TSTP Solution File: MGT065+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : MGT065+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n028.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 22:31:16 EDT 2022
% Result : Theorem 24.97s 25.17s
% Output : Proof 24.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : MGT065+1 : TPTP v8.1.0. Released v2.4.0.
% 0.10/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 9 08:44:47 EDT 2022
% 0.12/0.33 % CPUTime :
% 24.97/25.17 (* PROOF-FOUND *)
% 24.97/25.17 % SZS status Theorem
% 24.97/25.17 (* BEGIN-PROOF *)
% 24.97/25.17 % SZS output start Proof
% 24.97/25.17 Theorem theorem_11 : (forall X : zenon_U, (forall T0 : zenon_U, (forall T1 : zenon_U, (forall T2 : zenon_U, (((organization X)/\(((robust_position X)\/(fragile_position X))/\((has_endowment X)/\(((age X T0) = (zero))/\((greater (sigma) (zero))/\((greater (tau) (zero))/\((greater (eta) (zero))/\((smaller_or_equal (age X T1) (sigma))/\((smaller_or_equal (age X T1) (tau))/\((smaller_or_equal (age X T1) (eta))/\((greater (age X T2) (sigma))/\((greater (age X T2) (tau))/\(greater (age X T2) (eta))))))))))))))->((greater (hazard_of_mortality X T2) (hazard_of_mortality X T1))/\((hazard_of_mortality X T1) = (hazard_of_mortality X T0)))))))).
% 24.97/25.17 Proof.
% 24.97/25.17 assert (zenon_L1_ : forall (zenon_TX_u : zenon_U), (~(~(has_immunity zenon_TX_u zenon_E))) -> (~(has_immunity zenon_TX_u zenon_E)) -> False).
% 24.97/25.17 do 1 intro. intros zenon_H12 zenon_H13.
% 24.97/25.17 exact (zenon_H12 zenon_H13).
% 24.97/25.17 (* end of lemma zenon_L1_ *)
% 24.97/25.17 assert (zenon_L2_ : (~((high) = (high))) -> False).
% 24.97/25.17 do 0 intro. intros zenon_H15.
% 24.97/25.17 apply zenon_H15. apply refl_equal.
% 24.97/25.17 (* end of lemma zenon_L2_ *)
% 24.97/25.17 assert (zenon_L3_ : (~((mod2) = (mod2))) -> False).
% 24.97/25.17 do 0 intro. intros zenon_H16.
% 24.97/25.17 apply zenon_H16. apply refl_equal.
% 24.97/25.17 (* end of lemma zenon_L3_ *)
% 24.97/25.17 assert (zenon_L4_ : (~((low) = (low))) -> False).
% 24.97/25.17 do 0 intro. intros zenon_H17.
% 24.97/25.17 apply zenon_H17. apply refl_equal.
% 24.97/25.17 (* end of lemma zenon_L4_ *)
% 24.97/25.17 assert (zenon_L5_ : forall (zenon_TT1_ba : zenon_U) (zenon_TX_u : zenon_U), (greater (eta) (age zenon_TX_u zenon_TT1_ba)) -> (~(smaller_or_equal (age zenon_TX_u zenon_TT1_ba) (eta))) -> False).
% 24.97/25.17 do 2 intro. intros zenon_H18 zenon_H19.
% 24.97/25.17 generalize (definition_smaller_or_equal (age zenon_TX_u zenon_TT1_ba)). zenon_intro zenon_H1b.
% 24.97/25.17 generalize (zenon_H1b (eta)). zenon_intro zenon_H1c.
% 24.97/25.17 apply (zenon_equiv_s _ _ zenon_H1c); [ zenon_intro zenon_H19; zenon_intro zenon_H1f | zenon_intro zenon_H1e; zenon_intro zenon_H1d ].
% 24.97/25.17 apply (zenon_notor_s _ _ zenon_H1f). zenon_intro zenon_H21. zenon_intro zenon_H20.
% 24.97/25.17 generalize (definition_smaller (age zenon_TX_u zenon_TT1_ba)). zenon_intro zenon_H22.
% 24.97/25.17 generalize (zenon_H22 (eta)). zenon_intro zenon_H23.
% 24.97/25.17 apply (zenon_equiv_s _ _ zenon_H23); [ zenon_intro zenon_H21; zenon_intro zenon_H25 | zenon_intro zenon_H24; zenon_intro zenon_H18 ].
% 24.97/25.17 exact (zenon_H25 zenon_H18).
% 24.97/25.17 exact (zenon_H21 zenon_H24).
% 24.97/25.17 exact (zenon_H19 zenon_H1e).
% 24.97/25.17 (* end of lemma zenon_L5_ *)
% 24.97/25.17 assert (zenon_L6_ : forall (zenon_TT1_ba : zenon_U) (zenon_TX_u : zenon_U), (forall T : zenon_U, ((organization zenon_TX_u)->(((has_immunity zenon_TX_u T)->((hazard_of_mortality zenon_TX_u T) = (very_low)))/\((~(has_immunity zenon_TX_u T))->((((is_aligned zenon_TX_u T)/\(positional_advantage zenon_TX_u T))->((hazard_of_mortality zenon_TX_u T) = (low)))/\((((~(is_aligned zenon_TX_u T))/\(positional_advantage zenon_TX_u T))->((hazard_of_mortality zenon_TX_u T) = (mod1)))/\((((is_aligned zenon_TX_u T)/\(~(positional_advantage zenon_TX_u T)))->((hazard_of_mortality zenon_TX_u T) = (mod2)))/\(((~(is_aligned zenon_TX_u T))/\(~(positional_advantage zenon_TX_u T)))->((hazard_of_mortality zenon_TX_u T) = (high)))))))))) -> (organization zenon_TX_u) -> (has_immunity zenon_TX_u zenon_TT1_ba) -> (~((very_low) = (hazard_of_mortality zenon_TX_u zenon_TT1_ba))) -> False).
% 24.97/25.17 do 2 intro. intros zenon_H0 zenon_H26 zenon_H27 zenon_H28.
% 24.97/25.17 generalize (zenon_H0 zenon_TT1_ba). zenon_intro zenon_H29.
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ].
% 24.97/25.17 exact (zenon_H2b zenon_H26).
% 24.97/25.17 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H2d. zenon_intro zenon_H2c.
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ].
% 24.97/25.17 exact (zenon_H2f zenon_H27).
% 24.97/25.17 apply zenon_H28. apply sym_equal. exact zenon_H2e.
% 24.97/25.17 (* end of lemma zenon_L6_ *)
% 24.97/25.17 assert (zenon_L7_ : forall (zenon_TT1_ba : zenon_U) (zenon_TX_u : zenon_U), (~((very_low) = (hazard_of_mortality zenon_TX_u zenon_TT1_ba))) -> (has_immunity zenon_TX_u zenon_TT1_ba) -> (organization zenon_TX_u) -> False).
% 24.97/25.17 do 2 intro. intros zenon_H28 zenon_H27 zenon_H26.
% 24.97/25.17 generalize (assumption_17 zenon_TX_u). zenon_intro zenon_H0.
% 24.97/25.17 apply (zenon_L6_ zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.17 (* end of lemma zenon_L7_ *)
% 24.97/25.17 assert (zenon_L8_ : forall (zenon_TT1_ba : 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)))))) -> (~((very_low) = (hazard_of_mortality zenon_TX_u zenon_TT1_ba))) -> (greater (eta) (age zenon_TX_u zenon_TT1_ba)) -> False).
% 24.97/25.17 do 2 intro. intros zenon_H30 zenon_H28 zenon_H18.
% 24.97/25.17 generalize (zenon_H30 zenon_TT1_ba). zenon_intro zenon_H31.
% 24.97/25.17 apply (zenon_and_s _ _ zenon_H31). zenon_intro zenon_H26. zenon_intro zenon_H32.
% 24.97/25.17 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H34. zenon_intro zenon_H33.
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_H34); [ zenon_intro zenon_H19 | zenon_intro zenon_H27 ].
% 24.97/25.17 apply (zenon_L5_ zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.17 apply (zenon_L7_ zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.17 (* end of lemma zenon_L8_ *)
% 24.97/25.17 assert (zenon_L9_ : forall (zenon_TT1_ba : zenon_U) (zenon_TX_u : zenon_U), (~(greater (low) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))) -> (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_ba)) -> False).
% 24.97/25.17 do 2 intro. intros zenon_H35 zenon_H30 zenon_H18.
% 24.97/25.17 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [ zenon_intro zenon_H36 | zenon_intro zenon_H28 ].
% 24.97/25.17 cut ((greater (low) (very_low)) = (greater (low) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))).
% 24.97/25.17 intro zenon_D_pnotp.
% 24.97/25.17 apply zenon_H35.
% 24.97/25.17 rewrite <- zenon_D_pnotp.
% 24.97/25.17 exact assumption_18c.
% 24.97/25.17 cut (((very_low) = (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [idtac | apply NNPP; zenon_intro zenon_H28].
% 24.97/25.17 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H17].
% 24.97/25.17 congruence.
% 24.97/25.17 apply zenon_H17. apply refl_equal.
% 24.97/25.17 exact (zenon_H28 zenon_H36).
% 24.97/25.17 apply (zenon_L8_ zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.17 (* end of lemma zenon_L9_ *)
% 24.97/25.17 assert (zenon_L10_ : forall (zenon_TT1_ba : 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 (mod2) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))) -> (greater (eta) (age zenon_TX_u zenon_TT1_ba)) -> (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)))))) -> False).
% 24.97/25.17 do 2 intro. intros zenon_H37 zenon_H38 zenon_H18 zenon_H30.
% 24.97/25.17 elim (classic (greater (low) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [ zenon_intro zenon_H39 | zenon_intro zenon_H35 ].
% 24.97/25.17 generalize (zenon_H37 (mod2)). zenon_intro zenon_H3a.
% 24.97/25.17 generalize (zenon_H3a (low)). zenon_intro zenon_H3b.
% 24.97/25.17 generalize (zenon_H3b (hazard_of_mortality zenon_TX_u zenon_TT1_ba)). zenon_intro zenon_H3c.
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_H3c); [ zenon_intro zenon_H3e | zenon_intro zenon_H3d ].
% 24.97/25.17 exact (zenon_H3e assumption_18e).
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_H3d); [ zenon_intro zenon_H35 | zenon_intro zenon_H3f ].
% 24.97/25.17 exact (zenon_H35 zenon_H39).
% 24.97/25.17 exact (zenon_H38 zenon_H3f).
% 24.97/25.17 apply (zenon_L9_ zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.17 (* end of lemma zenon_L10_ *)
% 24.97/25.17 assert (zenon_L11_ : forall (zenon_TT1_ba : 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 (high) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))) -> (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_ba)) -> False).
% 24.97/25.17 do 2 intro. intros zenon_H37 zenon_H40 zenon_H30 zenon_H18.
% 24.97/25.17 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [ zenon_intro zenon_H3f | zenon_intro zenon_H38 ].
% 24.97/25.17 generalize (zenon_H37 (high)). zenon_intro zenon_H41.
% 24.97/25.17 generalize (zenon_H41 (mod2)). zenon_intro zenon_H42.
% 24.97/25.17 generalize (zenon_H42 (hazard_of_mortality zenon_TX_u zenon_TT1_ba)). zenon_intro zenon_H43.
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H45 | zenon_intro zenon_H44 ].
% 24.97/25.17 exact (zenon_H45 assumption_18d).
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_H44); [ zenon_intro zenon_H38 | zenon_intro zenon_H46 ].
% 24.97/25.17 exact (zenon_H38 zenon_H3f).
% 24.97/25.17 exact (zenon_H40 zenon_H46).
% 24.97/25.17 apply (zenon_L10_ zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.17 (* end of lemma zenon_L11_ *)
% 24.97/25.17 assert (zenon_L12_ : forall (zenon_TT1_ba : 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)))))) -> ((hazard_of_mortality zenon_TX_u zenon_E) = (high)) -> (~(greater (hazard_of_mortality zenon_TX_u zenon_E) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))) -> (greater (eta) (age zenon_TX_u zenon_TT1_ba)) -> (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)))))) -> False).
% 24.97/25.17 do 2 intro. intros zenon_H37 zenon_H47 zenon_H48 zenon_H18 zenon_H30.
% 24.97/25.17 elim (classic (greater (high) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [ zenon_intro zenon_H46 | zenon_intro zenon_H40 ].
% 24.97/25.17 cut ((greater (high) (hazard_of_mortality zenon_TX_u zenon_TT1_ba)) = (greater (hazard_of_mortality zenon_TX_u zenon_E) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))).
% 24.97/25.17 intro zenon_D_pnotp.
% 24.97/25.17 apply zenon_H48.
% 24.97/25.17 rewrite <- zenon_D_pnotp.
% 24.97/25.17 exact zenon_H46.
% 24.97/25.17 cut (((hazard_of_mortality zenon_TX_u zenon_TT1_ba) = (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [idtac | apply NNPP; zenon_intro zenon_H49].
% 24.97/25.17 cut (((high) = (hazard_of_mortality zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H4a].
% 24.97/25.17 congruence.
% 24.97/25.17 elim (classic ((hazard_of_mortality zenon_TX_u zenon_E) = (hazard_of_mortality zenon_TX_u zenon_E))); [ zenon_intro zenon_H4b | zenon_intro zenon_H4c ].
% 24.97/25.17 cut (((hazard_of_mortality zenon_TX_u zenon_E) = (hazard_of_mortality zenon_TX_u zenon_E)) = ((high) = (hazard_of_mortality zenon_TX_u zenon_E))).
% 24.97/25.17 intro zenon_D_pnotp.
% 24.97/25.17 apply zenon_H4a.
% 24.97/25.17 rewrite <- zenon_D_pnotp.
% 24.97/25.17 exact zenon_H4b.
% 24.97/25.17 cut (((hazard_of_mortality zenon_TX_u zenon_E) = (hazard_of_mortality zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H4c].
% 24.97/25.17 cut (((hazard_of_mortality zenon_TX_u zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H4d].
% 24.97/25.17 congruence.
% 24.97/25.17 exact (zenon_H4d zenon_H47).
% 24.97/25.17 apply zenon_H4c. apply refl_equal.
% 24.97/25.17 apply zenon_H4c. apply refl_equal.
% 24.97/25.17 apply zenon_H49. apply refl_equal.
% 24.97/25.17 apply (zenon_L11_ zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.17 (* end of lemma zenon_L12_ *)
% 24.97/25.17 assert (zenon_L13_ : forall (zenon_TT2_de : zenon_U) (zenon_TX_u : zenon_U), (((~(is_aligned zenon_TX_u zenon_TT2_de))/\(~(positional_advantage zenon_TX_u zenon_TT2_de)))->((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (high))) -> (~(positional_advantage zenon_TX_u zenon_TT2_de)) -> (~(is_aligned zenon_TX_u zenon_TT2_de)) -> (~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (high))) -> False).
% 24.97/25.17 do 2 intro. intros zenon_H4e zenon_H4f zenon_H50 zenon_H51.
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_H4e); [ zenon_intro zenon_H54 | zenon_intro zenon_H53 ].
% 24.97/25.17 apply (zenon_notand_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ].
% 24.97/25.17 exact (zenon_H56 zenon_H50).
% 24.97/25.17 exact (zenon_H55 zenon_H4f).
% 24.97/25.17 exact (zenon_H51 zenon_H53).
% 24.97/25.17 (* end of lemma zenon_L13_ *)
% 24.97/25.17 assert (zenon_L14_ : forall (zenon_TT2_de : zenon_U) (zenon_TX_u : zenon_U), ((~(has_immunity zenon_TX_u zenon_TT2_de))->((((is_aligned zenon_TX_u zenon_TT2_de)/\(positional_advantage zenon_TX_u zenon_TT2_de))->((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (low)))/\((((~(is_aligned zenon_TX_u zenon_TT2_de))/\(positional_advantage zenon_TX_u zenon_TT2_de))->((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (mod1)))/\((((is_aligned zenon_TX_u zenon_TT2_de)/\(~(positional_advantage zenon_TX_u zenon_TT2_de)))->((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (mod2)))/\(((~(is_aligned zenon_TX_u zenon_TT2_de))/\(~(positional_advantage zenon_TX_u zenon_TT2_de)))->((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (high))))))) -> (~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (low))) -> (~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (mod2))) -> (~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (high))) -> (~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (mod1))) -> (~(has_immunity zenon_TX_u zenon_TT2_de)) -> False).
% 24.97/25.17 do 2 intro. intros zenon_H57 zenon_H58 zenon_H59 zenon_H51 zenon_H5a zenon_H5b.
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H5d | zenon_intro zenon_H5c ].
% 24.97/25.17 exact (zenon_H5d zenon_H5b).
% 24.97/25.17 apply (zenon_and_s _ _ zenon_H5c). zenon_intro zenon_H5f. zenon_intro zenon_H5e.
% 24.97/25.17 apply (zenon_and_s _ _ zenon_H5e). zenon_intro zenon_H61. zenon_intro zenon_H60.
% 24.97/25.17 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H62. zenon_intro zenon_H4e.
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_H5f); [ zenon_intro zenon_H64 | zenon_intro zenon_H63 ].
% 24.97/25.17 apply (zenon_notand_s _ _ zenon_H64); [ zenon_intro zenon_H50 | zenon_intro zenon_H4f ].
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_H61); [ zenon_intro zenon_H66 | zenon_intro zenon_H65 ].
% 24.97/25.17 apply (zenon_notand_s _ _ zenon_H66); [ zenon_intro zenon_H56 | zenon_intro zenon_H4f ].
% 24.97/25.17 exact (zenon_H56 zenon_H50).
% 24.97/25.17 apply (zenon_L13_ zenon_TT2_de zenon_TX_u); trivial.
% 24.97/25.17 exact (zenon_H5a zenon_H65).
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_H62); [ zenon_intro zenon_H68 | zenon_intro zenon_H67 ].
% 24.97/25.17 apply (zenon_notand_s _ _ zenon_H68); [ zenon_intro zenon_H50 | zenon_intro zenon_H55 ].
% 24.97/25.17 apply (zenon_L13_ zenon_TT2_de zenon_TX_u); trivial.
% 24.97/25.17 exact (zenon_H55 zenon_H4f).
% 24.97/25.17 exact (zenon_H59 zenon_H67).
% 24.97/25.17 exact (zenon_H58 zenon_H63).
% 24.97/25.17 (* end of lemma zenon_L14_ *)
% 24.97/25.17 assert (zenon_L15_ : forall (zenon_TT2_de : zenon_U) (zenon_TX_u : zenon_U), (~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (very_low))) -> (~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (mod1))) -> (~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (high))) -> (~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (mod2))) -> (~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (low))) -> (organization zenon_TX_u) -> False).
% 24.97/25.17 do 2 intro. intros zenon_H69 zenon_H5a zenon_H51 zenon_H59 zenon_H58 zenon_H26.
% 24.97/25.17 generalize (assumption_17 zenon_TX_u). zenon_intro zenon_H0.
% 24.97/25.17 generalize (zenon_H0 zenon_TT2_de). zenon_intro zenon_H6a.
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_H6a); [ zenon_intro zenon_H2b | zenon_intro zenon_H6b ].
% 24.97/25.17 exact (zenon_H2b zenon_H26).
% 24.97/25.17 apply (zenon_and_s _ _ zenon_H6b). zenon_intro zenon_H6c. zenon_intro zenon_H57.
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_H6c); [ zenon_intro zenon_H5b | zenon_intro zenon_H6d ].
% 24.97/25.17 apply (zenon_L14_ zenon_TT2_de zenon_TX_u); trivial.
% 24.97/25.17 exact (zenon_H69 zenon_H6d).
% 24.97/25.17 (* end of lemma zenon_L15_ *)
% 24.97/25.17 assert (zenon_L16_ : forall (zenon_TT2_de : zenon_U) (zenon_TX_u : zenon_U), (organization zenon_TX_u) -> (~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (low))) -> (~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (mod2))) -> (~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (high))) -> (~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (very_low))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (low))) -> False).
% 24.97/25.17 do 2 intro. intros zenon_H26 zenon_H58 zenon_H59 zenon_H51 zenon_H69 zenon_H37 zenon_H6e.
% 24.97/25.17 elim (classic ((~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (mod1)))/\(~(greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (mod1))))); [ zenon_intro zenon_H6f | zenon_intro zenon_H70 ].
% 24.97/25.17 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H5a. zenon_intro zenon_H71.
% 24.97/25.17 apply (zenon_L15_ zenon_TT2_de zenon_TX_u); trivial.
% 24.97/25.17 cut ((greater (mod1) (low)) = (greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (low))).
% 24.97/25.17 intro zenon_D_pnotp.
% 24.97/25.17 apply zenon_H6e.
% 24.97/25.17 rewrite <- zenon_D_pnotp.
% 24.97/25.17 exact assumption_18b.
% 24.97/25.17 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H17].
% 24.97/25.17 cut (((mod1) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))); [idtac | apply NNPP; zenon_intro zenon_H72].
% 24.97/25.17 congruence.
% 24.97/25.17 apply (zenon_notand_s _ _ zenon_H70); [ zenon_intro zenon_H74 | zenon_intro zenon_H73 ].
% 24.97/25.17 apply zenon_H74. zenon_intro zenon_H65.
% 24.97/25.17 elim (classic ((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))); [ zenon_intro zenon_H75 | zenon_intro zenon_H76 ].
% 24.97/25.17 cut (((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (hazard_of_mortality zenon_TX_u zenon_TT2_de)) = ((mod1) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))).
% 24.97/25.17 intro zenon_D_pnotp.
% 24.97/25.17 apply zenon_H72.
% 24.97/25.17 rewrite <- zenon_D_pnotp.
% 24.97/25.17 exact zenon_H75.
% 24.97/25.17 cut (((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 24.97/25.17 cut (((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H5a].
% 24.97/25.17 congruence.
% 24.97/25.17 exact (zenon_H5a zenon_H65).
% 24.97/25.17 apply zenon_H76. apply refl_equal.
% 24.97/25.17 apply zenon_H76. apply refl_equal.
% 24.97/25.17 apply zenon_H73. zenon_intro zenon_H77.
% 24.97/25.17 generalize (zenon_H37 (hazard_of_mortality zenon_TX_u zenon_TT2_de)). zenon_intro zenon_H78.
% 24.97/25.17 generalize (zenon_H78 (mod1)). zenon_intro zenon_H79.
% 24.97/25.17 generalize (zenon_H79 (low)). zenon_intro zenon_H7a.
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_H7a); [ zenon_intro zenon_H71 | zenon_intro zenon_H7b ].
% 24.97/25.17 exact (zenon_H71 zenon_H77).
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_H7b); [ zenon_intro zenon_H7d | zenon_intro zenon_H7c ].
% 24.97/25.17 exact (zenon_H7d assumption_18b).
% 24.97/25.17 exact (zenon_H6e zenon_H7c).
% 24.97/25.17 apply zenon_H17. apply refl_equal.
% 24.97/25.17 (* end of lemma zenon_L16_ *)
% 24.97/25.17 assert (zenon_L17_ : (~((very_low) = (very_low))) -> False).
% 24.97/25.17 do 0 intro. intros zenon_H7e.
% 24.97/25.17 apply zenon_H7e. apply refl_equal.
% 24.97/25.17 (* end of lemma zenon_L17_ *)
% 24.97/25.17 assert (zenon_L18_ : forall (zenon_TT2_de : zenon_U) (zenon_TX_u : zenon_U), (organization zenon_TX_u) -> (~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (high))) -> (~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (very_low))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (very_low))) -> False).
% 24.97/25.17 do 2 intro. intros zenon_H26 zenon_H51 zenon_H69 zenon_H37 zenon_H7f.
% 24.97/25.17 elim (classic ((~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (low)))/\(~(greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (low))))); [ zenon_intro zenon_H80 | zenon_intro zenon_H81 ].
% 24.97/25.17 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H58. zenon_intro zenon_H6e.
% 24.97/25.17 elim (classic ((~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (mod2)))/\(~(greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (mod2))))); [ zenon_intro zenon_H82 | zenon_intro zenon_H83 ].
% 24.97/25.17 apply (zenon_and_s _ _ zenon_H82). zenon_intro zenon_H59. zenon_intro zenon_H84.
% 24.97/25.17 apply (zenon_L16_ zenon_TT2_de zenon_TX_u); trivial.
% 24.97/25.17 cut ((greater (mod2) (low)) = (greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (low))).
% 24.97/25.17 intro zenon_D_pnotp.
% 24.97/25.17 apply zenon_H6e.
% 24.97/25.17 rewrite <- zenon_D_pnotp.
% 24.97/25.17 exact assumption_18e.
% 24.97/25.17 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H17].
% 24.97/25.17 cut (((mod2) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))); [idtac | apply NNPP; zenon_intro zenon_H85].
% 24.97/25.17 congruence.
% 24.97/25.17 apply (zenon_notand_s _ _ zenon_H83); [ zenon_intro zenon_H87 | zenon_intro zenon_H86 ].
% 24.97/25.17 apply zenon_H87. zenon_intro zenon_H67.
% 24.97/25.17 elim (classic ((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))); [ zenon_intro zenon_H75 | zenon_intro zenon_H76 ].
% 24.97/25.17 cut (((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (hazard_of_mortality zenon_TX_u zenon_TT2_de)) = ((mod2) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))).
% 24.97/25.17 intro zenon_D_pnotp.
% 24.97/25.17 apply zenon_H85.
% 24.97/25.17 rewrite <- zenon_D_pnotp.
% 24.97/25.17 exact zenon_H75.
% 24.97/25.17 cut (((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 24.97/25.17 cut (((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 24.97/25.17 congruence.
% 24.97/25.17 exact (zenon_H59 zenon_H67).
% 24.97/25.17 apply zenon_H76. apply refl_equal.
% 24.97/25.17 apply zenon_H76. apply refl_equal.
% 24.97/25.17 apply zenon_H86. zenon_intro zenon_H88.
% 24.97/25.17 generalize (zenon_H37 (hazard_of_mortality zenon_TX_u zenon_TT2_de)). zenon_intro zenon_H78.
% 24.97/25.17 generalize (zenon_H78 (mod2)). zenon_intro zenon_H89.
% 24.97/25.17 generalize (zenon_H89 (low)). zenon_intro zenon_H8a.
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H84 | zenon_intro zenon_H8b ].
% 24.97/25.17 exact (zenon_H84 zenon_H88).
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_H8b); [ zenon_intro zenon_H3e | zenon_intro zenon_H7c ].
% 24.97/25.17 exact (zenon_H3e assumption_18e).
% 24.97/25.17 exact (zenon_H6e zenon_H7c).
% 24.97/25.17 apply zenon_H17. apply refl_equal.
% 24.97/25.17 cut ((greater (low) (very_low)) = (greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (very_low))).
% 24.97/25.17 intro zenon_D_pnotp.
% 24.97/25.17 apply zenon_H7f.
% 24.97/25.17 rewrite <- zenon_D_pnotp.
% 24.97/25.17 exact assumption_18c.
% 24.97/25.17 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H7e].
% 24.97/25.17 cut (((low) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 24.97/25.17 congruence.
% 24.97/25.17 apply (zenon_notand_s _ _ zenon_H81); [ zenon_intro zenon_H8e | zenon_intro zenon_H8d ].
% 24.97/25.17 apply zenon_H8e. zenon_intro zenon_H63.
% 24.97/25.17 elim (classic ((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))); [ zenon_intro zenon_H75 | zenon_intro zenon_H76 ].
% 24.97/25.17 cut (((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (hazard_of_mortality zenon_TX_u zenon_TT2_de)) = ((low) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))).
% 24.97/25.17 intro zenon_D_pnotp.
% 24.97/25.17 apply zenon_H8c.
% 24.97/25.17 rewrite <- zenon_D_pnotp.
% 24.97/25.17 exact zenon_H75.
% 24.97/25.17 cut (((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 24.97/25.17 cut (((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (low))); [idtac | apply NNPP; zenon_intro zenon_H58].
% 24.97/25.17 congruence.
% 24.97/25.17 exact (zenon_H58 zenon_H63).
% 24.97/25.17 apply zenon_H76. apply refl_equal.
% 24.97/25.17 apply zenon_H76. apply refl_equal.
% 24.97/25.17 apply zenon_H8d. zenon_intro zenon_H7c.
% 24.97/25.17 generalize (zenon_H37 (hazard_of_mortality zenon_TX_u zenon_TT2_de)). zenon_intro zenon_H78.
% 24.97/25.17 generalize (zenon_H78 (low)). zenon_intro zenon_H8f.
% 24.97/25.17 generalize (zenon_H8f (very_low)). zenon_intro zenon_H90.
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_H90); [ zenon_intro zenon_H6e | zenon_intro zenon_H91 ].
% 24.97/25.17 exact (zenon_H6e zenon_H7c).
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_H91); [ zenon_intro zenon_H93 | zenon_intro zenon_H92 ].
% 24.97/25.17 exact (zenon_H93 assumption_18c).
% 24.97/25.17 exact (zenon_H7f zenon_H92).
% 24.97/25.17 apply zenon_H7e. apply refl_equal.
% 24.97/25.17 (* end of lemma zenon_L18_ *)
% 24.97/25.17 assert (zenon_L19_ : forall (zenon_TT2_de : 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)))))) -> (~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (mod1))) -> (~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (high))) -> (~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (mod2))) -> (~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (low))) -> (greater (age zenon_TX_u zenon_TT2_de) (eta)) -> False).
% 24.97/25.17 do 2 intro. intros zenon_H30 zenon_H5a zenon_H51 zenon_H59 zenon_H58 zenon_H94.
% 24.97/25.17 generalize (zenon_H30 zenon_TT2_de). zenon_intro zenon_H95.
% 24.97/25.17 apply (zenon_and_s _ _ zenon_H95). zenon_intro zenon_H26. zenon_intro zenon_H96.
% 24.97/25.17 apply (zenon_and_s _ _ zenon_H96). zenon_intro zenon_H98. zenon_intro zenon_H97.
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_H97); [ zenon_intro zenon_H99 | zenon_intro zenon_H5b ].
% 24.97/25.17 exact (zenon_H99 zenon_H94).
% 24.97/25.17 generalize (assumption_17 zenon_TX_u). zenon_intro zenon_H0.
% 24.97/25.17 generalize (zenon_H0 zenon_TT2_de). zenon_intro zenon_H6a.
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_H6a); [ zenon_intro zenon_H2b | zenon_intro zenon_H6b ].
% 24.97/25.17 exact (zenon_H2b zenon_H26).
% 24.97/25.17 apply (zenon_and_s _ _ zenon_H6b). zenon_intro zenon_H6c. zenon_intro zenon_H57.
% 24.97/25.17 apply (zenon_L14_ zenon_TT2_de zenon_TX_u); trivial.
% 24.97/25.17 (* end of lemma zenon_L19_ *)
% 24.97/25.17 assert (zenon_L20_ : forall (zenon_TT2_de : zenon_U) (zenon_TX_u : zenon_U), (greater (age zenon_TX_u zenon_TT2_de) (eta)) -> (~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (low))) -> (~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (mod2))) -> (~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (high))) -> (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)))))) -> (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_TT2_de) (low))) -> False).
% 24.97/25.17 do 2 intro. intros zenon_H94 zenon_H58 zenon_H59 zenon_H51 zenon_H30 zenon_H37 zenon_H6e.
% 24.97/25.17 elim (classic ((~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (mod1)))/\(~(greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (mod1))))); [ zenon_intro zenon_H6f | zenon_intro zenon_H70 ].
% 24.97/25.17 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H5a. zenon_intro zenon_H71.
% 24.97/25.17 apply (zenon_L19_ zenon_TT2_de zenon_TX_u); trivial.
% 24.97/25.17 cut ((greater (mod1) (low)) = (greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (low))).
% 24.97/25.17 intro zenon_D_pnotp.
% 24.97/25.17 apply zenon_H6e.
% 24.97/25.17 rewrite <- zenon_D_pnotp.
% 24.97/25.17 exact assumption_18b.
% 24.97/25.17 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H17].
% 24.97/25.17 cut (((mod1) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))); [idtac | apply NNPP; zenon_intro zenon_H72].
% 24.97/25.17 congruence.
% 24.97/25.17 apply (zenon_notand_s _ _ zenon_H70); [ zenon_intro zenon_H74 | zenon_intro zenon_H73 ].
% 24.97/25.17 apply zenon_H74. zenon_intro zenon_H65.
% 24.97/25.17 elim (classic ((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))); [ zenon_intro zenon_H75 | zenon_intro zenon_H76 ].
% 24.97/25.17 cut (((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (hazard_of_mortality zenon_TX_u zenon_TT2_de)) = ((mod1) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))).
% 24.97/25.17 intro zenon_D_pnotp.
% 24.97/25.17 apply zenon_H72.
% 24.97/25.17 rewrite <- zenon_D_pnotp.
% 24.97/25.17 exact zenon_H75.
% 24.97/25.17 cut (((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 24.97/25.17 cut (((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (mod1))); [idtac | apply NNPP; zenon_intro zenon_H5a].
% 24.97/25.17 congruence.
% 24.97/25.17 exact (zenon_H5a zenon_H65).
% 24.97/25.17 apply zenon_H76. apply refl_equal.
% 24.97/25.17 apply zenon_H76. apply refl_equal.
% 24.97/25.17 apply zenon_H73. zenon_intro zenon_H77.
% 24.97/25.17 generalize (zenon_H37 (hazard_of_mortality zenon_TX_u zenon_TT2_de)). zenon_intro zenon_H78.
% 24.97/25.17 generalize (zenon_H78 (mod1)). zenon_intro zenon_H79.
% 24.97/25.17 generalize (zenon_H79 (low)). zenon_intro zenon_H7a.
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_H7a); [ zenon_intro zenon_H71 | zenon_intro zenon_H7b ].
% 24.97/25.17 exact (zenon_H71 zenon_H77).
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_H7b); [ zenon_intro zenon_H7d | zenon_intro zenon_H7c ].
% 24.97/25.17 exact (zenon_H7d assumption_18b).
% 24.97/25.17 exact (zenon_H6e zenon_H7c).
% 24.97/25.17 apply zenon_H17. apply refl_equal.
% 24.97/25.17 (* end of lemma zenon_L20_ *)
% 24.97/25.17 assert (zenon_L21_ : forall (zenon_TT2_de : 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)))))) -> (~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (mod2))) -> (~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (low))) -> (greater (age zenon_TX_u zenon_TT2_de) (eta)) -> (~(greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (low))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> (~(greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (mod2))) -> False).
% 24.97/25.17 do 2 intro. intros zenon_H30 zenon_H59 zenon_H58 zenon_H94 zenon_H6e zenon_H37 zenon_H84.
% 24.97/25.17 elim (classic ((~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (high)))/\(~(greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (high))))); [ zenon_intro zenon_H9a | zenon_intro zenon_H9b ].
% 24.97/25.17 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H51. zenon_intro zenon_H9c.
% 24.97/25.17 apply (zenon_L20_ zenon_TT2_de zenon_TX_u); trivial.
% 24.97/25.17 cut ((greater (high) (mod2)) = (greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (mod2))).
% 24.97/25.17 intro zenon_D_pnotp.
% 24.97/25.17 apply zenon_H84.
% 24.97/25.17 rewrite <- zenon_D_pnotp.
% 24.97/25.17 exact assumption_18d.
% 24.97/25.17 cut (((mod2) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H16].
% 24.97/25.17 cut (((high) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))); [idtac | apply NNPP; zenon_intro zenon_H9d].
% 24.97/25.17 congruence.
% 24.97/25.17 apply (zenon_notand_s _ _ zenon_H9b); [ zenon_intro zenon_H9f | zenon_intro zenon_H9e ].
% 24.97/25.17 apply zenon_H9f. zenon_intro zenon_H53.
% 24.97/25.17 elim (classic ((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))); [ zenon_intro zenon_H75 | zenon_intro zenon_H76 ].
% 24.97/25.17 cut (((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (hazard_of_mortality zenon_TX_u zenon_TT2_de)) = ((high) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))).
% 24.97/25.17 intro zenon_D_pnotp.
% 24.97/25.17 apply zenon_H9d.
% 24.97/25.17 rewrite <- zenon_D_pnotp.
% 24.97/25.17 exact zenon_H75.
% 24.97/25.17 cut (((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 24.97/25.17 cut (((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (high))); [idtac | apply NNPP; zenon_intro zenon_H51].
% 24.97/25.17 congruence.
% 24.97/25.17 exact (zenon_H51 zenon_H53).
% 24.97/25.17 apply zenon_H76. apply refl_equal.
% 24.97/25.17 apply zenon_H76. apply refl_equal.
% 24.97/25.17 apply zenon_H9e. zenon_intro zenon_Ha0.
% 24.97/25.17 generalize (zenon_H37 (hazard_of_mortality zenon_TX_u zenon_TT2_de)). zenon_intro zenon_H78.
% 24.97/25.17 generalize (zenon_H78 (high)). zenon_intro zenon_Ha1.
% 24.97/25.17 generalize (zenon_Ha1 (mod2)). zenon_intro zenon_Ha2.
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_Ha2); [ zenon_intro zenon_H9c | zenon_intro zenon_Ha3 ].
% 24.97/25.17 exact (zenon_H9c zenon_Ha0).
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_Ha3); [ zenon_intro zenon_H45 | zenon_intro zenon_H88 ].
% 24.97/25.17 exact (zenon_H45 assumption_18d).
% 24.97/25.17 exact (zenon_H84 zenon_H88).
% 24.97/25.17 apply zenon_H16. apply refl_equal.
% 24.97/25.17 (* end of lemma zenon_L21_ *)
% 24.97/25.17 assert (zenon_L22_ : forall (zenon_TT2_de : zenon_U) (zenon_TX_u : zenon_U), (greater (age zenon_TX_u zenon_TT2_de) (eta)) -> (~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (low))) -> (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)))))) -> (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_TT2_de) (low))) -> False).
% 24.97/25.17 do 2 intro. intros zenon_H94 zenon_H58 zenon_H30 zenon_H37 zenon_H6e.
% 24.97/25.17 elim (classic ((~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (mod2)))/\(~(greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (mod2))))); [ zenon_intro zenon_H82 | zenon_intro zenon_H83 ].
% 24.97/25.17 apply (zenon_and_s _ _ zenon_H82). zenon_intro zenon_H59. zenon_intro zenon_H84.
% 24.97/25.17 apply (zenon_L21_ zenon_TT2_de zenon_TX_u); trivial.
% 24.97/25.17 cut ((greater (mod2) (low)) = (greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (low))).
% 24.97/25.17 intro zenon_D_pnotp.
% 24.97/25.17 apply zenon_H6e.
% 24.97/25.17 rewrite <- zenon_D_pnotp.
% 24.97/25.17 exact assumption_18e.
% 24.97/25.17 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H17].
% 24.97/25.17 cut (((mod2) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))); [idtac | apply NNPP; zenon_intro zenon_H85].
% 24.97/25.17 congruence.
% 24.97/25.17 apply (zenon_notand_s _ _ zenon_H83); [ zenon_intro zenon_H87 | zenon_intro zenon_H86 ].
% 24.97/25.17 apply zenon_H87. zenon_intro zenon_H67.
% 24.97/25.17 elim (classic ((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))); [ zenon_intro zenon_H75 | zenon_intro zenon_H76 ].
% 24.97/25.17 cut (((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (hazard_of_mortality zenon_TX_u zenon_TT2_de)) = ((mod2) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))).
% 24.97/25.17 intro zenon_D_pnotp.
% 24.97/25.17 apply zenon_H85.
% 24.97/25.17 rewrite <- zenon_D_pnotp.
% 24.97/25.17 exact zenon_H75.
% 24.97/25.17 cut (((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 24.97/25.17 cut (((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (mod2))); [idtac | apply NNPP; zenon_intro zenon_H59].
% 24.97/25.17 congruence.
% 24.97/25.17 exact (zenon_H59 zenon_H67).
% 24.97/25.17 apply zenon_H76. apply refl_equal.
% 24.97/25.17 apply zenon_H76. apply refl_equal.
% 24.97/25.17 apply zenon_H86. zenon_intro zenon_H88.
% 24.97/25.17 generalize (zenon_H37 (hazard_of_mortality zenon_TX_u zenon_TT2_de)). zenon_intro zenon_H78.
% 24.97/25.17 generalize (zenon_H78 (mod2)). zenon_intro zenon_H89.
% 24.97/25.17 generalize (zenon_H89 (low)). zenon_intro zenon_H8a.
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H84 | zenon_intro zenon_H8b ].
% 24.97/25.17 exact (zenon_H84 zenon_H88).
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_H8b); [ zenon_intro zenon_H3e | zenon_intro zenon_H7c ].
% 24.97/25.17 exact (zenon_H3e assumption_18e).
% 24.97/25.17 exact (zenon_H6e zenon_H7c).
% 24.97/25.17 apply zenon_H17. apply refl_equal.
% 24.97/25.17 (* end of lemma zenon_L22_ *)
% 24.97/25.17 assert (zenon_L23_ : forall (zenon_TT2_de : 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 (age zenon_TX_u zenon_TT2_de) (eta)) -> (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_TT2_de) (very_low))) -> False).
% 24.97/25.17 do 2 intro. intros zenon_H30 zenon_H94 zenon_H37 zenon_H7f.
% 24.97/25.17 elim (classic ((~((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (low)))/\(~(greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (low))))); [ zenon_intro zenon_H80 | zenon_intro zenon_H81 ].
% 24.97/25.17 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H58. zenon_intro zenon_H6e.
% 24.97/25.17 apply (zenon_L22_ zenon_TT2_de zenon_TX_u); trivial.
% 24.97/25.17 cut ((greater (low) (very_low)) = (greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (very_low))).
% 24.97/25.17 intro zenon_D_pnotp.
% 24.97/25.17 apply zenon_H7f.
% 24.97/25.17 rewrite <- zenon_D_pnotp.
% 24.97/25.17 exact assumption_18c.
% 24.97/25.17 cut (((very_low) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_H7e].
% 24.97/25.17 cut (((low) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 24.97/25.17 congruence.
% 24.97/25.17 apply (zenon_notand_s _ _ zenon_H81); [ zenon_intro zenon_H8e | zenon_intro zenon_H8d ].
% 24.97/25.17 apply zenon_H8e. zenon_intro zenon_H63.
% 24.97/25.17 elim (classic ((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))); [ zenon_intro zenon_H75 | zenon_intro zenon_H76 ].
% 24.97/25.17 cut (((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (hazard_of_mortality zenon_TX_u zenon_TT2_de)) = ((low) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))).
% 24.97/25.17 intro zenon_D_pnotp.
% 24.97/25.17 apply zenon_H8c.
% 24.97/25.17 rewrite <- zenon_D_pnotp.
% 24.97/25.17 exact zenon_H75.
% 24.97/25.17 cut (((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 24.97/25.17 cut (((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (low))); [idtac | apply NNPP; zenon_intro zenon_H58].
% 24.97/25.17 congruence.
% 24.97/25.17 exact (zenon_H58 zenon_H63).
% 24.97/25.17 apply zenon_H76. apply refl_equal.
% 24.97/25.17 apply zenon_H76. apply refl_equal.
% 24.97/25.17 apply zenon_H8d. zenon_intro zenon_H7c.
% 24.97/25.17 generalize (zenon_H37 (hazard_of_mortality zenon_TX_u zenon_TT2_de)). zenon_intro zenon_H78.
% 24.97/25.17 generalize (zenon_H78 (low)). zenon_intro zenon_H8f.
% 24.97/25.17 generalize (zenon_H8f (very_low)). zenon_intro zenon_H90.
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_H90); [ zenon_intro zenon_H6e | zenon_intro zenon_H91 ].
% 24.97/25.17 exact (zenon_H6e zenon_H7c).
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_H91); [ zenon_intro zenon_H93 | zenon_intro zenon_H92 ].
% 24.97/25.17 exact (zenon_H93 assumption_18c).
% 24.97/25.17 exact (zenon_H7f zenon_H92).
% 24.97/25.17 apply zenon_H7e. apply refl_equal.
% 24.97/25.17 (* end of lemma zenon_L23_ *)
% 24.97/25.17 assert (zenon_L24_ : forall (zenon_TT1_ba : zenon_U) (zenon_TT2_de : 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_TT2_de) (eta)) -> (~(greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))) -> (has_immunity zenon_TX_u zenon_TT1_ba) -> (organization zenon_TX_u) -> False).
% 24.97/25.17 do 3 intro. intros zenon_H37 zenon_H30 zenon_H94 zenon_Ha4 zenon_H27 zenon_H26.
% 24.97/25.17 generalize (assumption_17 zenon_TX_u). zenon_intro zenon_H0.
% 24.97/25.17 generalize (zenon_H0 zenon_TT1_ba). zenon_intro zenon_H29.
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ].
% 24.97/25.17 exact (zenon_H2b zenon_H26).
% 24.97/25.17 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H2d. zenon_intro zenon_H2c.
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ].
% 24.97/25.17 exact (zenon_H2f zenon_H27).
% 24.97/25.17 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [ zenon_intro zenon_H36 | zenon_intro zenon_H28 ].
% 24.97/25.17 elim (classic (greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (very_low))); [ zenon_intro zenon_H92 | zenon_intro zenon_H7f ].
% 24.97/25.17 cut ((greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (very_low)) = (greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))).
% 24.97/25.17 intro zenon_D_pnotp.
% 24.97/25.17 apply zenon_Ha4.
% 24.97/25.17 rewrite <- zenon_D_pnotp.
% 24.97/25.17 exact zenon_H92.
% 24.97/25.17 cut (((very_low) = (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [idtac | apply NNPP; zenon_intro zenon_H28].
% 24.97/25.17 cut (((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 24.97/25.17 congruence.
% 24.97/25.17 apply zenon_H76. apply refl_equal.
% 24.97/25.17 exact (zenon_H28 zenon_H36).
% 24.97/25.17 apply (zenon_L23_ zenon_TT2_de zenon_TX_u); trivial.
% 24.97/25.17 elim (classic ((hazard_of_mortality zenon_TX_u zenon_TT1_ba) = (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H49 ].
% 24.97/25.17 cut (((hazard_of_mortality zenon_TX_u zenon_TT1_ba) = (hazard_of_mortality zenon_TX_u zenon_TT1_ba)) = ((very_low) = (hazard_of_mortality zenon_TX_u zenon_TT1_ba))).
% 24.97/25.17 intro zenon_D_pnotp.
% 24.97/25.17 apply zenon_H28.
% 24.97/25.17 rewrite <- zenon_D_pnotp.
% 24.97/25.17 exact zenon_Ha5.
% 24.97/25.17 cut (((hazard_of_mortality zenon_TX_u zenon_TT1_ba) = (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [idtac | apply NNPP; zenon_intro zenon_H49].
% 24.97/25.17 cut (((hazard_of_mortality zenon_TX_u zenon_TT1_ba) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Ha6].
% 24.97/25.17 congruence.
% 24.97/25.17 exact (zenon_Ha6 zenon_H2e).
% 24.97/25.17 apply zenon_H49. apply refl_equal.
% 24.97/25.17 apply zenon_H49. apply refl_equal.
% 24.97/25.17 (* end of lemma zenon_L24_ *)
% 24.97/25.17 assert (zenon_L25_ : forall (zenon_TT1_ba : zenon_U) (zenon_TT2_de : 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_TT2_de) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))) -> (greater (age zenon_TX_u zenon_TT2_de) (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 (eta) (age zenon_TX_u zenon_TT1_ba)) -> False).
% 24.97/25.17 do 3 intro. intros zenon_H37 zenon_Ha4 zenon_H94 zenon_H30 zenon_H18.
% 24.97/25.17 generalize (zenon_H30 zenon_TT1_ba). zenon_intro zenon_H31.
% 24.97/25.17 apply (zenon_and_s _ _ zenon_H31). zenon_intro zenon_H26. zenon_intro zenon_H32.
% 24.97/25.17 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H34. zenon_intro zenon_H33.
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_H34); [ zenon_intro zenon_H19 | zenon_intro zenon_H27 ].
% 24.97/25.17 apply (zenon_L5_ zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.17 apply (zenon_L24_ zenon_TT1_ba zenon_TT2_de zenon_TX_u); trivial.
% 24.97/25.17 (* end of lemma zenon_L25_ *)
% 24.97/25.17 assert (zenon_L26_ : forall (zenon_TT2_de : zenon_U) (zenon_TT1_ba : 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_TT2_de) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))) -> (greater (age zenon_TX_u zenon_TT2_de) (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 (eta) (age zenon_TX_u zenon_TT1_ba)) -> False).
% 24.97/25.17 do 3 intro. intros zenon_H37 zenon_Ha4 zenon_H94 zenon_H30 zenon_H18.
% 24.97/25.17 apply (zenon_L25_ zenon_TT1_ba zenon_TT2_de zenon_TX_u); trivial.
% 24.97/25.17 (* end of lemma zenon_L26_ *)
% 24.97/25.17 assert (zenon_L27_ : forall (zenon_TT2_de : zenon_U) (zenon_TT1_ba : zenon_U) (zenon_TX_u : zenon_U), (greater (eta) (age zenon_TX_u zenon_TT1_ba)) -> (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_de) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))) -> (greater (age zenon_TX_u zenon_TT2_de) (eta)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> False).
% 24.97/25.17 do 3 intro. intros zenon_H18 zenon_H30 zenon_Ha4 zenon_H94 zenon_H37.
% 24.97/25.17 apply (zenon_L26_ zenon_TT2_de zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.17 (* end of lemma zenon_L27_ *)
% 24.97/25.17 assert (zenon_L28_ : (~((mod1) = (mod1))) -> False).
% 24.97/25.17 do 0 intro. intros zenon_Ha7.
% 24.97/25.17 apply zenon_Ha7. apply refl_equal.
% 24.97/25.17 (* end of lemma zenon_L28_ *)
% 24.97/25.17 assert (zenon_L29_ : forall (zenon_TT1_ba : 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 (mod1) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))) -> (greater (eta) (age zenon_TX_u zenon_TT1_ba)) -> (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)))))) -> False).
% 24.97/25.17 do 2 intro. intros zenon_H37 zenon_Ha8 zenon_H18 zenon_H30.
% 24.97/25.17 elim (classic (greater (low) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [ zenon_intro zenon_H39 | zenon_intro zenon_H35 ].
% 24.97/25.17 generalize (zenon_H37 (mod1)). zenon_intro zenon_Ha9.
% 24.97/25.17 generalize (zenon_Ha9 (low)). zenon_intro zenon_Haa.
% 24.97/25.17 generalize (zenon_Haa (hazard_of_mortality zenon_TX_u zenon_TT1_ba)). zenon_intro zenon_Hab.
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_Hab); [ zenon_intro zenon_H7d | zenon_intro zenon_Hac ].
% 24.97/25.17 exact (zenon_H7d assumption_18b).
% 24.97/25.17 apply (zenon_imply_s _ _ zenon_Hac); [ zenon_intro zenon_H35 | zenon_intro zenon_Had ].
% 24.97/25.17 exact (zenon_H35 zenon_H39).
% 24.97/25.17 exact (zenon_Ha8 zenon_Had).
% 24.97/25.17 apply (zenon_L9_ zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.17 (* end of lemma zenon_L29_ *)
% 24.97/25.17 assert (zenon_L30_ : forall (zenon_TT2_de : zenon_U) (zenon_TT1_ba : 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_TT2_de) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))) -> (greater (age zenon_TX_u zenon_TT2_de) (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 (eta) (age zenon_TX_u zenon_TT1_ba)) -> False).
% 24.97/25.17 do 3 intro. intros zenon_H37 zenon_Ha4 zenon_H94 zenon_H30 zenon_H18.
% 24.97/25.17 apply (zenon_L25_ zenon_TT1_ba zenon_TT2_de zenon_TX_u); trivial.
% 24.97/25.17 (* end of lemma zenon_L30_ *)
% 24.97/25.17 assert (zenon_L31_ : forall (zenon_TT2_de : zenon_U) (zenon_TT1_ba : 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_TT2_de) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))) -> (greater (age zenon_TX_u zenon_TT2_de) (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 (eta) (age zenon_TX_u zenon_TT1_ba)) -> False).
% 24.97/25.17 do 3 intro. intros zenon_H37 zenon_Ha4 zenon_H94 zenon_H30 zenon_H18.
% 24.97/25.17 apply (zenon_L25_ zenon_TT1_ba zenon_TT2_de zenon_TX_u); trivial.
% 24.97/25.17 (* end of lemma zenon_L31_ *)
% 24.97/25.17 assert (zenon_L32_ : forall (zenon_TT1_ba : zenon_U) (zenon_TT2_de : zenon_U) (zenon_TX_u : zenon_U), (greater (eta) (age zenon_TX_u zenon_TT1_ba)) -> (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_de) (eta)) -> (~(greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> False).
% 24.97/25.17 do 3 intro. intros zenon_H18 zenon_H30 zenon_H94 zenon_Ha4 zenon_H37.
% 24.97/25.17 apply (zenon_L31_ zenon_TT2_de zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.17 (* end of lemma zenon_L32_ *)
% 24.97/25.17 assert (zenon_L33_ : forall (zenon_TT1_ba : zenon_U) (zenon_TX_u : zenon_U), ((hazard_of_mortality zenon_TX_u zenon_E) = (low)) -> (~(greater (hazard_of_mortality zenon_TX_u zenon_E) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))) -> (greater (eta) (age zenon_TX_u zenon_TT1_ba)) -> (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)))))) -> False).
% 24.97/25.17 do 2 intro. intros zenon_Hae zenon_H48 zenon_H18 zenon_H30.
% 24.97/25.17 elim (classic (greater (low) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [ zenon_intro zenon_H39 | zenon_intro zenon_H35 ].
% 24.97/25.17 cut ((greater (low) (hazard_of_mortality zenon_TX_u zenon_TT1_ba)) = (greater (hazard_of_mortality zenon_TX_u zenon_E) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))).
% 24.97/25.17 intro zenon_D_pnotp.
% 24.97/25.17 apply zenon_H48.
% 24.97/25.17 rewrite <- zenon_D_pnotp.
% 24.97/25.17 exact zenon_H39.
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_TT1_ba) = (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [idtac | apply NNPP; zenon_intro zenon_H49].
% 24.97/25.18 cut (((low) = (hazard_of_mortality zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Haf].
% 24.97/25.18 congruence.
% 24.97/25.18 elim (classic ((hazard_of_mortality zenon_TX_u zenon_E) = (hazard_of_mortality zenon_TX_u zenon_E))); [ zenon_intro zenon_H4b | zenon_intro zenon_H4c ].
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_E) = (hazard_of_mortality zenon_TX_u zenon_E)) = ((low) = (hazard_of_mortality zenon_TX_u zenon_E))).
% 24.97/25.18 intro zenon_D_pnotp.
% 24.97/25.18 apply zenon_Haf.
% 24.97/25.18 rewrite <- zenon_D_pnotp.
% 24.97/25.18 exact zenon_H4b.
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_E) = (hazard_of_mortality zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H4c].
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_Hb0].
% 24.97/25.18 congruence.
% 24.97/25.18 exact (zenon_Hb0 zenon_Hae).
% 24.97/25.18 apply zenon_H4c. apply refl_equal.
% 24.97/25.18 apply zenon_H4c. apply refl_equal.
% 24.97/25.18 apply zenon_H49. apply refl_equal.
% 24.97/25.18 apply (zenon_L9_ zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.18 (* end of lemma zenon_L33_ *)
% 24.97/25.18 assert (zenon_L34_ : forall (zenon_TT2_de : zenon_U) (zenon_TT1_ba : zenon_U) (zenon_TX_u : zenon_U), (greater (eta) (age zenon_TX_u zenon_TT1_ba)) -> (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_de) (eta)) -> (~(greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_u zenon_E) = (low)) -> False).
% 24.97/25.18 do 3 intro. intros zenon_H18 zenon_H30 zenon_H94 zenon_Ha4 zenon_H37 zenon_Hae.
% 24.97/25.18 elim (classic ((low) = (hazard_of_mortality zenon_TX_u zenon_E))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Haf ].
% 24.97/25.18 elim (classic (greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (low))); [ zenon_intro zenon_H7c | zenon_intro zenon_H6e ].
% 24.97/25.18 elim (classic (greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (hazard_of_mortality zenon_TX_u zenon_E))); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb3 ].
% 24.97/25.18 elim (classic (greater (hazard_of_mortality zenon_TX_u zenon_E) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H48 ].
% 24.97/25.18 generalize (zenon_H37 (hazard_of_mortality zenon_TX_u zenon_TT2_de)). zenon_intro zenon_H78.
% 24.97/25.18 generalize (zenon_H78 (hazard_of_mortality zenon_TX_u zenon_E)). zenon_intro zenon_Hb5.
% 24.97/25.18 generalize (zenon_Hb5 (hazard_of_mortality zenon_TX_u zenon_TT1_ba)). zenon_intro zenon_Hb6.
% 24.97/25.18 apply (zenon_imply_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb3 | zenon_intro zenon_Hb7 ].
% 24.97/25.18 exact (zenon_Hb3 zenon_Hb2).
% 24.97/25.18 apply (zenon_imply_s _ _ zenon_Hb7); [ zenon_intro zenon_H48 | zenon_intro zenon_Hb8 ].
% 24.97/25.18 exact (zenon_H48 zenon_Hb4).
% 24.97/25.18 exact (zenon_Ha4 zenon_Hb8).
% 24.97/25.18 apply (zenon_L33_ zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.18 cut ((greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (low)) = (greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (hazard_of_mortality zenon_TX_u zenon_E))).
% 24.97/25.18 intro zenon_D_pnotp.
% 24.97/25.18 apply zenon_Hb3.
% 24.97/25.18 rewrite <- zenon_D_pnotp.
% 24.97/25.18 exact zenon_H7c.
% 24.97/25.18 cut (((low) = (hazard_of_mortality zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Haf].
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 24.97/25.18 congruence.
% 24.97/25.18 apply zenon_H76. apply refl_equal.
% 24.97/25.18 exact (zenon_Haf zenon_Hb1).
% 24.97/25.18 elim (classic (greater (hazard_of_mortality zenon_TX_u zenon_E) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H48 ].
% 24.97/25.18 elim (classic (greater (low) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [ zenon_intro zenon_H39 | zenon_intro zenon_H35 ].
% 24.97/25.18 cut ((greater (low) (hazard_of_mortality zenon_TX_u zenon_TT1_ba)) = (greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))).
% 24.97/25.18 intro zenon_D_pnotp.
% 24.97/25.18 apply zenon_Ha4.
% 24.97/25.18 rewrite <- zenon_D_pnotp.
% 24.97/25.18 exact zenon_H39.
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_TT1_ba) = (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [idtac | apply NNPP; zenon_intro zenon_H49].
% 24.97/25.18 cut (((low) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 24.97/25.18 congruence.
% 24.97/25.18 elim (classic ((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))); [ zenon_intro zenon_H75 | zenon_intro zenon_H76 ].
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (hazard_of_mortality zenon_TX_u zenon_TT2_de)) = ((low) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))).
% 24.97/25.18 intro zenon_D_pnotp.
% 24.97/25.18 apply zenon_H8c.
% 24.97/25.18 rewrite <- zenon_D_pnotp.
% 24.97/25.18 exact zenon_H75.
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (low))); [idtac | apply NNPP; zenon_intro zenon_H58].
% 24.97/25.18 congruence.
% 24.97/25.18 apply (zenon_L22_ zenon_TT2_de zenon_TX_u); trivial.
% 24.97/25.18 apply zenon_H76. apply refl_equal.
% 24.97/25.18 apply zenon_H76. apply refl_equal.
% 24.97/25.18 apply zenon_H49. apply refl_equal.
% 24.97/25.18 cut ((greater (hazard_of_mortality zenon_TX_u zenon_E) (hazard_of_mortality zenon_TX_u zenon_TT1_ba)) = (greater (low) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))).
% 24.97/25.18 intro zenon_D_pnotp.
% 24.97/25.18 apply zenon_H35.
% 24.97/25.18 rewrite <- zenon_D_pnotp.
% 24.97/25.18 exact zenon_Hb4.
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_TT1_ba) = (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [idtac | apply NNPP; zenon_intro zenon_H49].
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_Hb0].
% 24.97/25.18 congruence.
% 24.97/25.18 elim (classic ((low) = (low))); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H17 ].
% 24.97/25.18 cut (((low) = (low)) = ((hazard_of_mortality zenon_TX_u zenon_E) = (low))).
% 24.97/25.18 intro zenon_D_pnotp.
% 24.97/25.18 apply zenon_Hb0.
% 24.97/25.18 rewrite <- zenon_D_pnotp.
% 24.97/25.18 exact zenon_Hb9.
% 24.97/25.18 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H17].
% 24.97/25.18 cut (((low) = (hazard_of_mortality zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Haf].
% 24.97/25.18 congruence.
% 24.97/25.18 exact (zenon_Haf zenon_Hb1).
% 24.97/25.18 apply zenon_H17. apply refl_equal.
% 24.97/25.18 apply zenon_H17. apply refl_equal.
% 24.97/25.18 apply zenon_H49. apply refl_equal.
% 24.97/25.18 apply (zenon_L33_ zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.18 elim (classic ((hazard_of_mortality zenon_TX_u zenon_E) = (hazard_of_mortality zenon_TX_u zenon_E))); [ zenon_intro zenon_H4b | zenon_intro zenon_H4c ].
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_E) = (hazard_of_mortality zenon_TX_u zenon_E)) = ((low) = (hazard_of_mortality zenon_TX_u zenon_E))).
% 24.97/25.18 intro zenon_D_pnotp.
% 24.97/25.18 apply zenon_Haf.
% 24.97/25.18 rewrite <- zenon_D_pnotp.
% 24.97/25.18 exact zenon_H4b.
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_E) = (hazard_of_mortality zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H4c].
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_Hb0].
% 24.97/25.18 congruence.
% 24.97/25.18 exact (zenon_Hb0 zenon_Hae).
% 24.97/25.18 apply zenon_H4c. apply refl_equal.
% 24.97/25.18 apply zenon_H4c. apply refl_equal.
% 24.97/25.18 (* end of lemma zenon_L34_ *)
% 24.97/25.18 assert (zenon_L35_ : forall (zenon_TT2_de : zenon_U) (zenon_TX_u : zenon_U), (greater (age zenon_TX_u zenon_TT2_de) (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_TT2_de) (hazard_of_mortality zenon_TX_u zenon_E))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_u zenon_E) = (very_low)) -> False).
% 24.97/25.18 do 2 intro. intros zenon_H94 zenon_H30 zenon_Hb3 zenon_H37 zenon_Hba.
% 24.97/25.18 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_u zenon_E))); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hbc ].
% 24.97/25.18 elim (classic (greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (very_low))); [ zenon_intro zenon_H92 | zenon_intro zenon_H7f ].
% 24.97/25.18 cut ((greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (very_low)) = (greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (hazard_of_mortality zenon_TX_u zenon_E))).
% 24.97/25.18 intro zenon_D_pnotp.
% 24.97/25.18 apply zenon_Hb3.
% 24.97/25.18 rewrite <- zenon_D_pnotp.
% 24.97/25.18 exact zenon_H92.
% 24.97/25.18 cut (((very_low) = (hazard_of_mortality zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Hbc].
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 24.97/25.18 congruence.
% 24.97/25.18 apply zenon_H76. apply refl_equal.
% 24.97/25.18 exact (zenon_Hbc zenon_Hbb).
% 24.97/25.18 apply (zenon_L23_ zenon_TT2_de zenon_TX_u); trivial.
% 24.97/25.18 elim (classic ((hazard_of_mortality zenon_TX_u zenon_E) = (hazard_of_mortality zenon_TX_u zenon_E))); [ zenon_intro zenon_H4b | zenon_intro zenon_H4c ].
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_E) = (hazard_of_mortality zenon_TX_u zenon_E)) = ((very_low) = (hazard_of_mortality zenon_TX_u zenon_E))).
% 24.97/25.18 intro zenon_D_pnotp.
% 24.97/25.18 apply zenon_Hbc.
% 24.97/25.18 rewrite <- zenon_D_pnotp.
% 24.97/25.18 exact zenon_H4b.
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_E) = (hazard_of_mortality zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H4c].
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_E) = (very_low))); [idtac | apply NNPP; zenon_intro zenon_Hbd].
% 24.97/25.18 congruence.
% 24.97/25.18 exact (zenon_Hbd zenon_Hba).
% 24.97/25.18 apply zenon_H4c. apply refl_equal.
% 24.97/25.18 apply zenon_H4c. apply refl_equal.
% 24.97/25.18 (* end of lemma zenon_L35_ *)
% 24.97/25.18 assert (zenon_L36_ : (~((eta) = (eta))) -> False).
% 24.97/25.18 do 0 intro. intros zenon_Hbe.
% 24.97/25.18 apply zenon_Hbe. apply refl_equal.
% 24.97/25.18 (* end of lemma zenon_L36_ *)
% 24.97/25.18 assert (zenon_L37_ : forall (zenon_TT0_hm : zenon_U) (zenon_TX_u : zenon_U), ((age zenon_TX_u zenon_TT0_hm) = (zero)) -> (greater (eta) (zero)) -> (~(smaller_or_equal (age zenon_TX_u zenon_TT0_hm) (eta))) -> False).
% 24.97/25.18 do 2 intro. intros zenon_Hbf zenon_Hc0 zenon_Hc1.
% 24.97/25.18 generalize (definition_smaller_or_equal (age zenon_TX_u zenon_TT0_hm)). zenon_intro zenon_Hc3.
% 24.97/25.18 generalize (zenon_Hc3 (eta)). zenon_intro zenon_Hc4.
% 24.97/25.18 apply (zenon_equiv_s _ _ zenon_Hc4); [ zenon_intro zenon_Hc1; zenon_intro zenon_Hc7 | zenon_intro zenon_Hc6; zenon_intro zenon_Hc5 ].
% 24.97/25.18 apply (zenon_notor_s _ _ zenon_Hc7). zenon_intro zenon_Hc9. zenon_intro zenon_Hc8.
% 24.97/25.18 generalize (definition_smaller (age zenon_TX_u zenon_TT0_hm)). zenon_intro zenon_Hca.
% 24.97/25.18 generalize (zenon_Hca (eta)). zenon_intro zenon_Hcb.
% 24.97/25.18 apply (zenon_equiv_s _ _ zenon_Hcb); [ zenon_intro zenon_Hc9; zenon_intro zenon_Hce | zenon_intro zenon_Hcd; zenon_intro zenon_Hcc ].
% 24.97/25.18 elim (classic ((zero) = (age zenon_TX_u zenon_TT0_hm))); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd0 ].
% 24.97/25.18 cut ((greater (eta) (zero)) = (greater (eta) (age zenon_TX_u zenon_TT0_hm))).
% 24.97/25.18 intro zenon_D_pnotp.
% 24.97/25.18 apply zenon_Hce.
% 24.97/25.18 rewrite <- zenon_D_pnotp.
% 24.97/25.18 exact zenon_Hc0.
% 24.97/25.18 cut (((zero) = (age zenon_TX_u zenon_TT0_hm))); [idtac | apply NNPP; zenon_intro zenon_Hd0].
% 24.97/25.18 cut (((eta) = (eta))); [idtac | apply NNPP; zenon_intro zenon_Hbe].
% 24.97/25.18 congruence.
% 24.97/25.18 apply zenon_Hbe. apply refl_equal.
% 24.97/25.18 exact (zenon_Hd0 zenon_Hcf).
% 24.97/25.18 apply zenon_Hd0. apply sym_equal. exact zenon_Hbf.
% 24.97/25.18 exact (zenon_Hc9 zenon_Hcd).
% 24.97/25.18 exact (zenon_Hc1 zenon_Hc6).
% 24.97/25.18 (* end of lemma zenon_L37_ *)
% 24.97/25.18 assert (zenon_L38_ : forall (zenon_TT0_hm : zenon_U) (zenon_TT1_ba : zenon_U) (zenon_TX_u : zenon_U), (~((hazard_of_mortality zenon_TX_u zenon_TT1_ba) = (hazard_of_mortality zenon_TX_u zenon_TT0_hm))) -> (has_immunity zenon_TX_u zenon_TT1_ba) -> (has_immunity zenon_TX_u zenon_TT0_hm) -> (organization zenon_TX_u) -> False).
% 24.97/25.18 do 3 intro. intros zenon_Hd1 zenon_H27 zenon_Hd2 zenon_H26.
% 24.97/25.18 generalize (assumption_17 zenon_TX_u). zenon_intro zenon_H0.
% 24.97/25.18 generalize (zenon_H0 zenon_TT0_hm). zenon_intro zenon_Hd3.
% 24.97/25.18 apply (zenon_imply_s _ _ zenon_Hd3); [ zenon_intro zenon_H2b | zenon_intro zenon_Hd4 ].
% 24.97/25.18 exact (zenon_H2b zenon_H26).
% 24.97/25.18 apply (zenon_and_s _ _ zenon_Hd4). zenon_intro zenon_Hd6. zenon_intro zenon_Hd5.
% 24.97/25.18 apply (zenon_imply_s _ _ zenon_Hd6); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hd7 ].
% 24.97/25.18 exact (zenon_Hd8 zenon_Hd2).
% 24.97/25.18 generalize (zenon_H0 zenon_TT1_ba). zenon_intro zenon_H29.
% 24.97/25.18 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ].
% 24.97/25.18 exact (zenon_H2b zenon_H26).
% 24.97/25.18 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H2d. zenon_intro zenon_H2c.
% 24.97/25.18 apply (zenon_imply_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ].
% 24.97/25.18 exact (zenon_H2f zenon_H27).
% 24.97/25.18 elim (classic ((hazard_of_mortality zenon_TX_u zenon_TT0_hm) = (hazard_of_mortality zenon_TX_u zenon_TT0_hm))); [ zenon_intro zenon_Hd9 | zenon_intro zenon_Hda ].
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_TT0_hm) = (hazard_of_mortality zenon_TX_u zenon_TT0_hm)) = ((hazard_of_mortality zenon_TX_u zenon_TT1_ba) = (hazard_of_mortality zenon_TX_u zenon_TT0_hm))).
% 24.97/25.18 intro zenon_D_pnotp.
% 24.97/25.18 apply zenon_Hd1.
% 24.97/25.18 rewrite <- zenon_D_pnotp.
% 24.97/25.18 exact zenon_Hd9.
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_TT0_hm) = (hazard_of_mortality zenon_TX_u zenon_TT0_hm))); [idtac | apply NNPP; zenon_intro zenon_Hda].
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_TT0_hm) = (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [idtac | apply NNPP; zenon_intro zenon_Hdb].
% 24.97/25.18 congruence.
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_TT0_hm) = (very_low)) = ((hazard_of_mortality zenon_TX_u zenon_TT0_hm) = (hazard_of_mortality zenon_TX_u zenon_TT1_ba))).
% 24.97/25.18 intro zenon_D_pnotp.
% 24.97/25.18 apply zenon_Hdb.
% 24.97/25.18 rewrite <- zenon_D_pnotp.
% 24.97/25.18 exact zenon_Hd7.
% 24.97/25.18 cut (((very_low) = (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [idtac | apply NNPP; zenon_intro zenon_H28].
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_TT0_hm) = (hazard_of_mortality zenon_TX_u zenon_TT0_hm))); [idtac | apply NNPP; zenon_intro zenon_Hda].
% 24.97/25.18 congruence.
% 24.97/25.18 apply zenon_Hda. apply refl_equal.
% 24.97/25.18 apply zenon_H28. apply sym_equal. exact zenon_H2e.
% 24.97/25.18 apply zenon_Hda. apply refl_equal.
% 24.97/25.18 apply zenon_Hda. apply refl_equal.
% 24.97/25.18 (* end of lemma zenon_L38_ *)
% 24.97/25.18 assert (zenon_L39_ : forall (zenon_TT1_ba : zenon_U) (zenon_TX_u : zenon_U), ((age zenon_TX_u zenon_TT1_ba) = (eta)) -> (~(smaller_or_equal (age zenon_TX_u zenon_TT1_ba) (eta))) -> False).
% 24.97/25.18 do 2 intro. intros zenon_Hdc zenon_H19.
% 24.97/25.18 generalize (definition_smaller_or_equal (age zenon_TX_u zenon_TT1_ba)). zenon_intro zenon_H1b.
% 24.97/25.18 generalize (zenon_H1b (eta)). zenon_intro zenon_H1c.
% 24.97/25.18 apply (zenon_equiv_s _ _ zenon_H1c); [ zenon_intro zenon_H19; zenon_intro zenon_H1f | zenon_intro zenon_H1e; zenon_intro zenon_H1d ].
% 24.97/25.18 apply (zenon_notor_s _ _ zenon_H1f). zenon_intro zenon_H21. zenon_intro zenon_H20.
% 24.97/25.18 exact (zenon_H20 zenon_Hdc).
% 24.97/25.18 exact (zenon_H19 zenon_H1e).
% 24.97/25.18 (* end of lemma zenon_L39_ *)
% 24.97/25.18 assert (zenon_L40_ : forall (zenon_TT1_ba : 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)))))) -> (~((very_low) = (hazard_of_mortality zenon_TX_u zenon_TT1_ba))) -> ((age zenon_TX_u zenon_TT1_ba) = (eta)) -> False).
% 24.97/25.18 do 2 intro. intros zenon_H30 zenon_H28 zenon_Hdc.
% 24.97/25.18 generalize (zenon_H30 zenon_TT1_ba). zenon_intro zenon_H31.
% 24.97/25.18 apply (zenon_and_s _ _ zenon_H31). zenon_intro zenon_H26. zenon_intro zenon_H32.
% 24.97/25.18 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H34. zenon_intro zenon_H33.
% 24.97/25.18 apply (zenon_imply_s _ _ zenon_H34); [ zenon_intro zenon_H19 | zenon_intro zenon_H27 ].
% 24.97/25.18 apply (zenon_L39_ zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.18 apply (zenon_L7_ zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.18 (* end of lemma zenon_L40_ *)
% 24.97/25.18 assert (zenon_L41_ : forall (zenon_TT1_ba : zenon_U) (zenon_TX_u : zenon_U), (~(greater (low) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))) -> (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_ba) = (eta)) -> False).
% 24.97/25.18 do 2 intro. intros zenon_H35 zenon_H30 zenon_Hdc.
% 24.97/25.18 elim (classic ((very_low) = (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [ zenon_intro zenon_H36 | zenon_intro zenon_H28 ].
% 24.97/25.18 cut ((greater (low) (very_low)) = (greater (low) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))).
% 24.97/25.18 intro zenon_D_pnotp.
% 24.97/25.18 apply zenon_H35.
% 24.97/25.18 rewrite <- zenon_D_pnotp.
% 24.97/25.18 exact assumption_18c.
% 24.97/25.18 cut (((very_low) = (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [idtac | apply NNPP; zenon_intro zenon_H28].
% 24.97/25.18 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H17].
% 24.97/25.18 congruence.
% 24.97/25.18 apply zenon_H17. apply refl_equal.
% 24.97/25.18 exact (zenon_H28 zenon_H36).
% 24.97/25.18 apply (zenon_L40_ zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.18 (* end of lemma zenon_L41_ *)
% 24.97/25.18 assert (zenon_L42_ : forall (zenon_TT1_ba : 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 (mod2) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))) -> ((age zenon_TX_u zenon_TT1_ba) = (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)))))) -> False).
% 24.97/25.18 do 2 intro. intros zenon_H37 zenon_H38 zenon_Hdc zenon_H30.
% 24.97/25.18 elim (classic (greater (low) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [ zenon_intro zenon_H39 | zenon_intro zenon_H35 ].
% 24.97/25.18 generalize (zenon_H37 (mod2)). zenon_intro zenon_H3a.
% 24.97/25.18 generalize (zenon_H3a (low)). zenon_intro zenon_H3b.
% 24.97/25.18 generalize (zenon_H3b (hazard_of_mortality zenon_TX_u zenon_TT1_ba)). zenon_intro zenon_H3c.
% 24.97/25.18 apply (zenon_imply_s _ _ zenon_H3c); [ zenon_intro zenon_H3e | zenon_intro zenon_H3d ].
% 24.97/25.18 exact (zenon_H3e assumption_18e).
% 24.97/25.18 apply (zenon_imply_s _ _ zenon_H3d); [ zenon_intro zenon_H35 | zenon_intro zenon_H3f ].
% 24.97/25.18 exact (zenon_H35 zenon_H39).
% 24.97/25.18 exact (zenon_H38 zenon_H3f).
% 24.97/25.18 apply (zenon_L41_ zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.18 (* end of lemma zenon_L42_ *)
% 24.97/25.18 assert (zenon_L43_ : forall (zenon_TT1_ba : 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 (high) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))) -> (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_ba) = (eta)) -> False).
% 24.97/25.18 do 2 intro. intros zenon_H37 zenon_H40 zenon_H30 zenon_Hdc.
% 24.97/25.18 elim (classic (greater (mod2) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [ zenon_intro zenon_H3f | zenon_intro zenon_H38 ].
% 24.97/25.18 generalize (zenon_H37 (high)). zenon_intro zenon_H41.
% 24.97/25.18 generalize (zenon_H41 (mod2)). zenon_intro zenon_H42.
% 24.97/25.18 generalize (zenon_H42 (hazard_of_mortality zenon_TX_u zenon_TT1_ba)). zenon_intro zenon_H43.
% 24.97/25.18 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H45 | zenon_intro zenon_H44 ].
% 24.97/25.18 exact (zenon_H45 assumption_18d).
% 24.97/25.18 apply (zenon_imply_s _ _ zenon_H44); [ zenon_intro zenon_H38 | zenon_intro zenon_H46 ].
% 24.97/25.18 exact (zenon_H38 zenon_H3f).
% 24.97/25.18 exact (zenon_H40 zenon_H46).
% 24.97/25.18 apply (zenon_L42_ zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.18 (* end of lemma zenon_L43_ *)
% 24.97/25.18 assert (zenon_L44_ : forall (zenon_TT1_ba : 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)))))) -> ((hazard_of_mortality zenon_TX_u zenon_E) = (high)) -> (~(greater (hazard_of_mortality zenon_TX_u zenon_E) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))) -> ((age zenon_TX_u zenon_TT1_ba) = (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)))))) -> False).
% 24.97/25.18 do 2 intro. intros zenon_H37 zenon_H47 zenon_H48 zenon_Hdc zenon_H30.
% 24.97/25.18 elim (classic (greater (high) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [ zenon_intro zenon_H46 | zenon_intro zenon_H40 ].
% 24.97/25.18 cut ((greater (high) (hazard_of_mortality zenon_TX_u zenon_TT1_ba)) = (greater (hazard_of_mortality zenon_TX_u zenon_E) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))).
% 24.97/25.18 intro zenon_D_pnotp.
% 24.97/25.18 apply zenon_H48.
% 24.97/25.18 rewrite <- zenon_D_pnotp.
% 24.97/25.18 exact zenon_H46.
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_TT1_ba) = (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [idtac | apply NNPP; zenon_intro zenon_H49].
% 24.97/25.18 cut (((high) = (hazard_of_mortality zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H4a].
% 24.97/25.18 congruence.
% 24.97/25.18 elim (classic ((hazard_of_mortality zenon_TX_u zenon_E) = (hazard_of_mortality zenon_TX_u zenon_E))); [ zenon_intro zenon_H4b | zenon_intro zenon_H4c ].
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_E) = (hazard_of_mortality zenon_TX_u zenon_E)) = ((high) = (hazard_of_mortality zenon_TX_u zenon_E))).
% 24.97/25.18 intro zenon_D_pnotp.
% 24.97/25.18 apply zenon_H4a.
% 24.97/25.18 rewrite <- zenon_D_pnotp.
% 24.97/25.18 exact zenon_H4b.
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_E) = (hazard_of_mortality zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H4c].
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_E) = (high))); [idtac | apply NNPP; zenon_intro zenon_H4d].
% 24.97/25.18 congruence.
% 24.97/25.18 exact (zenon_H4d zenon_H47).
% 24.97/25.18 apply zenon_H4c. apply refl_equal.
% 24.97/25.18 apply zenon_H4c. apply refl_equal.
% 24.97/25.18 apply zenon_H49. apply refl_equal.
% 24.97/25.18 apply (zenon_L43_ zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.18 (* end of lemma zenon_L44_ *)
% 24.97/25.18 assert (zenon_L45_ : forall (zenon_TT1_ba : zenon_U) (zenon_TT2_de : 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_TT2_de) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))) -> (greater (age zenon_TX_u zenon_TT2_de) (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)))))) -> ((age zenon_TX_u zenon_TT1_ba) = (eta)) -> False).
% 24.97/25.18 do 3 intro. intros zenon_H37 zenon_Ha4 zenon_H94 zenon_H30 zenon_Hdc.
% 24.97/25.18 generalize (zenon_H30 zenon_TT1_ba). zenon_intro zenon_H31.
% 24.97/25.18 apply (zenon_and_s _ _ zenon_H31). zenon_intro zenon_H26. zenon_intro zenon_H32.
% 24.97/25.18 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H34. zenon_intro zenon_H33.
% 24.97/25.18 apply (zenon_imply_s _ _ zenon_H34); [ zenon_intro zenon_H19 | zenon_intro zenon_H27 ].
% 24.97/25.18 apply (zenon_L39_ zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.18 apply (zenon_L24_ zenon_TT1_ba zenon_TT2_de zenon_TX_u); trivial.
% 24.97/25.18 (* end of lemma zenon_L45_ *)
% 24.97/25.18 assert (zenon_L46_ : forall (zenon_TT2_de : zenon_U) (zenon_TT1_ba : 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_TT2_de) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))) -> (greater (age zenon_TX_u zenon_TT2_de) (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)))))) -> ((age zenon_TX_u zenon_TT1_ba) = (eta)) -> False).
% 24.97/25.18 do 3 intro. intros zenon_H37 zenon_Ha4 zenon_H94 zenon_H30 zenon_Hdc.
% 24.97/25.18 apply (zenon_L45_ zenon_TT1_ba zenon_TT2_de zenon_TX_u); trivial.
% 24.97/25.18 (* end of lemma zenon_L46_ *)
% 24.97/25.18 assert (zenon_L47_ : forall (zenon_TT2_de : zenon_U) (zenon_TT1_ba : zenon_U) (zenon_TX_u : zenon_U), ((age zenon_TX_u zenon_TT1_ba) = (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_TT2_de) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))) -> (greater (age zenon_TX_u zenon_TT2_de) (eta)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> False).
% 24.97/25.18 do 3 intro. intros zenon_Hdc zenon_H30 zenon_Ha4 zenon_H94 zenon_H37.
% 24.97/25.18 apply (zenon_L46_ zenon_TT2_de zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.18 (* end of lemma zenon_L47_ *)
% 24.97/25.18 assert (zenon_L48_ : forall (zenon_TT1_ba : 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 (mod1) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))) -> ((age zenon_TX_u zenon_TT1_ba) = (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)))))) -> False).
% 24.97/25.18 do 2 intro. intros zenon_H37 zenon_Ha8 zenon_Hdc zenon_H30.
% 24.97/25.18 elim (classic (greater (low) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [ zenon_intro zenon_H39 | zenon_intro zenon_H35 ].
% 24.97/25.18 generalize (zenon_H37 (mod1)). zenon_intro zenon_Ha9.
% 24.97/25.18 generalize (zenon_Ha9 (low)). zenon_intro zenon_Haa.
% 24.97/25.18 generalize (zenon_Haa (hazard_of_mortality zenon_TX_u zenon_TT1_ba)). zenon_intro zenon_Hab.
% 24.97/25.18 apply (zenon_imply_s _ _ zenon_Hab); [ zenon_intro zenon_H7d | zenon_intro zenon_Hac ].
% 24.97/25.18 exact (zenon_H7d assumption_18b).
% 24.97/25.18 apply (zenon_imply_s _ _ zenon_Hac); [ zenon_intro zenon_H35 | zenon_intro zenon_Had ].
% 24.97/25.18 exact (zenon_H35 zenon_H39).
% 24.97/25.18 exact (zenon_Ha8 zenon_Had).
% 24.97/25.18 apply (zenon_L41_ zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.18 (* end of lemma zenon_L48_ *)
% 24.97/25.18 assert (zenon_L49_ : forall (zenon_TT2_de : zenon_U) (zenon_TT1_ba : 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_TT2_de) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))) -> (greater (age zenon_TX_u zenon_TT2_de) (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)))))) -> ((age zenon_TX_u zenon_TT1_ba) = (eta)) -> False).
% 24.97/25.18 do 3 intro. intros zenon_H37 zenon_Ha4 zenon_H94 zenon_H30 zenon_Hdc.
% 24.97/25.18 apply (zenon_L45_ zenon_TT1_ba zenon_TT2_de zenon_TX_u); trivial.
% 24.97/25.18 (* end of lemma zenon_L49_ *)
% 24.97/25.18 assert (zenon_L50_ : forall (zenon_TT2_de : zenon_U) (zenon_TT1_ba : 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_TT2_de) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))) -> (greater (age zenon_TX_u zenon_TT2_de) (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)))))) -> ((age zenon_TX_u zenon_TT1_ba) = (eta)) -> False).
% 24.97/25.18 do 3 intro. intros zenon_H37 zenon_Ha4 zenon_H94 zenon_H30 zenon_Hdc.
% 24.97/25.18 apply (zenon_L45_ zenon_TT1_ba zenon_TT2_de zenon_TX_u); trivial.
% 24.97/25.18 (* end of lemma zenon_L50_ *)
% 24.97/25.18 assert (zenon_L51_ : forall (zenon_TT1_ba : zenon_U) (zenon_TT2_de : zenon_U) (zenon_TX_u : zenon_U), ((age zenon_TX_u zenon_TT1_ba) = (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_TT2_de) (eta)) -> (~(greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> False).
% 24.97/25.18 do 3 intro. intros zenon_Hdc zenon_H30 zenon_H94 zenon_Ha4 zenon_H37.
% 24.97/25.18 apply (zenon_L50_ zenon_TT2_de zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.18 (* end of lemma zenon_L51_ *)
% 24.97/25.18 assert (zenon_L52_ : forall (zenon_TT1_ba : zenon_U) (zenon_TX_u : zenon_U), ((hazard_of_mortality zenon_TX_u zenon_E) = (low)) -> (~(greater (hazard_of_mortality zenon_TX_u zenon_E) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))) -> ((age zenon_TX_u zenon_TT1_ba) = (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)))))) -> False).
% 24.97/25.18 do 2 intro. intros zenon_Hae zenon_H48 zenon_Hdc zenon_H30.
% 24.97/25.18 elim (classic (greater (low) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [ zenon_intro zenon_H39 | zenon_intro zenon_H35 ].
% 24.97/25.18 cut ((greater (low) (hazard_of_mortality zenon_TX_u zenon_TT1_ba)) = (greater (hazard_of_mortality zenon_TX_u zenon_E) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))).
% 24.97/25.18 intro zenon_D_pnotp.
% 24.97/25.18 apply zenon_H48.
% 24.97/25.18 rewrite <- zenon_D_pnotp.
% 24.97/25.18 exact zenon_H39.
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_TT1_ba) = (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [idtac | apply NNPP; zenon_intro zenon_H49].
% 24.97/25.18 cut (((low) = (hazard_of_mortality zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Haf].
% 24.97/25.18 congruence.
% 24.97/25.18 elim (classic ((hazard_of_mortality zenon_TX_u zenon_E) = (hazard_of_mortality zenon_TX_u zenon_E))); [ zenon_intro zenon_H4b | zenon_intro zenon_H4c ].
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_E) = (hazard_of_mortality zenon_TX_u zenon_E)) = ((low) = (hazard_of_mortality zenon_TX_u zenon_E))).
% 24.97/25.18 intro zenon_D_pnotp.
% 24.97/25.18 apply zenon_Haf.
% 24.97/25.18 rewrite <- zenon_D_pnotp.
% 24.97/25.18 exact zenon_H4b.
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_E) = (hazard_of_mortality zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H4c].
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_Hb0].
% 24.97/25.18 congruence.
% 24.97/25.18 exact (zenon_Hb0 zenon_Hae).
% 24.97/25.18 apply zenon_H4c. apply refl_equal.
% 24.97/25.18 apply zenon_H4c. apply refl_equal.
% 24.97/25.18 apply zenon_H49. apply refl_equal.
% 24.97/25.18 apply (zenon_L41_ zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.18 (* end of lemma zenon_L52_ *)
% 24.97/25.18 assert (zenon_L53_ : forall (zenon_TT2_de : zenon_U) (zenon_TT1_ba : zenon_U) (zenon_TX_u : zenon_U), ((age zenon_TX_u zenon_TT1_ba) = (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_TT2_de) (eta)) -> (~(greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((greater x y)->((greater y z)->(greater x z)))))) -> ((hazard_of_mortality zenon_TX_u zenon_E) = (low)) -> False).
% 24.97/25.18 do 3 intro. intros zenon_Hdc zenon_H30 zenon_H94 zenon_Ha4 zenon_H37 zenon_Hae.
% 24.97/25.18 elim (classic ((low) = (hazard_of_mortality zenon_TX_u zenon_E))); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Haf ].
% 24.97/25.18 elim (classic (greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (low))); [ zenon_intro zenon_H7c | zenon_intro zenon_H6e ].
% 24.97/25.18 elim (classic (greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (hazard_of_mortality zenon_TX_u zenon_E))); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb3 ].
% 24.97/25.18 elim (classic (greater (hazard_of_mortality zenon_TX_u zenon_E) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H48 ].
% 24.97/25.18 generalize (zenon_H37 (hazard_of_mortality zenon_TX_u zenon_TT2_de)). zenon_intro zenon_H78.
% 24.97/25.18 generalize (zenon_H78 (hazard_of_mortality zenon_TX_u zenon_E)). zenon_intro zenon_Hb5.
% 24.97/25.18 generalize (zenon_Hb5 (hazard_of_mortality zenon_TX_u zenon_TT1_ba)). zenon_intro zenon_Hb6.
% 24.97/25.18 apply (zenon_imply_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb3 | zenon_intro zenon_Hb7 ].
% 24.97/25.18 exact (zenon_Hb3 zenon_Hb2).
% 24.97/25.18 apply (zenon_imply_s _ _ zenon_Hb7); [ zenon_intro zenon_H48 | zenon_intro zenon_Hb8 ].
% 24.97/25.18 exact (zenon_H48 zenon_Hb4).
% 24.97/25.18 exact (zenon_Ha4 zenon_Hb8).
% 24.97/25.18 apply (zenon_L52_ zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.18 cut ((greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (low)) = (greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (hazard_of_mortality zenon_TX_u zenon_E))).
% 24.97/25.18 intro zenon_D_pnotp.
% 24.97/25.18 apply zenon_Hb3.
% 24.97/25.18 rewrite <- zenon_D_pnotp.
% 24.97/25.18 exact zenon_H7c.
% 24.97/25.18 cut (((low) = (hazard_of_mortality zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Haf].
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 24.97/25.18 congruence.
% 24.97/25.18 apply zenon_H76. apply refl_equal.
% 24.97/25.18 exact (zenon_Haf zenon_Hb1).
% 24.97/25.18 elim (classic (greater (hazard_of_mortality zenon_TX_u zenon_E) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H48 ].
% 24.97/25.18 elim (classic (greater (low) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [ zenon_intro zenon_H39 | zenon_intro zenon_H35 ].
% 24.97/25.18 cut ((greater (low) (hazard_of_mortality zenon_TX_u zenon_TT1_ba)) = (greater (hazard_of_mortality zenon_TX_u zenon_TT2_de) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))).
% 24.97/25.18 intro zenon_D_pnotp.
% 24.97/25.18 apply zenon_Ha4.
% 24.97/25.18 rewrite <- zenon_D_pnotp.
% 24.97/25.18 exact zenon_H39.
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_TT1_ba) = (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [idtac | apply NNPP; zenon_intro zenon_H49].
% 24.97/25.18 cut (((low) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 24.97/25.18 congruence.
% 24.97/25.18 elim (classic ((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))); [ zenon_intro zenon_H75 | zenon_intro zenon_H76 ].
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (hazard_of_mortality zenon_TX_u zenon_TT2_de)) = ((low) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))).
% 24.97/25.18 intro zenon_D_pnotp.
% 24.97/25.18 apply zenon_H8c.
% 24.97/25.18 rewrite <- zenon_D_pnotp.
% 24.97/25.18 exact zenon_H75.
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (hazard_of_mortality zenon_TX_u zenon_TT2_de))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_TT2_de) = (low))); [idtac | apply NNPP; zenon_intro zenon_H58].
% 24.97/25.18 congruence.
% 24.97/25.18 apply (zenon_L22_ zenon_TT2_de zenon_TX_u); trivial.
% 24.97/25.18 apply zenon_H76. apply refl_equal.
% 24.97/25.18 apply zenon_H76. apply refl_equal.
% 24.97/25.18 apply zenon_H49. apply refl_equal.
% 24.97/25.18 cut ((greater (hazard_of_mortality zenon_TX_u zenon_E) (hazard_of_mortality zenon_TX_u zenon_TT1_ba)) = (greater (low) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))).
% 24.97/25.18 intro zenon_D_pnotp.
% 24.97/25.18 apply zenon_H35.
% 24.97/25.18 rewrite <- zenon_D_pnotp.
% 24.97/25.18 exact zenon_Hb4.
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_TT1_ba) = (hazard_of_mortality zenon_TX_u zenon_TT1_ba))); [idtac | apply NNPP; zenon_intro zenon_H49].
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_Hb0].
% 24.97/25.18 congruence.
% 24.97/25.18 elim (classic ((low) = (low))); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H17 ].
% 24.97/25.18 cut (((low) = (low)) = ((hazard_of_mortality zenon_TX_u zenon_E) = (low))).
% 24.97/25.18 intro zenon_D_pnotp.
% 24.97/25.18 apply zenon_Hb0.
% 24.97/25.18 rewrite <- zenon_D_pnotp.
% 24.97/25.18 exact zenon_Hb9.
% 24.97/25.18 cut (((low) = (low))); [idtac | apply NNPP; zenon_intro zenon_H17].
% 24.97/25.18 cut (((low) = (hazard_of_mortality zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_Haf].
% 24.97/25.18 congruence.
% 24.97/25.18 exact (zenon_Haf zenon_Hb1).
% 24.97/25.18 apply zenon_H17. apply refl_equal.
% 24.97/25.18 apply zenon_H17. apply refl_equal.
% 24.97/25.18 apply zenon_H49. apply refl_equal.
% 24.97/25.18 apply (zenon_L52_ zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.18 elim (classic ((hazard_of_mortality zenon_TX_u zenon_E) = (hazard_of_mortality zenon_TX_u zenon_E))); [ zenon_intro zenon_H4b | zenon_intro zenon_H4c ].
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_E) = (hazard_of_mortality zenon_TX_u zenon_E)) = ((low) = (hazard_of_mortality zenon_TX_u zenon_E))).
% 24.97/25.18 intro zenon_D_pnotp.
% 24.97/25.18 apply zenon_Haf.
% 24.97/25.18 rewrite <- zenon_D_pnotp.
% 24.97/25.18 exact zenon_H4b.
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_E) = (hazard_of_mortality zenon_TX_u zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H4c].
% 24.97/25.18 cut (((hazard_of_mortality zenon_TX_u zenon_E) = (low))); [idtac | apply NNPP; zenon_intro zenon_Hb0].
% 24.97/25.18 congruence.
% 24.97/25.18 exact (zenon_Hb0 zenon_Hae).
% 24.97/25.18 apply zenon_H4c. apply refl_equal.
% 24.97/25.18 apply zenon_H4c. apply refl_equal.
% 24.97/25.18 (* end of lemma zenon_L53_ *)
% 24.97/25.18 apply NNPP. intro zenon_G.
% 24.97/25.18 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_H37 | zenon_intro zenon_Hdd ].
% 24.97/25.18 apply (zenon_notallex_s (fun X : zenon_U => (forall T0 : zenon_U, (forall T1 : zenon_U, (forall T2 : zenon_U, (((organization X)/\(((robust_position X)\/(fragile_position X))/\((has_endowment X)/\(((age X T0) = (zero))/\((greater (sigma) (zero))/\((greater (tau) (zero))/\((greater (eta) (zero))/\((smaller_or_equal (age X T1) (sigma))/\((smaller_or_equal (age X T1) (tau))/\((smaller_or_equal (age X T1) (eta))/\((greater (age X T2) (sigma))/\((greater (age X T2) (tau))/\(greater (age X T2) (eta))))))))))))))->((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_Hde; idtac ].
% 24.97/25.18 elim zenon_Hde. zenon_intro zenon_TX_u. zenon_intro zenon_Hdf.
% 24.97/25.18 apply (zenon_notallex_s (fun T0 : zenon_U => (forall T1 : zenon_U, (forall T2 : zenon_U, (((organization zenon_TX_u)/\(((robust_position zenon_TX_u)\/(fragile_position zenon_TX_u))/\((has_endowment zenon_TX_u)/\(((age zenon_TX_u T0) = (zero))/\((greater (sigma) (zero))/\((greater (tau) (zero))/\((greater (eta) (zero))/\((smaller_or_equal (age zenon_TX_u T1) (sigma))/\((smaller_or_equal (age zenon_TX_u T1) (tau))/\((smaller_or_equal (age zenon_TX_u T1) (eta))/\((greater (age zenon_TX_u T2) (sigma))/\((greater (age zenon_TX_u T2) (tau))/\(greater (age zenon_TX_u T2) (eta))))))))))))))->((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_Hdf); [ zenon_intro zenon_He0; idtac ].
% 24.97/25.18 elim zenon_He0. zenon_intro zenon_TT0_hm. zenon_intro zenon_He1.
% 24.97/25.18 apply (zenon_notallex_s (fun T1 : zenon_U => (forall T2 : zenon_U, (((organization zenon_TX_u)/\(((robust_position zenon_TX_u)\/(fragile_position zenon_TX_u))/\((has_endowment zenon_TX_u)/\(((age zenon_TX_u zenon_TT0_hm) = (zero))/\((greater (sigma) (zero))/\((greater (tau) (zero))/\((greater (eta) (zero))/\((smaller_or_equal (age zenon_TX_u T1) (sigma))/\((smaller_or_equal (age zenon_TX_u T1) (tau))/\((smaller_or_equal (age zenon_TX_u T1) (eta))/\((greater (age zenon_TX_u T2) (sigma))/\((greater (age zenon_TX_u T2) (tau))/\(greater (age zenon_TX_u T2) (eta))))))))))))))->((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_hm)))))) zenon_He1); [ zenon_intro zenon_He2; idtac ].
% 24.97/25.18 elim zenon_He2. zenon_intro zenon_TT1_ba. zenon_intro zenon_He3.
% 24.97/25.18 apply (zenon_notallex_s (fun T2 : zenon_U => (((organization zenon_TX_u)/\(((robust_position zenon_TX_u)\/(fragile_position zenon_TX_u))/\((has_endowment zenon_TX_u)/\(((age zenon_TX_u zenon_TT0_hm) = (zero))/\((greater (sigma) (zero))/\((greater (tau) (zero))/\((greater (eta) (zero))/\((smaller_or_equal (age zenon_TX_u zenon_TT1_ba) (sigma))/\((smaller_or_equal (age zenon_TX_u zenon_TT1_ba) (tau))/\((smaller_or_equal (age zenon_TX_u zenon_TT1_ba) (eta))/\((greater (age zenon_TX_u T2) (sigma))/\((greater (age zenon_TX_u T2) (tau))/\(greater (age zenon_TX_u T2) (eta))))))))))))))->((greater (hazard_of_mortality zenon_TX_u T2) (hazard_of_mortality zenon_TX_u zenon_TT1_ba))/\((hazard_of_mortality zenon_TX_u zenon_TT1_ba) = (hazard_of_mortality zenon_TX_u zenon_TT0_hm))))) zenon_He3); [ zenon_intro zenon_He4; idtac ].
% 24.97/25.18 elim zenon_He4. zenon_intro zenon_TT2_de. zenon_intro zenon_He5.
% 24.97/25.18 apply (zenon_notimply_s _ _ zenon_He5). zenon_intro zenon_He7. zenon_intro zenon_He6.
% 24.97/25.18 apply (zenon_and_s _ _ zenon_He7). zenon_intro zenon_H26. zenon_intro zenon_He8.
% 24.97/25.18 apply (zenon_and_s _ _ zenon_He8). zenon_intro zenon_Hea. zenon_intro zenon_He9.
% 24.97/25.18 apply (zenon_and_s _ _ zenon_He9). zenon_intro zenon_Hec. zenon_intro zenon_Heb.
% 24.97/25.18 apply (zenon_and_s _ _ zenon_Heb). zenon_intro zenon_Hbf. zenon_intro zenon_Hed.
% 24.97/25.18 apply (zenon_and_s _ _ zenon_Hed). zenon_intro zenon_Hef. zenon_intro zenon_Hee.
% 24.97/25.18 apply (zenon_and_s _ _ zenon_Hee). zenon_intro zenon_Hf1. zenon_intro zenon_Hf0.
% 24.97/25.18 apply (zenon_and_s _ _ zenon_Hf0). zenon_intro zenon_Hc0. zenon_intro zenon_Hf2.
% 24.97/25.18 apply (zenon_and_s _ _ zenon_Hf2). zenon_intro zenon_Hf4. zenon_intro zenon_Hf3.
% 24.97/25.18 apply (zenon_and_s _ _ zenon_Hf3). zenon_intro zenon_Hf6. zenon_intro zenon_Hf5.
% 24.97/25.18 apply (zenon_and_s _ _ zenon_Hf5). zenon_intro zenon_H1e. zenon_intro zenon_Hf7.
% 24.97/25.18 apply (zenon_and_s _ _ zenon_Hf7). zenon_intro zenon_Hf9. zenon_intro zenon_Hf8.
% 24.97/25.18 apply (zenon_and_s _ _ zenon_Hf8). zenon_intro zenon_Hfa. zenon_intro zenon_H94.
% 24.97/25.18 generalize (definition_1 zenon_TX_u). zenon_intro zenon_Hfb.
% 24.97/25.18 apply (zenon_equiv_s _ _ zenon_Hfb); [ zenon_intro zenon_Hfd; zenon_intro zenon_Hfc | zenon_intro zenon_Hec; zenon_intro zenon_H30 ].
% 24.97/25.18 exact (zenon_Hfd zenon_Hec).
% 24.97/25.18 generalize (definition_smaller_or_equal (age zenon_TX_u zenon_TT1_ba)). zenon_intro zenon_H1b.
% 24.97/25.18 generalize (zenon_H1b (eta)). zenon_intro zenon_H1c.
% 24.97/25.18 apply (zenon_equiv_s _ _ zenon_H1c); [ zenon_intro zenon_H19; zenon_intro zenon_H1f | zenon_intro zenon_H1e; zenon_intro zenon_H1d ].
% 24.97/25.18 exact (zenon_H19 zenon_H1e).
% 24.97/25.18 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H24 | zenon_intro zenon_Hdc ].
% 24.97/25.18 generalize (definition_smaller (age zenon_TX_u zenon_TT1_ba)). zenon_intro zenon_H22.
% 24.97/25.18 generalize (zenon_H22 (eta)). zenon_intro zenon_H23.
% 24.97/25.18 apply (zenon_equiv_s _ _ zenon_H23); [ zenon_intro zenon_H21; zenon_intro zenon_H25 | zenon_intro zenon_H24; zenon_intro zenon_H18 ].
% 24.97/25.18 exact (zenon_H21 zenon_H24).
% 24.97/25.18 apply (zenon_notand_s _ _ zenon_He6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Hd1 ].
% 24.97/25.18 apply (zenon_L27_ zenon_TT2_de zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.18 generalize (zenon_H30 zenon_TT0_hm). zenon_intro zenon_Hfe.
% 24.97/25.18 apply (zenon_and_s _ _ zenon_Hfe). zenon_intro zenon_H26. zenon_intro zenon_Hff.
% 24.97/25.18 apply (zenon_and_s _ _ zenon_Hff). zenon_intro zenon_H101. zenon_intro zenon_H100.
% 24.97/25.18 apply (zenon_imply_s _ _ zenon_H101); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hd2 ].
% 24.97/25.18 apply (zenon_L37_ zenon_TT0_hm zenon_TX_u); trivial.
% 24.97/25.18 generalize (zenon_H30 zenon_TT1_ba). zenon_intro zenon_H31.
% 24.97/25.18 apply (zenon_and_s _ _ zenon_H31). zenon_intro zenon_H26. zenon_intro zenon_H32.
% 24.97/25.18 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H34. zenon_intro zenon_H33.
% 24.97/25.18 apply (zenon_imply_s _ _ zenon_H34); [ zenon_intro zenon_H19 | zenon_intro zenon_H27 ].
% 24.97/25.18 apply (zenon_L5_ zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.18 apply (zenon_L38_ zenon_TT0_hm zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.18 apply (zenon_notand_s _ _ zenon_He6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Hd1 ].
% 24.97/25.18 apply (zenon_L47_ zenon_TT2_de zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.18 generalize (zenon_H30 zenon_TT0_hm). zenon_intro zenon_Hfe.
% 24.97/25.18 apply (zenon_and_s _ _ zenon_Hfe). zenon_intro zenon_H26. zenon_intro zenon_Hff.
% 24.97/25.18 apply (zenon_and_s _ _ zenon_Hff). zenon_intro zenon_H101. zenon_intro zenon_H100.
% 24.97/25.18 apply (zenon_imply_s _ _ zenon_H101); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hd2 ].
% 24.97/25.18 apply (zenon_L37_ zenon_TT0_hm zenon_TX_u); trivial.
% 24.97/25.18 generalize (zenon_H30 zenon_TT1_ba). zenon_intro zenon_H31.
% 24.97/25.18 apply (zenon_and_s _ _ zenon_H31). zenon_intro zenon_H26. zenon_intro zenon_H32.
% 24.97/25.18 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H34. zenon_intro zenon_H33.
% 24.97/25.18 apply (zenon_imply_s _ _ zenon_H34); [ zenon_intro zenon_H19 | zenon_intro zenon_H27 ].
% 24.97/25.18 apply (zenon_L39_ zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.18 apply (zenon_L38_ zenon_TT0_hm zenon_TT1_ba zenon_TX_u); trivial.
% 24.97/25.18 apply zenon_Hdd. zenon_intro zenon_Tx_jy. apply NNPP. zenon_intro zenon_H103.
% 24.97/25.18 apply zenon_H103. zenon_intro zenon_Ty_ka. apply NNPP. zenon_intro zenon_H105.
% 24.97/25.18 apply zenon_H105. zenon_intro zenon_Tz_kc. apply NNPP. zenon_intro zenon_H107.
% 24.97/25.18 apply (zenon_notimply_s _ _ zenon_H107). zenon_intro zenon_H109. zenon_intro zenon_H108.
% 24.97/25.18 apply (zenon_notimply_s _ _ zenon_H108). zenon_intro zenon_H10b. zenon_intro zenon_H10a.
% 24.97/25.18 generalize (meaning_postulate_greater_transitive zenon_Tx_jy). zenon_intro zenon_H10c.
% 24.97/25.18 generalize (zenon_H10c zenon_Ty_ka). zenon_intro zenon_H10d.
% 24.97/25.18 generalize (zenon_H10d zenon_Tz_kc). zenon_intro zenon_H10e.
% 24.97/25.18 apply (zenon_imply_s _ _ zenon_H10e); [ zenon_intro zenon_H110 | zenon_intro zenon_H10f ].
% 24.97/25.18 apply (zenon_notand_s _ _ zenon_H110); [ zenon_intro zenon_H112 | zenon_intro zenon_H111 ].
% 24.97/25.18 exact (zenon_H112 zenon_H109).
% 24.97/25.18 exact (zenon_H111 zenon_H10b).
% 24.97/25.18 exact (zenon_H10a zenon_H10f).
% 24.97/25.18 Qed.
% 24.97/25.18 % SZS output end Proof
% 24.97/25.18 (* END-PROOF *)
% 24.97/25.18 nodes searched: 1244637
% 24.97/25.18 max branch formulas: 1392
% 24.97/25.18 proof nodes created: 19869
% 24.97/25.18 formulas created: 502094
% 24.97/25.18
%------------------------------------------------------------------------------