112.46 apply zenon_H16a. apply refl_equal. % 112.12/112.46 apply zenon_H62. apply refl_equal. % 112.12/112.46 cut ((greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.46 intro zenon_D_pnotp. % 112.12/112.46 apply zenon_H114. % 112.12/112.46 rewrite <- zenon_D_pnotp. % 112.12/112.46 exact zenon_H17e. % 112.12/112.46 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.46 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 112.12/112.46 congruence. % 112.12/112.46 elim (classic ((high) = (high))); [ zenon_intro zenon_H180 | zenon_intro zenon_H113 ]. % 112.12/112.47 cut (((high) = (high)) = ((hazard_of_mortality zenon_TX_y zenon_E) = (high))). % 112.12/112.47 intro zenon_D_pnotp. % 112.12/112.47 apply zenon_H11c. % 112.12/112.47 rewrite <- zenon_D_pnotp. % 112.12/112.47 exact zenon_H180. % 112.12/112.47 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113]. % 112.12/112.47 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H119]. % 112.12/112.47 congruence. % 112.12/112.47 exact (zenon_H119 zenon_H17d). % 112.12/112.47 apply zenon_H113. apply refl_equal. % 112.12/112.47 apply zenon_H113. apply refl_equal. % 112.12/112.47 apply zenon_H62. apply refl_equal. % 112.12/112.47 apply (zenon_L49_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.47 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.47 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.47 intro zenon_D_pnotp. % 112.12/112.47 apply zenon_H119. % 112.12/112.47 rewrite <- zenon_D_pnotp. % 112.12/112.47 exact zenon_H11a. % 112.12/112.47 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.47 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 112.12/112.47 congruence. % 112.12/112.47 exact (zenon_H11c zenon_H116). % 112.12/112.47 apply zenon_H11b. apply refl_equal. % 112.12/112.47 apply zenon_H11b. apply refl_equal. % 112.12/112.47 (* end of lemma zenon_L246_ *) % 112.12/112.47 assert (zenon_L247_ : forall (zenon_TT2_la : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (((~(is_aligned zenon_TX_y zenon_E))/\(~(positional_advantage zenon_TX_y zenon_E)))->((hazard_of_mortality zenon_TX_y zenon_E) = (high))) -> (~(positional_advantage zenon_TX_y zenon_E)) -> (~(is_aligned zenon_TX_y zenon_E)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> False). % 112.12/112.47 do 4 intro. intros zenon_H181 zenon_H182 zenon_H183 zenon_H1a zenon_H37 zenon_H35 zenon_H38 zenon_Hec zenon_H1f zenon_H148 zenon_H292 zenon_H17c zenon_H34. % 112.12/112.47 apply (zenon_imply_s _ _ zenon_H181); [ zenon_intro zenon_H184 | zenon_intro zenon_H116 ]. % 112.12/112.47 apply (zenon_notand_s _ _ zenon_H184); [ zenon_intro zenon_H186 | zenon_intro zenon_H185 ]. % 112.12/112.47 exact (zenon_H186 zenon_H183). % 112.12/112.47 exact (zenon_H185 zenon_H182). % 112.12/112.47 apply (zenon_L246_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.47 (* end of lemma zenon_L247_ *) % 112.12/112.47 assert (zenon_L248_ : forall (zenon_TT2_la : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))) -> False). % 112.12/112.47 do 3 intro. intros zenon_Hf3 zenon_H1f zenon_Hec zenon_H292 zenon_H35 zenon_H0 zenon_H148 zenon_H1a zenon_H34 zenon_H167. % 112.12/112.47 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (high))))); [ zenon_intro zenon_H189 | zenon_intro zenon_H18a ]. % 112.12/112.47 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H136. zenon_intro zenon_H18b. % 112.12/112.47 apply (zenon_L243_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.47 cut ((greater (high) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))). % 112.12/112.47 intro zenon_D_pnotp. % 112.12/112.47 apply zenon_H167. % 112.12/112.47 rewrite <- zenon_D_pnotp. % 112.12/112.47 exact assumption_18d. % 112.12/112.47 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 112.12/112.47 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 112.12/112.47 congruence. % 112.12/112.47 apply (zenon_notand_s _ _ zenon_H18a); [ zenon_intro zenon_H18d | zenon_intro zenon_H18c ]. % 112.12/112.47 apply zenon_H18d. zenon_intro zenon_H137. % 112.12/112.47 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.12/112.47 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.12/112.47 intro zenon_D_pnotp. % 112.12/112.47 apply zenon_H17f. % 112.12/112.47 rewrite <- zenon_D_pnotp. % 112.12/112.47 exact zenon_H16d. % 112.12/112.47 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.47 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 112.12/112.47 congruence. % 112.12/112.47 exact (zenon_H136 zenon_H137). % 112.12/112.47 apply zenon_H16a. apply refl_equal. % 112.12/112.47 apply zenon_H16a. apply refl_equal. % 112.12/112.47 apply zenon_H18c. zenon_intro zenon_H18e. % 112.12/112.47 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.12/112.47 generalize (zenon_H18f (high)). zenon_intro zenon_H190. % 112.12/112.47 generalize (zenon_H190 (mod2)). zenon_intro zenon_H191. % 112.12/112.47 apply (zenon_imply_s _ _ zenon_H191); [ zenon_intro zenon_H18b | zenon_intro zenon_H192 ]. % 112.12/112.47 exact (zenon_H18b zenon_H18e). % 112.12/112.47 apply (zenon_imply_s _ _ zenon_H192); [ zenon_intro zenon_H9b | zenon_intro zenon_H179 ]. % 112.12/112.47 exact (zenon_H9b assumption_18d). % 112.12/112.47 exact (zenon_H167 zenon_H179). % 112.12/112.47 apply zenon_H83. apply refl_equal. % 112.12/112.47 (* end of lemma zenon_L248_ *) % 112.12/112.47 assert (zenon_L249_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2)) -> False). % 112.12/112.48 do 4 intro. intros zenon_H1a zenon_H148 zenon_H0 zenon_H35 zenon_H292 zenon_Hec zenon_H1f zenon_Hf3 zenon_H17c zenon_H34 zenon_H32. % 112.12/112.48 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H115 | zenon_intro zenon_H5e ]. % 112.12/112.48 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ]. % 112.12/112.48 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H17c. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H179. % 112.12/112.48 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.48 congruence. % 112.12/112.48 apply zenon_H16a. apply refl_equal. % 112.12/112.48 exact (zenon_H5e zenon_H115). % 112.12/112.48 apply (zenon_L248_ zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.48 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H5e. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H61. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31]. % 112.12/112.48 congruence. % 112.12/112.48 exact (zenon_H31 zenon_H32). % 112.12/112.48 apply zenon_H62. apply refl_equal. % 112.12/112.48 apply zenon_H62. apply refl_equal. % 112.12/112.48 (* end of lemma zenon_L249_ *) % 112.12/112.48 assert (zenon_L250_ : forall (zenon_TT2_la : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (~((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> False). % 112.12/112.48 do 4 intro. intros zenon_H34 zenon_H1f zenon_Hec zenon_H72 zenon_H17c zenon_H1a zenon_H148 zenon_H0 zenon_H35 zenon_H292 zenon_Hf3 zenon_H37 zenon_H187. % 112.12/112.48 generalize (zenon_Hf3 zenon_TT0_hz). zenon_intro zenon_Hf4. % 112.12/112.48 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcd ]. % 112.12/112.48 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ]. % 112.12/112.48 exact (zenon_H27 zenon_H1f). % 112.12/112.48 exact (zenon_Hf2 zenon_Hec). % 112.12/112.48 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88. % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ]. % 112.12/112.48 exact (zenon_H27 zenon_H1f). % 112.12/112.48 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a. % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H8b); [ zenon_intro zenon_H24 | zenon_intro zenon_H188 ]. % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ]. % 112.12/112.48 exact (zenon_H1e zenon_H24). % 112.12/112.48 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d. % 112.12/112.48 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f. % 112.12/112.48 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H30. zenon_intro zenon_H28. % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H8e); [ zenon_intro zenon_H91 | zenon_intro zenon_H6b ]. % 112.12/112.48 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 112.12/112.48 apply (zenon_L31_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 112.12/112.48 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ]. % 112.12/112.48 apply (zenon_L31_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.48 exact (zenon_H2e zenon_H29). % 112.12/112.48 apply (zenon_L249_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.48 apply zenon_H72. apply sym_equal. exact zenon_H6b. % 112.12/112.48 apply zenon_H187. apply sym_equal. exact zenon_H188. % 112.12/112.48 (* end of lemma zenon_L250_ *) % 112.12/112.48 assert (zenon_L251_ : forall (zenon_TT2_la : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (~((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> False). % 112.12/112.48 do 4 intro. intros zenon_H34 zenon_H193 zenon_H1f zenon_Hec zenon_H17c zenon_H1a zenon_H148 zenon_H0 zenon_H35 zenon_H292 zenon_Hf3 zenon_H37 zenon_H187. % 112.12/112.48 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 112.12/112.48 cut ((greater (mod1) (low)) = (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H193. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact assumption_18b. % 112.12/112.48 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 112.12/112.48 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 112.12/112.48 congruence. % 112.12/112.48 apply zenon_H59. apply refl_equal. % 112.12/112.48 exact (zenon_H72 zenon_H71). % 112.12/112.48 apply (zenon_L250_ zenon_TT2_la zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.48 (* end of lemma zenon_L251_ *) % 112.12/112.48 assert (zenon_L252_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))) -> False). % 112.12/112.48 do 3 intro. intros zenon_H34 zenon_H1a zenon_H148 zenon_H35 zenon_H292 zenon_Hec zenon_H1f zenon_Hf3 zenon_H167. % 112.12/112.48 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0. % 112.12/112.48 apply (zenon_L248_ zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.48 (* end of lemma zenon_L252_ *) % 112.12/112.48 assert (zenon_L253_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))) -> (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> False). % 112.12/112.48 do 3 intro. intros zenon_H34 zenon_H167 zenon_H1f zenon_Hec zenon_H292 zenon_H35 zenon_H148 zenon_H1a. % 112.12/112.48 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3. % 112.12/112.48 apply (zenon_L252_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.48 (* end of lemma zenon_L253_ *) % 112.12/112.48 assert (zenon_L254_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))) -> False). % 112.12/112.48 do 3 intro. intros zenon_H1a zenon_H148 zenon_H35 zenon_H292 zenon_Hec zenon_H1f zenon_H34 zenon_H194. % 112.12/112.48 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))))); [ zenon_intro zenon_H195 | zenon_intro zenon_H196 ]. % 112.12/112.48 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H13b. zenon_intro zenon_H167. % 112.12/112.48 apply (zenon_L253_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.48 cut ((greater (mod2) (mod1)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H194. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact assumption_19. % 112.12/112.48 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 112.12/112.48 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 112.12/112.48 congruence. % 112.12/112.48 apply (zenon_notand_s _ _ zenon_H196); [ zenon_intro zenon_H198 | zenon_intro zenon_H197 ]. % 112.12/112.48 apply zenon_H198. zenon_intro zenon_H146. % 112.12/112.48 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H16c. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H16d. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 112.12/112.48 congruence. % 112.12/112.48 exact (zenon_H13b zenon_H146). % 112.12/112.48 apply zenon_H16a. apply refl_equal. % 112.12/112.48 apply zenon_H16a. apply refl_equal. % 112.12/112.48 apply zenon_H197. zenon_intro zenon_H179. % 112.12/112.48 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.12/112.48 generalize (zenon_H18f (mod2)). zenon_intro zenon_H199. % 112.12/112.48 generalize (zenon_H199 (mod1)). zenon_intro zenon_H19a. % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H19a); [ zenon_intro zenon_H167 | zenon_intro zenon_H19b ]. % 112.12/112.48 exact (zenon_H167 zenon_H179). % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H19b); [ zenon_intro zenon_H69 | zenon_intro zenon_H19c ]. % 112.12/112.48 exact (zenon_H69 assumption_19). % 112.12/112.48 exact (zenon_H194 zenon_H19c). % 112.12/112.48 apply zenon_H59. apply refl_equal. % 112.12/112.48 (* end of lemma zenon_L254_ *) % 112.12/112.48 assert (zenon_L255_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))) -> False). % 112.12/112.48 do 3 intro. intros zenon_H1a zenon_H148 zenon_H35 zenon_H292 zenon_Hec zenon_H1f zenon_H34 zenon_H1a9. % 112.12/112.48 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))))); [ zenon_intro zenon_H195 | zenon_intro zenon_H196 ]. % 112.12/112.48 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H13b. zenon_intro zenon_H167. % 112.12/112.48 apply (zenon_L253_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.48 cut ((greater (mod2) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H1a9. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact assumption_18e. % 112.12/112.48 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.12/112.48 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 112.12/112.48 congruence. % 112.12/112.48 apply (zenon_notand_s _ _ zenon_H196); [ zenon_intro zenon_H198 | zenon_intro zenon_H197 ]. % 112.12/112.48 apply zenon_H198. zenon_intro zenon_H146. % 112.12/112.48 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H16c. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H16d. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 112.12/112.48 congruence. % 112.12/112.48 exact (zenon_H13b zenon_H146). % 112.12/112.48 apply zenon_H16a. apply refl_equal. % 112.12/112.48 apply zenon_H16a. apply refl_equal. % 112.12/112.48 apply zenon_H197. zenon_intro zenon_H179. % 112.12/112.48 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.12/112.48 generalize (zenon_H18f (mod2)). zenon_intro zenon_H199. % 112.12/112.48 generalize (zenon_H199 (low)). zenon_intro zenon_H1c6. % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H1c6); [ zenon_intro zenon_H167 | zenon_intro zenon_H1c7 ]. % 112.12/112.48 exact (zenon_H167 zenon_H179). % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H1c7); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H1b1 ]. % 112.12/112.48 exact (zenon_Hc2 assumption_18e). % 112.12/112.48 exact (zenon_H1a9 zenon_H1b1). % 112.12/112.48 apply zenon_H6a. apply refl_equal. % 112.12/112.48 (* end of lemma zenon_L255_ *) % 112.12/112.48 assert (zenon_L256_ : forall (zenon_TT2_la : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (low)) -> False). % 112.12/112.48 do 3 intro. intros zenon_H1f zenon_Hec zenon_H292 zenon_H35 zenon_H148 zenon_H1a zenon_H1a5 zenon_H34 zenon_H1b8. % 112.12/112.48 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1ba ]. % 112.12/112.48 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1a9 ]. % 112.12/112.48 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H1a5. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H1b1. % 112.12/112.48 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.48 congruence. % 112.12/112.48 apply zenon_H16a. apply refl_equal. % 112.12/112.48 exact (zenon_H1ba zenon_H1b9). % 112.12/112.48 apply (zenon_L255_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.48 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((low) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H1ba. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H11a. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 112.12/112.48 congruence. % 112.12/112.48 exact (zenon_H1bb zenon_H1b8). % 112.12/112.48 apply zenon_H11b. apply refl_equal. % 112.12/112.48 apply zenon_H11b. apply refl_equal. % 112.12/112.48 (* end of lemma zenon_L256_ *) % 112.12/112.48 assert (zenon_L257_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> False). % 112.12/112.48 do 4 intro. intros zenon_H34 zenon_H1f zenon_H1a zenon_H187 zenon_H17c zenon_H37 zenon_H38 zenon_Hec zenon_H292 zenon_H35 zenon_H148. % 112.12/112.48 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3. % 112.12/112.48 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0. % 112.12/112.48 generalize (zenon_H0 zenon_E). zenon_intro zenon_H239. % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H239); [ zenon_intro zenon_H27 | zenon_intro zenon_H23a ]. % 112.12/112.48 exact (zenon_H27 zenon_H1f). % 112.12/112.48 apply (zenon_and_s _ _ zenon_H23a). zenon_intro zenon_H23b. zenon_intro zenon_H238. % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H238); [ zenon_intro zenon_H111 | zenon_intro zenon_H22f ]. % 112.12/112.48 apply (zenon_L105_ zenon_TX_y); trivial. % 112.12/112.48 apply (zenon_and_s _ _ zenon_H22f). zenon_intro zenon_H231. zenon_intro zenon_H230. % 112.12/112.48 apply (zenon_and_s _ _ zenon_H230). zenon_intro zenon_H233. zenon_intro zenon_H232. % 112.12/112.48 apply (zenon_and_s _ _ zenon_H232). zenon_intro zenon_H234. zenon_intro zenon_H181. % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H231); [ zenon_intro zenon_H235 | zenon_intro zenon_H1b8 ]. % 112.12/112.48 apply (zenon_notand_s _ _ zenon_H235); [ zenon_intro zenon_H183 | zenon_intro zenon_H182 ]. % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H233); [ zenon_intro zenon_H236 | zenon_intro zenon_H21a ]. % 112.12/112.48 apply (zenon_notand_s _ _ zenon_H236); [ zenon_intro zenon_H186 | zenon_intro zenon_H182 ]. % 112.12/112.48 exact (zenon_H186 zenon_H183). % 112.12/112.48 apply (zenon_L247_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.48 elim (classic ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H23c | zenon_intro zenon_H21f ]. % 112.12/112.48 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))); [ zenon_intro zenon_H19c | zenon_intro zenon_H194 ]. % 112.12/112.48 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1a5 ]. % 112.12/112.48 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H17e | zenon_intro zenon_H117 ]. % 112.12/112.48 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.12/112.48 generalize (zenon_H18f (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H23d. % 112.12/112.48 generalize (zenon_H23d (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H23e. % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H23f ]. % 112.12/112.48 exact (zenon_H1a5 zenon_H1a4). % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H23f); [ zenon_intro zenon_H117 | zenon_intro zenon_H240 ]. % 112.12/112.48 exact (zenon_H117 zenon_H17e). % 112.12/112.48 exact (zenon_H17c zenon_H240). % 112.12/112.48 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H241 | zenon_intro zenon_H193 ]. % 112.12/112.48 cut ((greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H117. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H241. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.48 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 112.12/112.48 congruence. % 112.12/112.48 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H21f. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H11a. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 112.12/112.48 congruence. % 112.12/112.48 exact (zenon_H21e zenon_H21a). % 112.12/112.48 apply zenon_H11b. apply refl_equal. % 112.12/112.48 apply zenon_H11b. apply refl_equal. % 112.12/112.48 apply zenon_H62. apply refl_equal. % 112.12/112.48 apply (zenon_L251_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.48 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H1a5. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H19c. % 112.12/112.48 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.48 congruence. % 112.12/112.48 apply zenon_H16a. apply refl_equal. % 112.12/112.48 exact (zenon_H21f zenon_H23c). % 112.12/112.48 apply (zenon_L254_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.48 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H21f. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H11a. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 112.12/112.48 congruence. % 112.12/112.48 exact (zenon_H21e zenon_H21a). % 112.12/112.48 apply zenon_H11b. apply refl_equal. % 112.12/112.48 apply zenon_H11b. apply refl_equal. % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H234); [ zenon_intro zenon_H237 | zenon_intro zenon_H19e ]. % 112.12/112.48 apply (zenon_notand_s _ _ zenon_H237); [ zenon_intro zenon_H183 | zenon_intro zenon_H185 ]. % 112.12/112.48 apply (zenon_L247_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.48 exact (zenon_H185 zenon_H182). % 112.12/112.48 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H1a1 ]. % 112.12/112.48 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ]. % 112.12/112.48 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1a5 ]. % 112.12/112.48 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H17e | zenon_intro zenon_H117 ]. % 112.12/112.48 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.12/112.48 generalize (zenon_H18f (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H23d. % 112.12/112.48 generalize (zenon_H23d (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H23e. % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H23f ]. % 112.12/112.48 exact (zenon_H1a5 zenon_H1a4). % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H23f); [ zenon_intro zenon_H117 | zenon_intro zenon_H240 ]. % 112.12/112.48 exact (zenon_H117 zenon_H17e). % 112.12/112.48 exact (zenon_H17c zenon_H240). % 112.12/112.48 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1c4 ]. % 112.12/112.48 cut ((greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H117. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H1c3. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.48 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 112.12/112.48 congruence. % 112.12/112.48 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H1a1. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H11a. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 112.12/112.48 congruence. % 112.12/112.48 exact (zenon_H1a2 zenon_H19e). % 112.12/112.48 apply zenon_H11b. apply refl_equal. % 112.12/112.48 apply zenon_H11b. apply refl_equal. % 112.12/112.48 apply zenon_H62. apply refl_equal. % 112.12/112.48 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H241 | zenon_intro zenon_H193 ]. % 112.12/112.48 generalize (zenon_H34 (mod2)). zenon_intro zenon_H16e. % 112.12/112.48 generalize (zenon_H16e (mod1)). zenon_intro zenon_H16f. % 112.12/112.48 generalize (zenon_H16f (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H28e. % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H28e); [ zenon_intro zenon_H69 | zenon_intro zenon_H28f ]. % 112.12/112.48 exact (zenon_H69 assumption_19). % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H28f); [ zenon_intro zenon_H193 | zenon_intro zenon_H1c3 ]. % 112.12/112.48 exact (zenon_H193 zenon_H241). % 112.12/112.48 exact (zenon_H1c4 zenon_H1c3). % 112.12/112.48 apply (zenon_L251_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.48 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H1a5. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H179. % 112.12/112.48 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.48 congruence. % 112.12/112.48 apply zenon_H16a. apply refl_equal. % 112.12/112.48 exact (zenon_H1a1 zenon_H1a3). % 112.12/112.48 apply (zenon_L248_ zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.48 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H1a1. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H11a. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 112.12/112.48 congruence. % 112.12/112.48 exact (zenon_H1a2 zenon_H19e). % 112.12/112.48 apply zenon_H11b. apply refl_equal. % 112.12/112.48 apply zenon_H11b. apply refl_equal. % 112.12/112.48 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1a5 ]. % 112.12/112.48 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1a9 ]. % 112.12/112.48 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H17c. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H1b1. % 112.12/112.48 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.48 congruence. % 112.12/112.48 apply zenon_H16a. apply refl_equal. % 112.12/112.48 apply (zenon_L250_ zenon_TT2_la zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.48 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H1a9. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H1a4. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.48 congruence. % 112.12/112.48 apply zenon_H16a. apply refl_equal. % 112.12/112.48 exact (zenon_H1bb zenon_H1b8). % 112.12/112.48 apply (zenon_L256_ zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.48 (* end of lemma zenon_L257_ *) % 112.12/112.48 assert (zenon_L258_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> False). % 112.12/112.48 do 4 intro. intros zenon_H34 zenon_Had zenon_H1f zenon_H1a zenon_H17c zenon_H37 zenon_H38 zenon_Hec zenon_H292 zenon_H35 zenon_H148. % 112.12/112.48 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H242 | zenon_intro zenon_H187 ]. % 112.12/112.48 cut ((greater (low) (very_low)) = (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_Had. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact assumption_18c. % 112.12/112.48 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H187]. % 112.12/112.48 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.12/112.48 congruence. % 112.12/112.48 apply zenon_H6a. apply refl_equal. % 112.12/112.48 exact (zenon_H187 zenon_H242). % 112.12/112.48 apply (zenon_L257_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.48 (* end of lemma zenon_L258_ *) % 112.12/112.48 assert (zenon_L259_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (greater (tau) (sigma)) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (organization zenon_TX_y) -> False). % 112.12/112.48 do 4 intro. intros zenon_H34 zenon_H193 zenon_H148 zenon_H35 zenon_H292 zenon_Hec zenon_H38 zenon_H37 zenon_H17c zenon_H1a zenon_H1f. % 112.12/112.48 elim (classic (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_Hac | zenon_intro zenon_Had ]. % 112.12/112.48 generalize (zenon_H34 (mod1)). zenon_intro zenon_Ha7. % 112.12/112.48 generalize (zenon_Ha7 (low)). zenon_intro zenon_Ha8. % 112.12/112.48 generalize (zenon_Ha8 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H243. % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H243); [ zenon_intro zenon_H7f | zenon_intro zenon_H244 ]. % 112.12/112.48 exact (zenon_H7f assumption_18b). % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H244); [ zenon_intro zenon_Had | zenon_intro zenon_H241 ]. % 112.12/112.48 exact (zenon_Had zenon_Hac). % 112.12/112.48 exact (zenon_H193 zenon_H241). % 112.12/112.48 apply (zenon_L258_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.48 (* end of lemma zenon_L259_ *) % 112.12/112.48 assert (zenon_L260_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (greater (sigma) (age zenon_TX_y zenon_TT1_bg)) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> False). % 112.12/112.48 do 4 intro. intros zenon_H34 zenon_H1c4 zenon_H1f zenon_H1a zenon_H17c zenon_H37 zenon_H38 zenon_Hec zenon_H292 zenon_H35 zenon_H148. % 112.12/112.48 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H241 | zenon_intro zenon_H193 ]. % 112.12/112.48 generalize (zenon_H34 (mod2)). zenon_intro zenon_H16e. % 112.12/112.48 generalize (zenon_H16e (mod1)). zenon_intro zenon_H16f. % 112.12/112.48 generalize (zenon_H16f (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H28e. % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H28e); [ zenon_intro zenon_H69 | zenon_intro zenon_H28f ]. % 112.12/112.48 exact (zenon_H69 assumption_19). % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H28f); [ zenon_intro zenon_H193 | zenon_intro zenon_H1c3 ]. % 112.12/112.48 exact (zenon_H193 zenon_H241). % 112.12/112.48 exact (zenon_H1c4 zenon_H1c3). % 112.12/112.48 apply (zenon_L259_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.48 (* end of lemma zenon_L260_ *) % 112.12/112.48 assert (zenon_L261_ : forall (zenon_TT2_la : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (high)) -> False). % 112.12/112.48 do 4 intro. intros zenon_H1f zenon_Hec zenon_H1a zenon_H26e zenon_Hf3 zenon_H292 zenon_H35 zenon_H148 zenon_H17c zenon_H34 zenon_H116. % 112.12/112.48 elim (classic ((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H17d | zenon_intro zenon_H119 ]. % 112.12/112.48 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H17e | zenon_intro zenon_H117 ]. % 112.12/112.48 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H118 | zenon_intro zenon_H114 ]. % 112.12/112.48 cut ((greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H17c. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H118. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.48 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 112.12/112.48 congruence. % 112.12/112.48 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H17f. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H16d. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 112.12/112.48 congruence. % 112.12/112.48 apply (zenon_L244_ zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.48 apply zenon_H16a. apply refl_equal. % 112.12/112.48 apply zenon_H16a. apply refl_equal. % 112.12/112.48 apply zenon_H62. apply refl_equal. % 112.12/112.48 cut ((greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H114. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H17e. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 112.12/112.48 congruence. % 112.12/112.48 elim (classic ((high) = (high))); [ zenon_intro zenon_H180 | zenon_intro zenon_H113 ]. % 112.12/112.48 cut (((high) = (high)) = ((hazard_of_mortality zenon_TX_y zenon_E) = (high))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H11c. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H180. % 112.12/112.48 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113]. % 112.12/112.48 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H119]. % 112.12/112.48 congruence. % 112.12/112.48 exact (zenon_H119 zenon_H17d). % 112.12/112.48 apply zenon_H113. apply refl_equal. % 112.12/112.48 apply zenon_H113. apply refl_equal. % 112.12/112.48 apply zenon_H62. apply refl_equal. % 112.12/112.48 apply (zenon_L207_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.48 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H119. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H11a. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 112.12/112.48 congruence. % 112.12/112.48 exact (zenon_H11c zenon_H116). % 112.12/112.48 apply zenon_H11b. apply refl_equal. % 112.12/112.48 apply zenon_H11b. apply refl_equal. % 112.12/112.48 (* end of lemma zenon_L261_ *) % 112.12/112.48 assert (zenon_L262_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> False). % 112.12/112.48 do 3 intro. intros zenon_H34 zenon_H1c2 zenon_H2c zenon_H26e zenon_H1a zenon_Hec zenon_H1f zenon_Hf3. % 112.12/112.48 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H118 | zenon_intro zenon_H114 ]. % 112.12/112.48 cut ((greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H1c2. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H118. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.48 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 112.12/112.48 congruence. % 112.12/112.48 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H94. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H61. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 112.12/112.48 congruence. % 112.12/112.48 exact (zenon_H2b zenon_H2c). % 112.12/112.48 apply zenon_H62. apply refl_equal. % 112.12/112.48 apply zenon_H62. apply refl_equal. % 112.12/112.48 apply zenon_H62. apply refl_equal. % 112.12/112.48 apply (zenon_L217_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.48 (* end of lemma zenon_L262_ *) % 112.12/112.48 assert (zenon_L263_ : forall (zenon_TT2_la : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (((~(is_aligned zenon_TX_y zenon_TT1_bg))/\(~(positional_advantage zenon_TX_y zenon_TT1_bg)))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))) -> (~(positional_advantage zenon_TX_y zenon_TT1_bg)) -> (~(is_aligned zenon_TX_y zenon_TT1_bg)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> False). % 112.12/112.48 do 4 intro. intros zenon_H28 zenon_H29 zenon_H2a zenon_H26e zenon_H1a zenon_Hec zenon_H1f zenon_Hf3 zenon_H148 zenon_H0 zenon_H35 zenon_H292 zenon_H17c zenon_H34. % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ]. % 112.12/112.48 apply (zenon_notand_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ]. % 112.12/112.48 exact (zenon_H2f zenon_H2a). % 112.12/112.48 exact (zenon_H2e zenon_H29). % 112.12/112.48 elim (classic ((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H281 | zenon_intro zenon_H94 ]. % 112.12/112.48 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H1c2 ]. % 112.12/112.48 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H118 | zenon_intro zenon_H114 ]. % 112.12/112.48 cut ((greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H17c. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H118. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.48 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 112.12/112.48 congruence. % 112.12/112.48 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H17f. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H16d. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 112.12/112.48 congruence. % 112.12/112.48 apply (zenon_L243_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.48 apply zenon_H16a. apply refl_equal. % 112.12/112.48 apply zenon_H16a. apply refl_equal. % 112.12/112.48 apply zenon_H62. apply refl_equal. % 112.12/112.48 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H114. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H1c5. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 112.12/112.48 congruence. % 112.12/112.48 elim (classic ((high) = (high))); [ zenon_intro zenon_H180 | zenon_intro zenon_H113 ]. % 112.12/112.48 cut (((high) = (high)) = ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H2b. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H180. % 112.12/112.48 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113]. % 112.12/112.48 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 112.12/112.48 congruence. % 112.12/112.48 exact (zenon_H94 zenon_H281). % 112.12/112.48 apply zenon_H113. apply refl_equal. % 112.12/112.48 apply zenon_H113. apply refl_equal. % 112.12/112.48 apply zenon_H62. apply refl_equal. % 112.12/112.48 apply (zenon_L262_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.48 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H94. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H61. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 112.12/112.48 congruence. % 112.12/112.48 exact (zenon_H2b zenon_H2c). % 112.12/112.48 apply zenon_H62. apply refl_equal. % 112.12/112.48 apply zenon_H62. apply refl_equal. % 112.12/112.48 (* end of lemma zenon_L263_ *) % 112.12/112.48 assert (zenon_L264_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (((~(is_aligned zenon_TX_y zenon_TT1_bg))/\(~(positional_advantage zenon_TX_y zenon_TT1_bg)))->((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (greater (tau) (sigma)) -> (~(is_aligned zenon_TX_y zenon_TT1_bg)) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod1)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> False). % 112.12/112.48 do 4 intro. intros zenon_H28 zenon_H26e zenon_H38 zenon_H2a zenon_H92 zenon_H1a zenon_H148 zenon_H0 zenon_H35 zenon_H292 zenon_Hec zenon_H1f zenon_Hf3 zenon_H17c zenon_H34. % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ]. % 112.12/112.48 apply (zenon_notand_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ]. % 112.12/112.48 exact (zenon_H2f zenon_H2a). % 112.12/112.48 apply zenon_H2e. zenon_intro zenon_H36. % 112.12/112.48 apply (zenon_L155_ zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.48 elim (classic ((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H281 | zenon_intro zenon_H94 ]. % 112.12/112.48 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H1c2 ]. % 112.12/112.48 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H118 | zenon_intro zenon_H114 ]. % 112.12/112.48 cut ((greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H17c. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H118. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.48 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 112.12/112.48 congruence. % 112.12/112.48 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H17f. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H16d. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 112.12/112.48 congruence. % 112.12/112.48 apply (zenon_L243_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.48 apply zenon_H16a. apply refl_equal. % 112.12/112.48 apply zenon_H16a. apply refl_equal. % 112.12/112.48 apply zenon_H62. apply refl_equal. % 112.12/112.48 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H114. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H1c5. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 112.12/112.48 congruence. % 112.12/112.48 elim (classic ((high) = (high))); [ zenon_intro zenon_H180 | zenon_intro zenon_H113 ]. % 112.12/112.48 cut (((high) = (high)) = ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H2b. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H180. % 112.12/112.48 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113]. % 112.12/112.48 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 112.12/112.48 congruence. % 112.12/112.48 exact (zenon_H94 zenon_H281). % 112.12/112.48 apply zenon_H113. apply refl_equal. % 112.12/112.48 apply zenon_H113. apply refl_equal. % 112.12/112.48 apply zenon_H62. apply refl_equal. % 112.12/112.48 apply (zenon_L176_ zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.48 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H94. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H61. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 112.12/112.48 congruence. % 112.12/112.48 exact (zenon_H2b zenon_H2c). % 112.12/112.48 apply zenon_H62. apply refl_equal. % 112.12/112.48 apply zenon_H62. apply refl_equal. % 112.12/112.48 (* end of lemma zenon_L264_ *) % 112.12/112.48 assert (zenon_L265_ : forall (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low)) -> False). % 112.12/112.48 do 2 intro. intros zenon_H34 zenon_H1c4 zenon_H6b. % 112.12/112.48 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H241 | zenon_intro zenon_H193 ]. % 112.12/112.48 generalize (zenon_H34 (mod2)). zenon_intro zenon_H16e. % 112.12/112.48 generalize (zenon_H16e (mod1)). zenon_intro zenon_H16f. % 112.12/112.48 generalize (zenon_H16f (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H28e. % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H28e); [ zenon_intro zenon_H69 | zenon_intro zenon_H28f ]. % 112.12/112.48 exact (zenon_H69 assumption_19). % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H28f); [ zenon_intro zenon_H193 | zenon_intro zenon_H1c3 ]. % 112.12/112.48 exact (zenon_H193 zenon_H241). % 112.12/112.48 exact (zenon_H1c4 zenon_H1c3). % 112.12/112.48 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 112.12/112.48 cut ((greater (mod1) (low)) = (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H193. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact assumption_18b. % 112.12/112.48 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 112.12/112.48 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 112.12/112.48 congruence. % 112.12/112.48 apply zenon_H59. apply refl_equal. % 112.12/112.48 exact (zenon_H72 zenon_H71). % 112.12/112.48 apply zenon_H72. apply sym_equal. exact zenon_H6b. % 112.12/112.48 (* end of lemma zenon_L265_ *) % 112.12/112.48 assert (zenon_L266_ : forall (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low)) -> False). % 112.12/112.48 do 2 intro. intros zenon_H34 zenon_H2c zenon_H1c2 zenon_H6b. % 112.12/112.48 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H118 | zenon_intro zenon_H114 ]. % 112.12/112.48 cut ((greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H1c2. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H118. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.48 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 112.12/112.48 congruence. % 112.12/112.48 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H94. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H61. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 112.12/112.48 congruence. % 112.12/112.48 exact (zenon_H2b zenon_H2c). % 112.12/112.48 apply zenon_H62. apply refl_equal. % 112.12/112.48 apply zenon_H62. apply refl_equal. % 112.12/112.48 apply zenon_H62. apply refl_equal. % 112.12/112.48 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1c4 ]. % 112.12/112.48 generalize (zenon_H34 (high)). zenon_intro zenon_H1fa. % 112.12/112.48 generalize (zenon_H1fa (mod2)). zenon_intro zenon_H1fb. % 112.12/112.48 generalize (zenon_H1fb (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H27e. % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H27e); [ zenon_intro zenon_H9b | zenon_intro zenon_H27f ]. % 112.12/112.48 exact (zenon_H9b assumption_18d). % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H27f); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H118 ]. % 112.12/112.48 exact (zenon_H1c4 zenon_H1c3). % 112.12/112.48 exact (zenon_H114 zenon_H118). % 112.12/112.48 apply (zenon_L265_ zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.48 (* end of lemma zenon_L266_ *) % 112.12/112.48 assert (zenon_L267_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, ((organization zenon_TX_y)->(((has_immunity zenon_TX_y T)->((hazard_of_mortality zenon_TX_y T) = (very_low)))/\((~(has_immunity zenon_TX_y T))->((((is_aligned zenon_TX_y T)/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (low)))/\((((~(is_aligned zenon_TX_y T))/\(positional_advantage zenon_TX_y T))->((hazard_of_mortality zenon_TX_y T) = (mod1)))/\((((is_aligned zenon_TX_y T)/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (mod2)))/\(((~(is_aligned zenon_TX_y T))/\(~(positional_advantage zenon_TX_y T)))->((hazard_of_mortality zenon_TX_y T) = (high)))))))))) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (greater (tau) (sigma)) -> (~((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> False). % 112.12/112.48 do 4 intro. intros zenon_H34 zenon_H1f zenon_H1a zenon_H148 zenon_H0 zenon_H35 zenon_H292 zenon_Hec zenon_Hf3 zenon_H26e zenon_H17c zenon_H38 zenon_H187. % 112.12/112.48 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88. % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ]. % 112.12/112.48 exact (zenon_H27 zenon_H1f). % 112.12/112.48 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a. % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H8b); [ zenon_intro zenon_H24 | zenon_intro zenon_H188 ]. % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ]. % 112.12/112.48 exact (zenon_H1e zenon_H24). % 112.12/112.48 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d. % 112.12/112.48 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f. % 112.12/112.48 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H30. zenon_intro zenon_H28. % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H8e); [ zenon_intro zenon_H91 | zenon_intro zenon_H6b ]. % 112.12/112.48 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H90); [ zenon_intro zenon_H93 | zenon_intro zenon_H92 ]. % 112.12/112.48 apply (zenon_notand_s _ _ zenon_H93); [ zenon_intro zenon_H2f | zenon_intro zenon_H29 ]. % 112.12/112.48 exact (zenon_H2f zenon_H2a). % 112.12/112.48 apply (zenon_L263_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.48 apply (zenon_L264_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 112.12/112.48 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ]. % 112.12/112.48 apply (zenon_L263_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.48 exact (zenon_H2e zenon_H29). % 112.12/112.48 apply (zenon_L249_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H90); [ zenon_intro zenon_H93 | zenon_intro zenon_H92 ]. % 112.12/112.48 apply (zenon_notand_s _ _ zenon_H93); [ zenon_intro zenon_H2f | zenon_intro zenon_H29 ]. % 112.12/112.48 apply zenon_H2f. zenon_intro zenon_H82. % 112.12/112.48 apply (zenon_L156_ zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 112.12/112.48 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ]. % 112.12/112.48 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ]. % 112.12/112.48 apply (zenon_notand_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ]. % 112.12/112.48 exact (zenon_H2f zenon_H2a). % 112.12/112.48 exact (zenon_H2e zenon_H29). % 112.12/112.48 elim (classic ((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H281 | zenon_intro zenon_H94 ]. % 112.12/112.48 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H1c2 ]. % 112.12/112.48 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H118 | zenon_intro zenon_H114 ]. % 112.12/112.48 cut ((greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.48 intro zenon_D_pnotp. % 112.12/112.48 apply zenon_H17c. % 112.12/112.48 rewrite <- zenon_D_pnotp. % 112.12/112.48 exact zenon_H118. % 112.12/112.48 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.48 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 112.12/112.49 congruence. % 112.12/112.49 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H17f. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H16d. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 112.12/112.49 congruence. % 112.12/112.49 apply (zenon_L243_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.49 apply zenon_H16a. apply refl_equal. % 112.12/112.49 apply zenon_H16a. apply refl_equal. % 112.12/112.49 apply zenon_H62. apply refl_equal. % 112.12/112.49 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H114. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H1c5. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 112.12/112.49 congruence. % 112.12/112.49 elim (classic ((high) = (high))); [ zenon_intro zenon_H180 | zenon_intro zenon_H113 ]. % 112.12/112.49 cut (((high) = (high)) = ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H2b. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H180. % 112.12/112.49 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113]. % 112.12/112.49 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 112.12/112.49 congruence. % 112.12/112.49 exact (zenon_H94 zenon_H281). % 112.12/112.49 apply zenon_H113. apply refl_equal. % 112.12/112.49 apply zenon_H113. apply refl_equal. % 112.12/112.49 apply zenon_H62. apply refl_equal. % 112.12/112.49 apply (zenon_L266_ zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.49 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = ((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H94. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H61. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 112.12/112.49 congruence. % 112.12/112.49 exact (zenon_H2b zenon_H2c). % 112.12/112.49 apply zenon_H62. apply refl_equal. % 112.12/112.49 apply zenon_H62. apply refl_equal. % 112.12/112.49 exact (zenon_H2e zenon_H29). % 112.12/112.49 apply (zenon_L249_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 112.12/112.49 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ]. % 112.12/112.49 apply (zenon_L264_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.49 apply zenon_H2e. zenon_intro zenon_H36. % 112.12/112.49 apply (zenon_L155_ zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.49 apply (zenon_L146_ zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.49 apply zenon_H187. apply sym_equal. exact zenon_H188. % 112.12/112.49 (* end of lemma zenon_L267_ *) % 112.12/112.49 assert (zenon_L268_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (greater (tau) (sigma)) -> (~((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> False). % 112.12/112.49 do 4 intro. intros zenon_H34 zenon_H1f zenon_H1a zenon_H148 zenon_H35 zenon_H292 zenon_Hec zenon_H26e zenon_H17c zenon_H38 zenon_H187. % 112.12/112.49 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3. % 112.12/112.49 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0. % 112.12/112.49 apply (zenon_L267_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.49 (* end of lemma zenon_L268_ *) % 112.12/112.49 assert (zenon_L269_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (greater (tau) (sigma)) -> False). % 112.12/112.49 do 4 intro. intros zenon_H34 zenon_Had zenon_H1f zenon_H1a zenon_H148 zenon_H35 zenon_H292 zenon_Hec zenon_H26e zenon_H17c zenon_H38. % 112.12/112.49 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H242 | zenon_intro zenon_H187 ]. % 112.12/112.49 cut ((greater (low) (very_low)) = (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_Had. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact assumption_18c. % 112.12/112.49 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H187]. % 112.12/112.49 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 112.12/112.49 congruence. % 112.12/112.49 apply zenon_H6a. apply refl_equal. % 112.12/112.49 exact (zenon_H187 zenon_H242). % 112.12/112.49 apply (zenon_L268_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.49 (* end of lemma zenon_L269_ *) % 112.12/112.49 assert (zenon_L270_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (greater (tau) (sigma)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (organization zenon_TX_y) -> False). % 112.12/112.49 do 4 intro. intros zenon_H34 zenon_H193 zenon_H38 zenon_H17c zenon_H26e zenon_Hec zenon_H292 zenon_H35 zenon_H148 zenon_H1a zenon_H1f. % 112.12/112.49 elim (classic (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_Hac | zenon_intro zenon_Had ]. % 112.12/112.49 generalize (zenon_H34 (mod1)). zenon_intro zenon_Ha7. % 112.12/112.49 generalize (zenon_Ha7 (low)). zenon_intro zenon_Ha8. % 112.12/112.49 generalize (zenon_Ha8 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H243. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H243); [ zenon_intro zenon_H7f | zenon_intro zenon_H244 ]. % 112.12/112.49 exact (zenon_H7f assumption_18b). % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H244); [ zenon_intro zenon_Had | zenon_intro zenon_H241 ]. % 112.12/112.49 exact (zenon_Had zenon_Hac). % 112.12/112.49 exact (zenon_H193 zenon_H241). % 112.12/112.49 apply (zenon_L269_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.49 (* end of lemma zenon_L270_ *) % 112.12/112.49 assert (zenon_L271_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TT1_bg : zenon_U) (zenon_TX_y : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (organization zenon_TX_y) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (greater (tau) (sigma)) -> False). % 112.12/112.49 do 4 intro. intros zenon_H34 zenon_H1c4 zenon_H1f zenon_H1a zenon_H148 zenon_H35 zenon_H292 zenon_Hec zenon_H26e zenon_H17c zenon_H38. % 112.12/112.49 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H241 | zenon_intro zenon_H193 ]. % 112.12/112.49 generalize (zenon_H34 (mod2)). zenon_intro zenon_H16e. % 112.12/112.49 generalize (zenon_H16e (mod1)). zenon_intro zenon_H16f. % 112.12/112.49 generalize (zenon_H16f (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H28e. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H28e); [ zenon_intro zenon_H69 | zenon_intro zenon_H28f ]. % 112.12/112.49 exact (zenon_H69 assumption_19). % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H28f); [ zenon_intro zenon_H193 | zenon_intro zenon_H1c3 ]. % 112.12/112.49 exact (zenon_H193 zenon_H241). % 112.12/112.49 exact (zenon_H1c4 zenon_H1c3). % 112.12/112.49 apply (zenon_L270_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.49 (* end of lemma zenon_L271_ *) % 112.12/112.49 assert (zenon_L272_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (mod2)) -> False). % 112.12/112.49 do 4 intro. intros zenon_H1a zenon_H148 zenon_H35 zenon_H292 zenon_Hec zenon_H1f zenon_H17c zenon_H38 zenon_H26e zenon_H34 zenon_H19e. % 112.12/112.49 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H1a1 ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1a5 ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H17e | zenon_intro zenon_H117 ]. % 112.12/112.49 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.12/112.49 generalize (zenon_H18f (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H23d. % 112.12/112.49 generalize (zenon_H23d (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H23e. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H23f ]. % 112.12/112.49 exact (zenon_H1a5 zenon_H1a4). % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H23f); [ zenon_intro zenon_H117 | zenon_intro zenon_H240 ]. % 112.12/112.49 exact (zenon_H117 zenon_H17e). % 112.12/112.49 exact (zenon_H17c zenon_H240). % 112.12/112.49 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1c4 ]. % 112.12/112.49 cut ((greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H117. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H1c3. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.49 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 112.12/112.49 congruence. % 112.12/112.49 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H1a1. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H11a. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 112.12/112.49 congruence. % 112.12/112.49 exact (zenon_H1a2 zenon_H19e). % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply zenon_H62. apply refl_equal. % 112.12/112.49 apply (zenon_L271_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.49 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H1a5. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H179. % 112.12/112.49 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.49 congruence. % 112.12/112.49 apply zenon_H16a. apply refl_equal. % 112.12/112.49 exact (zenon_H1a1 zenon_H1a3). % 112.12/112.49 apply (zenon_L253_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.49 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H1a1. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H11a. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 112.12/112.49 congruence. % 112.12/112.49 exact (zenon_H1a2 zenon_H19e). % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 (* end of lemma zenon_L272_ *) % 112.12/112.49 assert (zenon_L273_ : forall (zenon_TT1_bg : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (((is_aligned zenon_TX_y zenon_E)/\(~(positional_advantage zenon_TX_y zenon_E)))->((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))) -> (~(positional_advantage zenon_TX_y zenon_E)) -> (((~(is_aligned zenon_TX_y zenon_E))/\(~(positional_advantage zenon_TX_y zenon_E)))->((hazard_of_mortality zenon_TX_y zenon_E) = (high))) -> (forall T : zenon_U, (((organization zenon_TX_y)/\((age zenon_TX_y T) = (zero)))->(is_aligned zenon_TX_y T))) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))) -> (greater (tau) (sigma)) -> ((age zenon_TX_y zenon_TT1_bg) = (sigma)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> False). % 112.12/112.49 do 4 intro. intros zenon_H234 zenon_H182 zenon_H181 zenon_Hf3 zenon_H1a zenon_H148 zenon_H35 zenon_H292 zenon_Hec zenon_H1f zenon_H17c zenon_H38 zenon_H26e zenon_H34. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H234); [ zenon_intro zenon_H237 | zenon_intro zenon_H19e ]. % 112.12/112.49 apply (zenon_notand_s _ _ zenon_H237); [ zenon_intro zenon_H183 | zenon_intro zenon_H185 ]. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H181); [ zenon_intro zenon_H184 | zenon_intro zenon_H116 ]. % 112.12/112.49 apply (zenon_notand_s _ _ zenon_H184); [ zenon_intro zenon_H186 | zenon_intro zenon_H185 ]. % 112.12/112.49 exact (zenon_H186 zenon_H183). % 112.12/112.49 exact (zenon_H185 zenon_H182). % 112.12/112.49 apply (zenon_L261_ zenon_TT2_la zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.49 exact (zenon_H185 zenon_H182). % 112.12/112.49 apply (zenon_L272_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.49 (* end of lemma zenon_L273_ *) % 112.12/112.49 assert (zenon_L274_ : forall (zenon_TT2_la : zenon_U) (zenon_TT0_hz : zenon_U) (zenon_TX_y : zenon_U), (organization zenon_TX_y) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (very_low))) -> False). % 112.12/112.49 do 3 intro. intros zenon_H1f zenon_Hec zenon_H292 zenon_H35 zenon_H148 zenon_H1a zenon_H34 zenon_H294. % 112.12/112.49 elim (classic ((~((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (low)))/\(~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))))); [ zenon_intro zenon_H295 | zenon_intro zenon_H296 ]. % 112.12/112.49 apply (zenon_and_s _ _ zenon_H295). zenon_intro zenon_H1a8. zenon_intro zenon_H1a9. % 112.12/112.49 apply (zenon_L255_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.49 cut ((greater (low) (very_low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (very_low))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H294. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact assumption_18c. % 112.12/112.49 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 112.12/112.49 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H155]. % 112.12/112.49 congruence. % 112.12/112.49 apply (zenon_notand_s _ _ zenon_H296); [ zenon_intro zenon_H298 | zenon_intro zenon_H297 ]. % 112.12/112.49 apply zenon_H298. zenon_intro zenon_H15b. % 112.12/112.49 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H16d | zenon_intro zenon_H16a ]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = ((low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H155. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H16d. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1a8]. % 112.12/112.49 congruence. % 112.12/112.49 exact (zenon_H1a8 zenon_H15b). % 112.12/112.49 apply zenon_H16a. apply refl_equal. % 112.12/112.49 apply zenon_H16a. apply refl_equal. % 112.12/112.49 apply zenon_H297. zenon_intro zenon_H1b1. % 112.12/112.49 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.12/112.49 generalize (zenon_H18f (low)). zenon_intro zenon_H299. % 112.12/112.49 generalize (zenon_H299 (very_low)). zenon_intro zenon_H29a. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H29a); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H29b ]. % 112.12/112.49 exact (zenon_H1a9 zenon_H1b1). % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H29b); [ zenon_intro zenon_Hff | zenon_intro zenon_H29c ]. % 112.12/112.49 exact (zenon_Hff assumption_18c). % 112.12/112.49 exact (zenon_H294 zenon_H29c). % 112.12/112.49 apply zenon_Hf5. apply refl_equal. % 112.12/112.49 (* end of lemma zenon_L274_ *) % 112.12/112.49 assert (zenon_L275_ : forall (zenon_TT0_hz : zenon_U) (zenon_TT2_la : zenon_U) (zenon_TX_y : zenon_U), (~(forall T : zenon_U, ((organization zenon_TX_y)/\(((smaller_or_equal (age zenon_TX_y T) (eta))->(has_immunity zenon_TX_y T))/\((greater (age zenon_TX_y T) (eta))->(~(has_immunity zenon_TX_y T))))))) -> (greater (age zenon_TX_y zenon_TT2_la) (sigma)) -> (forall T : zenon_U, (((smaller_or_equal (age zenon_TX_y T) (tau))->(~(positional_advantage zenon_TX_y T)))/\((greater (age zenon_TX_y T) (tau))->(positional_advantage zenon_TX_y T)))) -> ((age zenon_TX_y zenon_TT2_la) = (tau)) -> ((age zenon_TX_y zenon_TT0_hz) = (zero)) -> (organization zenon_TX_y) -> (~(greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_y zenon_E) = (very_low)) -> False). % 112.12/112.49 do 3 intro. intros zenon_H1a zenon_H148 zenon_H35 zenon_H292 zenon_Hec zenon_H1f zenon_H1a5 zenon_H34 zenon_H1e0. % 112.12/112.49 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e2 ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (very_low))); [ zenon_intro zenon_H29c | zenon_intro zenon_H294 ]. % 112.12/112.49 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (very_low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H1a5. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H29c. % 112.12/112.49 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1e2]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.49 congruence. % 112.12/112.49 apply zenon_H16a. apply refl_equal. % 112.12/112.49 exact (zenon_H1e2 zenon_H1e1). % 112.12/112.49 apply (zenon_L274_ zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.49 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H1e2. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H11a. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 112.12/112.49 congruence. % 112.12/112.49 exact (zenon_H1e5 zenon_H1e0). % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 (* end of lemma zenon_L275_ *) % 112.12/112.49 apply NNPP. intro zenon_G. % 112.12/112.49 elim (classic (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z))))))); [ zenon_intro zenon_H34 | zenon_intro zenon_H29d ]. % 112.12/112.49 apply (zenon_notallex_s (fun X : zenon_U => (forall T0 : zenon_U, (forall T1 : zenon_U, (forall T2 : zenon_U, (forall T3 : zenon_U, (((organization X)/\((robust_position X)/\((~(has_endowment X))/\(((age X T0) = (zero))/\((greater (sigma) (zero))/\((greater (tau) (zero))/\((smaller (sigma) (tau))/\((smaller_or_equal (age X T1) (sigma))/\((greater (age X T2) (sigma))/\((smaller_or_equal (age X T2) (tau))/\(greater (age X T3) (tau))))))))))))->((smaller (hazard_of_mortality X T3) (hazard_of_mortality X T1))/\((smaller (hazard_of_mortality X T1) (hazard_of_mortality X T2))/\((hazard_of_mortality X T1) = (hazard_of_mortality X T0)))))))))) zenon_G); [ zenon_intro zenon_H29e; idtac ]. % 112.12/112.49 elim zenon_H29e. zenon_intro zenon_TX_y. zenon_intro zenon_H29f. % 112.12/112.49 apply (zenon_notallex_s (fun T0 : zenon_U => (forall T1 : zenon_U, (forall T2 : zenon_U, (forall T3 : zenon_U, (((organization zenon_TX_y)/\((robust_position zenon_TX_y)/\((~(has_endowment zenon_TX_y))/\(((age zenon_TX_y T0) = (zero))/\((greater (sigma) (zero))/\((greater (tau) (zero))/\((smaller (sigma) (tau))/\((smaller_or_equal (age zenon_TX_y T1) (sigma))/\((greater (age zenon_TX_y T2) (sigma))/\((smaller_or_equal (age zenon_TX_y T2) (tau))/\(greater (age zenon_TX_y T3) (tau))))))))))))->((smaller (hazard_of_mortality zenon_TX_y T3) (hazard_of_mortality zenon_TX_y T1))/\((smaller (hazard_of_mortality zenon_TX_y T1) (hazard_of_mortality zenon_TX_y T2))/\((hazard_of_mortality zenon_TX_y T1) = (hazard_of_mortality zenon_TX_y T0))))))))) zenon_H29f); [ zenon_intro zenon_H2a0; idtac ]. % 112.12/112.49 elim zenon_H2a0. zenon_intro zenon_TT0_hz. zenon_intro zenon_H2a1. % 112.12/112.49 apply (zenon_notallex_s (fun T1 : zenon_U => (forall T2 : zenon_U, (forall T3 : zenon_U, (((organization zenon_TX_y)/\((robust_position zenon_TX_y)/\((~(has_endowment zenon_TX_y))/\(((age zenon_TX_y zenon_TT0_hz) = (zero))/\((greater (sigma) (zero))/\((greater (tau) (zero))/\((smaller (sigma) (tau))/\((smaller_or_equal (age zenon_TX_y T1) (sigma))/\((greater (age zenon_TX_y T2) (sigma))/\((smaller_or_equal (age zenon_TX_y T2) (tau))/\(greater (age zenon_TX_y T3) (tau))))))))))))->((smaller (hazard_of_mortality zenon_TX_y T3) (hazard_of_mortality zenon_TX_y T1))/\((smaller (hazard_of_mortality zenon_TX_y T1) (hazard_of_mortality zenon_TX_y T2))/\((hazard_of_mortality zenon_TX_y T1) = (hazard_of_mortality zenon_TX_y zenon_TT0_hz)))))))) zenon_H2a1); [ zenon_intro zenon_H2a2; idtac ]. % 112.12/112.49 elim zenon_H2a2. zenon_intro zenon_TT1_bg. zenon_intro zenon_H2a3. % 112.12/112.49 apply (zenon_notallex_s (fun T2 : zenon_U => (forall T3 : zenon_U, (((organization zenon_TX_y)/\((robust_position zenon_TX_y)/\((~(has_endowment zenon_TX_y))/\(((age zenon_TX_y zenon_TT0_hz) = (zero))/\((greater (sigma) (zero))/\((greater (tau) (zero))/\((smaller (sigma) (tau))/\((smaller_or_equal (age zenon_TX_y zenon_TT1_bg) (sigma))/\((greater (age zenon_TX_y T2) (sigma))/\((smaller_or_equal (age zenon_TX_y T2) (tau))/\(greater (age zenon_TX_y T3) (tau))))))))))))->((smaller (hazard_of_mortality zenon_TX_y T3) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))/\((smaller (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y T2))/\((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT0_hz))))))) zenon_H2a3); [ zenon_intro zenon_H2a4; idtac ]. % 112.12/112.49 elim zenon_H2a4. zenon_intro zenon_TT2_la. zenon_intro zenon_H2a5. % 112.12/112.49 apply (zenon_notallex_s (fun T3 : zenon_U => (((organization zenon_TX_y)/\((robust_position zenon_TX_y)/\((~(has_endowment zenon_TX_y))/\(((age zenon_TX_y zenon_TT0_hz) = (zero))/\((greater (sigma) (zero))/\((greater (tau) (zero))/\((smaller (sigma) (tau))/\((smaller_or_equal (age zenon_TX_y zenon_TT1_bg) (sigma))/\((greater (age zenon_TX_y zenon_TT2_la) (sigma))/\((smaller_or_equal (age zenon_TX_y zenon_TT2_la) (tau))/\(greater (age zenon_TX_y T3) (tau))))))))))))->((smaller (hazard_of_mortality zenon_TX_y T3) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))/\((smaller (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT2_la))/\((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT0_hz)))))) zenon_H2a5); [ zenon_intro zenon_H2a6; idtac ]. % 112.12/112.49 elim zenon_H2a6. zenon_intro zenon_TT3_x. zenon_intro zenon_H2a7. % 112.12/112.49 apply (zenon_notimply_s _ _ zenon_H2a7). zenon_intro zenon_H2a9. zenon_intro zenon_H2a8. % 112.12/112.49 apply (zenon_and_s _ _ zenon_H2a9). zenon_intro zenon_H1f. zenon_intro zenon_H2aa. % 112.12/112.49 apply (zenon_and_s _ _ zenon_H2aa). zenon_intro zenon_H2ac. zenon_intro zenon_H2ab. % 112.12/112.49 apply (zenon_and_s _ _ zenon_H2ab). zenon_intro zenon_H1d. zenon_intro zenon_H2ad. % 112.12/112.49 apply (zenon_and_s _ _ zenon_H2ad). zenon_intro zenon_Hec. zenon_intro zenon_H2ae. % 112.12/112.49 apply (zenon_and_s _ _ zenon_H2ae). zenon_intro zenon_H2b0. zenon_intro zenon_H2af. % 112.12/112.49 apply (zenon_and_s _ _ zenon_H2af). zenon_intro zenon_H24a. zenon_intro zenon_H2b1. % 112.12/112.49 apply (zenon_and_s _ _ zenon_H2b1). zenon_intro zenon_H2b3. zenon_intro zenon_H2b2. % 112.12/112.49 apply (zenon_and_s _ _ zenon_H2b2). zenon_intro zenon_H2b5. zenon_intro zenon_H2b4. % 112.12/112.49 apply (zenon_and_s _ _ zenon_H2b4). zenon_intro zenon_H148. zenon_intro zenon_H2b6. % 112.12/112.49 apply (zenon_and_s _ _ zenon_H2b6). zenon_intro zenon_H12c. zenon_intro zenon_H100. % 112.12/112.49 generalize (definition_4 zenon_TX_y). zenon_intro zenon_H2b7. % 112.12/112.49 apply (zenon_equiv_s _ _ zenon_H2b7); [ zenon_intro zenon_H2b9; zenon_intro zenon_H2b8 | zenon_intro zenon_H2ac; zenon_intro zenon_H35 ]. % 112.12/112.49 exact (zenon_H2b9 zenon_H2ac). % 112.12/112.49 generalize (definition_1 zenon_TX_y). zenon_intro zenon_H1b. % 112.12/112.49 apply (zenon_equiv_s _ _ zenon_H1b); [ zenon_intro zenon_H1d; zenon_intro zenon_H1a | zenon_intro zenon_H19; zenon_intro zenon_H1c ]. % 112.12/112.49 generalize (definition_smaller (sigma)). zenon_intro zenon_H2ba. % 112.12/112.49 generalize (zenon_H2ba (tau)). zenon_intro zenon_H2bb. % 112.12/112.49 apply (zenon_equiv_s _ _ zenon_H2bb); [ zenon_intro zenon_H2bc; zenon_intro zenon_H4b | zenon_intro zenon_H2b3; zenon_intro zenon_H38 ]. % 112.12/112.49 exact (zenon_H2bc zenon_H2b3). % 112.12/112.49 generalize (definition_smaller_or_equal (age zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H3d. % 112.12/112.49 generalize (zenon_H3d (sigma)). zenon_intro zenon_H2bd. % 112.12/112.49 apply (zenon_equiv_s _ _ zenon_H2bd); [ zenon_intro zenon_H2c0; zenon_intro zenon_H2bf | zenon_intro zenon_H2b5; zenon_intro zenon_H2be ]. % 112.12/112.49 exact (zenon_H2c0 zenon_H2b5). % 112.12/112.49 generalize (definition_smaller_or_equal (age zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H129. % 112.12/112.49 generalize (zenon_H129 (tau)). zenon_intro zenon_H12a. % 112.12/112.49 apply (zenon_equiv_s _ _ zenon_H12a); [ zenon_intro zenon_H128; zenon_intro zenon_H12d | zenon_intro zenon_H12c; zenon_intro zenon_H12b ]. % 112.12/112.49 exact (zenon_H128 zenon_H12c). % 112.12/112.49 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_H132 | zenon_intro zenon_H292 ]. % 112.12/112.49 generalize (definition_smaller (age zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H130. % 112.12/112.49 generalize (zenon_H130 (tau)). zenon_intro zenon_H131. % 112.12/112.49 apply (zenon_equiv_s _ _ zenon_H131); [ zenon_intro zenon_H12f; zenon_intro zenon_H133 | zenon_intro zenon_H132; zenon_intro zenon_H123 ]. % 112.12/112.49 exact (zenon_H12f zenon_H132). % 112.12/112.49 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_H2c1 | zenon_intro zenon_H26e ]. % 112.12/112.49 generalize (definition_smaller (age zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H44. % 112.12/112.49 generalize (zenon_H44 (sigma)). zenon_intro zenon_H2c2. % 112.12/112.49 apply (zenon_equiv_s _ _ zenon_H2c2); [ zenon_intro zenon_H2c3; zenon_intro zenon_H58 | zenon_intro zenon_H2c1; zenon_intro zenon_H37 ]. % 112.12/112.49 exact (zenon_H2c3 zenon_H2c1). % 112.12/112.49 apply (zenon_notand_s _ _ zenon_H2a8); [ zenon_intro zenon_H101 | zenon_intro zenon_H2c4 ]. % 112.12/112.49 apply (zenon_L40_ zenon_TT1_bg zenon_TT0_hz zenon_TT3_x zenon_TX_y); trivial. % 112.12/112.49 apply (zenon_notand_s _ _ zenon_H2c4); [ zenon_intro zenon_H2c5 | zenon_intro zenon_H25e ]. % 112.12/112.49 generalize (definition_smaller (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H2c6. % 112.12/112.49 generalize (zenon_H2c6 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H2c7. % 112.12/112.49 apply (zenon_equiv_s _ _ zenon_H2c7); [ zenon_intro zenon_H2c5; zenon_intro zenon_H17c | zenon_intro zenon_H2c8; zenon_intro zenon_H240 ]. % 112.12/112.49 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3. % 112.12/112.49 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0. % 112.12/112.49 generalize (zenon_H0 zenon_E). zenon_intro zenon_H239. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H239); [ zenon_intro zenon_H27 | zenon_intro zenon_H23a ]. % 112.12/112.49 exact (zenon_H27 zenon_H1f). % 112.12/112.49 apply (zenon_and_s _ _ zenon_H23a). zenon_intro zenon_H23b. zenon_intro zenon_H238. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H23b); [ zenon_intro zenon_H112 | zenon_intro zenon_H1e0 ]. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H238); [ zenon_intro zenon_H111 | zenon_intro zenon_H22f ]. % 112.12/112.49 exact (zenon_H111 zenon_H112). % 112.12/112.49 apply (zenon_and_s _ _ zenon_H22f). zenon_intro zenon_H231. zenon_intro zenon_H230. % 112.12/112.49 apply (zenon_and_s _ _ zenon_H230). zenon_intro zenon_H233. zenon_intro zenon_H232. % 112.12/112.49 apply (zenon_and_s _ _ zenon_H232). zenon_intro zenon_H234. zenon_intro zenon_H181. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H231); [ zenon_intro zenon_H235 | zenon_intro zenon_H1b8 ]. % 112.12/112.49 apply (zenon_notand_s _ _ zenon_H235); [ zenon_intro zenon_H183 | zenon_intro zenon_H182 ]. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H233); [ zenon_intro zenon_H236 | zenon_intro zenon_H21a ]. % 112.12/112.49 apply (zenon_notand_s _ _ zenon_H236); [ zenon_intro zenon_H186 | zenon_intro zenon_H182 ]. % 112.12/112.49 exact (zenon_H186 zenon_H183). % 112.12/112.49 apply (zenon_L66_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.49 elim (classic ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H23c | zenon_intro zenon_H21f ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))); [ zenon_intro zenon_H19c | zenon_intro zenon_H194 ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1a5 ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H17e | zenon_intro zenon_H117 ]. % 112.12/112.49 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.12/112.49 generalize (zenon_H18f (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H23d. % 112.12/112.49 generalize (zenon_H23d (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H23e. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H23f ]. % 112.12/112.49 exact (zenon_H1a5 zenon_H1a4). % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H23f); [ zenon_intro zenon_H117 | zenon_intro zenon_H240 ]. % 112.12/112.49 exact (zenon_H117 zenon_H17e). % 112.12/112.49 exact (zenon_H17c zenon_H240). % 112.12/112.49 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H241 | zenon_intro zenon_H193 ]. % 112.12/112.49 cut ((greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H117. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H241. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.49 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 112.12/112.49 congruence. % 112.12/112.49 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H21f. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H11a. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 112.12/112.49 congruence. % 112.12/112.49 exact (zenon_H21e zenon_H21a). % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply zenon_H62. apply refl_equal. % 112.12/112.49 apply (zenon_L135_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.49 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H1a5. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H19c. % 112.12/112.49 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.49 congruence. % 112.12/112.49 apply zenon_H16a. apply refl_equal. % 112.12/112.49 exact (zenon_H21f zenon_H23c). % 112.12/112.49 apply (zenon_L80_ zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.49 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H21f. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H11a. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 112.12/112.49 congruence. % 112.12/112.49 exact (zenon_H21e zenon_H21a). % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H234); [ zenon_intro zenon_H237 | zenon_intro zenon_H19e ]. % 112.12/112.49 apply (zenon_notand_s _ _ zenon_H237); [ zenon_intro zenon_H183 | zenon_intro zenon_H185 ]. % 112.12/112.49 apply (zenon_L66_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.49 exact (zenon_H185 zenon_H182). % 112.12/112.49 apply (zenon_L85_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.49 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1ba ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1a9 ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1a5 ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H17e | zenon_intro zenon_H117 ]. % 112.12/112.49 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.12/112.49 generalize (zenon_H18f (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H23d. % 112.12/112.49 generalize (zenon_H23d (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H23e. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H23f ]. % 112.12/112.49 exact (zenon_H1a5 zenon_H1a4). % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H23f); [ zenon_intro zenon_H117 | zenon_intro zenon_H240 ]. % 112.12/112.49 exact (zenon_H117 zenon_H17e). % 112.12/112.49 exact (zenon_H17c zenon_H240). % 112.12/112.49 apply (zenon_L136_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.49 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H1a5. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H1b1. % 112.12/112.49 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.49 congruence. % 112.12/112.49 apply zenon_H16a. apply refl_equal. % 112.12/112.49 exact (zenon_H1ba zenon_H1b9). % 112.12/112.49 apply (zenon_L103_ zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.49 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((low) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H1ba. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H11a. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 112.12/112.49 congruence. % 112.12/112.49 exact (zenon_H1bb zenon_H1b8). % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply (zenon_L131_ zenon_TX_y); trivial. % 112.12/112.49 exact (zenon_H2c5 zenon_H2c8). % 112.12/112.49 apply (zenon_L149_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.49 apply (zenon_notand_s _ _ zenon_H2a8); [ zenon_intro zenon_H101 | zenon_intro zenon_H2c4 ]. % 112.12/112.49 apply (zenon_L195_ zenon_TT3_x zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.49 apply (zenon_notand_s _ _ zenon_H2c4); [ zenon_intro zenon_H2c5 | zenon_intro zenon_H25e ]. % 112.12/112.49 generalize (definition_smaller (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H2c6. % 112.12/112.49 generalize (zenon_H2c6 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H2c7. % 112.12/112.49 apply (zenon_equiv_s _ _ zenon_H2c7); [ zenon_intro zenon_H2c5; zenon_intro zenon_H17c | zenon_intro zenon_H2c8; zenon_intro zenon_H240 ]. % 112.12/112.49 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3. % 112.12/112.49 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0. % 112.12/112.49 generalize (zenon_H0 zenon_E). zenon_intro zenon_H239. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H239); [ zenon_intro zenon_H27 | zenon_intro zenon_H23a ]. % 112.12/112.49 exact (zenon_H27 zenon_H1f). % 112.12/112.49 apply (zenon_and_s _ _ zenon_H23a). zenon_intro zenon_H23b. zenon_intro zenon_H238. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H23b); [ zenon_intro zenon_H112 | zenon_intro zenon_H1e0 ]. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H238); [ zenon_intro zenon_H111 | zenon_intro zenon_H22f ]. % 112.12/112.49 exact (zenon_H111 zenon_H112). % 112.12/112.49 apply (zenon_and_s _ _ zenon_H22f). zenon_intro zenon_H231. zenon_intro zenon_H230. % 112.12/112.49 apply (zenon_and_s _ _ zenon_H230). zenon_intro zenon_H233. zenon_intro zenon_H232. % 112.12/112.49 apply (zenon_and_s _ _ zenon_H232). zenon_intro zenon_H234. zenon_intro zenon_H181. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H231); [ zenon_intro zenon_H235 | zenon_intro zenon_H1b8 ]. % 112.12/112.49 apply (zenon_notand_s _ _ zenon_H235); [ zenon_intro zenon_H183 | zenon_intro zenon_H182 ]. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H233); [ zenon_intro zenon_H236 | zenon_intro zenon_H21a ]. % 112.12/112.49 apply (zenon_notand_s _ _ zenon_H236); [ zenon_intro zenon_H186 | zenon_intro zenon_H182 ]. % 112.12/112.49 exact (zenon_H186 zenon_H183). % 112.12/112.49 apply (zenon_L216_ zenon_TT0_hz zenon_TT1_bg zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.49 elim (classic ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H23c | zenon_intro zenon_H21f ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))); [ zenon_intro zenon_H19c | zenon_intro zenon_H194 ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1a5 ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H17e | zenon_intro zenon_H117 ]. % 112.12/112.49 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.12/112.49 generalize (zenon_H18f (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H23d. % 112.12/112.49 generalize (zenon_H23d (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H23e. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H23f ]. % 112.12/112.49 exact (zenon_H1a5 zenon_H1a4). % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H23f); [ zenon_intro zenon_H117 | zenon_intro zenon_H240 ]. % 112.12/112.49 exact (zenon_H117 zenon_H17e). % 112.12/112.49 exact (zenon_H17c zenon_H240). % 112.12/112.49 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H241 | zenon_intro zenon_H193 ]. % 112.12/112.49 cut ((greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H117. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H241. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.49 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 112.12/112.49 congruence. % 112.12/112.49 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H21f. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H11a. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 112.12/112.49 congruence. % 112.12/112.49 exact (zenon_H21e zenon_H21a). % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply zenon_H62. apply refl_equal. % 112.12/112.49 apply (zenon_L232_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.49 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H1a5. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H19c. % 112.12/112.49 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.49 congruence. % 112.12/112.49 apply zenon_H16a. apply refl_equal. % 112.12/112.49 exact (zenon_H21f zenon_H23c). % 112.12/112.49 apply (zenon_L227_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.49 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H21f. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H11a. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 112.12/112.49 congruence. % 112.12/112.49 exact (zenon_H21e zenon_H21a). % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply (zenon_L216_ zenon_TT0_hz zenon_TT1_bg zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.49 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1ba ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1a9 ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1a5 ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H17e | zenon_intro zenon_H117 ]. % 112.12/112.49 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.12/112.49 generalize (zenon_H18f (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H23d. % 112.12/112.49 generalize (zenon_H23d (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H23e. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H23f ]. % 112.12/112.49 exact (zenon_H1a5 zenon_H1a4). % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H23f); [ zenon_intro zenon_H117 | zenon_intro zenon_H240 ]. % 112.12/112.49 exact (zenon_H117 zenon_H17e). % 112.12/112.49 exact (zenon_H17c zenon_H240). % 112.12/112.49 elim (classic (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_Hac | zenon_intro zenon_Had ]. % 112.12/112.49 cut ((greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H117. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_Hac. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.49 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba]. % 112.12/112.49 congruence. % 112.12/112.49 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((low) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H1ba. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H11a. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 112.12/112.49 congruence. % 112.12/112.49 exact (zenon_H1bb zenon_H1b8). % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply zenon_H62. apply refl_equal. % 112.12/112.49 apply (zenon_L231_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.49 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H1a5. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H1b1. % 112.12/112.49 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.49 congruence. % 112.12/112.49 apply zenon_H16a. apply refl_equal. % 112.12/112.49 exact (zenon_H1ba zenon_H1b9). % 112.12/112.49 apply (zenon_L103_ zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.49 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((low) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H1ba. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H11a. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 112.12/112.49 congruence. % 112.12/112.49 exact (zenon_H1bb zenon_H1b8). % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply (zenon_L131_ zenon_TX_y); trivial. % 112.12/112.49 exact (zenon_H2c5 zenon_H2c8). % 112.12/112.49 apply (zenon_L236_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.49 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_H2c1 | zenon_intro zenon_H26e ]. % 112.12/112.49 generalize (definition_smaller (age zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H44. % 112.12/112.49 generalize (zenon_H44 (sigma)). zenon_intro zenon_H2c2. % 112.12/112.49 apply (zenon_equiv_s _ _ zenon_H2c2); [ zenon_intro zenon_H2c3; zenon_intro zenon_H58 | zenon_intro zenon_H2c1; zenon_intro zenon_H37 ]. % 112.12/112.49 exact (zenon_H2c3 zenon_H2c1). % 112.12/112.49 apply (zenon_notand_s _ _ zenon_H2a8); [ zenon_intro zenon_H101 | zenon_intro zenon_H2c4 ]. % 112.12/112.49 apply (zenon_L40_ zenon_TT1_bg zenon_TT0_hz zenon_TT3_x zenon_TX_y); trivial. % 112.12/112.49 apply (zenon_notand_s _ _ zenon_H2c4); [ zenon_intro zenon_H2c5 | zenon_intro zenon_H25e ]. % 112.12/112.49 generalize (definition_smaller (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H2c6. % 112.12/112.49 generalize (zenon_H2c6 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H2c7. % 112.12/112.49 apply (zenon_equiv_s _ _ zenon_H2c7); [ zenon_intro zenon_H2c5; zenon_intro zenon_H17c | zenon_intro zenon_H2c8; zenon_intro zenon_H240 ]. % 112.12/112.49 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3. % 112.12/112.49 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0. % 112.12/112.49 generalize (zenon_H0 zenon_E). zenon_intro zenon_H239. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H239); [ zenon_intro zenon_H27 | zenon_intro zenon_H23a ]. % 112.12/112.49 exact (zenon_H27 zenon_H1f). % 112.12/112.49 apply (zenon_and_s _ _ zenon_H23a). zenon_intro zenon_H23b. zenon_intro zenon_H238. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H23b); [ zenon_intro zenon_H112 | zenon_intro zenon_H1e0 ]. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H238); [ zenon_intro zenon_H111 | zenon_intro zenon_H22f ]. % 112.12/112.49 exact (zenon_H111 zenon_H112). % 112.12/112.49 apply (zenon_and_s _ _ zenon_H22f). zenon_intro zenon_H231. zenon_intro zenon_H230. % 112.12/112.49 apply (zenon_and_s _ _ zenon_H230). zenon_intro zenon_H233. zenon_intro zenon_H232. % 112.12/112.49 apply (zenon_and_s _ _ zenon_H232). zenon_intro zenon_H234. zenon_intro zenon_H181. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H231); [ zenon_intro zenon_H235 | zenon_intro zenon_H1b8 ]. % 112.12/112.49 apply (zenon_notand_s _ _ zenon_H235); [ zenon_intro zenon_H183 | zenon_intro zenon_H182 ]. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H233); [ zenon_intro zenon_H236 | zenon_intro zenon_H21a ]. % 112.12/112.49 apply (zenon_notand_s _ _ zenon_H236); [ zenon_intro zenon_H186 | zenon_intro zenon_H182 ]. % 112.12/112.49 exact (zenon_H186 zenon_H183). % 112.12/112.49 apply (zenon_L247_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.49 elim (classic ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H23c | zenon_intro zenon_H21f ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))); [ zenon_intro zenon_H19c | zenon_intro zenon_H194 ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1a5 ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H17e | zenon_intro zenon_H117 ]. % 112.12/112.49 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.12/112.49 generalize (zenon_H18f (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H23d. % 112.12/112.49 generalize (zenon_H23d (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H23e. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H23f ]. % 112.12/112.49 exact (zenon_H1a5 zenon_H1a4). % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H23f); [ zenon_intro zenon_H117 | zenon_intro zenon_H240 ]. % 112.12/112.49 exact (zenon_H117 zenon_H17e). % 112.12/112.49 exact (zenon_H17c zenon_H240). % 112.12/112.49 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H241 | zenon_intro zenon_H193 ]. % 112.12/112.49 cut ((greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H117. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H241. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.49 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 112.12/112.49 congruence. % 112.12/112.49 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H21f. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H11a. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 112.12/112.49 congruence. % 112.12/112.49 exact (zenon_H21e zenon_H21a). % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply zenon_H62. apply refl_equal. % 112.12/112.49 apply (zenon_L259_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.49 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H1a5. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H19c. % 112.12/112.49 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.49 congruence. % 112.12/112.49 apply zenon_H16a. apply refl_equal. % 112.12/112.49 exact (zenon_H21f zenon_H23c). % 112.12/112.49 apply (zenon_L254_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.49 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H21f. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H11a. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 112.12/112.49 congruence. % 112.12/112.49 exact (zenon_H21e zenon_H21a). % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H234); [ zenon_intro zenon_H237 | zenon_intro zenon_H19e ]. % 112.12/112.49 apply (zenon_notand_s _ _ zenon_H237); [ zenon_intro zenon_H183 | zenon_intro zenon_H185 ]. % 112.12/112.49 apply (zenon_L247_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.49 exact (zenon_H185 zenon_H182). % 112.12/112.49 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H1a1 ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1a5 ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H17e | zenon_intro zenon_H117 ]. % 112.12/112.49 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.12/112.49 generalize (zenon_H18f (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H23d. % 112.12/112.49 generalize (zenon_H23d (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H23e. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H23f ]. % 112.12/112.49 exact (zenon_H1a5 zenon_H1a4). % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H23f); [ zenon_intro zenon_H117 | zenon_intro zenon_H240 ]. % 112.12/112.49 exact (zenon_H117 zenon_H17e). % 112.12/112.49 exact (zenon_H17c zenon_H240). % 112.12/112.49 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1c4 ]. % 112.12/112.49 cut ((greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H117. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H1c3. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.49 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 112.12/112.49 congruence. % 112.12/112.49 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H1a1. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H11a. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 112.12/112.49 congruence. % 112.12/112.49 exact (zenon_H1a2 zenon_H19e). % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply zenon_H62. apply refl_equal. % 112.12/112.49 apply (zenon_L260_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.49 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H1a5. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H179. % 112.12/112.49 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.49 congruence. % 112.12/112.49 apply zenon_H16a. apply refl_equal. % 112.12/112.49 exact (zenon_H1a1 zenon_H1a3). % 112.12/112.49 apply (zenon_L248_ zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.49 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H1a1. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H11a. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 112.12/112.49 congruence. % 112.12/112.49 exact (zenon_H1a2 zenon_H19e). % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1ba ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1a9 ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1a5 ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H17e | zenon_intro zenon_H117 ]. % 112.12/112.49 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.12/112.49 generalize (zenon_H18f (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H23d. % 112.12/112.49 generalize (zenon_H23d (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H23e. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H23f ]. % 112.12/112.49 exact (zenon_H1a5 zenon_H1a4). % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H23f); [ zenon_intro zenon_H117 | zenon_intro zenon_H240 ]. % 112.12/112.49 exact (zenon_H117 zenon_H17e). % 112.12/112.49 exact (zenon_H17c zenon_H240). % 112.12/112.49 elim (classic (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_Hac | zenon_intro zenon_Had ]. % 112.12/112.49 cut ((greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H117. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_Hac. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.49 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba]. % 112.12/112.49 congruence. % 112.12/112.49 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((low) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H1ba. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H11a. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 112.12/112.49 congruence. % 112.12/112.49 exact (zenon_H1bb zenon_H1b8). % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply zenon_H62. apply refl_equal. % 112.12/112.49 apply (zenon_L258_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.49 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H1a5. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H1b1. % 112.12/112.49 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.49 congruence. % 112.12/112.49 apply zenon_H16a. apply refl_equal. % 112.12/112.49 exact (zenon_H1ba zenon_H1b9). % 112.12/112.49 apply (zenon_L255_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.49 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((low) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H1ba. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H11a. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 112.12/112.49 congruence. % 112.12/112.49 exact (zenon_H1bb zenon_H1b8). % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply (zenon_L131_ zenon_TX_y); trivial. % 112.12/112.49 exact (zenon_H2c5 zenon_H2c8). % 112.12/112.49 apply (zenon_L149_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial. % 112.12/112.49 apply (zenon_notand_s _ _ zenon_H2a8); [ zenon_intro zenon_H101 | zenon_intro zenon_H2c4 ]. % 112.12/112.49 apply (zenon_L195_ zenon_TT3_x zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.49 apply (zenon_notand_s _ _ zenon_H2c4); [ zenon_intro zenon_H2c5 | zenon_intro zenon_H25e ]. % 112.12/112.49 generalize (definition_smaller (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H2c6. % 112.12/112.49 generalize (zenon_H2c6 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H2c7. % 112.12/112.49 apply (zenon_equiv_s _ _ zenon_H2c7); [ zenon_intro zenon_H2c5; zenon_intro zenon_H17c | zenon_intro zenon_H2c8; zenon_intro zenon_H240 ]. % 112.12/112.49 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3. % 112.12/112.49 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0. % 112.12/112.49 generalize (zenon_H0 zenon_E). zenon_intro zenon_H239. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H239); [ zenon_intro zenon_H27 | zenon_intro zenon_H23a ]. % 112.12/112.49 exact (zenon_H27 zenon_H1f). % 112.12/112.49 apply (zenon_and_s _ _ zenon_H23a). zenon_intro zenon_H23b. zenon_intro zenon_H238. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H23b); [ zenon_intro zenon_H112 | zenon_intro zenon_H1e0 ]. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H238); [ zenon_intro zenon_H111 | zenon_intro zenon_H22f ]. % 112.12/112.49 exact (zenon_H111 zenon_H112). % 112.12/112.49 apply (zenon_and_s _ _ zenon_H22f). zenon_intro zenon_H231. zenon_intro zenon_H230. % 112.12/112.49 apply (zenon_and_s _ _ zenon_H230). zenon_intro zenon_H233. zenon_intro zenon_H232. % 112.12/112.49 apply (zenon_and_s _ _ zenon_H232). zenon_intro zenon_H234. zenon_intro zenon_H181. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H231); [ zenon_intro zenon_H235 | zenon_intro zenon_H1b8 ]. % 112.12/112.49 apply (zenon_notand_s _ _ zenon_H235); [ zenon_intro zenon_H183 | zenon_intro zenon_H182 ]. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H233); [ zenon_intro zenon_H236 | zenon_intro zenon_H21a ]. % 112.12/112.49 apply (zenon_notand_s _ _ zenon_H236); [ zenon_intro zenon_H186 | zenon_intro zenon_H182 ]. % 112.12/112.49 exact (zenon_H186 zenon_H183). % 112.12/112.49 apply (zenon_L273_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.49 elim (classic ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H23c | zenon_intro zenon_H21f ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))); [ zenon_intro zenon_H19c | zenon_intro zenon_H194 ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1a5 ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H17e | zenon_intro zenon_H117 ]. % 112.12/112.49 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.12/112.49 generalize (zenon_H18f (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H23d. % 112.12/112.49 generalize (zenon_H23d (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H23e. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H23f ]. % 112.12/112.49 exact (zenon_H1a5 zenon_H1a4). % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H23f); [ zenon_intro zenon_H117 | zenon_intro zenon_H240 ]. % 112.12/112.49 exact (zenon_H117 zenon_H17e). % 112.12/112.49 exact (zenon_H17c zenon_H240). % 112.12/112.49 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H241 | zenon_intro zenon_H193 ]. % 112.12/112.49 cut ((greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H117. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H241. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.49 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 112.12/112.49 congruence. % 112.12/112.49 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H21f. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H11a. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 112.12/112.49 congruence. % 112.12/112.49 exact (zenon_H21e zenon_H21a). % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply zenon_H62. apply refl_equal. % 112.12/112.49 apply (zenon_L270_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.49 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H1a5. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H19c. % 112.12/112.49 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.49 congruence. % 112.12/112.49 apply zenon_H16a. apply refl_equal. % 112.12/112.49 exact (zenon_H21f zenon_H23c). % 112.12/112.49 apply (zenon_L254_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.49 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H21f. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H11a. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 112.12/112.49 congruence. % 112.12/112.49 exact (zenon_H21e zenon_H21a). % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply (zenon_L273_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.49 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1ba ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1a9 ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1a5 ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H17e | zenon_intro zenon_H117 ]. % 112.12/112.49 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f. % 112.12/112.49 generalize (zenon_H18f (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H23d. % 112.12/112.49 generalize (zenon_H23d (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H23e. % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H23f ]. % 112.12/112.49 exact (zenon_H1a5 zenon_H1a4). % 112.12/112.49 apply (zenon_imply_s _ _ zenon_H23f); [ zenon_intro zenon_H117 | zenon_intro zenon_H240 ]. % 112.12/112.49 exact (zenon_H117 zenon_H17e). % 112.12/112.49 exact (zenon_H17c zenon_H240). % 112.12/112.49 elim (classic (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_Hac | zenon_intro zenon_Had ]. % 112.12/112.49 cut ((greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H117. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_Hac. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 112.12/112.49 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba]. % 112.12/112.49 congruence. % 112.12/112.49 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((low) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H1ba. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H11a. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 112.12/112.49 congruence. % 112.12/112.49 exact (zenon_H1bb zenon_H1b8). % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply zenon_H62. apply refl_equal. % 112.12/112.49 apply (zenon_L269_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.49 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H1a5. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H1b1. % 112.12/112.49 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.49 congruence. % 112.12/112.49 apply zenon_H16a. apply refl_equal. % 112.12/112.49 exact (zenon_H1ba zenon_H1b9). % 112.12/112.49 apply (zenon_L255_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.49 elim (classic ((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H11a | zenon_intro zenon_H11b ]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E)) = ((low) = (hazard_of_mortality zenon_TX_y zenon_E))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H1ba. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H11a. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 112.12/112.49 congruence. % 112.12/112.49 exact (zenon_H1bb zenon_H1b8). % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 apply zenon_H11b. apply refl_equal. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1a5 ]. % 112.12/112.49 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (very_low))); [ zenon_intro zenon_H29c | zenon_intro zenon_H294 ]. % 112.12/112.49 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (very_low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H17c. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H29c. % 112.12/112.49 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H187]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.49 congruence. % 112.12/112.49 apply zenon_H16a. apply refl_equal. % 112.12/112.49 apply (zenon_L268_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.49 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (hazard_of_mortality zenon_TX_y zenon_E)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (very_low))). % 112.12/112.49 intro zenon_D_pnotp. % 112.12/112.49 apply zenon_H294. % 112.12/112.49 rewrite <- zenon_D_pnotp. % 112.12/112.49 exact zenon_H1a4. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 112.12/112.49 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 112.12/112.49 congruence. % 112.12/112.49 apply zenon_H16a. apply refl_equal. % 112.12/112.49 exact (zenon_H1e5 zenon_H1e0). % 112.12/112.49 apply (zenon_L275_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial. % 112.12/112.49 exact (zenon_H2c5 zenon_H2c8). % 112.12/112.49 apply (zenon_L236_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial. % 112.12/112.49 exact (zenon_H1d zenon_H19). % 112.12/112.49 apply zenon_H29d. zenon_intro zenon_Tx_bbl. apply NNPP. zenon_intro zenon_H2ca. % 112.12/112.49 apply zenon_H2ca. zenon_intro zenon_Ty_bbn. apply NNPP. zenon_intro zenon_H2cc. % 112.12/112.49 apply zenon_H2cc. zenon_intro zenon_Tz_bbp. apply NNPP. zenon_intro zenon_H2ce. % 112.12/112.49 apply (zenon_notimply_s _ _ zenon_H2ce). zenon_intro zenon_H2d0. zenon_intro zenon_H2cf. % 0.13/112.50 apply (zenon_notimply_s _ _ zenon_H2cf). zenon_intro zenon_H2d2. zenon_intro zenon_H2d1. % 0.13/112.50 generalize (meaning_postulate_greater_transitive zenon_Tx_bbl). zenon_intro zenon_H2d3. % 0.13/112.50 generalize (zenon_H2d3 zenon_Ty_bbn). zenon_intro zenon_H2d4. % 0.13/112.50 generalize (zenon_H2d4 zenon_Tz_bbp). zenon_intro zenon_H2d5. % 0.13/112.50 apply (zenon_imply_s _ _ zenon_H2d5); [ zenon_intro zenon_H2d7 | zenon_intro zenon_H2d6 ]. % 0.13/112.50 apply (zenon_notand_s _ _ zenon_H2d7); [ zenon_intro zenon_H2d9 | zenon_intro zenon_H2d8 ]. % 0.13/112.50 exact (zenon_H2d9 zenon_H2d0). % 0.13/112.50 exact (zenon_H2d8 zenon_H2d2). % 0.13/112.50 exact (zenon_H2d1 zenon_H2d6). % 0.13/112.50 Qed. % 0.13/112.50 % SZS output end Proof % 0.13/112.50 (* END-PROOF *) % 0.13/112.50 nodes searched: 2860654 % 0.13/112.50 max branch formulas: 5105 % 0.13/112.50 proof nodes created: 29947 % 0.13/112.50 formulas created: 910178 % 0.13/112.50 %------------------------------------------------------------------------------