TSTP Solution File: MGT051+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : MGT051+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n024.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 22:31:11 EDT 2022
% Result : Theorem 34.50s 34.76s
% Output : Proof 34.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : MGT051+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 9 08:47:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 34.50/34.76 (* PROOF-FOUND *)
% 34.50/34.76 % SZS status Theorem
% 34.50/34.76 (* BEGIN-PROOF *)
% 34.50/34.76 % SZS output start Proof
% 34.50/34.76 Theorem theorem_4 : (forall X : zenon_U, (forall T0 : zenon_U, (forall T1 : zenon_U, (forall T2 : zenon_U, (forall T3 : zenon_U, (((organization X)/\((has_endowment X)/\((smaller_or_equal (age X T0) (age X T1))/\((smaller_or_equal (age X T1) (eta))/\((greater (age X T2) (eta))/\(greater (age X T3) (age X T2)))))))->((greater (hazard_of_mortality X T3) (hazard_of_mortality X T2))/\((greater (hazard_of_mortality X T2) (hazard_of_mortality X T1))/\((hazard_of_mortality X T1) = (hazard_of_mortality X T0)))))))))).
% 34.50/34.76 Proof.
% 34.50/34.76 assert (zenon_L1_ : forall (zenon_TT3_t : zenon_U) (zenon_TX_u : zenon_U), (~(greater_or_equal (capability zenon_TX_u zenon_TT3_t) (capability zenon_TX_u zenon_TT3_t))) -> False).
% 34.50/34.76 do 2 intro. intros zenon_H12.
% 34.50/34.76 generalize (definition_greater_or_equal (capability zenon_TX_u zenon_TT3_t)). zenon_intro zenon_H15.
% 34.50/34.76 generalize (zenon_H15 (capability zenon_TX_u zenon_TT3_t)). zenon_intro zenon_H16.
% 34.50/34.76 apply (zenon_equiv_s _ _ zenon_H16); [ zenon_intro zenon_H12; zenon_intro zenon_H19 | zenon_intro zenon_H18; zenon_intro zenon_H17 ].
% 34.50/34.76 apply (zenon_notor_s _ _ zenon_H19). zenon_intro zenon_H1b. zenon_intro zenon_H1a.
% 34.50/34.76 apply zenon_H1a. apply refl_equal.
% 34.50/34.76 exact (zenon_H12 zenon_H18).
% 34.50/34.76 (* end of lemma zenon_L1_ *)
% 34.50/34.76 assert (zenon_L2_ : forall (zenon_TT3_t : zenon_U) (zenon_TT2_bg : zenon_U) (zenon_TX_u : zenon_U), (forall Y : zenon_U, ((smaller (stock_of_knowledge zenon_TX_u zenon_TT2_bg) Y)\/(((stock_of_knowledge zenon_TX_u zenon_TT2_bg) = Y)\/(greater (stock_of_knowledge zenon_TX_u zenon_TT2_bg) Y)))) -> (~(greater (stock_of_knowledge zenon_TX_u zenon_TT3_t) (stock_of_knowledge zenon_TX_u zenon_TT2_bg))) -> (~((stock_of_knowledge zenon_TX_u zenon_TT3_t) = (stock_of_knowledge zenon_TX_u zenon_TT2_bg))) -> (~(greater (stock_of_knowledge zenon_TX_u zenon_TT2_bg) (stock_of_knowledge zenon_TX_u zenon_TT3_t))) -> False).
% 34.50/34.76 do 3 intro. intros zenon_H1c zenon_H1d zenon_H1e zenon_H1f.
% 34.50/34.76 generalize (zenon_H1c (stock_of_knowledge zenon_TX_u zenon_TT3_t)). zenon_intro zenon_H21.
% 34.50/34.76 apply (zenon_or_s _ _ zenon_H21); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ].
% 34.50/34.76 generalize (definition_smaller (stock_of_knowledge zenon_TX_u zenon_TT2_bg)). zenon_intro zenon_H24.
% 34.50/34.76 generalize (zenon_H24 (stock_of_knowledge zenon_TX_u zenon_TT3_t)). zenon_intro zenon_H25.
% 34.50/34.76 apply (zenon_equiv_s _ _ zenon_H25); [ zenon_intro zenon_H27; zenon_intro zenon_H1d | zenon_intro zenon_H23; zenon_intro zenon_H26 ].
% 34.50/34.76 exact (zenon_H27 zenon_H23).
% 34.50/34.76 exact (zenon_H1d zenon_H26).
% 34.50/34.76 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ].
% 34.50/34.76 apply zenon_H1e. apply sym_equal. exact zenon_H29.
% 34.50/34.76 exact (zenon_H1f zenon_H28).
% 34.50/34.76 (* end of lemma zenon_L2_ *)
% 34.50/34.76 assert (zenon_L3_ : forall (zenon_TT3_t : zenon_U) (zenon_TT2_bg : zenon_U) (zenon_TX_u : zenon_U), ((stock_of_knowledge zenon_TX_u zenon_TT2_bg) = (stock_of_knowledge zenon_TX_u zenon_E)) -> (forall Y : zenon_U, ((smaller (stock_of_knowledge zenon_TX_u zenon_TT2_bg) Y)\/(((stock_of_knowledge zenon_TX_u zenon_TT2_bg) = Y)\/(greater (stock_of_knowledge zenon_TX_u zenon_TT2_bg) Y)))) -> (~(greater (stock_of_knowledge zenon_TX_u zenon_TT2_bg) (stock_of_knowledge zenon_TX_u zenon_TT2_bg))) -> (organization zenon_TX_u) -> (forall T : zenon_U, ((organization zenon_TX_u)->((stock_of_knowledge zenon_TX_u T) = (stock_of_knowledge zenon_TX_u zenon_E)))) -> (~(smaller_or_equal (stock_of_knowledge zenon_TX_u zenon_TT3_t) (stock_of_knowledge zenon_TX_u zenon_TT2_bg))) -> False).
% 34.50/34.76 do 3 intro. intros zenon_H2a zenon_H1c zenon_H2b zenon_H2c zenon_H2d zenon_H2e.
% 34.50/34.76 generalize (definition_smaller_or_equal (stock_of_knowledge zenon_TX_u zenon_TT3_t)). zenon_intro zenon_H2f.
% 34.50/34.76 generalize (zenon_H2f (stock_of_knowledge zenon_TX_u zenon_TT2_bg)). zenon_intro zenon_H30.
% 34.50/34.76 apply (zenon_equiv_s _ _ zenon_H30); [ zenon_intro zenon_H2e; zenon_intro zenon_H33 | zenon_intro zenon_H32; zenon_intro zenon_H31 ].
% 34.50/34.76 apply (zenon_notor_s _ _ zenon_H33). zenon_intro zenon_H34. zenon_intro zenon_H1e.
% 34.50/34.76 generalize (definition_smaller (stock_of_knowledge zenon_TX_u zenon_TT3_t)). zenon_intro zenon_H35.
% 34.50/34.76 generalize (zenon_H35 (stock_of_knowledge zenon_TX_u zenon_TT2_bg)). zenon_intro zenon_H36.
% 34.50/34.76 apply (zenon_equiv_s _ _ zenon_H36); [ zenon_intro zenon_H34; zenon_intro zenon_H1f | zenon_intro zenon_H37; zenon_intro zenon_H28 ].
% 34.50/34.76 generalize (zenon_H2d zenon_TT3_t). zenon_intro zenon_H38.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H38); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ].
% 34.50/34.76 exact (zenon_H3a zenon_H2c).
% 34.50/34.76 elim (classic ((stock_of_knowledge zenon_TX_u zenon_E) = (stock_of_knowledge zenon_TX_u zenon_TT3_t))); [ zenon_intro zenon_H3b | zenon_intro zenon_H3c ].
% 34.50/34.76 elim (classic (greater (stock_of_knowledge zenon_TX_u zenon_TT3_t) (stock_of_knowledge zenon_TX_u zenon_TT2_bg))); [ zenon_intro zenon_H26 | zenon_intro zenon_H1d ].
% 34.50/34.76 elim (classic (greater (stock_of_knowledge zenon_TX_u zenon_E) (stock_of_knowledge zenon_TX_u zenon_TT2_bg))); [ zenon_intro zenon_H3d | zenon_intro zenon_H3e ].
% 34.50/34.76 cut ((greater (stock_of_knowledge zenon_TX_u zenon_E) (stock_of_knowledge zenon_TX_u zenon_TT2_bg)) = (greater (stock_of_knowledge zenon_TX_u zenon_TT2_bg) (stock_of_knowledge zenon_TX_u zenon_TT2_bg))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H2b.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_H3d.
% 34.50/34.76 cut (((stock_of_knowledge zenon_TX_u zenon_TT2_bg) = (stock_of_knowledge zenon_TX_u zenon_TT2_bg))); [idtac | apply NNPP; zenon_intro zenon_H3f].
% 34.50/34.76 cut (((stock_of_knowledge zenon_TX_u zenon_E) = (stock_of_knowledge zenon_TX_u zenon_TT2_bg))); [idtac | apply NNPP; zenon_intro zenon_H40].
% 34.50/34.76 congruence.
% 34.50/34.76 elim (classic ((stock_of_knowledge zenon_TX_u zenon_TT2_bg) = (stock_of_knowledge zenon_TX_u zenon_TT2_bg))); [ zenon_intro zenon_H41 | zenon_intro zenon_H3f ].
% 34.50/34.76 cut (((stock_of_knowledge zenon_TX_u zenon_TT2_bg) = (stock_of_knowledge zenon_TX_u zenon_TT2_bg)) = ((stock_of_knowledge zenon_TX_u zenon_E) = (stock_of_knowledge zenon_TX_u zenon_TT2_bg))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H40.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_H41.
% 34.50/34.76 cut (((stock_of_knowledge zenon_TX_u zenon_TT2_bg) = (stock_of_knowledge zenon_TX_u zenon_TT2_bg))); [idtac | apply NNPP; zenon_intro zenon_H3f].
% 34.50/34.76 cut (((stock_of_knowledge zenon_TX_u zenon_TT2_bg) = (stock_of_knowledge zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H42].
% 34.50/34.76 congruence.
% 34.50/34.76 exact (zenon_H42 zenon_H2a).
% 34.50/34.76 apply zenon_H3f. apply refl_equal.
% 34.50/34.76 apply zenon_H3f. apply refl_equal.
% 34.50/34.76 apply zenon_H3f. apply refl_equal.
% 34.50/34.76 cut ((greater (stock_of_knowledge zenon_TX_u zenon_TT3_t) (stock_of_knowledge zenon_TX_u zenon_TT2_bg)) = (greater (stock_of_knowledge zenon_TX_u zenon_E) (stock_of_knowledge zenon_TX_u zenon_TT2_bg))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H3e.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_H26.
% 34.50/34.76 cut (((stock_of_knowledge zenon_TX_u zenon_TT2_bg) = (stock_of_knowledge zenon_TX_u zenon_TT2_bg))); [idtac | apply NNPP; zenon_intro zenon_H3f].
% 34.50/34.76 cut (((stock_of_knowledge zenon_TX_u zenon_TT3_t) = (stock_of_knowledge zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H43].
% 34.50/34.76 congruence.
% 34.50/34.76 elim (classic ((stock_of_knowledge zenon_TX_u zenon_E) = (stock_of_knowledge zenon_TX_u zenon_E))); [ zenon_intro zenon_H44 | zenon_intro zenon_H45 ].
% 34.50/34.76 cut (((stock_of_knowledge zenon_TX_u zenon_E) = (stock_of_knowledge zenon_TX_u zenon_E)) = ((stock_of_knowledge zenon_TX_u zenon_TT3_t) = (stock_of_knowledge zenon_TX_u zenon_E))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H43.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_H44.
% 34.50/34.76 cut (((stock_of_knowledge zenon_TX_u zenon_E) = (stock_of_knowledge zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H45].
% 34.50/34.76 cut (((stock_of_knowledge zenon_TX_u zenon_E) = (stock_of_knowledge zenon_TX_u zenon_TT3_t))); [idtac | apply NNPP; zenon_intro zenon_H3c].
% 34.50/34.76 congruence.
% 34.50/34.76 exact (zenon_H3c zenon_H3b).
% 34.50/34.76 apply zenon_H45. apply refl_equal.
% 34.50/34.76 apply zenon_H45. apply refl_equal.
% 34.50/34.76 apply zenon_H3f. apply refl_equal.
% 34.50/34.76 apply (zenon_L2_ zenon_TT3_t zenon_TT2_bg zenon_TX_u); trivial.
% 34.50/34.76 elim (classic ((stock_of_knowledge zenon_TX_u zenon_TT3_t) = (stock_of_knowledge zenon_TX_u zenon_TT3_t))); [ zenon_intro zenon_H46 | zenon_intro zenon_H47 ].
% 34.50/34.76 cut (((stock_of_knowledge zenon_TX_u zenon_TT3_t) = (stock_of_knowledge zenon_TX_u zenon_TT3_t)) = ((stock_of_knowledge zenon_TX_u zenon_E) = (stock_of_knowledge zenon_TX_u zenon_TT3_t))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H3c.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_H46.
% 34.50/34.76 cut (((stock_of_knowledge zenon_TX_u zenon_TT3_t) = (stock_of_knowledge zenon_TX_u zenon_TT3_t))); [idtac | apply NNPP; zenon_intro zenon_H47].
% 34.50/34.76 cut (((stock_of_knowledge zenon_TX_u zenon_TT3_t) = (stock_of_knowledge zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H43].
% 34.50/34.76 congruence.
% 34.50/34.76 exact (zenon_H43 zenon_H39).
% 34.50/34.76 apply zenon_H47. apply refl_equal.
% 34.50/34.76 apply zenon_H47. apply refl_equal.
% 34.50/34.76 exact (zenon_H34 zenon_H37).
% 34.50/34.76 exact (zenon_H2e zenon_H32).
% 34.50/34.76 (* end of lemma zenon_L3_ *)
% 34.50/34.76 assert (zenon_L4_ : forall (zenon_TT3_t : zenon_U) (zenon_TT2_bg : zenon_U) (zenon_TX_u : zenon_U), (forall T : zenon_U, (((organization zenon_TX_u)/\(greater (age zenon_TX_u T) (age zenon_TX_u zenon_TT2_bg)))->(greater (internal_friction zenon_TX_u T) (internal_friction zenon_TX_u zenon_TT2_bg)))) -> (organization zenon_TX_u) -> (greater (age zenon_TX_u zenon_TT3_t) (age zenon_TX_u zenon_TT2_bg)) -> (~(greater (internal_friction zenon_TX_u zenon_TT3_t) (internal_friction zenon_TX_u zenon_TT2_bg))) -> False).
% 34.50/34.76 do 3 intro. intros zenon_H48 zenon_H2c zenon_H49 zenon_H4a.
% 34.50/34.76 generalize (zenon_H48 zenon_TT3_t). zenon_intro zenon_H4b.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H4b); [ zenon_intro zenon_H4d | zenon_intro zenon_H4c ].
% 34.50/34.76 apply (zenon_notand_s _ _ zenon_H4d); [ zenon_intro zenon_H3a | zenon_intro zenon_H4e ].
% 34.50/34.76 exact (zenon_H3a zenon_H2c).
% 34.50/34.76 exact (zenon_H4e zenon_H49).
% 34.50/34.76 exact (zenon_H4a zenon_H4c).
% 34.50/34.76 (* end of lemma zenon_L4_ *)
% 34.50/34.76 assert (zenon_L5_ : forall (zenon_TT3_t : zenon_U) (zenon_TX_u : zenon_U), (forall T : zenon_U, ((organization zenon_TX_u)->((external_ties zenon_TX_u T) = (external_ties zenon_TX_u zenon_E)))) -> (organization zenon_TX_u) -> (~((external_ties zenon_TX_u zenon_E) = (external_ties zenon_TX_u zenon_TT3_t))) -> False).
% 34.50/34.76 do 2 intro. intros zenon_H4f zenon_H2c zenon_H50.
% 34.50/34.76 generalize (zenon_H4f zenon_TT3_t). zenon_intro zenon_H51.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H51); [ zenon_intro zenon_H3a | zenon_intro zenon_H52 ].
% 34.50/34.76 exact (zenon_H3a zenon_H2c).
% 34.50/34.76 apply zenon_H50. apply sym_equal. exact zenon_H52.
% 34.50/34.76 (* end of lemma zenon_L5_ *)
% 34.50/34.76 assert (zenon_L6_ : forall (zenon_TT3_t : zenon_U) (zenon_TT2_bg : zenon_U) (zenon_TX_u : zenon_U), (forall Y : zenon_U, ((smaller (external_ties zenon_TX_u zenon_TT2_bg) Y)\/(((external_ties zenon_TX_u zenon_TT2_bg) = Y)\/(greater (external_ties zenon_TX_u zenon_TT2_bg) Y)))) -> (~(greater (external_ties zenon_TX_u zenon_TT3_t) (external_ties zenon_TX_u zenon_TT2_bg))) -> (~((external_ties zenon_TX_u zenon_TT3_t) = (external_ties zenon_TX_u zenon_TT2_bg))) -> (~(greater (external_ties zenon_TX_u zenon_TT2_bg) (external_ties zenon_TX_u zenon_TT3_t))) -> False).
% 34.50/34.76 do 3 intro. intros zenon_H53 zenon_H54 zenon_H55 zenon_H56.
% 34.50/34.76 generalize (zenon_H53 (external_ties zenon_TX_u zenon_TT3_t)). zenon_intro zenon_H57.
% 34.50/34.76 apply (zenon_or_s _ _ zenon_H57); [ zenon_intro zenon_H59 | zenon_intro zenon_H58 ].
% 34.50/34.76 generalize (definition_smaller (external_ties zenon_TX_u zenon_TT2_bg)). zenon_intro zenon_H5a.
% 34.50/34.76 generalize (zenon_H5a (external_ties zenon_TX_u zenon_TT3_t)). zenon_intro zenon_H5b.
% 34.50/34.76 apply (zenon_equiv_s _ _ zenon_H5b); [ zenon_intro zenon_H5d; zenon_intro zenon_H54 | zenon_intro zenon_H59; zenon_intro zenon_H5c ].
% 34.50/34.76 exact (zenon_H5d zenon_H59).
% 34.50/34.76 exact (zenon_H54 zenon_H5c).
% 34.50/34.76 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5f | zenon_intro zenon_H5e ].
% 34.50/34.76 apply zenon_H55. apply sym_equal. exact zenon_H5f.
% 34.50/34.76 exact (zenon_H56 zenon_H5e).
% 34.50/34.76 (* end of lemma zenon_L6_ *)
% 34.50/34.76 assert (zenon_L7_ : forall (zenon_TT3_t : zenon_U) (zenon_TT2_bg : zenon_U) (zenon_TX_u : zenon_U), (forall T : zenon_U, ((organization zenon_TX_u)->((external_ties zenon_TX_u T) = (external_ties zenon_TX_u zenon_E)))) -> (organization zenon_TX_u) -> ((external_ties zenon_TX_u zenon_TT2_bg) = (external_ties zenon_TX_u zenon_E)) -> (~(greater (external_ties zenon_TX_u zenon_TT3_t) (external_ties zenon_TX_u zenon_TT3_t))) -> (forall Y : zenon_U, ((smaller (external_ties zenon_TX_u zenon_TT2_bg) Y)\/(((external_ties zenon_TX_u zenon_TT2_bg) = Y)\/(greater (external_ties zenon_TX_u zenon_TT2_bg) Y)))) -> (~((external_ties zenon_TX_u zenon_TT3_t) = (external_ties zenon_TX_u zenon_TT2_bg))) -> (~(greater (external_ties zenon_TX_u zenon_TT2_bg) (external_ties zenon_TX_u zenon_TT3_t))) -> False).
% 34.50/34.76 do 3 intro. intros zenon_H4f zenon_H2c zenon_H60 zenon_H61 zenon_H53 zenon_H55 zenon_H56.
% 34.50/34.76 elim (classic (greater (external_ties zenon_TX_u zenon_TT3_t) (external_ties zenon_TX_u zenon_TT2_bg))); [ zenon_intro zenon_H5c | zenon_intro zenon_H54 ].
% 34.50/34.76 elim (classic (greater (external_ties zenon_TX_u zenon_TT3_t) (external_ties zenon_TX_u zenon_E))); [ zenon_intro zenon_H62 | zenon_intro zenon_H63 ].
% 34.50/34.76 cut ((greater (external_ties zenon_TX_u zenon_TT3_t) (external_ties zenon_TX_u zenon_E)) = (greater (external_ties zenon_TX_u zenon_TT3_t) (external_ties zenon_TX_u zenon_TT3_t))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H61.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_H62.
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_E) = (external_ties zenon_TX_u zenon_TT3_t))); [idtac | apply NNPP; zenon_intro zenon_H50].
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_TT3_t) = (external_ties zenon_TX_u zenon_TT3_t))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 34.50/34.76 congruence.
% 34.50/34.76 apply zenon_H64. apply refl_equal.
% 34.50/34.76 apply (zenon_L5_ zenon_TT3_t zenon_TX_u); trivial.
% 34.50/34.76 cut ((greater (external_ties zenon_TX_u zenon_TT3_t) (external_ties zenon_TX_u zenon_TT2_bg)) = (greater (external_ties zenon_TX_u zenon_TT3_t) (external_ties zenon_TX_u zenon_E))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H63.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_H5c.
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_TT2_bg) = (external_ties zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_TT3_t) = (external_ties zenon_TX_u zenon_TT3_t))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 34.50/34.76 congruence.
% 34.50/34.76 apply zenon_H64. apply refl_equal.
% 34.50/34.76 exact (zenon_H65 zenon_H60).
% 34.50/34.76 apply (zenon_L6_ zenon_TT3_t zenon_TT2_bg zenon_TX_u); trivial.
% 34.50/34.76 (* end of lemma zenon_L7_ *)
% 34.50/34.76 assert (zenon_L8_ : forall (zenon_TT3_t : zenon_U) (zenon_TT2_bg : zenon_U) (zenon_TX_u : zenon_U), (forall Y : zenon_U, ((smaller (external_ties zenon_TX_u zenon_TT2_bg) Y)\/(((external_ties zenon_TX_u zenon_TT2_bg) = Y)\/(greater (external_ties zenon_TX_u zenon_TT2_bg) Y)))) -> (~((external_ties zenon_TX_u zenon_TT3_t) = (external_ties zenon_TX_u zenon_TT2_bg))) -> (forall T : zenon_U, ((organization zenon_TX_u)->((external_ties zenon_TX_u T) = (external_ties zenon_TX_u zenon_E)))) -> (organization zenon_TX_u) -> (~(greater (external_ties zenon_TX_u zenon_TT3_t) (external_ties zenon_TX_u zenon_TT3_t))) -> (~(greater (external_ties zenon_TX_u zenon_E) (external_ties zenon_TX_u zenon_TT3_t))) -> ((external_ties zenon_TX_u zenon_TT2_bg) = (external_ties zenon_TX_u zenon_E)) -> False).
% 34.50/34.76 do 3 intro. intros zenon_H53 zenon_H55 zenon_H4f zenon_H2c zenon_H61 zenon_H66 zenon_H60.
% 34.50/34.76 elim (classic ((external_ties zenon_TX_u zenon_E) = (external_ties zenon_TX_u zenon_TT2_bg))); [ zenon_intro zenon_H67 | zenon_intro zenon_H68 ].
% 34.50/34.76 elim (classic (greater (external_ties zenon_TX_u zenon_TT2_bg) (external_ties zenon_TX_u zenon_TT3_t))); [ zenon_intro zenon_H5e | zenon_intro zenon_H56 ].
% 34.50/34.76 cut ((greater (external_ties zenon_TX_u zenon_TT2_bg) (external_ties zenon_TX_u zenon_TT3_t)) = (greater (external_ties zenon_TX_u zenon_E) (external_ties zenon_TX_u zenon_TT3_t))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H66.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_H5e.
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_TT3_t) = (external_ties zenon_TX_u zenon_TT3_t))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_TT2_bg) = (external_ties zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 34.50/34.76 congruence.
% 34.50/34.76 elim (classic ((external_ties zenon_TX_u zenon_E) = (external_ties zenon_TX_u zenon_E))); [ zenon_intro zenon_H69 | zenon_intro zenon_H6a ].
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_E) = (external_ties zenon_TX_u zenon_E)) = ((external_ties zenon_TX_u zenon_TT2_bg) = (external_ties zenon_TX_u zenon_E))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H65.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_H69.
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_E) = (external_ties zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_E) = (external_ties zenon_TX_u zenon_TT2_bg))); [idtac | apply NNPP; zenon_intro zenon_H68].
% 34.50/34.76 congruence.
% 34.50/34.76 exact (zenon_H68 zenon_H67).
% 34.50/34.76 apply zenon_H6a. apply refl_equal.
% 34.50/34.76 apply zenon_H6a. apply refl_equal.
% 34.50/34.76 apply zenon_H64. apply refl_equal.
% 34.50/34.76 apply (zenon_L7_ zenon_TT3_t zenon_TT2_bg zenon_TX_u); trivial.
% 34.50/34.76 elim (classic ((external_ties zenon_TX_u zenon_TT2_bg) = (external_ties zenon_TX_u zenon_TT2_bg))); [ zenon_intro zenon_H6b | zenon_intro zenon_H6c ].
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_TT2_bg) = (external_ties zenon_TX_u zenon_TT2_bg)) = ((external_ties zenon_TX_u zenon_E) = (external_ties zenon_TX_u zenon_TT2_bg))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H68.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_H6b.
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_TT2_bg) = (external_ties zenon_TX_u zenon_TT2_bg))); [idtac | apply NNPP; zenon_intro zenon_H6c].
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_TT2_bg) = (external_ties zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 34.50/34.76 congruence.
% 34.50/34.76 exact (zenon_H65 zenon_H60).
% 34.50/34.76 apply zenon_H6c. apply refl_equal.
% 34.50/34.76 apply zenon_H6c. apply refl_equal.
% 34.50/34.76 (* end of lemma zenon_L8_ *)
% 34.50/34.76 assert (zenon_L9_ : forall (zenon_TT2_bg : zenon_U) (zenon_TT3_t : zenon_U) (zenon_TX_u : zenon_U), (~((external_ties zenon_TX_u zenon_TT3_t) = (external_ties zenon_TX_u zenon_TT2_bg))) -> (~(greater (external_ties zenon_TX_u zenon_TT3_t) (external_ties zenon_TX_u zenon_TT2_bg))) -> (forall Y : zenon_U, ((smaller (external_ties zenon_TX_u zenon_TT2_bg) Y)\/(((external_ties zenon_TX_u zenon_TT2_bg) = Y)\/(greater (external_ties zenon_TX_u zenon_TT2_bg) Y)))) -> (forall T : zenon_U, ((organization zenon_TX_u)->((external_ties zenon_TX_u T) = (external_ties zenon_TX_u zenon_E)))) -> (organization zenon_TX_u) -> (~(greater (external_ties zenon_TX_u zenon_TT3_t) (external_ties zenon_TX_u zenon_TT3_t))) -> ((external_ties zenon_TX_u zenon_TT2_bg) = (external_ties zenon_TX_u zenon_E)) -> False).
% 34.50/34.76 do 3 intro. intros zenon_H55 zenon_H54 zenon_H53 zenon_H4f zenon_H2c zenon_H61 zenon_H60.
% 34.50/34.76 elim (classic ((external_ties zenon_TX_u zenon_E) = (external_ties zenon_TX_u zenon_TT2_bg))); [ zenon_intro zenon_H67 | zenon_intro zenon_H68 ].
% 34.50/34.76 elim (classic (greater (external_ties zenon_TX_u zenon_TT2_bg) (external_ties zenon_TX_u zenon_TT3_t))); [ zenon_intro zenon_H5e | zenon_intro zenon_H56 ].
% 34.50/34.76 elim (classic (greater (external_ties zenon_TX_u zenon_E) (external_ties zenon_TX_u zenon_TT3_t))); [ zenon_intro zenon_H6d | zenon_intro zenon_H66 ].
% 34.50/34.76 cut ((greater (external_ties zenon_TX_u zenon_E) (external_ties zenon_TX_u zenon_TT3_t)) = (greater (external_ties zenon_TX_u zenon_TT3_t) (external_ties zenon_TX_u zenon_TT3_t))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H61.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_H6d.
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_TT3_t) = (external_ties zenon_TX_u zenon_TT3_t))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_E) = (external_ties zenon_TX_u zenon_TT3_t))); [idtac | apply NNPP; zenon_intro zenon_H50].
% 34.50/34.76 congruence.
% 34.50/34.76 elim (classic ((external_ties zenon_TX_u zenon_TT3_t) = (external_ties zenon_TX_u zenon_TT3_t))); [ zenon_intro zenon_H6e | zenon_intro zenon_H64 ].
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_TT3_t) = (external_ties zenon_TX_u zenon_TT3_t)) = ((external_ties zenon_TX_u zenon_E) = (external_ties zenon_TX_u zenon_TT3_t))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H50.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_H6e.
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_TT3_t) = (external_ties zenon_TX_u zenon_TT3_t))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_TT3_t) = (external_ties zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H6f].
% 34.50/34.76 congruence.
% 34.50/34.76 generalize (zenon_H4f zenon_TT3_t). zenon_intro zenon_H51.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H51); [ zenon_intro zenon_H3a | zenon_intro zenon_H52 ].
% 34.50/34.76 exact (zenon_H3a zenon_H2c).
% 34.50/34.76 exact (zenon_H6f zenon_H52).
% 34.50/34.76 apply zenon_H64. apply refl_equal.
% 34.50/34.76 apply zenon_H64. apply refl_equal.
% 34.50/34.76 apply zenon_H64. apply refl_equal.
% 34.50/34.76 cut ((greater (external_ties zenon_TX_u zenon_TT2_bg) (external_ties zenon_TX_u zenon_TT3_t)) = (greater (external_ties zenon_TX_u zenon_E) (external_ties zenon_TX_u zenon_TT3_t))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H66.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_H5e.
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_TT3_t) = (external_ties zenon_TX_u zenon_TT3_t))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_TT2_bg) = (external_ties zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 34.50/34.76 congruence.
% 34.50/34.76 elim (classic ((external_ties zenon_TX_u zenon_E) = (external_ties zenon_TX_u zenon_E))); [ zenon_intro zenon_H69 | zenon_intro zenon_H6a ].
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_E) = (external_ties zenon_TX_u zenon_E)) = ((external_ties zenon_TX_u zenon_TT2_bg) = (external_ties zenon_TX_u zenon_E))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H65.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_H69.
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_E) = (external_ties zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_E) = (external_ties zenon_TX_u zenon_TT2_bg))); [idtac | apply NNPP; zenon_intro zenon_H68].
% 34.50/34.76 congruence.
% 34.50/34.76 exact (zenon_H68 zenon_H67).
% 34.50/34.76 apply zenon_H6a. apply refl_equal.
% 34.50/34.76 apply zenon_H6a. apply refl_equal.
% 34.50/34.76 apply zenon_H64. apply refl_equal.
% 34.50/34.76 apply (zenon_L6_ zenon_TT3_t zenon_TT2_bg zenon_TX_u); trivial.
% 34.50/34.76 elim (classic ((external_ties zenon_TX_u zenon_TT2_bg) = (external_ties zenon_TX_u zenon_TT2_bg))); [ zenon_intro zenon_H6b | zenon_intro zenon_H6c ].
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_TT2_bg) = (external_ties zenon_TX_u zenon_TT2_bg)) = ((external_ties zenon_TX_u zenon_E) = (external_ties zenon_TX_u zenon_TT2_bg))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H68.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_H6b.
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_TT2_bg) = (external_ties zenon_TX_u zenon_TT2_bg))); [idtac | apply NNPP; zenon_intro zenon_H6c].
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_TT2_bg) = (external_ties zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 34.50/34.76 congruence.
% 34.50/34.76 exact (zenon_H65 zenon_H60).
% 34.50/34.76 apply zenon_H6c. apply refl_equal.
% 34.50/34.76 apply zenon_H6c. apply refl_equal.
% 34.50/34.76 (* end of lemma zenon_L9_ *)
% 34.50/34.76 assert (zenon_L10_ : forall (zenon_TT2_bg : zenon_U) (zenon_TT3_t : zenon_U) (zenon_TX_u : zenon_U), (forall T0 : zenon_U, (forall T : zenon_U, ((organization zenon_TX_u)->(((greater (external_ties zenon_TX_u T) (external_ties zenon_TX_u T0))->(greater (position zenon_TX_u T) (position zenon_TX_u T0)))/\(((external_ties zenon_TX_u T) = (external_ties zenon_TX_u T0))->((position zenon_TX_u T) = (position zenon_TX_u T0))))))) -> (~(greater (position zenon_TX_u zenon_TT3_t) (position zenon_TX_u zenon_TT3_t))) -> (forall T : zenon_U, ((organization zenon_TX_u)->((external_ties zenon_TX_u T) = (external_ties zenon_TX_u zenon_E)))) -> (forall Y : zenon_U, ((smaller (external_ties zenon_TX_u zenon_TT2_bg) Y)\/(((external_ties zenon_TX_u zenon_TT2_bg) = Y)\/(greater (external_ties zenon_TX_u zenon_TT2_bg) Y)))) -> (~(greater (external_ties zenon_TX_u zenon_TT3_t) (external_ties zenon_TX_u zenon_TT2_bg))) -> (~((external_ties zenon_TX_u zenon_TT3_t) = (external_ties zenon_TX_u zenon_TT2_bg))) -> ((external_ties zenon_TX_u zenon_TT2_bg) = (external_ties zenon_TX_u zenon_E)) -> (organization zenon_TX_u) -> False).
% 34.50/34.76 do 3 intro. intros zenon_H70 zenon_H71 zenon_H4f zenon_H53 zenon_H54 zenon_H55 zenon_H60 zenon_H2c.
% 34.50/34.76 generalize (zenon_H70 zenon_TT3_t). zenon_intro zenon_H72.
% 34.50/34.76 generalize (zenon_H72 zenon_TT3_t). zenon_intro zenon_H73.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H73); [ zenon_intro zenon_H3a | zenon_intro zenon_H74 ].
% 34.50/34.76 exact (zenon_H3a zenon_H2c).
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H74). zenon_intro zenon_H76. zenon_intro zenon_H75.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H76); [ zenon_intro zenon_H61 | zenon_intro zenon_H77 ].
% 34.50/34.76 apply (zenon_L9_ zenon_TT2_bg zenon_TT3_t zenon_TX_u); trivial.
% 34.50/34.76 exact (zenon_H71 zenon_H77).
% 34.50/34.76 (* end of lemma zenon_L10_ *)
% 34.50/34.76 assert (zenon_L11_ : forall (zenon_TT2_bg : zenon_U) (zenon_TT3_t : zenon_U) (zenon_TX_u : zenon_U), ((position zenon_TX_u zenon_TT3_t) = (position zenon_TX_u zenon_TT2_bg)) -> (~(greater_or_equal (position zenon_TX_u zenon_TT2_bg) (position zenon_TX_u zenon_TT3_t))) -> False).
% 34.50/34.76 do 3 intro. intros zenon_H78 zenon_H79.
% 34.50/34.76 generalize (definition_greater_or_equal (position zenon_TX_u zenon_TT2_bg)). zenon_intro zenon_H7a.
% 34.50/34.76 generalize (zenon_H7a (position zenon_TX_u zenon_TT3_t)). zenon_intro zenon_H7b.
% 34.50/34.76 apply (zenon_equiv_s _ _ zenon_H7b); [ zenon_intro zenon_H79; zenon_intro zenon_H7e | zenon_intro zenon_H7d; zenon_intro zenon_H7c ].
% 34.50/34.76 apply (zenon_notor_s _ _ zenon_H7e). zenon_intro zenon_H80. zenon_intro zenon_H7f.
% 34.50/34.76 apply zenon_H7f. apply sym_equal. exact zenon_H78.
% 34.50/34.76 exact (zenon_H79 zenon_H7d).
% 34.50/34.76 (* end of lemma zenon_L11_ *)
% 34.50/34.76 assert (zenon_L12_ : forall (zenon_TT3_t : zenon_U) (zenon_TT2_bg : zenon_U) (zenon_TX_u : zenon_U), (smaller (hazard_of_mortality zenon_TX_u zenon_TT2_bg) (hazard_of_mortality zenon_TX_u zenon_TT3_t)) -> (~(greater (hazard_of_mortality zenon_TX_u zenon_TT3_t) (hazard_of_mortality zenon_TX_u zenon_TT2_bg))) -> False).
% 34.50/34.76 do 3 intro. intros zenon_H81 zenon_H82.
% 34.50/34.76 generalize (definition_smaller (hazard_of_mortality zenon_TX_u zenon_TT2_bg)). zenon_intro zenon_H83.
% 34.50/34.76 generalize (zenon_H83 (hazard_of_mortality zenon_TX_u zenon_TT3_t)). zenon_intro zenon_H84.
% 34.50/34.76 apply (zenon_equiv_s _ _ zenon_H84); [ zenon_intro zenon_H86; zenon_intro zenon_H82 | zenon_intro zenon_H81; zenon_intro zenon_H85 ].
% 34.50/34.76 exact (zenon_H86 zenon_H81).
% 34.50/34.76 exact (zenon_H82 zenon_H85).
% 34.50/34.76 (* end of lemma zenon_L12_ *)
% 34.50/34.76 assert (zenon_L13_ : forall (zenon_TT2_bg : zenon_U) (zenon_TT3_t : zenon_U) (zenon_TX_u : zenon_U), (forall T : zenon_U, (((organization zenon_TX_u)/\((~(has_immunity zenon_TX_u zenon_TT3_t))/\(~(has_immunity zenon_TX_u T))))->((((greater (capability zenon_TX_u T) (capability zenon_TX_u zenon_TT3_t))/\(greater_or_equal (position zenon_TX_u T) (position zenon_TX_u zenon_TT3_t)))->(smaller (hazard_of_mortality zenon_TX_u T) (hazard_of_mortality zenon_TX_u zenon_TT3_t)))/\((((greater_or_equal (capability zenon_TX_u T) (capability zenon_TX_u zenon_TT3_t))/\(greater (position zenon_TX_u T) (position zenon_TX_u zenon_TT3_t)))->(smaller (hazard_of_mortality zenon_TX_u T) (hazard_of_mortality zenon_TX_u zenon_TT3_t)))/\((((capability zenon_TX_u T) = (capability zenon_TX_u zenon_TT3_t))/\((position zenon_TX_u T) = (position zenon_TX_u zenon_TT3_t)))->((hazard_of_mortality zenon_TX_u T) = (hazard_of_mortality zenon_TX_u zenon_TT3_t))))))) -> (organization zenon_TX_u) -> (~(has_immunity zenon_TX_u zenon_TT3_t)) -> (~(has_immunity zenon_TX_u zenon_TT2_bg)) -> (greater (capability zenon_TX_u zenon_TT2_bg) (capability zenon_TX_u zenon_TT3_t)) -> ((position zenon_TX_u zenon_TT3_t) = (position zenon_TX_u zenon_TT2_bg)) -> (~(greater (hazard_of_mortality zenon_TX_u zenon_TT3_t) (hazard_of_mortality zenon_TX_u zenon_TT2_bg))) -> False).
% 34.50/34.76 do 3 intro. intros zenon_H87 zenon_H2c zenon_H88 zenon_H89 zenon_H8a zenon_H78 zenon_H82.
% 34.50/34.76 generalize (zenon_H87 zenon_TT2_bg). zenon_intro zenon_H8b.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H8b); [ zenon_intro zenon_H8d | zenon_intro zenon_H8c ].
% 34.50/34.76 apply (zenon_notand_s _ _ zenon_H8d); [ zenon_intro zenon_H3a | zenon_intro zenon_H8e ].
% 34.50/34.76 exact (zenon_H3a zenon_H2c).
% 34.50/34.76 apply (zenon_notand_s _ _ zenon_H8e); [ zenon_intro zenon_H90 | zenon_intro zenon_H8f ].
% 34.50/34.76 exact (zenon_H90 zenon_H88).
% 34.50/34.76 exact (zenon_H8f zenon_H89).
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H92. zenon_intro zenon_H91.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H92); [ zenon_intro zenon_H93 | zenon_intro zenon_H81 ].
% 34.50/34.76 apply (zenon_notand_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H79 ].
% 34.50/34.76 exact (zenon_H94 zenon_H8a).
% 34.50/34.76 apply (zenon_L11_ zenon_TT2_bg zenon_TT3_t zenon_TX_u); trivial.
% 34.50/34.76 apply (zenon_L12_ zenon_TT3_t zenon_TT2_bg zenon_TX_u); trivial.
% 34.50/34.76 (* end of lemma zenon_L13_ *)
% 34.50/34.76 assert (zenon_L14_ : forall (zenon_TT2_bg : zenon_U) (zenon_TT3_t : zenon_U) (zenon_TX_u : zenon_U), (((external_ties zenon_TX_u zenon_TT3_t) = (external_ties zenon_TX_u zenon_TT2_bg))->((position zenon_TX_u zenon_TT3_t) = (position zenon_TX_u zenon_TT2_bg))) -> (~(greater (hazard_of_mortality zenon_TX_u zenon_TT3_t) (hazard_of_mortality zenon_TX_u zenon_TT2_bg))) -> (greater (capability zenon_TX_u zenon_TT2_bg) (capability zenon_TX_u zenon_TT3_t)) -> (~(has_immunity zenon_TX_u zenon_TT2_bg)) -> (~(has_immunity zenon_TX_u zenon_TT3_t)) -> (forall T : zenon_U, (((organization zenon_TX_u)/\((~(has_immunity zenon_TX_u zenon_TT3_t))/\(~(has_immunity zenon_TX_u T))))->((((greater (capability zenon_TX_u T) (capability zenon_TX_u zenon_TT3_t))/\(greater_or_equal (position zenon_TX_u T) (position zenon_TX_u zenon_TT3_t)))->(smaller (hazard_of_mortality zenon_TX_u T) (hazard_of_mortality zenon_TX_u zenon_TT3_t)))/\((((greater_or_equal (capability zenon_TX_u T) (capability zenon_TX_u zenon_TT3_t))/\(greater (position zenon_TX_u T) (position zenon_TX_u zenon_TT3_t)))->(smaller (hazard_of_mortality zenon_TX_u T) (hazard_of_mortality zenon_TX_u zenon_TT3_t)))/\((((capability zenon_TX_u T) = (capability zenon_TX_u zenon_TT3_t))/\((position zenon_TX_u T) = (position zenon_TX_u zenon_TT3_t)))->((hazard_of_mortality zenon_TX_u T) = (hazard_of_mortality zenon_TX_u zenon_TT3_t))))))) -> (organization zenon_TX_u) -> ((external_ties zenon_TX_u zenon_TT2_bg) = (external_ties zenon_TX_u zenon_E)) -> (~(greater (external_ties zenon_TX_u zenon_TT3_t) (external_ties zenon_TX_u zenon_TT2_bg))) -> (forall Y : zenon_U, ((smaller (external_ties zenon_TX_u zenon_TT2_bg) Y)\/(((external_ties zenon_TX_u zenon_TT2_bg) = Y)\/(greater (external_ties zenon_TX_u zenon_TT2_bg) Y)))) -> (forall T : zenon_U, ((organization zenon_TX_u)->((external_ties zenon_TX_u T) = (external_ties zenon_TX_u zenon_E)))) -> (~(greater (position zenon_TX_u zenon_TT3_t) (position zenon_TX_u zenon_TT3_t))) -> (forall T0 : zenon_U, (forall T : zenon_U, ((organization zenon_TX_u)->(((greater (external_ties zenon_TX_u T) (external_ties zenon_TX_u T0))->(greater (position zenon_TX_u T) (position zenon_TX_u T0)))/\(((external_ties zenon_TX_u T) = (external_ties zenon_TX_u T0))->((position zenon_TX_u T) = (position zenon_TX_u T0))))))) -> False).
% 34.50/34.76 do 3 intro. intros zenon_H95 zenon_H82 zenon_H8a zenon_H89 zenon_H88 zenon_H87 zenon_H2c zenon_H60 zenon_H54 zenon_H53 zenon_H4f zenon_H71 zenon_H70.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_H55 | zenon_intro zenon_H78 ].
% 34.50/34.76 apply (zenon_L10_ zenon_TT2_bg zenon_TT3_t zenon_TX_u); trivial.
% 34.50/34.76 apply (zenon_L13_ zenon_TT2_bg zenon_TT3_t zenon_TX_u); trivial.
% 34.50/34.76 (* end of lemma zenon_L14_ *)
% 34.50/34.76 assert (zenon_L15_ : forall (zenon_TT2_bg : zenon_U) (zenon_TT3_t : zenon_U) (zenon_TX_u : zenon_U), (~((external_ties zenon_TX_u zenon_TT3_t) = (external_ties zenon_TX_u zenon_TT2_bg))) -> (~(greater (external_ties zenon_TX_u zenon_TT3_t) (external_ties zenon_TX_u zenon_TT2_bg))) -> (forall Y : zenon_U, ((smaller (external_ties zenon_TX_u zenon_TT2_bg) Y)\/(((external_ties zenon_TX_u zenon_TT2_bg) = Y)\/(greater (external_ties zenon_TX_u zenon_TT2_bg) Y)))) -> (~(greater (external_ties zenon_TX_u zenon_E) (external_ties zenon_TX_u zenon_TT3_t))) -> ((external_ties zenon_TX_u zenon_TT2_bg) = (external_ties zenon_TX_u zenon_E)) -> False).
% 34.50/34.76 do 3 intro. intros zenon_H55 zenon_H54 zenon_H53 zenon_H66 zenon_H60.
% 34.50/34.76 elim (classic ((external_ties zenon_TX_u zenon_E) = (external_ties zenon_TX_u zenon_TT2_bg))); [ zenon_intro zenon_H67 | zenon_intro zenon_H68 ].
% 34.50/34.76 elim (classic (greater (external_ties zenon_TX_u zenon_TT2_bg) (external_ties zenon_TX_u zenon_TT3_t))); [ zenon_intro zenon_H5e | zenon_intro zenon_H56 ].
% 34.50/34.76 cut ((greater (external_ties zenon_TX_u zenon_TT2_bg) (external_ties zenon_TX_u zenon_TT3_t)) = (greater (external_ties zenon_TX_u zenon_E) (external_ties zenon_TX_u zenon_TT3_t))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H66.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_H5e.
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_TT3_t) = (external_ties zenon_TX_u zenon_TT3_t))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_TT2_bg) = (external_ties zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 34.50/34.76 congruence.
% 34.50/34.76 elim (classic ((external_ties zenon_TX_u zenon_E) = (external_ties zenon_TX_u zenon_E))); [ zenon_intro zenon_H69 | zenon_intro zenon_H6a ].
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_E) = (external_ties zenon_TX_u zenon_E)) = ((external_ties zenon_TX_u zenon_TT2_bg) = (external_ties zenon_TX_u zenon_E))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H65.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_H69.
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_E) = (external_ties zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_E) = (external_ties zenon_TX_u zenon_TT2_bg))); [idtac | apply NNPP; zenon_intro zenon_H68].
% 34.50/34.76 congruence.
% 34.50/34.76 exact (zenon_H68 zenon_H67).
% 34.50/34.76 apply zenon_H6a. apply refl_equal.
% 34.50/34.76 apply zenon_H6a. apply refl_equal.
% 34.50/34.76 apply zenon_H64. apply refl_equal.
% 34.50/34.76 apply (zenon_L6_ zenon_TT3_t zenon_TT2_bg zenon_TX_u); trivial.
% 34.50/34.76 elim (classic ((external_ties zenon_TX_u zenon_TT2_bg) = (external_ties zenon_TX_u zenon_TT2_bg))); [ zenon_intro zenon_H6b | zenon_intro zenon_H6c ].
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_TT2_bg) = (external_ties zenon_TX_u zenon_TT2_bg)) = ((external_ties zenon_TX_u zenon_E) = (external_ties zenon_TX_u zenon_TT2_bg))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H68.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_H6b.
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_TT2_bg) = (external_ties zenon_TX_u zenon_TT2_bg))); [idtac | apply NNPP; zenon_intro zenon_H6c].
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_TT2_bg) = (external_ties zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 34.50/34.76 congruence.
% 34.50/34.76 exact (zenon_H65 zenon_H60).
% 34.50/34.76 apply zenon_H6c. apply refl_equal.
% 34.50/34.76 apply zenon_H6c. apply refl_equal.
% 34.50/34.76 (* end of lemma zenon_L15_ *)
% 34.50/34.76 assert (zenon_L16_ : forall (zenon_TT2_bg : zenon_U) (zenon_TT3_t : zenon_U) (zenon_TX_u : 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_u)->(((greater (external_ties zenon_TX_u T) (external_ties zenon_TX_u zenon_TT3_t))->(greater (position zenon_TX_u T) (position zenon_TX_u zenon_TT3_t)))/\(((external_ties zenon_TX_u T) = (external_ties zenon_TX_u zenon_TT3_t))->((position zenon_TX_u T) = (position zenon_TX_u zenon_TT3_t)))))) -> (organization zenon_TX_u) -> (~((external_ties zenon_TX_u zenon_TT3_t) = (external_ties zenon_TX_u zenon_TT2_bg))) -> (forall T0 : zenon_U, (forall T : zenon_U, ((organization zenon_TX_u)->(((greater (external_ties zenon_TX_u T) (external_ties zenon_TX_u T0))->(greater (position zenon_TX_u T) (position zenon_TX_u T0)))/\(((external_ties zenon_TX_u T) = (external_ties zenon_TX_u T0))->((position zenon_TX_u T) = (position zenon_TX_u T0))))))) -> (~(greater (position zenon_TX_u zenon_TT3_t) (position zenon_TX_u zenon_TT3_t))) -> (forall T : zenon_U, ((organization zenon_TX_u)->((external_ties zenon_TX_u T) = (external_ties zenon_TX_u zenon_E)))) -> (forall Y : zenon_U, ((smaller (external_ties zenon_TX_u zenon_TT2_bg) Y)\/(((external_ties zenon_TX_u zenon_TT2_bg) = Y)\/(greater (external_ties zenon_TX_u zenon_TT2_bg) Y)))) -> ((external_ties zenon_TX_u zenon_TT2_bg) = (external_ties zenon_TX_u zenon_E)) -> (forall T : zenon_U, (((organization zenon_TX_u)/\((~(has_immunity zenon_TX_u zenon_TT3_t))/\(~(has_immunity zenon_TX_u T))))->((((greater (capability zenon_TX_u T) (capability zenon_TX_u zenon_TT3_t))/\(greater_or_equal (position zenon_TX_u T) (position zenon_TX_u zenon_TT3_t)))->(smaller (hazard_of_mortality zenon_TX_u T) (hazard_of_mortality zenon_TX_u zenon_TT3_t)))/\((((greater_or_equal (capability zenon_TX_u T) (capability zenon_TX_u zenon_TT3_t))/\(greater (position zenon_TX_u T) (position zenon_TX_u zenon_TT3_t)))->(smaller (hazard_of_mortality zenon_TX_u T) (hazard_of_mortality zenon_TX_u zenon_TT3_t)))/\((((capability zenon_TX_u T) = (capability zenon_TX_u zenon_TT3_t))/\((position zenon_TX_u T) = (position zenon_TX_u zenon_TT3_t)))->((hazard_of_mortality zenon_TX_u T) = (hazard_of_mortality zenon_TX_u zenon_TT3_t))))))) -> (~(has_immunity zenon_TX_u zenon_TT3_t)) -> (~(has_immunity zenon_TX_u zenon_TT2_bg)) -> (greater (capability zenon_TX_u zenon_TT2_bg) (capability zenon_TX_u zenon_TT3_t)) -> (~(greater (hazard_of_mortality zenon_TX_u zenon_TT3_t) (hazard_of_mortality zenon_TX_u zenon_TT2_bg))) -> (((external_ties zenon_TX_u zenon_TT3_t) = (external_ties zenon_TX_u zenon_TT2_bg))->((position zenon_TX_u zenon_TT3_t) = (position zenon_TX_u zenon_TT2_bg))) -> False).
% 34.50/34.76 do 3 intro. intros zenon_H96 zenon_H72 zenon_H2c zenon_H55 zenon_H70 zenon_H71 zenon_H4f zenon_H53 zenon_H60 zenon_H87 zenon_H88 zenon_H89 zenon_H8a zenon_H82 zenon_H95.
% 34.50/34.76 generalize (zenon_H72 zenon_TT3_t). zenon_intro zenon_H73.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H73); [ zenon_intro zenon_H3a | zenon_intro zenon_H74 ].
% 34.50/34.76 exact (zenon_H3a zenon_H2c).
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H74). zenon_intro zenon_H76. zenon_intro zenon_H75.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H76); [ zenon_intro zenon_H61 | zenon_intro zenon_H77 ].
% 34.50/34.76 elim (classic (greater (external_ties zenon_TX_u zenon_TT3_t) (external_ties zenon_TX_u zenon_TT2_bg))); [ zenon_intro zenon_H5c | zenon_intro zenon_H54 ].
% 34.50/34.76 elim (classic (greater (external_ties zenon_TX_u zenon_TT3_t) (external_ties zenon_TX_u zenon_E))); [ zenon_intro zenon_H62 | zenon_intro zenon_H63 ].
% 34.50/34.76 elim (classic (greater (external_ties zenon_TX_u zenon_E) (external_ties zenon_TX_u zenon_TT3_t))); [ zenon_intro zenon_H6d | zenon_intro zenon_H66 ].
% 34.50/34.76 generalize (zenon_H96 (external_ties zenon_TX_u zenon_TT3_t)). zenon_intro zenon_H97.
% 34.50/34.76 generalize (zenon_H97 (external_ties zenon_TX_u zenon_E)). zenon_intro zenon_H98.
% 34.50/34.76 generalize (zenon_H98 (external_ties zenon_TX_u zenon_TT3_t)). zenon_intro zenon_H99.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H63 | zenon_intro zenon_H9a ].
% 34.50/34.76 exact (zenon_H63 zenon_H62).
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H9a); [ zenon_intro zenon_H66 | zenon_intro zenon_H9b ].
% 34.50/34.76 exact (zenon_H66 zenon_H6d).
% 34.50/34.76 exact (zenon_H61 zenon_H9b).
% 34.50/34.76 apply (zenon_L8_ zenon_TT3_t zenon_TT2_bg zenon_TX_u); trivial.
% 34.50/34.76 cut ((greater (external_ties zenon_TX_u zenon_TT3_t) (external_ties zenon_TX_u zenon_TT2_bg)) = (greater (external_ties zenon_TX_u zenon_TT3_t) (external_ties zenon_TX_u zenon_E))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H63.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_H5c.
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_TT2_bg) = (external_ties zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H65].
% 34.50/34.76 cut (((external_ties zenon_TX_u zenon_TT3_t) = (external_ties zenon_TX_u zenon_TT3_t))); [idtac | apply NNPP; zenon_intro zenon_H64].
% 34.50/34.76 congruence.
% 34.50/34.76 apply zenon_H64. apply refl_equal.
% 34.50/34.76 exact (zenon_H65 zenon_H60).
% 34.50/34.76 apply (zenon_L14_ zenon_TT2_bg zenon_TT3_t zenon_TX_u); trivial.
% 34.50/34.76 exact (zenon_H71 zenon_H77).
% 34.50/34.76 (* end of lemma zenon_L16_ *)
% 34.50/34.76 assert (zenon_L17_ : forall (zenon_TT3_t : zenon_U) (zenon_TX_u : zenon_U), (smaller (hazard_of_mortality zenon_TX_u zenon_TT3_t) (hazard_of_mortality zenon_TX_u zenon_TT3_t)) -> False).
% 34.50/34.76 do 2 intro. intros zenon_H9c.
% 34.50/34.76 generalize (definition_smaller (hazard_of_mortality zenon_TX_u zenon_TT3_t)). zenon_intro zenon_H9d.
% 34.50/34.76 generalize (zenon_H9d (hazard_of_mortality zenon_TX_u zenon_TT3_t)). zenon_intro zenon_H9e.
% 34.50/34.76 apply (zenon_equiv_s _ _ zenon_H9e); [ zenon_intro zenon_Ha1; zenon_intro zenon_Ha0 | zenon_intro zenon_H9c; zenon_intro zenon_H9f ].
% 34.50/34.76 exact (zenon_Ha1 zenon_H9c).
% 34.50/34.76 generalize (meaning_postulate_greater_strict (hazard_of_mortality zenon_TX_u zenon_TT3_t)). zenon_intro zenon_Ha2.
% 34.50/34.76 generalize (zenon_Ha2 (hazard_of_mortality zenon_TX_u zenon_TT3_t)). zenon_intro zenon_Ha3.
% 34.50/34.76 apply (zenon_notand_s _ _ zenon_Ha3); [ zenon_intro zenon_Ha0 | zenon_intro zenon_Ha0 ].
% 34.50/34.76 exact (zenon_Ha0 zenon_H9f).
% 34.50/34.76 exact (zenon_Ha0 zenon_H9f).
% 34.50/34.76 (* end of lemma zenon_L17_ *)
% 34.50/34.76 assert (zenon_L18_ : forall (zenon_TT2_bg : zenon_U) (zenon_TX_u : zenon_U), (~(smaller_or_equal (internal_friction zenon_TX_u zenon_TT2_bg) (internal_friction zenon_TX_u zenon_TT2_bg))) -> False).
% 34.50/34.76 do 2 intro. intros zenon_Ha4.
% 34.50/34.76 generalize (definition_smaller_or_equal (internal_friction zenon_TX_u zenon_TT2_bg)). zenon_intro zenon_Ha5.
% 34.50/34.76 generalize (zenon_Ha5 (internal_friction zenon_TX_u zenon_TT2_bg)). zenon_intro zenon_Ha6.
% 34.50/34.76 apply (zenon_equiv_s _ _ zenon_Ha6); [ zenon_intro zenon_Ha4; zenon_intro zenon_Ha9 | zenon_intro zenon_Ha8; zenon_intro zenon_Ha7 ].
% 34.50/34.76 apply (zenon_notor_s _ _ zenon_Ha9). zenon_intro zenon_Hab. zenon_intro zenon_Haa.
% 34.50/34.76 apply zenon_Haa. apply refl_equal.
% 34.50/34.76 exact (zenon_Ha4 zenon_Ha8).
% 34.50/34.76 (* end of lemma zenon_L18_ *)
% 34.50/34.76 assert (zenon_L19_ : forall (zenon_TT2_bg : zenon_U) (zenon_TX_u : zenon_U), (smaller (hazard_of_mortality zenon_TX_u zenon_TT2_bg) (hazard_of_mortality zenon_TX_u zenon_TT2_bg)) -> False).
% 34.50/34.76 do 2 intro. intros zenon_Hac.
% 34.50/34.76 generalize (definition_smaller (hazard_of_mortality zenon_TX_u zenon_TT2_bg)). zenon_intro zenon_H83.
% 34.50/34.76 generalize (zenon_H83 (hazard_of_mortality zenon_TX_u zenon_TT2_bg)). zenon_intro zenon_Had.
% 34.50/34.76 apply (zenon_equiv_s _ _ zenon_Had); [ zenon_intro zenon_Hb0; zenon_intro zenon_Haf | zenon_intro zenon_Hac; zenon_intro zenon_Hae ].
% 34.50/34.76 exact (zenon_Hb0 zenon_Hac).
% 34.50/34.76 generalize (meaning_postulate_greater_strict (hazard_of_mortality zenon_TX_u zenon_TT2_bg)). zenon_intro zenon_Hb1.
% 34.50/34.76 generalize (zenon_Hb1 (hazard_of_mortality zenon_TX_u zenon_TT2_bg)). zenon_intro zenon_Hb2.
% 34.50/34.76 apply (zenon_notand_s _ _ zenon_Hb2); [ zenon_intro zenon_Haf | zenon_intro zenon_Haf ].
% 34.50/34.76 exact (zenon_Haf zenon_Hae).
% 34.50/34.76 exact (zenon_Haf zenon_Hae).
% 34.50/34.76 (* end of lemma zenon_L19_ *)
% 34.50/34.76 assert (zenon_L20_ : forall (zenon_TT2_bg : zenon_U) (zenon_TT3_t : zenon_U) (zenon_TX_u : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (eta) (age zenon_TX_u zenon_TT3_t))) -> (~((eta) = (age zenon_TX_u zenon_TT3_t))) -> (forall T : zenon_U, ((organization zenon_TX_u)/\(((smaller_or_equal (age zenon_TX_u T) (eta))->(has_immunity zenon_TX_u T))/\((greater (age zenon_TX_u T) (eta))->(~(has_immunity zenon_TX_u T)))))) -> (greater (age zenon_TX_u zenon_TT3_t) (age zenon_TX_u zenon_TT2_bg)) -> (~(greater (hazard_of_mortality zenon_TX_u zenon_TT3_t) (hazard_of_mortality zenon_TX_u zenon_TT2_bg))) -> (~(has_immunity zenon_TX_u zenon_TT2_bg)) -> (organization zenon_TX_u) -> False).
% 34.50/34.76 do 3 intro. intros zenon_H96 zenon_Hb3 zenon_Hb4 zenon_Hb5 zenon_H49 zenon_H82 zenon_H89 zenon_H2c.
% 34.50/34.76 generalize (assumption_4 zenon_TX_u). zenon_intro zenon_Hb6.
% 34.50/34.76 generalize (meaning_postulate_greater_comparable (eta)). zenon_intro zenon_Hb7.
% 34.50/34.76 generalize (zenon_Hb6 zenon_TT2_bg). zenon_intro zenon_Hb8.
% 34.50/34.76 generalize (zenon_Hb8 zenon_TT2_bg). zenon_intro zenon_Hb9.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_Hb9); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ].
% 34.50/34.76 apply (zenon_notand_s _ _ zenon_Hbb); [ zenon_intro zenon_H3a | zenon_intro zenon_Hbc ].
% 34.50/34.76 exact (zenon_H3a zenon_H2c).
% 34.50/34.76 apply (zenon_notand_s _ _ zenon_Hbc); [ zenon_intro zenon_H8f | zenon_intro zenon_H8f ].
% 34.50/34.76 exact (zenon_H8f zenon_H89).
% 34.50/34.76 exact (zenon_H8f zenon_H89).
% 34.50/34.76 apply (zenon_and_s _ _ zenon_Hba). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_Hbe); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hac ].
% 34.50/34.76 apply (zenon_notand_s _ _ zenon_Hbf); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hc0 ].
% 34.50/34.76 generalize (assumption_6 zenon_TX_u). zenon_intro zenon_H70.
% 34.50/34.76 generalize (assumption_5 zenon_TX_u). zenon_intro zenon_Hc2.
% 34.50/34.76 generalize (zenon_H70 zenon_TT2_bg). zenon_intro zenon_Hc3.
% 34.50/34.76 generalize (zenon_Hc2 zenon_TT2_bg). zenon_intro zenon_Hc4.
% 34.50/34.76 generalize (zenon_Hc4 zenon_TT2_bg). zenon_intro zenon_Hc5.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_Hc5); [ zenon_intro zenon_H3a | zenon_intro zenon_Hc6 ].
% 34.50/34.76 exact (zenon_H3a zenon_H2c).
% 34.50/34.76 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_Hc8); [ zenon_intro zenon_Hca | zenon_intro zenon_Hc9 ].
% 34.50/34.76 apply (zenon_notand_s _ _ zenon_Hca); [ zenon_intro zenon_H2b | zenon_intro zenon_Ha4 ].
% 34.50/34.76 generalize (assumption_12 zenon_TX_u). zenon_intro zenon_Hcb.
% 34.50/34.76 generalize (assumption_11 zenon_TX_u). zenon_intro zenon_H1.
% 34.50/34.76 generalize (zenon_H1 zenon_E). zenon_intro zenon_H4f.
% 34.50/34.76 generalize (zenon_Hcb zenon_TT2_bg). zenon_intro zenon_H48.
% 34.50/34.76 generalize (assumption_10 zenon_TX_u). zenon_intro zenon_H0.
% 34.50/34.76 generalize (zenon_H0 zenon_E). zenon_intro zenon_H2d.
% 34.50/34.76 generalize (zenon_Hb7 (age zenon_TX_u zenon_TT3_t)). zenon_intro zenon_Hcc.
% 34.50/34.76 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_Hce | zenon_intro zenon_Hcd ].
% 34.50/34.76 generalize (definition_smaller (eta)). zenon_intro zenon_Hcf.
% 34.50/34.76 generalize (zenon_Hcf (age zenon_TX_u zenon_TT3_t)). zenon_intro zenon_Hd0.
% 34.50/34.76 apply (zenon_equiv_s _ _ zenon_Hd0); [ zenon_intro zenon_Hd3; zenon_intro zenon_Hd2 | zenon_intro zenon_Hce; zenon_intro zenon_Hd1 ].
% 34.50/34.76 exact (zenon_Hd3 zenon_Hce).
% 34.50/34.76 generalize (zenon_H4f zenon_TT2_bg). zenon_intro zenon_Hd4.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_Hd4); [ zenon_intro zenon_H3a | zenon_intro zenon_H60 ].
% 34.50/34.76 exact (zenon_H3a zenon_H2c).
% 34.50/34.76 generalize (zenon_Hb5 zenon_TT3_t). zenon_intro zenon_Hd5.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_Hd5). zenon_intro zenon_H2c. zenon_intro zenon_Hd6.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_Hd6). zenon_intro zenon_Hd8. zenon_intro zenon_Hd7.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_Hd7); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H88 ].
% 34.50/34.76 exact (zenon_Hd2 zenon_Hd1).
% 34.50/34.76 generalize (meaning_postulate_greater_comparable (external_ties zenon_TX_u zenon_TT2_bg)). zenon_intro zenon_H53.
% 34.50/34.76 generalize (zenon_H2d zenon_TT2_bg). zenon_intro zenon_Hd9.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_Hd9); [ zenon_intro zenon_H3a | zenon_intro zenon_H2a ].
% 34.50/34.76 exact (zenon_H3a zenon_H2c).
% 34.50/34.76 generalize (meaning_postulate_greater_comparable (stock_of_knowledge zenon_TX_u zenon_TT2_bg)). zenon_intro zenon_H1c.
% 34.50/34.76 generalize (zenon_Hb6 zenon_TT3_t). zenon_intro zenon_H87.
% 34.50/34.76 generalize (zenon_H87 zenon_TT3_t). zenon_intro zenon_Hda.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_Hda); [ zenon_intro zenon_Hdc | zenon_intro zenon_Hdb ].
% 34.50/34.76 apply (zenon_notand_s _ _ zenon_Hdc); [ zenon_intro zenon_H3a | zenon_intro zenon_Hdd ].
% 34.50/34.76 exact (zenon_H3a zenon_H2c).
% 34.50/34.76 apply (zenon_notand_s _ _ zenon_Hdd); [ zenon_intro zenon_H90 | zenon_intro zenon_H90 ].
% 34.50/34.76 exact (zenon_H90 zenon_H88).
% 34.50/34.76 exact (zenon_H90 zenon_H88).
% 34.50/34.76 apply (zenon_and_s _ _ zenon_Hdb). zenon_intro zenon_Hdf. zenon_intro zenon_Hde.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_Hde). zenon_intro zenon_He1. zenon_intro zenon_He0.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_He1); [ zenon_intro zenon_He2 | zenon_intro zenon_H9c ].
% 34.50/34.76 apply (zenon_notand_s _ _ zenon_He2); [ zenon_intro zenon_H12 | zenon_intro zenon_H71 ].
% 34.50/34.76 apply (zenon_L1_ zenon_TT3_t zenon_TX_u); trivial.
% 34.50/34.76 generalize (zenon_Hc4 zenon_TT3_t). zenon_intro zenon_He3.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_He3); [ zenon_intro zenon_H3a | zenon_intro zenon_He4 ].
% 34.50/34.76 exact (zenon_H3a zenon_H2c).
% 34.50/34.76 apply (zenon_and_s _ _ zenon_He4). zenon_intro zenon_He6. zenon_intro zenon_He5.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_He5). zenon_intro zenon_He8. zenon_intro zenon_He7.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_He8); [ zenon_intro zenon_Hea | zenon_intro zenon_He9 ].
% 34.50/34.76 apply (zenon_notand_s _ _ zenon_Hea); [ zenon_intro zenon_H2e | zenon_intro zenon_H4a ].
% 34.50/34.76 apply (zenon_L3_ zenon_TT3_t zenon_TT2_bg zenon_TX_u); trivial.
% 34.50/34.76 apply (zenon_L4_ zenon_TT3_t zenon_TT2_bg zenon_TX_u); trivial.
% 34.50/34.76 generalize (definition_smaller (capability zenon_TX_u zenon_TT3_t)). zenon_intro zenon_Heb.
% 34.50/34.76 generalize (zenon_Heb (capability zenon_TX_u zenon_TT2_bg)). zenon_intro zenon_Hec.
% 34.50/34.76 apply (zenon_equiv_s _ _ zenon_Hec); [ zenon_intro zenon_Hed; zenon_intro zenon_H94 | zenon_intro zenon_He9; zenon_intro zenon_H8a ].
% 34.50/34.76 exact (zenon_Hed zenon_He9).
% 34.50/34.76 generalize (zenon_Hc3 zenon_TT3_t). zenon_intro zenon_Hee.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_Hee); [ zenon_intro zenon_H3a | zenon_intro zenon_Hef ].
% 34.50/34.76 exact (zenon_H3a zenon_H2c).
% 34.50/34.76 apply (zenon_and_s _ _ zenon_Hef). zenon_intro zenon_Hf0. zenon_intro zenon_H95.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_H55 | zenon_intro zenon_H78 ].
% 34.50/34.76 generalize (zenon_H70 zenon_TT3_t). zenon_intro zenon_H72.
% 34.50/34.76 apply (zenon_L16_ zenon_TT2_bg zenon_TT3_t zenon_TX_u); trivial.
% 34.50/34.76 apply (zenon_L13_ zenon_TT2_bg zenon_TT3_t zenon_TX_u); trivial.
% 34.50/34.76 apply (zenon_L17_ zenon_TT3_t zenon_TX_u); trivial.
% 34.50/34.76 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf1 ].
% 34.50/34.76 exact (zenon_Hb4 zenon_Hf2).
% 34.50/34.76 exact (zenon_Hb3 zenon_Hf1).
% 34.50/34.76 apply (zenon_L18_ zenon_TT2_bg zenon_TX_u); trivial.
% 34.50/34.76 exact (zenon_Hc1 zenon_Hc9).
% 34.50/34.76 generalize (definition_greater_or_equal (position zenon_TX_u zenon_TT2_bg)). zenon_intro zenon_H7a.
% 34.50/34.76 generalize (zenon_H7a (position zenon_TX_u zenon_TT2_bg)). zenon_intro zenon_Hf3.
% 34.50/34.76 apply (zenon_equiv_s _ _ zenon_Hf3); [ zenon_intro zenon_Hc0; zenon_intro zenon_Hf6 | zenon_intro zenon_Hf5; zenon_intro zenon_Hf4 ].
% 34.50/34.76 apply (zenon_notor_s _ _ zenon_Hf6). zenon_intro zenon_Hf8. zenon_intro zenon_Hf7.
% 34.50/34.76 apply zenon_Hf7. apply refl_equal.
% 34.50/34.76 exact (zenon_Hc0 zenon_Hf5).
% 34.50/34.76 apply (zenon_L19_ zenon_TT2_bg zenon_TX_u); trivial.
% 34.50/34.76 (* end of lemma zenon_L20_ *)
% 34.50/34.76 assert (zenon_L21_ : forall (zenon_TT2_bg : zenon_U) (zenon_TX_u : zenon_U), ((greater (age zenon_TX_u zenon_TT2_bg) (eta))->(~(has_immunity zenon_TX_u zenon_TT2_bg))) -> (has_immunity zenon_TX_u zenon_TT2_bg) -> (greater (age zenon_TX_u zenon_TT2_bg) (eta)) -> False).
% 34.50/34.76 do 2 intro. intros zenon_Hf9 zenon_Hfa zenon_Hfb.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_Hf9); [ zenon_intro zenon_Hfc | zenon_intro zenon_H89 ].
% 34.50/34.76 exact (zenon_Hfc zenon_Hfb).
% 34.50/34.76 exact (zenon_H89 zenon_Hfa).
% 34.50/34.76 (* end of lemma zenon_L21_ *)
% 34.50/34.76 assert (zenon_L22_ : forall (zenon_TT2_bg : zenon_U) (zenon_TT3_t : zenon_U) (zenon_TX_u : 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_u)/\(((smaller_or_equal (age zenon_TX_u T) (eta))->(has_immunity zenon_TX_u T))/\((greater (age zenon_TX_u T) (eta))->(~(has_immunity zenon_TX_u T)))))) -> (greater (age zenon_TX_u zenon_TT3_t) (age zenon_TX_u zenon_TT2_bg)) -> (~(greater (hazard_of_mortality zenon_TX_u zenon_TT3_t) (hazard_of_mortality zenon_TX_u zenon_TT2_bg))) -> (greater (age zenon_TX_u zenon_TT2_bg) (eta)) -> False).
% 34.50/34.76 do 3 intro. intros zenon_H96 zenon_Hb5 zenon_H49 zenon_H82 zenon_Hfb.
% 34.50/34.76 generalize (zenon_Hb5 zenon_TT2_bg). zenon_intro zenon_Hfd.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_Hfd). zenon_intro zenon_H2c. zenon_intro zenon_Hfe.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_Hfe). zenon_intro zenon_Hff. zenon_intro zenon_Hf9.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_Hff); [ zenon_intro zenon_H100 | zenon_intro zenon_Hfa ].
% 34.50/34.76 generalize (definition_smaller_or_equal (age zenon_TX_u zenon_TT2_bg)). zenon_intro zenon_H101.
% 34.50/34.76 generalize (zenon_H101 (eta)). zenon_intro zenon_H102.
% 34.50/34.76 apply (zenon_equiv_s _ _ zenon_H102); [ zenon_intro zenon_H100; zenon_intro zenon_H105 | zenon_intro zenon_H104; zenon_intro zenon_H103 ].
% 34.50/34.76 apply (zenon_notor_s _ _ zenon_H105). zenon_intro zenon_H107. zenon_intro zenon_H106.
% 34.50/34.76 generalize (definition_smaller (age zenon_TX_u zenon_TT2_bg)). zenon_intro zenon_H108.
% 34.50/34.76 generalize (zenon_H108 (eta)). zenon_intro zenon_H109.
% 34.50/34.76 apply (zenon_equiv_s _ _ zenon_H109); [ zenon_intro zenon_H107; zenon_intro zenon_H10c | zenon_intro zenon_H10b; zenon_intro zenon_H10a ].
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_Hf9); [ zenon_intro zenon_Hfc | zenon_intro zenon_H89 ].
% 34.50/34.76 exact (zenon_Hfc zenon_Hfb).
% 34.50/34.76 elim (classic ((~((eta) = (age zenon_TX_u zenon_TT3_t)))/\(~(greater (eta) (age zenon_TX_u zenon_TT3_t))))); [ zenon_intro zenon_H10d | zenon_intro zenon_H10e ].
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H10d). zenon_intro zenon_Hb4. zenon_intro zenon_Hb3.
% 34.50/34.76 apply (zenon_L20_ zenon_TT2_bg zenon_TT3_t zenon_TX_u); trivial.
% 34.50/34.76 cut ((greater (age zenon_TX_u zenon_TT3_t) (age zenon_TX_u zenon_TT2_bg)) = (greater (eta) (age zenon_TX_u zenon_TT2_bg))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H10c.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_H49.
% 34.50/34.76 cut (((age zenon_TX_u zenon_TT2_bg) = (age zenon_TX_u zenon_TT2_bg))); [idtac | apply NNPP; zenon_intro zenon_H10f].
% 34.50/34.76 cut (((age zenon_TX_u zenon_TT3_t) = (eta))); [idtac | apply NNPP; zenon_intro zenon_H110].
% 34.50/34.76 congruence.
% 34.50/34.76 apply (zenon_notand_s _ _ zenon_H10e); [ zenon_intro zenon_H112 | zenon_intro zenon_H111 ].
% 34.50/34.76 apply zenon_H112. zenon_intro zenon_Hf2.
% 34.50/34.76 elim (classic ((eta) = (eta))); [ zenon_intro zenon_H113 | zenon_intro zenon_H114 ].
% 34.50/34.76 cut (((eta) = (eta)) = ((age zenon_TX_u zenon_TT3_t) = (eta))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H110.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_H113.
% 34.50/34.76 cut (((eta) = (eta))); [idtac | apply NNPP; zenon_intro zenon_H114].
% 34.50/34.76 cut (((eta) = (age zenon_TX_u zenon_TT3_t))); [idtac | apply NNPP; zenon_intro zenon_Hb4].
% 34.50/34.76 congruence.
% 34.50/34.76 exact (zenon_Hb4 zenon_Hf2).
% 34.50/34.76 apply zenon_H114. apply refl_equal.
% 34.50/34.76 apply zenon_H114. apply refl_equal.
% 34.50/34.76 apply zenon_H111. zenon_intro zenon_Hf1.
% 34.50/34.76 generalize (zenon_H96 (eta)). zenon_intro zenon_H115.
% 34.50/34.76 generalize (zenon_H115 (age zenon_TX_u zenon_TT3_t)). zenon_intro zenon_H116.
% 34.50/34.76 generalize (zenon_H116 (age zenon_TX_u zenon_TT2_bg)). zenon_intro zenon_H117.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H117); [ zenon_intro zenon_Hb3 | zenon_intro zenon_H118 ].
% 34.50/34.76 exact (zenon_Hb3 zenon_Hf1).
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H118); [ zenon_intro zenon_H4e | zenon_intro zenon_H10a ].
% 34.50/34.76 exact (zenon_H4e zenon_H49).
% 34.50/34.76 exact (zenon_H10c zenon_H10a).
% 34.50/34.76 apply zenon_H10f. apply refl_equal.
% 34.50/34.76 exact (zenon_H107 zenon_H10b).
% 34.50/34.76 exact (zenon_H100 zenon_H104).
% 34.50/34.76 apply (zenon_L21_ zenon_TT2_bg zenon_TX_u); trivial.
% 34.50/34.76 (* end of lemma zenon_L22_ *)
% 34.50/34.76 assert (zenon_L23_ : forall (zenon_TT1_kx : zenon_U) (zenon_TX_u : zenon_U), (greater (eta) (age zenon_TX_u zenon_TT1_kx)) -> (~(smaller_or_equal (age zenon_TX_u zenon_TT1_kx) (eta))) -> False).
% 34.50/34.76 do 2 intro. intros zenon_H119 zenon_H11a.
% 34.50/34.76 generalize (definition_smaller_or_equal (age zenon_TX_u zenon_TT1_kx)). zenon_intro zenon_H11c.
% 34.50/34.76 generalize (zenon_H11c (eta)). zenon_intro zenon_H11d.
% 34.50/34.76 apply (zenon_equiv_s _ _ zenon_H11d); [ zenon_intro zenon_H11a; zenon_intro zenon_H120 | zenon_intro zenon_H11f; zenon_intro zenon_H11e ].
% 34.50/34.76 apply (zenon_notor_s _ _ zenon_H120). zenon_intro zenon_H122. zenon_intro zenon_H121.
% 34.50/34.76 generalize (definition_smaller (age zenon_TX_u zenon_TT1_kx)). zenon_intro zenon_H123.
% 34.50/34.76 generalize (zenon_H123 (eta)). zenon_intro zenon_H124.
% 34.50/34.76 apply (zenon_equiv_s _ _ zenon_H124); [ zenon_intro zenon_H122; zenon_intro zenon_H126 | zenon_intro zenon_H125; zenon_intro zenon_H119 ].
% 34.50/34.76 exact (zenon_H126 zenon_H119).
% 34.50/34.76 exact (zenon_H122 zenon_H125).
% 34.50/34.76 exact (zenon_H11a zenon_H11f).
% 34.50/34.76 (* end of lemma zenon_L23_ *)
% 34.50/34.76 assert (zenon_L24_ : forall (zenon_TT1_kx : zenon_U) (zenon_TT2_bg : zenon_U) (zenon_TX_u : zenon_U), (forall T : zenon_U, ((organization zenon_TX_u)/\(((smaller_or_equal (age zenon_TX_u T) (eta))->(has_immunity zenon_TX_u T))/\((greater (age zenon_TX_u T) (eta))->(~(has_immunity zenon_TX_u T)))))) -> (~(greater (hazard_of_mortality zenon_TX_u zenon_TT2_bg) (hazard_of_mortality zenon_TX_u zenon_TT1_kx))) -> (has_immunity zenon_TX_u zenon_TT1_kx) -> (greater (age zenon_TX_u zenon_TT2_bg) (eta)) -> False).
% 34.50/34.76 do 3 intro. intros zenon_Hb5 zenon_H127 zenon_H128 zenon_Hfb.
% 34.50/34.76 generalize (zenon_Hb5 zenon_TT2_bg). zenon_intro zenon_Hfd.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_Hfd). zenon_intro zenon_H2c. zenon_intro zenon_Hfe.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_Hfe). zenon_intro zenon_Hff. zenon_intro zenon_Hf9.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_Hf9); [ zenon_intro zenon_Hfc | zenon_intro zenon_H89 ].
% 34.50/34.76 exact (zenon_Hfc zenon_Hfb).
% 34.50/34.76 generalize (assumption_3 zenon_TX_u). zenon_intro zenon_H129.
% 34.50/34.76 generalize (zenon_H129 zenon_TT1_kx). zenon_intro zenon_H12a.
% 34.50/34.76 generalize (zenon_H12a zenon_TT2_bg). zenon_intro zenon_H12b.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H12b); [ zenon_intro zenon_H12d | zenon_intro zenon_H12c ].
% 34.50/34.76 apply (zenon_notand_s _ _ zenon_H12d); [ zenon_intro zenon_H3a | zenon_intro zenon_H12e ].
% 34.50/34.76 exact (zenon_H3a zenon_H2c).
% 34.50/34.76 apply (zenon_notand_s _ _ zenon_H12e); [ zenon_intro zenon_H12f | zenon_intro zenon_H8f ].
% 34.50/34.76 exact (zenon_H12f zenon_H128).
% 34.50/34.76 exact (zenon_H8f zenon_H89).
% 34.50/34.76 exact (zenon_H127 zenon_H12c).
% 34.50/34.76 (* end of lemma zenon_L24_ *)
% 34.50/34.76 assert (zenon_L25_ : forall (zenon_TT1_kx : zenon_U) (zenon_TT2_bg : zenon_U) (zenon_TX_u : zenon_U), (greater (age zenon_TX_u zenon_TT2_bg) (eta)) -> (~(greater (hazard_of_mortality zenon_TX_u zenon_TT2_bg) (hazard_of_mortality zenon_TX_u zenon_TT1_kx))) -> (forall T : zenon_U, ((organization zenon_TX_u)/\(((smaller_or_equal (age zenon_TX_u T) (eta))->(has_immunity zenon_TX_u T))/\((greater (age zenon_TX_u T) (eta))->(~(has_immunity zenon_TX_u T)))))) -> (greater (eta) (age zenon_TX_u zenon_TT1_kx)) -> False).
% 34.50/34.76 do 3 intro. intros zenon_Hfb zenon_H127 zenon_Hb5 zenon_H119.
% 34.50/34.76 generalize (zenon_Hb5 zenon_TT1_kx). zenon_intro zenon_H130.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H130). zenon_intro zenon_H2c. zenon_intro zenon_H131.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H131). zenon_intro zenon_H133. zenon_intro zenon_H132.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H133); [ zenon_intro zenon_H11a | zenon_intro zenon_H128 ].
% 34.50/34.76 apply (zenon_L23_ zenon_TT1_kx zenon_TX_u); trivial.
% 34.50/34.76 apply (zenon_L24_ zenon_TT1_kx zenon_TT2_bg zenon_TX_u); trivial.
% 34.50/34.76 (* end of lemma zenon_L25_ *)
% 34.50/34.76 assert (zenon_L26_ : (~((eta) = (eta))) -> False).
% 34.50/34.76 do 0 intro. intros zenon_H114.
% 34.50/34.76 apply zenon_H114. apply refl_equal.
% 34.50/34.76 (* end of lemma zenon_L26_ *)
% 34.50/34.76 assert (zenon_L27_ : forall (zenon_TT1_kx : zenon_U) (zenon_TT0_ly : zenon_U) (zenon_TX_u : zenon_U), (organization zenon_TX_u) -> (has_immunity zenon_TX_u zenon_TT0_ly) -> (has_immunity zenon_TX_u zenon_TT1_kx) -> (~((hazard_of_mortality zenon_TX_u zenon_TT1_kx) = (hazard_of_mortality zenon_TX_u zenon_TT0_ly))) -> False).
% 34.50/34.76 do 3 intro. intros zenon_H2c zenon_H134 zenon_H128 zenon_H135.
% 34.50/34.76 generalize (assumption_2 zenon_TX_u). zenon_intro zenon_H137.
% 34.50/34.76 generalize (zenon_H137 zenon_TT0_ly). zenon_intro zenon_H138.
% 34.50/34.76 generalize (zenon_H138 zenon_TT1_kx). zenon_intro zenon_H139.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H139); [ zenon_intro zenon_H13b | zenon_intro zenon_H13a ].
% 34.50/34.76 apply (zenon_notand_s _ _ zenon_H13b); [ zenon_intro zenon_H3a | zenon_intro zenon_H13c ].
% 34.50/34.76 exact (zenon_H3a zenon_H2c).
% 34.50/34.76 apply (zenon_notand_s _ _ zenon_H13c); [ zenon_intro zenon_H13d | zenon_intro zenon_H12f ].
% 34.50/34.76 exact (zenon_H13d zenon_H134).
% 34.50/34.76 exact (zenon_H12f zenon_H128).
% 34.50/34.76 apply zenon_H135. apply sym_equal. exact zenon_H13a.
% 34.50/34.76 (* end of lemma zenon_L27_ *)
% 34.50/34.76 assert (zenon_L28_ : forall (zenon_TT1_kx : zenon_U) (zenon_TX_u : zenon_U), ((age zenon_TX_u zenon_TT1_kx) = (eta)) -> (~(smaller_or_equal (age zenon_TX_u zenon_TT1_kx) (eta))) -> False).
% 34.50/34.76 do 2 intro. intros zenon_H13e zenon_H11a.
% 34.50/34.76 generalize (definition_smaller_or_equal (age zenon_TX_u zenon_TT1_kx)). zenon_intro zenon_H11c.
% 34.50/34.76 generalize (zenon_H11c (eta)). zenon_intro zenon_H11d.
% 34.50/34.76 apply (zenon_equiv_s _ _ zenon_H11d); [ zenon_intro zenon_H11a; zenon_intro zenon_H120 | zenon_intro zenon_H11f; zenon_intro zenon_H11e ].
% 34.50/34.76 apply (zenon_notor_s _ _ zenon_H120). zenon_intro zenon_H122. zenon_intro zenon_H121.
% 34.50/34.76 exact (zenon_H121 zenon_H13e).
% 34.50/34.76 exact (zenon_H11a zenon_H11f).
% 34.50/34.76 (* end of lemma zenon_L28_ *)
% 34.50/34.76 assert (zenon_L29_ : forall (zenon_TT2_bg : zenon_U) (zenon_TT3_t : zenon_U) (zenon_TX_u : 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_u zenon_TT3_t) (hazard_of_mortality zenon_TX_u zenon_TT2_bg))) -> (greater (age zenon_TX_u zenon_TT3_t) (age zenon_TX_u zenon_TT2_bg)) -> (forall T : zenon_U, ((organization zenon_TX_u)/\(((smaller_or_equal (age zenon_TX_u T) (eta))->(has_immunity zenon_TX_u T))/\((greater (age zenon_TX_u T) (eta))->(~(has_immunity zenon_TX_u T)))))) -> (~((eta) = (age zenon_TX_u zenon_TT3_t))) -> (~(greater (eta) (age zenon_TX_u zenon_TT3_t))) -> (greater (age zenon_TX_u zenon_TT2_bg) (eta)) -> False).
% 34.50/34.76 do 3 intro. intros zenon_H96 zenon_H82 zenon_H49 zenon_Hb5 zenon_Hb4 zenon_Hb3 zenon_Hfb.
% 34.50/34.76 generalize (zenon_Hb5 zenon_TT2_bg). zenon_intro zenon_Hfd.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_Hfd). zenon_intro zenon_H2c. zenon_intro zenon_Hfe.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_Hfe). zenon_intro zenon_Hff. zenon_intro zenon_Hf9.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_Hf9); [ zenon_intro zenon_Hfc | zenon_intro zenon_H89 ].
% 34.50/34.76 exact (zenon_Hfc zenon_Hfb).
% 34.50/34.76 apply (zenon_L20_ zenon_TT2_bg zenon_TT3_t zenon_TX_u); trivial.
% 34.50/34.76 (* end of lemma zenon_L29_ *)
% 34.50/34.76 assert (zenon_L30_ : forall (zenon_TT3_t : zenon_U) (zenon_TT2_bg : zenon_U) (zenon_TX_u : 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_u zenon_TT2_bg) (eta)) -> (~(greater (eta) (age zenon_TX_u zenon_TT3_t))) -> (forall T : zenon_U, ((organization zenon_TX_u)/\(((smaller_or_equal (age zenon_TX_u T) (eta))->(has_immunity zenon_TX_u T))/\((greater (age zenon_TX_u T) (eta))->(~(has_immunity zenon_TX_u T)))))) -> (greater (age zenon_TX_u zenon_TT3_t) (age zenon_TX_u zenon_TT2_bg)) -> (~(greater (hazard_of_mortality zenon_TX_u zenon_TT3_t) (hazard_of_mortality zenon_TX_u zenon_TT2_bg))) -> False).
% 34.50/34.76 do 3 intro. intros zenon_H96 zenon_Hfb zenon_Hb3 zenon_Hb5 zenon_H49 zenon_H82.
% 34.50/34.76 elim (classic ((~((eta) = (age zenon_TX_u zenon_TT3_t)))/\(~(greater (eta) (age zenon_TX_u zenon_TT3_t))))); [ zenon_intro zenon_H10d | zenon_intro zenon_H10e ].
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H10d). zenon_intro zenon_Hb4. zenon_intro zenon_Hb3.
% 34.50/34.76 apply (zenon_L29_ zenon_TT2_bg zenon_TT3_t zenon_TX_u); trivial.
% 34.50/34.76 elim (classic (greater (age zenon_TX_u zenon_TT2_bg) (age zenon_TX_u zenon_TT3_t))); [ zenon_intro zenon_H13f | zenon_intro zenon_H140 ].
% 34.50/34.76 generalize (zenon_H96 (age zenon_TX_u zenon_TT3_t)). zenon_intro zenon_H141.
% 34.50/34.76 generalize (zenon_H141 (age zenon_TX_u zenon_TT2_bg)). zenon_intro zenon_H142.
% 34.50/34.76 generalize (zenon_H142 (age zenon_TX_u zenon_TT3_t)). zenon_intro zenon_H143.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H143); [ zenon_intro zenon_H4e | zenon_intro zenon_H144 ].
% 34.50/34.76 exact (zenon_H4e zenon_H49).
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H144); [ zenon_intro zenon_H140 | zenon_intro zenon_H145 ].
% 34.50/34.76 exact (zenon_H140 zenon_H13f).
% 34.50/34.76 cut ((greater (age zenon_TX_u zenon_TT3_t) (age zenon_TX_u zenon_TT3_t)) = (greater (eta) (age zenon_TX_u zenon_TT3_t))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_Hb3.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_H145.
% 34.50/34.76 cut (((age zenon_TX_u zenon_TT3_t) = (age zenon_TX_u zenon_TT3_t))); [idtac | apply NNPP; zenon_intro zenon_H146].
% 34.50/34.76 cut (((age zenon_TX_u zenon_TT3_t) = (eta))); [idtac | apply NNPP; zenon_intro zenon_H110].
% 34.50/34.76 congruence.
% 34.50/34.76 apply (zenon_notand_s _ _ zenon_H10e); [ zenon_intro zenon_H112 | zenon_intro zenon_H111 ].
% 34.50/34.76 apply zenon_H112. zenon_intro zenon_Hf2.
% 34.50/34.76 apply zenon_H110. apply sym_equal. exact zenon_Hf2.
% 34.50/34.76 exact (zenon_H111 zenon_Hb3).
% 34.50/34.76 apply zenon_H146. apply refl_equal.
% 34.50/34.76 elim (classic ((eta) = (age zenon_TX_u zenon_TT3_t))); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hb4 ].
% 34.50/34.76 cut ((greater (age zenon_TX_u zenon_TT2_bg) (eta)) = (greater (age zenon_TX_u zenon_TT2_bg) (age zenon_TX_u zenon_TT3_t))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H140.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_Hfb.
% 34.50/34.76 cut (((eta) = (age zenon_TX_u zenon_TT3_t))); [idtac | apply NNPP; zenon_intro zenon_Hb4].
% 34.50/34.76 cut (((age zenon_TX_u zenon_TT2_bg) = (age zenon_TX_u zenon_TT2_bg))); [idtac | apply NNPP; zenon_intro zenon_H10f].
% 34.50/34.76 congruence.
% 34.50/34.76 apply zenon_H10f. apply refl_equal.
% 34.50/34.76 exact (zenon_Hb4 zenon_Hf2).
% 34.50/34.76 elim (classic (greater (eta) (age zenon_TX_u zenon_TT3_t))); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hb3 ].
% 34.50/34.76 generalize (zenon_H96 (age zenon_TX_u zenon_TT2_bg)). zenon_intro zenon_H147.
% 34.50/34.76 generalize (zenon_H147 (eta)). zenon_intro zenon_H148.
% 34.50/34.76 generalize (zenon_H148 (age zenon_TX_u zenon_TT3_t)). zenon_intro zenon_H149.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H149); [ zenon_intro zenon_Hfc | zenon_intro zenon_H14a ].
% 34.50/34.76 exact (zenon_Hfc zenon_Hfb).
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H14a); [ zenon_intro zenon_Hb3 | zenon_intro zenon_H13f ].
% 34.50/34.76 exact (zenon_Hb3 zenon_Hf1).
% 34.50/34.76 exact (zenon_H140 zenon_H13f).
% 34.50/34.76 apply (zenon_L29_ zenon_TT2_bg zenon_TT3_t zenon_TX_u); trivial.
% 34.50/34.76 (* end of lemma zenon_L30_ *)
% 34.50/34.76 assert (zenon_L31_ : forall (zenon_TT2_bg : zenon_U) (zenon_TT3_t : zenon_U) (zenon_TT1_kx : zenon_U) (zenon_TX_u : 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_u zenon_TT1_kx) = (eta)) -> (~(greater (age zenon_TX_u zenon_TT1_kx) (age zenon_TX_u zenon_TT3_t))) -> (greater (age zenon_TX_u zenon_TT2_bg) (eta)) -> (forall T : zenon_U, ((organization zenon_TX_u)/\(((smaller_or_equal (age zenon_TX_u T) (eta))->(has_immunity zenon_TX_u T))/\((greater (age zenon_TX_u T) (eta))->(~(has_immunity zenon_TX_u T)))))) -> (greater (age zenon_TX_u zenon_TT3_t) (age zenon_TX_u zenon_TT2_bg)) -> (~(greater (hazard_of_mortality zenon_TX_u zenon_TT3_t) (hazard_of_mortality zenon_TX_u zenon_TT2_bg))) -> False).
% 34.50/34.76 do 4 intro. intros zenon_H96 zenon_H13e zenon_H14b zenon_Hfb zenon_Hb5 zenon_H49 zenon_H82.
% 34.50/34.76 elim (classic (greater (eta) (age zenon_TX_u zenon_TT3_t))); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hb3 ].
% 34.50/34.76 cut ((greater (eta) (age zenon_TX_u zenon_TT3_t)) = (greater (age zenon_TX_u zenon_TT1_kx) (age zenon_TX_u zenon_TT3_t))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H14b.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_Hf1.
% 34.50/34.76 cut (((age zenon_TX_u zenon_TT3_t) = (age zenon_TX_u zenon_TT3_t))); [idtac | apply NNPP; zenon_intro zenon_H146].
% 34.50/34.76 cut (((eta) = (age zenon_TX_u zenon_TT1_kx))); [idtac | apply NNPP; zenon_intro zenon_H14c].
% 34.50/34.76 congruence.
% 34.50/34.76 elim (classic ((age zenon_TX_u zenon_TT1_kx) = (age zenon_TX_u zenon_TT1_kx))); [ zenon_intro zenon_H14d | zenon_intro zenon_H14e ].
% 34.50/34.76 cut (((age zenon_TX_u zenon_TT1_kx) = (age zenon_TX_u zenon_TT1_kx)) = ((eta) = (age zenon_TX_u zenon_TT1_kx))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H14c.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_H14d.
% 34.50/34.76 cut (((age zenon_TX_u zenon_TT1_kx) = (age zenon_TX_u zenon_TT1_kx))); [idtac | apply NNPP; zenon_intro zenon_H14e].
% 34.50/34.76 cut (((age zenon_TX_u zenon_TT1_kx) = (eta))); [idtac | apply NNPP; zenon_intro zenon_H121].
% 34.50/34.76 congruence.
% 34.50/34.76 exact (zenon_H121 zenon_H13e).
% 34.50/34.76 apply zenon_H14e. apply refl_equal.
% 34.50/34.76 apply zenon_H14e. apply refl_equal.
% 34.50/34.76 apply zenon_H146. apply refl_equal.
% 34.50/34.76 apply (zenon_L30_ zenon_TT3_t zenon_TT2_bg zenon_TX_u); trivial.
% 34.50/34.76 (* end of lemma zenon_L31_ *)
% 34.50/34.76 assert (zenon_L32_ : forall (zenon_TT1_kx : zenon_U) (zenon_TT3_t : zenon_U) (zenon_TT2_bg : zenon_U) (zenon_TX_u : zenon_U), (greater (age zenon_TX_u zenon_TT2_bg) (eta)) -> (forall T : zenon_U, ((organization zenon_TX_u)/\(((smaller_or_equal (age zenon_TX_u T) (eta))->(has_immunity zenon_TX_u T))/\((greater (age zenon_TX_u T) (eta))->(~(has_immunity zenon_TX_u T)))))) -> (~(greater (hazard_of_mortality zenon_TX_u zenon_TT3_t) (hazard_of_mortality zenon_TX_u zenon_TT2_bg))) -> ((age zenon_TX_u zenon_TT1_kx) = (eta)) -> (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_u zenon_TT1_kx) (age zenon_TX_u zenon_TT2_bg))) -> (greater (age zenon_TX_u zenon_TT3_t) (age zenon_TX_u zenon_TT2_bg)) -> False).
% 34.50/34.76 do 4 intro. intros zenon_Hfb zenon_Hb5 zenon_H82 zenon_H13e zenon_H96 zenon_H14f zenon_H49.
% 34.50/34.76 elim (classic ((~((age zenon_TX_u zenon_TT1_kx) = (age zenon_TX_u zenon_TT3_t)))/\(~(greater (age zenon_TX_u zenon_TT1_kx) (age zenon_TX_u zenon_TT3_t))))); [ zenon_intro zenon_H150 | zenon_intro zenon_H151 ].
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H150). zenon_intro zenon_H152. zenon_intro zenon_H14b.
% 34.50/34.76 apply (zenon_L31_ zenon_TT2_bg zenon_TT3_t zenon_TT1_kx zenon_TX_u); trivial.
% 34.50/34.76 cut ((greater (age zenon_TX_u zenon_TT3_t) (age zenon_TX_u zenon_TT2_bg)) = (greater (age zenon_TX_u zenon_TT1_kx) (age zenon_TX_u zenon_TT2_bg))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H14f.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_H49.
% 34.50/34.76 cut (((age zenon_TX_u zenon_TT2_bg) = (age zenon_TX_u zenon_TT2_bg))); [idtac | apply NNPP; zenon_intro zenon_H10f].
% 34.50/34.76 cut (((age zenon_TX_u zenon_TT3_t) = (age zenon_TX_u zenon_TT1_kx))); [idtac | apply NNPP; zenon_intro zenon_H153].
% 34.50/34.76 congruence.
% 34.50/34.76 apply (zenon_notand_s _ _ zenon_H151); [ zenon_intro zenon_H155 | zenon_intro zenon_H154 ].
% 34.50/34.76 apply zenon_H155. zenon_intro zenon_H156.
% 34.50/34.76 elim (classic ((age zenon_TX_u zenon_TT1_kx) = (age zenon_TX_u zenon_TT1_kx))); [ zenon_intro zenon_H14d | zenon_intro zenon_H14e ].
% 34.50/34.76 cut (((age zenon_TX_u zenon_TT1_kx) = (age zenon_TX_u zenon_TT1_kx)) = ((age zenon_TX_u zenon_TT3_t) = (age zenon_TX_u zenon_TT1_kx))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H153.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_H14d.
% 34.50/34.76 cut (((age zenon_TX_u zenon_TT1_kx) = (age zenon_TX_u zenon_TT1_kx))); [idtac | apply NNPP; zenon_intro zenon_H14e].
% 34.50/34.76 cut (((age zenon_TX_u zenon_TT1_kx) = (age zenon_TX_u zenon_TT3_t))); [idtac | apply NNPP; zenon_intro zenon_H152].
% 34.50/34.76 congruence.
% 34.50/34.76 exact (zenon_H152 zenon_H156).
% 34.50/34.76 apply zenon_H14e. apply refl_equal.
% 34.50/34.76 apply zenon_H14e. apply refl_equal.
% 34.50/34.76 apply zenon_H154. zenon_intro zenon_H157.
% 34.50/34.76 generalize (zenon_H96 (age zenon_TX_u zenon_TT1_kx)). zenon_intro zenon_H158.
% 34.50/34.76 generalize (zenon_H158 (age zenon_TX_u zenon_TT3_t)). zenon_intro zenon_H159.
% 34.50/34.76 generalize (zenon_H159 (age zenon_TX_u zenon_TT2_bg)). zenon_intro zenon_H15a.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H15a); [ zenon_intro zenon_H14b | zenon_intro zenon_H15b ].
% 34.50/34.76 exact (zenon_H14b zenon_H157).
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H15b); [ zenon_intro zenon_H4e | zenon_intro zenon_H15c ].
% 34.50/34.76 exact (zenon_H4e zenon_H49).
% 34.50/34.76 exact (zenon_H14f zenon_H15c).
% 34.50/34.76 apply zenon_H10f. apply refl_equal.
% 34.50/34.76 (* end of lemma zenon_L32_ *)
% 34.50/34.76 assert (zenon_L33_ : forall (zenon_TT1_kx : zenon_U) (zenon_TT2_bg : zenon_U) (zenon_TT3_t : zenon_U) (zenon_TX_u : 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_u zenon_TT3_t) (hazard_of_mortality zenon_TX_u zenon_TT2_bg))) -> (greater (age zenon_TX_u zenon_TT3_t) (age zenon_TX_u zenon_TT2_bg)) -> (forall T : zenon_U, ((organization zenon_TX_u)/\(((smaller_or_equal (age zenon_TX_u T) (eta))->(has_immunity zenon_TX_u T))/\((greater (age zenon_TX_u T) (eta))->(~(has_immunity zenon_TX_u T)))))) -> (greater (age zenon_TX_u zenon_TT2_bg) (eta)) -> ((age zenon_TX_u zenon_TT1_kx) = (eta)) -> False).
% 34.50/34.76 do 4 intro. intros zenon_H96 zenon_H82 zenon_H49 zenon_Hb5 zenon_Hfb zenon_H13e.
% 34.50/34.76 generalize (zenon_Hb5 zenon_TT1_kx). zenon_intro zenon_H130.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H130). zenon_intro zenon_H2c. zenon_intro zenon_H131.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H131). zenon_intro zenon_H133. zenon_intro zenon_H132.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H133); [ zenon_intro zenon_H11a | zenon_intro zenon_H128 ].
% 34.50/34.76 apply (zenon_L28_ zenon_TT1_kx zenon_TX_u); trivial.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H132); [ zenon_intro zenon_H15d | zenon_intro zenon_H12f ].
% 34.50/34.76 elim (classic ((~((age zenon_TX_u zenon_TT1_kx) = (age zenon_TX_u zenon_TT2_bg)))/\(~(greater (age zenon_TX_u zenon_TT1_kx) (age zenon_TX_u zenon_TT2_bg))))); [ zenon_intro zenon_H15e | zenon_intro zenon_H15f ].
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H15e). zenon_intro zenon_H160. zenon_intro zenon_H14f.
% 34.50/34.76 apply (zenon_L32_ zenon_TT1_kx zenon_TT3_t zenon_TT2_bg zenon_TX_u); trivial.
% 34.50/34.76 cut ((greater (age zenon_TX_u zenon_TT2_bg) (eta)) = (greater (age zenon_TX_u zenon_TT1_kx) (eta))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H15d.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_Hfb.
% 34.50/34.76 cut (((eta) = (eta))); [idtac | apply NNPP; zenon_intro zenon_H114].
% 34.50/34.76 cut (((age zenon_TX_u zenon_TT2_bg) = (age zenon_TX_u zenon_TT1_kx))); [idtac | apply NNPP; zenon_intro zenon_H161].
% 34.50/34.76 congruence.
% 34.50/34.76 apply (zenon_notand_s _ _ zenon_H15f); [ zenon_intro zenon_H163 | zenon_intro zenon_H162 ].
% 34.50/34.76 apply zenon_H163. zenon_intro zenon_H164.
% 34.50/34.76 elim (classic ((age zenon_TX_u zenon_TT1_kx) = (age zenon_TX_u zenon_TT1_kx))); [ zenon_intro zenon_H14d | zenon_intro zenon_H14e ].
% 34.50/34.76 cut (((age zenon_TX_u zenon_TT1_kx) = (age zenon_TX_u zenon_TT1_kx)) = ((age zenon_TX_u zenon_TT2_bg) = (age zenon_TX_u zenon_TT1_kx))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H161.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_H14d.
% 34.50/34.76 cut (((age zenon_TX_u zenon_TT1_kx) = (age zenon_TX_u zenon_TT1_kx))); [idtac | apply NNPP; zenon_intro zenon_H14e].
% 34.50/34.76 cut (((age zenon_TX_u zenon_TT1_kx) = (age zenon_TX_u zenon_TT2_bg))); [idtac | apply NNPP; zenon_intro zenon_H160].
% 34.50/34.76 congruence.
% 34.50/34.76 exact (zenon_H160 zenon_H164).
% 34.50/34.76 apply zenon_H14e. apply refl_equal.
% 34.50/34.76 apply zenon_H14e. apply refl_equal.
% 34.50/34.76 apply zenon_H162. zenon_intro zenon_H15c.
% 34.50/34.76 generalize (zenon_H96 (age zenon_TX_u zenon_TT1_kx)). zenon_intro zenon_H158.
% 34.50/34.76 generalize (zenon_H158 (age zenon_TX_u zenon_TT2_bg)). zenon_intro zenon_H165.
% 34.50/34.76 generalize (zenon_H165 (eta)). zenon_intro zenon_H166.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H166); [ zenon_intro zenon_H14f | zenon_intro zenon_H167 ].
% 34.50/34.76 exact (zenon_H14f zenon_H15c).
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H167); [ zenon_intro zenon_Hfc | zenon_intro zenon_H168 ].
% 34.50/34.76 exact (zenon_Hfc zenon_Hfb).
% 34.50/34.76 exact (zenon_H15d zenon_H168).
% 34.50/34.76 apply zenon_H114. apply refl_equal.
% 34.50/34.76 exact (zenon_H12f zenon_H128).
% 34.50/34.76 (* end of lemma zenon_L33_ *)
% 34.50/34.76 assert (zenon_L34_ : forall (zenon_TT1_kx : zenon_U) (zenon_TT2_bg : zenon_U) (zenon_TX_u : zenon_U), (greater (age zenon_TX_u zenon_TT2_bg) (eta)) -> (~(greater (hazard_of_mortality zenon_TX_u zenon_TT2_bg) (hazard_of_mortality zenon_TX_u zenon_TT1_kx))) -> (forall T : zenon_U, ((organization zenon_TX_u)/\(((smaller_or_equal (age zenon_TX_u T) (eta))->(has_immunity zenon_TX_u T))/\((greater (age zenon_TX_u T) (eta))->(~(has_immunity zenon_TX_u T)))))) -> ((age zenon_TX_u zenon_TT1_kx) = (eta)) -> False).
% 34.50/34.76 do 3 intro. intros zenon_Hfb zenon_H127 zenon_Hb5 zenon_H13e.
% 34.50/34.76 generalize (zenon_Hb5 zenon_TT1_kx). zenon_intro zenon_H130.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H130). zenon_intro zenon_H2c. zenon_intro zenon_H131.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H131). zenon_intro zenon_H133. zenon_intro zenon_H132.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H133); [ zenon_intro zenon_H11a | zenon_intro zenon_H128 ].
% 34.50/34.76 apply (zenon_L28_ zenon_TT1_kx zenon_TX_u); trivial.
% 34.50/34.76 apply (zenon_L24_ zenon_TT1_kx zenon_TT2_bg zenon_TX_u); trivial.
% 34.50/34.76 (* end of lemma zenon_L34_ *)
% 34.50/34.76 assert (zenon_L35_ : forall (zenon_TT1_kx : zenon_U) (zenon_TT0_ly : zenon_U) (zenon_TX_u : zenon_U), (~((age zenon_TX_u zenon_TT0_ly) = (eta))) -> ((age zenon_TX_u zenon_TT0_ly) = (age zenon_TX_u zenon_TT1_kx)) -> ((age zenon_TX_u zenon_TT1_kx) = (eta)) -> False).
% 34.50/34.76 do 3 intro. intros zenon_H169 zenon_H16a zenon_H13e.
% 34.50/34.76 cut (((age zenon_TX_u zenon_TT0_ly) = (age zenon_TX_u zenon_TT1_kx)) = ((age zenon_TX_u zenon_TT0_ly) = (eta))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H169.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_H16a.
% 34.50/34.76 cut (((age zenon_TX_u zenon_TT1_kx) = (eta))); [idtac | apply NNPP; zenon_intro zenon_H121].
% 34.50/34.76 cut (((age zenon_TX_u zenon_TT0_ly) = (age zenon_TX_u zenon_TT0_ly))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 34.50/34.76 congruence.
% 34.50/34.76 apply zenon_H16b. apply refl_equal.
% 34.50/34.76 exact (zenon_H121 zenon_H13e).
% 34.50/34.76 (* end of lemma zenon_L35_ *)
% 34.50/34.76 apply NNPP. intro zenon_G.
% 34.50/34.76 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_H96 | zenon_intro zenon_H16c ].
% 34.50/34.76 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)/\((has_endowment X)/\((smaller_or_equal (age X T0) (age X T1))/\((smaller_or_equal (age X T1) (eta))/\((greater (age X T2) (eta))/\(greater (age X T3) (age X T2)))))))->((greater (hazard_of_mortality X T3) (hazard_of_mortality X T2))/\((greater (hazard_of_mortality X T2) (hazard_of_mortality X T1))/\((hazard_of_mortality X T1) = (hazard_of_mortality X T0)))))))))) zenon_G); [ zenon_intro zenon_H16d; idtac ].
% 34.50/34.76 elim zenon_H16d. zenon_intro zenon_TX_u. zenon_intro zenon_H16e.
% 34.50/34.76 apply (zenon_notallex_s (fun T0 : zenon_U => (forall T1 : zenon_U, (forall T2 : zenon_U, (forall T3 : zenon_U, (((organization zenon_TX_u)/\((has_endowment zenon_TX_u)/\((smaller_or_equal (age zenon_TX_u T0) (age zenon_TX_u T1))/\((smaller_or_equal (age zenon_TX_u T1) (eta))/\((greater (age zenon_TX_u T2) (eta))/\(greater (age zenon_TX_u T3) (age zenon_TX_u T2)))))))->((greater (hazard_of_mortality zenon_TX_u T3) (hazard_of_mortality zenon_TX_u T2))/\((greater (hazard_of_mortality zenon_TX_u T2) (hazard_of_mortality zenon_TX_u T1))/\((hazard_of_mortality zenon_TX_u T1) = (hazard_of_mortality zenon_TX_u T0))))))))) zenon_H16e); [ zenon_intro zenon_H16f; idtac ].
% 34.50/34.76 elim zenon_H16f. zenon_intro zenon_TT0_ly. zenon_intro zenon_H170.
% 34.50/34.76 apply (zenon_notallex_s (fun T1 : zenon_U => (forall T2 : zenon_U, (forall T3 : zenon_U, (((organization zenon_TX_u)/\((has_endowment zenon_TX_u)/\((smaller_or_equal (age zenon_TX_u zenon_TT0_ly) (age zenon_TX_u T1))/\((smaller_or_equal (age zenon_TX_u T1) (eta))/\((greater (age zenon_TX_u T2) (eta))/\(greater (age zenon_TX_u T3) (age zenon_TX_u T2)))))))->((greater (hazard_of_mortality zenon_TX_u T3) (hazard_of_mortality zenon_TX_u T2))/\((greater (hazard_of_mortality zenon_TX_u T2) (hazard_of_mortality zenon_TX_u T1))/\((hazard_of_mortality zenon_TX_u T1) = (hazard_of_mortality zenon_TX_u zenon_TT0_ly)))))))) zenon_H170); [ zenon_intro zenon_H171; idtac ].
% 34.50/34.76 elim zenon_H171. zenon_intro zenon_TT1_kx. zenon_intro zenon_H172.
% 34.50/34.76 apply (zenon_notallex_s (fun T2 : zenon_U => (forall T3 : zenon_U, (((organization zenon_TX_u)/\((has_endowment zenon_TX_u)/\((smaller_or_equal (age zenon_TX_u zenon_TT0_ly) (age zenon_TX_u zenon_TT1_kx))/\((smaller_or_equal (age zenon_TX_u zenon_TT1_kx) (eta))/\((greater (age zenon_TX_u T2) (eta))/\(greater (age zenon_TX_u T3) (age zenon_TX_u T2)))))))->((greater (hazard_of_mortality zenon_TX_u T3) (hazard_of_mortality zenon_TX_u T2))/\((greater (hazard_of_mortality zenon_TX_u T2) (hazard_of_mortality zenon_TX_u zenon_TT1_kx))/\((hazard_of_mortality zenon_TX_u zenon_TT1_kx) = (hazard_of_mortality zenon_TX_u zenon_TT0_ly))))))) zenon_H172); [ zenon_intro zenon_H173; idtac ].
% 34.50/34.76 elim zenon_H173. zenon_intro zenon_TT2_bg. zenon_intro zenon_H174.
% 34.50/34.76 apply (zenon_notallex_s (fun T3 : zenon_U => (((organization zenon_TX_u)/\((has_endowment zenon_TX_u)/\((smaller_or_equal (age zenon_TX_u zenon_TT0_ly) (age zenon_TX_u zenon_TT1_kx))/\((smaller_or_equal (age zenon_TX_u zenon_TT1_kx) (eta))/\((greater (age zenon_TX_u zenon_TT2_bg) (eta))/\(greater (age zenon_TX_u T3) (age zenon_TX_u zenon_TT2_bg)))))))->((greater (hazard_of_mortality zenon_TX_u T3) (hazard_of_mortality zenon_TX_u zenon_TT2_bg))/\((greater (hazard_of_mortality zenon_TX_u zenon_TT2_bg) (hazard_of_mortality zenon_TX_u zenon_TT1_kx))/\((hazard_of_mortality zenon_TX_u zenon_TT1_kx) = (hazard_of_mortality zenon_TX_u zenon_TT0_ly)))))) zenon_H174); [ zenon_intro zenon_H175; idtac ].
% 34.50/34.76 elim zenon_H175. zenon_intro zenon_TT3_t. zenon_intro zenon_H176.
% 34.50/34.76 apply (zenon_notimply_s _ _ zenon_H176). zenon_intro zenon_H178. zenon_intro zenon_H177.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H178). zenon_intro zenon_H2c. zenon_intro zenon_H179.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H179). zenon_intro zenon_H17b. zenon_intro zenon_H17a.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H17a). zenon_intro zenon_H17d. zenon_intro zenon_H17c.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H17c). zenon_intro zenon_H11f. zenon_intro zenon_H17e.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H17e). zenon_intro zenon_Hfb. zenon_intro zenon_H49.
% 34.50/34.76 generalize (definition_1 zenon_TX_u). zenon_intro zenon_H17f.
% 34.50/34.76 apply (zenon_equiv_s _ _ zenon_H17f); [ zenon_intro zenon_H181; zenon_intro zenon_H180 | zenon_intro zenon_H17b; zenon_intro zenon_Hb5 ].
% 34.50/34.76 exact (zenon_H181 zenon_H17b).
% 34.50/34.76 generalize (definition_smaller_or_equal (age zenon_TX_u zenon_TT0_ly)). zenon_intro zenon_H182.
% 34.50/34.76 generalize (zenon_H182 (age zenon_TX_u zenon_TT1_kx)). zenon_intro zenon_H183.
% 34.50/34.76 apply (zenon_equiv_s _ _ zenon_H183); [ zenon_intro zenon_H186; zenon_intro zenon_H185 | zenon_intro zenon_H17d; zenon_intro zenon_H184 ].
% 34.50/34.76 exact (zenon_H186 zenon_H17d).
% 34.50/34.76 generalize (definition_smaller_or_equal (age zenon_TX_u zenon_TT1_kx)). zenon_intro zenon_H11c.
% 34.50/34.76 generalize (zenon_H11c (eta)). zenon_intro zenon_H11d.
% 34.50/34.76 apply (zenon_equiv_s _ _ zenon_H11d); [ zenon_intro zenon_H11a; zenon_intro zenon_H120 | zenon_intro zenon_H11f; zenon_intro zenon_H11e ].
% 34.50/34.76 exact (zenon_H11a zenon_H11f).
% 34.50/34.76 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H125 | zenon_intro zenon_H13e ].
% 34.50/34.76 generalize (definition_smaller (age zenon_TX_u zenon_TT1_kx)). zenon_intro zenon_H123.
% 34.50/34.76 generalize (zenon_H123 (eta)). zenon_intro zenon_H124.
% 34.50/34.76 apply (zenon_equiv_s _ _ zenon_H124); [ zenon_intro zenon_H122; zenon_intro zenon_H126 | zenon_intro zenon_H125; zenon_intro zenon_H119 ].
% 34.50/34.76 exact (zenon_H122 zenon_H125).
% 34.50/34.76 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H187 | zenon_intro zenon_H16a ].
% 34.50/34.76 generalize (definition_smaller (age zenon_TX_u zenon_TT0_ly)). zenon_intro zenon_H188.
% 34.50/34.76 generalize (zenon_H188 (age zenon_TX_u zenon_TT1_kx)). zenon_intro zenon_H189.
% 34.50/34.76 apply (zenon_equiv_s _ _ zenon_H189); [ zenon_intro zenon_H18c; zenon_intro zenon_H18b | zenon_intro zenon_H187; zenon_intro zenon_H18a ].
% 34.50/34.76 exact (zenon_H18c zenon_H187).
% 34.50/34.76 apply (zenon_notand_s _ _ zenon_H177); [ zenon_intro zenon_H82 | zenon_intro zenon_H18d ].
% 34.50/34.76 apply (zenon_L22_ zenon_TT2_bg zenon_TT3_t zenon_TX_u); trivial.
% 34.50/34.76 apply (zenon_notand_s _ _ zenon_H18d); [ zenon_intro zenon_H127 | zenon_intro zenon_H135 ].
% 34.50/34.76 apply (zenon_L25_ zenon_TT1_kx zenon_TT2_bg zenon_TX_u); trivial.
% 34.50/34.76 generalize (zenon_Hb5 zenon_TT1_kx). zenon_intro zenon_H130.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H130). zenon_intro zenon_H2c. zenon_intro zenon_H131.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H131). zenon_intro zenon_H133. zenon_intro zenon_H132.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H133); [ zenon_intro zenon_H11a | zenon_intro zenon_H128 ].
% 34.50/34.76 apply (zenon_L23_ zenon_TT1_kx zenon_TX_u); trivial.
% 34.50/34.76 generalize (zenon_Hb5 zenon_TT0_ly). zenon_intro zenon_H18e.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H18e). zenon_intro zenon_H2c. zenon_intro zenon_H18f.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H18f). zenon_intro zenon_H191. zenon_intro zenon_H190.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H191); [ zenon_intro zenon_H192 | zenon_intro zenon_H134 ].
% 34.50/34.76 generalize (definition_smaller_or_equal (age zenon_TX_u zenon_TT0_ly)). zenon_intro zenon_H182.
% 34.50/34.76 generalize (zenon_H182 (eta)). zenon_intro zenon_H193.
% 34.50/34.76 apply (zenon_equiv_s _ _ zenon_H193); [ zenon_intro zenon_H192; zenon_intro zenon_H196 | zenon_intro zenon_H195; zenon_intro zenon_H194 ].
% 34.50/34.76 apply (zenon_notor_s _ _ zenon_H196). zenon_intro zenon_H197. zenon_intro zenon_H169.
% 34.50/34.76 generalize (definition_smaller (age zenon_TX_u zenon_TT0_ly)). zenon_intro zenon_H188.
% 34.50/34.76 generalize (zenon_H188 (eta)). zenon_intro zenon_H198.
% 34.50/34.76 apply (zenon_equiv_s _ _ zenon_H198); [ zenon_intro zenon_H197; zenon_intro zenon_H19b | zenon_intro zenon_H19a; zenon_intro zenon_H199 ].
% 34.50/34.76 generalize (zenon_H96 (eta)). zenon_intro zenon_H115.
% 34.50/34.76 generalize (zenon_H115 (age zenon_TX_u zenon_TT1_kx)). zenon_intro zenon_H19c.
% 34.50/34.76 generalize (zenon_H19c (age zenon_TX_u zenon_TT0_ly)). zenon_intro zenon_H19d.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H19d); [ zenon_intro zenon_H126 | zenon_intro zenon_H19e ].
% 34.50/34.76 exact (zenon_H126 zenon_H119).
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H19e); [ zenon_intro zenon_H18b | zenon_intro zenon_H199 ].
% 34.50/34.76 exact (zenon_H18b zenon_H18a).
% 34.50/34.76 exact (zenon_H19b zenon_H199).
% 34.50/34.76 exact (zenon_H197 zenon_H19a).
% 34.50/34.76 exact (zenon_H192 zenon_H195).
% 34.50/34.76 apply (zenon_L27_ zenon_TT1_kx zenon_TT0_ly zenon_TX_u); trivial.
% 34.50/34.76 apply (zenon_notand_s _ _ zenon_H177); [ zenon_intro zenon_H82 | zenon_intro zenon_H18d ].
% 34.50/34.76 apply (zenon_L22_ zenon_TT2_bg zenon_TT3_t zenon_TX_u); trivial.
% 34.50/34.76 apply (zenon_notand_s _ _ zenon_H18d); [ zenon_intro zenon_H127 | zenon_intro zenon_H135 ].
% 34.50/34.76 apply (zenon_L25_ zenon_TT1_kx zenon_TT2_bg zenon_TX_u); trivial.
% 34.50/34.76 generalize (zenon_Hb5 zenon_TT1_kx). zenon_intro zenon_H130.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H130). zenon_intro zenon_H2c. zenon_intro zenon_H131.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H131). zenon_intro zenon_H133. zenon_intro zenon_H132.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H133); [ zenon_intro zenon_H11a | zenon_intro zenon_H128 ].
% 34.50/34.76 apply (zenon_L23_ zenon_TT1_kx zenon_TX_u); trivial.
% 34.50/34.76 generalize (zenon_Hb5 zenon_TT0_ly). zenon_intro zenon_H18e.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H18e). zenon_intro zenon_H2c. zenon_intro zenon_H18f.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H18f). zenon_intro zenon_H191. zenon_intro zenon_H190.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H191); [ zenon_intro zenon_H192 | zenon_intro zenon_H134 ].
% 34.50/34.76 generalize (definition_smaller_or_equal (age zenon_TX_u zenon_TT0_ly)). zenon_intro zenon_H182.
% 34.50/34.76 generalize (zenon_H182 (eta)). zenon_intro zenon_H193.
% 34.50/34.76 apply (zenon_equiv_s _ _ zenon_H193); [ zenon_intro zenon_H192; zenon_intro zenon_H196 | zenon_intro zenon_H195; zenon_intro zenon_H194 ].
% 34.50/34.76 apply (zenon_notor_s _ _ zenon_H196). zenon_intro zenon_H197. zenon_intro zenon_H169.
% 34.50/34.76 generalize (definition_smaller (age zenon_TX_u zenon_TT0_ly)). zenon_intro zenon_H188.
% 34.50/34.76 generalize (zenon_H188 (eta)). zenon_intro zenon_H198.
% 34.50/34.76 apply (zenon_equiv_s _ _ zenon_H198); [ zenon_intro zenon_H197; zenon_intro zenon_H19b | zenon_intro zenon_H19a; zenon_intro zenon_H199 ].
% 34.50/34.76 cut ((greater (eta) (age zenon_TX_u zenon_TT1_kx)) = (greater (eta) (age zenon_TX_u zenon_TT0_ly))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H19b.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_H119.
% 34.50/34.76 cut (((age zenon_TX_u zenon_TT1_kx) = (age zenon_TX_u zenon_TT0_ly))); [idtac | apply NNPP; zenon_intro zenon_H19f].
% 34.50/34.76 cut (((eta) = (eta))); [idtac | apply NNPP; zenon_intro zenon_H114].
% 34.50/34.76 congruence.
% 34.50/34.76 apply zenon_H114. apply refl_equal.
% 34.50/34.76 apply zenon_H19f. apply sym_equal. exact zenon_H16a.
% 34.50/34.76 exact (zenon_H197 zenon_H19a).
% 34.50/34.76 exact (zenon_H192 zenon_H195).
% 34.50/34.76 apply (zenon_L27_ zenon_TT1_kx zenon_TT0_ly zenon_TX_u); trivial.
% 34.50/34.76 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H187 | zenon_intro zenon_H16a ].
% 34.50/34.76 generalize (definition_smaller (age zenon_TX_u zenon_TT0_ly)). zenon_intro zenon_H188.
% 34.50/34.76 generalize (zenon_H188 (age zenon_TX_u zenon_TT1_kx)). zenon_intro zenon_H189.
% 34.50/34.76 apply (zenon_equiv_s _ _ zenon_H189); [ zenon_intro zenon_H18c; zenon_intro zenon_H18b | zenon_intro zenon_H187; zenon_intro zenon_H18a ].
% 34.50/34.76 exact (zenon_H18c zenon_H187).
% 34.50/34.76 apply (zenon_notand_s _ _ zenon_H177); [ zenon_intro zenon_H82 | zenon_intro zenon_H18d ].
% 34.50/34.76 apply (zenon_L33_ zenon_TT1_kx zenon_TT2_bg zenon_TT3_t zenon_TX_u); trivial.
% 34.50/34.76 apply (zenon_notand_s _ _ zenon_H18d); [ zenon_intro zenon_H127 | zenon_intro zenon_H135 ].
% 34.50/34.76 apply (zenon_L34_ zenon_TT1_kx zenon_TT2_bg zenon_TX_u); trivial.
% 34.50/34.76 generalize (zenon_Hb5 zenon_TT0_ly). zenon_intro zenon_H18e.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H18e). zenon_intro zenon_H2c. zenon_intro zenon_H18f.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H18f). zenon_intro zenon_H191. zenon_intro zenon_H190.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H191); [ zenon_intro zenon_H192 | zenon_intro zenon_H134 ].
% 34.50/34.76 generalize (definition_smaller_or_equal (age zenon_TX_u zenon_TT0_ly)). zenon_intro zenon_H182.
% 34.50/34.76 generalize (zenon_H182 (eta)). zenon_intro zenon_H193.
% 34.50/34.76 apply (zenon_equiv_s _ _ zenon_H193); [ zenon_intro zenon_H192; zenon_intro zenon_H196 | zenon_intro zenon_H195; zenon_intro zenon_H194 ].
% 34.50/34.76 apply (zenon_notor_s _ _ zenon_H196). zenon_intro zenon_H197. zenon_intro zenon_H169.
% 34.50/34.76 generalize (definition_smaller (age zenon_TX_u zenon_TT0_ly)). zenon_intro zenon_H188.
% 34.50/34.76 generalize (zenon_H188 (eta)). zenon_intro zenon_H198.
% 34.50/34.76 apply (zenon_equiv_s _ _ zenon_H198); [ zenon_intro zenon_H197; zenon_intro zenon_H19b | zenon_intro zenon_H19a; zenon_intro zenon_H199 ].
% 34.50/34.76 elim (classic ((~((eta) = (age zenon_TX_u zenon_TT1_kx)))/\(~(greater (eta) (age zenon_TX_u zenon_TT1_kx))))); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H1a1 ].
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H1a0). zenon_intro zenon_H14c. zenon_intro zenon_H126.
% 34.50/34.76 apply zenon_H14c. apply sym_equal. exact zenon_H13e.
% 34.50/34.76 cut ((greater (age zenon_TX_u zenon_TT1_kx) (age zenon_TX_u zenon_TT0_ly)) = (greater (eta) (age zenon_TX_u zenon_TT0_ly))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H19b.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_H18a.
% 34.50/34.76 cut (((age zenon_TX_u zenon_TT0_ly) = (age zenon_TX_u zenon_TT0_ly))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 34.50/34.76 cut (((age zenon_TX_u zenon_TT1_kx) = (eta))); [idtac | apply NNPP; zenon_intro zenon_H121].
% 34.50/34.76 congruence.
% 34.50/34.76 apply (zenon_notand_s _ _ zenon_H1a1); [ zenon_intro zenon_H1a3 | zenon_intro zenon_H1a2 ].
% 34.50/34.76 apply zenon_H1a3. zenon_intro zenon_H1a4.
% 34.50/34.76 elim (classic ((eta) = (eta))); [ zenon_intro zenon_H113 | zenon_intro zenon_H114 ].
% 34.50/34.76 cut (((eta) = (eta)) = ((age zenon_TX_u zenon_TT1_kx) = (eta))).
% 34.50/34.76 intro zenon_D_pnotp.
% 34.50/34.76 apply zenon_H121.
% 34.50/34.76 rewrite <- zenon_D_pnotp.
% 34.50/34.76 exact zenon_H113.
% 34.50/34.76 cut (((eta) = (eta))); [idtac | apply NNPP; zenon_intro zenon_H114].
% 34.50/34.76 cut (((eta) = (age zenon_TX_u zenon_TT1_kx))); [idtac | apply NNPP; zenon_intro zenon_H14c].
% 34.50/34.76 congruence.
% 34.50/34.76 exact (zenon_H14c zenon_H1a4).
% 34.50/34.76 apply zenon_H114. apply refl_equal.
% 34.50/34.76 apply zenon_H114. apply refl_equal.
% 34.50/34.76 apply zenon_H1a2. zenon_intro zenon_H119.
% 34.50/34.76 generalize (zenon_H96 (eta)). zenon_intro zenon_H115.
% 34.50/34.76 generalize (zenon_H115 (age zenon_TX_u zenon_TT1_kx)). zenon_intro zenon_H19c.
% 34.50/34.76 generalize (zenon_H19c (age zenon_TX_u zenon_TT0_ly)). zenon_intro zenon_H19d.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H19d); [ zenon_intro zenon_H126 | zenon_intro zenon_H19e ].
% 34.50/34.76 exact (zenon_H126 zenon_H119).
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H19e); [ zenon_intro zenon_H18b | zenon_intro zenon_H199 ].
% 34.50/34.76 exact (zenon_H18b zenon_H18a).
% 34.50/34.76 exact (zenon_H19b zenon_H199).
% 34.50/34.76 apply zenon_H16b. apply refl_equal.
% 34.50/34.76 exact (zenon_H197 zenon_H19a).
% 34.50/34.76 exact (zenon_H192 zenon_H195).
% 34.50/34.76 generalize (zenon_Hb5 zenon_TT1_kx). zenon_intro zenon_H130.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H130). zenon_intro zenon_H2c. zenon_intro zenon_H131.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H131). zenon_intro zenon_H133. zenon_intro zenon_H132.
% 34.50/34.76 apply (zenon_imply_s _ _ zenon_H133); [ zenon_intro zenon_H11a | zenon_intro zenon_H128 ].
% 34.50/34.76 apply (zenon_L28_ zenon_TT1_kx zenon_TX_u); trivial.
% 34.50/34.76 apply (zenon_L27_ zenon_TT1_kx zenon_TT0_ly zenon_TX_u); trivial.
% 34.50/34.76 apply (zenon_notand_s _ _ zenon_H177); [ zenon_intro zenon_H82 | zenon_intro zenon_H18d ].
% 34.50/34.76 apply (zenon_L33_ zenon_TT1_kx zenon_TT2_bg zenon_TT3_t zenon_TX_u); trivial.
% 34.50/34.76 apply (zenon_notand_s _ _ zenon_H18d); [ zenon_intro zenon_H127 | zenon_intro zenon_H135 ].
% 34.50/34.76 apply (zenon_L34_ zenon_TT1_kx zenon_TT2_bg zenon_TX_u); trivial.
% 34.50/34.76 generalize (zenon_Hb5 zenon_TT1_kx). zenon_intro zenon_H130.
% 34.50/34.76 apply (zenon_and_s _ _ zenon_H130). zenon_intro zenon_H2c. zenon_intro zenon_H131.
% 34.50/34.77 apply (zenon_and_s _ _ zenon_H131). zenon_intro zenon_H133. zenon_intro zenon_H132.
% 34.50/34.77 apply (zenon_imply_s _ _ zenon_H133); [ zenon_intro zenon_H11a | zenon_intro zenon_H128 ].
% 34.50/34.77 apply (zenon_L28_ zenon_TT1_kx zenon_TX_u); trivial.
% 34.50/34.77 generalize (zenon_Hb5 zenon_TT0_ly). zenon_intro zenon_H18e.
% 34.50/34.77 apply (zenon_and_s _ _ zenon_H18e). zenon_intro zenon_H2c. zenon_intro zenon_H18f.
% 34.50/34.77 apply (zenon_and_s _ _ zenon_H18f). zenon_intro zenon_H191. zenon_intro zenon_H190.
% 34.50/34.77 apply (zenon_imply_s _ _ zenon_H191); [ zenon_intro zenon_H192 | zenon_intro zenon_H134 ].
% 34.50/34.77 generalize (definition_smaller_or_equal (age zenon_TX_u zenon_TT0_ly)). zenon_intro zenon_H182.
% 34.50/34.77 generalize (zenon_H182 (eta)). zenon_intro zenon_H193.
% 34.50/34.77 apply (zenon_equiv_s _ _ zenon_H193); [ zenon_intro zenon_H192; zenon_intro zenon_H196 | zenon_intro zenon_H195; zenon_intro zenon_H194 ].
% 34.50/34.77 apply (zenon_notor_s _ _ zenon_H196). zenon_intro zenon_H197. zenon_intro zenon_H169.
% 34.50/34.77 apply (zenon_L35_ zenon_TT1_kx zenon_TT0_ly zenon_TX_u); trivial.
% 34.50/34.77 exact (zenon_H192 zenon_H195).
% 34.50/34.77 apply (zenon_L27_ zenon_TT1_kx zenon_TT0_ly zenon_TX_u); trivial.
% 34.50/34.77 apply zenon_H16c. zenon_intro zenon_Tx_qf. apply NNPP. zenon_intro zenon_H1a6.
% 34.50/34.77 apply zenon_H1a6. zenon_intro zenon_Ty_qh. apply NNPP. zenon_intro zenon_H1a8.
% 34.50/34.77 apply zenon_H1a8. zenon_intro zenon_Tz_qj. apply NNPP. zenon_intro zenon_H1aa.
% 34.50/34.77 apply (zenon_notimply_s _ _ zenon_H1aa). zenon_intro zenon_H1ac. zenon_intro zenon_H1ab.
% 34.50/34.77 apply (zenon_notimply_s _ _ zenon_H1ab). zenon_intro zenon_H1ae. zenon_intro zenon_H1ad.
% 34.50/34.77 generalize (meaning_postulate_greater_transitive zenon_Tx_qf). zenon_intro zenon_H1af.
% 34.50/34.77 generalize (zenon_H1af zenon_Ty_qh). zenon_intro zenon_H1b0.
% 34.50/34.77 generalize (zenon_H1b0 zenon_Tz_qj). zenon_intro zenon_H1b1.
% 34.50/34.77 apply (zenon_imply_s _ _ zenon_H1b1); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H1b2 ].
% 34.50/34.77 apply (zenon_notand_s _ _ zenon_H1b3); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H1b4 ].
% 34.50/34.77 exact (zenon_H1b5 zenon_H1ac).
% 34.50/34.77 exact (zenon_H1b4 zenon_H1ae).
% 34.50/34.77 exact (zenon_H1ad zenon_H1b2).
% 34.50/34.77 Qed.
% 34.50/34.77 % SZS output end Proof
% 34.50/34.77 (* END-PROOF *)
% 34.50/34.77 nodes searched: 2981578
% 34.50/34.77 max branch formulas: 8989
% 34.50/34.77 proof nodes created: 12120
% 34.50/34.77 formulas created: 545779
% 34.50/34.77
%------------------------------------------------------------------------------