TSTP Solution File: MGT063+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : MGT063+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 22:31:15 EDT 2022
% Result : Theorem 45.50s 45.65s
% Output : Proof 45.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : MGT063+1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.12 % Command : run_zenon %s %d
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 9 09:21:36 EDT 2022
% 0.13/0.33 % CPUTime :
% 45.50/45.65 (* PROOF-FOUND *)
% 45.50/45.65 % SZS status Theorem
% 45.50/45.65 (* BEGIN-PROOF *)
% 45.50/45.65 % SZS output start Proof
% 45.50/45.65 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)))))))))).
% 45.50/45.65 Proof.
% 45.50/45.65 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).
% 45.50/45.65 do 2 intro. intros zenon_H15 zenon_H16.
% 45.50/45.65 exact (zenon_H15 zenon_H16).
% 45.50/45.65 (* end of lemma zenon_L1_ *)
% 45.50/45.65 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).
% 45.50/45.65 do 1 intro. intros zenon_H19 zenon_H1a.
% 45.50/45.65 generalize (definition_1 zenon_TX_y). zenon_intro zenon_H1b.
% 45.50/45.65 apply (zenon_equiv_s _ _ zenon_H1b); [ zenon_intro zenon_H1d; zenon_intro zenon_H1a | zenon_intro zenon_H19; zenon_intro zenon_H1c ].
% 45.50/45.65 exact (zenon_H1d zenon_H19).
% 45.50/45.65 exact (zenon_H1a zenon_H1c).
% 45.50/45.65 (* end of lemma zenon_L2_ *)
% 45.50/45.65 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).
% 45.50/45.65 do 2 intro. intros zenon_H1e zenon_H1f zenon_H1a.
% 45.50/45.65 apply zenon_H1e. zenon_intro zenon_H21.
% 45.50/45.65 generalize (assumption_1 zenon_TX_y). zenon_intro zenon_H22.
% 45.50/45.65 generalize (zenon_H22 zenon_TT1_bg). zenon_intro zenon_H23.
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_H23); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ].
% 45.50/45.65 apply (zenon_notand_s _ _ zenon_H25); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ].
% 45.50/45.65 exact (zenon_H27 zenon_H1f).
% 45.50/45.65 apply zenon_H26. zenon_intro zenon_H19.
% 45.50/45.65 apply (zenon_L2_ zenon_TX_y); trivial.
% 45.50/45.65 exact (zenon_H24 zenon_H21).
% 45.50/45.65 (* end of lemma zenon_L3_ *)
% 45.50/45.65 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).
% 45.50/45.65 do 2 intro. intros zenon_H28 zenon_H29 zenon_H2a zenon_H2b.
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ].
% 45.50/45.65 apply (zenon_notand_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ].
% 45.50/45.65 exact (zenon_H2f zenon_H2a).
% 45.50/45.65 exact (zenon_H2e zenon_H29).
% 45.50/45.65 exact (zenon_H2b zenon_H2c).
% 45.50/45.65 (* end of lemma zenon_L4_ *)
% 45.50/45.65 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).
% 45.50/45.65 do 2 intro. intros zenon_H30 zenon_H29 zenon_H28 zenon_H2b zenon_H31.
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ].
% 45.50/45.65 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ].
% 45.50/45.65 apply (zenon_L4_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.65 exact (zenon_H2e zenon_H29).
% 45.50/45.65 exact (zenon_H31 zenon_H32).
% 45.50/45.65 (* end of lemma zenon_L5_ *)
% 45.50/45.65 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).
% 45.50/45.65 do 2 intro. intros zenon_H34 zenon_H35 zenon_H36 zenon_H37 zenon_H38.
% 45.50/45.65 generalize (zenon_H35 zenon_TT1_bg). zenon_intro zenon_H39.
% 45.50/45.65 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_H3b. zenon_intro zenon_H3a.
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_H3b); [ zenon_intro zenon_H3c | zenon_intro zenon_H29 ].
% 45.50/45.65 generalize (definition_smaller_or_equal (age zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H3d.
% 45.50/45.65 generalize (zenon_H3d (tau)). zenon_intro zenon_H3e.
% 45.50/45.65 apply (zenon_equiv_s _ _ zenon_H3e); [ zenon_intro zenon_H3c; zenon_intro zenon_H41 | zenon_intro zenon_H40; zenon_intro zenon_H3f ].
% 45.50/45.65 apply (zenon_notor_s _ _ zenon_H41). zenon_intro zenon_H43. zenon_intro zenon_H42.
% 45.50/45.65 generalize (definition_smaller (age zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H44.
% 45.50/45.65 generalize (zenon_H44 (tau)). zenon_intro zenon_H45.
% 45.50/45.65 apply (zenon_equiv_s _ _ zenon_H45); [ zenon_intro zenon_H43; zenon_intro zenon_H48 | zenon_intro zenon_H47; zenon_intro zenon_H46 ].
% 45.50/45.65 elim (classic ((~((tau) = (sigma)))/\(~(greater (tau) (sigma))))); [ zenon_intro zenon_H49 | zenon_intro zenon_H4a ].
% 45.50/45.65 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b.
% 45.50/45.65 exact (zenon_H4b zenon_H38).
% 45.50/45.65 cut ((greater (sigma) (age zenon_TX_y zenon_TT1_bg)) = (greater (tau) (age zenon_TX_y zenon_TT1_bg))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_H48.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact zenon_H37.
% 45.50/45.65 cut (((age zenon_TX_y zenon_TT1_bg) = (age zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H4d].
% 45.50/45.65 cut (((sigma) = (tau))); [idtac | apply NNPP; zenon_intro zenon_H4e].
% 45.50/45.65 congruence.
% 45.50/45.65 apply (zenon_notand_s _ _ zenon_H4a); [ zenon_intro zenon_H50 | zenon_intro zenon_H4f ].
% 45.50/45.65 apply zenon_H50. zenon_intro zenon_H51.
% 45.50/45.65 elim (classic ((tau) = (tau))); [ zenon_intro zenon_H52 | zenon_intro zenon_H53 ].
% 45.50/45.65 cut (((tau) = (tau)) = ((sigma) = (tau))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_H4e.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact zenon_H52.
% 45.50/45.65 cut (((tau) = (tau))); [idtac | apply NNPP; zenon_intro zenon_H53].
% 45.50/45.65 cut (((tau) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_H4c].
% 45.50/45.65 congruence.
% 45.50/45.65 exact (zenon_H4c zenon_H51).
% 45.50/45.65 apply zenon_H53. apply refl_equal.
% 45.50/45.65 apply zenon_H53. apply refl_equal.
% 45.50/45.65 apply zenon_H4f. zenon_intro zenon_H38.
% 45.50/45.65 generalize (zenon_H34 (tau)). zenon_intro zenon_H54.
% 45.50/45.65 generalize (zenon_H54 (sigma)). zenon_intro zenon_H55.
% 45.50/45.65 generalize (zenon_H55 (age zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H56.
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_H56); [ zenon_intro zenon_H4b | zenon_intro zenon_H57 ].
% 45.50/45.65 exact (zenon_H4b zenon_H38).
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H58 | zenon_intro zenon_H46 ].
% 45.50/45.65 exact (zenon_H58 zenon_H37).
% 45.50/45.65 exact (zenon_H48 zenon_H46).
% 45.50/45.65 apply zenon_H4d. apply refl_equal.
% 45.50/45.65 exact (zenon_H43 zenon_H47).
% 45.50/45.65 exact (zenon_H3c zenon_H40).
% 45.50/45.65 exact (zenon_H29 zenon_H36).
% 45.50/45.65 (* end of lemma zenon_L6_ *)
% 45.50/45.65 assert (zenon_L7_ : (~((mod1) = (mod1))) -> False).
% 45.50/45.65 do 0 intro. intros zenon_H59.
% 45.50/45.65 apply zenon_H59. apply refl_equal.
% 45.50/45.65 (* end of lemma zenon_L7_ *)
% 45.50/45.65 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).
% 45.50/45.65 do 2 intro. intros zenon_H32 zenon_H34 zenon_H5a.
% 45.50/45.65 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 ].
% 45.50/45.65 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H31. zenon_intro zenon_H5d.
% 45.50/45.65 exact (zenon_H31 zenon_H32).
% 45.50/45.65 cut ((greater (mod2) (mod1)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_H5a.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact assumption_19.
% 45.50/45.65 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 45.50/45.65 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 45.50/45.65 congruence.
% 45.50/45.65 apply (zenon_notand_s _ _ zenon_H5c); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ].
% 45.50/45.65 apply zenon_H60. zenon_intro zenon_H32.
% 45.50/45.65 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 ].
% 45.50/45.65 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))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_H5e.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact zenon_H61.
% 45.50/45.65 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].
% 45.50/45.65 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31].
% 45.50/45.65 congruence.
% 45.50/45.65 exact (zenon_H31 zenon_H32).
% 45.50/45.65 apply zenon_H62. apply refl_equal.
% 45.50/45.65 apply zenon_H62. apply refl_equal.
% 45.50/45.65 apply zenon_H5f. zenon_intro zenon_H63.
% 45.50/45.65 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64.
% 45.50/45.65 generalize (zenon_H64 (mod2)). zenon_intro zenon_H65.
% 45.50/45.65 generalize (zenon_H65 (mod1)). zenon_intro zenon_H66.
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H67 ].
% 45.50/45.65 exact (zenon_H5d zenon_H63).
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_H67); [ zenon_intro zenon_H69 | zenon_intro zenon_H68 ].
% 45.50/45.65 exact (zenon_H69 assumption_19).
% 45.50/45.65 exact (zenon_H5a zenon_H68).
% 45.50/45.65 apply zenon_H59. apply refl_equal.
% 45.50/45.65 (* end of lemma zenon_L8_ *)
% 45.50/45.65 assert (zenon_L9_ : (~((low) = (low))) -> False).
% 45.50/45.65 do 0 intro. intros zenon_H6a.
% 45.50/45.65 apply zenon_H6a. apply refl_equal.
% 45.50/45.65 (* end of lemma zenon_L9_ *)
% 45.50/45.65 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).
% 45.50/45.65 do 2 intro. intros zenon_H32 zenon_H6b zenon_H34 zenon_H6c.
% 45.50/45.65 elim (classic ((~((low) = (mod1)))/\(~(greater (low) (mod1))))); [ zenon_intro zenon_H6d | zenon_intro zenon_H6e ].
% 45.50/45.65 apply (zenon_and_s _ _ zenon_H6d). zenon_intro zenon_H70. zenon_intro zenon_H6f.
% 45.50/45.65 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ].
% 45.50/45.65 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1))); [ zenon_intro zenon_H68 | zenon_intro zenon_H5a ].
% 45.50/45.65 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1)) = (greater (low) (mod1))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_H6f.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact zenon_H68.
% 45.50/45.65 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 45.50/45.65 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low))); [idtac | apply NNPP; zenon_intro zenon_H73].
% 45.50/45.65 congruence.
% 45.50/45.65 elim (classic ((low) = (low))); [ zenon_intro zenon_H74 | zenon_intro zenon_H6a ].
% 45.50/45.65 cut (((low) = (low)) = ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_H73.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact zenon_H74.
% 45.50/45.65 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.65 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72].
% 45.50/45.65 congruence.
% 45.50/45.65 exact (zenon_H72 zenon_H71).
% 45.50/45.65 apply zenon_H6a. apply refl_equal.
% 45.50/45.65 apply zenon_H6a. apply refl_equal.
% 45.50/45.65 apply zenon_H59. apply refl_equal.
% 45.50/45.65 apply (zenon_L8_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.65 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 ].
% 45.50/45.65 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))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_H72.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact zenon_H61.
% 45.50/45.65 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].
% 45.50/45.65 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low))); [idtac | apply NNPP; zenon_intro zenon_H73].
% 45.50/45.65 congruence.
% 45.50/45.65 exact (zenon_H73 zenon_H6b).
% 45.50/45.65 apply zenon_H62. apply refl_equal.
% 45.50/45.65 apply zenon_H62. apply refl_equal.
% 45.50/45.65 cut ((greater (mod1) (low)) = (greater (low) (low))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_H6c.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact assumption_18b.
% 45.50/45.65 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.65 cut (((mod1) = (low))); [idtac | apply NNPP; zenon_intro zenon_H75].
% 45.50/45.65 congruence.
% 45.50/45.65 apply (zenon_notand_s _ _ zenon_H6e); [ zenon_intro zenon_H77 | zenon_intro zenon_H76 ].
% 45.50/45.65 apply zenon_H77. zenon_intro zenon_H78.
% 45.50/45.65 elim (classic ((low) = (low))); [ zenon_intro zenon_H74 | zenon_intro zenon_H6a ].
% 45.50/45.65 cut (((low) = (low)) = ((mod1) = (low))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_H75.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact zenon_H74.
% 45.50/45.65 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.65 cut (((low) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H70].
% 45.50/45.65 congruence.
% 45.50/45.65 exact (zenon_H70 zenon_H78).
% 45.50/45.65 apply zenon_H6a. apply refl_equal.
% 45.50/45.65 apply zenon_H6a. apply refl_equal.
% 45.50/45.65 apply zenon_H76. zenon_intro zenon_H79.
% 45.50/45.65 generalize (zenon_H34 (low)). zenon_intro zenon_H7a.
% 45.50/45.65 generalize (zenon_H7a (mod1)). zenon_intro zenon_H7b.
% 45.50/45.65 generalize (zenon_H7b (low)). zenon_intro zenon_H7c.
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_H7c); [ zenon_intro zenon_H6f | zenon_intro zenon_H7d ].
% 45.50/45.65 exact (zenon_H6f zenon_H79).
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_H7d); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ].
% 45.50/45.65 exact (zenon_H7f assumption_18b).
% 45.50/45.65 exact (zenon_H6c zenon_H7e).
% 45.50/45.65 apply zenon_H6a. apply refl_equal.
% 45.50/45.65 (* end of lemma zenon_L10_ *)
% 45.50/45.65 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).
% 45.50/45.65 do 2 intro. intros zenon_H34 zenon_H6b zenon_H32.
% 45.50/45.65 generalize (meaning_postulate_greater_strict (low)). zenon_intro zenon_H80.
% 45.50/45.65 generalize (zenon_H80 (low)). zenon_intro zenon_H81.
% 45.50/45.65 apply (zenon_notand_s _ _ zenon_H81); [ zenon_intro zenon_H6c | zenon_intro zenon_H6c ].
% 45.50/45.65 apply (zenon_L10_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.65 apply (zenon_L10_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.65 (* end of lemma zenon_L11_ *)
% 45.50/45.65 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).
% 45.50/45.65 do 2 intro. intros zenon_H30 zenon_H38 zenon_H37 zenon_H35 zenon_H82 zenon_H34 zenon_H6b.
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ].
% 45.50/45.65 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ].
% 45.50/45.65 exact (zenon_H2a zenon_H82).
% 45.50/45.65 apply zenon_H2e. zenon_intro zenon_H36.
% 45.50/45.65 apply (zenon_L6_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.65 apply (zenon_L11_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.65 (* end of lemma zenon_L12_ *)
% 45.50/45.65 assert (zenon_L13_ : (~((mod2) = (mod2))) -> False).
% 45.50/45.65 do 0 intro. intros zenon_H83.
% 45.50/45.65 apply zenon_H83. apply refl_equal.
% 45.50/45.65 (* end of lemma zenon_L13_ *)
% 45.50/45.65 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).
% 45.50/45.65 do 2 intro. intros zenon_H38 zenon_H37 zenon_H35 zenon_H31 zenon_H84 zenon_H1a zenon_H1f zenon_H0 zenon_H34 zenon_H5d.
% 45.50/45.65 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 ].
% 45.50/45.65 apply (zenon_and_s _ _ zenon_H85). zenon_intro zenon_H2b. zenon_intro zenon_H87.
% 45.50/45.65 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88.
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ].
% 45.50/45.65 exact (zenon_H27 zenon_H1f).
% 45.50/45.65 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a.
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ].
% 45.50/45.65 apply (zenon_L3_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.65 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d.
% 45.50/45.65 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f.
% 45.50/45.65 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H30. zenon_intro zenon_H28.
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_H8e); [ zenon_intro zenon_H91 | zenon_intro zenon_H6b ].
% 45.50/45.65 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ].
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_H90); [ zenon_intro zenon_H93 | zenon_intro zenon_H92 ].
% 45.50/45.65 apply (zenon_notand_s _ _ zenon_H93); [ zenon_intro zenon_H2f | zenon_intro zenon_H29 ].
% 45.50/45.65 exact (zenon_H2f zenon_H2a).
% 45.50/45.65 apply (zenon_L5_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.65 exact (zenon_H84 zenon_H92).
% 45.50/45.65 apply (zenon_L5_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_H90); [ zenon_intro zenon_H93 | zenon_intro zenon_H92 ].
% 45.50/45.65 apply (zenon_notand_s _ _ zenon_H93); [ zenon_intro zenon_H2f | zenon_intro zenon_H29 ].
% 45.50/45.65 apply zenon_H2f. zenon_intro zenon_H82.
% 45.50/45.65 apply (zenon_L12_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.65 apply (zenon_L5_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.65 exact (zenon_H84 zenon_H92).
% 45.50/45.65 cut ((greater (high) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod2))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_H5d.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact assumption_18d.
% 45.50/45.65 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83].
% 45.50/45.65 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H94].
% 45.50/45.65 congruence.
% 45.50/45.65 apply (zenon_notand_s _ _ zenon_H86); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ].
% 45.50/45.65 apply zenon_H96. zenon_intro zenon_H2c.
% 45.50/45.65 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 ].
% 45.50/45.65 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))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_H94.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact zenon_H61.
% 45.50/45.65 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].
% 45.50/45.65 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b].
% 45.50/45.65 congruence.
% 45.50/45.65 exact (zenon_H2b zenon_H2c).
% 45.50/45.65 apply zenon_H62. apply refl_equal.
% 45.50/45.65 apply zenon_H62. apply refl_equal.
% 45.50/45.65 apply zenon_H95. zenon_intro zenon_H97.
% 45.50/45.65 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64.
% 45.50/45.65 generalize (zenon_H64 (high)). zenon_intro zenon_H98.
% 45.50/45.65 generalize (zenon_H98 (mod2)). zenon_intro zenon_H99.
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H87 | zenon_intro zenon_H9a ].
% 45.50/45.65 exact (zenon_H87 zenon_H97).
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_H9a); [ zenon_intro zenon_H9b | zenon_intro zenon_H63 ].
% 45.50/45.65 exact (zenon_H9b assumption_18d).
% 45.50/45.65 exact (zenon_H5d zenon_H63).
% 45.50/45.65 apply zenon_H83. apply refl_equal.
% 45.50/45.65 (* end of lemma zenon_L14_ *)
% 45.50/45.65 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).
% 45.50/45.65 do 2 intro. intros zenon_H0 zenon_H1f zenon_H1a zenon_H84 zenon_H35 zenon_H37 zenon_H38 zenon_H34 zenon_H5a.
% 45.50/45.65 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 ].
% 45.50/45.65 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H31. zenon_intro zenon_H5d.
% 45.50/45.65 apply (zenon_L14_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.65 cut ((greater (mod2) (mod1)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_H5a.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact assumption_19.
% 45.50/45.65 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 45.50/45.65 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 45.50/45.65 congruence.
% 45.50/45.65 apply (zenon_notand_s _ _ zenon_H5c); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ].
% 45.50/45.65 apply zenon_H60. zenon_intro zenon_H32.
% 45.50/45.65 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 ].
% 45.50/45.65 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))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_H5e.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact zenon_H61.
% 45.50/45.65 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].
% 45.50/45.65 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31].
% 45.50/45.65 congruence.
% 45.50/45.65 exact (zenon_H31 zenon_H32).
% 45.50/45.65 apply zenon_H62. apply refl_equal.
% 45.50/45.65 apply zenon_H62. apply refl_equal.
% 45.50/45.65 apply zenon_H5f. zenon_intro zenon_H63.
% 45.50/45.65 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64.
% 45.50/45.65 generalize (zenon_H64 (mod2)). zenon_intro zenon_H65.
% 45.50/45.65 generalize (zenon_H65 (mod1)). zenon_intro zenon_H66.
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H67 ].
% 45.50/45.65 exact (zenon_H5d zenon_H63).
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_H67); [ zenon_intro zenon_H69 | zenon_intro zenon_H68 ].
% 45.50/45.65 exact (zenon_H69 assumption_19).
% 45.50/45.65 exact (zenon_H5a zenon_H68).
% 45.50/45.65 apply zenon_H59. apply refl_equal.
% 45.50/45.65 (* end of lemma zenon_L15_ *)
% 45.50/45.65 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).
% 45.50/45.65 do 2 intro. intros zenon_H28 zenon_H38 zenon_H37 zenon_H35 zenon_H34 zenon_H2a zenon_H2b.
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ].
% 45.50/45.65 apply (zenon_notand_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ].
% 45.50/45.65 exact (zenon_H2f zenon_H2a).
% 45.50/45.65 apply zenon_H2e. zenon_intro zenon_H36.
% 45.50/45.65 apply (zenon_L6_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.65 exact (zenon_H2b zenon_H2c).
% 45.50/45.65 (* end of lemma zenon_L16_ *)
% 45.50/45.65 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).
% 45.50/45.65 do 2 intro. intros zenon_H92 zenon_H34 zenon_H6c zenon_H6b.
% 45.50/45.65 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ].
% 45.50/45.65 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low))); [ zenon_intro zenon_H9c | zenon_intro zenon_H9d ].
% 45.50/45.65 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low)) = (greater (low) (low))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_H6c.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact zenon_H9c.
% 45.50/45.65 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.65 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low))); [idtac | apply NNPP; zenon_intro zenon_H73].
% 45.50/45.65 congruence.
% 45.50/45.65 elim (classic ((low) = (low))); [ zenon_intro zenon_H74 | zenon_intro zenon_H6a ].
% 45.50/45.65 cut (((low) = (low)) = ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_H73.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact zenon_H74.
% 45.50/45.65 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.65 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72].
% 45.50/45.65 congruence.
% 45.50/45.65 exact (zenon_H72 zenon_H71).
% 45.50/45.65 apply zenon_H6a. apply refl_equal.
% 45.50/45.65 apply zenon_H6a. apply refl_equal.
% 45.50/45.65 apply zenon_H6a. apply refl_equal.
% 45.50/45.65 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 ].
% 45.50/45.65 apply (zenon_and_s _ _ zenon_H9e). zenon_intro zenon_H84. zenon_intro zenon_H5a.
% 45.50/45.65 exact (zenon_H84 zenon_H92).
% 45.50/45.65 cut ((greater (mod1) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_H9d.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact assumption_18b.
% 45.50/45.65 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.65 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_Ha0].
% 45.50/45.65 congruence.
% 45.50/45.65 apply (zenon_notand_s _ _ zenon_H9f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Ha1 ].
% 45.50/45.65 apply zenon_Ha2. zenon_intro zenon_H92.
% 45.50/45.65 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 ].
% 45.50/45.65 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))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_Ha0.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact zenon_H61.
% 45.50/45.65 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].
% 45.50/45.65 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H84].
% 45.50/45.65 congruence.
% 45.50/45.65 exact (zenon_H84 zenon_H92).
% 45.50/45.65 apply zenon_H62. apply refl_equal.
% 45.50/45.65 apply zenon_H62. apply refl_equal.
% 45.50/45.65 apply zenon_Ha1. zenon_intro zenon_H68.
% 45.50/45.65 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64.
% 45.50/45.65 generalize (zenon_H64 (mod1)). zenon_intro zenon_Ha3.
% 45.50/45.65 generalize (zenon_Ha3 (low)). zenon_intro zenon_Ha4.
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_Ha4); [ zenon_intro zenon_H5a | zenon_intro zenon_Ha5 ].
% 45.50/45.65 exact (zenon_H5a zenon_H68).
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_Ha5); [ zenon_intro zenon_H7f | zenon_intro zenon_H9c ].
% 45.50/45.65 exact (zenon_H7f assumption_18b).
% 45.50/45.65 exact (zenon_H9d zenon_H9c).
% 45.50/45.65 apply zenon_H6a. apply refl_equal.
% 45.50/45.65 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 ].
% 45.50/45.65 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))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_H72.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact zenon_H61.
% 45.50/45.65 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].
% 45.50/45.65 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low))); [idtac | apply NNPP; zenon_intro zenon_H73].
% 45.50/45.65 congruence.
% 45.50/45.65 exact (zenon_H73 zenon_H6b).
% 45.50/45.65 apply zenon_H62. apply refl_equal.
% 45.50/45.65 apply zenon_H62. apply refl_equal.
% 45.50/45.65 (* end of lemma zenon_L17_ *)
% 45.50/45.65 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).
% 45.50/45.65 do 2 intro. intros zenon_H34 zenon_Ha6 zenon_H92 zenon_H6b.
% 45.50/45.65 elim (classic (greater (low) (mod1))); [ zenon_intro zenon_H79 | zenon_intro zenon_H6f ].
% 45.50/45.65 generalize (zenon_H34 (mod1)). zenon_intro zenon_Ha7.
% 45.50/45.65 generalize (zenon_Ha7 (low)). zenon_intro zenon_Ha8.
% 45.50/45.65 generalize (zenon_Ha8 (mod1)). zenon_intro zenon_Ha9.
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_Ha9); [ zenon_intro zenon_H7f | zenon_intro zenon_Haa ].
% 45.50/45.65 exact (zenon_H7f assumption_18b).
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_Haa); [ zenon_intro zenon_H6f | zenon_intro zenon_Hab ].
% 45.50/45.65 exact (zenon_H6f zenon_H79).
% 45.50/45.65 exact (zenon_Ha6 zenon_Hab).
% 45.50/45.65 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ].
% 45.50/45.65 elim (classic (greater (low) (low))); [ zenon_intro zenon_H7e | zenon_intro zenon_H6c ].
% 45.50/45.65 elim (classic (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_Hac | zenon_intro zenon_Had ].
% 45.50/45.65 cut ((greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (low) (mod1))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_H6f.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact zenon_Hac.
% 45.50/45.65 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H84].
% 45.50/45.65 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.65 congruence.
% 45.50/45.65 apply zenon_H6a. apply refl_equal.
% 45.50/45.65 exact (zenon_H84 zenon_H92).
% 45.50/45.65 cut ((greater (low) (low)) = (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_Had.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact zenon_H7e.
% 45.50/45.65 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72].
% 45.50/45.65 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.65 congruence.
% 45.50/45.65 apply zenon_H6a. apply refl_equal.
% 45.50/45.65 exact (zenon_H72 zenon_H71).
% 45.50/45.65 apply (zenon_L17_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.65 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 ].
% 45.50/45.65 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))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_H72.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact zenon_H61.
% 45.50/45.65 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].
% 45.50/45.65 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low))); [idtac | apply NNPP; zenon_intro zenon_H73].
% 45.50/45.65 congruence.
% 45.50/45.65 exact (zenon_H73 zenon_H6b).
% 45.50/45.65 apply zenon_H62. apply refl_equal.
% 45.50/45.65 apply zenon_H62. apply refl_equal.
% 45.50/45.65 (* end of lemma zenon_L18_ *)
% 45.50/45.65 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).
% 45.50/45.65 do 2 intro. intros zenon_H34 zenon_H0 zenon_H1f zenon_H1a zenon_H2b zenon_H38 zenon_H37 zenon_H35 zenon_H31 zenon_Ha6.
% 45.50/45.65 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88.
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ].
% 45.50/45.65 exact (zenon_H27 zenon_H1f).
% 45.50/45.65 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a.
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ].
% 45.50/45.65 apply (zenon_L3_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.65 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d.
% 45.50/45.65 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f.
% 45.50/45.65 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H30. zenon_intro zenon_H28.
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_H8e); [ zenon_intro zenon_H91 | zenon_intro zenon_H6b ].
% 45.50/45.65 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ].
% 45.50/45.65 apply (zenon_L16_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.65 apply (zenon_L5_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_H90); [ zenon_intro zenon_H93 | zenon_intro zenon_H92 ].
% 45.50/45.65 apply (zenon_notand_s _ _ zenon_H93); [ zenon_intro zenon_H2f | zenon_intro zenon_H29 ].
% 45.50/45.65 apply zenon_H2f. zenon_intro zenon_H82.
% 45.50/45.65 apply (zenon_L12_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.65 apply (zenon_L5_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.65 apply (zenon_L18_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.65 (* end of lemma zenon_L19_ *)
% 45.50/45.65 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).
% 45.50/45.65 do 3 intro. intros zenon_H35 zenon_H37 zenon_H38 zenon_H1a zenon_H1f zenon_H0 zenon_Hae zenon_H34 zenon_Haf.
% 45.50/45.65 elim (classic ((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hb1 ].
% 45.50/45.65 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1))); [ zenon_intro zenon_H68 | zenon_intro zenon_H5a ].
% 45.50/45.65 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))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_Hae.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact zenon_H68.
% 45.50/45.65 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hb1].
% 45.50/45.65 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].
% 45.50/45.65 congruence.
% 45.50/45.65 apply zenon_H62. apply refl_equal.
% 45.50/45.65 exact (zenon_Hb1 zenon_Hb0).
% 45.50/45.65 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 ].
% 45.50/45.65 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb5 ].
% 45.50/45.65 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))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_Hae.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact zenon_Hb4.
% 45.50/45.65 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].
% 45.50/45.65 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_Ha0].
% 45.50/45.65 congruence.
% 45.50/45.65 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 ].
% 45.50/45.65 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))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_Ha0.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact zenon_H61.
% 45.50/45.65 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].
% 45.50/45.65 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H84].
% 45.50/45.65 congruence.
% 45.50/45.65 apply (zenon_L15_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.65 apply zenon_H62. apply refl_equal.
% 45.50/45.65 apply zenon_H62. apply refl_equal.
% 45.50/45.65 apply zenon_Hb6. apply refl_equal.
% 45.50/45.65 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))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_Hb5.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact zenon_Hb2.
% 45.50/45.65 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].
% 45.50/45.65 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_Hb7].
% 45.50/45.65 congruence.
% 45.50/45.65 elim (classic ((mod1) = (mod1))); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H59 ].
% 45.50/45.65 cut (((mod1) = (mod1)) = ((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (mod1))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_Hb7.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact zenon_Hb8.
% 45.50/45.65 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 45.50/45.65 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hb1].
% 45.50/45.65 congruence.
% 45.50/45.65 exact (zenon_Hb1 zenon_Hb0).
% 45.50/45.65 apply zenon_H59. apply refl_equal.
% 45.50/45.65 apply zenon_H59. apply refl_equal.
% 45.50/45.65 apply zenon_Hb6. apply refl_equal.
% 45.50/45.65 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 ].
% 45.50/45.65 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H31. zenon_intro zenon_H5d.
% 45.50/45.65 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 ].
% 45.50/45.65 apply (zenon_and_s _ _ zenon_H85). zenon_intro zenon_H2b. zenon_intro zenon_H87.
% 45.50/45.65 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb5 ].
% 45.50/45.65 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))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_Hb3.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact zenon_Hb4.
% 45.50/45.65 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].
% 45.50/45.65 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hb1].
% 45.50/45.65 congruence.
% 45.50/45.65 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 ].
% 45.50/45.65 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))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_Hb1.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact zenon_Hb9.
% 45.50/45.65 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].
% 45.50/45.65 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_Hb7].
% 45.50/45.65 congruence.
% 45.50/45.65 exact (zenon_Hb7 zenon_Haf).
% 45.50/45.65 apply zenon_Hb6. apply refl_equal.
% 45.50/45.65 apply zenon_Hb6. apply refl_equal.
% 45.50/45.65 apply zenon_Hb6. apply refl_equal.
% 45.50/45.65 elim (classic ((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hb1 ].
% 45.50/45.65 elim (classic (greater (mod1) (mod1))); [ zenon_intro zenon_Hab | zenon_intro zenon_Ha6 ].
% 45.50/45.65 cut ((greater (mod1) (mod1)) = (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT3_x))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_Hb5.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact zenon_Hab.
% 45.50/45.65 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hb1].
% 45.50/45.65 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 45.50/45.65 congruence.
% 45.50/45.65 apply zenon_H59. apply refl_equal.
% 45.50/45.65 exact (zenon_Hb1 zenon_Hb0).
% 45.50/45.65 apply (zenon_L19_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.65 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 ].
% 45.50/45.65 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))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_Hb1.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact zenon_Hb9.
% 45.50/45.65 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].
% 45.50/45.65 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_Hb7].
% 45.50/45.65 congruence.
% 45.50/45.65 exact (zenon_Hb7 zenon_Haf).
% 45.50/45.65 apply zenon_Hb6. apply refl_equal.
% 45.50/45.65 apply zenon_Hb6. apply refl_equal.
% 45.50/45.65 cut ((greater (high) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod2))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_H5d.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact assumption_18d.
% 45.50/45.65 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83].
% 45.50/45.65 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H94].
% 45.50/45.65 congruence.
% 45.50/45.65 apply (zenon_notand_s _ _ zenon_H86); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ].
% 45.50/45.65 apply zenon_H96. zenon_intro zenon_H2c.
% 45.50/45.65 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 ].
% 45.50/45.65 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))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_H94.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact zenon_H61.
% 45.50/45.65 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].
% 45.50/45.65 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b].
% 45.50/45.65 congruence.
% 45.50/45.65 exact (zenon_H2b zenon_H2c).
% 45.50/45.65 apply zenon_H62. apply refl_equal.
% 45.50/45.65 apply zenon_H62. apply refl_equal.
% 45.50/45.65 apply zenon_H95. zenon_intro zenon_H97.
% 45.50/45.65 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64.
% 45.50/45.65 generalize (zenon_H64 (high)). zenon_intro zenon_H98.
% 45.50/45.65 generalize (zenon_H98 (mod2)). zenon_intro zenon_H99.
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H87 | zenon_intro zenon_H9a ].
% 45.50/45.65 exact (zenon_H87 zenon_H97).
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_H9a); [ zenon_intro zenon_H9b | zenon_intro zenon_H63 ].
% 45.50/45.65 exact (zenon_H9b assumption_18d).
% 45.50/45.65 exact (zenon_H5d zenon_H63).
% 45.50/45.65 apply zenon_H83. apply refl_equal.
% 45.50/45.65 cut ((greater (mod2) (mod1)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_H5a.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact assumption_19.
% 45.50/45.65 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 45.50/45.65 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 45.50/45.65 congruence.
% 45.50/45.65 apply (zenon_notand_s _ _ zenon_H5c); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ].
% 45.50/45.65 apply zenon_H60. zenon_intro zenon_H32.
% 45.50/45.65 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 ].
% 45.50/45.65 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))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_H5e.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact zenon_H61.
% 45.50/45.65 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].
% 45.50/45.65 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31].
% 45.50/45.65 congruence.
% 45.50/45.65 exact (zenon_H31 zenon_H32).
% 45.50/45.65 apply zenon_H62. apply refl_equal.
% 45.50/45.65 apply zenon_H62. apply refl_equal.
% 45.50/45.65 apply zenon_H5f. zenon_intro zenon_H63.
% 45.50/45.65 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64.
% 45.50/45.65 generalize (zenon_H64 (mod2)). zenon_intro zenon_H65.
% 45.50/45.65 generalize (zenon_H65 (mod1)). zenon_intro zenon_H66.
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H67 ].
% 45.50/45.65 exact (zenon_H5d zenon_H63).
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_H67); [ zenon_intro zenon_H69 | zenon_intro zenon_H68 ].
% 45.50/45.65 exact (zenon_H69 assumption_19).
% 45.50/45.65 exact (zenon_H5a zenon_H68).
% 45.50/45.65 apply zenon_H59. apply refl_equal.
% 45.50/45.65 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 ].
% 45.50/45.65 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))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_Hb1.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact zenon_Hb9.
% 45.50/45.65 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].
% 45.50/45.65 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_Hb7].
% 45.50/45.65 congruence.
% 45.50/45.65 exact (zenon_Hb7 zenon_Haf).
% 45.50/45.65 apply zenon_Hb6. apply refl_equal.
% 45.50/45.65 apply zenon_Hb6. apply refl_equal.
% 45.50/45.65 (* end of lemma zenon_L20_ *)
% 45.50/45.65 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).
% 45.50/45.65 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.
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_Hba); [ zenon_intro zenon_Hbd | zenon_intro zenon_Haf ].
% 45.50/45.65 apply (zenon_notand_s _ _ zenon_Hbd); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hbe ].
% 45.50/45.65 exact (zenon_Hbf zenon_Hbc).
% 45.50/45.65 exact (zenon_Hbe zenon_Hbb).
% 45.50/45.65 apply (zenon_L20_ zenon_TT3_x zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.65 (* end of lemma zenon_L21_ *)
% 45.50/45.65 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).
% 45.50/45.65 do 2 intro. intros zenon_H0 zenon_H1f zenon_H1a zenon_H31 zenon_H35 zenon_H37 zenon_H38 zenon_H5d zenon_H34 zenon_H9d.
% 45.50/45.65 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 ].
% 45.50/45.65 apply (zenon_and_s _ _ zenon_H9e). zenon_intro zenon_H84. zenon_intro zenon_H5a.
% 45.50/45.65 apply (zenon_L14_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.65 cut ((greater (mod1) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_H9d.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact assumption_18b.
% 45.50/45.65 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.65 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_Ha0].
% 45.50/45.65 congruence.
% 45.50/45.65 apply (zenon_notand_s _ _ zenon_H9f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Ha1 ].
% 45.50/45.65 apply zenon_Ha2. zenon_intro zenon_H92.
% 45.50/45.65 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 ].
% 45.50/45.65 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))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_Ha0.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact zenon_H61.
% 45.50/45.65 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].
% 45.50/45.65 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H84].
% 45.50/45.65 congruence.
% 45.50/45.65 exact (zenon_H84 zenon_H92).
% 45.50/45.65 apply zenon_H62. apply refl_equal.
% 45.50/45.65 apply zenon_H62. apply refl_equal.
% 45.50/45.65 apply zenon_Ha1. zenon_intro zenon_H68.
% 45.50/45.65 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64.
% 45.50/45.65 generalize (zenon_H64 (mod1)). zenon_intro zenon_Ha3.
% 45.50/45.65 generalize (zenon_Ha3 (low)). zenon_intro zenon_Ha4.
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_Ha4); [ zenon_intro zenon_H5a | zenon_intro zenon_Ha5 ].
% 45.50/45.65 exact (zenon_H5a zenon_H68).
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_Ha5); [ zenon_intro zenon_H7f | zenon_intro zenon_H9c ].
% 45.50/45.65 exact (zenon_H7f assumption_18b).
% 45.50/45.65 exact (zenon_H9d zenon_H9c).
% 45.50/45.65 apply zenon_H6a. apply refl_equal.
% 45.50/45.65 (* end of lemma zenon_L22_ *)
% 45.50/45.65 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).
% 45.50/45.65 do 2 intro. intros zenon_H38 zenon_H37 zenon_H35 zenon_H1a zenon_H1f zenon_H0 zenon_H34 zenon_H9d.
% 45.50/45.65 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 ].
% 45.50/45.65 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H31. zenon_intro zenon_H5d.
% 45.50/45.65 apply (zenon_L22_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.65 cut ((greater (mod2) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_H9d.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact assumption_18e.
% 45.50/45.65 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.65 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 45.50/45.65 congruence.
% 45.50/45.65 apply (zenon_notand_s _ _ zenon_H5c); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ].
% 45.50/45.65 apply zenon_H60. zenon_intro zenon_H32.
% 45.50/45.65 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 ].
% 45.50/45.65 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))).
% 45.50/45.65 intro zenon_D_pnotp.
% 45.50/45.65 apply zenon_H5e.
% 45.50/45.65 rewrite <- zenon_D_pnotp.
% 45.50/45.65 exact zenon_H61.
% 45.50/45.65 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].
% 45.50/45.65 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31].
% 45.50/45.65 congruence.
% 45.50/45.65 exact (zenon_H31 zenon_H32).
% 45.50/45.65 apply zenon_H62. apply refl_equal.
% 45.50/45.65 apply zenon_H62. apply refl_equal.
% 45.50/45.65 apply zenon_H5f. zenon_intro zenon_H63.
% 45.50/45.65 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64.
% 45.50/45.65 generalize (zenon_H64 (mod2)). zenon_intro zenon_H65.
% 45.50/45.65 generalize (zenon_H65 (low)). zenon_intro zenon_Hc0.
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_Hc0); [ zenon_intro zenon_H5d | zenon_intro zenon_Hc1 ].
% 45.50/45.65 exact (zenon_H5d zenon_H63).
% 45.50/45.65 apply (zenon_imply_s _ _ zenon_Hc1); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H9c ].
% 45.50/45.65 exact (zenon_Hc2 assumption_18e).
% 45.50/45.65 exact (zenon_H9d zenon_H9c).
% 45.50/45.65 apply zenon_H6a. apply refl_equal.
% 45.50/45.65 (* end of lemma zenon_L23_ *)
% 45.50/45.65 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).
% 45.50/45.66 do 3 intro. intros zenon_Hc3 zenon_Hbb zenon_H0 zenon_H1f zenon_H1a zenon_H35 zenon_H37 zenon_H38 zenon_Hae zenon_H34.
% 45.50/45.66 apply (zenon_and_s _ _ zenon_Hc3). zenon_intro zenon_Hc5. zenon_intro zenon_Hc4.
% 45.50/45.66 apply (zenon_and_s _ _ zenon_Hc4). zenon_intro zenon_Hba. zenon_intro zenon_Hc6.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_Hc5); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hc7 ].
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_Hc8); [ zenon_intro zenon_Hbc | zenon_intro zenon_Hbe ].
% 45.50/45.66 apply (zenon_L21_ zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial.
% 45.50/45.66 exact (zenon_Hbe zenon_Hbb).
% 45.50/45.66 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hca ].
% 45.50/45.66 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low))); [ zenon_intro zenon_H9c | zenon_intro zenon_H9d ].
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_Hae.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H9c.
% 45.50/45.66 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hca].
% 45.50/45.66 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].
% 45.50/45.66 congruence.
% 45.50/45.66 apply zenon_H62. apply refl_equal.
% 45.50/45.66 exact (zenon_Hca zenon_Hc9).
% 45.50/45.66 apply (zenon_L23_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.66 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 ].
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_Hca.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_Hb9.
% 45.50/45.66 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].
% 45.50/45.66 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (low))); [idtac | apply NNPP; zenon_intro zenon_Hcb].
% 45.50/45.66 congruence.
% 45.50/45.66 exact (zenon_Hcb zenon_Hc7).
% 45.50/45.66 apply zenon_Hb6. apply refl_equal.
% 45.50/45.66 apply zenon_Hb6. apply refl_equal.
% 45.50/45.66 (* end of lemma zenon_L24_ *)
% 45.50/45.66 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).
% 45.50/45.66 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.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_Hcc); [ zenon_intro zenon_H15 | zenon_intro zenon_Hc3 ].
% 45.50/45.66 exact (zenon_H15 zenon_H16).
% 45.50/45.66 apply (zenon_L24_ zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial.
% 45.50/45.66 (* end of lemma zenon_L25_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 3 intro. intros zenon_H1f zenon_Hcd zenon_H2a zenon_Hce.
% 45.50/45.66 generalize (definition_2 zenon_TX_y). zenon_intro zenon_Hd0.
% 45.50/45.66 generalize (zenon_Hd0 zenon_TT0_hz). zenon_intro zenon_Hd1.
% 45.50/45.66 generalize (zenon_Hd1 zenon_TT1_bg). zenon_intro zenon_Hd2.
% 45.50/45.66 apply (zenon_equiv_s _ _ zenon_Hd2); [ zenon_intro zenon_Hce; zenon_intro zenon_Hd5 | zenon_intro zenon_Hd4; zenon_intro zenon_Hd3 ].
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_Hd5); [ zenon_intro zenon_H27 | zenon_intro zenon_Hd6 ].
% 45.50/45.66 exact (zenon_H27 zenon_H1f).
% 45.50/45.66 apply zenon_Hd6. zenon_intro zenon_Hd7.
% 45.50/45.66 apply (zenon_equiv_s _ _ zenon_Hd7); [ zenon_intro zenon_Hd8; zenon_intro zenon_H2a | zenon_intro zenon_Hcd; zenon_intro zenon_H82 ].
% 45.50/45.66 exact (zenon_Hd8 zenon_Hcd).
% 45.50/45.66 exact (zenon_H2a zenon_H82).
% 45.50/45.66 exact (zenon_Hce zenon_Hd4).
% 45.50/45.66 (* end of lemma zenon_L26_ *)
% 45.50/45.66 assert (zenon_L27_ : (~((sigma) = (sigma))) -> False).
% 45.50/45.66 do 0 intro. intros zenon_Hd9.
% 45.50/45.66 apply zenon_Hd9. apply refl_equal.
% 45.50/45.66 (* end of lemma zenon_L27_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 2 intro. intros zenon_H37 zenon_H34 zenon_Hda zenon_Hdb.
% 45.50/45.66 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 ].
% 45.50/45.66 apply (zenon_and_s _ _ zenon_Hdc). zenon_intro zenon_Hde. zenon_intro zenon_H58.
% 45.50/45.66 exact (zenon_H58 zenon_H37).
% 45.50/45.66 cut ((greater (age zenon_TX_y zenon_TT1_bg) (sigma)) = (greater (sigma) (sigma))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_Hda.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_Hdb.
% 45.50/45.66 cut (((sigma) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hd9].
% 45.50/45.66 cut (((age zenon_TX_y zenon_TT1_bg) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hdf].
% 45.50/45.66 congruence.
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_Hdd); [ zenon_intro zenon_He1 | zenon_intro zenon_He0 ].
% 45.50/45.66 apply zenon_He1. zenon_intro zenon_He2.
% 45.50/45.66 elim (classic ((sigma) = (sigma))); [ zenon_intro zenon_He3 | zenon_intro zenon_Hd9 ].
% 45.50/45.66 cut (((sigma) = (sigma)) = ((age zenon_TX_y zenon_TT1_bg) = (sigma))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_Hdf.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_He3.
% 45.50/45.66 cut (((sigma) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hd9].
% 45.50/45.66 cut (((sigma) = (age zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_Hde].
% 45.50/45.66 congruence.
% 45.50/45.66 exact (zenon_Hde zenon_He2).
% 45.50/45.66 apply zenon_Hd9. apply refl_equal.
% 45.50/45.66 apply zenon_Hd9. apply refl_equal.
% 45.50/45.66 apply zenon_He0. zenon_intro zenon_H37.
% 45.50/45.66 generalize (zenon_H34 (sigma)). zenon_intro zenon_He4.
% 45.50/45.66 generalize (zenon_He4 (age zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_He5.
% 45.50/45.66 generalize (zenon_He5 (sigma)). zenon_intro zenon_He6.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_He6); [ zenon_intro zenon_H58 | zenon_intro zenon_He7 ].
% 45.50/45.66 exact (zenon_H58 zenon_H37).
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_He7); [ zenon_intro zenon_He9 | zenon_intro zenon_He8 ].
% 45.50/45.66 exact (zenon_He9 zenon_Hdb).
% 45.50/45.66 exact (zenon_Hda zenon_He8).
% 45.50/45.66 apply zenon_Hd9. apply refl_equal.
% 45.50/45.66 (* end of lemma zenon_L28_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 2 intro. intros zenon_H34 zenon_Hea zenon_Hdb zenon_H37.
% 45.50/45.66 generalize (zenon_Hea (sigma)). zenon_intro zenon_Heb.
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_Heb); [ zenon_intro zenon_Hda | zenon_intro zenon_Hda ].
% 45.50/45.66 apply (zenon_L28_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.66 apply (zenon_L28_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.66 (* end of lemma zenon_L29_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 3 intro. intros zenon_H34 zenon_H1f zenon_Hec zenon_H37 zenon_H2a zenon_Hcd zenon_Hed.
% 45.50/45.66 generalize (meaning_postulate_greater_strict (sigma)). zenon_intro zenon_Hea.
% 45.50/45.66 generalize (zenon_Hed zenon_TT0_hz). zenon_intro zenon_Hee.
% 45.50/45.66 generalize (zenon_Hee zenon_TT1_bg). zenon_intro zenon_Hef.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_Hef); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf0 ].
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ].
% 45.50/45.66 exact (zenon_H27 zenon_H1f).
% 45.50/45.66 exact (zenon_Hf2 zenon_Hec).
% 45.50/45.66 apply (zenon_equiv_s _ _ zenon_Hf0); [ zenon_intro zenon_He9; zenon_intro zenon_Hce | zenon_intro zenon_Hdb; zenon_intro zenon_Hd4 ].
% 45.50/45.66 apply (zenon_L26_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.66 apply (zenon_L29_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.66 (* end of lemma zenon_L30_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 3 intro. intros zenon_H34 zenon_Hcd zenon_H2a zenon_H37 zenon_Hec zenon_H1f.
% 45.50/45.66 generalize (assumption_15 zenon_TX_y). zenon_intro zenon_Hed.
% 45.50/45.66 apply (zenon_L30_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.66 (* end of lemma zenon_L31_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 3 intro. intros zenon_H34 zenon_H0 zenon_H1f zenon_H1a zenon_Hcd zenon_H37 zenon_Hec zenon_H31 zenon_H2b zenon_H73.
% 45.50/45.66 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ].
% 45.50/45.66 exact (zenon_H27 zenon_H1f).
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ].
% 45.50/45.66 apply (zenon_L3_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d.
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f.
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H30. zenon_intro zenon_H28.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H8e); [ zenon_intro zenon_H91 | zenon_intro zenon_H6b ].
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ].
% 45.50/45.66 apply (zenon_L31_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.66 apply (zenon_L5_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.66 exact (zenon_H73 zenon_H6b).
% 45.50/45.66 (* end of lemma zenon_L32_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 3 intro. intros zenon_H34 zenon_Hf3 zenon_H1f zenon_Hec zenon_H0 zenon_H1a zenon_H37 zenon_H31 zenon_H2b zenon_H73.
% 45.50/45.66 generalize (zenon_Hf3 zenon_TT0_hz). zenon_intro zenon_Hf4.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcd ].
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ].
% 45.50/45.66 exact (zenon_H27 zenon_H1f).
% 45.50/45.66 exact (zenon_Hf2 zenon_Hec).
% 45.50/45.66 apply (zenon_L32_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.66 (* end of lemma zenon_L33_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 3 intro. intros zenon_H34 zenon_H73 zenon_H2b zenon_H31 zenon_H37 zenon_H1a zenon_Hec zenon_H1f zenon_Hf3.
% 45.50/45.66 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0.
% 45.50/45.66 apply (zenon_L33_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.66 (* end of lemma zenon_L34_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 3 intro. intros zenon_H34 zenon_H1f zenon_Hec zenon_H1a zenon_H37 zenon_H31 zenon_H2b zenon_H73.
% 45.50/45.66 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3.
% 45.50/45.66 apply (zenon_L34_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.66 (* end of lemma zenon_L35_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 3 intro. intros zenon_H73 zenon_H31 zenon_H37 zenon_H1a zenon_Hec zenon_H1f zenon_H34 zenon_H5d.
% 45.50/45.66 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 ].
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H85). zenon_intro zenon_H2b. zenon_intro zenon_H87.
% 45.50/45.66 apply (zenon_L35_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.66 cut ((greater (high) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod2))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H5d.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact assumption_18d.
% 45.50/45.66 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83].
% 45.50/45.66 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H94].
% 45.50/45.66 congruence.
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_H86); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ].
% 45.50/45.66 apply zenon_H96. zenon_intro zenon_H2c.
% 45.50/45.66 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 ].
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H94.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H61.
% 45.50/45.66 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].
% 45.50/45.66 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b].
% 45.50/45.66 congruence.
% 45.50/45.66 exact (zenon_H2b zenon_H2c).
% 45.50/45.66 apply zenon_H62. apply refl_equal.
% 45.50/45.66 apply zenon_H62. apply refl_equal.
% 45.50/45.66 apply zenon_H95. zenon_intro zenon_H97.
% 45.50/45.66 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64.
% 45.50/45.66 generalize (zenon_H64 (high)). zenon_intro zenon_H98.
% 45.50/45.66 generalize (zenon_H98 (mod2)). zenon_intro zenon_H99.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H87 | zenon_intro zenon_H9a ].
% 45.50/45.66 exact (zenon_H87 zenon_H97).
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H9a); [ zenon_intro zenon_H9b | zenon_intro zenon_H63 ].
% 45.50/45.66 exact (zenon_H9b assumption_18d).
% 45.50/45.66 exact (zenon_H5d zenon_H63).
% 45.50/45.66 apply zenon_H83. apply refl_equal.
% 45.50/45.66 (* end of lemma zenon_L36_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 3 intro. intros zenon_H1f zenon_Hec zenon_H1a zenon_H37 zenon_H73 zenon_H34 zenon_H9d.
% 45.50/45.66 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 ].
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H31. zenon_intro zenon_H5d.
% 45.50/45.66 apply (zenon_L36_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.66 cut ((greater (mod2) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H9d.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact assumption_18e.
% 45.50/45.66 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.66 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 45.50/45.66 congruence.
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_H5c); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ].
% 45.50/45.66 apply zenon_H60. zenon_intro zenon_H32.
% 45.50/45.66 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 ].
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H5e.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H61.
% 45.50/45.66 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].
% 45.50/45.66 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31].
% 45.50/45.66 congruence.
% 45.50/45.66 exact (zenon_H31 zenon_H32).
% 45.50/45.66 apply zenon_H62. apply refl_equal.
% 45.50/45.66 apply zenon_H62. apply refl_equal.
% 45.50/45.66 apply zenon_H5f. zenon_intro zenon_H63.
% 45.50/45.66 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64.
% 45.50/45.66 generalize (zenon_H64 (mod2)). zenon_intro zenon_H65.
% 45.50/45.66 generalize (zenon_H65 (low)). zenon_intro zenon_Hc0.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_Hc0); [ zenon_intro zenon_H5d | zenon_intro zenon_Hc1 ].
% 45.50/45.66 exact (zenon_H5d zenon_H63).
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_Hc1); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H9c ].
% 45.50/45.66 exact (zenon_Hc2 assumption_18e).
% 45.50/45.66 exact (zenon_H9d zenon_H9c).
% 45.50/45.66 apply zenon_H6a. apply refl_equal.
% 45.50/45.66 (* end of lemma zenon_L37_ *)
% 45.50/45.66 assert (zenon_L38_ : (~((very_low) = (very_low))) -> False).
% 45.50/45.66 do 0 intro. intros zenon_Hf5.
% 45.50/45.66 apply zenon_Hf5. apply refl_equal.
% 45.50/45.66 (* end of lemma zenon_L38_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 3 intro. intros zenon_H37 zenon_H1a zenon_Hec zenon_H1f zenon_H34 zenon_Hf6.
% 45.50/45.66 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 ].
% 45.50/45.66 apply (zenon_and_s _ _ zenon_Hf7). zenon_intro zenon_H73. zenon_intro zenon_H9d.
% 45.50/45.66 apply (zenon_L37_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.66 cut ((greater (low) (very_low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (very_low))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_Hf6.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact assumption_18c.
% 45.50/45.66 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5].
% 45.50/45.66 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72].
% 45.50/45.66 congruence.
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_Hf8); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hf9 ].
% 45.50/45.66 apply zenon_Hfa. zenon_intro zenon_H6b.
% 45.50/45.66 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 ].
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H72.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H61.
% 45.50/45.66 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].
% 45.50/45.66 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low))); [idtac | apply NNPP; zenon_intro zenon_H73].
% 45.50/45.66 congruence.
% 45.50/45.66 exact (zenon_H73 zenon_H6b).
% 45.50/45.66 apply zenon_H62. apply refl_equal.
% 45.50/45.66 apply zenon_H62. apply refl_equal.
% 45.50/45.66 apply zenon_Hf9. zenon_intro zenon_H9c.
% 45.50/45.66 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64.
% 45.50/45.66 generalize (zenon_H64 (low)). zenon_intro zenon_Hfb.
% 45.50/45.66 generalize (zenon_Hfb (very_low)). zenon_intro zenon_Hfc.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_Hfc); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfd ].
% 45.50/45.66 exact (zenon_H9d zenon_H9c).
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_Hfd); [ zenon_intro zenon_Hff | zenon_intro zenon_Hfe ].
% 45.50/45.66 exact (zenon_Hff assumption_18c).
% 45.50/45.66 exact (zenon_Hf6 zenon_Hfe).
% 45.50/45.66 apply zenon_Hf5. apply refl_equal.
% 45.50/45.66 (* end of lemma zenon_L39_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 4 intro. intros zenon_H34 zenon_H100 zenon_Hec zenon_H1a zenon_H35 zenon_H37 zenon_H38 zenon_H1f zenon_H101.
% 45.50/45.66 generalize (definition_smaller (hazard_of_mortality zenon_TX_y zenon_TT3_x)). zenon_intro zenon_H102.
% 45.50/45.66 generalize (zenon_H102 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H103.
% 45.50/45.66 apply (zenon_equiv_s _ _ zenon_H103); [ zenon_intro zenon_H101; zenon_intro zenon_Hae | zenon_intro zenon_H105; zenon_intro zenon_H104 ].
% 45.50/45.66 generalize (zenon_H35 zenon_TT3_x). zenon_intro zenon_H106.
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H106). zenon_intro zenon_H108. zenon_intro zenon_H107.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H107); [ zenon_intro zenon_H109 | zenon_intro zenon_Hbb ].
% 45.50/45.66 exact (zenon_H109 zenon_H100).
% 45.50/45.66 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0.
% 45.50/45.66 generalize (zenon_H0 zenon_TT3_x). zenon_intro zenon_H10a.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H10a); [ zenon_intro zenon_H27 | zenon_intro zenon_H10b ].
% 45.50/45.66 exact (zenon_H27 zenon_H1f).
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H10b). zenon_intro zenon_H10c. zenon_intro zenon_Hcc.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H10c); [ zenon_intro zenon_H16 | zenon_intro zenon_H10d ].
% 45.50/45.66 apply (zenon_L25_ zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial.
% 45.50/45.66 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_H10e | zenon_intro zenon_H10f ].
% 45.50/45.66 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (very_low))); [ zenon_intro zenon_Hfe | zenon_intro zenon_Hf6 ].
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_Hae.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_Hfe.
% 45.50/45.66 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_H10f].
% 45.50/45.66 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].
% 45.50/45.66 congruence.
% 45.50/45.66 apply zenon_H62. apply refl_equal.
% 45.50/45.66 exact (zenon_H10f zenon_H10e).
% 45.50/45.66 apply (zenon_L39_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.66 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 ].
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H10f.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_Hb9.
% 45.50/45.66 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].
% 45.50/45.66 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H110].
% 45.50/45.66 congruence.
% 45.50/45.66 exact (zenon_H110 zenon_H10d).
% 45.50/45.66 apply zenon_Hb6. apply refl_equal.
% 45.50/45.66 apply zenon_Hb6. apply refl_equal.
% 45.50/45.66 exact (zenon_H101 zenon_H105).
% 45.50/45.66 (* end of lemma zenon_L40_ *)
% 45.50/45.66 assert (zenon_L41_ : forall (zenon_TX_y : zenon_U), (~(~(has_immunity zenon_TX_y zenon_E))) -> (~(has_immunity zenon_TX_y zenon_E)) -> False).
% 45.50/45.66 do 1 intro. intros zenon_H111 zenon_H112.
% 45.50/45.66 exact (zenon_H111 zenon_H112).
% 45.50/45.66 (* end of lemma zenon_L41_ *)
% 45.50/45.66 assert (zenon_L42_ : (~((high) = (high))) -> False).
% 45.50/45.66 do 0 intro. intros zenon_H113.
% 45.50/45.66 apply zenon_H113. apply refl_equal.
% 45.50/45.66 (* end of lemma zenon_L42_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 3 intro. intros zenon_H8c zenon_H38 zenon_H37 zenon_H35 zenon_H34 zenon_H1f zenon_Hec zenon_Hcd zenon_Hed zenon_H5e.
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d.
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f.
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H30. zenon_intro zenon_H28.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ].
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ].
% 45.50/45.66 apply (zenon_L30_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.66 apply zenon_H2e. zenon_intro zenon_H36.
% 45.50/45.66 apply (zenon_L6_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.66 apply zenon_H5e. apply sym_equal. exact zenon_H32.
% 45.50/45.66 (* end of lemma zenon_L43_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 3 intro. intros zenon_H34 zenon_H5e zenon_H38 zenon_H35 zenon_Hcd zenon_H37 zenon_Hec zenon_H1a zenon_H1f zenon_H0.
% 45.50/45.66 generalize (assumption_15 zenon_TX_y). zenon_intro zenon_Hed.
% 45.50/45.66 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ].
% 45.50/45.66 exact (zenon_H27 zenon_H1f).
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ].
% 45.50/45.66 apply (zenon_L3_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.66 apply (zenon_L43_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.66 (* end of lemma zenon_L44_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 3 intro. intros zenon_H34 zenon_Hf3 zenon_H1f zenon_Hec zenon_H5e zenon_H38 zenon_H35 zenon_H37 zenon_H1a zenon_H0.
% 45.50/45.66 generalize (zenon_Hf3 zenon_TT0_hz). zenon_intro zenon_Hf4.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcd ].
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ].
% 45.50/45.66 exact (zenon_H27 zenon_H1f).
% 45.50/45.66 exact (zenon_Hf2 zenon_Hec).
% 45.50/45.66 apply (zenon_L44_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.66 (* end of lemma zenon_L45_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 3 intro. intros zenon_H34 zenon_H1a zenon_H37 zenon_H35 zenon_H38 zenon_H5e zenon_Hec zenon_H1f zenon_Hf3.
% 45.50/45.66 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0.
% 45.50/45.66 apply (zenon_L45_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.66 (* end of lemma zenon_L46_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 3 intro. intros zenon_H34 zenon_H1f zenon_Hec zenon_H5e zenon_H38 zenon_H35 zenon_H37 zenon_H1a.
% 45.50/45.66 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3.
% 45.50/45.66 apply (zenon_L46_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.66 (* end of lemma zenon_L47_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 3 intro. intros zenon_H34 zenon_H114 zenon_H1f zenon_Hec zenon_H38 zenon_H35 zenon_H37 zenon_H1a.
% 45.50/45.66 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H115 | zenon_intro zenon_H5e ].
% 45.50/45.66 cut ((greater (high) (mod2)) = (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H114.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact assumption_18d.
% 45.50/45.66 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 45.50/45.66 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113].
% 45.50/45.66 congruence.
% 45.50/45.66 apply zenon_H113. apply refl_equal.
% 45.50/45.66 exact (zenon_H5e zenon_H115).
% 45.50/45.66 apply (zenon_L47_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.66 (* end of lemma zenon_L48_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 3 intro. intros zenon_H34 zenon_H116 zenon_H117 zenon_H1a zenon_H37 zenon_H35 zenon_H38 zenon_Hec zenon_H1f.
% 45.50/45.66 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H118 | zenon_intro zenon_H114 ].
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H117.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H118.
% 45.50/45.66 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].
% 45.50/45.66 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H119].
% 45.50/45.66 congruence.
% 45.50/45.66 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 ].
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H119.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H11a.
% 45.50/45.66 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.66 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c].
% 45.50/45.66 congruence.
% 45.50/45.66 exact (zenon_H11c zenon_H116).
% 45.50/45.66 apply zenon_H11b. apply refl_equal.
% 45.50/45.66 apply zenon_H11b. apply refl_equal.
% 45.50/45.66 apply zenon_H62. apply refl_equal.
% 45.50/45.66 apply (zenon_L48_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.66 (* end of lemma zenon_L49_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 2 intro. intros zenon_H11d zenon_H1f zenon_H1a.
% 45.50/45.66 apply zenon_H11d. zenon_intro zenon_H11f.
% 45.50/45.66 generalize (assumption_1 zenon_TX_y). zenon_intro zenon_H22.
% 45.50/45.66 generalize (zenon_H22 zenon_TT2_la). zenon_intro zenon_H120.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H120); [ zenon_intro zenon_H25 | zenon_intro zenon_H121 ].
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_H25); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ].
% 45.50/45.66 exact (zenon_H27 zenon_H1f).
% 45.50/45.66 apply zenon_H26. zenon_intro zenon_H19.
% 45.50/45.66 apply (zenon_L2_ zenon_TX_y); trivial.
% 45.50/45.66 exact (zenon_H121 zenon_H11f).
% 45.50/45.66 (* end of lemma zenon_L50_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 2 intro. intros zenon_H35 zenon_H122 zenon_H123.
% 45.50/45.66 generalize (zenon_H35 zenon_TT2_la). zenon_intro zenon_H124.
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H124). zenon_intro zenon_H126. zenon_intro zenon_H125.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H126); [ zenon_intro zenon_H128 | zenon_intro zenon_H127 ].
% 45.50/45.66 generalize (definition_smaller_or_equal (age zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H129.
% 45.50/45.66 generalize (zenon_H129 (tau)). zenon_intro zenon_H12a.
% 45.50/45.66 apply (zenon_equiv_s _ _ zenon_H12a); [ zenon_intro zenon_H128; zenon_intro zenon_H12d | zenon_intro zenon_H12c; zenon_intro zenon_H12b ].
% 45.50/45.66 apply (zenon_notor_s _ _ zenon_H12d). zenon_intro zenon_H12f. zenon_intro zenon_H12e.
% 45.50/45.66 generalize (definition_smaller (age zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H130.
% 45.50/45.66 generalize (zenon_H130 (tau)). zenon_intro zenon_H131.
% 45.50/45.66 apply (zenon_equiv_s _ _ zenon_H131); [ zenon_intro zenon_H12f; zenon_intro zenon_H133 | zenon_intro zenon_H132; zenon_intro zenon_H123 ].
% 45.50/45.66 exact (zenon_H133 zenon_H123).
% 45.50/45.66 exact (zenon_H12f zenon_H132).
% 45.50/45.66 exact (zenon_H128 zenon_H12c).
% 45.50/45.66 exact (zenon_H127 zenon_H122).
% 45.50/45.66 (* end of lemma zenon_L51_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 2 intro. intros zenon_H134 zenon_H123 zenon_H35 zenon_H135 zenon_H136.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H134); [ zenon_intro zenon_H138 | zenon_intro zenon_H137 ].
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_H138); [ zenon_intro zenon_H13a | zenon_intro zenon_H139 ].
% 45.50/45.66 exact (zenon_H13a zenon_H135).
% 45.50/45.66 apply zenon_H139. zenon_intro zenon_H122.
% 45.50/45.66 apply (zenon_L51_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.66 exact (zenon_H136 zenon_H137).
% 45.50/45.66 (* end of lemma zenon_L52_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 2 intro. intros zenon_H0 zenon_H1f zenon_H1a zenon_H136 zenon_H123 zenon_H35 zenon_H13b.
% 45.50/45.66 generalize (zenon_H0 zenon_TT2_la). zenon_intro zenon_H13c.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H13c); [ zenon_intro zenon_H27 | zenon_intro zenon_H13d ].
% 45.50/45.66 exact (zenon_H27 zenon_H1f).
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H13d). zenon_intro zenon_H13f. zenon_intro zenon_H13e.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H13e); [ zenon_intro zenon_H11d | zenon_intro zenon_H140 ].
% 45.50/45.66 apply (zenon_L50_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H140). zenon_intro zenon_H142. zenon_intro zenon_H141.
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H141). zenon_intro zenon_H144. zenon_intro zenon_H143.
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H143). zenon_intro zenon_H145. zenon_intro zenon_H134.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H145); [ zenon_intro zenon_H147 | zenon_intro zenon_H146 ].
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_H147); [ zenon_intro zenon_H135 | zenon_intro zenon_H139 ].
% 45.50/45.66 apply (zenon_L52_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.66 apply zenon_H139. zenon_intro zenon_H122.
% 45.50/45.66 apply (zenon_L51_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.66 exact (zenon_H13b zenon_H146).
% 45.50/45.66 (* end of lemma zenon_L53_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 2 intro. intros zenon_H11d zenon_H121.
% 45.50/45.66 exact (zenon_H11d zenon_H121).
% 45.50/45.66 (* end of lemma zenon_L54_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 3 intro. intros zenon_Hed zenon_H148 zenon_H149 zenon_Hcd zenon_Hec zenon_H1f.
% 45.50/45.66 generalize (zenon_Hed zenon_TT0_hz). zenon_intro zenon_Hee.
% 45.50/45.66 generalize (zenon_Hee zenon_TT2_la). zenon_intro zenon_H14a.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H14a); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H14b ].
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ].
% 45.50/45.66 exact (zenon_H27 zenon_H1f).
% 45.50/45.66 exact (zenon_Hf2 zenon_Hec).
% 45.50/45.66 apply (zenon_equiv_s _ _ zenon_H14b); [ zenon_intro zenon_H14e; zenon_intro zenon_H14d | zenon_intro zenon_H148; zenon_intro zenon_H14c ].
% 45.50/45.66 exact (zenon_H14e zenon_H148).
% 45.50/45.66 generalize (definition_2 zenon_TX_y). zenon_intro zenon_Hd0.
% 45.50/45.66 generalize (zenon_Hd0 zenon_TT0_hz). zenon_intro zenon_Hd1.
% 45.50/45.66 generalize (zenon_Hd1 zenon_TT2_la). zenon_intro zenon_H14f.
% 45.50/45.66 apply (zenon_equiv_s _ _ zenon_H14f); [ zenon_intro zenon_H14d; zenon_intro zenon_H151 | zenon_intro zenon_H14c; zenon_intro zenon_H150 ].
% 45.50/45.66 exact (zenon_H14d zenon_H14c).
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H150). zenon_intro zenon_H1f. zenon_intro zenon_H152.
% 45.50/45.66 apply (zenon_notequiv_s _ _ zenon_H152); [ zenon_intro zenon_Hd8; zenon_intro zenon_H149 | zenon_intro zenon_Hcd; zenon_intro zenon_H135 ].
% 45.50/45.66 exact (zenon_Hd8 zenon_Hcd).
% 45.50/45.66 exact (zenon_H135 zenon_H149).
% 45.50/45.66 (* end of lemma zenon_L55_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 3 intro. intros zenon_H134 zenon_H127 zenon_Hed zenon_H148 zenon_Hcd zenon_Hec zenon_H1f zenon_H136.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H134); [ zenon_intro zenon_H138 | zenon_intro zenon_H137 ].
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_H138); [ zenon_intro zenon_H13a | zenon_intro zenon_H139 ].
% 45.50/45.66 apply zenon_H13a. zenon_intro zenon_H149.
% 45.50/45.66 apply (zenon_L55_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.66 exact (zenon_H139 zenon_H127).
% 45.50/45.66 exact (zenon_H136 zenon_H137).
% 45.50/45.66 (* end of lemma zenon_L56_ *)
% 45.50/45.66 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).
% 45.50/45.66 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.
% 45.50/45.66 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H156 | zenon_intro zenon_H157 ].
% 45.50/45.66 cut ((greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = (greater (mod2) (mod2))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H153.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H156.
% 45.50/45.66 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b].
% 45.50/45.66 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83].
% 45.50/45.66 congruence.
% 45.50/45.66 apply zenon_H83. apply refl_equal.
% 45.50/45.66 exact (zenon_H13b zenon_H146).
% 45.50/45.66 elim (classic ((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H158 | zenon_intro zenon_H159 ].
% 45.50/45.66 cut ((greater (mod2) (mod1)) = (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT2_la))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H157.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact assumption_19.
% 45.50/45.66 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 45.50/45.66 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83].
% 45.50/45.66 congruence.
% 45.50/45.66 apply zenon_H83. apply refl_equal.
% 45.50/45.66 exact (zenon_H159 zenon_H158).
% 45.50/45.66 generalize (zenon_H0 zenon_TT2_la). zenon_intro zenon_H13c.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H13c); [ zenon_intro zenon_H27 | zenon_intro zenon_H13d ].
% 45.50/45.66 exact (zenon_H27 zenon_H1f).
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H13d). zenon_intro zenon_H13f. zenon_intro zenon_H13e.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H13f); [ zenon_intro zenon_H121 | zenon_intro zenon_H15a ].
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H13e); [ zenon_intro zenon_H11d | zenon_intro zenon_H140 ].
% 45.50/45.66 exact (zenon_H11d zenon_H121).
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H140). zenon_intro zenon_H142. zenon_intro zenon_H141.
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H141). zenon_intro zenon_H144. zenon_intro zenon_H143.
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H143). zenon_intro zenon_H145. zenon_intro zenon_H134.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H142); [ zenon_intro zenon_H15c | zenon_intro zenon_H15b ].
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_H15c); [ zenon_intro zenon_H135 | zenon_intro zenon_H127 ].
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H144); [ zenon_intro zenon_H15e | zenon_intro zenon_H15d ].
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_H15e); [ zenon_intro zenon_H13a | zenon_intro zenon_H127 ].
% 45.50/45.66 exact (zenon_H13a zenon_H135).
% 45.50/45.66 apply (zenon_L56_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.66 apply zenon_H159. apply sym_equal. exact zenon_H15d.
% 45.50/45.66 apply (zenon_L56_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.66 apply zenon_H155. apply sym_equal. exact zenon_H15b.
% 45.50/45.66 apply zenon_H154. apply sym_equal. exact zenon_H15a.
% 45.50/45.66 (* end of lemma zenon_L57_ *)
% 45.50/45.66 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).
% 45.50/45.66 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.
% 45.50/45.66 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H160 | zenon_intro zenon_H155 ].
% 45.50/45.66 cut ((greater (mod1) (low)) = (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT2_la))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H15f.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact assumption_18b.
% 45.50/45.66 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H155].
% 45.50/45.66 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 45.50/45.66 congruence.
% 45.50/45.66 apply zenon_H59. apply refl_equal.
% 45.50/45.66 exact (zenon_H155 zenon_H160).
% 45.50/45.66 elim (classic (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H161 | zenon_intro zenon_H162 ].
% 45.50/45.66 generalize (zenon_H34 (mod1)). zenon_intro zenon_Ha7.
% 45.50/45.66 generalize (zenon_Ha7 (low)). zenon_intro zenon_Ha8.
% 45.50/45.66 generalize (zenon_Ha8 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H163.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H163); [ zenon_intro zenon_H7f | zenon_intro zenon_H164 ].
% 45.50/45.66 exact (zenon_H7f assumption_18b).
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H164); [ zenon_intro zenon_H162 | zenon_intro zenon_H165 ].
% 45.50/45.66 exact (zenon_H162 zenon_H161).
% 45.50/45.66 exact (zenon_H15f zenon_H165).
% 45.50/45.66 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H166 | zenon_intro zenon_H154 ].
% 45.50/45.66 cut ((greater (low) (very_low)) = (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT2_la))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H162.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact assumption_18c.
% 45.50/45.66 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H154].
% 45.50/45.66 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.66 congruence.
% 45.50/45.66 apply zenon_H6a. apply refl_equal.
% 45.50/45.66 exact (zenon_H154 zenon_H166).
% 45.50/45.66 apply (zenon_L57_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.66 (* end of lemma zenon_L58_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 3 intro. intros zenon_H34 zenon_H167 zenon_H0 zenon_H1f zenon_H136 zenon_Hec zenon_Hcd zenon_H148 zenon_Hed zenon_H146.
% 45.50/45.66 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 ].
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H167.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H168.
% 45.50/45.66 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b].
% 45.50/45.66 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].
% 45.50/45.66 congruence.
% 45.50/45.66 apply zenon_H16a. apply refl_equal.
% 45.50/45.66 exact (zenon_H13b zenon_H146).
% 45.50/45.66 elim (classic (greater (mod2) (mod2))); [ zenon_intro zenon_H16b | zenon_intro zenon_H153 ].
% 45.50/45.66 cut ((greater (mod2) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H167.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H16b.
% 45.50/45.66 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83].
% 45.50/45.66 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16c].
% 45.50/45.66 congruence.
% 45.50/45.66 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 ].
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H16c.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H16d.
% 45.50/45.66 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].
% 45.50/45.66 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b].
% 45.50/45.66 congruence.
% 45.50/45.66 exact (zenon_H13b zenon_H146).
% 45.50/45.66 apply zenon_H16a. apply refl_equal.
% 45.50/45.66 apply zenon_H16a. apply refl_equal.
% 45.50/45.66 apply zenon_H83. apply refl_equal.
% 45.50/45.66 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H156 | zenon_intro zenon_H157 ].
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H169.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H156.
% 45.50/45.66 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].
% 45.50/45.66 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16c].
% 45.50/45.66 congruence.
% 45.50/45.66 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 ].
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H16c.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H16d.
% 45.50/45.66 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].
% 45.50/45.66 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b].
% 45.50/45.66 congruence.
% 45.50/45.66 exact (zenon_H13b zenon_H146).
% 45.50/45.66 apply zenon_H16a. apply refl_equal.
% 45.50/45.66 apply zenon_H16a. apply refl_equal.
% 45.50/45.66 apply zenon_H16a. apply refl_equal.
% 45.50/45.66 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H165 | zenon_intro zenon_H15f ].
% 45.50/45.66 generalize (zenon_H34 (mod2)). zenon_intro zenon_H16e.
% 45.50/45.66 generalize (zenon_H16e (mod1)). zenon_intro zenon_H16f.
% 45.50/45.66 generalize (zenon_H16f (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H170.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H170); [ zenon_intro zenon_H69 | zenon_intro zenon_H171 ].
% 45.50/45.66 exact (zenon_H69 assumption_19).
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H171); [ zenon_intro zenon_H15f | zenon_intro zenon_H156 ].
% 45.50/45.66 exact (zenon_H15f zenon_H165).
% 45.50/45.66 exact (zenon_H157 zenon_H156).
% 45.50/45.66 apply (zenon_L58_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.66 (* end of lemma zenon_L59_ *)
% 45.50/45.66 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).
% 45.50/45.66 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.
% 45.50/45.66 generalize (zenon_Hf3 zenon_TT0_hz). zenon_intro zenon_Hf4.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcd ].
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ].
% 45.50/45.66 exact (zenon_H27 zenon_H1f).
% 45.50/45.66 exact (zenon_Hf2 zenon_Hec).
% 45.50/45.66 generalize (assumption_15 zenon_TX_y). zenon_intro zenon_Hed.
% 45.50/45.66 generalize (meaning_postulate_greater_comparable (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H172.
% 45.50/45.66 generalize (zenon_H172 (mod2)). zenon_intro zenon_H173.
% 45.50/45.66 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H175 | zenon_intro zenon_H174 ].
% 45.50/45.66 generalize (definition_smaller (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H176.
% 45.50/45.66 generalize (zenon_H176 (mod2)). zenon_intro zenon_H177.
% 45.50/45.66 apply (zenon_equiv_s _ _ zenon_H177); [ zenon_intro zenon_H178; zenon_intro zenon_H157 | zenon_intro zenon_H175; zenon_intro zenon_H156 ].
% 45.50/45.66 exact (zenon_H178 zenon_H175).
% 45.50/45.66 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [ zenon_intro zenon_H146 | zenon_intro zenon_H13b ].
% 45.50/45.66 cut ((greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = (greater (mod2) (mod2))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H153.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H156.
% 45.50/45.66 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b].
% 45.50/45.66 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83].
% 45.50/45.66 congruence.
% 45.50/45.66 apply zenon_H83. apply refl_equal.
% 45.50/45.66 exact (zenon_H13b zenon_H146).
% 45.50/45.66 apply (zenon_L53_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.66 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H146 | zenon_intro zenon_H179 ].
% 45.50/45.66 apply (zenon_L59_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.66 exact (zenon_H167 zenon_H179).
% 45.50/45.66 (* end of lemma zenon_L60_ *)
% 45.50/45.66 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).
% 45.50/45.66 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.
% 45.50/45.66 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H17a | zenon_intro zenon_H16c ].
% 45.50/45.66 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ].
% 45.50/45.66 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2)) = (greater (mod2) (mod2))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H153.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H179.
% 45.50/45.66 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83].
% 45.50/45.66 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b].
% 45.50/45.66 congruence.
% 45.50/45.66 elim (classic ((mod2) = (mod2))); [ zenon_intro zenon_H17b | zenon_intro zenon_H83 ].
% 45.50/45.66 cut (((mod2) = (mod2)) = ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H13b.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H17b.
% 45.50/45.66 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83].
% 45.50/45.66 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16c].
% 45.50/45.66 congruence.
% 45.50/45.66 exact (zenon_H16c zenon_H17a).
% 45.50/45.66 apply zenon_H83. apply refl_equal.
% 45.50/45.66 apply zenon_H83. apply refl_equal.
% 45.50/45.66 apply zenon_H83. apply refl_equal.
% 45.50/45.66 apply (zenon_L60_ zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.66 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 ].
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H16c.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H16d.
% 45.50/45.66 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].
% 45.50/45.66 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b].
% 45.50/45.66 congruence.
% 45.50/45.66 exact (zenon_H13b zenon_H146).
% 45.50/45.66 apply zenon_H16a. apply refl_equal.
% 45.50/45.66 apply zenon_H16a. apply refl_equal.
% 45.50/45.66 (* end of lemma zenon_L61_ *)
% 45.50/45.66 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).
% 45.50/45.66 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.
% 45.50/45.66 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H156 | zenon_intro zenon_H157 ].
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H169.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H156.
% 45.50/45.66 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].
% 45.50/45.66 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16c].
% 45.50/45.66 congruence.
% 45.50/45.66 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 ].
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H16c.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H16d.
% 45.50/45.66 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].
% 45.50/45.66 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b].
% 45.50/45.66 congruence.
% 45.50/45.66 exact (zenon_H13b zenon_H146).
% 45.50/45.66 apply zenon_H16a. apply refl_equal.
% 45.50/45.66 apply zenon_H16a. apply refl_equal.
% 45.50/45.66 apply zenon_H16a. apply refl_equal.
% 45.50/45.66 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H17a | zenon_intro zenon_H16c ].
% 45.50/45.66 elim (classic (greater (mod2) (mod2))); [ zenon_intro zenon_H16b | zenon_intro zenon_H153 ].
% 45.50/45.66 cut ((greater (mod2) (mod2)) = (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT2_la))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H157.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H16b.
% 45.50/45.66 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16c].
% 45.50/45.66 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83].
% 45.50/45.66 congruence.
% 45.50/45.66 apply zenon_H83. apply refl_equal.
% 45.50/45.66 exact (zenon_H16c zenon_H17a).
% 45.50/45.66 apply (zenon_L61_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.66 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 ].
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H16c.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H16d.
% 45.50/45.66 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].
% 45.50/45.66 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b].
% 45.50/45.66 congruence.
% 45.50/45.66 exact (zenon_H13b zenon_H146).
% 45.50/45.66 apply zenon_H16a. apply refl_equal.
% 45.50/45.66 apply zenon_H16a. apply refl_equal.
% 45.50/45.66 (* end of lemma zenon_L62_ *)
% 45.50/45.66 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).
% 45.50/45.66 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.
% 45.50/45.66 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 ].
% 45.50/45.66 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ].
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H17c.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H179.
% 45.50/45.66 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 45.50/45.66 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].
% 45.50/45.66 congruence.
% 45.50/45.66 apply zenon_H16a. apply refl_equal.
% 45.50/45.66 apply (zenon_L44_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H167.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H168.
% 45.50/45.66 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b].
% 45.50/45.66 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].
% 45.50/45.66 congruence.
% 45.50/45.66 apply zenon_H16a. apply refl_equal.
% 45.50/45.66 exact (zenon_H13b zenon_H146).
% 45.50/45.66 apply (zenon_L62_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.66 (* end of lemma zenon_L63_ *)
% 45.50/45.66 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).
% 45.50/45.66 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.
% 45.50/45.66 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0.
% 45.50/45.66 generalize (zenon_Hf3 zenon_TT0_hz). zenon_intro zenon_Hf4.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcd ].
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ].
% 45.50/45.66 exact (zenon_H27 zenon_H1f).
% 45.50/45.66 exact (zenon_Hf2 zenon_Hec).
% 45.50/45.66 generalize (zenon_H0 zenon_TT2_la). zenon_intro zenon_H13c.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H13c); [ zenon_intro zenon_H27 | zenon_intro zenon_H13d ].
% 45.50/45.66 exact (zenon_H27 zenon_H1f).
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H13d). zenon_intro zenon_H13f. zenon_intro zenon_H13e.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H13e); [ zenon_intro zenon_H11d | zenon_intro zenon_H140 ].
% 45.50/45.66 apply (zenon_L50_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H140). zenon_intro zenon_H142. zenon_intro zenon_H141.
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H141). zenon_intro zenon_H144. zenon_intro zenon_H143.
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H143). zenon_intro zenon_H145. zenon_intro zenon_H134.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H145); [ zenon_intro zenon_H147 | zenon_intro zenon_H146 ].
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_H147); [ zenon_intro zenon_H135 | zenon_intro zenon_H139 ].
% 45.50/45.66 apply (zenon_L52_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.66 apply zenon_H139. zenon_intro zenon_H122.
% 45.50/45.66 apply (zenon_L51_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.66 apply (zenon_L63_ zenon_TT2_la zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.66 (* end of lemma zenon_L64_ *)
% 45.50/45.66 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).
% 45.50/45.66 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.
% 45.50/45.66 elim (classic ((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H17d | zenon_intro zenon_H119 ].
% 45.50/45.66 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 ].
% 45.50/45.66 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H118 | zenon_intro zenon_H114 ].
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H17c.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H118.
% 45.50/45.66 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].
% 45.50/45.66 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f].
% 45.50/45.66 congruence.
% 45.50/45.66 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 ].
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H17f.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H16d.
% 45.50/45.66 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].
% 45.50/45.66 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136].
% 45.50/45.66 congruence.
% 45.50/45.66 apply (zenon_L64_ zenon_TT0_hz zenon_TT1_bg zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.66 apply zenon_H16a. apply refl_equal.
% 45.50/45.66 apply zenon_H16a. apply refl_equal.
% 45.50/45.66 apply zenon_H62. apply refl_equal.
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H114.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H17e.
% 45.50/45.66 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].
% 45.50/45.66 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c].
% 45.50/45.66 congruence.
% 45.50/45.66 elim (classic ((high) = (high))); [ zenon_intro zenon_H180 | zenon_intro zenon_H113 ].
% 45.50/45.66 cut (((high) = (high)) = ((hazard_of_mortality zenon_TX_y zenon_E) = (high))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H11c.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H180.
% 45.50/45.66 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113].
% 45.50/45.66 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H119].
% 45.50/45.66 congruence.
% 45.50/45.66 exact (zenon_H119 zenon_H17d).
% 45.50/45.66 apply zenon_H113. apply refl_equal.
% 45.50/45.66 apply zenon_H113. apply refl_equal.
% 45.50/45.66 apply zenon_H62. apply refl_equal.
% 45.50/45.66 apply (zenon_L49_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.66 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 ].
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H119.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H11a.
% 45.50/45.66 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.66 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c].
% 45.50/45.66 congruence.
% 45.50/45.66 exact (zenon_H11c zenon_H116).
% 45.50/45.66 apply zenon_H11b. apply refl_equal.
% 45.50/45.66 apply zenon_H11b. apply refl_equal.
% 45.50/45.66 (* end of lemma zenon_L65_ *)
% 45.50/45.66 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).
% 45.50/45.66 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.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H181); [ zenon_intro zenon_H184 | zenon_intro zenon_H116 ].
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_H184); [ zenon_intro zenon_H186 | zenon_intro zenon_H185 ].
% 45.50/45.66 exact (zenon_H186 zenon_H183).
% 45.50/45.66 exact (zenon_H185 zenon_H182).
% 45.50/45.66 apply (zenon_L65_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.66 (* end of lemma zenon_L66_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 2 intro. intros zenon_H134 zenon_H127 zenon_H135 zenon_H136.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H134); [ zenon_intro zenon_H138 | zenon_intro zenon_H137 ].
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_H138); [ zenon_intro zenon_H13a | zenon_intro zenon_H139 ].
% 45.50/45.66 exact (zenon_H13a zenon_H135).
% 45.50/45.66 exact (zenon_H139 zenon_H127).
% 45.50/45.66 exact (zenon_H136 zenon_H137).
% 45.50/45.66 (* end of lemma zenon_L67_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 2 intro. intros zenon_H1e zenon_H24.
% 45.50/45.66 exact (zenon_H1e zenon_H24).
% 45.50/45.66 (* end of lemma zenon_L68_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 3 intro. intros zenon_H34 zenon_H187 zenon_Hec zenon_H37 zenon_Hcd zenon_H35 zenon_H38 zenon_H5e zenon_H1f zenon_H0.
% 45.50/45.66 generalize (assumption_15 zenon_TX_y). zenon_intro zenon_Hed.
% 45.50/45.66 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ].
% 45.50/45.66 exact (zenon_H27 zenon_H1f).
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H8b); [ zenon_intro zenon_H24 | zenon_intro zenon_H188 ].
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ].
% 45.50/45.66 exact (zenon_H1e zenon_H24).
% 45.50/45.66 apply (zenon_L43_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.66 apply zenon_H187. apply sym_equal. exact zenon_H188.
% 45.50/45.66 (* end of lemma zenon_L69_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 2 intro. intros zenon_H34 zenon_H146 zenon_H169 zenon_H15b.
% 45.50/45.66 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H156 | zenon_intro zenon_H157 ].
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H169.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H156.
% 45.50/45.66 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].
% 45.50/45.66 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16c].
% 45.50/45.66 congruence.
% 45.50/45.66 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 ].
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H16c.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H16d.
% 45.50/45.66 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].
% 45.50/45.66 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b].
% 45.50/45.66 congruence.
% 45.50/45.66 exact (zenon_H13b zenon_H146).
% 45.50/45.66 apply zenon_H16a. apply refl_equal.
% 45.50/45.66 apply zenon_H16a. apply refl_equal.
% 45.50/45.66 apply zenon_H16a. apply refl_equal.
% 45.50/45.66 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H165 | zenon_intro zenon_H15f ].
% 45.50/45.66 generalize (zenon_H34 (mod2)). zenon_intro zenon_H16e.
% 45.50/45.66 generalize (zenon_H16e (mod1)). zenon_intro zenon_H16f.
% 45.50/45.66 generalize (zenon_H16f (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H170.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H170); [ zenon_intro zenon_H69 | zenon_intro zenon_H171 ].
% 45.50/45.66 exact (zenon_H69 assumption_19).
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H171); [ zenon_intro zenon_H15f | zenon_intro zenon_H156 ].
% 45.50/45.66 exact (zenon_H15f zenon_H165).
% 45.50/45.66 exact (zenon_H157 zenon_H156).
% 45.50/45.66 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H160 | zenon_intro zenon_H155 ].
% 45.50/45.66 cut ((greater (mod1) (low)) = (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT2_la))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H15f.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact assumption_18b.
% 45.50/45.66 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H155].
% 45.50/45.66 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 45.50/45.66 congruence.
% 45.50/45.66 apply zenon_H59. apply refl_equal.
% 45.50/45.66 exact (zenon_H155 zenon_H160).
% 45.50/45.66 apply zenon_H155. apply sym_equal. exact zenon_H15b.
% 45.50/45.66 (* end of lemma zenon_L70_ *)
% 45.50/45.66 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).
% 45.50/45.66 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.
% 45.50/45.66 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 ].
% 45.50/45.66 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ].
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H17c.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H179.
% 45.50/45.66 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 45.50/45.66 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].
% 45.50/45.66 congruence.
% 45.50/45.66 apply zenon_H16a. apply refl_equal.
% 45.50/45.66 apply (zenon_L69_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H167.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H168.
% 45.50/45.66 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b].
% 45.50/45.66 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].
% 45.50/45.66 congruence.
% 45.50/45.66 apply zenon_H16a. apply refl_equal.
% 45.50/45.66 exact (zenon_H13b zenon_H146).
% 45.50/45.66 apply (zenon_L70_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.66 (* end of lemma zenon_L71_ *)
% 45.50/45.66 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).
% 45.50/45.66 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.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H145); [ zenon_intro zenon_H147 | zenon_intro zenon_H146 ].
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_H147); [ zenon_intro zenon_H135 | zenon_intro zenon_H139 ].
% 45.50/45.66 apply (zenon_L52_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.66 apply zenon_H139. zenon_intro zenon_H122.
% 45.50/45.66 apply (zenon_L51_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.66 apply (zenon_L71_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.66 (* end of lemma zenon_L72_ *)
% 45.50/45.66 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).
% 45.50/45.66 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.
% 45.50/45.66 generalize (zenon_H0 zenon_TT2_la). zenon_intro zenon_H13c.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H13c); [ zenon_intro zenon_H27 | zenon_intro zenon_H13d ].
% 45.50/45.66 exact (zenon_H27 zenon_H1f).
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H13d). zenon_intro zenon_H13f. zenon_intro zenon_H13e.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H13e); [ zenon_intro zenon_H11d | zenon_intro zenon_H140 ].
% 45.50/45.66 apply (zenon_L50_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H140). zenon_intro zenon_H142. zenon_intro zenon_H141.
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H141). zenon_intro zenon_H144. zenon_intro zenon_H143.
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H143). zenon_intro zenon_H145. zenon_intro zenon_H134.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H142); [ zenon_intro zenon_H15c | zenon_intro zenon_H15b ].
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_H15c); [ zenon_intro zenon_H135 | zenon_intro zenon_H127 ].
% 45.50/45.66 apply (zenon_L52_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H145); [ zenon_intro zenon_H147 | zenon_intro zenon_H146 ].
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_H147); [ zenon_intro zenon_H135 | zenon_intro zenon_H139 ].
% 45.50/45.66 apply (zenon_L67_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.66 exact (zenon_H139 zenon_H127).
% 45.50/45.66 apply (zenon_L63_ zenon_TT2_la zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.66 apply (zenon_L72_ zenon_TT0_hz zenon_TT1_bg zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.66 (* end of lemma zenon_L73_ *)
% 45.50/45.66 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).
% 45.50/45.66 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.
% 45.50/45.66 generalize (zenon_Hf3 zenon_TT0_hz). zenon_intro zenon_Hf4.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcd ].
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ].
% 45.50/45.66 exact (zenon_H27 zenon_H1f).
% 45.50/45.66 exact (zenon_Hf2 zenon_Hec).
% 45.50/45.66 apply (zenon_L73_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.66 (* end of lemma zenon_L74_ *)
% 45.50/45.66 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).
% 45.50/45.66 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.
% 45.50/45.66 elim (classic ((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H17d | zenon_intro zenon_H119 ].
% 45.50/45.66 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 ].
% 45.50/45.66 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H118 | zenon_intro zenon_H114 ].
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H17c.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H118.
% 45.50/45.66 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].
% 45.50/45.66 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f].
% 45.50/45.66 congruence.
% 45.50/45.66 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 ].
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H17f.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H16d.
% 45.50/45.66 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].
% 45.50/45.66 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136].
% 45.50/45.66 congruence.
% 45.50/45.66 apply (zenon_L74_ zenon_TT1_bg zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.66 apply zenon_H16a. apply refl_equal.
% 45.50/45.66 apply zenon_H16a. apply refl_equal.
% 45.50/45.66 apply zenon_H62. apply refl_equal.
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H114.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H17e.
% 45.50/45.66 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].
% 45.50/45.66 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c].
% 45.50/45.66 congruence.
% 45.50/45.66 elim (classic ((high) = (high))); [ zenon_intro zenon_H180 | zenon_intro zenon_H113 ].
% 45.50/45.66 cut (((high) = (high)) = ((hazard_of_mortality zenon_TX_y zenon_E) = (high))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H11c.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H180.
% 45.50/45.66 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113].
% 45.50/45.66 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H119].
% 45.50/45.66 congruence.
% 45.50/45.66 exact (zenon_H119 zenon_H17d).
% 45.50/45.66 apply zenon_H113. apply refl_equal.
% 45.50/45.66 apply zenon_H113. apply refl_equal.
% 45.50/45.66 apply zenon_H62. apply refl_equal.
% 45.50/45.66 apply (zenon_L49_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.66 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 ].
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H119.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H11a.
% 45.50/45.66 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.66 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c].
% 45.50/45.66 congruence.
% 45.50/45.66 exact (zenon_H11c zenon_H116).
% 45.50/45.66 apply zenon_H11b. apply refl_equal.
% 45.50/45.66 apply zenon_H11b. apply refl_equal.
% 45.50/45.66 (* end of lemma zenon_L75_ *)
% 45.50/45.66 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).
% 45.50/45.66 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.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H181); [ zenon_intro zenon_H184 | zenon_intro zenon_H116 ].
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_H184); [ zenon_intro zenon_H186 | zenon_intro zenon_H185 ].
% 45.50/45.66 exact (zenon_H186 zenon_H183).
% 45.50/45.66 exact (zenon_H185 zenon_H182).
% 45.50/45.66 apply (zenon_L75_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.66 (* end of lemma zenon_L76_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 2 intro. intros zenon_H13b zenon_H35 zenon_H123 zenon_H136 zenon_H1a zenon_H1f.
% 45.50/45.66 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0.
% 45.50/45.66 apply (zenon_L53_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.66 (* end of lemma zenon_L77_ *)
% 45.50/45.66 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).
% 45.50/45.66 do 2 intro. intros zenon_H1f zenon_H1a zenon_H123 zenon_H35 zenon_H13b zenon_H34 zenon_H167.
% 45.50/45.66 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 ].
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H136. zenon_intro zenon_H18b.
% 45.50/45.66 apply (zenon_L77_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.66 cut ((greater (high) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H167.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact assumption_18d.
% 45.50/45.66 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83].
% 45.50/45.66 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f].
% 45.50/45.66 congruence.
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_H18a); [ zenon_intro zenon_H18d | zenon_intro zenon_H18c ].
% 45.50/45.66 apply zenon_H18d. zenon_intro zenon_H137.
% 45.50/45.66 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 ].
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H17f.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H16d.
% 45.50/45.66 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].
% 45.50/45.66 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136].
% 45.50/45.66 congruence.
% 45.50/45.66 exact (zenon_H136 zenon_H137).
% 45.50/45.66 apply zenon_H16a. apply refl_equal.
% 45.50/45.66 apply zenon_H16a. apply refl_equal.
% 45.50/45.66 apply zenon_H18c. zenon_intro zenon_H18e.
% 45.50/45.66 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.50/45.66 generalize (zenon_H18f (high)). zenon_intro zenon_H190.
% 45.50/45.66 generalize (zenon_H190 (mod2)). zenon_intro zenon_H191.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H191); [ zenon_intro zenon_H18b | zenon_intro zenon_H192 ].
% 45.50/45.66 exact (zenon_H18b zenon_H18e).
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H192); [ zenon_intro zenon_H9b | zenon_intro zenon_H179 ].
% 45.50/45.66 exact (zenon_H9b assumption_18d).
% 45.50/45.66 exact (zenon_H167 zenon_H179).
% 45.50/45.66 apply zenon_H83. apply refl_equal.
% 45.50/45.66 (* end of lemma zenon_L78_ *)
% 45.50/45.66 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).
% 45.50/45.66 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.
% 45.50/45.66 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ].
% 45.50/45.66 cut ((greater (mod1) (low)) = (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H193.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact assumption_18b.
% 45.50/45.66 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72].
% 45.50/45.66 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 45.50/45.66 congruence.
% 45.50/45.66 apply zenon_H59. apply refl_equal.
% 45.50/45.66 exact (zenon_H72 zenon_H71).
% 45.50/45.66 generalize (zenon_Hf3 zenon_TT0_hz). zenon_intro zenon_Hf4.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcd ].
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ].
% 45.50/45.66 exact (zenon_H27 zenon_H1f).
% 45.50/45.66 exact (zenon_Hf2 zenon_Hec).
% 45.50/45.66 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ].
% 45.50/45.66 exact (zenon_H27 zenon_H1f).
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H8b); [ zenon_intro zenon_H24 | zenon_intro zenon_H188 ].
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ].
% 45.50/45.66 exact (zenon_H1e zenon_H24).
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d.
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f.
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H30. zenon_intro zenon_H28.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H8e); [ zenon_intro zenon_H91 | zenon_intro zenon_H6b ].
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ].
% 45.50/45.66 apply (zenon_L31_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ].
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ].
% 45.50/45.66 apply (zenon_L31_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.66 exact (zenon_H2e zenon_H29).
% 45.50/45.66 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H115 | zenon_intro zenon_H5e ].
% 45.50/45.66 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ].
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H17c.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H179.
% 45.50/45.66 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 45.50/45.66 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].
% 45.50/45.66 congruence.
% 45.50/45.66 apply zenon_H16a. apply refl_equal.
% 45.50/45.66 exact (zenon_H5e zenon_H115).
% 45.50/45.66 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 ].
% 45.50/45.66 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H136. zenon_intro zenon_H18b.
% 45.50/45.66 apply (zenon_L73_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.66 cut ((greater (high) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H167.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact assumption_18d.
% 45.50/45.66 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83].
% 45.50/45.66 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f].
% 45.50/45.66 congruence.
% 45.50/45.66 apply (zenon_notand_s _ _ zenon_H18a); [ zenon_intro zenon_H18d | zenon_intro zenon_H18c ].
% 45.50/45.66 apply zenon_H18d. zenon_intro zenon_H137.
% 45.50/45.66 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 ].
% 45.50/45.66 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))).
% 45.50/45.66 intro zenon_D_pnotp.
% 45.50/45.66 apply zenon_H17f.
% 45.50/45.66 rewrite <- zenon_D_pnotp.
% 45.50/45.66 exact zenon_H16d.
% 45.50/45.66 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].
% 45.50/45.66 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136].
% 45.50/45.66 congruence.
% 45.50/45.66 exact (zenon_H136 zenon_H137).
% 45.50/45.66 apply zenon_H16a. apply refl_equal.
% 45.50/45.66 apply zenon_H16a. apply refl_equal.
% 45.50/45.66 apply zenon_H18c. zenon_intro zenon_H18e.
% 45.50/45.66 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.50/45.66 generalize (zenon_H18f (high)). zenon_intro zenon_H190.
% 45.50/45.66 generalize (zenon_H190 (mod2)). zenon_intro zenon_H191.
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H191); [ zenon_intro zenon_H18b | zenon_intro zenon_H192 ].
% 45.50/45.66 exact (zenon_H18b zenon_H18e).
% 45.50/45.66 apply (zenon_imply_s _ _ zenon_H192); [ zenon_intro zenon_H9b | zenon_intro zenon_H179 ].
% 45.50/45.66 exact (zenon_H9b assumption_18d).
% 45.50/45.66 exact (zenon_H167 zenon_H179).
% 45.50/45.66 apply zenon_H83. apply refl_equal.
% 45.50/45.66 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H5e.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H61.
% 45.50/45.67 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].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H31 zenon_H32).
% 45.50/45.67 apply zenon_H62. apply refl_equal.
% 45.50/45.67 apply zenon_H62. apply refl_equal.
% 45.50/45.67 apply zenon_H72. apply sym_equal. exact zenon_H6b.
% 45.50/45.67 apply zenon_H187. apply sym_equal. exact zenon_H188.
% 45.50/45.67 (* end of lemma zenon_L79_ *)
% 45.50/45.67 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).
% 45.50/45.67 do 2 intro. intros zenon_H35 zenon_H123 zenon_H1a zenon_H1f zenon_H34 zenon_H194.
% 45.50/45.67 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 ].
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H13b. zenon_intro zenon_H167.
% 45.50/45.67 apply (zenon_L78_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.67 cut ((greater (mod2) (mod1)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H194.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact assumption_19.
% 45.50/45.67 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 45.50/45.67 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16c].
% 45.50/45.67 congruence.
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H196); [ zenon_intro zenon_H198 | zenon_intro zenon_H197 ].
% 45.50/45.67 apply zenon_H198. zenon_intro zenon_H146.
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H16c.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H16d.
% 45.50/45.67 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].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H13b zenon_H146).
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 apply zenon_H197. zenon_intro zenon_H179.
% 45.50/45.67 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.50/45.67 generalize (zenon_H18f (mod2)). zenon_intro zenon_H199.
% 45.50/45.67 generalize (zenon_H199 (mod1)). zenon_intro zenon_H19a.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H19a); [ zenon_intro zenon_H167 | zenon_intro zenon_H19b ].
% 45.50/45.67 exact (zenon_H167 zenon_H179).
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H19b); [ zenon_intro zenon_H69 | zenon_intro zenon_H19c ].
% 45.50/45.67 exact (zenon_H69 assumption_19).
% 45.50/45.67 exact (zenon_H194 zenon_H19c).
% 45.50/45.67 apply zenon_H59. apply refl_equal.
% 45.50/45.67 (* end of lemma zenon_L80_ *)
% 45.50/45.67 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).
% 45.50/45.67 do 2 intro. intros zenon_H13b zenon_H35 zenon_H123 zenon_H1a zenon_H1f zenon_H0 zenon_H34 zenon_H167.
% 45.50/45.67 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 ].
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H136. zenon_intro zenon_H18b.
% 45.50/45.67 apply (zenon_L53_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.67 cut ((greater (high) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H167.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact assumption_18d.
% 45.50/45.67 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83].
% 45.50/45.67 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f].
% 45.50/45.67 congruence.
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H18a); [ zenon_intro zenon_H18d | zenon_intro zenon_H18c ].
% 45.50/45.67 apply zenon_H18d. zenon_intro zenon_H137.
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H17f.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H16d.
% 45.50/45.67 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].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H136 zenon_H137).
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 apply zenon_H18c. zenon_intro zenon_H18e.
% 45.50/45.67 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.50/45.67 generalize (zenon_H18f (high)). zenon_intro zenon_H190.
% 45.50/45.67 generalize (zenon_H190 (mod2)). zenon_intro zenon_H191.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H191); [ zenon_intro zenon_H18b | zenon_intro zenon_H192 ].
% 45.50/45.67 exact (zenon_H18b zenon_H18e).
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H192); [ zenon_intro zenon_H9b | zenon_intro zenon_H179 ].
% 45.50/45.67 exact (zenon_H9b assumption_18d).
% 45.50/45.67 exact (zenon_H167 zenon_H179).
% 45.50/45.67 apply zenon_H83. apply refl_equal.
% 45.50/45.67 (* end of lemma zenon_L81_ *)
% 45.50/45.67 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).
% 45.50/45.67 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.
% 45.50/45.67 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H19f | zenon_intro zenon_H1a0 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H19d.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H19f.
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.67 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1].
% 45.50/45.67 congruence.
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1a1.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H11a.
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H1a2 zenon_H19e).
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H1a1 ].
% 45.50/45.67 elim (classic (greater (mod2) (mod2))); [ zenon_intro zenon_H16b | zenon_intro zenon_H153 ].
% 45.50/45.67 cut ((greater (mod2) (mod2)) = (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_E))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1a0.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H16b.
% 45.50/45.67 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1].
% 45.50/45.67 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83].
% 45.50/45.67 congruence.
% 45.50/45.67 apply zenon_H83. apply refl_equal.
% 45.50/45.67 exact (zenon_H1a1 zenon_H1a3).
% 45.50/45.67 apply (zenon_L60_ zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1a1.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H11a.
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H1a2 zenon_H19e).
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 (* end of lemma zenon_L82_ *)
% 45.50/45.67 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).
% 45.50/45.67 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.
% 45.50/45.67 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 ].
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H136. zenon_intro zenon_H18b.
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H167.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H1a4.
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2].
% 45.50/45.67 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].
% 45.50/45.67 congruence.
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 exact (zenon_H1a2 zenon_H19e).
% 45.50/45.67 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H1a1 ].
% 45.50/45.67 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1a5.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H179.
% 45.50/45.67 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1].
% 45.50/45.67 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].
% 45.50/45.67 congruence.
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 exact (zenon_H1a1 zenon_H1a3).
% 45.50/45.67 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 ].
% 45.50/45.67 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H19f | zenon_intro zenon_H1a0 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1a5.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H19f.
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.67 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16c].
% 45.50/45.67 congruence.
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H16c.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H16d.
% 45.50/45.67 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].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b].
% 45.50/45.67 congruence.
% 45.50/45.67 apply (zenon_L53_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1a0.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H1a6.
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2].
% 45.50/45.67 congruence.
% 45.50/45.67 elim (classic ((mod2) = (mod2))); [ zenon_intro zenon_H17b | zenon_intro zenon_H83 ].
% 45.50/45.67 cut (((mod2) = (mod2)) = ((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1a2.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H17b.
% 45.50/45.67 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83].
% 45.50/45.67 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H1a1 zenon_H1a3).
% 45.50/45.67 apply zenon_H83. apply refl_equal.
% 45.50/45.67 apply zenon_H83. apply refl_equal.
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 apply (zenon_L82_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1a1.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H11a.
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H1a2 zenon_H19e).
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 cut ((greater (high) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H167.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact assumption_18d.
% 45.50/45.67 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83].
% 45.50/45.67 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f].
% 45.50/45.67 congruence.
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H18a); [ zenon_intro zenon_H18d | zenon_intro zenon_H18c ].
% 45.50/45.67 apply zenon_H18d. zenon_intro zenon_H137.
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H17f.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H16d.
% 45.50/45.67 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].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H136 zenon_H137).
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 apply zenon_H18c. zenon_intro zenon_H18e.
% 45.50/45.67 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.50/45.67 generalize (zenon_H18f (high)). zenon_intro zenon_H190.
% 45.50/45.67 generalize (zenon_H190 (mod2)). zenon_intro zenon_H191.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H191); [ zenon_intro zenon_H18b | zenon_intro zenon_H192 ].
% 45.50/45.67 exact (zenon_H18b zenon_H18e).
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H192); [ zenon_intro zenon_H9b | zenon_intro zenon_H179 ].
% 45.50/45.67 exact (zenon_H9b assumption_18d).
% 45.50/45.67 exact (zenon_H167 zenon_H179).
% 45.50/45.67 apply zenon_H83. apply refl_equal.
% 45.50/45.67 (* end of lemma zenon_L83_ *)
% 45.50/45.67 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).
% 45.50/45.67 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.
% 45.50/45.67 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H1a1 ].
% 45.50/45.67 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1a5.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H179.
% 45.50/45.67 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1].
% 45.50/45.67 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].
% 45.50/45.67 congruence.
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 exact (zenon_H1a1 zenon_H1a3).
% 45.50/45.67 apply (zenon_L83_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1a1.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H11a.
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H1a2 zenon_H19e).
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 (* end of lemma zenon_L84_ *)
% 45.50/45.67 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).
% 45.50/45.67 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.
% 45.50/45.67 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 ].
% 45.50/45.67 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H17c.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H179.
% 45.50/45.67 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 45.50/45.67 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].
% 45.50/45.67 congruence.
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 apply (zenon_L45_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H167.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H1a4.
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2].
% 45.50/45.67 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].
% 45.50/45.67 congruence.
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 exact (zenon_H1a2 zenon_H19e).
% 45.50/45.67 apply (zenon_L84_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.67 (* end of lemma zenon_L85_ *)
% 45.50/45.67 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).
% 45.50/45.67 do 2 intro. intros zenon_H145 zenon_H127 zenon_H134 zenon_H136 zenon_H13b.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H145); [ zenon_intro zenon_H147 | zenon_intro zenon_H146 ].
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H147); [ zenon_intro zenon_H135 | zenon_intro zenon_H139 ].
% 45.50/45.67 apply (zenon_L67_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.67 exact (zenon_H139 zenon_H127).
% 45.50/45.67 exact (zenon_H13b zenon_H146).
% 45.50/45.67 (* end of lemma zenon_L86_ *)
% 45.50/45.67 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).
% 45.50/45.67 do 2 intro. intros zenon_H0 zenon_H1f zenon_H1a zenon_H1a7 zenon_H136 zenon_H13b zenon_H1a8.
% 45.50/45.67 generalize (zenon_H0 zenon_TT2_la). zenon_intro zenon_H13c.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H13c); [ zenon_intro zenon_H27 | zenon_intro zenon_H13d ].
% 45.50/45.67 exact (zenon_H27 zenon_H1f).
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H13d). zenon_intro zenon_H13f. zenon_intro zenon_H13e.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H13e); [ zenon_intro zenon_H11d | zenon_intro zenon_H140 ].
% 45.50/45.67 apply (zenon_L50_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H140). zenon_intro zenon_H142. zenon_intro zenon_H141.
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H141). zenon_intro zenon_H144. zenon_intro zenon_H143.
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H143). zenon_intro zenon_H145. zenon_intro zenon_H134.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H142); [ zenon_intro zenon_H15c | zenon_intro zenon_H15b ].
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H15c); [ zenon_intro zenon_H135 | zenon_intro zenon_H127 ].
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H144); [ zenon_intro zenon_H15e | zenon_intro zenon_H15d ].
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H15e); [ zenon_intro zenon_H13a | zenon_intro zenon_H127 ].
% 45.50/45.67 exact (zenon_H13a zenon_H135).
% 45.50/45.67 apply (zenon_L67_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.67 exact (zenon_H1a7 zenon_H15d).
% 45.50/45.67 apply (zenon_L86_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.67 exact (zenon_H1a8 zenon_H15b).
% 45.50/45.67 (* end of lemma zenon_L87_ *)
% 45.50/45.67 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).
% 45.50/45.67 do 2 intro. intros zenon_H1a8 zenon_H13b zenon_H136 zenon_H1a zenon_H1f zenon_H0 zenon_H34 zenon_H1a9.
% 45.50/45.67 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 ].
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H1aa). zenon_intro zenon_H1a7. zenon_intro zenon_H194.
% 45.50/45.67 apply (zenon_L87_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.67 cut ((greater (mod1) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1a9.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact assumption_18b.
% 45.50/45.67 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.67 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 45.50/45.67 congruence.
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H1ab); [ zenon_intro zenon_H1ad | zenon_intro zenon_H1ac ].
% 45.50/45.67 apply zenon_H1ad. zenon_intro zenon_H15d.
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H159.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H16d.
% 45.50/45.67 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].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H1a7].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H1a7 zenon_H15d).
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 apply zenon_H1ac. zenon_intro zenon_H19c.
% 45.50/45.67 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.50/45.67 generalize (zenon_H18f (mod1)). zenon_intro zenon_H1ae.
% 45.50/45.67 generalize (zenon_H1ae (low)). zenon_intro zenon_H1af.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H1af); [ zenon_intro zenon_H194 | zenon_intro zenon_H1b0 ].
% 45.50/45.67 exact (zenon_H194 zenon_H19c).
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H1b0); [ zenon_intro zenon_H7f | zenon_intro zenon_H1b1 ].
% 45.50/45.67 exact (zenon_H7f assumption_18b).
% 45.50/45.67 exact (zenon_H1a9 zenon_H1b1).
% 45.50/45.67 apply zenon_H6a. apply refl_equal.
% 45.50/45.67 (* end of lemma zenon_L88_ *)
% 45.50/45.67 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).
% 45.50/45.67 do 2 intro. intros zenon_H34 zenon_H1b2 zenon_H6c zenon_H0 zenon_H1f zenon_H1a zenon_H136 zenon_H13b.
% 45.50/45.67 generalize (definition_smaller (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H176.
% 45.50/45.67 generalize (zenon_H176 (low)). zenon_intro zenon_H1b3.
% 45.50/45.67 apply (zenon_equiv_s _ _ zenon_H1b3); [ zenon_intro zenon_H1b4; zenon_intro zenon_H162 | zenon_intro zenon_H1b2; zenon_intro zenon_H161 ].
% 45.50/45.67 exact (zenon_H1b4 zenon_H1b2).
% 45.50/45.67 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (low))); [ zenon_intro zenon_H15b | zenon_intro zenon_H1a8 ].
% 45.50/45.67 cut ((greater (low) (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = (greater (low) (low))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H6c.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H161.
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1a8].
% 45.50/45.67 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.67 congruence.
% 45.50/45.67 apply zenon_H6a. apply refl_equal.
% 45.50/45.67 exact (zenon_H1a8 zenon_H15b).
% 45.50/45.67 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1a9 ].
% 45.50/45.67 generalize (zenon_H34 (low)). zenon_intro zenon_H7a.
% 45.50/45.67 generalize (zenon_H7a (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H1b5.
% 45.50/45.67 generalize (zenon_H1b5 (low)). zenon_intro zenon_H1b6.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H1b6); [ zenon_intro zenon_H162 | zenon_intro zenon_H1b7 ].
% 45.50/45.67 exact (zenon_H162 zenon_H161).
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H1b7); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H7e ].
% 45.50/45.67 exact (zenon_H1a9 zenon_H1b1).
% 45.50/45.67 exact (zenon_H6c zenon_H7e).
% 45.50/45.67 apply (zenon_L88_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.67 (* end of lemma zenon_L89_ *)
% 45.50/45.67 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).
% 45.50/45.67 do 3 intro. intros zenon_H0 zenon_H1f zenon_H1a7 zenon_H136 zenon_Hec zenon_Hcd zenon_H148 zenon_Hed zenon_H154.
% 45.50/45.67 generalize (zenon_H0 zenon_TT2_la). zenon_intro zenon_H13c.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H13c); [ zenon_intro zenon_H27 | zenon_intro zenon_H13d ].
% 45.50/45.67 exact (zenon_H27 zenon_H1f).
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H13d). zenon_intro zenon_H13f. zenon_intro zenon_H13e.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H13f); [ zenon_intro zenon_H121 | zenon_intro zenon_H15a ].
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H13e); [ zenon_intro zenon_H11d | zenon_intro zenon_H140 ].
% 45.50/45.67 exact (zenon_H11d zenon_H121).
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H140). zenon_intro zenon_H142. zenon_intro zenon_H141.
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H141). zenon_intro zenon_H144. zenon_intro zenon_H143.
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H143). zenon_intro zenon_H145. zenon_intro zenon_H134.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H144); [ zenon_intro zenon_H15e | zenon_intro zenon_H15d ].
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H15e); [ zenon_intro zenon_H13a | zenon_intro zenon_H127 ].
% 45.50/45.67 apply zenon_H13a. zenon_intro zenon_H149.
% 45.50/45.67 apply (zenon_L55_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.67 apply (zenon_L56_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.67 exact (zenon_H1a7 zenon_H15d).
% 45.50/45.67 apply zenon_H154. apply sym_equal. exact zenon_H15a.
% 45.50/45.67 (* end of lemma zenon_L90_ *)
% 45.50/45.67 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).
% 45.50/45.67 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.
% 45.50/45.67 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1ba ].
% 45.50/45.67 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1a9 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1a5.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H1b1.
% 45.50/45.67 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba].
% 45.50/45.67 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].
% 45.50/45.67 congruence.
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 exact (zenon_H1ba zenon_H1b9).
% 45.50/45.67 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 ].
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H1aa). zenon_intro zenon_H1a7. zenon_intro zenon_H194.
% 45.50/45.67 apply (zenon_L90_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.67 cut ((greater (mod1) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1a9.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact assumption_18b.
% 45.50/45.67 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.67 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 45.50/45.67 congruence.
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H1ab); [ zenon_intro zenon_H1ad | zenon_intro zenon_H1ac ].
% 45.50/45.67 apply zenon_H1ad. zenon_intro zenon_H15d.
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H159.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H16d.
% 45.50/45.67 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].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H1a7].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H1a7 zenon_H15d).
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 apply zenon_H1ac. zenon_intro zenon_H19c.
% 45.50/45.67 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.50/45.67 generalize (zenon_H18f (mod1)). zenon_intro zenon_H1ae.
% 45.50/45.67 generalize (zenon_H1ae (low)). zenon_intro zenon_H1af.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H1af); [ zenon_intro zenon_H194 | zenon_intro zenon_H1b0 ].
% 45.50/45.67 exact (zenon_H194 zenon_H19c).
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H1b0); [ zenon_intro zenon_H7f | zenon_intro zenon_H1b1 ].
% 45.50/45.67 exact (zenon_H7f assumption_18b).
% 45.50/45.67 exact (zenon_H1a9 zenon_H1b1).
% 45.50/45.67 apply zenon_H6a. apply refl_equal.
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1ba.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H11a.
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H1bb zenon_H1b8).
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 (* end of lemma zenon_L91_ *)
% 45.50/45.67 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).
% 45.50/45.67 do 2 intro. intros zenon_H162 zenon_H0 zenon_H1f zenon_H155 zenon_H13b zenon_H35 zenon_H123 zenon_H136.
% 45.50/45.67 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H166 | zenon_intro zenon_H154 ].
% 45.50/45.67 cut ((greater (low) (very_low)) = (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT2_la))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H162.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact assumption_18c.
% 45.50/45.67 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H154].
% 45.50/45.67 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.67 congruence.
% 45.50/45.67 apply zenon_H6a. apply refl_equal.
% 45.50/45.67 exact (zenon_H154 zenon_H166).
% 45.50/45.67 generalize (zenon_H0 zenon_TT2_la). zenon_intro zenon_H13c.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H13c); [ zenon_intro zenon_H27 | zenon_intro zenon_H13d ].
% 45.50/45.67 exact (zenon_H27 zenon_H1f).
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H13d). zenon_intro zenon_H13f. zenon_intro zenon_H13e.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H13f); [ zenon_intro zenon_H121 | zenon_intro zenon_H15a ].
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H13e); [ zenon_intro zenon_H11d | zenon_intro zenon_H140 ].
% 45.50/45.67 exact (zenon_H11d zenon_H121).
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H140). zenon_intro zenon_H142. zenon_intro zenon_H141.
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H141). zenon_intro zenon_H144. zenon_intro zenon_H143.
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H143). zenon_intro zenon_H145. zenon_intro zenon_H134.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H142); [ zenon_intro zenon_H15c | zenon_intro zenon_H15b ].
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H15c); [ zenon_intro zenon_H135 | zenon_intro zenon_H127 ].
% 45.50/45.67 apply (zenon_L52_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.67 apply (zenon_L86_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.67 apply zenon_H155. apply sym_equal. exact zenon_H15b.
% 45.50/45.67 apply zenon_H154. apply sym_equal. exact zenon_H15a.
% 45.50/45.67 (* end of lemma zenon_L92_ *)
% 45.50/45.67 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).
% 45.50/45.67 do 2 intro. intros zenon_H0 zenon_H1f zenon_H13b zenon_H35 zenon_H123 zenon_H136 zenon_H34 zenon_H6c zenon_H1b1.
% 45.50/45.67 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 ].
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H1bc). zenon_intro zenon_H155. zenon_intro zenon_H162.
% 45.50/45.67 apply (zenon_L92_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.67 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low)) = (greater (low) (low))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H6c.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H1b1.
% 45.50/45.67 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1a8].
% 45.50/45.67 congruence.
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H1bd); [ zenon_intro zenon_H1bf | zenon_intro zenon_H1be ].
% 45.50/45.67 apply zenon_H1bf. zenon_intro zenon_H160.
% 45.50/45.67 elim (classic ((low) = (low))); [ zenon_intro zenon_H74 | zenon_intro zenon_H6a ].
% 45.50/45.67 cut (((low) = (low)) = ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (low))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1a8.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H74.
% 45.50/45.67 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.67 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H155].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H155 zenon_H160).
% 45.50/45.67 apply zenon_H6a. apply refl_equal.
% 45.50/45.67 apply zenon_H6a. apply refl_equal.
% 45.50/45.67 apply zenon_H1be. zenon_intro zenon_H161.
% 45.50/45.67 generalize (zenon_H34 (low)). zenon_intro zenon_H7a.
% 45.50/45.67 generalize (zenon_H7a (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H1b5.
% 45.50/45.67 generalize (zenon_H1b5 (low)). zenon_intro zenon_H1b6.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H1b6); [ zenon_intro zenon_H162 | zenon_intro zenon_H1b7 ].
% 45.50/45.67 exact (zenon_H162 zenon_H161).
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H1b7); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H7e ].
% 45.50/45.67 exact (zenon_H1a9 zenon_H1b1).
% 45.50/45.67 exact (zenon_H6c zenon_H7e).
% 45.50/45.67 apply zenon_H6a. apply refl_equal.
% 45.50/45.67 (* end of lemma zenon_L93_ *)
% 45.50/45.67 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).
% 45.50/45.67 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.
% 45.50/45.67 generalize (zenon_H172 (low)). zenon_intro zenon_H1c0.
% 45.50/45.67 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H1c1 ].
% 45.50/45.67 apply (zenon_L89_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.67 apply (zenon_or_s _ _ zenon_H1c1); [ zenon_intro zenon_H15b | zenon_intro zenon_H1b1 ].
% 45.50/45.67 elim (classic (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H161 | zenon_intro zenon_H162 ].
% 45.50/45.67 cut ((greater (low) (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = (greater (low) (low))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H6c.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H161.
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1a8].
% 45.50/45.67 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.67 congruence.
% 45.50/45.67 apply zenon_H6a. apply refl_equal.
% 45.50/45.67 exact (zenon_H1a8 zenon_H15b).
% 45.50/45.67 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H166 | zenon_intro zenon_H154 ].
% 45.50/45.67 cut ((greater (low) (very_low)) = (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT2_la))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H162.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact assumption_18c.
% 45.50/45.67 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H154].
% 45.50/45.67 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.67 congruence.
% 45.50/45.67 apply zenon_H6a. apply refl_equal.
% 45.50/45.67 exact (zenon_H154 zenon_H166).
% 45.50/45.67 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H160 | zenon_intro zenon_H155 ].
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H162.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H168.
% 45.50/45.67 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].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1a8].
% 45.50/45.67 congruence.
% 45.50/45.67 elim (classic ((low) = (low))); [ zenon_intro zenon_H74 | zenon_intro zenon_H6a ].
% 45.50/45.67 cut (((low) = (low)) = ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (low))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1a8.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H74.
% 45.50/45.67 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.67 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H155].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H155 zenon_H160).
% 45.50/45.67 apply zenon_H6a. apply refl_equal.
% 45.50/45.67 apply zenon_H6a. apply refl_equal.
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 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 ].
% 45.50/45.67 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1a9 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H169.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H1b1.
% 45.50/45.67 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H155].
% 45.50/45.67 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].
% 45.50/45.67 congruence.
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 apply zenon_H155. apply sym_equal. exact zenon_H15b.
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1a9.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H1a4.
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb].
% 45.50/45.67 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].
% 45.50/45.67 congruence.
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 exact (zenon_H1bb zenon_H1b8).
% 45.50/45.67 apply (zenon_L91_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H155.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H16d.
% 45.50/45.67 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].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1a8].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H1a8 zenon_H15b).
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 apply (zenon_L93_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.67 (* end of lemma zenon_L94_ *)
% 45.50/45.67 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).
% 45.50/45.67 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.
% 45.50/45.67 generalize (meaning_postulate_greater_comparable (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H172.
% 45.50/45.67 generalize (zenon_H172 (mod2)). zenon_intro zenon_H173.
% 45.50/45.67 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H175 | zenon_intro zenon_H174 ].
% 45.50/45.67 generalize (definition_smaller (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H176.
% 45.50/45.67 generalize (zenon_H176 (mod2)). zenon_intro zenon_H177.
% 45.50/45.67 apply (zenon_equiv_s _ _ zenon_H177); [ zenon_intro zenon_H178; zenon_intro zenon_H157 | zenon_intro zenon_H175; zenon_intro zenon_H156 ].
% 45.50/45.67 exact (zenon_H178 zenon_H175).
% 45.50/45.67 elim (classic ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [ zenon_intro zenon_H146 | zenon_intro zenon_H13b ].
% 45.50/45.67 cut ((greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = (greater (mod2) (mod2))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H153.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H156.
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b].
% 45.50/45.67 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83].
% 45.50/45.67 congruence.
% 45.50/45.67 apply zenon_H83. apply refl_equal.
% 45.50/45.67 exact (zenon_H13b zenon_H146).
% 45.50/45.67 apply (zenon_L94_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.67 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H146 | zenon_intro zenon_H179 ].
% 45.50/45.67 apply (zenon_L59_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.67 exact (zenon_H167 zenon_H179).
% 45.50/45.67 (* end of lemma zenon_L95_ *)
% 45.50/45.67 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).
% 45.50/45.67 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.
% 45.50/45.67 generalize (zenon_Hf3 zenon_TT0_hz). zenon_intro zenon_Hf4.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcd ].
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ].
% 45.50/45.67 exact (zenon_H27 zenon_H1f).
% 45.50/45.67 exact (zenon_Hf2 zenon_Hec).
% 45.50/45.67 generalize (assumption_15 zenon_TX_y). zenon_intro zenon_Hed.
% 45.50/45.67 generalize (meaning_postulate_greater_strict (low)). zenon_intro zenon_H80.
% 45.50/45.67 generalize (zenon_H80 (low)). zenon_intro zenon_H81.
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H81); [ zenon_intro zenon_H6c | zenon_intro zenon_H6c ].
% 45.50/45.67 apply (zenon_L95_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.67 apply (zenon_L95_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.67 (* end of lemma zenon_L96_ *)
% 45.50/45.67 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).
% 45.50/45.67 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.
% 45.50/45.67 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1c4 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1c2.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H1c3.
% 45.50/45.67 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].
% 45.50/45.67 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 45.50/45.67 congruence.
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H5e.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H61.
% 45.50/45.67 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].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H31 zenon_H32).
% 45.50/45.67 apply zenon_H62. apply refl_equal.
% 45.50/45.67 apply zenon_H62. apply refl_equal.
% 45.50/45.67 apply zenon_H62. apply refl_equal.
% 45.50/45.67 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H115 | zenon_intro zenon_H5e ].
% 45.50/45.67 elim (classic (greater (mod2) (mod2))); [ zenon_intro zenon_H16b | zenon_intro zenon_H153 ].
% 45.50/45.67 cut ((greater (mod2) (mod2)) = (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1c4.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H16b.
% 45.50/45.67 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 45.50/45.67 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83].
% 45.50/45.67 congruence.
% 45.50/45.67 apply zenon_H83. apply refl_equal.
% 45.50/45.67 exact (zenon_H5e zenon_H115).
% 45.50/45.67 apply (zenon_L96_ zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H5e.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H61.
% 45.50/45.67 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].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H31 zenon_H32).
% 45.50/45.67 apply zenon_H62. apply refl_equal.
% 45.50/45.67 apply zenon_H62. apply refl_equal.
% 45.50/45.67 (* end of lemma zenon_L97_ *)
% 45.50/45.67 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).
% 45.50/45.67 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.
% 45.50/45.67 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H115 | zenon_intro zenon_H5e ].
% 45.50/45.67 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H17c.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H179.
% 45.50/45.67 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 45.50/45.67 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].
% 45.50/45.67 congruence.
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 exact (zenon_H5e zenon_H115).
% 45.50/45.67 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 ].
% 45.50/45.67 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1c4 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H17c.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H1c3.
% 45.50/45.67 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].
% 45.50/45.67 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16c].
% 45.50/45.67 congruence.
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H16c.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H16d.
% 45.50/45.67 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].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b].
% 45.50/45.67 congruence.
% 45.50/45.67 apply (zenon_L81_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 apply zenon_H62. apply refl_equal.
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1c4.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H1c5.
% 45.50/45.67 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].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31].
% 45.50/45.67 congruence.
% 45.50/45.67 elim (classic ((mod2) = (mod2))); [ zenon_intro zenon_H17b | zenon_intro zenon_H83 ].
% 45.50/45.67 cut (((mod2) = (mod2)) = ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H31.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H17b.
% 45.50/45.67 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83].
% 45.50/45.67 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H5e zenon_H115).
% 45.50/45.67 apply zenon_H83. apply refl_equal.
% 45.50/45.67 apply zenon_H83. apply refl_equal.
% 45.50/45.67 apply zenon_H62. apply refl_equal.
% 45.50/45.67 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 ].
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H136. zenon_intro zenon_H18b.
% 45.50/45.67 apply (zenon_L97_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.67 cut ((greater (high) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H167.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact assumption_18d.
% 45.50/45.67 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83].
% 45.50/45.67 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f].
% 45.50/45.67 congruence.
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H18a); [ zenon_intro zenon_H18d | zenon_intro zenon_H18c ].
% 45.50/45.67 apply zenon_H18d. zenon_intro zenon_H137.
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H17f.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H16d.
% 45.50/45.67 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].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H136 zenon_H137).
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 apply zenon_H18c. zenon_intro zenon_H18e.
% 45.50/45.67 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.50/45.67 generalize (zenon_H18f (high)). zenon_intro zenon_H190.
% 45.50/45.67 generalize (zenon_H190 (mod2)). zenon_intro zenon_H191.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H191); [ zenon_intro zenon_H18b | zenon_intro zenon_H192 ].
% 45.50/45.67 exact (zenon_H18b zenon_H18e).
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H192); [ zenon_intro zenon_H9b | zenon_intro zenon_H179 ].
% 45.50/45.67 exact (zenon_H9b assumption_18d).
% 45.50/45.67 exact (zenon_H167 zenon_H179).
% 45.50/45.67 apply zenon_H83. apply refl_equal.
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H5e.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H61.
% 45.50/45.67 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].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H31 zenon_H32).
% 45.50/45.67 apply zenon_H62. apply refl_equal.
% 45.50/45.67 apply zenon_H62. apply refl_equal.
% 45.50/45.67 (* end of lemma zenon_L98_ *)
% 45.50/45.67 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).
% 45.50/45.67 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.
% 45.50/45.67 generalize (zenon_Hf3 zenon_TT0_hz). zenon_intro zenon_Hf4.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcd ].
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ].
% 45.50/45.67 exact (zenon_H27 zenon_H1f).
% 45.50/45.67 exact (zenon_Hf2 zenon_Hec).
% 45.50/45.67 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ].
% 45.50/45.67 exact (zenon_H27 zenon_H1f).
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H8b); [ zenon_intro zenon_H24 | zenon_intro zenon_H188 ].
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ].
% 45.50/45.67 exact (zenon_H1e zenon_H24).
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d.
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f.
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H30. zenon_intro zenon_H28.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H8e); [ zenon_intro zenon_H91 | zenon_intro zenon_H6b ].
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ].
% 45.50/45.67 apply (zenon_L31_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ].
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ].
% 45.50/45.67 apply (zenon_L31_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.67 exact (zenon_H2e zenon_H29).
% 45.50/45.67 apply (zenon_L98_ zenon_TT1_bg zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.67 apply zenon_H72. apply sym_equal. exact zenon_H6b.
% 45.50/45.67 apply zenon_H187. apply sym_equal. exact zenon_H188.
% 45.50/45.67 (* end of lemma zenon_L99_ *)
% 45.50/45.67 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).
% 45.50/45.67 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.
% 45.50/45.67 generalize (meaning_postulate_greater_comparable (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H172.
% 45.50/45.67 apply (zenon_L94_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.67 (* end of lemma zenon_L100_ *)
% 45.50/45.67 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).
% 45.50/45.67 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.
% 45.50/45.67 generalize (zenon_Hf3 zenon_TT0_hz). zenon_intro zenon_Hf4.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcd ].
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ].
% 45.50/45.67 exact (zenon_H27 zenon_H1f).
% 45.50/45.67 exact (zenon_Hf2 zenon_Hec).
% 45.50/45.67 generalize (assumption_15 zenon_TX_y). zenon_intro zenon_Hed.
% 45.50/45.67 generalize (meaning_postulate_greater_strict (low)). zenon_intro zenon_H80.
% 45.50/45.67 generalize (zenon_H80 (low)). zenon_intro zenon_H81.
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H81); [ zenon_intro zenon_H6c | zenon_intro zenon_H6c ].
% 45.50/45.67 apply (zenon_L100_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.67 apply (zenon_L100_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.67 (* end of lemma zenon_L101_ *)
% 45.50/45.67 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).
% 45.50/45.67 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.
% 45.50/45.67 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 ].
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H136. zenon_intro zenon_H18b.
% 45.50/45.67 apply (zenon_L101_ zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.67 cut ((greater (high) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H167.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact assumption_18d.
% 45.50/45.67 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83].
% 45.50/45.67 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f].
% 45.50/45.67 congruence.
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H18a); [ zenon_intro zenon_H18d | zenon_intro zenon_H18c ].
% 45.50/45.67 apply zenon_H18d. zenon_intro zenon_H137.
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H17f.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H16d.
% 45.50/45.67 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].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H136 zenon_H137).
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 apply zenon_H18c. zenon_intro zenon_H18e.
% 45.50/45.67 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.50/45.67 generalize (zenon_H18f (high)). zenon_intro zenon_H190.
% 45.50/45.67 generalize (zenon_H190 (mod2)). zenon_intro zenon_H191.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H191); [ zenon_intro zenon_H18b | zenon_intro zenon_H192 ].
% 45.50/45.67 exact (zenon_H18b zenon_H18e).
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H192); [ zenon_intro zenon_H9b | zenon_intro zenon_H179 ].
% 45.50/45.67 exact (zenon_H9b assumption_18d).
% 45.50/45.67 exact (zenon_H167 zenon_H179).
% 45.50/45.67 apply zenon_H83. apply refl_equal.
% 45.50/45.67 (* end of lemma zenon_L102_ *)
% 45.50/45.67 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).
% 45.50/45.67 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.
% 45.50/45.67 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 ].
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H13b. zenon_intro zenon_H167.
% 45.50/45.67 apply (zenon_L102_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.67 cut ((greater (mod2) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1a9.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact assumption_18e.
% 45.50/45.67 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.67 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16c].
% 45.50/45.67 congruence.
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H196); [ zenon_intro zenon_H198 | zenon_intro zenon_H197 ].
% 45.50/45.67 apply zenon_H198. zenon_intro zenon_H146.
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H16c.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H16d.
% 45.50/45.67 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].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H13b zenon_H146).
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 apply zenon_H197. zenon_intro zenon_H179.
% 45.50/45.67 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.50/45.67 generalize (zenon_H18f (mod2)). zenon_intro zenon_H199.
% 45.50/45.67 generalize (zenon_H199 (low)). zenon_intro zenon_H1c6.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H1c6); [ zenon_intro zenon_H167 | zenon_intro zenon_H1c7 ].
% 45.50/45.67 exact (zenon_H167 zenon_H179).
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H1c7); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H1b1 ].
% 45.50/45.67 exact (zenon_Hc2 assumption_18e).
% 45.50/45.67 exact (zenon_H1a9 zenon_H1b1).
% 45.50/45.67 apply zenon_H6a. apply refl_equal.
% 45.50/45.67 (* end of lemma zenon_L103_ *)
% 45.50/45.67 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).
% 45.50/45.67 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.
% 45.50/45.67 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1ba ].
% 45.50/45.67 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1a9 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1a5.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H1b1.
% 45.50/45.67 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba].
% 45.50/45.67 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].
% 45.50/45.67 congruence.
% 45.50/45.67 apply zenon_H16a. apply refl_equal.
% 45.50/45.67 exact (zenon_H1ba zenon_H1b9).
% 45.50/45.67 apply (zenon_L103_ zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1ba.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H11a.
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H1bb zenon_H1b8).
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 (* end of lemma zenon_L104_ *)
% 45.50/45.67 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).
% 45.50/45.67 do 1 intro. intros zenon_H111 zenon_H1f zenon_H1a.
% 45.50/45.67 apply zenon_H111. zenon_intro zenon_H1c8.
% 45.50/45.67 generalize (assumption_1 zenon_TX_y). zenon_intro zenon_H22.
% 45.50/45.67 generalize (zenon_H22 zenon_E). zenon_intro zenon_H1c9.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H1c9); [ zenon_intro zenon_H25 | zenon_intro zenon_H112 ].
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H25); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ].
% 45.50/45.67 exact (zenon_H27 zenon_H1f).
% 45.50/45.67 apply zenon_H26. zenon_intro zenon_H19.
% 45.50/45.67 apply (zenon_L2_ zenon_TX_y); trivial.
% 45.50/45.67 exact (zenon_H112 zenon_H1c8).
% 45.50/45.67 (* end of lemma zenon_L105_ *)
% 45.50/45.67 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).
% 45.50/45.67 do 1 intro. intros zenon_H116 zenon_H34 zenon_H1ca.
% 45.50/45.67 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 ].
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H1cb). zenon_intro zenon_H11c. zenon_intro zenon_H1cd.
% 45.50/45.67 exact (zenon_H11c zenon_H116).
% 45.50/45.67 cut ((greater (high) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (mod2))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1ca.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact assumption_18d.
% 45.50/45.67 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83].
% 45.50/45.67 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H119].
% 45.50/45.67 congruence.
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H1cc); [ zenon_intro zenon_H1cf | zenon_intro zenon_H1ce ].
% 45.50/45.67 apply zenon_H1cf. zenon_intro zenon_H116.
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H119.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H11a.
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H11c zenon_H116).
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 apply zenon_H1ce. zenon_intro zenon_H1d0.
% 45.50/45.67 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H1d1.
% 45.50/45.67 generalize (zenon_H1d1 (high)). zenon_intro zenon_H1d2.
% 45.50/45.67 generalize (zenon_H1d2 (mod2)). zenon_intro zenon_H1d3.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H1d3); [ zenon_intro zenon_H1cd | zenon_intro zenon_H1d4 ].
% 45.50/45.67 exact (zenon_H1cd zenon_H1d0).
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H1d4); [ zenon_intro zenon_H9b | zenon_intro zenon_H1d5 ].
% 45.50/45.67 exact (zenon_H9b assumption_18d).
% 45.50/45.67 exact (zenon_H1ca zenon_H1d5).
% 45.50/45.67 apply zenon_H83. apply refl_equal.
% 45.50/45.67 (* end of lemma zenon_L106_ *)
% 45.50/45.67 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).
% 45.50/45.67 do 1 intro. intros zenon_H116 zenon_H34 zenon_H1d6.
% 45.50/45.67 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 ].
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H1d7). zenon_intro zenon_H1a2. zenon_intro zenon_H1ca.
% 45.50/45.67 apply (zenon_L106_ zenon_TX_y); trivial.
% 45.50/45.67 cut ((greater (mod2) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (low))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1d6.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact assumption_18e.
% 45.50/45.67 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.67 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1].
% 45.50/45.67 congruence.
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H1d8); [ zenon_intro zenon_H1da | zenon_intro zenon_H1d9 ].
% 45.50/45.67 apply zenon_H1da. zenon_intro zenon_H19e.
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1a1.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H11a.
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H1a2 zenon_H19e).
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 apply zenon_H1d9. zenon_intro zenon_H1d5.
% 45.50/45.67 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H1d1.
% 45.50/45.67 generalize (zenon_H1d1 (mod2)). zenon_intro zenon_H1db.
% 45.50/45.67 generalize (zenon_H1db (low)). zenon_intro zenon_H1dc.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H1dc); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1dd ].
% 45.50/45.67 exact (zenon_H1ca zenon_H1d5).
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H1dd); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H1de ].
% 45.50/45.67 exact (zenon_Hc2 assumption_18e).
% 45.50/45.67 exact (zenon_H1d6 zenon_H1de).
% 45.50/45.67 apply zenon_H6a. apply refl_equal.
% 45.50/45.67 (* end of lemma zenon_L107_ *)
% 45.50/45.67 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).
% 45.50/45.67 do 1 intro. intros zenon_H116 zenon_H34 zenon_H1df zenon_H1e0.
% 45.50/45.67 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e2 ].
% 45.50/45.67 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (very_low))); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H1e4 ].
% 45.50/45.67 cut ((greater (hazard_of_mortality zenon_TX_y zenon_E) (very_low)) = (greater (very_low) (very_low))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1df.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H1e3.
% 45.50/45.67 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5].
% 45.50/45.67 congruence.
% 45.50/45.67 elim (classic ((very_low) = (very_low))); [ zenon_intro zenon_H1e6 | zenon_intro zenon_Hf5 ].
% 45.50/45.67 cut (((very_low) = (very_low)) = ((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1e5.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H1e6.
% 45.50/45.67 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5].
% 45.50/45.67 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1e2].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H1e2 zenon_H1e1).
% 45.50/45.67 apply zenon_Hf5. apply refl_equal.
% 45.50/45.67 apply zenon_Hf5. apply refl_equal.
% 45.50/45.67 apply zenon_Hf5. apply refl_equal.
% 45.50/45.67 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 ].
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H1e7). zenon_intro zenon_H1bb. zenon_intro zenon_H1d6.
% 45.50/45.67 apply (zenon_L107_ zenon_TX_y); trivial.
% 45.50/45.67 cut ((greater (low) (very_low)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (very_low))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1e4.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact assumption_18c.
% 45.50/45.67 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5].
% 45.50/45.67 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba].
% 45.50/45.67 congruence.
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H1e8); [ zenon_intro zenon_H1ea | zenon_intro zenon_H1e9 ].
% 45.50/45.67 apply zenon_H1ea. zenon_intro zenon_H1b8.
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1ba.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H11a.
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H1bb zenon_H1b8).
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 apply zenon_H1e9. zenon_intro zenon_H1de.
% 45.50/45.67 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H1d1.
% 45.50/45.67 generalize (zenon_H1d1 (low)). zenon_intro zenon_H1eb.
% 45.50/45.67 generalize (zenon_H1eb (very_low)). zenon_intro zenon_H1ec.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H1ec); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H1ed ].
% 45.50/45.67 exact (zenon_H1d6 zenon_H1de).
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H1ed); [ zenon_intro zenon_Hff | zenon_intro zenon_H1e3 ].
% 45.50/45.67 exact (zenon_Hff assumption_18c).
% 45.50/45.67 exact (zenon_H1e4 zenon_H1e3).
% 45.50/45.67 apply zenon_Hf5. apply refl_equal.
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1e2.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H11a.
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H1e5 zenon_H1e0).
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 (* end of lemma zenon_L108_ *)
% 45.50/45.67 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).
% 45.50/45.67 do 1 intro. intros zenon_H116 zenon_H1ee zenon_H34 zenon_H1e0.
% 45.50/45.67 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e2 ].
% 45.50/45.67 elim (classic (greater (very_low) (very_low))); [ zenon_intro zenon_H1ef | zenon_intro zenon_H1df ].
% 45.50/45.67 elim (classic (greater (very_low) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H1f1 ].
% 45.50/45.67 cut ((greater (very_low) (hazard_of_mortality zenon_TX_y zenon_E)) = (greater (very_low) (high))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1ee.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H1f0.
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c].
% 45.50/45.67 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5].
% 45.50/45.67 congruence.
% 45.50/45.67 apply zenon_Hf5. apply refl_equal.
% 45.50/45.67 exact (zenon_H11c zenon_H116).
% 45.50/45.67 cut ((greater (very_low) (very_low)) = (greater (very_low) (hazard_of_mortality zenon_TX_y zenon_E))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1f1.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H1ef.
% 45.50/45.67 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1e2].
% 45.50/45.67 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5].
% 45.50/45.67 congruence.
% 45.50/45.67 apply zenon_Hf5. apply refl_equal.
% 45.50/45.67 exact (zenon_H1e2 zenon_H1e1).
% 45.50/45.67 apply (zenon_L108_ zenon_TX_y); trivial.
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1e2.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H11a.
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H1e5 zenon_H1e0).
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 (* end of lemma zenon_L109_ *)
% 45.50/45.67 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).
% 45.50/45.67 do 0 intro. intros zenon_H34 zenon_H1f2.
% 45.50/45.67 elim (classic ((~((high) = (mod2)))/\(~(greater (high) (mod2))))); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H1f4 ].
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H1f3). zenon_intro zenon_H1f5. zenon_intro zenon_H9b.
% 45.50/45.67 exact (zenon_H9b assumption_18d).
% 45.50/45.67 cut ((greater (mod2) (low)) = (greater (high) (low))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1f2.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact assumption_18e.
% 45.50/45.67 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.67 cut (((mod2) = (high))); [idtac | apply NNPP; zenon_intro zenon_H1f6].
% 45.50/45.67 congruence.
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H1f4); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H1f7 ].
% 45.50/45.67 apply zenon_H1f8. zenon_intro zenon_H1f9.
% 45.50/45.67 elim (classic ((high) = (high))); [ zenon_intro zenon_H180 | zenon_intro zenon_H113 ].
% 45.50/45.67 cut (((high) = (high)) = ((mod2) = (high))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1f6.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H180.
% 45.50/45.67 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113].
% 45.50/45.67 cut (((high) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1f5].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H1f5 zenon_H1f9).
% 45.50/45.67 apply zenon_H113. apply refl_equal.
% 45.50/45.67 apply zenon_H113. apply refl_equal.
% 45.50/45.67 apply zenon_H1f7. zenon_intro assumption_18d.
% 45.50/45.67 generalize (zenon_H34 (high)). zenon_intro zenon_H1fa.
% 45.50/45.67 generalize (zenon_H1fa (mod2)). zenon_intro zenon_H1fb.
% 45.50/45.67 generalize (zenon_H1fb (low)). zenon_intro zenon_H1fc.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H1fc); [ zenon_intro zenon_H9b | zenon_intro zenon_H1fd ].
% 45.50/45.67 exact (zenon_H9b assumption_18d).
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H1fd); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H1fe ].
% 45.50/45.67 exact (zenon_Hc2 assumption_18e).
% 45.50/45.67 exact (zenon_H1f2 zenon_H1fe).
% 45.50/45.67 apply zenon_H6a. apply refl_equal.
% 45.50/45.67 (* end of lemma zenon_L110_ *)
% 45.50/45.67 assert (zenon_L111_ : (~(greater (low) (high))) -> ((very_low) = (high)) -> False).
% 45.50/45.67 do 0 intro. intros zenon_H1ff zenon_H200.
% 45.50/45.67 cut ((greater (low) (very_low)) = (greater (low) (high))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1ff.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact assumption_18c.
% 45.50/45.67 cut (((very_low) = (high))); [idtac | apply NNPP; zenon_intro zenon_H201].
% 45.50/45.67 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.67 congruence.
% 45.50/45.67 apply zenon_H6a. apply refl_equal.
% 45.50/45.67 exact (zenon_H201 zenon_H200).
% 45.50/45.67 (* end of lemma zenon_L111_ *)
% 45.50/45.67 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).
% 45.50/45.67 do 0 intro. intros zenon_H34 zenon_H202 zenon_H200.
% 45.50/45.67 generalize (zenon_H202 (low)). zenon_intro zenon_H203.
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H203); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H1ff ].
% 45.50/45.67 apply (zenon_L110_); trivial.
% 45.50/45.67 apply (zenon_L111_); trivial.
% 45.50/45.67 (* end of lemma zenon_L112_ *)
% 45.50/45.67 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).
% 45.50/45.67 do 0 intro. intros zenon_H34 zenon_H200.
% 45.50/45.67 generalize (meaning_postulate_greater_strict (high)). zenon_intro zenon_H202.
% 45.50/45.67 apply (zenon_L112_); trivial.
% 45.50/45.67 (* end of lemma zenon_L113_ *)
% 45.50/45.67 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).
% 45.50/45.67 do 0 intro. intros zenon_H34 zenon_H1ff zenon_H204.
% 45.50/45.67 elim (classic ((~((low) = (very_low)))/\(~(greater (low) (very_low))))); [ zenon_intro zenon_H205 | zenon_intro zenon_H206 ].
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H205). zenon_intro zenon_H207. zenon_intro zenon_Hff.
% 45.50/45.67 exact (zenon_Hff assumption_18c).
% 45.50/45.67 cut ((greater (very_low) (high)) = (greater (low) (high))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1ff.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H204.
% 45.50/45.67 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113].
% 45.50/45.67 cut (((very_low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H208].
% 45.50/45.67 congruence.
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H206); [ zenon_intro zenon_H20a | zenon_intro zenon_H209 ].
% 45.50/45.67 apply zenon_H20a. zenon_intro zenon_H20b.
% 45.50/45.67 elim (classic ((low) = (low))); [ zenon_intro zenon_H74 | zenon_intro zenon_H6a ].
% 45.50/45.67 cut (((low) = (low)) = ((very_low) = (low))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H208.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H74.
% 45.50/45.67 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.67 cut (((low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H207].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H207 zenon_H20b).
% 45.50/45.67 apply zenon_H6a. apply refl_equal.
% 45.50/45.67 apply zenon_H6a. apply refl_equal.
% 45.50/45.67 apply zenon_H209. zenon_intro assumption_18c.
% 45.50/45.67 generalize (zenon_H34 (low)). zenon_intro zenon_H7a.
% 45.50/45.67 generalize (zenon_H7a (very_low)). zenon_intro zenon_H20c.
% 45.50/45.67 generalize (zenon_H20c (high)). zenon_intro zenon_H20d.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H20d); [ zenon_intro zenon_Hff | zenon_intro zenon_H20e ].
% 45.50/45.67 exact (zenon_Hff assumption_18c).
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H20e); [ zenon_intro zenon_H1ee | zenon_intro zenon_H20f ].
% 45.50/45.67 exact (zenon_H1ee zenon_H204).
% 45.50/45.67 exact (zenon_H1ff zenon_H20f).
% 45.50/45.67 apply zenon_H113. apply refl_equal.
% 45.50/45.67 (* end of lemma zenon_L114_ *)
% 45.50/45.67 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).
% 45.50/45.67 do 0 intro. intros zenon_H34 zenon_H202 zenon_H204.
% 45.50/45.67 generalize (zenon_H202 (low)). zenon_intro zenon_H203.
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H203); [ zenon_intro zenon_H1f2 | zenon_intro zenon_H1ff ].
% 45.50/45.67 apply (zenon_L110_); trivial.
% 45.50/45.67 apply (zenon_L114_); trivial.
% 45.50/45.67 (* end of lemma zenon_L115_ *)
% 45.50/45.67 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).
% 45.50/45.67 do 0 intro. intros zenon_H34 zenon_H204.
% 45.50/45.67 generalize (meaning_postulate_greater_strict (high)). zenon_intro zenon_H202.
% 45.50/45.67 apply (zenon_L115_); trivial.
% 45.50/45.67 (* end of lemma zenon_L116_ *)
% 45.50/45.67 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).
% 45.50/45.67 do 1 intro. intros zenon_H34 zenon_H210 zenon_H116 zenon_H1e0.
% 45.50/45.67 generalize (zenon_H210 (high)). zenon_intro zenon_H211.
% 45.50/45.67 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H213 | zenon_intro zenon_H212 ].
% 45.50/45.67 generalize (definition_smaller (very_low)). zenon_intro zenon_H214.
% 45.50/45.67 generalize (zenon_H214 (high)). zenon_intro zenon_H215.
% 45.50/45.67 apply (zenon_equiv_s _ _ zenon_H215); [ zenon_intro zenon_H218; zenon_intro zenon_H217 | zenon_intro zenon_H213; zenon_intro zenon_H216 ].
% 45.50/45.67 exact (zenon_H218 zenon_H213).
% 45.50/45.67 generalize (meaning_postulate_greater_strict (high)). zenon_intro zenon_H202.
% 45.50/45.67 generalize (zenon_H202 (very_low)). zenon_intro zenon_H219.
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H219); [ zenon_intro zenon_H217 | zenon_intro zenon_H1ee ].
% 45.50/45.67 exact (zenon_H217 zenon_H216).
% 45.50/45.67 apply (zenon_L109_ zenon_TX_y); trivial.
% 45.50/45.67 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H200 | zenon_intro zenon_H204 ].
% 45.50/45.67 apply (zenon_L113_); trivial.
% 45.50/45.67 apply (zenon_L116_); trivial.
% 45.50/45.67 (* end of lemma zenon_L117_ *)
% 45.50/45.67 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).
% 45.50/45.67 do 1 intro. intros zenon_H181 zenon_H182 zenon_H183 zenon_H34 zenon_H1e0.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H181); [ zenon_intro zenon_H184 | zenon_intro zenon_H116 ].
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H184); [ zenon_intro zenon_H186 | zenon_intro zenon_H185 ].
% 45.50/45.67 exact (zenon_H186 zenon_H183).
% 45.50/45.67 exact (zenon_H185 zenon_H182).
% 45.50/45.67 generalize (meaning_postulate_greater_comparable (very_low)). zenon_intro zenon_H210.
% 45.50/45.67 apply (zenon_L117_ zenon_TX_y); trivial.
% 45.50/45.67 (* end of lemma zenon_L118_ *)
% 45.50/45.67 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).
% 45.50/45.67 do 1 intro. intros zenon_H21a zenon_H34 zenon_H1d6.
% 45.50/45.67 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 ].
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H21b). zenon_intro zenon_H21e. zenon_intro zenon_H21d.
% 45.50/45.67 exact (zenon_H21e zenon_H21a).
% 45.50/45.67 cut ((greater (mod1) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (low))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1d6.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact assumption_18b.
% 45.50/45.67 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.67 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f].
% 45.50/45.67 congruence.
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H21c); [ zenon_intro zenon_H221 | zenon_intro zenon_H220 ].
% 45.50/45.67 apply zenon_H221. zenon_intro zenon_H21a.
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H21f.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H11a.
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H21e zenon_H21a).
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 apply zenon_H220. zenon_intro zenon_H222.
% 45.50/45.67 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H1d1.
% 45.50/45.67 generalize (zenon_H1d1 (mod1)). zenon_intro zenon_H223.
% 45.50/45.67 generalize (zenon_H223 (low)). zenon_intro zenon_H224.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H224); [ zenon_intro zenon_H21d | zenon_intro zenon_H225 ].
% 45.50/45.67 exact (zenon_H21d zenon_H222).
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H225); [ zenon_intro zenon_H7f | zenon_intro zenon_H1de ].
% 45.50/45.67 exact (zenon_H7f assumption_18b).
% 45.50/45.67 exact (zenon_H1d6 zenon_H1de).
% 45.50/45.67 apply zenon_H6a. apply refl_equal.
% 45.50/45.67 (* end of lemma zenon_L119_ *)
% 45.50/45.67 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).
% 45.50/45.67 do 1 intro. intros zenon_H21a zenon_H34 zenon_H1df zenon_H1e0.
% 45.50/45.67 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e2 ].
% 45.50/45.67 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (very_low))); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H1e4 ].
% 45.50/45.67 cut ((greater (hazard_of_mortality zenon_TX_y zenon_E) (very_low)) = (greater (very_low) (very_low))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1df.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H1e3.
% 45.50/45.67 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5].
% 45.50/45.67 congruence.
% 45.50/45.67 elim (classic ((very_low) = (very_low))); [ zenon_intro zenon_H1e6 | zenon_intro zenon_Hf5 ].
% 45.50/45.67 cut (((very_low) = (very_low)) = ((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1e5.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H1e6.
% 45.50/45.67 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5].
% 45.50/45.67 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1e2].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H1e2 zenon_H1e1).
% 45.50/45.67 apply zenon_Hf5. apply refl_equal.
% 45.50/45.67 apply zenon_Hf5. apply refl_equal.
% 45.50/45.67 apply zenon_Hf5. apply refl_equal.
% 45.50/45.67 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 ].
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H1e7). zenon_intro zenon_H1bb. zenon_intro zenon_H1d6.
% 45.50/45.67 apply (zenon_L119_ zenon_TX_y); trivial.
% 45.50/45.67 cut ((greater (low) (very_low)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (very_low))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1e4.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact assumption_18c.
% 45.50/45.67 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5].
% 45.50/45.67 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba].
% 45.50/45.67 congruence.
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H1e8); [ zenon_intro zenon_H1ea | zenon_intro zenon_H1e9 ].
% 45.50/45.67 apply zenon_H1ea. zenon_intro zenon_H1b8.
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1ba.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H11a.
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H1bb zenon_H1b8).
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 apply zenon_H1e9. zenon_intro zenon_H1de.
% 45.50/45.67 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H1d1.
% 45.50/45.67 generalize (zenon_H1d1 (low)). zenon_intro zenon_H1eb.
% 45.50/45.67 generalize (zenon_H1eb (very_low)). zenon_intro zenon_H1ec.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H1ec); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H1ed ].
% 45.50/45.67 exact (zenon_H1d6 zenon_H1de).
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H1ed); [ zenon_intro zenon_Hff | zenon_intro zenon_H1e3 ].
% 45.50/45.67 exact (zenon_Hff assumption_18c).
% 45.50/45.67 exact (zenon_H1e4 zenon_H1e3).
% 45.50/45.67 apply zenon_Hf5. apply refl_equal.
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1e2.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H11a.
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H1e5 zenon_H1e0).
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 (* end of lemma zenon_L120_ *)
% 45.50/45.67 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).
% 45.50/45.67 do 1 intro. intros zenon_H34 zenon_H6c zenon_H21a zenon_H1e0.
% 45.50/45.67 elim (classic (greater (very_low) (low))); [ zenon_intro zenon_H226 | zenon_intro zenon_H227 ].
% 45.50/45.67 generalize (zenon_H34 (low)). zenon_intro zenon_H7a.
% 45.50/45.67 generalize (zenon_H7a (very_low)). zenon_intro zenon_H20c.
% 45.50/45.67 generalize (zenon_H20c (low)). zenon_intro zenon_H228.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H228); [ zenon_intro zenon_Hff | zenon_intro zenon_H229 ].
% 45.50/45.67 exact (zenon_Hff assumption_18c).
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H229); [ zenon_intro zenon_H227 | zenon_intro zenon_H7e ].
% 45.50/45.67 exact (zenon_H227 zenon_H226).
% 45.50/45.67 exact (zenon_H6c zenon_H7e).
% 45.50/45.67 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e2 ].
% 45.50/45.67 elim (classic (greater (very_low) (very_low))); [ zenon_intro zenon_H1ef | zenon_intro zenon_H1df ].
% 45.50/45.67 elim (classic (greater (very_low) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H1f1 ].
% 45.50/45.67 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (low))); [ zenon_intro zenon_H1de | zenon_intro zenon_H1d6 ].
% 45.50/45.67 generalize (zenon_H34 (very_low)). zenon_intro zenon_H22a.
% 45.50/45.67 generalize (zenon_H22a (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H22b.
% 45.50/45.67 generalize (zenon_H22b (low)). zenon_intro zenon_H22c.
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H22c); [ zenon_intro zenon_H1f1 | zenon_intro zenon_H22d ].
% 45.50/45.67 exact (zenon_H1f1 zenon_H1f0).
% 45.50/45.67 apply (zenon_imply_s _ _ zenon_H22d); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H226 ].
% 45.50/45.67 exact (zenon_H1d6 zenon_H1de).
% 45.50/45.67 exact (zenon_H227 zenon_H226).
% 45.50/45.67 apply (zenon_L119_ zenon_TX_y); trivial.
% 45.50/45.67 cut ((greater (very_low) (very_low)) = (greater (very_low) (hazard_of_mortality zenon_TX_y zenon_E))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1f1.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H1ef.
% 45.50/45.67 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1e2].
% 45.50/45.67 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5].
% 45.50/45.67 congruence.
% 45.50/45.67 apply zenon_Hf5. apply refl_equal.
% 45.50/45.67 exact (zenon_H1e2 zenon_H1e1).
% 45.50/45.67 apply (zenon_L120_ zenon_TX_y); trivial.
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1e2.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H11a.
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H1e5 zenon_H1e0).
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 apply zenon_H11b. apply refl_equal.
% 45.50/45.67 (* end of lemma zenon_L121_ *)
% 45.50/45.67 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).
% 45.50/45.67 do 1 intro. intros zenon_H34 zenon_H21a zenon_H1e0.
% 45.50/45.67 generalize (meaning_postulate_greater_strict (low)). zenon_intro zenon_H80.
% 45.50/45.67 generalize (zenon_H80 (low)). zenon_intro zenon_H81.
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H81); [ zenon_intro zenon_H6c | zenon_intro zenon_H6c ].
% 45.50/45.67 apply (zenon_L121_ zenon_TX_y); trivial.
% 45.50/45.67 apply (zenon_L121_ zenon_TX_y); trivial.
% 45.50/45.67 (* end of lemma zenon_L122_ *)
% 45.50/45.67 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).
% 45.50/45.67 do 1 intro. intros zenon_H19e zenon_H34 zenon_H1d6.
% 45.50/45.67 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 ].
% 45.50/45.67 apply (zenon_and_s _ _ zenon_H1d7). zenon_intro zenon_H1a2. zenon_intro zenon_H1ca.
% 45.50/45.67 exact (zenon_H1a2 zenon_H19e).
% 45.50/45.67 cut ((greater (mod2) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (low))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1d6.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact assumption_18e.
% 45.50/45.67 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.67 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1].
% 45.50/45.67 congruence.
% 45.50/45.67 apply (zenon_notand_s _ _ zenon_H1d8); [ zenon_intro zenon_H1da | zenon_intro zenon_H1d9 ].
% 45.50/45.67 apply zenon_H1da. zenon_intro zenon_H19e.
% 45.50/45.67 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 ].
% 45.50/45.67 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))).
% 45.50/45.67 intro zenon_D_pnotp.
% 45.50/45.67 apply zenon_H1a1.
% 45.50/45.67 rewrite <- zenon_D_pnotp.
% 45.50/45.67 exact zenon_H11a.
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.67 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2].
% 45.50/45.67 congruence.
% 45.50/45.67 exact (zenon_H1a2 zenon_H19e).
% 45.50/45.68 apply zenon_H11b. apply refl_equal.
% 45.50/45.68 apply zenon_H11b. apply refl_equal.
% 45.50/45.68 apply zenon_H1d9. zenon_intro zenon_H1d5.
% 45.50/45.68 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H1d1.
% 45.50/45.68 generalize (zenon_H1d1 (mod2)). zenon_intro zenon_H1db.
% 45.50/45.68 generalize (zenon_H1db (low)). zenon_intro zenon_H1dc.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H1dc); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1dd ].
% 45.50/45.68 exact (zenon_H1ca zenon_H1d5).
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H1dd); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H1de ].
% 45.50/45.68 exact (zenon_Hc2 assumption_18e).
% 45.50/45.68 exact (zenon_H1d6 zenon_H1de).
% 45.50/45.68 apply zenon_H6a. apply refl_equal.
% 45.50/45.68 (* end of lemma zenon_L123_ *)
% 45.50/45.68 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).
% 45.50/45.68 do 1 intro. intros zenon_H19e zenon_H34 zenon_H1df zenon_H1e0.
% 45.50/45.68 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e2 ].
% 45.50/45.68 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (very_low))); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H1e4 ].
% 45.50/45.68 cut ((greater (hazard_of_mortality zenon_TX_y zenon_E) (very_low)) = (greater (very_low) (very_low))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H1df.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_H1e3.
% 45.50/45.68 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5].
% 45.50/45.68 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5].
% 45.50/45.68 congruence.
% 45.50/45.68 elim (classic ((very_low) = (very_low))); [ zenon_intro zenon_H1e6 | zenon_intro zenon_Hf5 ].
% 45.50/45.68 cut (((very_low) = (very_low)) = ((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H1e5.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_H1e6.
% 45.50/45.68 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5].
% 45.50/45.68 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1e2].
% 45.50/45.68 congruence.
% 45.50/45.68 exact (zenon_H1e2 zenon_H1e1).
% 45.50/45.68 apply zenon_Hf5. apply refl_equal.
% 45.50/45.68 apply zenon_Hf5. apply refl_equal.
% 45.50/45.68 apply zenon_Hf5. apply refl_equal.
% 45.50/45.68 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 ].
% 45.50/45.68 apply (zenon_and_s _ _ zenon_H1e7). zenon_intro zenon_H1bb. zenon_intro zenon_H1d6.
% 45.50/45.68 apply (zenon_L123_ zenon_TX_y); trivial.
% 45.50/45.68 cut ((greater (low) (very_low)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (very_low))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H1e4.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact assumption_18c.
% 45.50/45.68 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5].
% 45.50/45.68 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba].
% 45.50/45.68 congruence.
% 45.50/45.68 apply (zenon_notand_s _ _ zenon_H1e8); [ zenon_intro zenon_H1ea | zenon_intro zenon_H1e9 ].
% 45.50/45.68 apply zenon_H1ea. zenon_intro zenon_H1b8.
% 45.50/45.68 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 ].
% 45.50/45.68 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))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H1ba.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_H11a.
% 45.50/45.68 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.68 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb].
% 45.50/45.68 congruence.
% 45.50/45.68 exact (zenon_H1bb zenon_H1b8).
% 45.50/45.68 apply zenon_H11b. apply refl_equal.
% 45.50/45.68 apply zenon_H11b. apply refl_equal.
% 45.50/45.68 apply zenon_H1e9. zenon_intro zenon_H1de.
% 45.50/45.68 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H1d1.
% 45.50/45.68 generalize (zenon_H1d1 (low)). zenon_intro zenon_H1eb.
% 45.50/45.68 generalize (zenon_H1eb (very_low)). zenon_intro zenon_H1ec.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H1ec); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H1ed ].
% 45.50/45.68 exact (zenon_H1d6 zenon_H1de).
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H1ed); [ zenon_intro zenon_Hff | zenon_intro zenon_H1e3 ].
% 45.50/45.68 exact (zenon_Hff assumption_18c).
% 45.50/45.68 exact (zenon_H1e4 zenon_H1e3).
% 45.50/45.68 apply zenon_Hf5. apply refl_equal.
% 45.50/45.68 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 ].
% 45.50/45.68 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))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H1e2.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_H11a.
% 45.50/45.68 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.68 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5].
% 45.50/45.68 congruence.
% 45.50/45.68 exact (zenon_H1e5 zenon_H1e0).
% 45.50/45.68 apply zenon_H11b. apply refl_equal.
% 45.50/45.68 apply zenon_H11b. apply refl_equal.
% 45.50/45.68 (* end of lemma zenon_L124_ *)
% 45.50/45.68 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).
% 45.50/45.68 do 1 intro. intros zenon_H19e zenon_H227 zenon_H34 zenon_H1e0.
% 45.50/45.68 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e2 ].
% 45.50/45.68 elim (classic (greater (very_low) (very_low))); [ zenon_intro zenon_H1ef | zenon_intro zenon_H1df ].
% 45.50/45.68 elim (classic (greater (very_low) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H1f1 ].
% 45.50/45.68 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (low))); [ zenon_intro zenon_H1de | zenon_intro zenon_H1d6 ].
% 45.50/45.68 generalize (zenon_H34 (very_low)). zenon_intro zenon_H22a.
% 45.50/45.68 generalize (zenon_H22a (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H22b.
% 45.50/45.68 generalize (zenon_H22b (low)). zenon_intro zenon_H22c.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H22c); [ zenon_intro zenon_H1f1 | zenon_intro zenon_H22d ].
% 45.50/45.68 exact (zenon_H1f1 zenon_H1f0).
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H22d); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H226 ].
% 45.50/45.68 exact (zenon_H1d6 zenon_H1de).
% 45.50/45.68 exact (zenon_H227 zenon_H226).
% 45.50/45.68 apply (zenon_L123_ zenon_TX_y); trivial.
% 45.50/45.68 cut ((greater (very_low) (very_low)) = (greater (very_low) (hazard_of_mortality zenon_TX_y zenon_E))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H1f1.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_H1ef.
% 45.50/45.68 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1e2].
% 45.50/45.68 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5].
% 45.50/45.68 congruence.
% 45.50/45.68 apply zenon_Hf5. apply refl_equal.
% 45.50/45.68 exact (zenon_H1e2 zenon_H1e1).
% 45.50/45.68 apply (zenon_L124_ zenon_TX_y); trivial.
% 45.50/45.68 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 ].
% 45.50/45.68 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))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H1e2.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_H11a.
% 45.50/45.68 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.68 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5].
% 45.50/45.68 congruence.
% 45.50/45.68 exact (zenon_H1e5 zenon_H1e0).
% 45.50/45.68 apply zenon_H11b. apply refl_equal.
% 45.50/45.68 apply zenon_H11b. apply refl_equal.
% 45.50/45.68 (* end of lemma zenon_L125_ *)
% 45.50/45.68 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).
% 45.50/45.68 do 1 intro. intros zenon_H34 zenon_H1e0 zenon_H19e.
% 45.50/45.68 generalize (meaning_postulate_greater_strict (low)). zenon_intro zenon_H80.
% 45.50/45.68 generalize (zenon_H80 (very_low)). zenon_intro zenon_H22e.
% 45.50/45.68 apply (zenon_notand_s _ _ zenon_H22e); [ zenon_intro zenon_Hff | zenon_intro zenon_H227 ].
% 45.50/45.68 exact (zenon_Hff assumption_18c).
% 45.50/45.68 apply (zenon_L125_ zenon_TX_y); trivial.
% 45.50/45.68 (* end of lemma zenon_L126_ *)
% 45.50/45.68 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).
% 45.50/45.68 do 1 intro. intros zenon_H1b8 zenon_H34 zenon_H1df zenon_H1e0.
% 45.50/45.68 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e2 ].
% 45.50/45.68 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_E) (very_low))); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H1e4 ].
% 45.50/45.68 cut ((greater (hazard_of_mortality zenon_TX_y zenon_E) (very_low)) = (greater (very_low) (very_low))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H1df.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_H1e3.
% 45.50/45.68 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5].
% 45.50/45.68 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5].
% 45.50/45.68 congruence.
% 45.50/45.68 elim (classic ((very_low) = (very_low))); [ zenon_intro zenon_H1e6 | zenon_intro zenon_Hf5 ].
% 45.50/45.68 cut (((very_low) = (very_low)) = ((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H1e5.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_H1e6.
% 45.50/45.68 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5].
% 45.50/45.68 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1e2].
% 45.50/45.68 congruence.
% 45.50/45.68 exact (zenon_H1e2 zenon_H1e1).
% 45.50/45.68 apply zenon_Hf5. apply refl_equal.
% 45.50/45.68 apply zenon_Hf5. apply refl_equal.
% 45.50/45.68 apply zenon_Hf5. apply refl_equal.
% 45.50/45.68 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 ].
% 45.50/45.68 apply (zenon_and_s _ _ zenon_H1e7). zenon_intro zenon_H1bb. zenon_intro zenon_H1d6.
% 45.50/45.68 exact (zenon_H1bb zenon_H1b8).
% 45.50/45.68 cut ((greater (low) (very_low)) = (greater (hazard_of_mortality zenon_TX_y zenon_E) (very_low))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H1e4.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact assumption_18c.
% 45.50/45.68 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5].
% 45.50/45.68 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba].
% 45.50/45.68 congruence.
% 45.50/45.68 apply (zenon_notand_s _ _ zenon_H1e8); [ zenon_intro zenon_H1ea | zenon_intro zenon_H1e9 ].
% 45.50/45.68 apply zenon_H1ea. zenon_intro zenon_H1b8.
% 45.50/45.68 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 ].
% 45.50/45.68 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))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H1ba.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_H11a.
% 45.50/45.68 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.68 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb].
% 45.50/45.68 congruence.
% 45.50/45.68 exact (zenon_H1bb zenon_H1b8).
% 45.50/45.68 apply zenon_H11b. apply refl_equal.
% 45.50/45.68 apply zenon_H11b. apply refl_equal.
% 45.50/45.68 apply zenon_H1e9. zenon_intro zenon_H1de.
% 45.50/45.68 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H1d1.
% 45.50/45.68 generalize (zenon_H1d1 (low)). zenon_intro zenon_H1eb.
% 45.50/45.68 generalize (zenon_H1eb (very_low)). zenon_intro zenon_H1ec.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H1ec); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H1ed ].
% 45.50/45.68 exact (zenon_H1d6 zenon_H1de).
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H1ed); [ zenon_intro zenon_Hff | zenon_intro zenon_H1e3 ].
% 45.50/45.68 exact (zenon_Hff assumption_18c).
% 45.50/45.68 exact (zenon_H1e4 zenon_H1e3).
% 45.50/45.68 apply zenon_Hf5. apply refl_equal.
% 45.50/45.68 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 ].
% 45.50/45.68 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))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H1e2.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_H11a.
% 45.50/45.68 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.68 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5].
% 45.50/45.68 congruence.
% 45.50/45.68 exact (zenon_H1e5 zenon_H1e0).
% 45.50/45.68 apply zenon_H11b. apply refl_equal.
% 45.50/45.68 apply zenon_H11b. apply refl_equal.
% 45.50/45.68 (* end of lemma zenon_L127_ *)
% 45.50/45.68 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).
% 45.50/45.68 do 1 intro. intros zenon_H1b8 zenon_H227 zenon_H34 zenon_H1e0.
% 45.50/45.68 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e2 ].
% 45.50/45.68 elim (classic (greater (very_low) (very_low))); [ zenon_intro zenon_H1ef | zenon_intro zenon_H1df ].
% 45.50/45.68 elim (classic (greater (very_low) (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H1f1 ].
% 45.50/45.68 cut ((greater (very_low) (hazard_of_mortality zenon_TX_y zenon_E)) = (greater (very_low) (low))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H227.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_H1f0.
% 45.50/45.68 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb].
% 45.50/45.68 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5].
% 45.50/45.68 congruence.
% 45.50/45.68 apply zenon_Hf5. apply refl_equal.
% 45.50/45.68 exact (zenon_H1bb zenon_H1b8).
% 45.50/45.68 cut ((greater (very_low) (very_low)) = (greater (very_low) (hazard_of_mortality zenon_TX_y zenon_E))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H1f1.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_H1ef.
% 45.50/45.68 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1e2].
% 45.50/45.68 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5].
% 45.50/45.68 congruence.
% 45.50/45.68 apply zenon_Hf5. apply refl_equal.
% 45.50/45.68 exact (zenon_H1e2 zenon_H1e1).
% 45.50/45.68 apply (zenon_L127_ zenon_TX_y); trivial.
% 45.50/45.68 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 ].
% 45.50/45.68 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))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H1e2.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_H11a.
% 45.50/45.68 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.68 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5].
% 45.50/45.68 congruence.
% 45.50/45.68 exact (zenon_H1e5 zenon_H1e0).
% 45.50/45.68 apply zenon_H11b. apply refl_equal.
% 45.50/45.68 apply zenon_H11b. apply refl_equal.
% 45.50/45.68 (* end of lemma zenon_L128_ *)
% 45.50/45.68 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).
% 45.50/45.68 do 1 intro. intros zenon_H34 zenon_H1e0 zenon_H1b8.
% 45.50/45.68 generalize (meaning_postulate_greater_strict (low)). zenon_intro zenon_H80.
% 45.50/45.68 generalize (zenon_H80 (very_low)). zenon_intro zenon_H22e.
% 45.50/45.68 apply (zenon_notand_s _ _ zenon_H22e); [ zenon_intro zenon_Hff | zenon_intro zenon_H227 ].
% 45.50/45.68 exact (zenon_Hff assumption_18c).
% 45.50/45.68 apply (zenon_L128_ zenon_TX_y); trivial.
% 45.50/45.68 (* end of lemma zenon_L129_ *)
% 45.50/45.68 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).
% 45.50/45.68 do 1 intro. intros zenon_H22f zenon_H34 zenon_H1e0.
% 45.50/45.68 apply (zenon_and_s _ _ zenon_H22f). zenon_intro zenon_H231. zenon_intro zenon_H230.
% 45.50/45.68 apply (zenon_and_s _ _ zenon_H230). zenon_intro zenon_H233. zenon_intro zenon_H232.
% 45.50/45.68 apply (zenon_and_s _ _ zenon_H232). zenon_intro zenon_H234. zenon_intro zenon_H181.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H231); [ zenon_intro zenon_H235 | zenon_intro zenon_H1b8 ].
% 45.50/45.68 apply (zenon_notand_s _ _ zenon_H235); [ zenon_intro zenon_H183 | zenon_intro zenon_H182 ].
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H233); [ zenon_intro zenon_H236 | zenon_intro zenon_H21a ].
% 45.50/45.68 apply (zenon_notand_s _ _ zenon_H236); [ zenon_intro zenon_H186 | zenon_intro zenon_H182 ].
% 45.50/45.68 exact (zenon_H186 zenon_H183).
% 45.50/45.68 apply (zenon_L118_ zenon_TX_y); trivial.
% 45.50/45.68 apply (zenon_L122_ zenon_TX_y); trivial.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H234); [ zenon_intro zenon_H237 | zenon_intro zenon_H19e ].
% 45.50/45.68 apply (zenon_notand_s _ _ zenon_H237); [ zenon_intro zenon_H183 | zenon_intro zenon_H185 ].
% 45.50/45.68 apply (zenon_L118_ zenon_TX_y); trivial.
% 45.50/45.68 exact (zenon_H185 zenon_H182).
% 45.50/45.68 apply (zenon_L126_ zenon_TX_y); trivial.
% 45.50/45.68 apply (zenon_L129_ zenon_TX_y); trivial.
% 45.50/45.68 (* end of lemma zenon_L130_ *)
% 45.50/45.68 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).
% 45.50/45.68 do 1 intro. intros zenon_H34 zenon_H238 zenon_H1e0 zenon_H1a zenon_H1f.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H238); [ zenon_intro zenon_H111 | zenon_intro zenon_H22f ].
% 45.50/45.68 apply (zenon_L105_ zenon_TX_y); trivial.
% 45.50/45.68 apply (zenon_L130_ zenon_TX_y); trivial.
% 45.50/45.68 (* end of lemma zenon_L131_ *)
% 45.50/45.68 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).
% 45.50/45.68 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.
% 45.50/45.68 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0.
% 45.50/45.68 generalize (zenon_H0 zenon_E). zenon_intro zenon_H239.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H239); [ zenon_intro zenon_H27 | zenon_intro zenon_H23a ].
% 45.50/45.68 exact (zenon_H27 zenon_H1f).
% 45.50/45.68 apply (zenon_and_s _ _ zenon_H23a). zenon_intro zenon_H23b. zenon_intro zenon_H238.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H23b); [ zenon_intro zenon_H112 | zenon_intro zenon_H1e0 ].
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H238); [ zenon_intro zenon_H111 | zenon_intro zenon_H22f ].
% 45.50/45.68 exact (zenon_H111 zenon_H112).
% 45.50/45.68 apply (zenon_and_s _ _ zenon_H22f). zenon_intro zenon_H231. zenon_intro zenon_H230.
% 45.50/45.68 apply (zenon_and_s _ _ zenon_H230). zenon_intro zenon_H233. zenon_intro zenon_H232.
% 45.50/45.68 apply (zenon_and_s _ _ zenon_H232). zenon_intro zenon_H234. zenon_intro zenon_H181.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H231); [ zenon_intro zenon_H235 | zenon_intro zenon_H1b8 ].
% 45.50/45.68 apply (zenon_notand_s _ _ zenon_H235); [ zenon_intro zenon_H183 | zenon_intro zenon_H182 ].
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H233); [ zenon_intro zenon_H236 | zenon_intro zenon_H21a ].
% 45.50/45.68 apply (zenon_notand_s _ _ zenon_H236); [ zenon_intro zenon_H186 | zenon_intro zenon_H182 ].
% 45.50/45.68 exact (zenon_H186 zenon_H183).
% 45.50/45.68 apply (zenon_L76_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 elim (classic ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H23c | zenon_intro zenon_H21f ].
% 45.50/45.68 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))); [ zenon_intro zenon_H19c | zenon_intro zenon_H194 ].
% 45.50/45.68 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 ].
% 45.50/45.68 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 ].
% 45.50/45.68 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.50/45.68 generalize (zenon_H18f (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H23d.
% 45.50/45.68 generalize (zenon_H23d (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H23e.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H23f ].
% 45.50/45.68 exact (zenon_H1a5 zenon_H1a4).
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H23f); [ zenon_intro zenon_H117 | zenon_intro zenon_H240 ].
% 45.50/45.68 exact (zenon_H117 zenon_H17e).
% 45.50/45.68 exact (zenon_H17c zenon_H240).
% 45.50/45.68 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H241 | zenon_intro zenon_H193 ].
% 45.50/45.68 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))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H117.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_H241.
% 45.50/45.68 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].
% 45.50/45.68 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f].
% 45.50/45.68 congruence.
% 45.50/45.68 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 ].
% 45.50/45.68 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))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H21f.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_H11a.
% 45.50/45.68 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.68 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e].
% 45.50/45.68 congruence.
% 45.50/45.68 exact (zenon_H21e zenon_H21a).
% 45.50/45.68 apply zenon_H11b. apply refl_equal.
% 45.50/45.68 apply zenon_H11b. apply refl_equal.
% 45.50/45.68 apply zenon_H62. apply refl_equal.
% 45.50/45.68 apply (zenon_L79_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 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))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H1a5.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_H19c.
% 45.50/45.68 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f].
% 45.50/45.68 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].
% 45.50/45.68 congruence.
% 45.50/45.68 apply zenon_H16a. apply refl_equal.
% 45.50/45.68 exact (zenon_H21f zenon_H23c).
% 45.50/45.68 apply (zenon_L80_ zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.68 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 ].
% 45.50/45.68 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))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H21f.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_H11a.
% 45.50/45.68 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.68 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e].
% 45.50/45.68 congruence.
% 45.50/45.68 exact (zenon_H21e zenon_H21a).
% 45.50/45.68 apply zenon_H11b. apply refl_equal.
% 45.50/45.68 apply zenon_H11b. apply refl_equal.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H234); [ zenon_intro zenon_H237 | zenon_intro zenon_H19e ].
% 45.50/45.68 apply (zenon_notand_s _ _ zenon_H237); [ zenon_intro zenon_H183 | zenon_intro zenon_H185 ].
% 45.50/45.68 apply (zenon_L76_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 exact (zenon_H185 zenon_H182).
% 45.50/45.68 apply (zenon_L85_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 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 ].
% 45.50/45.68 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1a9 ].
% 45.50/45.68 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))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H17c.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_H1b1.
% 45.50/45.68 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72].
% 45.50/45.68 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].
% 45.50/45.68 congruence.
% 45.50/45.68 apply zenon_H16a. apply refl_equal.
% 45.50/45.68 apply (zenon_L99_ zenon_TT2_la zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.68 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))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H1a9.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_H1a4.
% 45.50/45.68 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb].
% 45.50/45.68 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].
% 45.50/45.68 congruence.
% 45.50/45.68 apply zenon_H16a. apply refl_equal.
% 45.50/45.68 exact (zenon_H1bb zenon_H1b8).
% 45.50/45.68 apply (zenon_L104_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.50/45.68 apply (zenon_L131_ zenon_TX_y); trivial.
% 45.50/45.68 (* end of lemma zenon_L132_ *)
% 45.50/45.68 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).
% 45.50/45.68 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.
% 45.50/45.68 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3.
% 45.50/45.68 apply (zenon_L132_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 (* end of lemma zenon_L133_ *)
% 45.50/45.68 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).
% 45.50/45.68 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.
% 45.50/45.68 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H242 | zenon_intro zenon_H187 ].
% 45.50/45.68 cut ((greater (low) (very_low)) = (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_Had.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact assumption_18c.
% 45.50/45.68 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H187].
% 45.50/45.68 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.68 congruence.
% 45.50/45.68 apply zenon_H6a. apply refl_equal.
% 45.50/45.68 exact (zenon_H187 zenon_H242).
% 45.50/45.68 apply (zenon_L133_ zenon_TT1_bg zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.68 (* end of lemma zenon_L134_ *)
% 45.50/45.68 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).
% 45.50/45.68 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.
% 45.50/45.68 elim (classic (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_Hac | zenon_intro zenon_Had ].
% 45.50/45.68 generalize (zenon_H34 (mod1)). zenon_intro zenon_Ha7.
% 45.50/45.68 generalize (zenon_Ha7 (low)). zenon_intro zenon_Ha8.
% 45.50/45.68 generalize (zenon_Ha8 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H243.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H243); [ zenon_intro zenon_H7f | zenon_intro zenon_H244 ].
% 45.50/45.68 exact (zenon_H7f assumption_18b).
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H244); [ zenon_intro zenon_Had | zenon_intro zenon_H241 ].
% 45.50/45.68 exact (zenon_Had zenon_Hac).
% 45.50/45.68 exact (zenon_H193 zenon_H241).
% 45.50/45.68 apply (zenon_L134_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 (* end of lemma zenon_L135_ *)
% 45.50/45.68 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).
% 45.50/45.68 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.
% 45.50/45.68 elim (classic (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_Hac | zenon_intro zenon_Had ].
% 45.50/45.68 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))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H117.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_Hac.
% 45.50/45.68 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].
% 45.50/45.68 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba].
% 45.50/45.68 congruence.
% 45.50/45.68 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 ].
% 45.50/45.68 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))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H1ba.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_H11a.
% 45.50/45.68 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.68 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb].
% 45.50/45.68 congruence.
% 45.50/45.68 exact (zenon_H1bb zenon_H1b8).
% 45.50/45.68 apply zenon_H11b. apply refl_equal.
% 45.50/45.68 apply zenon_H11b. apply refl_equal.
% 45.50/45.68 apply zenon_H62. apply refl_equal.
% 45.50/45.68 apply (zenon_L134_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 (* end of lemma zenon_L136_ *)
% 45.50/45.68 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).
% 45.50/45.68 do 2 intro. intros zenon_H245 zenon_H1f zenon_H1a.
% 45.50/45.68 apply zenon_H245. zenon_intro zenon_H246.
% 45.50/45.68 generalize (assumption_1 zenon_TX_y). zenon_intro zenon_H22.
% 45.50/45.68 generalize (zenon_H22 zenon_TT0_hz). zenon_intro zenon_H247.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H247); [ zenon_intro zenon_H25 | zenon_intro zenon_H248 ].
% 45.50/45.68 apply (zenon_notand_s _ _ zenon_H25); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ].
% 45.50/45.68 exact (zenon_H27 zenon_H1f).
% 45.50/45.68 apply zenon_H26. zenon_intro zenon_H19.
% 45.50/45.68 apply (zenon_L2_ zenon_TX_y); trivial.
% 45.50/45.68 exact (zenon_H248 zenon_H246).
% 45.50/45.68 (* end of lemma zenon_L137_ *)
% 45.50/45.68 assert (zenon_L138_ : (~((tau) = (tau))) -> False).
% 45.50/45.68 do 0 intro. intros zenon_H53.
% 45.50/45.68 apply zenon_H53. apply refl_equal.
% 45.50/45.68 (* end of lemma zenon_L138_ *)
% 45.50/45.68 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).
% 45.50/45.68 do 2 intro. intros zenon_H249 zenon_H24a zenon_Hec.
% 45.50/45.68 elim (classic ((zero) = (age zenon_TX_y zenon_TT0_hz))); [ zenon_intro zenon_H24b | zenon_intro zenon_H24c ].
% 45.50/45.68 cut ((greater (tau) (zero)) = (greater (tau) (age zenon_TX_y zenon_TT0_hz))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H249.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_H24a.
% 45.50/45.68 cut (((zero) = (age zenon_TX_y zenon_TT0_hz))); [idtac | apply NNPP; zenon_intro zenon_H24c].
% 45.50/45.68 cut (((tau) = (tau))); [idtac | apply NNPP; zenon_intro zenon_H53].
% 45.50/45.68 congruence.
% 45.50/45.68 apply zenon_H53. apply refl_equal.
% 45.50/45.68 exact (zenon_H24c zenon_H24b).
% 45.50/45.68 apply zenon_H24c. apply sym_equal. exact zenon_Hec.
% 45.50/45.68 (* end of lemma zenon_L139_ *)
% 45.50/45.68 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).
% 45.50/45.68 do 2 intro. intros zenon_H35 zenon_H24d zenon_H24a zenon_Hec.
% 45.50/45.68 generalize (zenon_H35 zenon_TT0_hz). zenon_intro zenon_H24e.
% 45.50/45.68 apply (zenon_and_s _ _ zenon_H24e). zenon_intro zenon_H250. zenon_intro zenon_H24f.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H250); [ zenon_intro zenon_H252 | zenon_intro zenon_H251 ].
% 45.50/45.68 generalize (definition_smaller_or_equal (age zenon_TX_y zenon_TT0_hz)). zenon_intro zenon_H253.
% 45.50/45.68 generalize (zenon_H253 (tau)). zenon_intro zenon_H254.
% 45.50/45.68 apply (zenon_equiv_s _ _ zenon_H254); [ zenon_intro zenon_H252; zenon_intro zenon_H257 | zenon_intro zenon_H256; zenon_intro zenon_H255 ].
% 45.50/45.68 apply (zenon_notor_s _ _ zenon_H257). zenon_intro zenon_H259. zenon_intro zenon_H258.
% 45.50/45.68 generalize (definition_smaller (age zenon_TX_y zenon_TT0_hz)). zenon_intro zenon_H25a.
% 45.50/45.68 generalize (zenon_H25a (tau)). zenon_intro zenon_H25b.
% 45.50/45.68 apply (zenon_equiv_s _ _ zenon_H25b); [ zenon_intro zenon_H259; zenon_intro zenon_H249 | zenon_intro zenon_H25d; zenon_intro zenon_H25c ].
% 45.50/45.68 apply (zenon_L139_ zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.68 exact (zenon_H259 zenon_H25d).
% 45.50/45.68 exact (zenon_H252 zenon_H256).
% 45.50/45.68 exact (zenon_H251 zenon_H24d).
% 45.50/45.68 (* end of lemma zenon_L140_ *)
% 45.50/45.68 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).
% 45.50/45.68 do 3 intro. intros zenon_H25e zenon_H32 zenon_H25f.
% 45.50/45.68 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))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H25e.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_H32.
% 45.50/45.68 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT0_hz))); [idtac | apply NNPP; zenon_intro zenon_H260].
% 45.50/45.68 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].
% 45.50/45.68 congruence.
% 45.50/45.68 apply zenon_H62. apply refl_equal.
% 45.50/45.68 apply zenon_H260. apply sym_equal. exact zenon_H25f.
% 45.50/45.68 (* end of lemma zenon_L141_ *)
% 45.50/45.68 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).
% 45.50/45.68 do 3 intro. intros zenon_H261 zenon_Hec zenon_H24a zenon_H35 zenon_Hcd zenon_H25e zenon_H32.
% 45.50/45.68 apply (zenon_and_s _ _ zenon_H261). zenon_intro zenon_H263. zenon_intro zenon_H262.
% 45.50/45.68 apply (zenon_and_s _ _ zenon_H262). zenon_intro zenon_H265. zenon_intro zenon_H264.
% 45.50/45.68 apply (zenon_and_s _ _ zenon_H264). zenon_intro zenon_H267. zenon_intro zenon_H266.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H267); [ zenon_intro zenon_H268 | zenon_intro zenon_H25f ].
% 45.50/45.68 apply (zenon_notand_s _ _ zenon_H268); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H269 ].
% 45.50/45.68 exact (zenon_Hd8 zenon_Hcd).
% 45.50/45.68 apply zenon_H269. zenon_intro zenon_H24d.
% 45.50/45.68 apply (zenon_L140_ zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.68 apply (zenon_L141_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 (* end of lemma zenon_L142_ *)
% 45.50/45.68 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).
% 45.50/45.68 do 3 intro. intros zenon_H0 zenon_H1f zenon_H1a zenon_Hcd zenon_H35 zenon_H24a zenon_Hec zenon_H25e zenon_H32.
% 45.50/45.68 generalize (zenon_H0 zenon_TT0_hz). zenon_intro zenon_H26a.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H26a); [ zenon_intro zenon_H27 | zenon_intro zenon_H26b ].
% 45.50/45.68 exact (zenon_H27 zenon_H1f).
% 45.50/45.68 apply (zenon_and_s _ _ zenon_H26b). zenon_intro zenon_H26d. zenon_intro zenon_H26c.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H26c); [ zenon_intro zenon_H245 | zenon_intro zenon_H261 ].
% 45.50/45.68 apply (zenon_L137_ zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.68 apply (zenon_L142_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.68 (* end of lemma zenon_L143_ *)
% 45.50/45.68 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).
% 45.50/45.68 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.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ].
% 45.50/45.68 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ].
% 45.50/45.68 apply (zenon_L31_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.68 exact (zenon_H2e zenon_H29).
% 45.50/45.68 apply (zenon_L143_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.68 (* end of lemma zenon_L144_ *)
% 45.50/45.68 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).
% 45.50/45.68 do 2 intro. intros zenon_H32 zenon_H6b zenon_H34 zenon_H6c.
% 45.50/45.68 elim (classic ((~((low) = (mod1)))/\(~(greater (low) (mod1))))); [ zenon_intro zenon_H6d | zenon_intro zenon_H6e ].
% 45.50/45.68 apply (zenon_and_s _ _ zenon_H6d). zenon_intro zenon_H70. zenon_intro zenon_H6f.
% 45.50/45.68 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ].
% 45.50/45.68 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1))); [ zenon_intro zenon_H68 | zenon_intro zenon_H5a ].
% 45.50/45.68 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1)) = (greater (low) (mod1))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H6f.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_H68.
% 45.50/45.68 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 45.50/45.68 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low))); [idtac | apply NNPP; zenon_intro zenon_H73].
% 45.50/45.68 congruence.
% 45.50/45.68 elim (classic ((low) = (low))); [ zenon_intro zenon_H74 | zenon_intro zenon_H6a ].
% 45.50/45.68 cut (((low) = (low)) = ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H73.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_H74.
% 45.50/45.68 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.68 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72].
% 45.50/45.68 congruence.
% 45.50/45.68 exact (zenon_H72 zenon_H71).
% 45.50/45.68 apply zenon_H6a. apply refl_equal.
% 45.50/45.68 apply zenon_H6a. apply refl_equal.
% 45.50/45.68 apply zenon_H59. apply refl_equal.
% 45.50/45.68 apply (zenon_L8_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 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 ].
% 45.50/45.68 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))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H72.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_H61.
% 45.50/45.68 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].
% 45.50/45.68 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low))); [idtac | apply NNPP; zenon_intro zenon_H73].
% 45.50/45.68 congruence.
% 45.50/45.68 exact (zenon_H73 zenon_H6b).
% 45.50/45.68 apply zenon_H62. apply refl_equal.
% 45.50/45.68 apply zenon_H62. apply refl_equal.
% 45.50/45.68 cut ((greater (mod1) (low)) = (greater (low) (low))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H6c.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact assumption_18b.
% 45.50/45.68 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.68 cut (((mod1) = (low))); [idtac | apply NNPP; zenon_intro zenon_H75].
% 45.50/45.68 congruence.
% 45.50/45.68 apply (zenon_notand_s _ _ zenon_H6e); [ zenon_intro zenon_H77 | zenon_intro zenon_H76 ].
% 45.50/45.68 apply zenon_H77. zenon_intro zenon_H78.
% 45.50/45.68 elim (classic ((low) = (low))); [ zenon_intro zenon_H74 | zenon_intro zenon_H6a ].
% 45.50/45.68 cut (((low) = (low)) = ((mod1) = (low))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H75.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_H74.
% 45.50/45.68 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.68 cut (((low) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H70].
% 45.50/45.68 congruence.
% 45.50/45.68 exact (zenon_H70 zenon_H78).
% 45.50/45.68 apply zenon_H6a. apply refl_equal.
% 45.50/45.68 apply zenon_H6a. apply refl_equal.
% 45.50/45.68 apply zenon_H76. zenon_intro zenon_H79.
% 45.50/45.68 generalize (zenon_H34 (low)). zenon_intro zenon_H7a.
% 45.50/45.68 generalize (zenon_H7a (mod1)). zenon_intro zenon_H7b.
% 45.50/45.68 generalize (zenon_H7b (low)). zenon_intro zenon_H7c.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H7c); [ zenon_intro zenon_H6f | zenon_intro zenon_H7d ].
% 45.50/45.68 exact (zenon_H6f zenon_H79).
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H7d); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ].
% 45.50/45.68 exact (zenon_H7f assumption_18b).
% 45.50/45.68 exact (zenon_H6c zenon_H7e).
% 45.50/45.68 apply zenon_H6a. apply refl_equal.
% 45.50/45.68 (* end of lemma zenon_L145_ *)
% 45.50/45.68 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).
% 45.50/45.68 do 2 intro. intros zenon_H34 zenon_H6b zenon_H32.
% 45.50/45.68 generalize (meaning_postulate_greater_strict (low)). zenon_intro zenon_H80.
% 45.50/45.68 generalize (zenon_H80 (low)). zenon_intro zenon_H81.
% 45.50/45.68 apply (zenon_notand_s _ _ zenon_H81); [ zenon_intro zenon_H6c | zenon_intro zenon_H6c ].
% 45.50/45.68 apply (zenon_L145_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 apply (zenon_L145_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 (* end of lemma zenon_L146_ *)
% 45.50/45.68 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).
% 45.50/45.68 do 3 intro. intros zenon_H30 zenon_H38 zenon_H37 zenon_H35 zenon_H1f zenon_Hec zenon_Hcd zenon_Hed zenon_H34 zenon_H6b.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ].
% 45.50/45.68 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ].
% 45.50/45.68 apply (zenon_L30_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.68 apply zenon_H2e. zenon_intro zenon_H36.
% 45.50/45.68 apply (zenon_L6_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 apply (zenon_L146_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 (* end of lemma zenon_L147_ *)
% 45.50/45.68 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).
% 45.50/45.68 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.
% 45.50/45.68 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d.
% 45.50/45.68 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f.
% 45.50/45.68 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H30. zenon_intro zenon_H28.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H8e); [ zenon_intro zenon_H91 | zenon_intro zenon_H6b ].
% 45.50/45.68 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ].
% 45.50/45.68 apply (zenon_L30_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.68 apply (zenon_L144_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 apply (zenon_L147_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 (* end of lemma zenon_L148_ *)
% 45.50/45.68 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).
% 45.50/45.68 do 3 intro. intros zenon_H34 zenon_H1f zenon_Hec zenon_H38 zenon_H35 zenon_H24a zenon_H25e zenon_H37 zenon_H1a.
% 45.50/45.68 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3.
% 45.50/45.68 generalize (assumption_15 zenon_TX_y). zenon_intro zenon_Hed.
% 45.50/45.68 generalize (zenon_Hf3 zenon_TT0_hz). zenon_intro zenon_Hf4.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcd ].
% 45.50/45.68 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ].
% 45.50/45.68 exact (zenon_H27 zenon_H1f).
% 45.50/45.68 exact (zenon_Hf2 zenon_Hec).
% 45.50/45.68 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0.
% 45.50/45.68 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ].
% 45.50/45.68 exact (zenon_H27 zenon_H1f).
% 45.50/45.68 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ].
% 45.50/45.68 apply (zenon_L3_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 apply (zenon_L148_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 (* end of lemma zenon_L149_ *)
% 45.50/45.68 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).
% 45.50/45.68 do 3 intro. intros zenon_Hed zenon_Hcd zenon_H2a zenon_He9 zenon_Hec zenon_H1f.
% 45.50/45.68 generalize (zenon_Hed zenon_TT0_hz). zenon_intro zenon_Hee.
% 45.50/45.68 generalize (zenon_Hee zenon_TT1_bg). zenon_intro zenon_Hef.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_Hef); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hf0 ].
% 45.50/45.68 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ].
% 45.50/45.68 exact (zenon_H27 zenon_H1f).
% 45.50/45.68 exact (zenon_Hf2 zenon_Hec).
% 45.50/45.68 apply (zenon_equiv_s _ _ zenon_Hf0); [ zenon_intro zenon_He9; zenon_intro zenon_Hce | zenon_intro zenon_Hdb; zenon_intro zenon_Hd4 ].
% 45.50/45.68 apply (zenon_L26_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.68 exact (zenon_He9 zenon_Hdb).
% 45.50/45.68 (* end of lemma zenon_L150_ *)
% 45.50/45.68 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).
% 45.50/45.68 do 3 intro. intros zenon_Hf4 zenon_Hed zenon_H2a zenon_He9 zenon_Hec zenon_H1f.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcd ].
% 45.50/45.68 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ].
% 45.50/45.68 exact (zenon_H27 zenon_H1f).
% 45.50/45.68 exact (zenon_Hf2 zenon_Hec).
% 45.50/45.68 apply (zenon_L150_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.68 (* end of lemma zenon_L151_ *)
% 45.50/45.68 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).
% 45.50/45.68 do 3 intro. intros zenon_Hf3 zenon_H1f zenon_Hec zenon_Hed zenon_H2a zenon_He9.
% 45.50/45.68 generalize (zenon_Hf3 zenon_TT0_hz). zenon_intro zenon_Hf4.
% 45.50/45.68 apply (zenon_L151_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.68 (* end of lemma zenon_L152_ *)
% 45.50/45.68 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).
% 45.50/45.68 do 3 intro. intros zenon_He9 zenon_H2a zenon_Hec zenon_H1f zenon_Hf3.
% 45.50/45.68 generalize (assumption_15 zenon_TX_y). zenon_intro zenon_Hed.
% 45.50/45.68 apply (zenon_L152_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.50/45.68 (* end of lemma zenon_L153_ *)
% 45.50/45.68 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).
% 45.50/45.68 do 3 intro. intros zenon_H30 zenon_H29 zenon_He9 zenon_Hec zenon_H1f zenon_Hf3 zenon_H31.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ].
% 45.50/45.68 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ].
% 45.50/45.68 apply (zenon_L153_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 exact (zenon_H2e zenon_H29).
% 45.50/45.68 exact (zenon_H31 zenon_H32).
% 45.50/45.68 (* end of lemma zenon_L154_ *)
% 45.50/45.68 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).
% 45.50/45.68 do 2 intro. intros zenon_H35 zenon_H36 zenon_H38 zenon_H26e.
% 45.50/45.68 generalize (zenon_H35 zenon_TT1_bg). zenon_intro zenon_H39.
% 45.50/45.68 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_H3b. zenon_intro zenon_H3a.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H3b); [ zenon_intro zenon_H3c | zenon_intro zenon_H29 ].
% 45.50/45.68 generalize (definition_smaller_or_equal (age zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H3d.
% 45.50/45.68 generalize (zenon_H3d (tau)). zenon_intro zenon_H3e.
% 45.50/45.68 apply (zenon_equiv_s _ _ zenon_H3e); [ zenon_intro zenon_H3c; zenon_intro zenon_H41 | zenon_intro zenon_H40; zenon_intro zenon_H3f ].
% 45.50/45.68 apply (zenon_notor_s _ _ zenon_H41). zenon_intro zenon_H43. zenon_intro zenon_H42.
% 45.50/45.68 generalize (definition_smaller (age zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H44.
% 45.50/45.68 generalize (zenon_H44 (tau)). zenon_intro zenon_H45.
% 45.50/45.68 apply (zenon_equiv_s _ _ zenon_H45); [ zenon_intro zenon_H43; zenon_intro zenon_H48 | zenon_intro zenon_H47; zenon_intro zenon_H46 ].
% 45.50/45.68 elim (classic ((sigma) = (age zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_He2 | zenon_intro zenon_Hde ].
% 45.50/45.68 cut ((greater (tau) (sigma)) = (greater (tau) (age zenon_TX_y zenon_TT1_bg))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H48.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_H38.
% 45.50/45.68 cut (((sigma) = (age zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_Hde].
% 45.50/45.68 cut (((tau) = (tau))); [idtac | apply NNPP; zenon_intro zenon_H53].
% 45.50/45.68 congruence.
% 45.50/45.68 apply zenon_H53. apply refl_equal.
% 45.50/45.68 exact (zenon_Hde zenon_He2).
% 45.50/45.68 apply zenon_Hde. apply sym_equal. exact zenon_H26e.
% 45.50/45.68 exact (zenon_H43 zenon_H47).
% 45.50/45.68 exact (zenon_H3c zenon_H40).
% 45.50/45.68 exact (zenon_H29 zenon_H36).
% 45.50/45.68 (* end of lemma zenon_L155_ *)
% 45.50/45.68 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).
% 45.50/45.68 do 2 intro. intros zenon_H30 zenon_H26e zenon_H38 zenon_H35 zenon_H82 zenon_H34 zenon_H6b.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ].
% 45.50/45.68 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ].
% 45.50/45.68 exact (zenon_H2a zenon_H82).
% 45.50/45.68 apply zenon_H2e. zenon_intro zenon_H36.
% 45.50/45.68 apply (zenon_L155_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 apply (zenon_L11_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 (* end of lemma zenon_L156_ *)
% 45.50/45.68 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).
% 45.50/45.68 do 3 intro. intros zenon_H30 zenon_H29 zenon_He9 zenon_Hec zenon_H1f zenon_Hf3 zenon_H34 zenon_H6b.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ].
% 45.50/45.68 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ].
% 45.50/45.68 apply (zenon_L153_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 exact (zenon_H2e zenon_H29).
% 45.50/45.68 apply (zenon_L11_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 (* end of lemma zenon_L157_ *)
% 45.50/45.68 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).
% 45.50/45.68 do 3 intro. intros zenon_H30 zenon_H26e zenon_H38 zenon_H35 zenon_He9 zenon_Hec zenon_H1f zenon_Hf3 zenon_H34 zenon_H6b.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ].
% 45.50/45.68 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ].
% 45.50/45.68 apply (zenon_L153_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 apply zenon_H2e. zenon_intro zenon_H36.
% 45.50/45.68 apply (zenon_L155_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 apply (zenon_L146_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 (* end of lemma zenon_L158_ *)
% 45.50/45.68 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).
% 45.50/45.68 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.
% 45.50/45.68 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ].
% 45.50/45.68 exact (zenon_H27 zenon_H1f).
% 45.50/45.68 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ].
% 45.50/45.68 apply (zenon_L3_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d.
% 45.50/45.68 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f.
% 45.50/45.68 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H30. zenon_intro zenon_H28.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H8e); [ zenon_intro zenon_H91 | zenon_intro zenon_H6b ].
% 45.50/45.68 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ].
% 45.50/45.68 apply (zenon_L153_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 apply (zenon_L154_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 apply (zenon_L158_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 (* end of lemma zenon_L159_ *)
% 45.50/45.68 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).
% 45.50/45.68 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.
% 45.50/45.68 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 ].
% 45.50/45.68 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H31. zenon_intro zenon_H5d.
% 45.50/45.68 apply (zenon_L159_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 cut ((greater (mod2) (mod1)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H5a.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact assumption_19.
% 45.50/45.68 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 45.50/45.68 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 45.50/45.68 congruence.
% 45.50/45.68 apply (zenon_notand_s _ _ zenon_H5c); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ].
% 45.50/45.68 apply zenon_H60. zenon_intro zenon_H32.
% 45.50/45.68 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 ].
% 45.50/45.68 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))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H5e.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_H61.
% 45.50/45.68 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].
% 45.50/45.68 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31].
% 45.50/45.68 congruence.
% 45.50/45.68 exact (zenon_H31 zenon_H32).
% 45.50/45.68 apply zenon_H62. apply refl_equal.
% 45.50/45.68 apply zenon_H62. apply refl_equal.
% 45.50/45.68 apply zenon_H5f. zenon_intro zenon_H63.
% 45.50/45.68 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64.
% 45.50/45.68 generalize (zenon_H64 (mod2)). zenon_intro zenon_H65.
% 45.50/45.68 generalize (zenon_H65 (mod1)). zenon_intro zenon_H66.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H67 ].
% 45.50/45.68 exact (zenon_H5d zenon_H63).
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H67); [ zenon_intro zenon_H69 | zenon_intro zenon_H68 ].
% 45.50/45.68 exact (zenon_H69 assumption_19).
% 45.50/45.68 exact (zenon_H5a zenon_H68).
% 45.50/45.68 apply zenon_H59. apply refl_equal.
% 45.50/45.68 (* end of lemma zenon_L160_ *)
% 45.50/45.68 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).
% 45.50/45.68 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.
% 45.50/45.68 elim (classic ((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hb1 ].
% 45.50/45.68 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1))); [ zenon_intro zenon_H68 | zenon_intro zenon_H5a ].
% 45.50/45.68 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))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_Hae.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_H68.
% 45.50/45.68 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hb1].
% 45.50/45.68 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].
% 45.50/45.68 congruence.
% 45.50/45.68 apply zenon_H62. apply refl_equal.
% 45.50/45.68 exact (zenon_Hb1 zenon_Hb0).
% 45.50/45.68 apply (zenon_L160_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 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 ].
% 45.50/45.68 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))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_Hb1.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_Hb9.
% 45.50/45.68 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].
% 45.50/45.68 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_Hb7].
% 45.50/45.68 congruence.
% 45.50/45.68 exact (zenon_Hb7 zenon_Haf).
% 45.50/45.68 apply zenon_Hb6. apply refl_equal.
% 45.50/45.68 apply zenon_Hb6. apply refl_equal.
% 45.50/45.68 (* end of lemma zenon_L161_ *)
% 45.50/45.68 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).
% 45.50/45.68 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.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_Hba); [ zenon_intro zenon_Hbd | zenon_intro zenon_Haf ].
% 45.50/45.68 apply (zenon_notand_s _ _ zenon_Hbd); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hbe ].
% 45.50/45.68 exact (zenon_Hbf zenon_Hbc).
% 45.50/45.68 exact (zenon_Hbe zenon_Hbb).
% 45.50/45.68 apply (zenon_L161_ zenon_TT3_x zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 (* end of lemma zenon_L162_ *)
% 45.50/45.68 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).
% 45.50/45.68 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.
% 45.50/45.68 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 ].
% 45.50/45.68 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H31. zenon_intro zenon_H5d.
% 45.50/45.68 apply (zenon_L159_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 cut ((greater (mod2) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H9d.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact assumption_18e.
% 45.50/45.68 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.68 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 45.50/45.68 congruence.
% 45.50/45.68 apply (zenon_notand_s _ _ zenon_H5c); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ].
% 45.50/45.68 apply zenon_H60. zenon_intro zenon_H32.
% 45.50/45.68 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 ].
% 45.50/45.68 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))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_H5e.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_H61.
% 45.50/45.68 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].
% 45.50/45.68 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31].
% 45.50/45.68 congruence.
% 45.50/45.68 exact (zenon_H31 zenon_H32).
% 45.50/45.68 apply zenon_H62. apply refl_equal.
% 45.50/45.68 apply zenon_H62. apply refl_equal.
% 45.50/45.68 apply zenon_H5f. zenon_intro zenon_H63.
% 45.50/45.68 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64.
% 45.50/45.68 generalize (zenon_H64 (mod2)). zenon_intro zenon_H65.
% 45.50/45.68 generalize (zenon_H65 (low)). zenon_intro zenon_Hc0.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_Hc0); [ zenon_intro zenon_H5d | zenon_intro zenon_Hc1 ].
% 45.50/45.68 exact (zenon_H5d zenon_H63).
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_Hc1); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H9c ].
% 45.50/45.68 exact (zenon_Hc2 assumption_18e).
% 45.50/45.68 exact (zenon_H9d zenon_H9c).
% 45.50/45.68 apply zenon_H6a. apply refl_equal.
% 45.50/45.68 (* end of lemma zenon_L163_ *)
% 45.50/45.68 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).
% 45.50/45.68 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.
% 45.50/45.68 generalize (zenon_H0 zenon_TT3_x). zenon_intro zenon_H10a.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H10a); [ zenon_intro zenon_H27 | zenon_intro zenon_H10b ].
% 45.50/45.68 exact (zenon_H27 zenon_H1f).
% 45.50/45.68 apply (zenon_and_s _ _ zenon_H10b). zenon_intro zenon_H10c. zenon_intro zenon_Hcc.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_H10c); [ zenon_intro zenon_H16 | zenon_intro zenon_H10d ].
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_Hcc); [ zenon_intro zenon_H15 | zenon_intro zenon_Hc3 ].
% 45.50/45.68 exact (zenon_H15 zenon_H16).
% 45.50/45.68 apply (zenon_and_s _ _ zenon_Hc3). zenon_intro zenon_Hc5. zenon_intro zenon_Hc4.
% 45.50/45.68 apply (zenon_and_s _ _ zenon_Hc4). zenon_intro zenon_Hba. zenon_intro zenon_Hc6.
% 45.50/45.68 apply (zenon_imply_s _ _ zenon_Hc5); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hc7 ].
% 45.50/45.68 apply (zenon_notand_s _ _ zenon_Hc8); [ zenon_intro zenon_Hbc | zenon_intro zenon_Hbe ].
% 45.50/45.68 apply (zenon_L162_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial.
% 45.50/45.68 exact (zenon_Hbe zenon_Hbb).
% 45.50/45.68 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hca ].
% 45.50/45.68 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low))); [ zenon_intro zenon_H9c | zenon_intro zenon_H9d ].
% 45.50/45.68 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))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_Hae.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_H9c.
% 45.50/45.68 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_Hca].
% 45.50/45.68 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].
% 45.50/45.68 congruence.
% 45.50/45.68 apply zenon_H62. apply refl_equal.
% 45.50/45.68 exact (zenon_Hca zenon_Hc9).
% 45.50/45.68 apply (zenon_L163_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.68 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 ].
% 45.50/45.68 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))).
% 45.50/45.68 intro zenon_D_pnotp.
% 45.50/45.68 apply zenon_Hca.
% 45.50/45.68 rewrite <- zenon_D_pnotp.
% 45.50/45.68 exact zenon_Hb9.
% 45.50/45.68 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].
% 45.50/45.68 cut (((hazard_of_mortality zenon_TX_y zenon_TT3_x) = (low))); [idtac | apply NNPP; zenon_intro zenon_Hcb].
% 45.50/45.69 congruence.
% 45.50/45.69 exact (zenon_Hcb zenon_Hc7).
% 45.50/45.69 apply zenon_Hb6. apply refl_equal.
% 45.50/45.69 apply zenon_Hb6. apply refl_equal.
% 45.50/45.69 apply zenon_H10f. apply sym_equal. exact zenon_H10d.
% 45.50/45.69 (* end of lemma zenon_L164_ *)
% 45.50/45.69 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).
% 45.50/45.69 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.
% 45.50/45.69 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0.
% 45.50/45.69 apply (zenon_L164_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial.
% 45.50/45.69 (* end of lemma zenon_L165_ *)
% 45.50/45.69 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).
% 45.50/45.69 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.
% 45.50/45.69 elim (classic ((sigma) = (age zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_He2 | zenon_intro zenon_Hde ].
% 45.50/45.69 elim (classic (greater (age zenon_TX_y zenon_TT1_bg) (sigma))); [ zenon_intro zenon_Hdb | zenon_intro zenon_He9 ].
% 45.50/45.69 cut ((greater (age zenon_TX_y zenon_TT1_bg) (sigma)) = (greater (sigma) (sigma))).
% 45.50/45.69 intro zenon_D_pnotp.
% 45.50/45.69 apply zenon_Hda.
% 45.50/45.69 rewrite <- zenon_D_pnotp.
% 45.50/45.69 exact zenon_Hdb.
% 45.50/45.69 cut (((sigma) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hd9].
% 45.50/45.69 cut (((age zenon_TX_y zenon_TT1_bg) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hdf].
% 45.50/45.69 congruence.
% 45.50/45.69 elim (classic ((sigma) = (sigma))); [ zenon_intro zenon_He3 | zenon_intro zenon_Hd9 ].
% 45.50/45.69 cut (((sigma) = (sigma)) = ((age zenon_TX_y zenon_TT1_bg) = (sigma))).
% 45.50/45.69 intro zenon_D_pnotp.
% 45.50/45.69 apply zenon_Hdf.
% 45.50/45.69 rewrite <- zenon_D_pnotp.
% 45.50/45.69 exact zenon_He3.
% 45.50/45.69 cut (((sigma) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hd9].
% 45.50/45.69 cut (((sigma) = (age zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_Hde].
% 45.50/45.69 congruence.
% 45.50/45.69 exact (zenon_Hde zenon_He2).
% 45.50/45.69 apply zenon_Hd9. apply refl_equal.
% 45.50/45.69 apply zenon_Hd9. apply refl_equal.
% 45.50/45.69 apply zenon_Hd9. apply refl_equal.
% 45.50/45.69 apply (zenon_L165_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial.
% 45.50/45.69 elim (classic ((age zenon_TX_y zenon_TT1_bg) = (age zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H26f | zenon_intro zenon_H4d ].
% 45.50/45.69 cut (((age zenon_TX_y zenon_TT1_bg) = (age zenon_TX_y zenon_TT1_bg)) = ((sigma) = (age zenon_TX_y zenon_TT1_bg))).
% 45.50/45.69 intro zenon_D_pnotp.
% 45.50/45.69 apply zenon_Hde.
% 45.50/45.69 rewrite <- zenon_D_pnotp.
% 45.50/45.69 exact zenon_H26f.
% 45.50/45.69 cut (((age zenon_TX_y zenon_TT1_bg) = (age zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H4d].
% 45.50/45.69 cut (((age zenon_TX_y zenon_TT1_bg) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hdf].
% 45.50/45.69 congruence.
% 45.50/45.69 exact (zenon_Hdf zenon_H26e).
% 45.50/45.69 apply zenon_H4d. apply refl_equal.
% 45.50/45.69 apply zenon_H4d. apply refl_equal.
% 45.50/45.69 (* end of lemma zenon_L166_ *)
% 45.50/45.69 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).
% 45.50/45.69 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.
% 45.50/45.69 generalize (meaning_postulate_greater_strict (sigma)). zenon_intro zenon_Hea.
% 45.50/45.69 generalize (zenon_Hea (sigma)). zenon_intro zenon_Heb.
% 45.50/45.69 apply (zenon_notand_s _ _ zenon_Heb); [ zenon_intro zenon_Hda | zenon_intro zenon_Hda ].
% 45.50/45.69 apply (zenon_L166_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial.
% 45.50/45.69 apply (zenon_L166_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial.
% 45.50/45.69 (* end of lemma zenon_L167_ *)
% 45.50/45.69 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).
% 45.50/45.69 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.
% 45.50/45.69 generalize (zenon_H35 zenon_TT3_x). zenon_intro zenon_H106.
% 45.50/45.69 apply (zenon_and_s _ _ zenon_H106). zenon_intro zenon_H108. zenon_intro zenon_H107.
% 45.50/45.69 apply (zenon_imply_s _ _ zenon_H107); [ zenon_intro zenon_H109 | zenon_intro zenon_Hbb ].
% 45.50/45.69 exact (zenon_H109 zenon_H100).
% 45.50/45.69 apply (zenon_L167_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial.
% 45.50/45.69 (* end of lemma zenon_L168_ *)
% 45.50/45.69 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).
% 45.50/45.69 do 4 intro. intros zenon_H34 zenon_H100 zenon_H10f zenon_H26e zenon_H38 zenon_H35 zenon_Hec zenon_H1a zenon_Hae zenon_H1f.
% 45.50/45.69 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3.
% 45.50/45.69 apply (zenon_L168_ zenon_TT0_hz zenon_TT3_x zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.69 (* end of lemma zenon_L169_ *)
% 45.50/45.69 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).
% 45.50/45.69 do 4 intro. intros zenon_H34 zenon_H270 zenon_H100 zenon_H26e zenon_H38 zenon_H35 zenon_Hec zenon_H1a zenon_Hae zenon_H1f.
% 45.50/45.69 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_H10e | zenon_intro zenon_H10f ].
% 45.50/45.69 cut ((greater (low) (very_low)) = (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT3_x))).
% 45.50/45.69 intro zenon_D_pnotp.
% 45.50/45.69 apply zenon_H270.
% 45.50/45.69 rewrite <- zenon_D_pnotp.
% 45.50/45.69 exact assumption_18c.
% 45.50/45.69 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_H10f].
% 45.50/45.69 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.50/45.69 congruence.
% 45.50/45.69 apply zenon_H6a. apply refl_equal.
% 45.50/45.69 exact (zenon_H10f zenon_H10e).
% 45.50/45.69 apply (zenon_L169_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial.
% 45.50/45.69 (* end of lemma zenon_L170_ *)
% 45.50/45.69 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).
% 45.50/45.69 do 4 intro. intros zenon_H34 zenon_Hb5 zenon_H1f zenon_Hae zenon_H1a zenon_Hec zenon_H35 zenon_H38 zenon_H26e zenon_H100.
% 45.50/45.69 elim (classic (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_H271 | zenon_intro zenon_H270 ].
% 45.50/45.69 generalize (zenon_H34 (mod1)). zenon_intro zenon_Ha7.
% 45.50/45.69 generalize (zenon_Ha7 (low)). zenon_intro zenon_Ha8.
% 45.50/45.69 generalize (zenon_Ha8 (hazard_of_mortality zenon_TX_y zenon_TT3_x)). zenon_intro zenon_H272.
% 45.50/45.69 apply (zenon_imply_s _ _ zenon_H272); [ zenon_intro zenon_H7f | zenon_intro zenon_H273 ].
% 45.50/45.69 exact (zenon_H7f assumption_18b).
% 45.50/45.69 apply (zenon_imply_s _ _ zenon_H273); [ zenon_intro zenon_H270 | zenon_intro zenon_Hb4 ].
% 45.50/45.69 exact (zenon_H270 zenon_H271).
% 45.50/45.69 exact (zenon_Hb5 zenon_Hb4).
% 45.50/45.69 apply (zenon_L170_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial.
% 45.50/45.69 (* end of lemma zenon_L171_ *)
% 45.50/45.69 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).
% 45.50/45.69 do 4 intro. intros zenon_H34 zenon_H274 zenon_H100 zenon_H26e zenon_H38 zenon_H35 zenon_Hec zenon_H1a zenon_Hae zenon_H1f.
% 45.50/45.69 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb5 ].
% 45.50/45.69 generalize (zenon_H34 (mod2)). zenon_intro zenon_H16e.
% 45.50/45.69 generalize (zenon_H16e (mod1)). zenon_intro zenon_H16f.
% 45.50/45.69 generalize (zenon_H16f (hazard_of_mortality zenon_TX_y zenon_TT3_x)). zenon_intro zenon_H275.
% 45.50/45.69 apply (zenon_imply_s _ _ zenon_H275); [ zenon_intro zenon_H69 | zenon_intro zenon_H276 ].
% 45.50/45.69 exact (zenon_H69 assumption_19).
% 45.50/45.69 apply (zenon_imply_s _ _ zenon_H276); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H277 ].
% 45.50/45.69 exact (zenon_Hb5 zenon_Hb4).
% 45.50/45.69 exact (zenon_H274 zenon_H277).
% 45.50/45.69 apply (zenon_L171_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial.
% 45.50/45.69 (* end of lemma zenon_L172_ *)
% 45.50/45.69 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).
% 45.50/45.69 do 4 intro. intros zenon_H34 zenon_H278 zenon_H1f zenon_Hae zenon_H1a zenon_Hec zenon_H35 zenon_H38 zenon_H26e zenon_H100.
% 45.50/45.69 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_H277 | zenon_intro zenon_H274 ].
% 45.50/45.69 generalize (zenon_H34 (high)). zenon_intro zenon_H1fa.
% 45.50/45.69 generalize (zenon_H1fa (mod2)). zenon_intro zenon_H1fb.
% 45.50/45.69 generalize (zenon_H1fb (hazard_of_mortality zenon_TX_y zenon_TT3_x)). zenon_intro zenon_H279.
% 45.50/45.69 apply (zenon_imply_s _ _ zenon_H279); [ zenon_intro zenon_H9b | zenon_intro zenon_H27a ].
% 45.50/45.69 exact (zenon_H9b assumption_18d).
% 45.50/45.69 apply (zenon_imply_s _ _ zenon_H27a); [ zenon_intro zenon_H274 | zenon_intro zenon_H27b ].
% 45.50/45.69 exact (zenon_H274 zenon_H277).
% 45.50/45.69 exact (zenon_H278 zenon_H27b).
% 45.50/45.69 apply (zenon_L172_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial.
% 45.50/45.69 (* end of lemma zenon_L173_ *)
% 45.50/45.69 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).
% 45.50/45.69 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.
% 45.50/45.69 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_H27b | zenon_intro zenon_H278 ].
% 45.50/45.69 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))).
% 45.50/45.69 intro zenon_D_pnotp.
% 45.50/45.69 apply zenon_H27c.
% 45.50/45.69 rewrite <- zenon_D_pnotp.
% 45.50/45.69 exact zenon_H27b.
% 45.50/45.69 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].
% 45.50/45.69 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H119].
% 45.50/45.69 congruence.
% 45.50/45.69 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 ].
% 45.50/45.69 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))).
% 45.50/45.69 intro zenon_D_pnotp.
% 45.50/45.69 apply zenon_H119.
% 45.50/45.69 rewrite <- zenon_D_pnotp.
% 45.50/45.69 exact zenon_H11a.
% 45.50/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.50/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c].
% 45.50/45.69 congruence.
% 45.50/45.69 exact (zenon_H11c zenon_H116).
% 45.50/45.69 apply zenon_H11b. apply refl_equal.
% 45.50/45.69 apply zenon_H11b. apply refl_equal.
% 45.50/45.69 apply zenon_Hb6. apply refl_equal.
% 45.50/45.69 apply (zenon_L173_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial.
% 45.50/45.69 (* end of lemma zenon_L174_ *)
% 45.50/45.69 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).
% 45.50/45.69 do 2 intro. intros zenon_H1c4 zenon_H92.
% 45.50/45.69 elim (classic ((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H27d | zenon_intro zenon_Ha0 ].
% 45.50/45.69 cut ((greater (mod2) (mod1)) = (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))).
% 45.50/45.69 intro zenon_D_pnotp.
% 45.50/45.69 apply zenon_H1c4.
% 45.50/45.69 rewrite <- zenon_D_pnotp.
% 45.50/45.69 exact assumption_19.
% 45.50/45.69 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_Ha0].
% 45.50/45.69 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83].
% 45.50/45.69 congruence.
% 45.50/45.69 apply zenon_H83. apply refl_equal.
% 45.50/45.69 exact (zenon_Ha0 zenon_H27d).
% 45.50/45.69 apply zenon_Ha0. apply sym_equal. exact zenon_H92.
% 45.50/45.69 (* end of lemma zenon_L175_ *)
% 45.50/45.69 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).
% 45.50/45.69 do 2 intro. intros zenon_H34 zenon_H2c zenon_H1c2 zenon_H92.
% 45.50/45.69 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H118 | zenon_intro zenon_H114 ].
% 45.50/45.69 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))).
% 45.50/45.69 intro zenon_D_pnotp.
% 45.50/45.69 apply zenon_H1c2.
% 45.50/45.69 rewrite <- zenon_D_pnotp.
% 45.50/45.69 exact zenon_H118.
% 45.50/45.69 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].
% 45.50/45.69 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H94].
% 45.50/45.69 congruence.
% 45.50/45.69 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 ].
% 45.50/45.69 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))).
% 45.50/45.69 intro zenon_D_pnotp.
% 45.50/45.69 apply zenon_H94.
% 45.50/45.69 rewrite <- zenon_D_pnotp.
% 45.50/45.69 exact zenon_H61.
% 45.50/45.69 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].
% 45.50/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b].
% 45.50/45.69 congruence.
% 45.50/45.69 exact (zenon_H2b zenon_H2c).
% 45.50/45.69 apply zenon_H62. apply refl_equal.
% 45.50/45.69 apply zenon_H62. apply refl_equal.
% 45.50/45.69 apply zenon_H62. apply refl_equal.
% 45.50/45.69 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1c4 ].
% 45.50/45.69 generalize (zenon_H34 (high)). zenon_intro zenon_H1fa.
% 45.50/45.69 generalize (zenon_H1fa (mod2)). zenon_intro zenon_H1fb.
% 45.50/45.69 generalize (zenon_H1fb (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H27e.
% 45.50/45.69 apply (zenon_imply_s _ _ zenon_H27e); [ zenon_intro zenon_H9b | zenon_intro zenon_H27f ].
% 45.50/45.69 exact (zenon_H9b assumption_18d).
% 45.50/45.69 apply (zenon_imply_s _ _ zenon_H27f); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H118 ].
% 45.50/45.69 exact (zenon_H1c4 zenon_H1c3).
% 45.50/45.69 exact (zenon_H114 zenon_H118).
% 45.50/45.69 apply (zenon_L175_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.69 (* end of lemma zenon_L176_ *)
% 45.50/45.69 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).
% 45.50/45.69 do 2 intro. intros zenon_H92 zenon_H34 zenon_H280 zenon_H2c.
% 45.50/45.69 elim (classic ((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H281 | zenon_intro zenon_H94 ].
% 45.50/45.69 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (high))); [ zenon_intro zenon_H97 | zenon_intro zenon_H87 ].
% 45.50/45.69 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (high)) = (greater (high) (high))).
% 45.50/45.69 intro zenon_D_pnotp.
% 45.50/45.69 apply zenon_H280.
% 45.50/45.69 rewrite <- zenon_D_pnotp.
% 45.50/45.69 exact zenon_H97.
% 45.50/45.69 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113].
% 45.50/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b].
% 45.50/45.69 congruence.
% 45.50/45.69 elim (classic ((high) = (high))); [ zenon_intro zenon_H180 | zenon_intro zenon_H113 ].
% 45.50/45.69 cut (((high) = (high)) = ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))).
% 45.50/45.69 intro zenon_D_pnotp.
% 45.50/45.69 apply zenon_H2b.
% 45.50/45.69 rewrite <- zenon_D_pnotp.
% 45.50/45.69 exact zenon_H180.
% 45.50/45.69 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113].
% 45.50/45.69 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H94].
% 45.50/45.69 congruence.
% 45.50/45.69 exact (zenon_H94 zenon_H281).
% 45.50/45.69 apply zenon_H113. apply refl_equal.
% 45.50/45.69 apply zenon_H113. apply refl_equal.
% 45.50/45.69 apply zenon_H113. apply refl_equal.
% 45.50/45.69 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 ].
% 45.50/45.69 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))).
% 45.50/45.69 intro zenon_D_pnotp.
% 45.50/45.69 apply zenon_H87.
% 45.50/45.69 rewrite <- zenon_D_pnotp.
% 45.50/45.69 exact zenon_H1c5.
% 45.50/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b].
% 45.50/45.69 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].
% 45.50/45.69 congruence.
% 45.50/45.69 apply zenon_H62. apply refl_equal.
% 45.50/45.69 exact (zenon_H2b zenon_H2c).
% 45.50/45.69 apply (zenon_L176_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.69 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 ].
% 45.50/45.69 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))).
% 45.50/45.69 intro zenon_D_pnotp.
% 45.50/45.69 apply zenon_H94.
% 45.50/45.69 rewrite <- zenon_D_pnotp.
% 45.50/45.69 exact zenon_H61.
% 45.50/45.69 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].
% 45.50/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b].
% 45.50/45.69 congruence.
% 45.50/45.69 exact (zenon_H2b zenon_H2c).
% 45.50/45.69 apply zenon_H62. apply refl_equal.
% 45.50/45.69 apply zenon_H62. apply refl_equal.
% 45.50/45.69 (* end of lemma zenon_L177_ *)
% 45.50/45.69 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).
% 45.50/45.69 do 2 intro. intros zenon_H28 zenon_H26e zenon_H38 zenon_H35 zenon_H2a zenon_H282 zenon_H92.
% 45.50/45.69 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ].
% 45.50/45.69 apply (zenon_notand_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ].
% 45.50/45.69 exact (zenon_H2f zenon_H2a).
% 45.50/45.69 apply zenon_H2e. zenon_intro zenon_H36.
% 45.50/45.69 apply (zenon_L155_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.69 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1c4 ].
% 45.50/45.69 cut ((greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (mod2) (high))).
% 45.50/45.69 intro zenon_D_pnotp.
% 45.50/45.69 apply zenon_H282.
% 45.50/45.69 rewrite <- zenon_D_pnotp.
% 45.50/45.69 exact zenon_H1c3.
% 45.50/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b].
% 45.50/45.69 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83].
% 45.50/45.69 congruence.
% 45.50/45.69 apply zenon_H83. apply refl_equal.
% 45.50/45.69 exact (zenon_H2b zenon_H2c).
% 45.50/45.69 apply (zenon_L175_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.69 (* end of lemma zenon_L178_ *)
% 45.50/45.69 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).
% 45.50/45.69 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.
% 45.50/45.69 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88.
% 45.50/45.69 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ].
% 45.50/45.69 exact (zenon_H27 zenon_H1f).
% 45.50/45.69 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a.
% 45.50/45.69 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ].
% 45.50/45.69 apply (zenon_L3_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.50/45.69 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d.
% 45.50/45.69 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f.
% 45.50/45.69 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H30. zenon_intro zenon_H28.
% 45.55/45.69 apply (zenon_imply_s _ _ zenon_H8e); [ zenon_intro zenon_H91 | zenon_intro zenon_H6b ].
% 45.55/45.69 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ].
% 45.55/45.69 apply (zenon_imply_s _ _ zenon_H90); [ zenon_intro zenon_H93 | zenon_intro zenon_H92 ].
% 45.55/45.69 apply (zenon_notand_s _ _ zenon_H93); [ zenon_intro zenon_H2f | zenon_intro zenon_H29 ].
% 45.55/45.69 exact (zenon_H2f zenon_H2a).
% 45.55/45.69 apply (zenon_L4_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.69 apply (zenon_L178_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.69 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ].
% 45.55/45.69 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ].
% 45.55/45.69 apply (zenon_L4_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.69 exact (zenon_H2e zenon_H29).
% 45.55/45.69 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_H277 | zenon_intro zenon_H274 ].
% 45.55/45.69 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))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_Hae.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_H277.
% 45.55/45.69 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].
% 45.55/45.69 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 45.55/45.69 congruence.
% 45.55/45.69 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 ].
% 45.55/45.69 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))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_H5e.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_H61.
% 45.55/45.69 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].
% 45.55/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31].
% 45.55/45.69 congruence.
% 45.55/45.69 exact (zenon_H31 zenon_H32).
% 45.55/45.69 apply zenon_H62. apply refl_equal.
% 45.55/45.69 apply zenon_H62. apply refl_equal.
% 45.55/45.69 apply zenon_Hb6. apply refl_equal.
% 45.55/45.69 apply (zenon_L172_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial.
% 45.55/45.69 apply zenon_H72. apply sym_equal. exact zenon_H6b.
% 45.55/45.69 (* end of lemma zenon_L179_ *)
% 45.55/45.69 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).
% 45.55/45.69 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.
% 45.55/45.69 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0.
% 45.55/45.69 cut ((greater (low) (very_low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (hazard_of_mortality zenon_TX_y zenon_TT3_x))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_Hae.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact assumption_18c.
% 45.55/45.69 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_H10f].
% 45.55/45.69 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72].
% 45.55/45.69 congruence.
% 45.55/45.69 apply (zenon_L179_ zenon_TT0_hz zenon_TT3_x zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.69 apply (zenon_L169_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial.
% 45.55/45.69 (* end of lemma zenon_L180_ *)
% 45.55/45.69 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).
% 45.55/45.69 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.
% 45.55/45.69 elim (classic (greater (mod2) (high))); [ zenon_intro zenon_H283 | zenon_intro zenon_H282 ].
% 45.55/45.69 generalize (zenon_H34 (high)). zenon_intro zenon_H1fa.
% 45.55/45.69 generalize (zenon_H1fa (mod2)). zenon_intro zenon_H1fb.
% 45.55/45.69 generalize (zenon_H1fb (high)). zenon_intro zenon_H284.
% 45.55/45.69 apply (zenon_imply_s _ _ zenon_H284); [ zenon_intro zenon_H9b | zenon_intro zenon_H285 ].
% 45.55/45.69 exact (zenon_H9b assumption_18d).
% 45.55/45.69 apply (zenon_imply_s _ _ zenon_H285); [ zenon_intro zenon_H282 | zenon_intro zenon_H286 ].
% 45.55/45.69 exact (zenon_H282 zenon_H283).
% 45.55/45.69 exact (zenon_H280 zenon_H286).
% 45.55/45.69 apply (zenon_L180_ zenon_TT0_hz zenon_TT3_x zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.69 (* end of lemma zenon_L181_ *)
% 45.55/45.69 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).
% 45.55/45.69 do 4 intro. intros zenon_H34 zenon_H1f zenon_H1a zenon_H35 zenon_H38 zenon_H26e zenon_H2b zenon_Hae zenon_Hec zenon_H100.
% 45.55/45.69 generalize (meaning_postulate_greater_strict (high)). zenon_intro zenon_H202.
% 45.55/45.69 generalize (zenon_H202 (high)). zenon_intro zenon_H287.
% 45.55/45.69 apply (zenon_notand_s _ _ zenon_H287); [ zenon_intro zenon_H280 | zenon_intro zenon_H280 ].
% 45.55/45.69 apply (zenon_L181_ zenon_TT0_hz zenon_TT3_x zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.69 apply (zenon_L181_ zenon_TT0_hz zenon_TT3_x zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.69 (* end of lemma zenon_L182_ *)
% 45.55/45.69 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).
% 45.55/45.69 do 4 intro. intros zenon_H100 zenon_H26e zenon_H38 zenon_H35 zenon_Hec zenon_H1a zenon_Hae zenon_H1f zenon_H34 zenon_H116.
% 45.55/45.69 elim (classic ((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H17d | zenon_intro zenon_H119 ].
% 45.55/45.69 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 ].
% 45.55/45.69 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_H27b | zenon_intro zenon_H278 ].
% 45.55/45.69 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))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_Hae.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_H27b.
% 45.55/45.69 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].
% 45.55/45.69 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H94].
% 45.55/45.69 congruence.
% 45.55/45.69 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 ].
% 45.55/45.69 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))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_H94.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_H61.
% 45.55/45.69 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].
% 45.55/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b].
% 45.55/45.69 congruence.
% 45.55/45.69 apply (zenon_L182_ zenon_TT0_hz zenon_TT3_x zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.69 apply zenon_H62. apply refl_equal.
% 45.55/45.69 apply zenon_H62. apply refl_equal.
% 45.55/45.69 apply zenon_Hb6. apply refl_equal.
% 45.55/45.69 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))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_H278.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_H288.
% 45.55/45.69 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].
% 45.55/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c].
% 45.55/45.69 congruence.
% 45.55/45.69 elim (classic ((high) = (high))); [ zenon_intro zenon_H180 | zenon_intro zenon_H113 ].
% 45.55/45.69 cut (((high) = (high)) = ((hazard_of_mortality zenon_TX_y zenon_E) = (high))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_H11c.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_H180.
% 45.55/45.69 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113].
% 45.55/45.69 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H119].
% 45.55/45.69 congruence.
% 45.55/45.69 exact (zenon_H119 zenon_H17d).
% 45.55/45.69 apply zenon_H113. apply refl_equal.
% 45.55/45.69 apply zenon_H113. apply refl_equal.
% 45.55/45.69 apply zenon_Hb6. apply refl_equal.
% 45.55/45.69 apply (zenon_L174_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial.
% 45.55/45.69 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 ].
% 45.55/45.69 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))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_H119.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_H11a.
% 45.55/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c].
% 45.55/45.69 congruence.
% 45.55/45.69 exact (zenon_H11c zenon_H116).
% 45.55/45.69 apply zenon_H11b. apply refl_equal.
% 45.55/45.69 apply zenon_H11b. apply refl_equal.
% 45.55/45.69 (* end of lemma zenon_L183_ *)
% 45.55/45.69 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).
% 45.55/45.69 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.
% 45.55/45.69 apply (zenon_imply_s _ _ zenon_H181); [ zenon_intro zenon_H184 | zenon_intro zenon_H116 ].
% 45.55/45.69 apply (zenon_notand_s _ _ zenon_H184); [ zenon_intro zenon_H186 | zenon_intro zenon_H185 ].
% 45.55/45.69 exact (zenon_H186 zenon_H183).
% 45.55/45.69 exact (zenon_H185 zenon_H182).
% 45.55/45.69 apply (zenon_L183_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial.
% 45.55/45.69 (* end of lemma zenon_L184_ *)
% 45.55/45.69 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).
% 45.55/45.69 do 3 intro. intros zenon_H1f zenon_H1a zenon_Hec zenon_Hf3 zenon_H31 zenon_H35 zenon_H38 zenon_H34 zenon_Hda zenon_H26e.
% 45.55/45.69 elim (classic ((sigma) = (age zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_He2 | zenon_intro zenon_Hde ].
% 45.55/45.69 elim (classic (greater (age zenon_TX_y zenon_TT1_bg) (sigma))); [ zenon_intro zenon_Hdb | zenon_intro zenon_He9 ].
% 45.55/45.69 cut ((greater (age zenon_TX_y zenon_TT1_bg) (sigma)) = (greater (sigma) (sigma))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_Hda.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_Hdb.
% 45.55/45.69 cut (((sigma) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hd9].
% 45.55/45.69 cut (((age zenon_TX_y zenon_TT1_bg) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hdf].
% 45.55/45.69 congruence.
% 45.55/45.69 elim (classic ((sigma) = (sigma))); [ zenon_intro zenon_He3 | zenon_intro zenon_Hd9 ].
% 45.55/45.69 cut (((sigma) = (sigma)) = ((age zenon_TX_y zenon_TT1_bg) = (sigma))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_Hdf.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_He3.
% 45.55/45.69 cut (((sigma) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hd9].
% 45.55/45.69 cut (((sigma) = (age zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_Hde].
% 45.55/45.69 congruence.
% 45.55/45.69 exact (zenon_Hde zenon_He2).
% 45.55/45.69 apply zenon_Hd9. apply refl_equal.
% 45.55/45.69 apply zenon_Hd9. apply refl_equal.
% 45.55/45.69 apply zenon_Hd9. apply refl_equal.
% 45.55/45.69 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0.
% 45.55/45.69 apply (zenon_L159_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.69 elim (classic ((age zenon_TX_y zenon_TT1_bg) = (age zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H26f | zenon_intro zenon_H4d ].
% 45.55/45.69 cut (((age zenon_TX_y zenon_TT1_bg) = (age zenon_TX_y zenon_TT1_bg)) = ((sigma) = (age zenon_TX_y zenon_TT1_bg))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_Hde.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_H26f.
% 45.55/45.69 cut (((age zenon_TX_y zenon_TT1_bg) = (age zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H4d].
% 45.55/45.69 cut (((age zenon_TX_y zenon_TT1_bg) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hdf].
% 45.55/45.69 congruence.
% 45.55/45.69 exact (zenon_Hdf zenon_H26e).
% 45.55/45.69 apply zenon_H4d. apply refl_equal.
% 45.55/45.69 apply zenon_H4d. apply refl_equal.
% 45.55/45.69 (* end of lemma zenon_L185_ *)
% 45.55/45.69 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).
% 45.55/45.69 do 3 intro. intros zenon_H34 zenon_H26e zenon_H38 zenon_H35 zenon_H31 zenon_Hf3 zenon_Hec zenon_H1a zenon_H1f.
% 45.55/45.69 generalize (meaning_postulate_greater_strict (sigma)). zenon_intro zenon_Hea.
% 45.55/45.69 generalize (zenon_Hea (sigma)). zenon_intro zenon_Heb.
% 45.55/45.69 apply (zenon_notand_s _ _ zenon_Heb); [ zenon_intro zenon_Hda | zenon_intro zenon_Hda ].
% 45.55/45.69 apply (zenon_L185_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.69 apply (zenon_L185_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.69 (* end of lemma zenon_L186_ *)
% 45.55/45.69 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).
% 45.55/45.69 do 3 intro. intros zenon_H34 zenon_H1f zenon_H1a zenon_Hec zenon_H31 zenon_H35 zenon_H38 zenon_H26e.
% 45.55/45.69 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3.
% 45.55/45.69 apply (zenon_L186_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.69 (* end of lemma zenon_L187_ *)
% 45.55/45.69 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).
% 45.55/45.69 do 3 intro. intros zenon_H26e zenon_H38 zenon_H35 zenon_Hec zenon_H1a zenon_H1f zenon_H34 zenon_H5a.
% 45.55/45.69 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 ].
% 45.55/45.69 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H31. zenon_intro zenon_H5d.
% 45.55/45.69 apply (zenon_L187_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.69 cut ((greater (mod2) (mod1)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_H5a.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact assumption_19.
% 45.55/45.69 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 45.55/45.69 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 45.55/45.69 congruence.
% 45.55/45.69 apply (zenon_notand_s _ _ zenon_H5c); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ].
% 45.55/45.69 apply zenon_H60. zenon_intro zenon_H32.
% 45.55/45.69 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 ].
% 45.55/45.69 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))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_H5e.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_H61.
% 45.55/45.69 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].
% 45.55/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31].
% 45.55/45.69 congruence.
% 45.55/45.69 exact (zenon_H31 zenon_H32).
% 45.55/45.69 apply zenon_H62. apply refl_equal.
% 45.55/45.69 apply zenon_H62. apply refl_equal.
% 45.55/45.69 apply zenon_H5f. zenon_intro zenon_H63.
% 45.55/45.69 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64.
% 45.55/45.69 generalize (zenon_H64 (mod2)). zenon_intro zenon_H65.
% 45.55/45.69 generalize (zenon_H65 (mod1)). zenon_intro zenon_H66.
% 45.55/45.69 apply (zenon_imply_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H67 ].
% 45.55/45.69 exact (zenon_H5d zenon_H63).
% 45.55/45.69 apply (zenon_imply_s _ _ zenon_H67); [ zenon_intro zenon_H69 | zenon_intro zenon_H68 ].
% 45.55/45.69 exact (zenon_H69 assumption_19).
% 45.55/45.69 exact (zenon_H5a zenon_H68).
% 45.55/45.69 apply zenon_H59. apply refl_equal.
% 45.55/45.69 (* end of lemma zenon_L188_ *)
% 45.55/45.69 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).
% 45.55/45.69 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.
% 45.55/45.69 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_H277 | zenon_intro zenon_H274 ].
% 45.55/45.69 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))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_H27c.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_H277.
% 45.55/45.69 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].
% 45.55/45.69 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1].
% 45.55/45.69 congruence.
% 45.55/45.69 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 ].
% 45.55/45.69 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))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_H1a1.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_H11a.
% 45.55/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2].
% 45.55/45.69 congruence.
% 45.55/45.69 exact (zenon_H1a2 zenon_H19e).
% 45.55/45.69 apply zenon_H11b. apply refl_equal.
% 45.55/45.69 apply zenon_H11b. apply refl_equal.
% 45.55/45.69 apply zenon_Hb6. apply refl_equal.
% 45.55/45.69 apply (zenon_L172_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial.
% 45.55/45.69 (* end of lemma zenon_L189_ *)
% 45.55/45.69 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).
% 45.55/45.69 do 4 intro. intros zenon_H1f zenon_Hae zenon_H1a zenon_Hec zenon_H35 zenon_H38 zenon_H26e zenon_H100 zenon_H34 zenon_H19e.
% 45.55/45.69 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H1a1 ].
% 45.55/45.69 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 ].
% 45.55/45.69 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_H277 | zenon_intro zenon_H274 ].
% 45.55/45.69 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))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_Hae.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_H277.
% 45.55/45.69 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].
% 45.55/45.69 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 45.55/45.69 congruence.
% 45.55/45.69 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 ].
% 45.55/45.69 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))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_H5e.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_H61.
% 45.55/45.69 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].
% 45.55/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31].
% 45.55/45.69 congruence.
% 45.55/45.69 apply (zenon_L187_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.69 apply zenon_H62. apply refl_equal.
% 45.55/45.69 apply zenon_H62. apply refl_equal.
% 45.55/45.69 apply zenon_Hb6. apply refl_equal.
% 45.55/45.69 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))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_H274.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_H288.
% 45.55/45.69 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].
% 45.55/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2].
% 45.55/45.69 congruence.
% 45.55/45.69 elim (classic ((mod2) = (mod2))); [ zenon_intro zenon_H17b | zenon_intro zenon_H83 ].
% 45.55/45.69 cut (((mod2) = (mod2)) = ((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_H1a2.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_H17b.
% 45.55/45.69 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83].
% 45.55/45.69 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1].
% 45.55/45.69 congruence.
% 45.55/45.69 exact (zenon_H1a1 zenon_H1a3).
% 45.55/45.69 apply zenon_H83. apply refl_equal.
% 45.55/45.69 apply zenon_H83. apply refl_equal.
% 45.55/45.69 apply zenon_Hb6. apply refl_equal.
% 45.55/45.69 apply (zenon_L189_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial.
% 45.55/45.69 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 ].
% 45.55/45.69 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))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_H1a1.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_H11a.
% 45.55/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2].
% 45.55/45.69 congruence.
% 45.55/45.69 exact (zenon_H1a2 zenon_H19e).
% 45.55/45.69 apply zenon_H11b. apply refl_equal.
% 45.55/45.69 apply zenon_H11b. apply refl_equal.
% 45.55/45.69 (* end of lemma zenon_L190_ *)
% 45.55/45.69 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).
% 45.55/45.69 do 3 intro. intros zenon_H26e zenon_H38 zenon_H35 zenon_Hec zenon_H1a zenon_H1f zenon_H34 zenon_H9d.
% 45.55/45.69 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 ].
% 45.55/45.69 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H31. zenon_intro zenon_H5d.
% 45.55/45.69 apply (zenon_L187_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.69 cut ((greater (mod2) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_H9d.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact assumption_18e.
% 45.55/45.69 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.55/45.69 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 45.55/45.69 congruence.
% 45.55/45.69 apply (zenon_notand_s _ _ zenon_H5c); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ].
% 45.55/45.69 apply zenon_H60. zenon_intro zenon_H32.
% 45.55/45.69 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 ].
% 45.55/45.69 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))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_H5e.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_H61.
% 45.55/45.69 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].
% 45.55/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31].
% 45.55/45.69 congruence.
% 45.55/45.69 exact (zenon_H31 zenon_H32).
% 45.55/45.69 apply zenon_H62. apply refl_equal.
% 45.55/45.69 apply zenon_H62. apply refl_equal.
% 45.55/45.69 apply zenon_H5f. zenon_intro zenon_H63.
% 45.55/45.69 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64.
% 45.55/45.69 generalize (zenon_H64 (mod2)). zenon_intro zenon_H65.
% 45.55/45.69 generalize (zenon_H65 (low)). zenon_intro zenon_Hc0.
% 45.55/45.69 apply (zenon_imply_s _ _ zenon_Hc0); [ zenon_intro zenon_H5d | zenon_intro zenon_Hc1 ].
% 45.55/45.69 exact (zenon_H5d zenon_H63).
% 45.55/45.69 apply (zenon_imply_s _ _ zenon_Hc1); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H9c ].
% 45.55/45.69 exact (zenon_Hc2 assumption_18e).
% 45.55/45.69 exact (zenon_H9d zenon_H9c).
% 45.55/45.69 apply zenon_H6a. apply refl_equal.
% 45.55/45.69 (* end of lemma zenon_L191_ *)
% 45.55/45.69 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).
% 45.55/45.69 do 4 intro. intros zenon_H1f zenon_H1a zenon_Hec zenon_H35 zenon_H38 zenon_H26e zenon_Hae zenon_H100 zenon_H34 zenon_H1b8.
% 45.55/45.69 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1ba ].
% 45.55/45.69 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (low))); [ zenon_intro zenon_H9c | zenon_intro zenon_H9d ].
% 45.55/45.69 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 ].
% 45.55/45.69 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 ].
% 45.55/45.69 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64.
% 45.55/45.69 generalize (zenon_H64 (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H28b.
% 45.55/45.69 generalize (zenon_H28b (hazard_of_mortality zenon_TX_y zenon_TT3_x)). zenon_intro zenon_H28c.
% 45.55/45.69 apply (zenon_imply_s _ _ zenon_H28c); [ zenon_intro zenon_H28a | zenon_intro zenon_H28d ].
% 45.55/45.69 exact (zenon_H28a zenon_H289).
% 45.55/45.69 apply (zenon_imply_s _ _ zenon_H28d); [ zenon_intro zenon_H27c | zenon_intro zenon_H104 ].
% 45.55/45.69 exact (zenon_H27c zenon_H288).
% 45.55/45.69 exact (zenon_Hae zenon_H104).
% 45.55/45.69 elim (classic (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_H271 | zenon_intro zenon_H270 ].
% 45.55/45.69 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))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_H27c.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_H271.
% 45.55/45.69 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].
% 45.55/45.69 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba].
% 45.55/45.69 congruence.
% 45.55/45.69 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 ].
% 45.55/45.69 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))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_H1ba.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_H11a.
% 45.55/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb].
% 45.55/45.69 congruence.
% 45.55/45.69 exact (zenon_H1bb zenon_H1b8).
% 45.55/45.69 apply zenon_H11b. apply refl_equal.
% 45.55/45.69 apply zenon_H11b. apply refl_equal.
% 45.55/45.69 apply zenon_Hb6. apply refl_equal.
% 45.55/45.69 apply (zenon_L170_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial.
% 45.55/45.69 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))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_H28a.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_H9c.
% 45.55/45.69 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba].
% 45.55/45.69 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].
% 45.55/45.69 congruence.
% 45.55/45.69 apply zenon_H62. apply refl_equal.
% 45.55/45.69 exact (zenon_H1ba zenon_H1b9).
% 45.55/45.69 apply (zenon_L191_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.69 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 ].
% 45.55/45.69 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))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_H1ba.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_H11a.
% 45.55/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb].
% 45.55/45.69 congruence.
% 45.55/45.69 exact (zenon_H1bb zenon_H1b8).
% 45.55/45.69 apply zenon_H11b. apply refl_equal.
% 45.55/45.69 apply zenon_H11b. apply refl_equal.
% 45.55/45.69 (* end of lemma zenon_L192_ *)
% 45.55/45.69 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).
% 45.55/45.69 do 3 intro. intros zenon_H1f zenon_H1a zenon_Hec zenon_H35 zenon_H38 zenon_H26e zenon_H34 zenon_Hf6.
% 45.55/45.69 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 ].
% 45.55/45.69 apply (zenon_and_s _ _ zenon_Hf7). zenon_intro zenon_H73. zenon_intro zenon_H9d.
% 45.55/45.69 apply (zenon_L191_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.69 cut ((greater (low) (very_low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (very_low))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_Hf6.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact assumption_18c.
% 45.55/45.69 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5].
% 45.55/45.69 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72].
% 45.55/45.69 congruence.
% 45.55/45.69 apply (zenon_notand_s _ _ zenon_Hf8); [ zenon_intro zenon_Hfa | zenon_intro zenon_Hf9 ].
% 45.55/45.69 apply zenon_Hfa. zenon_intro zenon_H6b.
% 45.55/45.69 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 ].
% 45.55/45.69 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))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_H72.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_H61.
% 45.55/45.69 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].
% 45.55/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (low))); [idtac | apply NNPP; zenon_intro zenon_H73].
% 45.55/45.69 congruence.
% 45.55/45.69 exact (zenon_H73 zenon_H6b).
% 45.55/45.69 apply zenon_H62. apply refl_equal.
% 45.55/45.69 apply zenon_H62. apply refl_equal.
% 45.55/45.69 apply zenon_Hf9. zenon_intro zenon_H9c.
% 45.55/45.69 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64.
% 45.55/45.69 generalize (zenon_H64 (low)). zenon_intro zenon_Hfb.
% 45.55/45.69 generalize (zenon_Hfb (very_low)). zenon_intro zenon_Hfc.
% 45.55/45.69 apply (zenon_imply_s _ _ zenon_Hfc); [ zenon_intro zenon_H9d | zenon_intro zenon_Hfd ].
% 45.55/45.69 exact (zenon_H9d zenon_H9c).
% 45.55/45.69 apply (zenon_imply_s _ _ zenon_Hfd); [ zenon_intro zenon_Hff | zenon_intro zenon_Hfe ].
% 45.55/45.69 exact (zenon_Hff assumption_18c).
% 45.55/45.69 exact (zenon_Hf6 zenon_Hfe).
% 45.55/45.69 apply zenon_Hf5. apply refl_equal.
% 45.55/45.69 (* end of lemma zenon_L193_ *)
% 45.55/45.69 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).
% 45.55/45.69 do 3 intro. intros zenon_H26e zenon_H38 zenon_H35 zenon_Hec zenon_H1a zenon_H1f zenon_H28a zenon_H34 zenon_H1e0.
% 45.55/45.69 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e2 ].
% 45.55/45.69 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (very_low))); [ zenon_intro zenon_Hfe | zenon_intro zenon_Hf6 ].
% 45.55/45.69 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))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_H28a.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_Hfe.
% 45.55/45.69 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1e2].
% 45.55/45.69 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].
% 45.55/45.69 congruence.
% 45.55/45.69 apply zenon_H62. apply refl_equal.
% 45.55/45.69 exact (zenon_H1e2 zenon_H1e1).
% 45.55/45.69 apply (zenon_L193_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.69 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 ].
% 45.55/45.69 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))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_H1e2.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_H11a.
% 45.55/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5].
% 45.55/45.69 congruence.
% 45.55/45.69 exact (zenon_H1e5 zenon_H1e0).
% 45.55/45.69 apply zenon_H11b. apply refl_equal.
% 45.55/45.69 apply zenon_H11b. apply refl_equal.
% 45.55/45.69 (* end of lemma zenon_L194_ *)
% 45.55/45.69 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).
% 45.55/45.69 do 4 intro. intros zenon_H34 zenon_H1f zenon_H1a zenon_H35 zenon_H38 zenon_H26e zenon_Hec zenon_H100 zenon_H101.
% 45.55/45.69 generalize (definition_smaller (hazard_of_mortality zenon_TX_y zenon_TT3_x)). zenon_intro zenon_H102.
% 45.55/45.69 generalize (zenon_H102 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H103.
% 45.55/45.69 apply (zenon_equiv_s _ _ zenon_H103); [ zenon_intro zenon_H101; zenon_intro zenon_Hae | zenon_intro zenon_H105; zenon_intro zenon_H104 ].
% 45.55/45.69 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0.
% 45.55/45.69 generalize (zenon_H0 zenon_E). zenon_intro zenon_H239.
% 45.55/45.69 apply (zenon_imply_s _ _ zenon_H239); [ zenon_intro zenon_H27 | zenon_intro zenon_H23a ].
% 45.55/45.69 exact (zenon_H27 zenon_H1f).
% 45.55/45.69 apply (zenon_and_s _ _ zenon_H23a). zenon_intro zenon_H23b. zenon_intro zenon_H238.
% 45.55/45.69 apply (zenon_imply_s _ _ zenon_H23b); [ zenon_intro zenon_H112 | zenon_intro zenon_H1e0 ].
% 45.55/45.69 apply (zenon_imply_s _ _ zenon_H238); [ zenon_intro zenon_H111 | zenon_intro zenon_H22f ].
% 45.55/45.69 exact (zenon_H111 zenon_H112).
% 45.55/45.69 apply (zenon_and_s _ _ zenon_H22f). zenon_intro zenon_H231. zenon_intro zenon_H230.
% 45.55/45.69 apply (zenon_and_s _ _ zenon_H230). zenon_intro zenon_H233. zenon_intro zenon_H232.
% 45.55/45.69 apply (zenon_and_s _ _ zenon_H232). zenon_intro zenon_H234. zenon_intro zenon_H181.
% 45.55/45.69 apply (zenon_imply_s _ _ zenon_H231); [ zenon_intro zenon_H235 | zenon_intro zenon_H1b8 ].
% 45.55/45.69 apply (zenon_notand_s _ _ zenon_H235); [ zenon_intro zenon_H183 | zenon_intro zenon_H182 ].
% 45.55/45.69 apply (zenon_imply_s _ _ zenon_H233); [ zenon_intro zenon_H236 | zenon_intro zenon_H21a ].
% 45.55/45.69 apply (zenon_notand_s _ _ zenon_H236); [ zenon_intro zenon_H186 | zenon_intro zenon_H182 ].
% 45.55/45.69 exact (zenon_H186 zenon_H183).
% 45.55/45.69 apply (zenon_L184_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial.
% 45.55/45.69 elim (classic ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H23c | zenon_intro zenon_H21f ].
% 45.55/45.69 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (mod1))); [ zenon_intro zenon_H68 | zenon_intro zenon_H5a ].
% 45.55/45.69 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 ].
% 45.55/45.69 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 ].
% 45.55/45.69 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H64.
% 45.55/45.69 generalize (zenon_H64 (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H28b.
% 45.55/45.69 generalize (zenon_H28b (hazard_of_mortality zenon_TX_y zenon_TT3_x)). zenon_intro zenon_H28c.
% 45.55/45.69 apply (zenon_imply_s _ _ zenon_H28c); [ zenon_intro zenon_H28a | zenon_intro zenon_H28d ].
% 45.55/45.69 exact (zenon_H28a zenon_H289).
% 45.55/45.69 apply (zenon_imply_s _ _ zenon_H28d); [ zenon_intro zenon_H27c | zenon_intro zenon_H104 ].
% 45.55/45.69 exact (zenon_H27c zenon_H288).
% 45.55/45.69 exact (zenon_Hae zenon_H104).
% 45.55/45.69 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb5 ].
% 45.55/45.69 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))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_H27c.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_Hb4.
% 45.55/45.69 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].
% 45.55/45.69 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f].
% 45.55/45.69 congruence.
% 45.55/45.69 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 ].
% 45.55/45.69 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))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_H21f.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_H11a.
% 45.55/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e].
% 45.55/45.69 congruence.
% 45.55/45.69 exact (zenon_H21e zenon_H21a).
% 45.55/45.69 apply zenon_H11b. apply refl_equal.
% 45.55/45.69 apply zenon_H11b. apply refl_equal.
% 45.55/45.69 apply zenon_Hb6. apply refl_equal.
% 45.55/45.69 apply (zenon_L171_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial.
% 45.55/45.69 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))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_H28a.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_H68.
% 45.55/45.69 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f].
% 45.55/45.69 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].
% 45.55/45.69 congruence.
% 45.55/45.69 apply zenon_H62. apply refl_equal.
% 45.55/45.69 exact (zenon_H21f zenon_H23c).
% 45.55/45.69 apply (zenon_L188_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.69 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 ].
% 45.55/45.69 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))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_H21f.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_H11a.
% 45.55/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e].
% 45.55/45.69 congruence.
% 45.55/45.69 exact (zenon_H21e zenon_H21a).
% 45.55/45.69 apply zenon_H11b. apply refl_equal.
% 45.55/45.69 apply zenon_H11b. apply refl_equal.
% 45.55/45.69 apply (zenon_imply_s _ _ zenon_H234); [ zenon_intro zenon_H237 | zenon_intro zenon_H19e ].
% 45.55/45.69 apply (zenon_notand_s _ _ zenon_H237); [ zenon_intro zenon_H183 | zenon_intro zenon_H185 ].
% 45.55/45.69 apply (zenon_L184_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial.
% 45.55/45.69 exact (zenon_H185 zenon_H182).
% 45.55/45.69 apply (zenon_L190_ zenon_TT0_hz zenon_TT3_x zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.69 apply (zenon_L192_ zenon_TT3_x zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.69 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 ].
% 45.55/45.69 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT1_bg) (very_low))); [ zenon_intro zenon_Hfe | zenon_intro zenon_Hf6 ].
% 45.55/45.69 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))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_Hae.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_Hfe.
% 45.55/45.69 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT3_x))); [idtac | apply NNPP; zenon_intro zenon_H10f].
% 45.55/45.69 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].
% 45.55/45.69 congruence.
% 45.55/45.69 apply zenon_H62. apply refl_equal.
% 45.55/45.69 apply (zenon_L169_ zenon_TT0_hz zenon_TT1_bg zenon_TT3_x zenon_TX_y); trivial.
% 45.55/45.69 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))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_Hf6.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_H289.
% 45.55/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5].
% 45.55/45.69 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].
% 45.55/45.69 congruence.
% 45.55/45.69 apply zenon_H62. apply refl_equal.
% 45.55/45.69 exact (zenon_H1e5 zenon_H1e0).
% 45.55/45.69 apply (zenon_L194_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.69 exact (zenon_H101 zenon_H105).
% 45.55/45.69 (* end of lemma zenon_L195_ *)
% 45.55/45.69 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).
% 45.55/45.69 do 3 intro. intros zenon_H30 zenon_H29 zenon_Hed zenon_Hcd zenon_He9 zenon_Hec zenon_H1f zenon_H5e.
% 45.55/45.69 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ].
% 45.55/45.69 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ].
% 45.55/45.69 apply (zenon_L150_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.69 exact (zenon_H2e zenon_H29).
% 45.55/45.69 apply zenon_H5e. apply sym_equal. exact zenon_H32.
% 45.55/45.69 (* end of lemma zenon_L196_ *)
% 45.55/45.69 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).
% 45.55/45.69 do 3 intro. intros zenon_H8c zenon_H5e zenon_H1f zenon_Hec zenon_He9 zenon_Hcd zenon_Hed zenon_H72.
% 45.55/45.69 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d.
% 45.55/45.69 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f.
% 45.55/45.69 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H30. zenon_intro zenon_H28.
% 45.55/45.69 apply (zenon_imply_s _ _ zenon_H8e); [ zenon_intro zenon_H91 | zenon_intro zenon_H6b ].
% 45.55/45.69 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ].
% 45.55/45.69 apply (zenon_L150_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.69 apply (zenon_L196_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.69 apply zenon_H72. apply sym_equal. exact zenon_H6b.
% 45.55/45.69 (* end of lemma zenon_L197_ *)
% 45.55/45.69 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).
% 45.55/45.69 do 3 intro. intros zenon_H0 zenon_H1f zenon_H1a zenon_Hed zenon_Hcd zenon_He9 zenon_Hec zenon_H5e zenon_H72.
% 45.55/45.69 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88.
% 45.55/45.69 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ].
% 45.55/45.69 exact (zenon_H27 zenon_H1f).
% 45.55/45.69 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a.
% 45.55/45.69 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ].
% 45.55/45.69 apply (zenon_L3_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.69 apply (zenon_L197_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.69 (* end of lemma zenon_L198_ *)
% 45.55/45.69 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).
% 45.55/45.69 do 3 intro. intros zenon_Hf4 zenon_H0 zenon_H1f zenon_H1a zenon_Hed zenon_He9 zenon_Hec zenon_H5e zenon_H72.
% 45.55/45.69 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcd ].
% 45.55/45.69 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ].
% 45.55/45.69 exact (zenon_H27 zenon_H1f).
% 45.55/45.69 exact (zenon_Hf2 zenon_Hec).
% 45.55/45.69 apply (zenon_L198_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.69 (* end of lemma zenon_L199_ *)
% 45.55/45.69 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).
% 45.55/45.69 do 3 intro. intros zenon_Hf3 zenon_H1f zenon_Hec zenon_H1a zenon_He9 zenon_H5e zenon_H72.
% 45.55/45.69 generalize (assumption_15 zenon_TX_y). zenon_intro zenon_Hed.
% 45.55/45.69 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0.
% 45.55/45.69 generalize (zenon_Hf3 zenon_TT0_hz). zenon_intro zenon_Hf4.
% 45.55/45.69 apply (zenon_L199_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.69 (* end of lemma zenon_L200_ *)
% 45.55/45.69 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).
% 45.55/45.69 do 3 intro. intros zenon_H72 zenon_H5e zenon_H1a zenon_Hec zenon_H1f zenon_Hf3 zenon_Hda zenon_H26e.
% 45.55/45.69 elim (classic ((sigma) = (age zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_He2 | zenon_intro zenon_Hde ].
% 45.55/45.69 elim (classic (greater (age zenon_TX_y zenon_TT1_bg) (sigma))); [ zenon_intro zenon_Hdb | zenon_intro zenon_He9 ].
% 45.55/45.69 cut ((greater (age zenon_TX_y zenon_TT1_bg) (sigma)) = (greater (sigma) (sigma))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_Hda.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_Hdb.
% 45.55/45.69 cut (((sigma) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hd9].
% 45.55/45.69 cut (((age zenon_TX_y zenon_TT1_bg) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hdf].
% 45.55/45.69 congruence.
% 45.55/45.69 elim (classic ((sigma) = (sigma))); [ zenon_intro zenon_He3 | zenon_intro zenon_Hd9 ].
% 45.55/45.69 cut (((sigma) = (sigma)) = ((age zenon_TX_y zenon_TT1_bg) = (sigma))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_Hdf.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_He3.
% 45.55/45.69 cut (((sigma) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hd9].
% 45.55/45.69 cut (((sigma) = (age zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_Hde].
% 45.55/45.69 congruence.
% 45.55/45.69 exact (zenon_Hde zenon_He2).
% 45.55/45.69 apply zenon_Hd9. apply refl_equal.
% 45.55/45.69 apply zenon_Hd9. apply refl_equal.
% 45.55/45.69 apply zenon_Hd9. apply refl_equal.
% 45.55/45.69 apply (zenon_L200_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.69 elim (classic ((age zenon_TX_y zenon_TT1_bg) = (age zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H26f | zenon_intro zenon_H4d ].
% 45.55/45.69 cut (((age zenon_TX_y zenon_TT1_bg) = (age zenon_TX_y zenon_TT1_bg)) = ((sigma) = (age zenon_TX_y zenon_TT1_bg))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_Hde.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_H26f.
% 45.55/45.69 cut (((age zenon_TX_y zenon_TT1_bg) = (age zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H4d].
% 45.55/45.69 cut (((age zenon_TX_y zenon_TT1_bg) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hdf].
% 45.55/45.69 congruence.
% 45.55/45.69 exact (zenon_Hdf zenon_H26e).
% 45.55/45.69 apply zenon_H4d. apply refl_equal.
% 45.55/45.69 apply zenon_H4d. apply refl_equal.
% 45.55/45.69 (* end of lemma zenon_L201_ *)
% 45.55/45.69 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).
% 45.55/45.69 do 3 intro. intros zenon_Hea zenon_H26e zenon_H72 zenon_H5e zenon_H1a zenon_Hec zenon_H1f zenon_Hf3.
% 45.55/45.69 generalize (zenon_Hea (sigma)). zenon_intro zenon_Heb.
% 45.55/45.69 apply (zenon_notand_s _ _ zenon_Heb); [ zenon_intro zenon_Hda | zenon_intro zenon_Hda ].
% 45.55/45.69 apply (zenon_L201_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.69 apply (zenon_L201_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.69 (* end of lemma zenon_L202_ *)
% 45.55/45.69 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).
% 45.55/45.69 do 3 intro. intros zenon_Hf3 zenon_H1f zenon_Hec zenon_H1a zenon_H5e zenon_H72 zenon_H26e.
% 45.55/45.69 generalize (meaning_postulate_greater_strict (sigma)). zenon_intro zenon_Hea.
% 45.55/45.69 apply (zenon_L202_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.69 (* end of lemma zenon_L203_ *)
% 45.55/45.69 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).
% 45.55/45.69 do 3 intro. intros zenon_H26e zenon_H72 zenon_H5e zenon_H1a zenon_Hec zenon_H1f.
% 45.55/45.69 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3.
% 45.55/45.69 apply (zenon_L203_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.69 (* end of lemma zenon_L204_ *)
% 45.55/45.69 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).
% 45.55/45.69 do 3 intro. intros zenon_H34 zenon_H1c4 zenon_H1f zenon_Hec zenon_H1a zenon_H5e zenon_H26e.
% 45.55/45.69 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H241 | zenon_intro zenon_H193 ].
% 45.55/45.69 generalize (zenon_H34 (mod2)). zenon_intro zenon_H16e.
% 45.55/45.69 generalize (zenon_H16e (mod1)). zenon_intro zenon_H16f.
% 45.55/45.69 generalize (zenon_H16f (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H28e.
% 45.55/45.69 apply (zenon_imply_s _ _ zenon_H28e); [ zenon_intro zenon_H69 | zenon_intro zenon_H28f ].
% 45.55/45.69 exact (zenon_H69 assumption_19).
% 45.55/45.69 apply (zenon_imply_s _ _ zenon_H28f); [ zenon_intro zenon_H193 | zenon_intro zenon_H1c3 ].
% 45.55/45.69 exact (zenon_H193 zenon_H241).
% 45.55/45.69 exact (zenon_H1c4 zenon_H1c3).
% 45.55/45.69 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ].
% 45.55/45.69 cut ((greater (mod1) (low)) = (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_H193.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact assumption_18b.
% 45.55/45.69 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72].
% 45.55/45.69 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 45.55/45.69 congruence.
% 45.55/45.69 apply zenon_H59. apply refl_equal.
% 45.55/45.69 exact (zenon_H72 zenon_H71).
% 45.55/45.69 apply (zenon_L204_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.69 (* end of lemma zenon_L205_ *)
% 45.55/45.69 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).
% 45.55/45.69 do 3 intro. intros zenon_H34 zenon_H114 zenon_H26e zenon_H1a zenon_Hec zenon_H1f.
% 45.55/45.69 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H115 | zenon_intro zenon_H5e ].
% 45.55/45.69 cut ((greater (high) (mod2)) = (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_H114.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact assumption_18d.
% 45.55/45.69 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 45.55/45.69 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113].
% 45.55/45.69 congruence.
% 45.55/45.69 apply zenon_H113. apply refl_equal.
% 45.55/45.69 exact (zenon_H5e zenon_H115).
% 45.55/45.69 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1c4 ].
% 45.55/45.69 generalize (zenon_H34 (high)). zenon_intro zenon_H1fa.
% 45.55/45.69 generalize (zenon_H1fa (mod2)). zenon_intro zenon_H1fb.
% 45.55/45.69 generalize (zenon_H1fb (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H27e.
% 45.55/45.69 apply (zenon_imply_s _ _ zenon_H27e); [ zenon_intro zenon_H9b | zenon_intro zenon_H27f ].
% 45.55/45.69 exact (zenon_H9b assumption_18d).
% 45.55/45.69 apply (zenon_imply_s _ _ zenon_H27f); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H118 ].
% 45.55/45.69 exact (zenon_H1c4 zenon_H1c3).
% 45.55/45.69 exact (zenon_H114 zenon_H118).
% 45.55/45.69 apply (zenon_L205_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.69 (* end of lemma zenon_L206_ *)
% 45.55/45.69 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).
% 45.55/45.69 do 3 intro. intros zenon_H34 zenon_H116 zenon_H117 zenon_H1f zenon_Hec zenon_H1a zenon_H26e.
% 45.55/45.69 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H118 | zenon_intro zenon_H114 ].
% 45.55/45.69 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))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_H117.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_H118.
% 45.55/45.69 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].
% 45.55/45.69 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H119].
% 45.55/45.69 congruence.
% 45.55/45.69 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 ].
% 45.55/45.69 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))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_H119.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact zenon_H11a.
% 45.55/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.69 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c].
% 45.55/45.69 congruence.
% 45.55/45.69 exact (zenon_H11c zenon_H116).
% 45.55/45.69 apply zenon_H11b. apply refl_equal.
% 45.55/45.69 apply zenon_H11b. apply refl_equal.
% 45.55/45.69 apply zenon_H62. apply refl_equal.
% 45.55/45.69 apply (zenon_L206_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.69 (* end of lemma zenon_L207_ *)
% 45.55/45.69 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).
% 45.55/45.69 do 3 intro. intros zenon_H193 zenon_Hf3 zenon_H1f zenon_Hec zenon_H1a zenon_H5e zenon_H26e.
% 45.55/45.69 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ].
% 45.55/45.69 cut ((greater (mod1) (low)) = (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))).
% 45.55/45.69 intro zenon_D_pnotp.
% 45.55/45.69 apply zenon_H193.
% 45.55/45.69 rewrite <- zenon_D_pnotp.
% 45.55/45.69 exact assumption_18b.
% 45.55/45.69 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72].
% 45.55/45.69 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 45.55/45.69 congruence.
% 45.55/45.69 apply zenon_H59. apply refl_equal.
% 45.55/45.69 exact (zenon_H72 zenon_H71).
% 45.55/45.69 apply (zenon_L203_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.69 (* end of lemma zenon_L208_ *)
% 45.55/45.69 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).
% 45.55/45.69 do 3 intro. intros zenon_H34 zenon_H1c4 zenon_H26e zenon_H5e zenon_H1a zenon_Hec zenon_H1f zenon_Hf3.
% 45.55/45.70 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H241 | zenon_intro zenon_H193 ].
% 45.55/45.70 generalize (zenon_H34 (mod2)). zenon_intro zenon_H16e.
% 45.55/45.70 generalize (zenon_H16e (mod1)). zenon_intro zenon_H16f.
% 45.55/45.70 generalize (zenon_H16f (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H28e.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H28e); [ zenon_intro zenon_H69 | zenon_intro zenon_H28f ].
% 45.55/45.70 exact (zenon_H69 assumption_19).
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H28f); [ zenon_intro zenon_H193 | zenon_intro zenon_H1c3 ].
% 45.55/45.70 exact (zenon_H193 zenon_H241).
% 45.55/45.70 exact (zenon_H1c4 zenon_H1c3).
% 45.55/45.70 apply (zenon_L208_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 (* end of lemma zenon_L209_ *)
% 45.55/45.70 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).
% 45.55/45.70 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.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H145); [ zenon_intro zenon_H147 | zenon_intro zenon_H146 ].
% 45.55/45.70 apply (zenon_notand_s _ _ zenon_H147); [ zenon_intro zenon_H135 | zenon_intro zenon_H139 ].
% 45.55/45.70 apply (zenon_L67_ zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 exact (zenon_H139 zenon_H127).
% 45.55/45.70 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 ].
% 45.55/45.70 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ].
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H17c.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H179.
% 45.55/45.70 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 45.55/45.70 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].
% 45.55/45.70 congruence.
% 45.55/45.70 apply zenon_H16a. apply refl_equal.
% 45.55/45.70 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1c4 ].
% 45.55/45.70 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.55/45.70 generalize (zenon_H18f (mod2)). zenon_intro zenon_H199.
% 45.55/45.70 generalize (zenon_H199 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H290.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H290); [ zenon_intro zenon_H167 | zenon_intro zenon_H291 ].
% 45.55/45.70 exact (zenon_H167 zenon_H179).
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H291); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H240 ].
% 45.55/45.70 exact (zenon_H1c4 zenon_H1c3).
% 45.55/45.70 exact (zenon_H17c zenon_H240).
% 45.55/45.70 apply (zenon_L209_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H167.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H168.
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b].
% 45.55/45.70 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].
% 45.55/45.70 congruence.
% 45.55/45.70 apply zenon_H16a. apply refl_equal.
% 45.55/45.70 exact (zenon_H13b zenon_H146).
% 45.55/45.70 apply (zenon_L62_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 (* end of lemma zenon_L210_ *)
% 45.55/45.70 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).
% 45.55/45.70 do 4 intro. intros zenon_H34 zenon_Hf3 zenon_H1f zenon_Hec zenon_H1a zenon_H26e zenon_H17c zenon_H146 zenon_H15b.
% 45.55/45.70 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 ].
% 45.55/45.70 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ].
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H17c.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H179.
% 45.55/45.70 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 45.55/45.70 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].
% 45.55/45.70 congruence.
% 45.55/45.70 apply zenon_H16a. apply refl_equal.
% 45.55/45.70 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1c4 ].
% 45.55/45.70 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.55/45.70 generalize (zenon_H18f (mod2)). zenon_intro zenon_H199.
% 45.55/45.70 generalize (zenon_H199 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H290.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H290); [ zenon_intro zenon_H167 | zenon_intro zenon_H291 ].
% 45.55/45.70 exact (zenon_H167 zenon_H179).
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H291); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H240 ].
% 45.55/45.70 exact (zenon_H1c4 zenon_H1c3).
% 45.55/45.70 exact (zenon_H17c zenon_H240).
% 45.55/45.70 apply (zenon_L209_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H167.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H168.
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b].
% 45.55/45.70 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].
% 45.55/45.70 congruence.
% 45.55/45.70 apply zenon_H16a. apply refl_equal.
% 45.55/45.70 exact (zenon_H13b zenon_H146).
% 45.55/45.70 apply (zenon_L70_ zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 (* end of lemma zenon_L211_ *)
% 45.55/45.70 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).
% 45.55/45.70 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.
% 45.55/45.70 generalize (zenon_H0 zenon_TT2_la). zenon_intro zenon_H13c.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H13c); [ zenon_intro zenon_H27 | zenon_intro zenon_H13d ].
% 45.55/45.70 exact (zenon_H27 zenon_H1f).
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H13d). zenon_intro zenon_H13f. zenon_intro zenon_H13e.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H13e); [ zenon_intro zenon_H11d | zenon_intro zenon_H140 ].
% 45.55/45.70 apply (zenon_L50_ zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H140). zenon_intro zenon_H142. zenon_intro zenon_H141.
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H141). zenon_intro zenon_H144. zenon_intro zenon_H143.
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H143). zenon_intro zenon_H145. zenon_intro zenon_H134.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H142); [ zenon_intro zenon_H15c | zenon_intro zenon_H15b ].
% 45.55/45.70 apply (zenon_notand_s _ _ zenon_H15c); [ zenon_intro zenon_H135 | zenon_intro zenon_H127 ].
% 45.55/45.70 apply (zenon_L52_ zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 apply (zenon_L210_ zenon_TT0_hz zenon_TT1_bg zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H145); [ zenon_intro zenon_H147 | zenon_intro zenon_H146 ].
% 45.55/45.70 apply (zenon_notand_s _ _ zenon_H147); [ zenon_intro zenon_H135 | zenon_intro zenon_H139 ].
% 45.55/45.70 apply (zenon_L52_ zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 apply zenon_H139. zenon_intro zenon_H122.
% 45.55/45.70 apply (zenon_L51_ zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 apply (zenon_L211_ zenon_TT2_la zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.70 (* end of lemma zenon_L212_ *)
% 45.55/45.70 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).
% 45.55/45.70 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.
% 45.55/45.70 elim (classic ((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H17d | zenon_intro zenon_H119 ].
% 45.55/45.70 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 ].
% 45.55/45.70 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H118 | zenon_intro zenon_H114 ].
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H17c.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H118.
% 45.55/45.70 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].
% 45.55/45.70 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f].
% 45.55/45.70 congruence.
% 45.55/45.70 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 ].
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H17f.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H16d.
% 45.55/45.70 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].
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136].
% 45.55/45.70 congruence.
% 45.55/45.70 apply (zenon_L212_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 apply zenon_H16a. apply refl_equal.
% 45.55/45.70 apply zenon_H16a. apply refl_equal.
% 45.55/45.70 apply zenon_H62. apply refl_equal.
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H114.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H17e.
% 45.55/45.70 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].
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c].
% 45.55/45.70 congruence.
% 45.55/45.70 elim (classic ((high) = (high))); [ zenon_intro zenon_H180 | zenon_intro zenon_H113 ].
% 45.55/45.70 cut (((high) = (high)) = ((hazard_of_mortality zenon_TX_y zenon_E) = (high))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H11c.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H180.
% 45.55/45.70 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113].
% 45.55/45.70 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H119].
% 45.55/45.70 congruence.
% 45.55/45.70 exact (zenon_H119 zenon_H17d).
% 45.55/45.70 apply zenon_H113. apply refl_equal.
% 45.55/45.70 apply zenon_H113. apply refl_equal.
% 45.55/45.70 apply zenon_H62. apply refl_equal.
% 45.55/45.70 apply (zenon_L207_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 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 ].
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H119.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H11a.
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c].
% 45.55/45.70 congruence.
% 45.55/45.70 exact (zenon_H11c zenon_H116).
% 45.55/45.70 apply zenon_H11b. apply refl_equal.
% 45.55/45.70 apply zenon_H11b. apply refl_equal.
% 45.55/45.70 (* end of lemma zenon_L213_ *)
% 45.55/45.70 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).
% 45.55/45.70 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.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H181); [ zenon_intro zenon_H184 | zenon_intro zenon_H116 ].
% 45.55/45.70 apply (zenon_notand_s _ _ zenon_H184); [ zenon_intro zenon_H186 | zenon_intro zenon_H185 ].
% 45.55/45.70 exact (zenon_H186 zenon_H183).
% 45.55/45.70 exact (zenon_H185 zenon_H182).
% 45.55/45.70 apply (zenon_L213_ zenon_TT2_la zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.70 (* end of lemma zenon_L214_ *)
% 45.55/45.70 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).
% 45.55/45.70 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.
% 45.55/45.70 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1c4 ].
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H117.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H1c3.
% 45.55/45.70 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].
% 45.55/45.70 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1].
% 45.55/45.70 congruence.
% 45.55/45.70 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 ].
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H1a1.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H11a.
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2].
% 45.55/45.70 congruence.
% 45.55/45.70 exact (zenon_H1a2 zenon_H19e).
% 45.55/45.70 apply zenon_H11b. apply refl_equal.
% 45.55/45.70 apply zenon_H11b. apply refl_equal.
% 45.55/45.70 apply zenon_H62. apply refl_equal.
% 45.55/45.70 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H241 | zenon_intro zenon_H193 ].
% 45.55/45.70 generalize (zenon_H34 (mod2)). zenon_intro zenon_H16e.
% 45.55/45.70 generalize (zenon_H16e (mod1)). zenon_intro zenon_H16f.
% 45.55/45.70 generalize (zenon_H16f (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H28e.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H28e); [ zenon_intro zenon_H69 | zenon_intro zenon_H28f ].
% 45.55/45.70 exact (zenon_H69 assumption_19).
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H28f); [ zenon_intro zenon_H193 | zenon_intro zenon_H1c3 ].
% 45.55/45.70 exact (zenon_H193 zenon_H241).
% 45.55/45.70 exact (zenon_H1c4 zenon_H1c3).
% 45.55/45.70 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ].
% 45.55/45.70 cut ((greater (mod1) (low)) = (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H193.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact assumption_18b.
% 45.55/45.70 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72].
% 45.55/45.70 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 45.55/45.70 congruence.
% 45.55/45.70 apply zenon_H59. apply refl_equal.
% 45.55/45.70 exact (zenon_H72 zenon_H71).
% 45.55/45.70 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 ].
% 45.55/45.70 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ].
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H17c.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H179.
% 45.55/45.70 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 45.55/45.70 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].
% 45.55/45.70 congruence.
% 45.55/45.70 apply zenon_H16a. apply refl_equal.
% 45.55/45.70 apply (zenon_L204_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H167.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H1a4.
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2].
% 45.55/45.70 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].
% 45.55/45.70 congruence.
% 45.55/45.70 apply zenon_H16a. apply refl_equal.
% 45.55/45.70 exact (zenon_H1a2 zenon_H19e).
% 45.55/45.70 apply (zenon_L84_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 (* end of lemma zenon_L215_ *)
% 45.55/45.70 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).
% 45.55/45.70 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.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H234); [ zenon_intro zenon_H237 | zenon_intro zenon_H19e ].
% 45.55/45.70 apply (zenon_notand_s _ _ zenon_H237); [ zenon_intro zenon_H183 | zenon_intro zenon_H185 ].
% 45.55/45.70 apply (zenon_L214_ zenon_TT2_la zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.70 exact (zenon_H185 zenon_H182).
% 45.55/45.70 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H1a1 ].
% 45.55/45.70 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ].
% 45.55/45.70 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 ].
% 45.55/45.70 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 ].
% 45.55/45.70 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.55/45.70 generalize (zenon_H18f (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H23d.
% 45.55/45.70 generalize (zenon_H23d (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H23e.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H23f ].
% 45.55/45.70 exact (zenon_H1a5 zenon_H1a4).
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H23f); [ zenon_intro zenon_H117 | zenon_intro zenon_H240 ].
% 45.55/45.70 exact (zenon_H117 zenon_H17e).
% 45.55/45.70 exact (zenon_H17c zenon_H240).
% 45.55/45.70 apply (zenon_L215_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H1a5.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H179.
% 45.55/45.70 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1].
% 45.55/45.70 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].
% 45.55/45.70 congruence.
% 45.55/45.70 apply zenon_H16a. apply refl_equal.
% 45.55/45.70 exact (zenon_H1a1 zenon_H1a3).
% 45.55/45.70 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 ].
% 45.55/45.70 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1c4 ].
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H17c.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H1c3.
% 45.55/45.70 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].
% 45.55/45.70 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16c].
% 45.55/45.70 congruence.
% 45.55/45.70 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 ].
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H16c.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H16d.
% 45.55/45.70 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].
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b].
% 45.55/45.70 congruence.
% 45.55/45.70 apply (zenon_L81_ zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 apply zenon_H16a. apply refl_equal.
% 45.55/45.70 apply zenon_H16a. apply refl_equal.
% 45.55/45.70 apply zenon_H62. apply refl_equal.
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H1c4.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H17e.
% 45.55/45.70 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].
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2].
% 45.55/45.70 congruence.
% 45.55/45.70 elim (classic ((mod2) = (mod2))); [ zenon_intro zenon_H17b | zenon_intro zenon_H83 ].
% 45.55/45.70 cut (((mod2) = (mod2)) = ((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H1a2.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H17b.
% 45.55/45.70 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83].
% 45.55/45.70 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1].
% 45.55/45.70 congruence.
% 45.55/45.70 exact (zenon_H1a1 zenon_H1a3).
% 45.55/45.70 apply zenon_H83. apply refl_equal.
% 45.55/45.70 apply zenon_H83. apply refl_equal.
% 45.55/45.70 apply zenon_H62. apply refl_equal.
% 45.55/45.70 apply (zenon_L215_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 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 ].
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H1a1.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H11a.
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2].
% 45.55/45.70 congruence.
% 45.55/45.70 exact (zenon_H1a2 zenon_H19e).
% 45.55/45.70 apply zenon_H11b. apply refl_equal.
% 45.55/45.70 apply zenon_H11b. apply refl_equal.
% 45.55/45.70 (* end of lemma zenon_L216_ *)
% 45.55/45.70 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).
% 45.55/45.70 do 3 intro. intros zenon_H34 zenon_H114 zenon_Hf3 zenon_H1f zenon_Hec zenon_H1a zenon_H26e.
% 45.55/45.70 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H115 | zenon_intro zenon_H5e ].
% 45.55/45.70 cut ((greater (high) (mod2)) = (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H114.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact assumption_18d.
% 45.55/45.70 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 45.55/45.70 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113].
% 45.55/45.70 congruence.
% 45.55/45.70 apply zenon_H113. apply refl_equal.
% 45.55/45.70 exact (zenon_H5e zenon_H115).
% 45.55/45.70 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1c4 ].
% 45.55/45.70 generalize (zenon_H34 (high)). zenon_intro zenon_H1fa.
% 45.55/45.70 generalize (zenon_H1fa (mod2)). zenon_intro zenon_H1fb.
% 45.55/45.70 generalize (zenon_H1fb (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H27e.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H27e); [ zenon_intro zenon_H9b | zenon_intro zenon_H27f ].
% 45.55/45.70 exact (zenon_H9b assumption_18d).
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H27f); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H118 ].
% 45.55/45.70 exact (zenon_H1c4 zenon_H1c3).
% 45.55/45.70 exact (zenon_H114 zenon_H118).
% 45.55/45.70 apply (zenon_L209_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 (* end of lemma zenon_L217_ *)
% 45.55/45.70 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).
% 45.55/45.70 do 3 intro. intros zenon_H34 zenon_H2c zenon_H280 zenon_H26e zenon_H1a zenon_Hec zenon_H1f zenon_Hf3.
% 45.55/45.70 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H118 | zenon_intro zenon_H114 ].
% 45.55/45.70 cut ((greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg)) = (greater (high) (high))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H280.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H118.
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b].
% 45.55/45.70 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113].
% 45.55/45.70 congruence.
% 45.55/45.70 apply zenon_H113. apply refl_equal.
% 45.55/45.70 exact (zenon_H2b zenon_H2c).
% 45.55/45.70 apply (zenon_L217_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 (* end of lemma zenon_L218_ *)
% 45.55/45.70 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).
% 45.55/45.70 do 3 intro. intros zenon_H34 zenon_H2c zenon_H280 zenon_H26e zenon_H1a zenon_Hec zenon_H1f zenon_Hf3.
% 45.55/45.70 apply (zenon_L218_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 (* end of lemma zenon_L219_ *)
% 45.55/45.70 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).
% 45.55/45.70 do 3 intro. intros zenon_H34 zenon_H280 zenon_Hf3 zenon_H1f zenon_Hec zenon_H1a zenon_H26e zenon_H2c.
% 45.55/45.70 apply (zenon_L219_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.70 (* end of lemma zenon_L220_ *)
% 45.55/45.70 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).
% 45.55/45.70 do 3 intro. intros zenon_H34 zenon_H2c zenon_H26e zenon_H1a zenon_Hec zenon_H1f zenon_Hf3.
% 45.55/45.70 generalize (meaning_postulate_greater_strict (high)). zenon_intro zenon_H202.
% 45.55/45.70 generalize (zenon_H202 (high)). zenon_intro zenon_H287.
% 45.55/45.70 apply (zenon_notand_s _ _ zenon_H287); [ zenon_intro zenon_H280 | zenon_intro zenon_H280 ].
% 45.55/45.70 apply (zenon_L220_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 apply (zenon_L220_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 (* end of lemma zenon_L221_ *)
% 45.55/45.70 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).
% 45.55/45.70 do 3 intro. intros zenon_H28 zenon_H38 zenon_H35 zenon_H2a zenon_H34 zenon_H26e zenon_H1a zenon_Hec zenon_H1f zenon_Hf3.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ].
% 45.55/45.70 apply (zenon_notand_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ].
% 45.55/45.70 exact (zenon_H2f zenon_H2a).
% 45.55/45.70 apply zenon_H2e. zenon_intro zenon_H36.
% 45.55/45.70 apply (zenon_L155_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 apply (zenon_L221_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 (* end of lemma zenon_L222_ *)
% 45.55/45.70 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).
% 45.55/45.70 do 3 intro. intros zenon_H28 zenon_H29 zenon_H2a zenon_H34 zenon_H26e zenon_H1a zenon_Hec zenon_H1f zenon_Hf3.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ].
% 45.55/45.70 apply (zenon_notand_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ].
% 45.55/45.70 exact (zenon_H2f zenon_H2a).
% 45.55/45.70 exact (zenon_H2e zenon_H29).
% 45.55/45.70 apply (zenon_L221_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 (* end of lemma zenon_L223_ *)
% 45.55/45.70 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).
% 45.55/45.70 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.
% 45.55/45.70 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 ].
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H136. zenon_intro zenon_H18b.
% 45.55/45.70 apply (zenon_L212_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 cut ((greater (high) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H167.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact assumption_18d.
% 45.55/45.70 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83].
% 45.55/45.70 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f].
% 45.55/45.70 congruence.
% 45.55/45.70 apply (zenon_notand_s _ _ zenon_H18a); [ zenon_intro zenon_H18d | zenon_intro zenon_H18c ].
% 45.55/45.70 apply zenon_H18d. zenon_intro zenon_H137.
% 45.55/45.70 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 ].
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H17f.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H16d.
% 45.55/45.70 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].
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136].
% 45.55/45.70 congruence.
% 45.55/45.70 exact (zenon_H136 zenon_H137).
% 45.55/45.70 apply zenon_H16a. apply refl_equal.
% 45.55/45.70 apply zenon_H16a. apply refl_equal.
% 45.55/45.70 apply zenon_H18c. zenon_intro zenon_H18e.
% 45.55/45.70 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.55/45.70 generalize (zenon_H18f (high)). zenon_intro zenon_H190.
% 45.55/45.70 generalize (zenon_H190 (mod2)). zenon_intro zenon_H191.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H191); [ zenon_intro zenon_H18b | zenon_intro zenon_H192 ].
% 45.55/45.70 exact (zenon_H18b zenon_H18e).
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H192); [ zenon_intro zenon_H9b | zenon_intro zenon_H179 ].
% 45.55/45.70 exact (zenon_H9b assumption_18d).
% 45.55/45.70 exact (zenon_H167 zenon_H179).
% 45.55/45.70 apply zenon_H83. apply refl_equal.
% 45.55/45.70 (* end of lemma zenon_L224_ *)
% 45.55/45.70 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).
% 45.55/45.70 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.
% 45.55/45.70 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ].
% 45.55/45.70 cut ((greater (mod1) (low)) = (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H193.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact assumption_18b.
% 45.55/45.70 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72].
% 45.55/45.70 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 45.55/45.70 congruence.
% 45.55/45.70 apply zenon_H59. apply refl_equal.
% 45.55/45.70 exact (zenon_H72 zenon_H71).
% 45.55/45.70 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ].
% 45.55/45.70 exact (zenon_H27 zenon_H1f).
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H8b); [ zenon_intro zenon_H24 | zenon_intro zenon_H188 ].
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ].
% 45.55/45.70 exact (zenon_H1e zenon_H24).
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d.
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f.
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H30. zenon_intro zenon_H28.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H8e); [ zenon_intro zenon_H91 | zenon_intro zenon_H6b ].
% 45.55/45.70 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ].
% 45.55/45.70 apply (zenon_L222_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ].
% 45.55/45.70 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ].
% 45.55/45.70 apply (zenon_L223_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 exact (zenon_H2e zenon_H29).
% 45.55/45.70 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H115 | zenon_intro zenon_H5e ].
% 45.55/45.70 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ].
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H17c.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H179.
% 45.55/45.70 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 45.55/45.70 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].
% 45.55/45.70 congruence.
% 45.55/45.70 apply zenon_H16a. apply refl_equal.
% 45.55/45.70 exact (zenon_H5e zenon_H115).
% 45.55/45.70 apply (zenon_L224_ zenon_TT0_hz zenon_TT1_bg zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 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 ].
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H5e.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H61.
% 45.55/45.70 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].
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31].
% 45.55/45.70 congruence.
% 45.55/45.70 exact (zenon_H31 zenon_H32).
% 45.55/45.70 apply zenon_H62. apply refl_equal.
% 45.55/45.70 apply zenon_H62. apply refl_equal.
% 45.55/45.70 apply zenon_H72. apply sym_equal. exact zenon_H6b.
% 45.55/45.70 apply zenon_H187. apply sym_equal. exact zenon_H188.
% 45.55/45.70 (* end of lemma zenon_L225_ *)
% 45.55/45.70 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).
% 45.55/45.70 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.
% 45.55/45.70 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H241 | zenon_intro zenon_H193 ].
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H117.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H241.
% 45.55/45.70 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].
% 45.55/45.70 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f].
% 45.55/45.70 congruence.
% 45.55/45.70 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 ].
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H21f.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H11a.
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e].
% 45.55/45.70 congruence.
% 45.55/45.70 exact (zenon_H21e zenon_H21a).
% 45.55/45.70 apply zenon_H11b. apply refl_equal.
% 45.55/45.70 apply zenon_H11b. apply refl_equal.
% 45.55/45.70 apply zenon_H62. apply refl_equal.
% 45.55/45.70 apply (zenon_L225_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 (* end of lemma zenon_L226_ *)
% 45.55/45.70 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).
% 45.55/45.70 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.
% 45.55/45.70 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 ].
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H13b. zenon_intro zenon_H167.
% 45.55/45.70 apply (zenon_L224_ zenon_TT0_hz zenon_TT1_bg zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 cut ((greater (mod2) (mod1)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H194.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact assumption_19.
% 45.55/45.70 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 45.55/45.70 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16c].
% 45.55/45.70 congruence.
% 45.55/45.70 apply (zenon_notand_s _ _ zenon_H196); [ zenon_intro zenon_H198 | zenon_intro zenon_H197 ].
% 45.55/45.70 apply zenon_H198. zenon_intro zenon_H146.
% 45.55/45.70 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 ].
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H16c.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H16d.
% 45.55/45.70 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].
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b].
% 45.55/45.70 congruence.
% 45.55/45.70 exact (zenon_H13b zenon_H146).
% 45.55/45.70 apply zenon_H16a. apply refl_equal.
% 45.55/45.70 apply zenon_H16a. apply refl_equal.
% 45.55/45.70 apply zenon_H197. zenon_intro zenon_H179.
% 45.55/45.70 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.55/45.70 generalize (zenon_H18f (mod2)). zenon_intro zenon_H199.
% 45.55/45.70 generalize (zenon_H199 (mod1)). zenon_intro zenon_H19a.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H19a); [ zenon_intro zenon_H167 | zenon_intro zenon_H19b ].
% 45.55/45.70 exact (zenon_H167 zenon_H179).
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H19b); [ zenon_intro zenon_H69 | zenon_intro zenon_H19c ].
% 45.55/45.70 exact (zenon_H69 assumption_19).
% 45.55/45.70 exact (zenon_H194 zenon_H19c).
% 45.55/45.70 apply zenon_H59. apply refl_equal.
% 45.55/45.70 (* end of lemma zenon_L227_ *)
% 45.55/45.70 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).
% 45.55/45.70 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.
% 45.55/45.70 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ].
% 45.55/45.70 exact (zenon_H27 zenon_H1f).
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H8b); [ zenon_intro zenon_H24 | zenon_intro zenon_H188 ].
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ].
% 45.55/45.70 exact (zenon_H1e zenon_H24).
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d.
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f.
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H30. zenon_intro zenon_H28.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H8e); [ zenon_intro zenon_H91 | zenon_intro zenon_H6b ].
% 45.55/45.70 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ].
% 45.55/45.70 apply (zenon_L222_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ].
% 45.55/45.70 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ].
% 45.55/45.70 apply (zenon_L223_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 exact (zenon_H2e zenon_H29).
% 45.55/45.70 apply (zenon_L98_ zenon_TT1_bg zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.70 apply zenon_H72. apply sym_equal. exact zenon_H6b.
% 45.55/45.70 apply zenon_H187. apply sym_equal. exact zenon_H188.
% 45.55/45.70 (* end of lemma zenon_L228_ *)
% 45.55/45.70 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).
% 45.55/45.70 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.
% 45.55/45.70 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0.
% 45.55/45.70 generalize (zenon_H0 zenon_E). zenon_intro zenon_H239.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H239); [ zenon_intro zenon_H27 | zenon_intro zenon_H23a ].
% 45.55/45.70 exact (zenon_H27 zenon_H1f).
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H23a). zenon_intro zenon_H23b. zenon_intro zenon_H238.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H23b); [ zenon_intro zenon_H112 | zenon_intro zenon_H1e0 ].
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H238); [ zenon_intro zenon_H111 | zenon_intro zenon_H22f ].
% 45.55/45.70 exact (zenon_H111 zenon_H112).
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H22f). zenon_intro zenon_H231. zenon_intro zenon_H230.
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H230). zenon_intro zenon_H233. zenon_intro zenon_H232.
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H232). zenon_intro zenon_H234. zenon_intro zenon_H181.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H231); [ zenon_intro zenon_H235 | zenon_intro zenon_H1b8 ].
% 45.55/45.70 apply (zenon_notand_s _ _ zenon_H235); [ zenon_intro zenon_H183 | zenon_intro zenon_H182 ].
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H233); [ zenon_intro zenon_H236 | zenon_intro zenon_H21a ].
% 45.55/45.70 apply (zenon_notand_s _ _ zenon_H236); [ zenon_intro zenon_H186 | zenon_intro zenon_H182 ].
% 45.55/45.70 exact (zenon_H186 zenon_H183).
% 45.55/45.70 apply (zenon_L214_ zenon_TT2_la zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.70 elim (classic ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H23c | zenon_intro zenon_H21f ].
% 45.55/45.70 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))); [ zenon_intro zenon_H19c | zenon_intro zenon_H194 ].
% 45.55/45.70 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 ].
% 45.55/45.70 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 ].
% 45.55/45.70 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.55/45.70 generalize (zenon_H18f (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H23d.
% 45.55/45.70 generalize (zenon_H23d (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H23e.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H23f ].
% 45.55/45.70 exact (zenon_H1a5 zenon_H1a4).
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H23f); [ zenon_intro zenon_H117 | zenon_intro zenon_H240 ].
% 45.55/45.70 exact (zenon_H117 zenon_H17e).
% 45.55/45.70 exact (zenon_H17c zenon_H240).
% 45.55/45.70 apply (zenon_L226_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H1a5.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H19c.
% 45.55/45.70 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f].
% 45.55/45.70 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].
% 45.55/45.70 congruence.
% 45.55/45.70 apply zenon_H16a. apply refl_equal.
% 45.55/45.70 exact (zenon_H21f zenon_H23c).
% 45.55/45.70 apply (zenon_L227_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 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 ].
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H21f.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H11a.
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e].
% 45.55/45.70 congruence.
% 45.55/45.70 exact (zenon_H21e zenon_H21a).
% 45.55/45.70 apply zenon_H11b. apply refl_equal.
% 45.55/45.70 apply zenon_H11b. apply refl_equal.
% 45.55/45.70 apply (zenon_L216_ zenon_TT0_hz zenon_TT1_bg zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 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 ].
% 45.55/45.70 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1a9 ].
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H17c.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H1b1.
% 45.55/45.70 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72].
% 45.55/45.70 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].
% 45.55/45.70 congruence.
% 45.55/45.70 apply zenon_H16a. apply refl_equal.
% 45.55/45.70 apply (zenon_L228_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H1a9.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H1a4.
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb].
% 45.55/45.70 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].
% 45.55/45.70 congruence.
% 45.55/45.70 apply zenon_H16a. apply refl_equal.
% 45.55/45.70 exact (zenon_H1bb zenon_H1b8).
% 45.55/45.70 apply (zenon_L104_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 apply (zenon_L131_ zenon_TX_y); trivial.
% 45.55/45.70 (* end of lemma zenon_L229_ *)
% 45.55/45.70 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).
% 45.55/45.70 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.
% 45.55/45.70 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3.
% 45.55/45.70 apply (zenon_L229_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 (* end of lemma zenon_L230_ *)
% 45.55/45.70 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).
% 45.55/45.70 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.
% 45.55/45.70 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H242 | zenon_intro zenon_H187 ].
% 45.55/45.70 cut ((greater (low) (very_low)) = (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_Had.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact assumption_18c.
% 45.55/45.70 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H187].
% 45.55/45.70 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.55/45.70 congruence.
% 45.55/45.70 apply zenon_H6a. apply refl_equal.
% 45.55/45.70 exact (zenon_H187 zenon_H242).
% 45.55/45.70 apply (zenon_L230_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 (* end of lemma zenon_L231_ *)
% 45.55/45.70 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).
% 45.55/45.70 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.
% 45.55/45.70 elim (classic (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_Hac | zenon_intro zenon_Had ].
% 45.55/45.70 generalize (zenon_H34 (mod1)). zenon_intro zenon_Ha7.
% 45.55/45.70 generalize (zenon_Ha7 (low)). zenon_intro zenon_Ha8.
% 45.55/45.70 generalize (zenon_Ha8 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H243.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H243); [ zenon_intro zenon_H7f | zenon_intro zenon_H244 ].
% 45.55/45.70 exact (zenon_H7f assumption_18b).
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H244); [ zenon_intro zenon_Had | zenon_intro zenon_H241 ].
% 45.55/45.70 exact (zenon_Had zenon_Hac).
% 45.55/45.70 exact (zenon_H193 zenon_H241).
% 45.55/45.70 apply (zenon_L231_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 (* end of lemma zenon_L232_ *)
% 45.55/45.70 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).
% 45.55/45.70 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.
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d.
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f.
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H30. zenon_intro zenon_H28.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ].
% 45.55/45.70 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ].
% 45.55/45.70 apply (zenon_L150_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.70 apply zenon_H2e. zenon_intro zenon_H36.
% 45.55/45.70 apply (zenon_L155_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 apply (zenon_L141_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 (* end of lemma zenon_L233_ *)
% 45.55/45.70 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).
% 45.55/45.70 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.
% 45.55/45.70 generalize (zenon_H0 zenon_TT0_hz). zenon_intro zenon_H26a.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H26a); [ zenon_intro zenon_H27 | zenon_intro zenon_H26b ].
% 45.55/45.70 exact (zenon_H27 zenon_H1f).
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H26b). zenon_intro zenon_H26d. zenon_intro zenon_H26c.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H26c); [ zenon_intro zenon_H245 | zenon_intro zenon_H261 ].
% 45.55/45.70 apply (zenon_L137_ zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H261). zenon_intro zenon_H263. zenon_intro zenon_H262.
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H262). zenon_intro zenon_H265. zenon_intro zenon_H264.
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H264). zenon_intro zenon_H267. zenon_intro zenon_H266.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H267); [ zenon_intro zenon_H268 | zenon_intro zenon_H25f ].
% 45.55/45.70 apply (zenon_notand_s _ _ zenon_H268); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H269 ].
% 45.55/45.70 exact (zenon_Hd8 zenon_Hcd).
% 45.55/45.70 apply zenon_H269. zenon_intro zenon_H24d.
% 45.55/45.70 apply (zenon_L140_ zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.70 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ].
% 45.55/45.70 exact (zenon_H27 zenon_H1f).
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ].
% 45.55/45.70 apply (zenon_L3_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 apply (zenon_L233_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 (* end of lemma zenon_L234_ *)
% 45.55/45.70 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).
% 45.55/45.70 do 3 intro. intros zenon_H25e zenon_H38 zenon_H24a zenon_H35 zenon_H1a zenon_Hec zenon_H1f zenon_Hf3 zenon_Hda zenon_H26e.
% 45.55/45.70 elim (classic ((sigma) = (age zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_He2 | zenon_intro zenon_Hde ].
% 45.55/45.70 elim (classic (greater (age zenon_TX_y zenon_TT1_bg) (sigma))); [ zenon_intro zenon_Hdb | zenon_intro zenon_He9 ].
% 45.55/45.70 cut ((greater (age zenon_TX_y zenon_TT1_bg) (sigma)) = (greater (sigma) (sigma))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_Hda.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_Hdb.
% 45.55/45.70 cut (((sigma) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hd9].
% 45.55/45.70 cut (((age zenon_TX_y zenon_TT1_bg) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hdf].
% 45.55/45.70 congruence.
% 45.55/45.70 elim (classic ((sigma) = (sigma))); [ zenon_intro zenon_He3 | zenon_intro zenon_Hd9 ].
% 45.55/45.70 cut (((sigma) = (sigma)) = ((age zenon_TX_y zenon_TT1_bg) = (sigma))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_Hdf.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_He3.
% 45.55/45.70 cut (((sigma) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hd9].
% 45.55/45.70 cut (((sigma) = (age zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_Hde].
% 45.55/45.70 congruence.
% 45.55/45.70 exact (zenon_Hde zenon_He2).
% 45.55/45.70 apply zenon_Hd9. apply refl_equal.
% 45.55/45.70 apply zenon_Hd9. apply refl_equal.
% 45.55/45.70 apply zenon_Hd9. apply refl_equal.
% 45.55/45.70 generalize (assumption_15 zenon_TX_y). zenon_intro zenon_Hed.
% 45.55/45.70 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0.
% 45.55/45.70 generalize (zenon_Hf3 zenon_TT0_hz). zenon_intro zenon_Hf4.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcd ].
% 45.55/45.70 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ].
% 45.55/45.70 exact (zenon_H27 zenon_H1f).
% 45.55/45.70 exact (zenon_Hf2 zenon_Hec).
% 45.55/45.70 apply (zenon_L234_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.70 elim (classic ((age zenon_TX_y zenon_TT1_bg) = (age zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H26f | zenon_intro zenon_H4d ].
% 45.55/45.70 cut (((age zenon_TX_y zenon_TT1_bg) = (age zenon_TX_y zenon_TT1_bg)) = ((sigma) = (age zenon_TX_y zenon_TT1_bg))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_Hde.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H26f.
% 45.55/45.70 cut (((age zenon_TX_y zenon_TT1_bg) = (age zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H4d].
% 45.55/45.70 cut (((age zenon_TX_y zenon_TT1_bg) = (sigma))); [idtac | apply NNPP; zenon_intro zenon_Hdf].
% 45.55/45.70 congruence.
% 45.55/45.70 exact (zenon_Hdf zenon_H26e).
% 45.55/45.70 apply zenon_H4d. apply refl_equal.
% 45.55/45.70 apply zenon_H4d. apply refl_equal.
% 45.55/45.70 (* end of lemma zenon_L235_ *)
% 45.55/45.70 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).
% 45.55/45.70 do 3 intro. intros zenon_H25e zenon_H26e zenon_H38 zenon_H24a zenon_H35 zenon_H1a zenon_Hec zenon_H1f.
% 45.55/45.70 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3.
% 45.55/45.70 generalize (meaning_postulate_greater_strict (sigma)). zenon_intro zenon_Hea.
% 45.55/45.70 generalize (zenon_Hea (sigma)). zenon_intro zenon_Heb.
% 45.55/45.70 apply (zenon_notand_s _ _ zenon_Heb); [ zenon_intro zenon_Hda | zenon_intro zenon_Hda ].
% 45.55/45.70 apply (zenon_L235_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 apply (zenon_L235_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 (* end of lemma zenon_L236_ *)
% 45.55/45.70 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).
% 45.55/45.70 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.
% 45.55/45.70 generalize (zenon_H0 zenon_TT2_la). zenon_intro zenon_H13c.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H13c); [ zenon_intro zenon_H27 | zenon_intro zenon_H13d ].
% 45.55/45.70 exact (zenon_H27 zenon_H1f).
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H13d). zenon_intro zenon_H13f. zenon_intro zenon_H13e.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H13f); [ zenon_intro zenon_H121 | zenon_intro zenon_H15a ].
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H13e); [ zenon_intro zenon_H11d | zenon_intro zenon_H140 ].
% 45.55/45.70 exact (zenon_H11d zenon_H121).
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H140). zenon_intro zenon_H142. zenon_intro zenon_H141.
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H141). zenon_intro zenon_H144. zenon_intro zenon_H143.
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H143). zenon_intro zenon_H145. zenon_intro zenon_H134.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H142); [ zenon_intro zenon_H15c | zenon_intro zenon_H15b ].
% 45.55/45.70 apply (zenon_notand_s _ _ zenon_H15c); [ zenon_intro zenon_H135 | zenon_intro zenon_H127 ].
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H134); [ zenon_intro zenon_H138 | zenon_intro zenon_H137 ].
% 45.55/45.70 apply (zenon_notand_s _ _ zenon_H138); [ zenon_intro zenon_H13a | zenon_intro zenon_H139 ].
% 45.55/45.70 exact (zenon_H13a zenon_H135).
% 45.55/45.70 apply zenon_H139. zenon_intro zenon_H122.
% 45.55/45.70 generalize (zenon_H35 zenon_TT2_la). zenon_intro zenon_H124.
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H124). zenon_intro zenon_H126. zenon_intro zenon_H125.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H126); [ zenon_intro zenon_H128 | zenon_intro zenon_H127 ].
% 45.55/45.70 generalize (definition_smaller_or_equal (age zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H129.
% 45.55/45.70 generalize (zenon_H129 (tau)). zenon_intro zenon_H12a.
% 45.55/45.70 apply (zenon_equiv_s _ _ zenon_H12a); [ zenon_intro zenon_H128; zenon_intro zenon_H12d | zenon_intro zenon_H12c; zenon_intro zenon_H12b ].
% 45.55/45.70 apply (zenon_notor_s _ _ zenon_H12d). zenon_intro zenon_H12f. zenon_intro zenon_H12e.
% 45.55/45.70 exact (zenon_H12e zenon_H292).
% 45.55/45.70 exact (zenon_H128 zenon_H12c).
% 45.55/45.70 exact (zenon_H127 zenon_H122).
% 45.55/45.70 exact (zenon_H136 zenon_H137).
% 45.55/45.70 apply (zenon_L56_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 apply zenon_H155. apply sym_equal. exact zenon_H15b.
% 45.55/45.70 apply zenon_H154. apply sym_equal. exact zenon_H15a.
% 45.55/45.70 (* end of lemma zenon_L237_ *)
% 45.55/45.70 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).
% 45.55/45.70 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.
% 45.55/45.70 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H166 | zenon_intro zenon_H154 ].
% 45.55/45.70 cut ((greater (low) (very_low)) = (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT2_la))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H162.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact assumption_18c.
% 45.55/45.70 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H154].
% 45.55/45.70 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.55/45.70 congruence.
% 45.55/45.70 apply zenon_H6a. apply refl_equal.
% 45.55/45.70 exact (zenon_H154 zenon_H166).
% 45.55/45.70 apply (zenon_L237_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 (* end of lemma zenon_L238_ *)
% 45.55/45.70 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).
% 45.55/45.70 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.
% 45.55/45.70 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H165 | zenon_intro zenon_H15f ].
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H169.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H165.
% 45.55/45.70 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].
% 45.55/45.70 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 45.55/45.70 congruence.
% 45.55/45.70 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 ].
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H159.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H16d.
% 45.55/45.70 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].
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H1a7].
% 45.55/45.70 congruence.
% 45.55/45.70 exact (zenon_H1a7 zenon_H15d).
% 45.55/45.70 apply zenon_H16a. apply refl_equal.
% 45.55/45.70 apply zenon_H16a. apply refl_equal.
% 45.55/45.70 apply zenon_H16a. apply refl_equal.
% 45.55/45.70 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H160 | zenon_intro zenon_H155 ].
% 45.55/45.70 cut ((greater (mod1) (low)) = (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT2_la))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H15f.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact assumption_18b.
% 45.55/45.70 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H155].
% 45.55/45.70 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 45.55/45.70 congruence.
% 45.55/45.70 apply zenon_H59. apply refl_equal.
% 45.55/45.70 exact (zenon_H155 zenon_H160).
% 45.55/45.70 elim (classic (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H161 | zenon_intro zenon_H162 ].
% 45.55/45.70 generalize (zenon_H34 (mod1)). zenon_intro zenon_Ha7.
% 45.55/45.70 generalize (zenon_Ha7 (low)). zenon_intro zenon_Ha8.
% 45.55/45.70 generalize (zenon_Ha8 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H163.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H163); [ zenon_intro zenon_H7f | zenon_intro zenon_H164 ].
% 45.55/45.70 exact (zenon_H7f assumption_18b).
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H164); [ zenon_intro zenon_H162 | zenon_intro zenon_H165 ].
% 45.55/45.70 exact (zenon_H162 zenon_H161).
% 45.55/45.70 exact (zenon_H15f zenon_H165).
% 45.55/45.70 apply (zenon_L238_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 (* end of lemma zenon_L239_ *)
% 45.55/45.70 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).
% 45.55/45.70 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.
% 45.55/45.70 elim (classic ((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H158 | zenon_intro zenon_H159 ].
% 45.55/45.70 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))); [ zenon_intro zenon_H19c | zenon_intro zenon_H194 ].
% 45.55/45.70 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1)) = (greater (mod1) (mod1))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_Ha6.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H19c.
% 45.55/45.70 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H1a7].
% 45.55/45.70 congruence.
% 45.55/45.70 elim (classic ((mod1) = (mod1))); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H59 ].
% 45.55/45.70 cut (((mod1) = (mod1)) = ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod1))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H1a7.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_Hb8.
% 45.55/45.70 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 45.55/45.70 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 45.55/45.70 congruence.
% 45.55/45.70 exact (zenon_H159 zenon_H158).
% 45.55/45.70 apply zenon_H59. apply refl_equal.
% 45.55/45.70 apply zenon_H59. apply refl_equal.
% 45.55/45.70 apply zenon_H59. apply refl_equal.
% 45.55/45.70 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 ].
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H194.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H168.
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H1a7].
% 45.55/45.70 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].
% 45.55/45.70 congruence.
% 45.55/45.70 apply zenon_H16a. apply refl_equal.
% 45.55/45.70 exact (zenon_H1a7 zenon_H15d).
% 45.55/45.70 apply (zenon_L239_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 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 ].
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H159.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H16d.
% 45.55/45.70 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].
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H1a7].
% 45.55/45.70 congruence.
% 45.55/45.70 exact (zenon_H1a7 zenon_H15d).
% 45.55/45.70 apply zenon_H16a. apply refl_equal.
% 45.55/45.70 apply zenon_H16a. apply refl_equal.
% 45.55/45.70 (* end of lemma zenon_L240_ *)
% 45.55/45.70 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).
% 45.55/45.70 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.
% 45.55/45.70 elim (classic (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [ zenon_intro zenon_H161 | zenon_intro zenon_H162 ].
% 45.55/45.70 cut ((greater (low) (hazard_of_mortality zenon_TX_y zenon_TT2_la)) = (greater (low) (mod1))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H6f.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H161.
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H1a7].
% 45.55/45.70 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.55/45.70 congruence.
% 45.55/45.70 apply zenon_H6a. apply refl_equal.
% 45.55/45.70 exact (zenon_H1a7 zenon_H15d).
% 45.55/45.70 elim (classic (greater (mod1) (mod1))); [ zenon_intro zenon_Hab | zenon_intro zenon_Ha6 ].
% 45.55/45.70 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))); [ zenon_intro zenon_H19c | zenon_intro zenon_H194 ].
% 45.55/45.70 cut ((greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1)) = (greater (low) (mod1))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H6f.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H19c.
% 45.55/45.70 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1a8].
% 45.55/45.70 congruence.
% 45.55/45.70 elim (classic ((low) = (low))); [ zenon_intro zenon_H74 | zenon_intro zenon_H6a ].
% 45.55/45.70 cut (((low) = (low)) = ((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (low))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H1a8.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H74.
% 45.55/45.70 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.55/45.70 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H155].
% 45.55/45.70 congruence.
% 45.55/45.70 apply (zenon_L238_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 apply zenon_H6a. apply refl_equal.
% 45.55/45.70 apply zenon_H6a. apply refl_equal.
% 45.55/45.70 apply zenon_H59. apply refl_equal.
% 45.55/45.70 cut ((greater (mod1) (mod1)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H194.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_Hab.
% 45.55/45.70 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 45.55/45.70 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H159].
% 45.55/45.70 congruence.
% 45.55/45.70 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 ].
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H159.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H16d.
% 45.55/45.70 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].
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H1a7].
% 45.55/45.70 congruence.
% 45.55/45.70 exact (zenon_H1a7 zenon_H15d).
% 45.55/45.70 apply zenon_H16a. apply refl_equal.
% 45.55/45.70 apply zenon_H16a. apply refl_equal.
% 45.55/45.70 apply zenon_H59. apply refl_equal.
% 45.55/45.70 apply (zenon_L240_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 (* end of lemma zenon_L241_ *)
% 45.55/45.70 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).
% 45.55/45.70 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.
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H140). zenon_intro zenon_H142. zenon_intro zenon_H141.
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H141). zenon_intro zenon_H144. zenon_intro zenon_H143.
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H143). zenon_intro zenon_H145. zenon_intro zenon_H134.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H144); [ zenon_intro zenon_H15e | zenon_intro zenon_H15d ].
% 45.55/45.70 apply (zenon_notand_s _ _ zenon_H15e); [ zenon_intro zenon_H13a | zenon_intro zenon_H127 ].
% 45.55/45.70 apply zenon_H13a. zenon_intro zenon_H149.
% 45.55/45.70 apply (zenon_L55_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 apply (zenon_L56_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 apply (zenon_L241_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 (* end of lemma zenon_L242_ *)
% 45.55/45.70 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).
% 45.55/45.70 do 3 intro. intros zenon_H34 zenon_H1a zenon_H148 zenon_H136 zenon_H0 zenon_H35 zenon_H292 zenon_Hec zenon_H1f zenon_Hf3.
% 45.55/45.70 generalize (assumption_15 zenon_TX_y). zenon_intro zenon_Hed.
% 45.55/45.70 generalize (zenon_Hf3 zenon_TT0_hz). zenon_intro zenon_Hf4.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcd ].
% 45.55/45.70 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ].
% 45.55/45.70 exact (zenon_H27 zenon_H1f).
% 45.55/45.70 exact (zenon_Hf2 zenon_Hec).
% 45.55/45.70 generalize (meaning_postulate_greater_strict (low)). zenon_intro zenon_H80.
% 45.55/45.70 generalize (zenon_H80 (mod1)). zenon_intro zenon_H293.
% 45.55/45.70 apply (zenon_notand_s _ _ zenon_H293); [ zenon_intro zenon_H6f | zenon_intro zenon_H7f ].
% 45.55/45.70 generalize (zenon_H0 zenon_TT2_la). zenon_intro zenon_H13c.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H13c); [ zenon_intro zenon_H27 | zenon_intro zenon_H13d ].
% 45.55/45.70 exact (zenon_H27 zenon_H1f).
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H13d). zenon_intro zenon_H13f. zenon_intro zenon_H13e.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H13e); [ zenon_intro zenon_H11d | zenon_intro zenon_H140 ].
% 45.55/45.70 apply (zenon_L50_ zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 apply (zenon_L242_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 exact (zenon_H7f assumption_18b).
% 45.55/45.70 (* end of lemma zenon_L243_ *)
% 45.55/45.70 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).
% 45.55/45.70 do 3 intro. intros zenon_H34 zenon_Hf3 zenon_H1f zenon_Hec zenon_H292 zenon_H35 zenon_H136 zenon_H148 zenon_H1a.
% 45.55/45.70 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0.
% 45.55/45.70 apply (zenon_L243_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 (* end of lemma zenon_L244_ *)
% 45.55/45.70 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).
% 45.55/45.70 do 3 intro. intros zenon_H34 zenon_H1a zenon_H148 zenon_H136 zenon_H35 zenon_H292 zenon_Hec zenon_H1f.
% 45.55/45.70 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3.
% 45.55/45.70 apply (zenon_L244_ zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.70 (* end of lemma zenon_L245_ *)
% 45.55/45.70 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).
% 45.55/45.70 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.
% 45.55/45.70 elim (classic ((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H17d | zenon_intro zenon_H119 ].
% 45.55/45.70 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 ].
% 45.55/45.70 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H118 | zenon_intro zenon_H114 ].
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H17c.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H118.
% 45.55/45.70 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].
% 45.55/45.70 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f].
% 45.55/45.70 congruence.
% 45.55/45.70 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 ].
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H17f.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H16d.
% 45.55/45.70 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].
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136].
% 45.55/45.70 congruence.
% 45.55/45.70 apply (zenon_L245_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 apply zenon_H16a. apply refl_equal.
% 45.55/45.70 apply zenon_H16a. apply refl_equal.
% 45.55/45.70 apply zenon_H62. apply refl_equal.
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H114.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H17e.
% 45.55/45.70 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].
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c].
% 45.55/45.70 congruence.
% 45.55/45.70 elim (classic ((high) = (high))); [ zenon_intro zenon_H180 | zenon_intro zenon_H113 ].
% 45.55/45.70 cut (((high) = (high)) = ((hazard_of_mortality zenon_TX_y zenon_E) = (high))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H11c.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H180.
% 45.55/45.70 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113].
% 45.55/45.70 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H119].
% 45.55/45.70 congruence.
% 45.55/45.70 exact (zenon_H119 zenon_H17d).
% 45.55/45.70 apply zenon_H113. apply refl_equal.
% 45.55/45.70 apply zenon_H113. apply refl_equal.
% 45.55/45.70 apply zenon_H62. apply refl_equal.
% 45.55/45.70 apply (zenon_L49_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 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 ].
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H119.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H11a.
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c].
% 45.55/45.70 congruence.
% 45.55/45.70 exact (zenon_H11c zenon_H116).
% 45.55/45.70 apply zenon_H11b. apply refl_equal.
% 45.55/45.70 apply zenon_H11b. apply refl_equal.
% 45.55/45.70 (* end of lemma zenon_L246_ *)
% 45.55/45.70 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).
% 45.55/45.70 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.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H181); [ zenon_intro zenon_H184 | zenon_intro zenon_H116 ].
% 45.55/45.70 apply (zenon_notand_s _ _ zenon_H184); [ zenon_intro zenon_H186 | zenon_intro zenon_H185 ].
% 45.55/45.70 exact (zenon_H186 zenon_H183).
% 45.55/45.70 exact (zenon_H185 zenon_H182).
% 45.55/45.70 apply (zenon_L246_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.70 (* end of lemma zenon_L247_ *)
% 45.55/45.70 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).
% 45.55/45.70 do 3 intro. intros zenon_Hf3 zenon_H1f zenon_Hec zenon_H292 zenon_H35 zenon_H0 zenon_H148 zenon_H1a zenon_H34 zenon_H167.
% 45.55/45.70 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 ].
% 45.55/45.70 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H136. zenon_intro zenon_H18b.
% 45.55/45.70 apply (zenon_L243_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.70 cut ((greater (high) (mod2)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H167.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact assumption_18d.
% 45.55/45.70 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H83].
% 45.55/45.70 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f].
% 45.55/45.70 congruence.
% 45.55/45.70 apply (zenon_notand_s _ _ zenon_H18a); [ zenon_intro zenon_H18d | zenon_intro zenon_H18c ].
% 45.55/45.70 apply zenon_H18d. zenon_intro zenon_H137.
% 45.55/45.70 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 ].
% 45.55/45.70 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))).
% 45.55/45.70 intro zenon_D_pnotp.
% 45.55/45.70 apply zenon_H17f.
% 45.55/45.70 rewrite <- zenon_D_pnotp.
% 45.55/45.70 exact zenon_H16d.
% 45.55/45.70 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].
% 45.55/45.70 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136].
% 45.55/45.70 congruence.
% 45.55/45.70 exact (zenon_H136 zenon_H137).
% 45.55/45.70 apply zenon_H16a. apply refl_equal.
% 45.55/45.70 apply zenon_H16a. apply refl_equal.
% 45.55/45.70 apply zenon_H18c. zenon_intro zenon_H18e.
% 45.55/45.70 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.55/45.70 generalize (zenon_H18f (high)). zenon_intro zenon_H190.
% 45.55/45.70 generalize (zenon_H190 (mod2)). zenon_intro zenon_H191.
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H191); [ zenon_intro zenon_H18b | zenon_intro zenon_H192 ].
% 45.55/45.70 exact (zenon_H18b zenon_H18e).
% 45.55/45.70 apply (zenon_imply_s _ _ zenon_H192); [ zenon_intro zenon_H9b | zenon_intro zenon_H179 ].
% 45.55/45.70 exact (zenon_H9b assumption_18d).
% 45.55/45.70 exact (zenon_H167 zenon_H179).
% 45.55/45.70 apply zenon_H83. apply refl_equal.
% 45.55/45.70 (* end of lemma zenon_L248_ *)
% 45.55/45.70 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).
% 45.55/45.71 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.
% 45.55/45.71 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H115 | zenon_intro zenon_H5e ].
% 45.55/45.71 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H17c.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H179.
% 45.55/45.71 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 45.55/45.71 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].
% 45.55/45.71 congruence.
% 45.55/45.71 apply zenon_H16a. apply refl_equal.
% 45.55/45.71 exact (zenon_H5e zenon_H115).
% 45.55/45.71 apply (zenon_L248_ zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.71 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 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H5e.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H61.
% 45.55/45.71 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].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H31].
% 45.55/45.71 congruence.
% 45.55/45.71 exact (zenon_H31 zenon_H32).
% 45.55/45.71 apply zenon_H62. apply refl_equal.
% 45.55/45.71 apply zenon_H62. apply refl_equal.
% 45.55/45.71 (* end of lemma zenon_L249_ *)
% 45.55/45.71 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).
% 45.55/45.71 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.
% 45.55/45.71 generalize (zenon_Hf3 zenon_TT0_hz). zenon_intro zenon_Hf4.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcd ].
% 45.55/45.71 apply (zenon_notand_s _ _ zenon_Hf1); [ zenon_intro zenon_H27 | zenon_intro zenon_Hf2 ].
% 45.55/45.71 exact (zenon_H27 zenon_H1f).
% 45.55/45.71 exact (zenon_Hf2 zenon_Hec).
% 45.55/45.71 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ].
% 45.55/45.71 exact (zenon_H27 zenon_H1f).
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H8b); [ zenon_intro zenon_H24 | zenon_intro zenon_H188 ].
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ].
% 45.55/45.71 exact (zenon_H1e zenon_H24).
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d.
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f.
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H30. zenon_intro zenon_H28.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H8e); [ zenon_intro zenon_H91 | zenon_intro zenon_H6b ].
% 45.55/45.71 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ].
% 45.55/45.71 apply (zenon_L31_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ].
% 45.55/45.71 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ].
% 45.55/45.71 apply (zenon_L31_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.71 exact (zenon_H2e zenon_H29).
% 45.55/45.71 apply (zenon_L249_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.71 apply zenon_H72. apply sym_equal. exact zenon_H6b.
% 45.55/45.71 apply zenon_H187. apply sym_equal. exact zenon_H188.
% 45.55/45.71 (* end of lemma zenon_L250_ *)
% 45.55/45.71 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).
% 45.55/45.71 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.
% 45.55/45.71 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ].
% 45.55/45.71 cut ((greater (mod1) (low)) = (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H193.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact assumption_18b.
% 45.55/45.71 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72].
% 45.55/45.71 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 45.55/45.71 congruence.
% 45.55/45.71 apply zenon_H59. apply refl_equal.
% 45.55/45.71 exact (zenon_H72 zenon_H71).
% 45.55/45.71 apply (zenon_L250_ zenon_TT2_la zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.71 (* end of lemma zenon_L251_ *)
% 45.55/45.71 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).
% 45.55/45.71 do 3 intro. intros zenon_H34 zenon_H1a zenon_H148 zenon_H35 zenon_H292 zenon_Hec zenon_H1f zenon_Hf3 zenon_H167.
% 45.55/45.71 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0.
% 45.55/45.71 apply (zenon_L248_ zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.71 (* end of lemma zenon_L252_ *)
% 45.55/45.71 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).
% 45.55/45.71 do 3 intro. intros zenon_H34 zenon_H167 zenon_H1f zenon_Hec zenon_H292 zenon_H35 zenon_H148 zenon_H1a.
% 45.55/45.71 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3.
% 45.55/45.71 apply (zenon_L252_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.71 (* end of lemma zenon_L253_ *)
% 45.55/45.71 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).
% 45.55/45.71 do 3 intro. intros zenon_H1a zenon_H148 zenon_H35 zenon_H292 zenon_Hec zenon_H1f zenon_H34 zenon_H194.
% 45.55/45.71 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 ].
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H13b. zenon_intro zenon_H167.
% 45.55/45.71 apply (zenon_L253_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.71 cut ((greater (mod2) (mod1)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H194.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact assumption_19.
% 45.55/45.71 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 45.55/45.71 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16c].
% 45.55/45.71 congruence.
% 45.55/45.71 apply (zenon_notand_s _ _ zenon_H196); [ zenon_intro zenon_H198 | zenon_intro zenon_H197 ].
% 45.55/45.71 apply zenon_H198. zenon_intro zenon_H146.
% 45.55/45.71 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 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H16c.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H16d.
% 45.55/45.71 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].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b].
% 45.55/45.71 congruence.
% 45.55/45.71 exact (zenon_H13b zenon_H146).
% 45.55/45.71 apply zenon_H16a. apply refl_equal.
% 45.55/45.71 apply zenon_H16a. apply refl_equal.
% 45.55/45.71 apply zenon_H197. zenon_intro zenon_H179.
% 45.55/45.71 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.55/45.71 generalize (zenon_H18f (mod2)). zenon_intro zenon_H199.
% 45.55/45.71 generalize (zenon_H199 (mod1)). zenon_intro zenon_H19a.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H19a); [ zenon_intro zenon_H167 | zenon_intro zenon_H19b ].
% 45.55/45.71 exact (zenon_H167 zenon_H179).
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H19b); [ zenon_intro zenon_H69 | zenon_intro zenon_H19c ].
% 45.55/45.71 exact (zenon_H69 assumption_19).
% 45.55/45.71 exact (zenon_H194 zenon_H19c).
% 45.55/45.71 apply zenon_H59. apply refl_equal.
% 45.55/45.71 (* end of lemma zenon_L254_ *)
% 45.55/45.71 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).
% 45.55/45.71 do 3 intro. intros zenon_H1a zenon_H148 zenon_H35 zenon_H292 zenon_Hec zenon_H1f zenon_H34 zenon_H1a9.
% 45.55/45.71 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 ].
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H195). zenon_intro zenon_H13b. zenon_intro zenon_H167.
% 45.55/45.71 apply (zenon_L253_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.71 cut ((greater (mod2) (low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H1a9.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact assumption_18e.
% 45.55/45.71 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.55/45.71 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H16c].
% 45.55/45.71 congruence.
% 45.55/45.71 apply (zenon_notand_s _ _ zenon_H196); [ zenon_intro zenon_H198 | zenon_intro zenon_H197 ].
% 45.55/45.71 apply zenon_H198. zenon_intro zenon_H146.
% 45.55/45.71 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 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H16c.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H16d.
% 45.55/45.71 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].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H13b].
% 45.55/45.71 congruence.
% 45.55/45.71 exact (zenon_H13b zenon_H146).
% 45.55/45.71 apply zenon_H16a. apply refl_equal.
% 45.55/45.71 apply zenon_H16a. apply refl_equal.
% 45.55/45.71 apply zenon_H197. zenon_intro zenon_H179.
% 45.55/45.71 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.55/45.71 generalize (zenon_H18f (mod2)). zenon_intro zenon_H199.
% 45.55/45.71 generalize (zenon_H199 (low)). zenon_intro zenon_H1c6.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H1c6); [ zenon_intro zenon_H167 | zenon_intro zenon_H1c7 ].
% 45.55/45.71 exact (zenon_H167 zenon_H179).
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H1c7); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H1b1 ].
% 45.55/45.71 exact (zenon_Hc2 assumption_18e).
% 45.55/45.71 exact (zenon_H1a9 zenon_H1b1).
% 45.55/45.71 apply zenon_H6a. apply refl_equal.
% 45.55/45.71 (* end of lemma zenon_L255_ *)
% 45.55/45.71 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).
% 45.55/45.71 do 3 intro. intros zenon_H1f zenon_Hec zenon_H292 zenon_H35 zenon_H148 zenon_H1a zenon_H1a5 zenon_H34 zenon_H1b8.
% 45.55/45.71 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1ba ].
% 45.55/45.71 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1a9 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H1a5.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H1b1.
% 45.55/45.71 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba].
% 45.55/45.71 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].
% 45.55/45.71 congruence.
% 45.55/45.71 apply zenon_H16a. apply refl_equal.
% 45.55/45.71 exact (zenon_H1ba zenon_H1b9).
% 45.55/45.71 apply (zenon_L255_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.71 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 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H1ba.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H11a.
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb].
% 45.55/45.71 congruence.
% 45.55/45.71 exact (zenon_H1bb zenon_H1b8).
% 45.55/45.71 apply zenon_H11b. apply refl_equal.
% 45.55/45.71 apply zenon_H11b. apply refl_equal.
% 45.55/45.71 (* end of lemma zenon_L256_ *)
% 45.55/45.71 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).
% 45.55/45.71 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.
% 45.55/45.71 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3.
% 45.55/45.71 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0.
% 45.55/45.71 generalize (zenon_H0 zenon_E). zenon_intro zenon_H239.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H239); [ zenon_intro zenon_H27 | zenon_intro zenon_H23a ].
% 45.55/45.71 exact (zenon_H27 zenon_H1f).
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H23a). zenon_intro zenon_H23b. zenon_intro zenon_H238.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H238); [ zenon_intro zenon_H111 | zenon_intro zenon_H22f ].
% 45.55/45.71 apply (zenon_L105_ zenon_TX_y); trivial.
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H22f). zenon_intro zenon_H231. zenon_intro zenon_H230.
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H230). zenon_intro zenon_H233. zenon_intro zenon_H232.
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H232). zenon_intro zenon_H234. zenon_intro zenon_H181.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H231); [ zenon_intro zenon_H235 | zenon_intro zenon_H1b8 ].
% 45.55/45.71 apply (zenon_notand_s _ _ zenon_H235); [ zenon_intro zenon_H183 | zenon_intro zenon_H182 ].
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H233); [ zenon_intro zenon_H236 | zenon_intro zenon_H21a ].
% 45.55/45.71 apply (zenon_notand_s _ _ zenon_H236); [ zenon_intro zenon_H186 | zenon_intro zenon_H182 ].
% 45.55/45.71 exact (zenon_H186 zenon_H183).
% 45.55/45.71 apply (zenon_L247_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 elim (classic ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H23c | zenon_intro zenon_H21f ].
% 45.55/45.71 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))); [ zenon_intro zenon_H19c | zenon_intro zenon_H194 ].
% 45.55/45.71 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 ].
% 45.55/45.71 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 ].
% 45.55/45.71 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.55/45.71 generalize (zenon_H18f (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H23d.
% 45.55/45.71 generalize (zenon_H23d (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H23e.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H23f ].
% 45.55/45.71 exact (zenon_H1a5 zenon_H1a4).
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H23f); [ zenon_intro zenon_H117 | zenon_intro zenon_H240 ].
% 45.55/45.71 exact (zenon_H117 zenon_H17e).
% 45.55/45.71 exact (zenon_H17c zenon_H240).
% 45.55/45.71 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H241 | zenon_intro zenon_H193 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H117.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H241.
% 45.55/45.71 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].
% 45.55/45.71 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f].
% 45.55/45.71 congruence.
% 45.55/45.71 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 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H21f.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H11a.
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e].
% 45.55/45.71 congruence.
% 45.55/45.71 exact (zenon_H21e zenon_H21a).
% 45.55/45.71 apply zenon_H11b. apply refl_equal.
% 45.55/45.71 apply zenon_H11b. apply refl_equal.
% 45.55/45.71 apply zenon_H62. apply refl_equal.
% 45.55/45.71 apply (zenon_L251_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H1a5.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H19c.
% 45.55/45.71 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f].
% 45.55/45.71 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].
% 45.55/45.71 congruence.
% 45.55/45.71 apply zenon_H16a. apply refl_equal.
% 45.55/45.71 exact (zenon_H21f zenon_H23c).
% 45.55/45.71 apply (zenon_L254_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.71 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 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H21f.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H11a.
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e].
% 45.55/45.71 congruence.
% 45.55/45.71 exact (zenon_H21e zenon_H21a).
% 45.55/45.71 apply zenon_H11b. apply refl_equal.
% 45.55/45.71 apply zenon_H11b. apply refl_equal.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H234); [ zenon_intro zenon_H237 | zenon_intro zenon_H19e ].
% 45.55/45.71 apply (zenon_notand_s _ _ zenon_H237); [ zenon_intro zenon_H183 | zenon_intro zenon_H185 ].
% 45.55/45.71 apply (zenon_L247_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 exact (zenon_H185 zenon_H182).
% 45.55/45.71 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H1a1 ].
% 45.55/45.71 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ].
% 45.55/45.71 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 ].
% 45.55/45.71 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 ].
% 45.55/45.71 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.55/45.71 generalize (zenon_H18f (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H23d.
% 45.55/45.71 generalize (zenon_H23d (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H23e.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H23f ].
% 45.55/45.71 exact (zenon_H1a5 zenon_H1a4).
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H23f); [ zenon_intro zenon_H117 | zenon_intro zenon_H240 ].
% 45.55/45.71 exact (zenon_H117 zenon_H17e).
% 45.55/45.71 exact (zenon_H17c zenon_H240).
% 45.55/45.71 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1c4 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H117.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H1c3.
% 45.55/45.71 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].
% 45.55/45.71 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1].
% 45.55/45.71 congruence.
% 45.55/45.71 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 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H1a1.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H11a.
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2].
% 45.55/45.71 congruence.
% 45.55/45.71 exact (zenon_H1a2 zenon_H19e).
% 45.55/45.71 apply zenon_H11b. apply refl_equal.
% 45.55/45.71 apply zenon_H11b. apply refl_equal.
% 45.55/45.71 apply zenon_H62. apply refl_equal.
% 45.55/45.71 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H241 | zenon_intro zenon_H193 ].
% 45.55/45.71 generalize (zenon_H34 (mod2)). zenon_intro zenon_H16e.
% 45.55/45.71 generalize (zenon_H16e (mod1)). zenon_intro zenon_H16f.
% 45.55/45.71 generalize (zenon_H16f (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H28e.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H28e); [ zenon_intro zenon_H69 | zenon_intro zenon_H28f ].
% 45.55/45.71 exact (zenon_H69 assumption_19).
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H28f); [ zenon_intro zenon_H193 | zenon_intro zenon_H1c3 ].
% 45.55/45.71 exact (zenon_H193 zenon_H241).
% 45.55/45.71 exact (zenon_H1c4 zenon_H1c3).
% 45.55/45.71 apply (zenon_L251_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H1a5.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H179.
% 45.55/45.71 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1].
% 45.55/45.71 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].
% 45.55/45.71 congruence.
% 45.55/45.71 apply zenon_H16a. apply refl_equal.
% 45.55/45.71 exact (zenon_H1a1 zenon_H1a3).
% 45.55/45.71 apply (zenon_L248_ zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.71 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 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H1a1.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H11a.
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2].
% 45.55/45.71 congruence.
% 45.55/45.71 exact (zenon_H1a2 zenon_H19e).
% 45.55/45.71 apply zenon_H11b. apply refl_equal.
% 45.55/45.71 apply zenon_H11b. apply refl_equal.
% 45.55/45.71 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 ].
% 45.55/45.71 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1a9 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H17c.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H1b1.
% 45.55/45.71 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72].
% 45.55/45.71 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].
% 45.55/45.71 congruence.
% 45.55/45.71 apply zenon_H16a. apply refl_equal.
% 45.55/45.71 apply (zenon_L250_ zenon_TT2_la zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H1a9.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H1a4.
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb].
% 45.55/45.71 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].
% 45.55/45.71 congruence.
% 45.55/45.71 apply zenon_H16a. apply refl_equal.
% 45.55/45.71 exact (zenon_H1bb zenon_H1b8).
% 45.55/45.71 apply (zenon_L256_ zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.71 (* end of lemma zenon_L257_ *)
% 45.55/45.71 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).
% 45.55/45.71 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.
% 45.55/45.71 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H242 | zenon_intro zenon_H187 ].
% 45.55/45.71 cut ((greater (low) (very_low)) = (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_Had.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact assumption_18c.
% 45.55/45.71 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H187].
% 45.55/45.71 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.55/45.71 congruence.
% 45.55/45.71 apply zenon_H6a. apply refl_equal.
% 45.55/45.71 exact (zenon_H187 zenon_H242).
% 45.55/45.71 apply (zenon_L257_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 (* end of lemma zenon_L258_ *)
% 45.55/45.71 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).
% 45.55/45.71 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.
% 45.55/45.71 elim (classic (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_Hac | zenon_intro zenon_Had ].
% 45.55/45.71 generalize (zenon_H34 (mod1)). zenon_intro zenon_Ha7.
% 45.55/45.71 generalize (zenon_Ha7 (low)). zenon_intro zenon_Ha8.
% 45.55/45.71 generalize (zenon_Ha8 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H243.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H243); [ zenon_intro zenon_H7f | zenon_intro zenon_H244 ].
% 45.55/45.71 exact (zenon_H7f assumption_18b).
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H244); [ zenon_intro zenon_Had | zenon_intro zenon_H241 ].
% 45.55/45.71 exact (zenon_Had zenon_Hac).
% 45.55/45.71 exact (zenon_H193 zenon_H241).
% 45.55/45.71 apply (zenon_L258_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 (* end of lemma zenon_L259_ *)
% 45.55/45.71 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).
% 45.55/45.71 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.
% 45.55/45.71 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H241 | zenon_intro zenon_H193 ].
% 45.55/45.71 generalize (zenon_H34 (mod2)). zenon_intro zenon_H16e.
% 45.55/45.71 generalize (zenon_H16e (mod1)). zenon_intro zenon_H16f.
% 45.55/45.71 generalize (zenon_H16f (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H28e.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H28e); [ zenon_intro zenon_H69 | zenon_intro zenon_H28f ].
% 45.55/45.71 exact (zenon_H69 assumption_19).
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H28f); [ zenon_intro zenon_H193 | zenon_intro zenon_H1c3 ].
% 45.55/45.71 exact (zenon_H193 zenon_H241).
% 45.55/45.71 exact (zenon_H1c4 zenon_H1c3).
% 45.55/45.71 apply (zenon_L259_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 (* end of lemma zenon_L260_ *)
% 45.55/45.71 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).
% 45.55/45.71 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.
% 45.55/45.71 elim (classic ((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H17d | zenon_intro zenon_H119 ].
% 45.55/45.71 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 ].
% 45.55/45.71 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H118 | zenon_intro zenon_H114 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H17c.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H118.
% 45.55/45.71 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].
% 45.55/45.71 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f].
% 45.55/45.71 congruence.
% 45.55/45.71 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 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H17f.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H16d.
% 45.55/45.71 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].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136].
% 45.55/45.71 congruence.
% 45.55/45.71 apply (zenon_L244_ zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.71 apply zenon_H16a. apply refl_equal.
% 45.55/45.71 apply zenon_H16a. apply refl_equal.
% 45.55/45.71 apply zenon_H62. apply refl_equal.
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H114.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H17e.
% 45.55/45.71 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].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c].
% 45.55/45.71 congruence.
% 45.55/45.71 elim (classic ((high) = (high))); [ zenon_intro zenon_H180 | zenon_intro zenon_H113 ].
% 45.55/45.71 cut (((high) = (high)) = ((hazard_of_mortality zenon_TX_y zenon_E) = (high))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H11c.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H180.
% 45.55/45.71 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113].
% 45.55/45.71 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H119].
% 45.55/45.71 congruence.
% 45.55/45.71 exact (zenon_H119 zenon_H17d).
% 45.55/45.71 apply zenon_H113. apply refl_equal.
% 45.55/45.71 apply zenon_H113. apply refl_equal.
% 45.55/45.71 apply zenon_H62. apply refl_equal.
% 45.55/45.71 apply (zenon_L207_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 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 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H119.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H11a.
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H11c].
% 45.55/45.71 congruence.
% 45.55/45.71 exact (zenon_H11c zenon_H116).
% 45.55/45.71 apply zenon_H11b. apply refl_equal.
% 45.55/45.71 apply zenon_H11b. apply refl_equal.
% 45.55/45.71 (* end of lemma zenon_L261_ *)
% 45.55/45.71 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).
% 45.55/45.71 do 3 intro. intros zenon_H34 zenon_H1c2 zenon_H2c zenon_H26e zenon_H1a zenon_Hec zenon_H1f zenon_Hf3.
% 45.55/45.71 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H118 | zenon_intro zenon_H114 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H1c2.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H118.
% 45.55/45.71 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].
% 45.55/45.71 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H94].
% 45.55/45.71 congruence.
% 45.55/45.71 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 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H94.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H61.
% 45.55/45.71 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].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b].
% 45.55/45.71 congruence.
% 45.55/45.71 exact (zenon_H2b zenon_H2c).
% 45.55/45.71 apply zenon_H62. apply refl_equal.
% 45.55/45.71 apply zenon_H62. apply refl_equal.
% 45.55/45.71 apply zenon_H62. apply refl_equal.
% 45.55/45.71 apply (zenon_L217_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 (* end of lemma zenon_L262_ *)
% 45.55/45.71 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).
% 45.55/45.71 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.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ].
% 45.55/45.71 apply (zenon_notand_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ].
% 45.55/45.71 exact (zenon_H2f zenon_H2a).
% 45.55/45.71 exact (zenon_H2e zenon_H29).
% 45.55/45.71 elim (classic ((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H281 | zenon_intro zenon_H94 ].
% 45.55/45.71 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 ].
% 45.55/45.71 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H118 | zenon_intro zenon_H114 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H17c.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H118.
% 45.55/45.71 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].
% 45.55/45.71 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f].
% 45.55/45.71 congruence.
% 45.55/45.71 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 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H17f.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H16d.
% 45.55/45.71 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].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136].
% 45.55/45.71 congruence.
% 45.55/45.71 apply (zenon_L243_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.71 apply zenon_H16a. apply refl_equal.
% 45.55/45.71 apply zenon_H16a. apply refl_equal.
% 45.55/45.71 apply zenon_H62. apply refl_equal.
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H114.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H1c5.
% 45.55/45.71 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].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b].
% 45.55/45.71 congruence.
% 45.55/45.71 elim (classic ((high) = (high))); [ zenon_intro zenon_H180 | zenon_intro zenon_H113 ].
% 45.55/45.71 cut (((high) = (high)) = ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H2b.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H180.
% 45.55/45.71 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113].
% 45.55/45.71 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H94].
% 45.55/45.71 congruence.
% 45.55/45.71 exact (zenon_H94 zenon_H281).
% 45.55/45.71 apply zenon_H113. apply refl_equal.
% 45.55/45.71 apply zenon_H113. apply refl_equal.
% 45.55/45.71 apply zenon_H62. apply refl_equal.
% 45.55/45.71 apply (zenon_L262_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 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 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H94.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H61.
% 45.55/45.71 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].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b].
% 45.55/45.71 congruence.
% 45.55/45.71 exact (zenon_H2b zenon_H2c).
% 45.55/45.71 apply zenon_H62. apply refl_equal.
% 45.55/45.71 apply zenon_H62. apply refl_equal.
% 45.55/45.71 (* end of lemma zenon_L263_ *)
% 45.55/45.71 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).
% 45.55/45.71 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.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ].
% 45.55/45.71 apply (zenon_notand_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ].
% 45.55/45.71 exact (zenon_H2f zenon_H2a).
% 45.55/45.71 apply zenon_H2e. zenon_intro zenon_H36.
% 45.55/45.71 apply (zenon_L155_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 elim (classic ((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H281 | zenon_intro zenon_H94 ].
% 45.55/45.71 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 ].
% 45.55/45.71 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H118 | zenon_intro zenon_H114 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H17c.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H118.
% 45.55/45.71 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].
% 45.55/45.71 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f].
% 45.55/45.71 congruence.
% 45.55/45.71 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 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H17f.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H16d.
% 45.55/45.71 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].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136].
% 45.55/45.71 congruence.
% 45.55/45.71 apply (zenon_L243_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.71 apply zenon_H16a. apply refl_equal.
% 45.55/45.71 apply zenon_H16a. apply refl_equal.
% 45.55/45.71 apply zenon_H62. apply refl_equal.
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H114.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H1c5.
% 45.55/45.71 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].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b].
% 45.55/45.71 congruence.
% 45.55/45.71 elim (classic ((high) = (high))); [ zenon_intro zenon_H180 | zenon_intro zenon_H113 ].
% 45.55/45.71 cut (((high) = (high)) = ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H2b.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H180.
% 45.55/45.71 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113].
% 45.55/45.71 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H94].
% 45.55/45.71 congruence.
% 45.55/45.71 exact (zenon_H94 zenon_H281).
% 45.55/45.71 apply zenon_H113. apply refl_equal.
% 45.55/45.71 apply zenon_H113. apply refl_equal.
% 45.55/45.71 apply zenon_H62. apply refl_equal.
% 45.55/45.71 apply (zenon_L176_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 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 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H94.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H61.
% 45.55/45.71 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].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b].
% 45.55/45.71 congruence.
% 45.55/45.71 exact (zenon_H2b zenon_H2c).
% 45.55/45.71 apply zenon_H62. apply refl_equal.
% 45.55/45.71 apply zenon_H62. apply refl_equal.
% 45.55/45.71 (* end of lemma zenon_L264_ *)
% 45.55/45.71 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).
% 45.55/45.71 do 2 intro. intros zenon_H34 zenon_H1c4 zenon_H6b.
% 45.55/45.71 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H241 | zenon_intro zenon_H193 ].
% 45.55/45.71 generalize (zenon_H34 (mod2)). zenon_intro zenon_H16e.
% 45.55/45.71 generalize (zenon_H16e (mod1)). zenon_intro zenon_H16f.
% 45.55/45.71 generalize (zenon_H16f (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H28e.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H28e); [ zenon_intro zenon_H69 | zenon_intro zenon_H28f ].
% 45.55/45.71 exact (zenon_H69 assumption_19).
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H28f); [ zenon_intro zenon_H193 | zenon_intro zenon_H1c3 ].
% 45.55/45.71 exact (zenon_H193 zenon_H241).
% 45.55/45.71 exact (zenon_H1c4 zenon_H1c3).
% 45.55/45.71 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ].
% 45.55/45.71 cut ((greater (mod1) (low)) = (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H193.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact assumption_18b.
% 45.55/45.71 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H72].
% 45.55/45.71 cut (((mod1) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 45.55/45.71 congruence.
% 45.55/45.71 apply zenon_H59. apply refl_equal.
% 45.55/45.71 exact (zenon_H72 zenon_H71).
% 45.55/45.71 apply zenon_H72. apply sym_equal. exact zenon_H6b.
% 45.55/45.71 (* end of lemma zenon_L265_ *)
% 45.55/45.71 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).
% 45.55/45.71 do 2 intro. intros zenon_H34 zenon_H2c zenon_H1c2 zenon_H6b.
% 45.55/45.71 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H118 | zenon_intro zenon_H114 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H1c2.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H118.
% 45.55/45.71 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].
% 45.55/45.71 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H94].
% 45.55/45.71 congruence.
% 45.55/45.71 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 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H94.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H61.
% 45.55/45.71 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].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b].
% 45.55/45.71 congruence.
% 45.55/45.71 exact (zenon_H2b zenon_H2c).
% 45.55/45.71 apply zenon_H62. apply refl_equal.
% 45.55/45.71 apply zenon_H62. apply refl_equal.
% 45.55/45.71 apply zenon_H62. apply refl_equal.
% 45.55/45.71 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1c4 ].
% 45.55/45.71 generalize (zenon_H34 (high)). zenon_intro zenon_H1fa.
% 45.55/45.71 generalize (zenon_H1fa (mod2)). zenon_intro zenon_H1fb.
% 45.55/45.71 generalize (zenon_H1fb (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H27e.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H27e); [ zenon_intro zenon_H9b | zenon_intro zenon_H27f ].
% 45.55/45.71 exact (zenon_H9b assumption_18d).
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H27f); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H118 ].
% 45.55/45.71 exact (zenon_H1c4 zenon_H1c3).
% 45.55/45.71 exact (zenon_H114 zenon_H118).
% 45.55/45.71 apply (zenon_L265_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 (* end of lemma zenon_L266_ *)
% 45.55/45.71 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).
% 45.55/45.71 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.
% 45.55/45.71 generalize (zenon_H0 zenon_TT1_bg). zenon_intro zenon_H88.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H27 | zenon_intro zenon_H89 ].
% 45.55/45.71 exact (zenon_H27 zenon_H1f).
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H8b); [ zenon_intro zenon_H24 | zenon_intro zenon_H188 ].
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H1e | zenon_intro zenon_H8c ].
% 45.55/45.71 exact (zenon_H1e zenon_H24).
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d.
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f.
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H30. zenon_intro zenon_H28.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H8e); [ zenon_intro zenon_H91 | zenon_intro zenon_H6b ].
% 45.55/45.71 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ].
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H90); [ zenon_intro zenon_H93 | zenon_intro zenon_H92 ].
% 45.55/45.71 apply (zenon_notand_s _ _ zenon_H93); [ zenon_intro zenon_H2f | zenon_intro zenon_H29 ].
% 45.55/45.71 exact (zenon_H2f zenon_H2a).
% 45.55/45.71 apply (zenon_L263_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 apply (zenon_L264_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ].
% 45.55/45.71 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ].
% 45.55/45.71 apply (zenon_L263_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 exact (zenon_H2e zenon_H29).
% 45.55/45.71 apply (zenon_L249_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H90); [ zenon_intro zenon_H93 | zenon_intro zenon_H92 ].
% 45.55/45.71 apply (zenon_notand_s _ _ zenon_H93); [ zenon_intro zenon_H2f | zenon_intro zenon_H29 ].
% 45.55/45.71 apply zenon_H2f. zenon_intro zenon_H82.
% 45.55/45.71 apply (zenon_L156_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ].
% 45.55/45.71 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ].
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ].
% 45.55/45.71 apply (zenon_notand_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ].
% 45.55/45.71 exact (zenon_H2f zenon_H2a).
% 45.55/45.71 exact (zenon_H2e zenon_H29).
% 45.55/45.71 elim (classic ((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H281 | zenon_intro zenon_H94 ].
% 45.55/45.71 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 ].
% 45.55/45.71 elim (classic (greater (high) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H118 | zenon_intro zenon_H114 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H17c.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H118.
% 45.55/45.71 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].
% 45.55/45.71 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H17f].
% 45.55/45.71 congruence.
% 45.55/45.71 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 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H17f.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H16d.
% 45.55/45.71 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].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (high))); [idtac | apply NNPP; zenon_intro zenon_H136].
% 45.55/45.71 congruence.
% 45.55/45.71 apply (zenon_L243_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.71 apply zenon_H16a. apply refl_equal.
% 45.55/45.71 apply zenon_H16a. apply refl_equal.
% 45.55/45.71 apply zenon_H62. apply refl_equal.
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H114.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H1c5.
% 45.55/45.71 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].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b].
% 45.55/45.71 congruence.
% 45.55/45.71 elim (classic ((high) = (high))); [ zenon_intro zenon_H180 | zenon_intro zenon_H113 ].
% 45.55/45.71 cut (((high) = (high)) = ((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H2b.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H180.
% 45.55/45.71 cut (((high) = (high))); [idtac | apply NNPP; zenon_intro zenon_H113].
% 45.55/45.71 cut (((high) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H94].
% 45.55/45.71 congruence.
% 45.55/45.71 exact (zenon_H94 zenon_H281).
% 45.55/45.71 apply zenon_H113. apply refl_equal.
% 45.55/45.71 apply zenon_H113. apply refl_equal.
% 45.55/45.71 apply zenon_H62. apply refl_equal.
% 45.55/45.71 apply (zenon_L266_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 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 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H94.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H61.
% 45.55/45.71 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].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_TT1_bg) = (high))); [idtac | apply NNPP; zenon_intro zenon_H2b].
% 45.55/45.71 congruence.
% 45.55/45.71 exact (zenon_H2b zenon_H2c).
% 45.55/45.71 apply zenon_H62. apply refl_equal.
% 45.55/45.71 apply zenon_H62. apply refl_equal.
% 45.55/45.71 exact (zenon_H2e zenon_H29).
% 45.55/45.71 apply (zenon_L249_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ].
% 45.55/45.71 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H2a | zenon_intro zenon_H2e ].
% 45.55/45.71 apply (zenon_L264_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 apply zenon_H2e. zenon_intro zenon_H36.
% 45.55/45.71 apply (zenon_L155_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 apply (zenon_L146_ zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 apply zenon_H187. apply sym_equal. exact zenon_H188.
% 45.55/45.71 (* end of lemma zenon_L267_ *)
% 45.55/45.71 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).
% 45.55/45.71 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.
% 45.55/45.71 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3.
% 45.55/45.71 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0.
% 45.55/45.71 apply (zenon_L267_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.71 (* end of lemma zenon_L268_ *)
% 45.55/45.71 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).
% 45.55/45.71 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.
% 45.55/45.71 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H242 | zenon_intro zenon_H187 ].
% 45.55/45.71 cut ((greater (low) (very_low)) = (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_Had.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact assumption_18c.
% 45.55/45.71 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H187].
% 45.55/45.71 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 45.55/45.71 congruence.
% 45.55/45.71 apply zenon_H6a. apply refl_equal.
% 45.55/45.71 exact (zenon_H187 zenon_H242).
% 45.55/45.71 apply (zenon_L268_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.71 (* end of lemma zenon_L269_ *)
% 45.55/45.71 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).
% 45.55/45.71 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.
% 45.55/45.71 elim (classic (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_Hac | zenon_intro zenon_Had ].
% 45.55/45.71 generalize (zenon_H34 (mod1)). zenon_intro zenon_Ha7.
% 45.55/45.71 generalize (zenon_Ha7 (low)). zenon_intro zenon_Ha8.
% 45.55/45.71 generalize (zenon_Ha8 (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H243.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H243); [ zenon_intro zenon_H7f | zenon_intro zenon_H244 ].
% 45.55/45.71 exact (zenon_H7f assumption_18b).
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H244); [ zenon_intro zenon_Had | zenon_intro zenon_H241 ].
% 45.55/45.71 exact (zenon_Had zenon_Hac).
% 45.55/45.71 exact (zenon_H193 zenon_H241).
% 45.55/45.71 apply (zenon_L269_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 (* end of lemma zenon_L270_ *)
% 45.55/45.71 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).
% 45.55/45.71 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.
% 45.55/45.71 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H241 | zenon_intro zenon_H193 ].
% 45.55/45.71 generalize (zenon_H34 (mod2)). zenon_intro zenon_H16e.
% 45.55/45.71 generalize (zenon_H16e (mod1)). zenon_intro zenon_H16f.
% 45.55/45.71 generalize (zenon_H16f (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H28e.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H28e); [ zenon_intro zenon_H69 | zenon_intro zenon_H28f ].
% 45.55/45.71 exact (zenon_H69 assumption_19).
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H28f); [ zenon_intro zenon_H193 | zenon_intro zenon_H1c3 ].
% 45.55/45.71 exact (zenon_H193 zenon_H241).
% 45.55/45.71 exact (zenon_H1c4 zenon_H1c3).
% 45.55/45.71 apply (zenon_L270_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 (* end of lemma zenon_L271_ *)
% 45.55/45.71 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).
% 45.55/45.71 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.
% 45.55/45.71 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H1a1 ].
% 45.55/45.71 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ].
% 45.55/45.71 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 ].
% 45.55/45.71 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 ].
% 45.55/45.71 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.55/45.71 generalize (zenon_H18f (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H23d.
% 45.55/45.71 generalize (zenon_H23d (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H23e.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H23f ].
% 45.55/45.71 exact (zenon_H1a5 zenon_H1a4).
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H23f); [ zenon_intro zenon_H117 | zenon_intro zenon_H240 ].
% 45.55/45.71 exact (zenon_H117 zenon_H17e).
% 45.55/45.71 exact (zenon_H17c zenon_H240).
% 45.55/45.71 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1c4 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H117.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H1c3.
% 45.55/45.71 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].
% 45.55/45.71 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1].
% 45.55/45.71 congruence.
% 45.55/45.71 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 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H1a1.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H11a.
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2].
% 45.55/45.71 congruence.
% 45.55/45.71 exact (zenon_H1a2 zenon_H19e).
% 45.55/45.71 apply zenon_H11b. apply refl_equal.
% 45.55/45.71 apply zenon_H11b. apply refl_equal.
% 45.55/45.71 apply zenon_H62. apply refl_equal.
% 45.55/45.71 apply (zenon_L271_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H1a5.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H179.
% 45.55/45.71 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1].
% 45.55/45.71 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].
% 45.55/45.71 congruence.
% 45.55/45.71 apply zenon_H16a. apply refl_equal.
% 45.55/45.71 exact (zenon_H1a1 zenon_H1a3).
% 45.55/45.71 apply (zenon_L253_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.71 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 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H1a1.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H11a.
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2].
% 45.55/45.71 congruence.
% 45.55/45.71 exact (zenon_H1a2 zenon_H19e).
% 45.55/45.71 apply zenon_H11b. apply refl_equal.
% 45.55/45.71 apply zenon_H11b. apply refl_equal.
% 45.55/45.71 (* end of lemma zenon_L272_ *)
% 45.55/45.71 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).
% 45.55/45.71 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.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H234); [ zenon_intro zenon_H237 | zenon_intro zenon_H19e ].
% 45.55/45.71 apply (zenon_notand_s _ _ zenon_H237); [ zenon_intro zenon_H183 | zenon_intro zenon_H185 ].
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H181); [ zenon_intro zenon_H184 | zenon_intro zenon_H116 ].
% 45.55/45.71 apply (zenon_notand_s _ _ zenon_H184); [ zenon_intro zenon_H186 | zenon_intro zenon_H185 ].
% 45.55/45.71 exact (zenon_H186 zenon_H183).
% 45.55/45.71 exact (zenon_H185 zenon_H182).
% 45.55/45.71 apply (zenon_L261_ zenon_TT2_la zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.71 exact (zenon_H185 zenon_H182).
% 45.55/45.71 apply (zenon_L272_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.71 (* end of lemma zenon_L273_ *)
% 45.55/45.71 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).
% 45.55/45.71 do 3 intro. intros zenon_H1f zenon_Hec zenon_H292 zenon_H35 zenon_H148 zenon_H1a zenon_H34 zenon_H294.
% 45.55/45.71 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 ].
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H295). zenon_intro zenon_H1a8. zenon_intro zenon_H1a9.
% 45.55/45.71 apply (zenon_L255_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.71 cut ((greater (low) (very_low)) = (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (very_low))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H294.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact assumption_18c.
% 45.55/45.71 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hf5].
% 45.55/45.71 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_TT2_la))); [idtac | apply NNPP; zenon_intro zenon_H155].
% 45.55/45.71 congruence.
% 45.55/45.71 apply (zenon_notand_s _ _ zenon_H296); [ zenon_intro zenon_H298 | zenon_intro zenon_H297 ].
% 45.55/45.71 apply zenon_H298. zenon_intro zenon_H15b.
% 45.55/45.71 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 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H155.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H16d.
% 45.55/45.71 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].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_TT2_la) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1a8].
% 45.55/45.71 congruence.
% 45.55/45.71 exact (zenon_H1a8 zenon_H15b).
% 45.55/45.71 apply zenon_H16a. apply refl_equal.
% 45.55/45.71 apply zenon_H16a. apply refl_equal.
% 45.55/45.71 apply zenon_H297. zenon_intro zenon_H1b1.
% 45.55/45.71 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.55/45.71 generalize (zenon_H18f (low)). zenon_intro zenon_H299.
% 45.55/45.71 generalize (zenon_H299 (very_low)). zenon_intro zenon_H29a.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H29a); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H29b ].
% 45.55/45.71 exact (zenon_H1a9 zenon_H1b1).
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H29b); [ zenon_intro zenon_Hff | zenon_intro zenon_H29c ].
% 45.55/45.71 exact (zenon_Hff assumption_18c).
% 45.55/45.71 exact (zenon_H294 zenon_H29c).
% 45.55/45.71 apply zenon_Hf5. apply refl_equal.
% 45.55/45.71 (* end of lemma zenon_L274_ *)
% 45.55/45.71 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).
% 45.55/45.71 do 3 intro. intros zenon_H1a zenon_H148 zenon_H35 zenon_H292 zenon_Hec zenon_H1f zenon_H1a5 zenon_H34 zenon_H1e0.
% 45.55/45.71 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e2 ].
% 45.55/45.71 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (very_low))); [ zenon_intro zenon_H29c | zenon_intro zenon_H294 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H1a5.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H29c.
% 45.55/45.71 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1e2].
% 45.55/45.71 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].
% 45.55/45.71 congruence.
% 45.55/45.71 apply zenon_H16a. apply refl_equal.
% 45.55/45.71 exact (zenon_H1e2 zenon_H1e1).
% 45.55/45.71 apply (zenon_L274_ zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.71 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 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H1e2.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H11a.
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5].
% 45.55/45.71 congruence.
% 45.55/45.71 exact (zenon_H1e5 zenon_H1e0).
% 45.55/45.71 apply zenon_H11b. apply refl_equal.
% 45.55/45.71 apply zenon_H11b. apply refl_equal.
% 45.55/45.71 (* end of lemma zenon_L275_ *)
% 45.55/45.71 apply NNPP. intro zenon_G.
% 45.55/45.71 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 ].
% 45.55/45.71 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 ].
% 45.55/45.71 elim zenon_H29e. zenon_intro zenon_TX_y. zenon_intro zenon_H29f.
% 45.55/45.71 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 ].
% 45.55/45.71 elim zenon_H2a0. zenon_intro zenon_TT0_hz. zenon_intro zenon_H2a1.
% 45.55/45.71 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 ].
% 45.55/45.71 elim zenon_H2a2. zenon_intro zenon_TT1_bg. zenon_intro zenon_H2a3.
% 45.55/45.71 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 ].
% 45.55/45.71 elim zenon_H2a4. zenon_intro zenon_TT2_la. zenon_intro zenon_H2a5.
% 45.55/45.71 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 ].
% 45.55/45.71 elim zenon_H2a6. zenon_intro zenon_TT3_x. zenon_intro zenon_H2a7.
% 45.55/45.71 apply (zenon_notimply_s _ _ zenon_H2a7). zenon_intro zenon_H2a9. zenon_intro zenon_H2a8.
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H2a9). zenon_intro zenon_H1f. zenon_intro zenon_H2aa.
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H2aa). zenon_intro zenon_H2ac. zenon_intro zenon_H2ab.
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H2ab). zenon_intro zenon_H1d. zenon_intro zenon_H2ad.
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H2ad). zenon_intro zenon_Hec. zenon_intro zenon_H2ae.
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H2ae). zenon_intro zenon_H2b0. zenon_intro zenon_H2af.
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H2af). zenon_intro zenon_H24a. zenon_intro zenon_H2b1.
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H2b1). zenon_intro zenon_H2b3. zenon_intro zenon_H2b2.
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H2b2). zenon_intro zenon_H2b5. zenon_intro zenon_H2b4.
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H2b4). zenon_intro zenon_H148. zenon_intro zenon_H2b6.
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H2b6). zenon_intro zenon_H12c. zenon_intro zenon_H100.
% 45.55/45.71 generalize (definition_4 zenon_TX_y). zenon_intro zenon_H2b7.
% 45.55/45.71 apply (zenon_equiv_s _ _ zenon_H2b7); [ zenon_intro zenon_H2b9; zenon_intro zenon_H2b8 | zenon_intro zenon_H2ac; zenon_intro zenon_H35 ].
% 45.55/45.71 exact (zenon_H2b9 zenon_H2ac).
% 45.55/45.71 generalize (definition_1 zenon_TX_y). zenon_intro zenon_H1b.
% 45.55/45.71 apply (zenon_equiv_s _ _ zenon_H1b); [ zenon_intro zenon_H1d; zenon_intro zenon_H1a | zenon_intro zenon_H19; zenon_intro zenon_H1c ].
% 45.55/45.71 generalize (definition_smaller (sigma)). zenon_intro zenon_H2ba.
% 45.55/45.71 generalize (zenon_H2ba (tau)). zenon_intro zenon_H2bb.
% 45.55/45.71 apply (zenon_equiv_s _ _ zenon_H2bb); [ zenon_intro zenon_H2bc; zenon_intro zenon_H4b | zenon_intro zenon_H2b3; zenon_intro zenon_H38 ].
% 45.55/45.71 exact (zenon_H2bc zenon_H2b3).
% 45.55/45.71 generalize (definition_smaller_or_equal (age zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H3d.
% 45.55/45.71 generalize (zenon_H3d (sigma)). zenon_intro zenon_H2bd.
% 45.55/45.71 apply (zenon_equiv_s _ _ zenon_H2bd); [ zenon_intro zenon_H2c0; zenon_intro zenon_H2bf | zenon_intro zenon_H2b5; zenon_intro zenon_H2be ].
% 45.55/45.71 exact (zenon_H2c0 zenon_H2b5).
% 45.55/45.71 generalize (definition_smaller_or_equal (age zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H129.
% 45.55/45.71 generalize (zenon_H129 (tau)). zenon_intro zenon_H12a.
% 45.55/45.71 apply (zenon_equiv_s _ _ zenon_H12a); [ zenon_intro zenon_H128; zenon_intro zenon_H12d | zenon_intro zenon_H12c; zenon_intro zenon_H12b ].
% 45.55/45.71 exact (zenon_H128 zenon_H12c).
% 45.55/45.71 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_H132 | zenon_intro zenon_H292 ].
% 45.55/45.71 generalize (definition_smaller (age zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H130.
% 45.55/45.71 generalize (zenon_H130 (tau)). zenon_intro zenon_H131.
% 45.55/45.71 apply (zenon_equiv_s _ _ zenon_H131); [ zenon_intro zenon_H12f; zenon_intro zenon_H133 | zenon_intro zenon_H132; zenon_intro zenon_H123 ].
% 45.55/45.71 exact (zenon_H12f zenon_H132).
% 45.55/45.71 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_H2c1 | zenon_intro zenon_H26e ].
% 45.55/45.71 generalize (definition_smaller (age zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H44.
% 45.55/45.71 generalize (zenon_H44 (sigma)). zenon_intro zenon_H2c2.
% 45.55/45.71 apply (zenon_equiv_s _ _ zenon_H2c2); [ zenon_intro zenon_H2c3; zenon_intro zenon_H58 | zenon_intro zenon_H2c1; zenon_intro zenon_H37 ].
% 45.55/45.71 exact (zenon_H2c3 zenon_H2c1).
% 45.55/45.71 apply (zenon_notand_s _ _ zenon_H2a8); [ zenon_intro zenon_H101 | zenon_intro zenon_H2c4 ].
% 45.55/45.71 apply (zenon_L40_ zenon_TT1_bg zenon_TT0_hz zenon_TT3_x zenon_TX_y); trivial.
% 45.55/45.71 apply (zenon_notand_s _ _ zenon_H2c4); [ zenon_intro zenon_H2c5 | zenon_intro zenon_H25e ].
% 45.55/45.71 generalize (definition_smaller (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H2c6.
% 45.55/45.71 generalize (zenon_H2c6 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H2c7.
% 45.55/45.71 apply (zenon_equiv_s _ _ zenon_H2c7); [ zenon_intro zenon_H2c5; zenon_intro zenon_H17c | zenon_intro zenon_H2c8; zenon_intro zenon_H240 ].
% 45.55/45.71 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3.
% 45.55/45.71 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0.
% 45.55/45.71 generalize (zenon_H0 zenon_E). zenon_intro zenon_H239.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H239); [ zenon_intro zenon_H27 | zenon_intro zenon_H23a ].
% 45.55/45.71 exact (zenon_H27 zenon_H1f).
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H23a). zenon_intro zenon_H23b. zenon_intro zenon_H238.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H23b); [ zenon_intro zenon_H112 | zenon_intro zenon_H1e0 ].
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H238); [ zenon_intro zenon_H111 | zenon_intro zenon_H22f ].
% 45.55/45.71 exact (zenon_H111 zenon_H112).
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H22f). zenon_intro zenon_H231. zenon_intro zenon_H230.
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H230). zenon_intro zenon_H233. zenon_intro zenon_H232.
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H232). zenon_intro zenon_H234. zenon_intro zenon_H181.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H231); [ zenon_intro zenon_H235 | zenon_intro zenon_H1b8 ].
% 45.55/45.71 apply (zenon_notand_s _ _ zenon_H235); [ zenon_intro zenon_H183 | zenon_intro zenon_H182 ].
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H233); [ zenon_intro zenon_H236 | zenon_intro zenon_H21a ].
% 45.55/45.71 apply (zenon_notand_s _ _ zenon_H236); [ zenon_intro zenon_H186 | zenon_intro zenon_H182 ].
% 45.55/45.71 exact (zenon_H186 zenon_H183).
% 45.55/45.71 apply (zenon_L66_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 elim (classic ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H23c | zenon_intro zenon_H21f ].
% 45.55/45.71 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))); [ zenon_intro zenon_H19c | zenon_intro zenon_H194 ].
% 45.55/45.71 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 ].
% 45.55/45.71 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 ].
% 45.55/45.71 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.55/45.71 generalize (zenon_H18f (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H23d.
% 45.55/45.71 generalize (zenon_H23d (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H23e.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H23f ].
% 45.55/45.71 exact (zenon_H1a5 zenon_H1a4).
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H23f); [ zenon_intro zenon_H117 | zenon_intro zenon_H240 ].
% 45.55/45.71 exact (zenon_H117 zenon_H17e).
% 45.55/45.71 exact (zenon_H17c zenon_H240).
% 45.55/45.71 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H241 | zenon_intro zenon_H193 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H117.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H241.
% 45.55/45.71 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].
% 45.55/45.71 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f].
% 45.55/45.71 congruence.
% 45.55/45.71 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 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H21f.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H11a.
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e].
% 45.55/45.71 congruence.
% 45.55/45.71 exact (zenon_H21e zenon_H21a).
% 45.55/45.71 apply zenon_H11b. apply refl_equal.
% 45.55/45.71 apply zenon_H11b. apply refl_equal.
% 45.55/45.71 apply zenon_H62. apply refl_equal.
% 45.55/45.71 apply (zenon_L135_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H1a5.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H19c.
% 45.55/45.71 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f].
% 45.55/45.71 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].
% 45.55/45.71 congruence.
% 45.55/45.71 apply zenon_H16a. apply refl_equal.
% 45.55/45.71 exact (zenon_H21f zenon_H23c).
% 45.55/45.71 apply (zenon_L80_ zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.71 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 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H21f.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H11a.
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e].
% 45.55/45.71 congruence.
% 45.55/45.71 exact (zenon_H21e zenon_H21a).
% 45.55/45.71 apply zenon_H11b. apply refl_equal.
% 45.55/45.71 apply zenon_H11b. apply refl_equal.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H234); [ zenon_intro zenon_H237 | zenon_intro zenon_H19e ].
% 45.55/45.71 apply (zenon_notand_s _ _ zenon_H237); [ zenon_intro zenon_H183 | zenon_intro zenon_H185 ].
% 45.55/45.71 apply (zenon_L66_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 exact (zenon_H185 zenon_H182).
% 45.55/45.71 apply (zenon_L85_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1ba ].
% 45.55/45.71 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1a9 ].
% 45.55/45.71 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 ].
% 45.55/45.71 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 ].
% 45.55/45.71 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.55/45.71 generalize (zenon_H18f (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H23d.
% 45.55/45.71 generalize (zenon_H23d (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H23e.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H23f ].
% 45.55/45.71 exact (zenon_H1a5 zenon_H1a4).
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H23f); [ zenon_intro zenon_H117 | zenon_intro zenon_H240 ].
% 45.55/45.71 exact (zenon_H117 zenon_H17e).
% 45.55/45.71 exact (zenon_H17c zenon_H240).
% 45.55/45.71 apply (zenon_L136_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H1a5.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H1b1.
% 45.55/45.71 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba].
% 45.55/45.71 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].
% 45.55/45.71 congruence.
% 45.55/45.71 apply zenon_H16a. apply refl_equal.
% 45.55/45.71 exact (zenon_H1ba zenon_H1b9).
% 45.55/45.71 apply (zenon_L103_ zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.71 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 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H1ba.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H11a.
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb].
% 45.55/45.71 congruence.
% 45.55/45.71 exact (zenon_H1bb zenon_H1b8).
% 45.55/45.71 apply zenon_H11b. apply refl_equal.
% 45.55/45.71 apply zenon_H11b. apply refl_equal.
% 45.55/45.71 apply (zenon_L131_ zenon_TX_y); trivial.
% 45.55/45.71 exact (zenon_H2c5 zenon_H2c8).
% 45.55/45.71 apply (zenon_L149_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.71 apply (zenon_notand_s _ _ zenon_H2a8); [ zenon_intro zenon_H101 | zenon_intro zenon_H2c4 ].
% 45.55/45.71 apply (zenon_L195_ zenon_TT3_x zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 apply (zenon_notand_s _ _ zenon_H2c4); [ zenon_intro zenon_H2c5 | zenon_intro zenon_H25e ].
% 45.55/45.71 generalize (definition_smaller (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H2c6.
% 45.55/45.71 generalize (zenon_H2c6 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H2c7.
% 45.55/45.71 apply (zenon_equiv_s _ _ zenon_H2c7); [ zenon_intro zenon_H2c5; zenon_intro zenon_H17c | zenon_intro zenon_H2c8; zenon_intro zenon_H240 ].
% 45.55/45.71 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3.
% 45.55/45.71 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0.
% 45.55/45.71 generalize (zenon_H0 zenon_E). zenon_intro zenon_H239.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H239); [ zenon_intro zenon_H27 | zenon_intro zenon_H23a ].
% 45.55/45.71 exact (zenon_H27 zenon_H1f).
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H23a). zenon_intro zenon_H23b. zenon_intro zenon_H238.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H23b); [ zenon_intro zenon_H112 | zenon_intro zenon_H1e0 ].
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H238); [ zenon_intro zenon_H111 | zenon_intro zenon_H22f ].
% 45.55/45.71 exact (zenon_H111 zenon_H112).
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H22f). zenon_intro zenon_H231. zenon_intro zenon_H230.
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H230). zenon_intro zenon_H233. zenon_intro zenon_H232.
% 45.55/45.71 apply (zenon_and_s _ _ zenon_H232). zenon_intro zenon_H234. zenon_intro zenon_H181.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H231); [ zenon_intro zenon_H235 | zenon_intro zenon_H1b8 ].
% 45.55/45.71 apply (zenon_notand_s _ _ zenon_H235); [ zenon_intro zenon_H183 | zenon_intro zenon_H182 ].
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H233); [ zenon_intro zenon_H236 | zenon_intro zenon_H21a ].
% 45.55/45.71 apply (zenon_notand_s _ _ zenon_H236); [ zenon_intro zenon_H186 | zenon_intro zenon_H182 ].
% 45.55/45.71 exact (zenon_H186 zenon_H183).
% 45.55/45.71 apply (zenon_L216_ zenon_TT0_hz zenon_TT1_bg zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.71 elim (classic ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H23c | zenon_intro zenon_H21f ].
% 45.55/45.71 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))); [ zenon_intro zenon_H19c | zenon_intro zenon_H194 ].
% 45.55/45.71 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 ].
% 45.55/45.71 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 ].
% 45.55/45.71 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.55/45.71 generalize (zenon_H18f (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H23d.
% 45.55/45.71 generalize (zenon_H23d (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H23e.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H23f ].
% 45.55/45.71 exact (zenon_H1a5 zenon_H1a4).
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H23f); [ zenon_intro zenon_H117 | zenon_intro zenon_H240 ].
% 45.55/45.71 exact (zenon_H117 zenon_H17e).
% 45.55/45.71 exact (zenon_H17c zenon_H240).
% 45.55/45.71 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H241 | zenon_intro zenon_H193 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H117.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H241.
% 45.55/45.71 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].
% 45.55/45.71 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f].
% 45.55/45.71 congruence.
% 45.55/45.71 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 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H21f.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H11a.
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e].
% 45.55/45.71 congruence.
% 45.55/45.71 exact (zenon_H21e zenon_H21a).
% 45.55/45.71 apply zenon_H11b. apply refl_equal.
% 45.55/45.71 apply zenon_H11b. apply refl_equal.
% 45.55/45.71 apply zenon_H62. apply refl_equal.
% 45.55/45.71 apply (zenon_L232_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H1a5.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H19c.
% 45.55/45.71 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f].
% 45.55/45.71 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].
% 45.55/45.71 congruence.
% 45.55/45.71 apply zenon_H16a. apply refl_equal.
% 45.55/45.71 exact (zenon_H21f zenon_H23c).
% 45.55/45.71 apply (zenon_L227_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.71 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 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H21f.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H11a.
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e].
% 45.55/45.71 congruence.
% 45.55/45.71 exact (zenon_H21e zenon_H21a).
% 45.55/45.71 apply zenon_H11b. apply refl_equal.
% 45.55/45.71 apply zenon_H11b. apply refl_equal.
% 45.55/45.71 apply (zenon_L216_ zenon_TT0_hz zenon_TT1_bg zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.71 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1ba ].
% 45.55/45.71 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1a9 ].
% 45.55/45.71 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 ].
% 45.55/45.71 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 ].
% 45.55/45.71 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.55/45.71 generalize (zenon_H18f (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H23d.
% 45.55/45.71 generalize (zenon_H23d (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H23e.
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H23f ].
% 45.55/45.71 exact (zenon_H1a5 zenon_H1a4).
% 45.55/45.71 apply (zenon_imply_s _ _ zenon_H23f); [ zenon_intro zenon_H117 | zenon_intro zenon_H240 ].
% 45.55/45.71 exact (zenon_H117 zenon_H17e).
% 45.55/45.71 exact (zenon_H17c zenon_H240).
% 45.55/45.71 elim (classic (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_Hac | zenon_intro zenon_Had ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H117.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_Hac.
% 45.55/45.71 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].
% 45.55/45.71 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba].
% 45.55/45.71 congruence.
% 45.55/45.71 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 ].
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H1ba.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H11a.
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.71 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb].
% 45.55/45.71 congruence.
% 45.55/45.71 exact (zenon_H1bb zenon_H1b8).
% 45.55/45.71 apply zenon_H11b. apply refl_equal.
% 45.55/45.71 apply zenon_H11b. apply refl_equal.
% 45.55/45.71 apply zenon_H62. apply refl_equal.
% 45.55/45.71 apply (zenon_L231_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.71 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))).
% 45.55/45.71 intro zenon_D_pnotp.
% 45.55/45.71 apply zenon_H1a5.
% 45.55/45.71 rewrite <- zenon_D_pnotp.
% 45.55/45.71 exact zenon_H1b1.
% 45.55/45.71 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba].
% 45.55/45.71 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].
% 45.55/45.71 congruence.
% 45.55/45.71 apply zenon_H16a. apply refl_equal.
% 45.55/45.71 exact (zenon_H1ba zenon_H1b9).
% 45.55/45.71 apply (zenon_L103_ zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.71 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 ].
% 45.55/45.71 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))).
% 45.55/45.72 intro zenon_D_pnotp.
% 45.55/45.72 apply zenon_H1ba.
% 45.55/45.72 rewrite <- zenon_D_pnotp.
% 45.55/45.72 exact zenon_H11a.
% 45.55/45.72 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.72 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb].
% 45.55/45.72 congruence.
% 45.55/45.72 exact (zenon_H1bb zenon_H1b8).
% 45.55/45.72 apply zenon_H11b. apply refl_equal.
% 45.55/45.72 apply zenon_H11b. apply refl_equal.
% 45.55/45.72 apply (zenon_L131_ zenon_TX_y); trivial.
% 45.55/45.72 exact (zenon_H2c5 zenon_H2c8).
% 45.55/45.72 apply (zenon_L236_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.72 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_H2c1 | zenon_intro zenon_H26e ].
% 45.55/45.72 generalize (definition_smaller (age zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H44.
% 45.55/45.72 generalize (zenon_H44 (sigma)). zenon_intro zenon_H2c2.
% 45.55/45.72 apply (zenon_equiv_s _ _ zenon_H2c2); [ zenon_intro zenon_H2c3; zenon_intro zenon_H58 | zenon_intro zenon_H2c1; zenon_intro zenon_H37 ].
% 45.55/45.72 exact (zenon_H2c3 zenon_H2c1).
% 45.55/45.72 apply (zenon_notand_s _ _ zenon_H2a8); [ zenon_intro zenon_H101 | zenon_intro zenon_H2c4 ].
% 45.55/45.72 apply (zenon_L40_ zenon_TT1_bg zenon_TT0_hz zenon_TT3_x zenon_TX_y); trivial.
% 45.55/45.72 apply (zenon_notand_s _ _ zenon_H2c4); [ zenon_intro zenon_H2c5 | zenon_intro zenon_H25e ].
% 45.55/45.72 generalize (definition_smaller (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H2c6.
% 45.55/45.72 generalize (zenon_H2c6 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H2c7.
% 45.55/45.72 apply (zenon_equiv_s _ _ zenon_H2c7); [ zenon_intro zenon_H2c5; zenon_intro zenon_H17c | zenon_intro zenon_H2c8; zenon_intro zenon_H240 ].
% 45.55/45.72 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3.
% 45.55/45.72 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0.
% 45.55/45.72 generalize (zenon_H0 zenon_E). zenon_intro zenon_H239.
% 45.55/45.72 apply (zenon_imply_s _ _ zenon_H239); [ zenon_intro zenon_H27 | zenon_intro zenon_H23a ].
% 45.55/45.72 exact (zenon_H27 zenon_H1f).
% 45.55/45.72 apply (zenon_and_s _ _ zenon_H23a). zenon_intro zenon_H23b. zenon_intro zenon_H238.
% 45.55/45.72 apply (zenon_imply_s _ _ zenon_H23b); [ zenon_intro zenon_H112 | zenon_intro zenon_H1e0 ].
% 45.55/45.72 apply (zenon_imply_s _ _ zenon_H238); [ zenon_intro zenon_H111 | zenon_intro zenon_H22f ].
% 45.55/45.72 exact (zenon_H111 zenon_H112).
% 45.55/45.72 apply (zenon_and_s _ _ zenon_H22f). zenon_intro zenon_H231. zenon_intro zenon_H230.
% 45.55/45.72 apply (zenon_and_s _ _ zenon_H230). zenon_intro zenon_H233. zenon_intro zenon_H232.
% 45.55/45.72 apply (zenon_and_s _ _ zenon_H232). zenon_intro zenon_H234. zenon_intro zenon_H181.
% 45.55/45.72 apply (zenon_imply_s _ _ zenon_H231); [ zenon_intro zenon_H235 | zenon_intro zenon_H1b8 ].
% 45.55/45.72 apply (zenon_notand_s _ _ zenon_H235); [ zenon_intro zenon_H183 | zenon_intro zenon_H182 ].
% 45.55/45.72 apply (zenon_imply_s _ _ zenon_H233); [ zenon_intro zenon_H236 | zenon_intro zenon_H21a ].
% 45.55/45.72 apply (zenon_notand_s _ _ zenon_H236); [ zenon_intro zenon_H186 | zenon_intro zenon_H182 ].
% 45.55/45.72 exact (zenon_H186 zenon_H183).
% 45.55/45.72 apply (zenon_L247_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.72 elim (classic ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H23c | zenon_intro zenon_H21f ].
% 45.55/45.72 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))); [ zenon_intro zenon_H19c | zenon_intro zenon_H194 ].
% 45.55/45.72 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 ].
% 45.55/45.72 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 ].
% 45.55/45.72 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.55/45.72 generalize (zenon_H18f (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H23d.
% 45.55/45.72 generalize (zenon_H23d (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H23e.
% 45.55/45.72 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H23f ].
% 45.55/45.72 exact (zenon_H1a5 zenon_H1a4).
% 45.55/45.72 apply (zenon_imply_s _ _ zenon_H23f); [ zenon_intro zenon_H117 | zenon_intro zenon_H240 ].
% 45.55/45.72 exact (zenon_H117 zenon_H17e).
% 45.55/45.72 exact (zenon_H17c zenon_H240).
% 45.55/45.72 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H241 | zenon_intro zenon_H193 ].
% 45.55/45.72 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))).
% 45.55/45.72 intro zenon_D_pnotp.
% 45.55/45.72 apply zenon_H117.
% 45.55/45.72 rewrite <- zenon_D_pnotp.
% 45.55/45.72 exact zenon_H241.
% 45.55/45.72 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].
% 45.55/45.72 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f].
% 45.55/45.72 congruence.
% 45.55/45.72 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 ].
% 45.55/45.72 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))).
% 45.55/45.72 intro zenon_D_pnotp.
% 45.55/45.72 apply zenon_H21f.
% 45.55/45.72 rewrite <- zenon_D_pnotp.
% 45.55/45.72 exact zenon_H11a.
% 45.55/45.72 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.72 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e].
% 45.55/45.72 congruence.
% 45.55/45.72 exact (zenon_H21e zenon_H21a).
% 45.55/45.72 apply zenon_H11b. apply refl_equal.
% 45.55/45.72 apply zenon_H11b. apply refl_equal.
% 45.55/45.72 apply zenon_H62. apply refl_equal.
% 45.55/45.72 apply (zenon_L259_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.72 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))).
% 45.55/45.72 intro zenon_D_pnotp.
% 45.55/45.72 apply zenon_H1a5.
% 45.55/45.72 rewrite <- zenon_D_pnotp.
% 45.55/45.72 exact zenon_H19c.
% 45.55/45.72 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f].
% 45.55/45.72 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].
% 45.55/45.72 congruence.
% 45.55/45.72 apply zenon_H16a. apply refl_equal.
% 45.55/45.72 exact (zenon_H21f zenon_H23c).
% 45.55/45.72 apply (zenon_L254_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.72 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 ].
% 45.55/45.72 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))).
% 45.55/45.72 intro zenon_D_pnotp.
% 45.55/45.72 apply zenon_H21f.
% 45.55/45.72 rewrite <- zenon_D_pnotp.
% 45.55/45.72 exact zenon_H11a.
% 45.55/45.72 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.72 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e].
% 45.55/45.72 congruence.
% 45.55/45.72 exact (zenon_H21e zenon_H21a).
% 45.55/45.72 apply zenon_H11b. apply refl_equal.
% 45.55/45.72 apply zenon_H11b. apply refl_equal.
% 45.55/45.72 apply (zenon_imply_s _ _ zenon_H234); [ zenon_intro zenon_H237 | zenon_intro zenon_H19e ].
% 45.55/45.72 apply (zenon_notand_s _ _ zenon_H237); [ zenon_intro zenon_H183 | zenon_intro zenon_H185 ].
% 45.55/45.72 apply (zenon_L247_ zenon_TT2_la zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.72 exact (zenon_H185 zenon_H182).
% 45.55/45.72 elim (classic ((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H1a1 ].
% 45.55/45.72 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod2))); [ zenon_intro zenon_H179 | zenon_intro zenon_H167 ].
% 45.55/45.72 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 ].
% 45.55/45.72 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 ].
% 45.55/45.72 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.55/45.72 generalize (zenon_H18f (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H23d.
% 45.55/45.72 generalize (zenon_H23d (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H23e.
% 45.55/45.72 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H23f ].
% 45.55/45.72 exact (zenon_H1a5 zenon_H1a4).
% 45.55/45.72 apply (zenon_imply_s _ _ zenon_H23f); [ zenon_intro zenon_H117 | zenon_intro zenon_H240 ].
% 45.55/45.72 exact (zenon_H117 zenon_H17e).
% 45.55/45.72 exact (zenon_H17c zenon_H240).
% 45.55/45.72 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H1c3 | zenon_intro zenon_H1c4 ].
% 45.55/45.72 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))).
% 45.55/45.72 intro zenon_D_pnotp.
% 45.55/45.72 apply zenon_H117.
% 45.55/45.72 rewrite <- zenon_D_pnotp.
% 45.55/45.72 exact zenon_H1c3.
% 45.55/45.72 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].
% 45.55/45.72 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1].
% 45.55/45.72 congruence.
% 45.55/45.72 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 ].
% 45.55/45.72 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))).
% 45.55/45.72 intro zenon_D_pnotp.
% 45.55/45.72 apply zenon_H1a1.
% 45.55/45.72 rewrite <- zenon_D_pnotp.
% 45.55/45.72 exact zenon_H11a.
% 45.55/45.72 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.72 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2].
% 45.55/45.72 congruence.
% 45.55/45.72 exact (zenon_H1a2 zenon_H19e).
% 45.55/45.72 apply zenon_H11b. apply refl_equal.
% 45.55/45.72 apply zenon_H11b. apply refl_equal.
% 45.55/45.72 apply zenon_H62. apply refl_equal.
% 45.55/45.72 apply (zenon_L260_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.72 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))).
% 45.55/45.72 intro zenon_D_pnotp.
% 45.55/45.72 apply zenon_H1a5.
% 45.55/45.72 rewrite <- zenon_D_pnotp.
% 45.55/45.72 exact zenon_H179.
% 45.55/45.72 cut (((mod2) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1a1].
% 45.55/45.72 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].
% 45.55/45.72 congruence.
% 45.55/45.72 apply zenon_H16a. apply refl_equal.
% 45.55/45.72 exact (zenon_H1a1 zenon_H1a3).
% 45.55/45.72 apply (zenon_L248_ zenon_TT2_la zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.72 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 ].
% 45.55/45.72 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))).
% 45.55/45.72 intro zenon_D_pnotp.
% 45.55/45.72 apply zenon_H1a1.
% 45.55/45.72 rewrite <- zenon_D_pnotp.
% 45.55/45.72 exact zenon_H11a.
% 45.55/45.72 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.72 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H1a2].
% 45.55/45.72 congruence.
% 45.55/45.72 exact (zenon_H1a2 zenon_H19e).
% 45.55/45.72 apply zenon_H11b. apply refl_equal.
% 45.55/45.72 apply zenon_H11b. apply refl_equal.
% 45.55/45.72 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1ba ].
% 45.55/45.72 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1a9 ].
% 45.55/45.72 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 ].
% 45.55/45.72 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 ].
% 45.55/45.72 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.55/45.72 generalize (zenon_H18f (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H23d.
% 45.55/45.72 generalize (zenon_H23d (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H23e.
% 45.55/45.72 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H23f ].
% 45.55/45.72 exact (zenon_H1a5 zenon_H1a4).
% 45.55/45.72 apply (zenon_imply_s _ _ zenon_H23f); [ zenon_intro zenon_H117 | zenon_intro zenon_H240 ].
% 45.55/45.72 exact (zenon_H117 zenon_H17e).
% 45.55/45.72 exact (zenon_H17c zenon_H240).
% 45.55/45.72 elim (classic (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_Hac | zenon_intro zenon_Had ].
% 45.55/45.72 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))).
% 45.55/45.72 intro zenon_D_pnotp.
% 45.55/45.72 apply zenon_H117.
% 45.55/45.72 rewrite <- zenon_D_pnotp.
% 45.55/45.72 exact zenon_Hac.
% 45.55/45.72 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].
% 45.55/45.72 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba].
% 45.55/45.72 congruence.
% 45.55/45.72 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 ].
% 45.55/45.72 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))).
% 45.55/45.72 intro zenon_D_pnotp.
% 45.55/45.72 apply zenon_H1ba.
% 45.55/45.72 rewrite <- zenon_D_pnotp.
% 45.55/45.72 exact zenon_H11a.
% 45.55/45.72 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.72 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb].
% 45.55/45.72 congruence.
% 45.55/45.72 exact (zenon_H1bb zenon_H1b8).
% 45.55/45.72 apply zenon_H11b. apply refl_equal.
% 45.55/45.72 apply zenon_H11b. apply refl_equal.
% 45.55/45.72 apply zenon_H62. apply refl_equal.
% 45.55/45.72 apply (zenon_L258_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.72 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))).
% 45.55/45.72 intro zenon_D_pnotp.
% 45.55/45.72 apply zenon_H1a5.
% 45.55/45.72 rewrite <- zenon_D_pnotp.
% 45.55/45.72 exact zenon_H1b1.
% 45.55/45.72 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba].
% 45.55/45.72 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].
% 45.55/45.72 congruence.
% 45.55/45.72 apply zenon_H16a. apply refl_equal.
% 45.55/45.72 exact (zenon_H1ba zenon_H1b9).
% 45.55/45.72 apply (zenon_L255_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.72 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 ].
% 45.55/45.72 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))).
% 45.55/45.72 intro zenon_D_pnotp.
% 45.55/45.72 apply zenon_H1ba.
% 45.55/45.72 rewrite <- zenon_D_pnotp.
% 45.55/45.72 exact zenon_H11a.
% 45.55/45.72 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.72 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb].
% 45.55/45.72 congruence.
% 45.55/45.72 exact (zenon_H1bb zenon_H1b8).
% 45.55/45.72 apply zenon_H11b. apply refl_equal.
% 45.55/45.72 apply zenon_H11b. apply refl_equal.
% 45.55/45.72 apply (zenon_L131_ zenon_TX_y); trivial.
% 45.55/45.72 exact (zenon_H2c5 zenon_H2c8).
% 45.55/45.72 apply (zenon_L149_ zenon_TT1_bg zenon_TT0_hz zenon_TX_y); trivial.
% 45.55/45.72 apply (zenon_notand_s _ _ zenon_H2a8); [ zenon_intro zenon_H101 | zenon_intro zenon_H2c4 ].
% 45.55/45.72 apply (zenon_L195_ zenon_TT3_x zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.72 apply (zenon_notand_s _ _ zenon_H2c4); [ zenon_intro zenon_H2c5 | zenon_intro zenon_H25e ].
% 45.55/45.72 generalize (definition_smaller (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H2c6.
% 45.55/45.72 generalize (zenon_H2c6 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H2c7.
% 45.55/45.72 apply (zenon_equiv_s _ _ zenon_H2c7); [ zenon_intro zenon_H2c5; zenon_intro zenon_H17c | zenon_intro zenon_H2c8; zenon_intro zenon_H240 ].
% 45.55/45.72 generalize (assumption_13 zenon_TX_y). zenon_intro zenon_Hf3.
% 45.55/45.72 generalize (assumption_17 zenon_TX_y). zenon_intro zenon_H0.
% 45.55/45.72 generalize (zenon_H0 zenon_E). zenon_intro zenon_H239.
% 45.55/45.72 apply (zenon_imply_s _ _ zenon_H239); [ zenon_intro zenon_H27 | zenon_intro zenon_H23a ].
% 45.55/45.72 exact (zenon_H27 zenon_H1f).
% 45.55/45.72 apply (zenon_and_s _ _ zenon_H23a). zenon_intro zenon_H23b. zenon_intro zenon_H238.
% 45.55/45.72 apply (zenon_imply_s _ _ zenon_H23b); [ zenon_intro zenon_H112 | zenon_intro zenon_H1e0 ].
% 45.55/45.72 apply (zenon_imply_s _ _ zenon_H238); [ zenon_intro zenon_H111 | zenon_intro zenon_H22f ].
% 45.55/45.72 exact (zenon_H111 zenon_H112).
% 45.55/45.72 apply (zenon_and_s _ _ zenon_H22f). zenon_intro zenon_H231. zenon_intro zenon_H230.
% 45.55/45.72 apply (zenon_and_s _ _ zenon_H230). zenon_intro zenon_H233. zenon_intro zenon_H232.
% 45.55/45.72 apply (zenon_and_s _ _ zenon_H232). zenon_intro zenon_H234. zenon_intro zenon_H181.
% 45.55/45.72 apply (zenon_imply_s _ _ zenon_H231); [ zenon_intro zenon_H235 | zenon_intro zenon_H1b8 ].
% 45.55/45.72 apply (zenon_notand_s _ _ zenon_H235); [ zenon_intro zenon_H183 | zenon_intro zenon_H182 ].
% 45.55/45.72 apply (zenon_imply_s _ _ zenon_H233); [ zenon_intro zenon_H236 | zenon_intro zenon_H21a ].
% 45.55/45.72 apply (zenon_notand_s _ _ zenon_H236); [ zenon_intro zenon_H186 | zenon_intro zenon_H182 ].
% 45.55/45.72 exact (zenon_H186 zenon_H183).
% 45.55/45.72 apply (zenon_L273_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.72 elim (classic ((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H23c | zenon_intro zenon_H21f ].
% 45.55/45.72 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (mod1))); [ zenon_intro zenon_H19c | zenon_intro zenon_H194 ].
% 45.55/45.72 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 ].
% 45.55/45.72 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 ].
% 45.55/45.72 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.55/45.72 generalize (zenon_H18f (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H23d.
% 45.55/45.72 generalize (zenon_H23d (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H23e.
% 45.55/45.72 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H23f ].
% 45.55/45.72 exact (zenon_H1a5 zenon_H1a4).
% 45.55/45.72 apply (zenon_imply_s _ _ zenon_H23f); [ zenon_intro zenon_H117 | zenon_intro zenon_H240 ].
% 45.55/45.72 exact (zenon_H117 zenon_H17e).
% 45.55/45.72 exact (zenon_H17c zenon_H240).
% 45.55/45.72 elim (classic (greater (mod1) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_H241 | zenon_intro zenon_H193 ].
% 45.55/45.72 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))).
% 45.55/45.72 intro zenon_D_pnotp.
% 45.55/45.72 apply zenon_H117.
% 45.55/45.72 rewrite <- zenon_D_pnotp.
% 45.55/45.72 exact zenon_H241.
% 45.55/45.72 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].
% 45.55/45.72 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f].
% 45.55/45.72 congruence.
% 45.55/45.72 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 ].
% 45.55/45.72 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))).
% 45.55/45.72 intro zenon_D_pnotp.
% 45.55/45.72 apply zenon_H21f.
% 45.55/45.72 rewrite <- zenon_D_pnotp.
% 45.55/45.72 exact zenon_H11a.
% 45.55/45.72 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.72 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e].
% 45.55/45.72 congruence.
% 45.55/45.72 exact (zenon_H21e zenon_H21a).
% 45.55/45.72 apply zenon_H11b. apply refl_equal.
% 45.55/45.72 apply zenon_H11b. apply refl_equal.
% 45.55/45.72 apply zenon_H62. apply refl_equal.
% 45.55/45.72 apply (zenon_L270_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.72 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))).
% 45.55/45.72 intro zenon_D_pnotp.
% 45.55/45.72 apply zenon_H1a5.
% 45.55/45.72 rewrite <- zenon_D_pnotp.
% 45.55/45.72 exact zenon_H19c.
% 45.55/45.72 cut (((mod1) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H21f].
% 45.55/45.72 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].
% 45.55/45.72 congruence.
% 45.55/45.72 apply zenon_H16a. apply refl_equal.
% 45.55/45.72 exact (zenon_H21f zenon_H23c).
% 45.55/45.72 apply (zenon_L254_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.72 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 ].
% 45.55/45.72 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))).
% 45.55/45.72 intro zenon_D_pnotp.
% 45.55/45.72 apply zenon_H21f.
% 45.55/45.72 rewrite <- zenon_D_pnotp.
% 45.55/45.72 exact zenon_H11a.
% 45.55/45.72 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.72 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H21e].
% 45.55/45.72 congruence.
% 45.55/45.72 exact (zenon_H21e zenon_H21a).
% 45.55/45.72 apply zenon_H11b. apply refl_equal.
% 45.55/45.72 apply zenon_H11b. apply refl_equal.
% 45.55/45.72 apply (zenon_L273_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.72 elim (classic ((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1ba ].
% 45.55/45.72 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (low))); [ zenon_intro zenon_H1b1 | zenon_intro zenon_H1a9 ].
% 45.55/45.72 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 ].
% 45.55/45.72 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 ].
% 45.55/45.72 generalize (zenon_H34 (hazard_of_mortality zenon_TX_y zenon_TT2_la)). zenon_intro zenon_H18f.
% 45.55/45.72 generalize (zenon_H18f (hazard_of_mortality zenon_TX_y zenon_E)). zenon_intro zenon_H23d.
% 45.55/45.72 generalize (zenon_H23d (hazard_of_mortality zenon_TX_y zenon_TT1_bg)). zenon_intro zenon_H23e.
% 45.55/45.72 apply (zenon_imply_s _ _ zenon_H23e); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H23f ].
% 45.55/45.72 exact (zenon_H1a5 zenon_H1a4).
% 45.55/45.72 apply (zenon_imply_s _ _ zenon_H23f); [ zenon_intro zenon_H117 | zenon_intro zenon_H240 ].
% 45.55/45.72 exact (zenon_H117 zenon_H17e).
% 45.55/45.72 exact (zenon_H17c zenon_H240).
% 45.55/45.72 elim (classic (greater (low) (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [ zenon_intro zenon_Hac | zenon_intro zenon_Had ].
% 45.55/45.72 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))).
% 45.55/45.72 intro zenon_D_pnotp.
% 45.55/45.72 apply zenon_H117.
% 45.55/45.72 rewrite <- zenon_D_pnotp.
% 45.55/45.72 exact zenon_Hac.
% 45.55/45.72 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].
% 45.55/45.72 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba].
% 45.55/45.72 congruence.
% 45.55/45.72 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 ].
% 45.55/45.72 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))).
% 45.55/45.72 intro zenon_D_pnotp.
% 45.55/45.72 apply zenon_H1ba.
% 45.55/45.72 rewrite <- zenon_D_pnotp.
% 45.55/45.72 exact zenon_H11a.
% 45.55/45.72 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.72 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb].
% 45.55/45.72 congruence.
% 45.55/45.72 exact (zenon_H1bb zenon_H1b8).
% 45.55/45.72 apply zenon_H11b. apply refl_equal.
% 45.55/45.72 apply zenon_H11b. apply refl_equal.
% 45.55/45.72 apply zenon_H62. apply refl_equal.
% 45.55/45.72 apply (zenon_L269_ zenon_TT0_hz zenon_TT2_la zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.72 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))).
% 45.55/45.72 intro zenon_D_pnotp.
% 45.55/45.72 apply zenon_H1a5.
% 45.55/45.72 rewrite <- zenon_D_pnotp.
% 45.55/45.72 exact zenon_H1b1.
% 45.55/45.72 cut (((low) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1ba].
% 45.55/45.72 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].
% 45.55/45.72 congruence.
% 45.55/45.72 apply zenon_H16a. apply refl_equal.
% 45.55/45.72 exact (zenon_H1ba zenon_H1b9).
% 45.55/45.72 apply (zenon_L255_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.72 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 ].
% 45.55/45.72 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))).
% 45.55/45.72 intro zenon_D_pnotp.
% 45.55/45.72 apply zenon_H1ba.
% 45.55/45.72 rewrite <- zenon_D_pnotp.
% 45.55/45.72 exact zenon_H11a.
% 45.55/45.72 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (hazard_of_mortality zenon_TX_y zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 45.55/45.72 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_H1bb].
% 45.55/45.72 congruence.
% 45.55/45.72 exact (zenon_H1bb zenon_H1b8).
% 45.55/45.72 apply zenon_H11b. apply refl_equal.
% 45.55/45.72 apply zenon_H11b. apply refl_equal.
% 45.55/45.72 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 ].
% 45.55/45.72 elim (classic (greater (hazard_of_mortality zenon_TX_y zenon_TT2_la) (very_low))); [ zenon_intro zenon_H29c | zenon_intro zenon_H294 ].
% 45.55/45.72 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))).
% 45.55/45.72 intro zenon_D_pnotp.
% 45.55/45.72 apply zenon_H17c.
% 45.55/45.72 rewrite <- zenon_D_pnotp.
% 45.55/45.72 exact zenon_H29c.
% 45.55/45.72 cut (((very_low) = (hazard_of_mortality zenon_TX_y zenon_TT1_bg))); [idtac | apply NNPP; zenon_intro zenon_H187].
% 45.55/45.72 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].
% 45.55/45.72 congruence.
% 45.55/45.72 apply zenon_H16a. apply refl_equal.
% 45.55/45.72 apply (zenon_L268_ zenon_TT1_bg zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.72 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))).
% 45.55/45.72 intro zenon_D_pnotp.
% 45.55/45.72 apply zenon_H294.
% 45.55/45.72 rewrite <- zenon_D_pnotp.
% 45.55/45.72 exact zenon_H1a4.
% 45.55/45.72 cut (((hazard_of_mortality zenon_TX_y zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H1e5].
% 45.55/45.72 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].
% 45.55/45.72 congruence.
% 45.55/45.72 apply zenon_H16a. apply refl_equal.
% 45.55/45.72 exact (zenon_H1e5 zenon_H1e0).
% 45.55/45.72 apply (zenon_L275_ zenon_TT0_hz zenon_TT2_la zenon_TX_y); trivial.
% 45.55/45.72 exact (zenon_H2c5 zenon_H2c8).
% 45.55/45.72 apply (zenon_L236_ zenon_TT0_hz zenon_TT1_bg zenon_TX_y); trivial.
% 45.55/45.72 exact (zenon_H1d zenon_H19).
% 45.55/45.72 apply zenon_H29d. zenon_intro zenon_Tx_bbl. apply NNPP. zenon_intro zenon_H2ca.
% 45.55/45.72 apply zenon_H2ca. zenon_intro zenon_Ty_bbn. apply NNPP. zenon_intro zenon_H2cc.
% 45.55/45.72 apply zenon_H2cc. zenon_intro zenon_Tz_bbp. apply NNPP. zenon_intro zenon_H2ce.
% 45.55/45.72 apply (zenon_notimply_s _ _ zenon_H2ce). zenon_intro zenon_H2d0. zenon_intro zenon_H2cf.
% 45.55/45.72 apply (zenon_notimply_s _ _ zenon_H2cf). zenon_intro zenon_H2d2. zenon_intro zenon_H2d1.
% 45.55/45.72 generalize (meaning_postulate_greater_transitive zenon_Tx_bbl). zenon_intro zenon_H2d3.
% 45.55/45.72 generalize (zenon_H2d3 zenon_Ty_bbn). zenon_intro zenon_H2d4.
% 45.55/45.72 generalize (zenon_H2d4 zenon_Tz_bbp). zenon_intro zenon_H2d5.
% 45.55/45.72 apply (zenon_imply_s _ _ zenon_H2d5); [ zenon_intro zenon_H2d7 | zenon_intro zenon_H2d6 ].
% 45.55/45.72 apply (zenon_notand_s _ _ zenon_H2d7); [ zenon_intro zenon_H2d9 | zenon_intro zenon_H2d8 ].
% 45.55/45.72 exact (zenon_H2d9 zenon_H2d0).
% 45.55/45.72 exact (zenon_H2d8 zenon_H2d2).
% 45.55/45.72 exact (zenon_H2d1 zenon_H2d6).
% 45.55/45.72 Qed.
% 45.55/45.72 % SZS output end Proof
% 45.55/45.72 (* END-PROOF *)
% 45.55/45.72 nodes searched: 2860654
% 45.55/45.72 max branch formulas: 5105
% 45.55/45.72 proof nodes created: 29947
% 45.55/45.72 formulas created: 908436
% 45.55/45.72
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