%------------------------------------------------------------------------------
% File     : SCT171_30 : TPTP v9.0.0. Released v8.2.0.
% Domain   : Social Choice Theory
% Problem  : Arrow's Impossibility Theorem line 309, 1000 axioms selected
% Version  : SCT171_3 with the conjecture removed
% English  :

% Refs     : [BN10]  Boehme & Nipkow (2010), Sledgehammer: Judgement Day
%          : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source   : [TPTP]
% Names    : 

% Status   : Satisfiable
% Rating   : 1.00 v8.2.0
% Syntax   : Number of formulae    : 2063 ( 253 unt; 785 typ;   0 def)
%            Number of atoms       : 3610 ( 585 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives : 2658 ( 326   ~;  59   |;  91   &)
%                                         ( 243 <=>;1939  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   6 avg)
%            Maximal term depth    :   13 (   2 avg)
%            Number of types       :  295 ( 294 usr)
%            Number of type conns  :  623 ( 324   >; 299   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  490 ( 490 usr; 167 con; 0-3 aty)
%            Number of variables   : 3775 (3754   !;  21   ?;3775   :)
% SPC      : TF0_SAT_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2011-08-09 17:56:11
%------------------------------------------------------------------------------
%----Should-be-implicit typings (294)
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tff(ty_ty_tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_141,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_142,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_143,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_144,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_145,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_146,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_147,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_148,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_149,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_150,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_151,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_152,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_153,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_154,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_155,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_156,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs_,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__157,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__158,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__159,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__160,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__161,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__162,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__163,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__164,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__165,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__166,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__167,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__168,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__169,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__170,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__171,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__172,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__173,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__174,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__175,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__176,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__177,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__178,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__179,type,
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tff(ty_ty_tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__180,type,
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tff(ty_ty_tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc,type,
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tff(ty_ty_tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc_181,type,
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tff(ty_ty_tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc_182,type,
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tff(ty_ty_tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc_183,type,
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tff(ty_ty_tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc_184,type,
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tff(ty_ty_tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc_185,type,
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tff(ty_ty_tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc_186,type,
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tff(ty_ty_tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc__Arrow__,type,
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%----Explicit typings (491)
tff(sy_c_Arrow__Order__Mirabelle__effngqiqbs_OIIA,type,
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tff(sy_c_Arrow__Order__Mirabelle__effngqiqbs_OLin,type,
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tff(sy_c_Arrow__Order__Mirabelle__effngqiqbs_OProf,type,
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tff(sy_c_Arrow__Order__Mirabelle__effngqiqbs_Oabove,type,
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tff(sy_c_Arrow__Order__Mirabelle__effngqiqbs_Obelow,type,
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tff(sy_c_Arrow__Order__Mirabelle__effngqiqbs_Odictator,type,
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tff(sy_c_Arrow__Order__Mirabelle__effngqiqbs_Omkbot,type,
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tff(sy_c_Arrow__Order__Mirabelle__effngqiqbs_Omktop,type,
    arrow_1630265669_mktop: fun_fu1679793515t_bool ).

tff(sy_c_Arrow__Order__Mirabelle__effngqiqbs_Ounanimity,type,
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tff(sy_c_Big__Operators_Ocomm__monoid__add__class_Osetsum_000tc__Nat__Onat_000tc__Na,type,
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tff(sy_c_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc_,type,
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tff(sy_c_COMBB_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order__,type,
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tff(sy_c_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__A,type,
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tff(sy_c_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__N,type,
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tff(sy_c_COMBB_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J,type,
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tff(sy_c_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc__,type,
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tff(sy_c_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc___187,type,
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tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__,type,
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tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs___188,type,
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tff(sy_c_COMBB_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc_,type,
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tff(sy_c_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc,type,
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tff(sy_c_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc_189,type,
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tff(sy_c_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc__Arrow_,type,
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tff(sy_c_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc__Arrow__190,type,
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tff(sy_c_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc__Nat__O,type,
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tff(sy_c_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc__fun_It,type,
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tff(sy_c_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc__fun_It_191,type,
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tff(sy_c_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool,type,
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tff(sy_c_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Nat__Onat,type,
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tff(sy_c_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__H,type,
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tff(sy_c_COMBC_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_Mtc_,type,
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tff(sy_c_COMBC_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__O,type,
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tff(sy_c_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__,type,
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tff(sy_c_COMBC_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc_,type,
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tff(sy_c_COMBI_000tc__Nat__Onat,type,
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tff(sy_c_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____effngqiqbs__O,type,
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tff(sy_c_COMBK_000tc__HOL__Obool_000tc__Nat__Onat,type,
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tff(sy_c_COMBK_000tc__HOL__Obool_000tc__Product____Type__Ounit,type,
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tff(sy_c_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____effn,type,
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tff(sy_c_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabell,type,
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tff(sy_c_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabel,type,
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tff(sy_c_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabelle____eff,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_Mtc_,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_Mtc__192,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_Mtc__193,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_Mtc__194,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_Mtc__195,type,
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tff(sy_c_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__Nat__Onat,type,
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tff(sy_c_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc__Arrow___,type,
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tff(sy_c_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc_,type,
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tff(sy_c_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc__prod_Itc,type,
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tff(sy_c_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__prod_Itc__Arrow__,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Arrow____Order____,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Product____Type__O,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_000tc__Nat__,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_000tc__fun_I,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_000tc__fun_I_196,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_000tc__fun_I_197,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_000tc__prod_,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__O,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__O_198,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__O_199,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effn,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effn_200,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effn_201,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____eff,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____eff_202,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____eff_203,type,
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tff(sy_c_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__,type,
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tff(sy_c_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs___205,type,
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tff(sy_c_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs___206,type,
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tff(sy_c_COMBS_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc__fun_It,type,
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tff(sy_c_COMBS_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc__fun_It_207,type,
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tff(sy_c_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool,type,
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tff(sy_c_Finite__Set_Ocard_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi,type,
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tff(sy_c_Finite__Set_Ocard_000tc__Nat__Onat,type,
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tff(sy_c_Finite__Set_Ocard_000tc__Product____Type__Ounit,type,
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tff(sy_c_Finite__Set_Ofinite_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi,type,
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tff(sy_c_Finite__Set_Ofinite_000tc__Nat__Onat,type,
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tff(sy_c_Fun_Oinj__on_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc_,type,
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tff(sy_c_Fun_Oinj__on_000tc__Nat__Onat_000tc__Nat__Onat,type,
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tff(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc__,type,
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tff(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc___208,type,
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tff(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc___209,type,
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tff(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc___210,type,
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tff(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc___211,type,
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tff(sy_c_FuncSet_OPi_000tc__HOL__Obool_000tc__Nat__Onat,type,
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tff(sy_c_FuncSet_OPi_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle__,type,
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tff(sy_c_FuncSet_OPi_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order____Mi,type,
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tff(sy_c_FuncSet_OPi_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order____M,type,
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tff(sy_c_FuncSet_OPi_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabelle_,type,
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tff(sy_c_FuncSet_OPi_000tc__Nat__Onat_000tc__Arrow____Order____Mirabelle____effngqiq,type,
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tff(sy_c_FuncSet_OPi_000tc__Nat__Onat_000tc__HOL__Obool,type,
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tff(sy_c_FuncSet_OPi_000tc__Nat__Onat_000tc__Product____Type__Ounit,type,
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tff(sy_c_FuncSet_OPi_000tc__Product____Type__Ounit_000tc__Nat__Onat,type,
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tff(sy_c_FuncSet_OPi_000tc__Product____Type__Ounit_000tc__fun_Itc__Arrow____Order___,type,
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tff(sy_c_FuncSet_OPi_000tc__Product____Type__Ounit_000tc__fun_Itc__fun_Itc__Arrow___,type,
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tff(sy_c_FuncSet_OPi_000tc__Product____Type__Ounit_000tc__fun_Itc__prod_Itc__Arrow__,type,
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tff(sy_c_FuncSet_OPi_000tc__Product____Type__Ounit_000tc__prod_Itc__Arrow____Order__,type,
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tff(sy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oind,type,
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tff(sy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oind_212,type,
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tff(sy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oind_213,type,
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tff(sy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oind_214,type,
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tff(sy_c_FuncSet_OPi_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqi,type,
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tff(sy_c_FuncSet_OPi_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqi_215,type,
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tff(sy_c_FuncSet_OPi_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqi_216,type,
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tff(sy_c_FuncSet_OPi_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngq,type,
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tff(sy_c_FuncSet_OPi_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngq_217,type,
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tff(sy_c_FuncSet_OPi_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngq_218,type,
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tff(sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal,type,
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tff(sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal_219,type,
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tff(sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal_220,type,
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tff(sy_c_Groups_Oone__class_Oone_000tc__Nat__Onat,type,
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tff(sy_c_Groups_Oplus__class_Oplus_000tc__Nat__Onat,type,
    plus_plus_nat: fun_nat_fun_nat_nat ).

tff(sy_c_Groups_Otimes__class_Otimes_000tc__Nat__Onat,type,
    times_times_nat: nat > fun_nat_nat ).

tff(sy_c_Groups_Ozero__class_Ozero_000tc__Nat__Onat,type,
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tff(sy_c_HOL_Obool_Obool__size,type,
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tff(sy_c_Hilbert__Choice_Oinv__into_000tc__Arrow____Order____Mirabelle____effngqiqbs,type,
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tff(sy_c_Hilbert__Choice_Oinv__into_000tc__Nat__Onat_000tc__Nat__Onat,type,
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tff(sy_c_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oal,type,
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tff(sy_c_Lattices_Osemilattice__sup__class_Osup_000tc__fun_Itc__Nat__Onat_Mtc__HOL__,type,
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tff(sy_c_Nat_OSuc,type,
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tff(sy_c_Nat_Onat_Onat__case_000tc__HOL__Obool,type,
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tff(sy_c_Nat_Onat_Onat__size,type,
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tff(sy_c_Nat_Osize__class_Osize_000tc__Nat__Onat,type,
    size_size_nat: fun_nat_nat ).

tff(sy_c_Orderings_Oord__class_Oless_000tc__HOL__Obool,type,
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tff(sy_c_Orderings_Oord__class_Oless_000tc__Nat__Onat,type,
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tff(sy_c_Orderings_Oord__class_Oless_000tc__fun_Itc__Arrow____Order____Mirabelle____,type,
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tff(sy_c_Orderings_Oord__class_Oless_000tc__fun_Itc__Arrow____Order____Mirabelle_____221,type,
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tff(sy_c_Orderings_Oord__class_Oless_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J,type,
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tff(sy_c_Orderings_Oord__class_Oless_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL,type,
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tff(sy_c_Orderings_Oord__class_Oless_000tc__fun_Itc__fun_Itc__Arrow____Order____Mira,type,
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tff(sy_c_Orderings_Oord__class_Oless_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Orde,type,
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tff(sy_c_Orderings_Oord__class_Oless_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Ord,type,
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tff(sy_c_Orderings_Oord__class_Oless_000tc__fun_Itc__prod_Itc__Arrow____Order____Mir,type,
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tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__HOL__Obool,type,
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tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__Nat__Onat,type,
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tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__Arrow____Order____Mirabelle,type,
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tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__Arrow____Order____Mirabelle_222,type,
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tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__Arrow____Order____Mirabelle_223,type,
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tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_,type,
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tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J,type,
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tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__Product____Type__Ounit_Mtc_,type,
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tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__fun_Itc__Arrow____Order____,type,
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tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____,type,
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tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow___,type,
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tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__prod_Itc__Arrow____Order___,type,
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tff(sy_c_Orderings_Otop__class_Otop_000tc__HOL__Obool,type,
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tff(sy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Arrow____Order____Mirabelle____e,type,
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tff(sy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Arrow____Order____Mirabelle____e_224,type,
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tff(sy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J,type,
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tff(sy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J,type,
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tff(sy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirab,type,
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tff(sy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order,type,
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tff(sy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Orde,type,
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tff(sy_c_Product__Type_OPair_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_,type,
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tff(sy_c_SetInterval_Oord__class_OatLeastAtMost_000tc__Nat__Onat,type,
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tff(sy_c_SetInterval_Oord__class_OatLeastLessThan_000tc__Nat__Onat,type,
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tff(sy_c_SetInterval_Oord__class_OatLeast_000tc__Nat__Onat,type,
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tff(sy_c_SetInterval_Oord__class_OgreaterThanAtMost_000tc__Nat__Onat,type,
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tff(sy_c_SetInterval_Oord__class_OgreaterThanLessThan_000tc__Nat__Onat,type,
    ord_gr660468384an_nat: nat > fun_nat_fun_nat_bool ).

tff(sy_c_SetInterval_Oord__class_OgreaterThan_000tc__Nat__Onat,type,
    ord_greaterThan_nat: fun_nat_fun_nat_bool ).

tff(sy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi,type,
    collec1597001935e_indi: fun_fu1712056765i_bool ).

tff(sy_c_Set_OCollect_000tc__Nat__Onat,type,
    collect_nat: fun_fu821463397t_bool ).

tff(sy_c_Set_OCollect_000tc__Product____Type__Ounit,type,
    collect_Product_unit: fun_fu391017725t_bool ).

tff(sy_c_Set_OCollect_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oin,type,
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tff(sy_c_Set_OCollect_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngq,type,
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tff(sy_c_Set_OCollect_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effng,type,
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tff(sy_c_Set_OCollect_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oa,type,
    collec1988958098le_alt: fun_fu1550952061t_bool ).

tff(sy_c_Set_Oimage_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000tc__N,type,
    image_1465793779di_nat: fun_Ar671024215di_nat > fun_fu1254370943t_bool ).

tff(sy_c_Set_Oimage_000tc__Nat__Onat_000tc__Nat__Onat,type,
    image_nat_nat: fun_nat_nat > fun_fu821463397t_bool ).

tff(sy_c_fFalse,type,
    fFalse: bool ).

tff(sy_c_fTrue,type,
    fTrue: bool ).

tff(sy_c_fconj,type,
    fconj: fun_bo1549164019l_bool ).

tff(sy_c_fequal_000tc__Nat__Onat,type,
    fequal_nat: fun_nat_fun_nat_bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__HOL__Obo,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc_,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc__225,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc__226,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc__227,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc__228,type,
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tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000tc__fun_Itc__229,type,
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tff(sy_c_member_000tc__fun_Itc__HOL__Obool_Mtc__fun_Itc__fun_Itc__Arrow____Order____,type,
    member1782492345t_bool: fun_fu1407717749l_bool ).

tff(sy_c_member_000tc__fun_Itc__HOL__Obool_Mtc__fun_Itc__prod_Itc__Arrow____Order___,type,
    member1133581546t_bool: fun_fu827796887l_bool ).

tff(sy_c_member_000tc__fun_Itc__HOL__Obool_Mtc__prod_Itc__Arrow____Order____Mirabell,type,
    member684813948le_alt: fun_fu662095797l_bool ).

tff(sy_c_member_000tc__fun_Itc__Nat__Onat_Mtc__Arrow____Order____Mirabelle____effngq,type,
    member1530714804e_indi: fun_fu1544203051l_bool ).

tff(sy_c_member_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J,type,
    member_fun_nat_bool: fun_fu1436348701l_bool ).

tff(sy_c_member_000tc__fun_Itc__Nat__Onat_Mtc__Product____Type__Ounit_J,type,
    member1024687843t_unit: fun_fu1028680969l_bool ).

tff(sy_c_member_000tc__fun_Itc__Product____Type__Ounit_Mtc__Nat__Onat_J,type,
    member87760213it_nat: fun_fu486305773l_bool ).

tff(sy_c_member_000tc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__Arrow____Order_,type,
    member364267905t_bool: fun_fu1172193141l_bool ).

tff(sy_c_member_000tc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__fun_Itc__Arrow_,type,
    member480326063t_bool: fun_fu1327602165l_bool ).

tff(sy_c_member_000tc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__prod_Itc__Arrow,type,
    member803887220t_bool: fun_fu1838150827l_bool ).

tff(sy_c_member_000tc__fun_Itc__Product____Type__Ounit_Mtc__prod_Itc__Arrow____Order,type,
    member869664626le_alt: fun_fu323675445l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__,type,
    member282602450e_indi: fun_fu1607936949l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs___392,type,
    member1020280587l_bool: fun_fu2080348917l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs___393,type,
    member2003579649t_unit: fun_fu1109942133l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs___394,type,
    member173038353t_bool: fun_fu1383920485l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____eff,type,
    member1247254528e_indi: fun_fu1843791925l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____eff_395,type,
    member1173995577l_bool: fun_fu2017702261l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____eff_396,type,
    member2091379247t_unit: fun_fu224426485l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef,type,
    member1220706259e_indi: fun_fu687131369l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_397,type,
    member340585612l_bool: fun_fu1253304283l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_398,type,
    member1729658242t_unit: fun_fu2020020679l_bool ).

tff(sy_c_member_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs_,type,
    member1558233923e_indi: fun_fu916781301l_bool ).

tff(sy_c_member_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__399,type,
    member1069471740t_bool: fun_fu864675765l_bool ).

tff(sy_c_member_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__400,type,
    member1303779570t_unit: fun_fu318801205l_bool ).

tff(sy_c_member_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_Mtc,type,
    member1333168212le_alt: fun_Pr1085078251l_bool ).

tff(sy_v_F,type,
    f: fun_fu2114379172t_bool ).

tff(sy_v_Lab____,type,
    lab: fun_Pr2067565481t_bool ).

tff(sy_v_Lba____,type,
    lba: fun_Pr2067565481t_bool ).

tff(sy_v_P____,type,
    p: fun_Ar274636406t_bool ).

tff(sy_v_a____,type,
    a: arrow_1893660431le_alt ).

tff(sy_v_b____,type,
    b: arrow_1893660431le_alt ).

tff(sy_v_c____,type,
    c: arrow_1893660431le_alt ).

tff(sy_v_d____,type,
    d: arrow_1893660431le_alt ).

tff(sy_v_e____,type,
    e: arrow_1893660431le_alt ).

tff(sy_v_h____,type,
    h: fun_Ar671024215di_nat ).

tff(sy_v_n____,type,
    n: nat ).

%----Relevant facts (1200)
tff(fact_0_assms_I3_J,axiom,
    hBOOL(hAPP_f1572141188l_bool(arrow_1335103695le_IIA,f)) ).

tff(fact_1_u,axiom,
    hBOOL(hAPP_f1572141188l_bool(arrow_320876018nimity,f)) ).

tff(fact_2__096c_A_126_061_Ad_096,axiom,
    c != d ).

tff(fact_3__096P_A_058_AProf_096,axiom,
    hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,p),arrow_5070731e_Prof)) ).

tff(fact_4_in__mkbot,axiom,
    ! [X_2: arrow_1893660431le_alt,Y_2: arrow_1893660431le_alt,L_3: fun_Pr2067565481t_bool,Z_2: arrow_1893660431le_alt] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Y_2)),hAPP_A1601437999t_bool(hAPP_f1761571331t_bool(arrow_1481558583_mkbot,L_3),Z_2)))
    <=> ( ( Y_2 != Z_2 )
        & ( ( X_2 = Z_2 )
         => ( X_2 != Y_2 ) )
        & ( ( X_2 != Z_2 )
         => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Y_2)),L_3)) ) ) ) ).

tff(fact_5_in__mktop,axiom,
    ! [X_2: arrow_1893660431le_alt,Y_2: arrow_1893660431le_alt,L_3: fun_Pr2067565481t_bool,Z_2: arrow_1893660431le_alt] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Y_2)),hAPP_A1601437999t_bool(hAPP_f1761571331t_bool(arrow_1630265669_mktop,L_3),Z_2)))
    <=> ( ( X_2 != Z_2 )
        & ( ( Y_2 = Z_2 )
         => ( X_2 != Y_2 ) )
        & ( ( Y_2 != Z_2 )
         => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Y_2)),L_3)) ) ) ) ).

tff(fact_6__C2_C,axiom,
    ! [P_1: fun_Ar274636406t_bool,Pa: fun_Ar274636406t_bool,A_34: arrow_1893660431le_alt,B_32: arrow_1893660431le_alt,Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt] :
      ( ( Aa != Ba )
     => ( ( A_34 != B_32 )
       => ( ( Aa != B_32 )
         => ( ( Ba != A_34 )
           => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,Pa),arrow_5070731e_Prof))
             => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,P_1),arrow_5070731e_Prof))
               => ( ! [I_1: arrow_856714788e_indi] :
                      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)),hAPP_A1646126530t_bool(Pa,I_1)))
                    <=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_34),B_32)),hAPP_A1646126530t_bool(P_1,I_1))) )
                 => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)),hAPP_f2008608496t_bool(f,Pa)))
                  <=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_34),B_32)),hAPP_f2008608496t_bool(f,P_1))) ) ) ) ) ) ) ) ) ).

tff(fact_7__C1_C,axiom,
    ! [P_1: fun_Ar274636406t_bool,Pa: fun_Ar274636406t_bool,A_34: arrow_1893660431le_alt,B_32: arrow_1893660431le_alt,Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt] :
      ( ( Aa != Ba )
     => ( ( A_34 != B_32 )
       => ( ( Aa != B_32 )
         => ( ( Ba != A_34 )
           => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,Pa),arrow_5070731e_Prof))
             => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,P_1),arrow_5070731e_Prof))
               => ( ! [I_1: arrow_856714788e_indi] :
                      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)),hAPP_A1646126530t_bool(Pa,I_1)))
                    <=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_34),B_32)),hAPP_A1646126530t_bool(P_1,I_1))) )
                 => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)),hAPP_f2008608496t_bool(f,Pa)))
                   => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_34),B_32)),hAPP_f2008608496t_bool(f,P_1))) ) ) ) ) ) ) ) ) ).

tff(fact_8__C4_C,axiom,
    ! [P_1: fun_Ar274636406t_bool,Pa: fun_Ar274636406t_bool,Ca: arrow_1893660431le_alt,Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt] :
      ( ( Aa != Ba )
     => ( ( Ba != Ca )
       => ( ( Aa != Ca )
         => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,Pa),arrow_5070731e_Prof))
           => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,P_1),arrow_5070731e_Prof))
             => ( ! [I_1: arrow_856714788e_indi] :
                    ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)),hAPP_A1646126530t_bool(Pa,I_1)))
                  <=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Ba),Ca)),hAPP_A1646126530t_bool(P_1,I_1))) )
               => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)),hAPP_f2008608496t_bool(f,Pa)))
                <=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Ba),Ca)),hAPP_f2008608496t_bool(f,P_1))) ) ) ) ) ) ) ) ).

tff(fact_9_pairwise__neutrality,axiom,
    ! [P_1: fun_Ar274636406t_bool,Pa: fun_Ar274636406t_bool,A_34: arrow_1893660431le_alt,B_32: arrow_1893660431le_alt,Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt] :
      ( ( Aa != Ba )
     => ( ( A_34 != B_32 )
       => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,Pa),arrow_5070731e_Prof))
         => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,P_1),arrow_5070731e_Prof))
           => ( ! [I_1: arrow_856714788e_indi] :
                  ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)),hAPP_A1646126530t_bool(Pa,I_1)))
                <=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_34),B_32)),hAPP_A1646126530t_bool(P_1,I_1))) )
             => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)),hAPP_f2008608496t_bool(f,Pa)))
              <=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_34),B_32)),hAPP_f2008608496t_bool(f,P_1))) ) ) ) ) ) ) ).

tff(fact_10__C3_C,axiom,
    ! [P_1: fun_Ar274636406t_bool,Pa: fun_Ar274636406t_bool,Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,Pa),arrow_5070731e_Prof))
       => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,P_1),arrow_5070731e_Prof))
         => ( ! [I_1: arrow_856714788e_indi] :
                ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)),hAPP_A1646126530t_bool(Pa,I_1)))
              <=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Ba),Aa)),hAPP_A1646126530t_bool(P_1,I_1))) )
           => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)),hAPP_f2008608496t_bool(f,Pa)))
            <=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Ba),Aa)),hAPP_f2008608496t_bool(f,P_1))) ) ) ) ) ) ).

tff(fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J,axiom,
    ! [I_1: arrow_856714788e_indi] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_A1646126530t_bool(p,I_1)))
    <=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A376526755di_nat(h,I_1)),n))
         => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_A1601437999t_bool(hAPP_f1761571331t_bool(arrow_1630265669_mktop,hAPP_A1646126530t_bool(p,I_1)),e))) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A376526755di_nat(h,I_1)),n))
         => ( ( ( hAPP_A376526755di_nat(h,I_1) = n )
             => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_216713899_above,hAPP_A1646126530t_bool(p,I_1)),c),e))) )
            & ( ( hAPP_A376526755di_nat(h,I_1) != n )
             => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_A1601437999t_bool(hAPP_f1761571331t_bool(arrow_1481558583_mkbot,hAPP_A1646126530t_bool(p,I_1)),e))) ) ) ) ) ) ).

tff(fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0,axiom,
    hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_A1646126530t_bool(p,hAPP_n1937165849e_indi(hilber1580028780di_nat(top_to788185952i_bool,h),n)))) ).

tff(fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
    hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_f2008608496t_bool(f,hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(ord_less_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1630265669_mktop),p)),e))),hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(fequal_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_A1889513822t_bool(hAPP_f2102110817t_bool(cOMBC_1486904681t_bool,hAPP_f1751344075t_bool(cOMBB_1876517692e_indi(arrow_216713899_above),p)),c)),e))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1481558583_mkbot),p)),e)))))) ).

tff(fact_14_PW,axiom,
    ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_f2008608496t_bool(f,p)))
  <=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_f2008608496t_bool(f,hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(ord_less_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1630265669_mktop),p)),e))),hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(fequal_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_A1889513822t_bool(hAPP_f2102110817t_bool(cOMBC_1486904681t_bool,hAPP_f1751344075t_bool(cOMBB_1876517692e_indi(arrow_216713899_above),p)),c)),e))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1481558583_mkbot),p)),e)))))) ) ).

tff(fact_15_split__paired__All,axiom,
    ! [Pa: fun_Pr2067565481t_bool] :
      ( ! [X1: produc472769767le_alt] : hBOOL(hAPP_P1178790471t_bool(Pa,X1))
    <=> ! [A_27: arrow_1893660431le_alt,B_25: arrow_1893660431le_alt] : hBOOL(hAPP_P1178790471t_bool(Pa,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_27),B_25))) ) ).

tff(fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai,axiom,
    hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(ord_less_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1630265669_mktop),p)),e))),hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(fequal_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_A1889513822t_bool(hAPP_f2102110817t_bool(cOMBC_1486904681t_bool,hAPP_f1751344075t_bool(cOMBB_1876517692e_indi(arrow_216713899_above),p)),c)),e))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1481558583_mkbot),p)),e)))),arrow_5070731e_Prof)) ).

tff(fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
    hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),e)),hAPP_f2008608496t_bool(f,hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(ord_less_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1630265669_mktop),p)),e))),hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(fequal_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_A1889513822t_bool(hAPP_f2102110817t_bool(cOMBC_1486904681t_bool,hAPP_f1751344075t_bool(cOMBB_1876517692e_indi(arrow_216713899_above),p)),c)),e))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1481558583_mkbot),p)),e)))))) ).

tff(fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
    hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,e),d)),hAPP_f2008608496t_bool(f,hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(ord_less_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1630265669_mktop),p)),e))),hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(fequal_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_A1889513822t_bool(hAPP_f2102110817t_bool(cOMBC_1486904681t_bool,hAPP_f1751344075t_bool(cOMBB_1876517692e_indi(arrow_216713899_above),p)),c)),e))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1481558583_mkbot),p)),e)))))) ).

tff(fact_19_n_I1_J,axiom,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,n),hAPP_f846027769ol_nat(finite1672073426e_indi,top_to788185952i_bool))) ).

tff(fact_20_injh,axiom,
    hBOOL(hAPP_f584385070l_bool(inj_on1960344199di_nat(h),top_to788185952i_bool)) ).

tff(fact_21_Pair__inject,axiom,
    ! [A_36: arrow_1893660431le_alt,B_34: arrow_1893660431le_alt,A_35: arrow_1893660431le_alt,B_33: arrow_1893660431le_alt] :
      ( ( hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_36),B_34) = hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_35),B_33) )
     => ~ ( ( A_36 = A_35 )
         => ( B_34 != B_33 ) ) ) ).

tff(fact_22_Pair__eq,axiom,
    ! [Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt,A_34: arrow_1893660431le_alt,B_32: arrow_1893660431le_alt] :
      ( ( hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba) = hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_34),B_32) )
    <=> ( ( Aa = A_34 )
        & ( Ba = B_32 ) ) ) ).

tff(fact_23_IIA__def,axiom,
    ! [Fa: fun_fu2114379172t_bool] :
      ( hBOOL(hAPP_f1572141188l_bool(arrow_1335103695le_IIA,Fa))
    <=> ! [X_1: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),arrow_5070731e_Prof))
         => ! [Xa: fun_Ar274636406t_bool] :
              ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,Xa),arrow_5070731e_Prof))
             => ! [A_27: arrow_1893660431le_alt,B_25: arrow_1893660431le_alt] :
                  ( ! [I_1: arrow_856714788e_indi] :
                      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_27),B_25)),hAPP_A1646126530t_bool(X_1,I_1)))
                    <=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_27),B_25)),hAPP_A1646126530t_bool(Xa,I_1))) )
                 => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_27),B_25)),hAPP_f2008608496t_bool(Fa,X_1)))
                  <=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_27),B_25)),hAPP_f2008608496t_bool(Fa,Xa))) ) ) ) ) ) ).

tff(fact_24_unanimity__def,axiom,
    ! [Fa: fun_fu2114379172t_bool] :
      ( hBOOL(hAPP_f1572141188l_bool(arrow_320876018nimity,Fa))
    <=> ! [X_1: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),arrow_5070731e_Prof))
         => ! [A_27: arrow_1893660431le_alt,B_25: arrow_1893660431le_alt] :
              ( ! [I_1: arrow_856714788e_indi] : hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_27),B_25)),hAPP_A1646126530t_bool(X_1,I_1)))
             => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_27),B_25)),hAPP_f2008608496t_bool(Fa,X_1))) ) ) ) ).

tff(fact_25_top1I,axiom,
    ! [X_2: fun_Pr2067565481t_bool] : hBOOL(hAPP_f52567537l_bool(top_to1312956197l_bool,X_2)) ).

tff(fact_26_top1I,axiom,
    ! [X_2: fun_Ar274636406t_bool] : hBOOL(hAPP_f995490902l_bool(top_to553140914l_bool,X_2)) ).

tff(fact_27_top1I,axiom,
    ! [X_2: fun_fu2114379172t_bool] : hBOOL(hAPP_f1572141188l_bool(top_to827110112l_bool,X_2)) ).

tff(fact_28_top1I,axiom,
    ! [X_2: produc472769767le_alt] : hBOOL(hAPP_P1178790471t_bool(top_to1138392227t_bool,X_2)) ).

tff(fact_29_top1I,axiom,
    ! [X_2: arrow_856714788e_indi] : hBOOL(hAPP_A997847300i_bool(top_to788185952i_bool,X_2)) ).

tff(fact_30_top1I,axiom,
    ! [X_2: nat] : hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,X_2)) ).

tff(fact_31_top1I,axiom,
    ! [X_2: product_unit] : hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,X_2)) ).

tff(fact_32_UNIV__I,axiom,
    ! [X_2: bool] : hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),top_to1647826457l_bool)) ).

tff(fact_33_UNIV__I,axiom,
    ! [X_2: arrow_856714788e_indi] : hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),top_to788185952i_bool)) ).

tff(fact_34_UNIV__I,axiom,
    ! [X_2: product_unit] : hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),top_to1257323279t_bool)) ).

tff(fact_35_UNIV__I,axiom,
    ! [X_2: produc472769767le_alt] : hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),top_to1138392227t_bool)) ).

tff(fact_36_UNIV__I,axiom,
    ! [X_2: fun_Ar274636406t_bool] : hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),top_to553140914l_bool)) ).

tff(fact_37_UNIV__I,axiom,
    ! [X_2: fun_fu2114379172t_bool] : hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),top_to827110112l_bool)) ).

tff(fact_38_UNIV__I,axiom,
    ! [X_2: fun_Pr2067565481t_bool] : hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),top_to1312956197l_bool)) ).

tff(fact_39_UNIV__I,axiom,
    ! [X_2: nat] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),top_top_fun_nat_bool)) ).

tff(fact_40_iso__tuple__UNIV__I,axiom,
    ! [X_2: bool] : hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),top_to1647826457l_bool)) ).

tff(fact_41_iso__tuple__UNIV__I,axiom,
    ! [X_2: arrow_856714788e_indi] : hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),top_to788185952i_bool)) ).

tff(fact_42_iso__tuple__UNIV__I,axiom,
    ! [X_2: product_unit] : hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),top_to1257323279t_bool)) ).

tff(fact_43_iso__tuple__UNIV__I,axiom,
    ! [X_2: produc472769767le_alt] : hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),top_to1138392227t_bool)) ).

tff(fact_44_iso__tuple__UNIV__I,axiom,
    ! [X_2: fun_Ar274636406t_bool] : hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),top_to553140914l_bool)) ).

tff(fact_45_iso__tuple__UNIV__I,axiom,
    ! [X_2: fun_fu2114379172t_bool] : hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),top_to827110112l_bool)) ).

tff(fact_46_iso__tuple__UNIV__I,axiom,
    ! [X_2: fun_Pr2067565481t_bool] : hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),top_to1312956197l_bool)) ).

tff(fact_47_iso__tuple__UNIV__I,axiom,
    ! [X_2: nat] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),top_top_fun_nat_bool)) ).

tff(fact_48_top__apply,axiom,
    ! [X_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(top_to1312956197l_bool,X_2))
    <=> hBOOL(top_top_bool) ) ).

tff(fact_49_top__apply,axiom,
    ! [X_2: fun_Ar274636406t_bool] :
      ( hBOOL(hAPP_f995490902l_bool(top_to553140914l_bool,X_2))
    <=> hBOOL(top_top_bool) ) ).

tff(fact_50_top__apply,axiom,
    ! [X_2: fun_fu2114379172t_bool] :
      ( hBOOL(hAPP_f1572141188l_bool(top_to827110112l_bool,X_2))
    <=> hBOOL(top_top_bool) ) ).

tff(fact_51_top__apply,axiom,
    ! [X_2: produc472769767le_alt] :
      ( hBOOL(hAPP_P1178790471t_bool(top_to1138392227t_bool,X_2))
    <=> hBOOL(top_top_bool) ) ).

tff(fact_52_top__apply,axiom,
    ! [X_2: arrow_856714788e_indi] :
      ( hBOOL(hAPP_A997847300i_bool(top_to788185952i_bool,X_2))
    <=> hBOOL(top_top_bool) ) ).

tff(fact_53_top__apply,axiom,
    ! [X_2: nat] :
      ( hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,X_2))
    <=> hBOOL(top_top_bool) ) ).

tff(fact_54_top__apply,axiom,
    ! [X_2: product_unit] :
      ( hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,X_2))
    <=> hBOOL(top_top_bool) ) ).

tff(fact_55_not__top__less,axiom,
    ! [Aa: fun_fu638310559l_bool] : ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,top_to1312956197l_bool),Aa)) ).

tff(fact_56_not__top__less,axiom,
    ! [Aa: fun_fu3835832l_bool] : ~ hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,top_to553140914l_bool),Aa)) ).

tff(fact_57_not__top__less,axiom,
    ! [Aa: fun_fu2098777574l_bool] : ~ hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,top_to827110112l_bool),Aa)) ).

tff(fact_58_not__top__less,axiom,
    ! [Aa: bool] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,top_top_bool),Aa)) ).

tff(fact_59_not__top__less,axiom,
    ! [Aa: fun_Pr2067565481t_bool] : ~ hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,top_to1138392227t_bool),Aa)) ).

tff(fact_60_not__top__less,axiom,
    ! [Aa: fun_Ar1809396326i_bool] : ~ hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,top_to788185952i_bool),Aa)) ).

tff(fact_61_not__top__less,axiom,
    ! [Aa: fun_nat_bool] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,top_top_fun_nat_bool),Aa)) ).

tff(fact_62_not__top__less,axiom,
    ! [Aa: fun_Pr1643180309t_bool] : ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,top_to1257323279t_bool),Aa)) ).

tff(fact_63_less__top,axiom,
    ! [Aa: fun_fu638310559l_bool] :
      ( ( Aa != top_to1312956197l_bool )
    <=> hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,Aa),top_to1312956197l_bool)) ) ).

tff(fact_64_less__top,axiom,
    ! [Aa: fun_fu3835832l_bool] :
      ( ( Aa != top_to553140914l_bool )
    <=> hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,Aa),top_to553140914l_bool)) ) ).

tff(fact_65_less__top,axiom,
    ! [Aa: fun_fu2098777574l_bool] :
      ( ( Aa != top_to827110112l_bool )
    <=> hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,Aa),top_to827110112l_bool)) ) ).

tff(fact_66_less__top,axiom,
    ! [Aa: bool] :
      ( ~ ( hBOOL(Aa)
        <=> hBOOL(top_top_bool) )
    <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),top_top_bool)) ) ).

tff(fact_67_less__top,axiom,
    ! [Aa: fun_Pr2067565481t_bool] :
      ( ( Aa != top_to1138392227t_bool )
    <=> hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,Aa),top_to1138392227t_bool)) ) ).

tff(fact_68_less__top,axiom,
    ! [Aa: fun_Ar1809396326i_bool] :
      ( ( Aa != top_to788185952i_bool )
    <=> hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Aa),top_to788185952i_bool)) ) ).

tff(fact_69_less__top,axiom,
    ! [Aa: fun_nat_bool] :
      ( ( Aa != top_top_fun_nat_bool )
    <=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),top_top_fun_nat_bool)) ) ).

tff(fact_70_less__top,axiom,
    ! [Aa: fun_Pr1643180309t_bool] :
      ( ( Aa != top_to1257323279t_bool )
    <=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),top_to1257323279t_bool)) ) ).

tff(fact_71_assms_I1_J,axiom,
    hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,f),pi_fun1746584570t_bool(arrow_5070731e_Prof,hAPP_f1104294872l_bool(cOMBK_1701906001t_bool,arrow_1361987423le_Lin)))) ).

tff(fact_72__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk,axiom,
    ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,e),d)),hAPP_f2008608496t_bool(f,hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(ord_less_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1630265669_mktop),p)),e))),hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(fequal_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_A1889513822t_bool(hAPP_f2102110817t_bool(cOMBC_1486904681t_bool,hAPP_f1751344075t_bool(cOMBB_1876517692e_indi(arrow_216713899_above),p)),c)),e))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1481558583_mkbot),p)),e))))))
  <=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,b),a)),hAPP_f2008608496t_bool(f,hAPP_f480276746t_bool(hAPP_f601594885t_bool(cOMBC_750853729t_bool,hAPP_f1344464862t_bool(hAPP_f1908974253t_bool(cOMBC_156709173t_bool,hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(ord_less_nat),h)),n))),lab)),lba)))) ) ).

tff(fact_73_dictator__def,axiom,
    ! [Fa: fun_fu2114379172t_bool,I: arrow_856714788e_indi] :
      ( hBOOL(hAPP_A997847300i_bool(hAPP_f399308031i_bool(arrow_1765888670ctator,Fa),I))
    <=> ! [X_1: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),arrow_5070731e_Prof))
         => ( hAPP_f2008608496t_bool(Fa,X_1) = hAPP_A1646126530t_bool(X_1,I) ) ) ) ).

tff(fact_74__096Lab_A_058_ALin_096,axiom,
    hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,lab),arrow_1361987423le_Lin)) ).

tff(fact_75__096Lba_A_058_ALin_096,axiom,
    hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,lba),arrow_1361987423le_Lin)) ).

tff(fact_76__096a_A_126_061_Ab_096,axiom,
    a != b ).

tff(fact_77__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096,axiom,
    hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,a),b)),lab)) ).

tff(fact_78__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096,axiom,
    hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,b),a)),lba)) ).

tff(fact_79__096_Ia_M_Ab_J_A_126_058_ALba_096,axiom,
    ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,a),b)),lba)) ).

tff(fact_80__096_Ib_M_Aa_J_A_126_058_ALab_096,axiom,
    ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,b),a)),lab)) ).

tff(fact_81_PiProf,axiom,
    ! [Na: nat] : hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_f480276746t_bool(hAPP_f601594885t_bool(cOMBC_750853729t_bool,hAPP_f1344464862t_bool(hAPP_f1908974253t_bool(cOMBC_156709173t_bool,hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(ord_less_nat),h)),Na))),lab)),lba)),arrow_5070731e_Prof)) ).

tff(fact_82__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_,axiom,
    ~ ! [Lab: fun_Pr2067565481t_bool] :
        ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,a),b)),Lab))
       => ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,Lab),arrow_1361987423le_Lin)) ) ).

tff(fact_83__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_,axiom,
    ~ ! [Lba: fun_Pr2067565481t_bool] :
        ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,b),a)),Lba))
       => ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,Lba),arrow_1361987423le_Lin)) ) ).

tff(fact_84__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk,axiom,
    ! [I_1: arrow_856714788e_indi] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A376526755di_nat(h,I_1)),n))
         => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,e),d)),hAPP_A1601437999t_bool(hAPP_f1761571331t_bool(arrow_1630265669_mktop,hAPP_A1646126530t_bool(p,I_1)),e))) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A376526755di_nat(h,I_1)),n))
         => ( ( ( hAPP_A376526755di_nat(h,I_1) = n )
             => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,e),d)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_216713899_above,hAPP_A1646126530t_bool(p,I_1)),c),e))) )
            & ( ( hAPP_A376526755di_nat(h,I_1) != n )
             => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,e),d)),hAPP_A1601437999t_bool(hAPP_f1761571331t_bool(arrow_1481558583_mkbot,hAPP_A1646126530t_bool(p,I_1)),e))) ) ) ) )
    <=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A376526755di_nat(h,I_1)),n))
         => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,b),a)),lab)) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A376526755di_nat(h,I_1)),n))
         => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,b),a)),lba)) ) ) ) ).

tff(fact_85_n_I2_J,axiom,
    ! [M: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),n))
     => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,b),a)),hAPP_f2008608496t_bool(f,hAPP_f480276746t_bool(hAPP_f601594885t_bool(cOMBC_750853729t_bool,hAPP_f1344464862t_bool(hAPP_f1908974253t_bool(cOMBC_156709173t_bool,hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(ord_less_nat),h)),M))),lab)),lba)))) ) ).

tff(fact_86_notin__Lin__iff,axiom,
    ! [X_2: arrow_1893660431le_alt,Y_2: arrow_1893660431le_alt,L_3: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,L_3),arrow_1361987423le_Lin))
     => ( ( X_2 != Y_2 )
       => ( ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Y_2)),L_3))
        <=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Y_2),X_2)),L_3)) ) ) ) ).

tff(fact_87_Lin__irrefl,axiom,
    ! [Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt,L_3: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,L_3),arrow_1361987423le_Lin))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)),L_3))
       => ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Ba),Aa)),L_3)) ) ) ).

tff(fact_88_mktop__Lin,axiom,
    ! [X_2: arrow_1893660431le_alt,L_3: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,L_3),arrow_1361987423le_Lin))
     => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_A1601437999t_bool(hAPP_f1761571331t_bool(arrow_1630265669_mktop,L_3),X_2)),arrow_1361987423le_Lin)) ) ).

tff(fact_89_mkbot__Lin,axiom,
    ! [X_2: arrow_1893660431le_alt,L_3: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,L_3),arrow_1361987423le_Lin))
     => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_A1601437999t_bool(hAPP_f1761571331t_bool(arrow_1481558583_mkbot,L_3),X_2)),arrow_1361987423le_Lin)) ) ).

tff(fact_90_above__Lin,axiom,
    ! [L_3: fun_Pr2067565481t_bool,X_2: arrow_1893660431le_alt,Y_2: arrow_1893660431le_alt] :
      ( ( X_2 != Y_2 )
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,L_3),arrow_1361987423le_Lin))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_216713899_above,L_3),X_2),Y_2)),arrow_1361987423le_Lin)) ) ) ).

tff(fact_91_const__Lin__Prof,axiom,
    ! [L_3: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,L_3),arrow_1361987423le_Lin))
     => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_f480276746t_bool(cOMBK_1650320063e_indi,L_3)),arrow_5070731e_Prof)) ) ).

tff(fact_92_linorder__cases,axiom,
    ! [X_32: nat,Y_30: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_32),Y_30))
     => ( ( X_32 != Y_30 )
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_30),X_32)) ) ) ).

tff(fact_93_order__less__asym,axiom,
    ! [X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
     => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2)) ) ).

tff(fact_94_order__less__asym,axiom,
    ! [X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
     => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2)) ) ).

tff(fact_95_order__less__asym,axiom,
    ! [X_2: fun_Ar1809396326i_bool,Y_2: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,X_2),Y_2))
     => ~ hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Y_2),X_2)) ) ).

tff(fact_96_order__less__asym,axiom,
    ! [X_31: nat,Y_29: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_31),Y_29))
     => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_29),X_31)) ) ).

tff(fact_97_xt1_I10_J,axiom,
    ! [Z_2: fun_nat_bool,Y_2: fun_nat_bool,X_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_2),Y_2))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_2),X_2)) ) ) ).

tff(fact_98_xt1_I10_J,axiom,
    ! [Z_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool,X_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_2),Y_2))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_2),X_2)) ) ) ).

tff(fact_99_xt1_I10_J,axiom,
    ! [Z_2: fun_Ar1809396326i_bool,Y_2: fun_Ar1809396326i_bool,X_2: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Z_2),Y_2))
       => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Z_2),X_2)) ) ) ).

tff(fact_100_xt1_I10_J,axiom,
    ! [Z_9: nat,Y_28: nat,X_30: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_28),X_30))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_9),Y_28))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_9),X_30)) ) ) ).

tff(fact_101_order__less__trans,axiom,
    ! [Z_2: fun_nat_bool,X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),Z_2))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Z_2)) ) ) ).

tff(fact_102_order__less__trans,axiom,
    ! [Z_2: fun_Pr1643180309t_bool,X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),Z_2))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Z_2)) ) ) ).

tff(fact_103_order__less__trans,axiom,
    ! [Z_2: fun_Ar1809396326i_bool,X_2: fun_Ar1809396326i_bool,Y_2: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Y_2),Z_2))
       => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,X_2),Z_2)) ) ) ).

tff(fact_104_order__less__trans,axiom,
    ! [Z_8: nat,X_29: nat,Y_27: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_29),Y_27))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_27),Z_8))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_29),Z_8)) ) ) ).

tff(fact_105_xt1_I2_J,axiom,
    ! [Ca: fun_nat_bool,Ba: fun_nat_bool,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa))
     => ( ( Ba = Ca )
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),Aa)) ) ) ).

tff(fact_106_xt1_I2_J,axiom,
    ! [Ca: fun_Pr1643180309t_bool,Ba: fun_Pr1643180309t_bool,Aa: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa))
     => ( ( Ba = Ca )
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),Aa)) ) ) ).

tff(fact_107_xt1_I2_J,axiom,
    ! [Ca: fun_Ar1809396326i_bool,Ba: fun_Ar1809396326i_bool,Aa: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Ba),Aa))
     => ( ( Ba = Ca )
       => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Ca),Aa)) ) ) ).

tff(fact_108_xt1_I2_J,axiom,
    ! [C_24: nat,B_31: nat,A_33: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_31),A_33))
     => ( ( B_31 = C_24 )
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_24),A_33)) ) ) ).

tff(fact_109_ord__less__eq__trans,axiom,
    ! [Ca: fun_nat_bool,Aa: fun_nat_bool,Ba: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba))
     => ( ( Ba = Ca )
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ca)) ) ) ).

tff(fact_110_ord__less__eq__trans,axiom,
    ! [Ca: fun_Pr1643180309t_bool,Aa: fun_Pr1643180309t_bool,Ba: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba))
     => ( ( Ba = Ca )
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ca)) ) ) ).

tff(fact_111_ord__less__eq__trans,axiom,
    ! [Ca: fun_Ar1809396326i_bool,Aa: fun_Ar1809396326i_bool,Ba: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Aa),Ba))
     => ( ( Ba = Ca )
       => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Aa),Ca)) ) ) ).

tff(fact_112_ord__less__eq__trans,axiom,
    ! [C_23: nat,A_32: nat,B_30: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_32),B_30))
     => ( ( B_30 = C_23 )
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_32),C_23)) ) ) ).

tff(fact_113_xt1_I1_J,axiom,
    ! [Ca: fun_nat_bool,Aa: fun_nat_bool,Ba: fun_nat_bool] :
      ( ( Aa = Ba )
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),Ba))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),Aa)) ) ) ).

tff(fact_114_xt1_I1_J,axiom,
    ! [Ca: fun_Pr1643180309t_bool,Aa: fun_Pr1643180309t_bool,Ba: fun_Pr1643180309t_bool] :
      ( ( Aa = Ba )
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),Ba))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),Aa)) ) ) ).

tff(fact_115_xt1_I1_J,axiom,
    ! [Ca: fun_Ar1809396326i_bool,Aa: fun_Ar1809396326i_bool,Ba: fun_Ar1809396326i_bool] :
      ( ( Aa = Ba )
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Ca),Ba))
       => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Ca),Aa)) ) ) ).

tff(fact_116_xt1_I1_J,axiom,
    ! [C_22: nat,A_31: nat,B_29: nat] :
      ( ( A_31 = B_29 )
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_22),B_29))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_22),A_31)) ) ) ).

tff(fact_117_ord__eq__less__trans,axiom,
    ! [Ca: fun_nat_bool,Aa: fun_nat_bool,Ba: fun_nat_bool] :
      ( ( Aa = Ba )
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Ca))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ca)) ) ) ).

tff(fact_118_ord__eq__less__trans,axiom,
    ! [Ca: fun_Pr1643180309t_bool,Aa: fun_Pr1643180309t_bool,Ba: fun_Pr1643180309t_bool] :
      ( ( Aa = Ba )
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Ca))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ca)) ) ) ).

tff(fact_119_ord__eq__less__trans,axiom,
    ! [Ca: fun_Ar1809396326i_bool,Aa: fun_Ar1809396326i_bool,Ba: fun_Ar1809396326i_bool] :
      ( ( Aa = Ba )
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Ba),Ca))
       => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Aa),Ca)) ) ) ).

tff(fact_120_ord__eq__less__trans,axiom,
    ! [C_21: nat,A_30: nat,B_28: nat] :
      ( ( A_30 = B_28 )
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_28),C_21))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_30),C_21)) ) ) ).

tff(fact_121_xt1_I9_J,axiom,
    ! [Ba: fun_nat_bool,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa))
     => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba)) ) ).

tff(fact_122_xt1_I9_J,axiom,
    ! [Ba: fun_Pr1643180309t_bool,Aa: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa))
     => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba)) ) ).

tff(fact_123_xt1_I9_J,axiom,
    ! [Ba: fun_Ar1809396326i_bool,Aa: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Ba),Aa))
     => ~ hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Aa),Ba)) ) ).

tff(fact_124_xt1_I9_J,axiom,
    ! [B_27: nat,A_29: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_27),A_29))
     => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_29),B_27)) ) ).

tff(fact_125_order__less__asym_H,axiom,
    ! [Aa: fun_nat_bool,Ba: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba))
     => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa)) ) ).

tff(fact_126_order__less__asym_H,axiom,
    ! [Aa: fun_Pr1643180309t_bool,Ba: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba))
     => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa)) ) ).

tff(fact_127_order__less__asym_H,axiom,
    ! [Aa: fun_Ar1809396326i_bool,Ba: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Aa),Ba))
     => ~ hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Ba),Aa)) ) ).

tff(fact_128_order__less__asym_H,axiom,
    ! [A_28: nat,B_26: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_28),B_26))
     => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_26),A_28)) ) ).

tff(fact_129_order__less__imp__triv,axiom,
    ! [Pa: bool,X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2))
       => hBOOL(Pa) ) ) ).

tff(fact_130_order__less__imp__triv,axiom,
    ! [Pa: bool,X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2))
       => hBOOL(Pa) ) ) ).

tff(fact_131_order__less__imp__triv,axiom,
    ! [Pa: bool,X_2: fun_Ar1809396326i_bool,Y_2: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Y_2),X_2))
       => hBOOL(Pa) ) ) ).

tff(fact_132_order__less__imp__triv,axiom,
    ! [Pa: bool,X_2: nat,Y_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2))
       => hBOOL(Pa) ) ) ).

tff(fact_133_order__less__imp__not__eq2,axiom,
    ! [X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
     => ( Y_2 != X_2 ) ) ).

tff(fact_134_order__less__imp__not__eq2,axiom,
    ! [X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
     => ( Y_2 != X_2 ) ) ).

tff(fact_135_order__less__imp__not__eq2,axiom,
    ! [X_2: fun_Ar1809396326i_bool,Y_2: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,X_2),Y_2))
     => ( Y_2 != X_2 ) ) ).

tff(fact_136_order__less__imp__not__eq2,axiom,
    ! [X_28: nat,Y_26: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_28),Y_26))
     => ( Y_26 != X_28 ) ) ).

tff(fact_137_order__less__imp__not__eq,axiom,
    ! [X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
     => ( X_2 != Y_2 ) ) ).

tff(fact_138_order__less__imp__not__eq,axiom,
    ! [X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
     => ( X_2 != Y_2 ) ) ).

tff(fact_139_order__less__imp__not__eq,axiom,
    ! [X_2: fun_Ar1809396326i_bool,Y_2: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,X_2),Y_2))
     => ( X_2 != Y_2 ) ) ).

tff(fact_140_order__less__imp__not__eq,axiom,
    ! [X_27: nat,Y_25: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_27),Y_25))
     => ( X_27 != Y_25 ) ) ).

tff(fact_141_order__less__imp__not__less,axiom,
    ! [X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
     => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2)) ) ).

tff(fact_142_order__less__imp__not__less,axiom,
    ! [X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
     => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2)) ) ).

tff(fact_143_order__less__imp__not__less,axiom,
    ! [X_2: fun_Ar1809396326i_bool,Y_2: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,X_2),Y_2))
     => ~ hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Y_2),X_2)) ) ).

tff(fact_144_order__less__imp__not__less,axiom,
    ! [X_26: nat,Y_24: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_26),Y_24))
     => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_24),X_26)) ) ).

tff(fact_145_order__less__not__sym,axiom,
    ! [X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
     => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2)) ) ).

tff(fact_146_order__less__not__sym,axiom,
    ! [X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
     => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2)) ) ).

tff(fact_147_order__less__not__sym,axiom,
    ! [X_2: fun_Ar1809396326i_bool,Y_2: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,X_2),Y_2))
     => ~ hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Y_2),X_2)) ) ).

tff(fact_148_order__less__not__sym,axiom,
    ! [X_25: nat,Y_23: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_25),Y_23))
     => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_23),X_25)) ) ).

tff(fact_149_less__imp__neq,axiom,
    ! [X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
     => ( X_2 != Y_2 ) ) ).

tff(fact_150_less__imp__neq,axiom,
    ! [X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
     => ( X_2 != Y_2 ) ) ).

tff(fact_151_less__imp__neq,axiom,
    ! [X_2: fun_Ar1809396326i_bool,Y_2: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,X_2),Y_2))
     => ( X_2 != Y_2 ) ) ).

tff(fact_152_less__imp__neq,axiom,
    ! [X_24: nat,Y_22: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_24),Y_22))
     => ( X_24 != Y_22 ) ) ).

tff(fact_153_linorder__neqE,axiom,
    ! [X_23: nat,Y_21: nat] :
      ( ( X_23 != Y_21 )
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_23),Y_21))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_21),X_23)) ) ) ).

tff(fact_154_linorder__antisym__conv3,axiom,
    ! [Y_2: nat,X_2: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
      <=> ( X_2 = Y_2 ) ) ) ).

tff(fact_155_linorder__less__linear,axiom,
    ! [X_22: nat,Y_20: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_22),Y_20))
      | ( X_22 = Y_20 )
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_20),X_22)) ) ).

tff(fact_156_not__less__iff__gr__or__eq,axiom,
    ! [X_2: nat,Y_2: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2))
        | ( X_2 = Y_2 ) ) ) ).

tff(fact_157_linorder__neq__iff,axiom,
    ! [X_2: nat,Y_2: nat] :
      ( ( X_2 != Y_2 )
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2)) ) ) ).

tff(fact_158_order__less__irrefl,axiom,
    ! [X_2: fun_nat_bool] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),X_2)) ).

tff(fact_159_order__less__irrefl,axiom,
    ! [X_2: fun_Pr1643180309t_bool] : ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),X_2)) ).

tff(fact_160_order__less__irrefl,axiom,
    ! [X_2: fun_Ar1809396326i_bool] : ~ hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,X_2),X_2)) ).

tff(fact_161_order__less__irrefl,axiom,
    ! [X_21: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_21),X_21)) ).

tff(fact_162_mem__def,axiom,
    ! [X_2: arrow_856714788e_indi,A: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A))
    <=> hBOOL(hAPP_A997847300i_bool(A,X_2)) ) ).

tff(fact_163_mem__def,axiom,
    ! [X_2: bool,A: fun_bool_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
    <=> hBOOL(hAPP_bool_bool(A,X_2)) ) ).

tff(fact_164_mem__def,axiom,
    ! [X_2: product_unit,A: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
    <=> hBOOL(hAPP_P1676879539t_bool(A,X_2)) ) ).

tff(fact_165_mem__def,axiom,
    ! [X_2: produc472769767le_alt,A: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A))
    <=> hBOOL(hAPP_P1178790471t_bool(A,X_2)) ) ).

tff(fact_166_mem__def,axiom,
    ! [X_2: fun_Ar274636406t_bool,A: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A))
    <=> hBOOL(hAPP_f995490902l_bool(A,X_2)) ) ).

tff(fact_167_mem__def,axiom,
    ! [X_2: fun_fu2114379172t_bool,A: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A))
    <=> hBOOL(hAPP_f1572141188l_bool(A,X_2)) ) ).

tff(fact_168_mem__def,axiom,
    ! [X_2: fun_Pr2067565481t_bool,A: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A))
    <=> hBOOL(hAPP_f52567537l_bool(A,X_2)) ) ).

tff(fact_169_mem__def,axiom,
    ! [X_2: nat,A: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
    <=> hBOOL(hAPP_nat_bool(A,X_2)) ) ).

tff(fact_170_Collect__def,axiom,
    ! [Pa: fun_Pr1643180309t_bool] : ( hAPP_f427533077t_bool(collect_Product_unit,Pa) = Pa ) ).

tff(fact_171_Collect__def,axiom,
    ! [Pa: fun_Ar1809396326i_bool] : ( hAPP_f1612707285i_bool(collec1597001935e_indi,Pa) = Pa ) ).

tff(fact_172_Collect__def,axiom,
    ! [Pa: fun_nat_bool] : ( hAPP_f800510211t_bool(collect_nat,Pa) = Pa ) ).

tff(fact_173_UNIV__def,axiom,
    top_to1312956197l_bool = hAPP_f1060563265l_bool(collec2125531966t_bool,hAPP_b1272691967l_bool(cOMBK_81143760t_bool,fTrue)) ).

tff(fact_174_UNIV__def,axiom,
    top_to553140914l_bool = hAPP_f819682389l_bool(collec1236161569t_bool,hAPP_b1078573912l_bool(cOMBK_445086735t_bool,fTrue)) ).

tff(fact_175_UNIV__def,axiom,
    top_to827110112l_bool = hAPP_f1181604821l_bool(collec71394895t_bool,hAPP_b1777246598l_bool(cOMBK_1279003709t_bool,fTrue)) ).

tff(fact_176_UNIV__def,axiom,
    top_to1138392227t_bool = hAPP_f1356305429t_bool(collec1988958098le_alt,hAPP_b128655177t_bool(cOMBK_198697344le_alt,fTrue)) ).

tff(fact_177_UNIV__def,axiom,
    top_to788185952i_bool = hAPP_f1612707285i_bool(collec1597001935e_indi,hAPP_b549570054i_bool(cOMBK_561380029e_indi,fTrue)) ).

tff(fact_178_UNIV__def,axiom,
    top_to1257323279t_bool = hAPP_f427533077t_bool(collect_Product_unit,hAPP_b1096750261t_bool(cOMBK_790042732t_unit,fTrue)) ).

tff(fact_179_UNIV__def,axiom,
    top_top_fun_nat_bool = hAPP_f800510211t_bool(collect_nat,hAPP_b1013836512t_bool(cOMBK_bool_nat,fTrue)) ).

tff(fact_180_in__above,axiom,
    ! [X_2: arrow_1893660431le_alt,Y_2: arrow_1893660431le_alt,L_3: fun_Pr2067565481t_bool,Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,L_3),arrow_1361987423le_Lin))
       => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Y_2)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_216713899_above,L_3),Aa),Ba)))
        <=> ( ( X_2 != Y_2 )
            & ( ( X_2 = Ba )
             => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Y_2)),L_3)) )
            & ( ( X_2 != Ba )
             => ( ( ( Y_2 = Ba )
                 => ( ( X_2 = Aa )
                    | hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Aa)),L_3)) ) )
                & ( ( Y_2 != Ba )
                 => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Y_2)),L_3)) ) ) ) ) ) ) ) ).

tff(fact_181_pred__equals__eq2,axiom,
    ! [S_1: fun_Pr2067565481t_bool,R_1: fun_Pr2067565481t_bool] :
      ( ! [X_1: arrow_1893660431le_alt,Xa: arrow_1893660431le_alt] :
          ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_1),Xa)),R_1))
        <=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_1),Xa)),S_1)) )
    <=> ( R_1 = S_1 ) ) ).

tff(fact_182_dictatorI,axiom,
    ! [I: arrow_856714788e_indi,Fa: fun_fu2114379172t_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,Fa),pi_fun1746584570t_bool(arrow_5070731e_Prof,hAPP_f1104294872l_bool(cOMBK_1701906001t_bool,arrow_1361987423le_Lin))))
     => ( ! [X_1: fun_Ar274636406t_bool] :
            ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),arrow_5070731e_Prof))
           => ! [A_27: arrow_1893660431le_alt,B_25: arrow_1893660431le_alt] :
                ( ( A_27 != B_25 )
               => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_27),B_25)),hAPP_A1646126530t_bool(X_1,I)))
                 => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,A_27),B_25)),hAPP_f2008608496t_bool(Fa,X_1))) ) ) )
       => hBOOL(hAPP_A997847300i_bool(hAPP_f399308031i_bool(arrow_1765888670ctator,Fa),I)) ) ) ).

tff(fact_183_n_I3_J,axiom,
    hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,a),b)),hAPP_f2008608496t_bool(f,hAPP_f480276746t_bool(hAPP_f601594885t_bool(cOMBC_750853729t_bool,hAPP_f1344464862t_bool(hAPP_f1908974253t_bool(cOMBC_156709173t_bool,hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))),lab)),lba)))) ).

tff(fact_184__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am,axiom,
    ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),e)),hAPP_f2008608496t_bool(f,hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(ord_less_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1630265669_mktop),p)),e))),hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(fequal_nat),h)),n))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_A1889513822t_bool(hAPP_f2102110817t_bool(cOMBC_1486904681t_bool,hAPP_f1751344075t_bool(cOMBB_1876517692e_indi(arrow_216713899_above),p)),c)),e))),hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,hAPP_f831214557t_bool(cOMBB_80760910e_indi(arrow_1481558583_mkbot),p)),e))))))
  <=> hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,a),b)),hAPP_f2008608496t_bool(f,hAPP_f480276746t_bool(hAPP_f601594885t_bool(cOMBC_750853729t_bool,hAPP_f1344464862t_bool(hAPP_f1908974253t_bool(cOMBC_156709173t_bool,hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))),lab)),lba)))) ) ).

tff(fact_185__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am,axiom,
    ! [I_1: arrow_856714788e_indi] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A376526755di_nat(h,I_1)),n))
         => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),e)),hAPP_A1601437999t_bool(hAPP_f1761571331t_bool(arrow_1630265669_mktop,hAPP_A1646126530t_bool(p,I_1)),e))) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A376526755di_nat(h,I_1)),n))
         => ( ( ( hAPP_A376526755di_nat(h,I_1) = n )
             => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),e)),hAPP_A1601437999t_bool(hAPP_A1058422557t_bool(hAPP_f1550387441t_bool(arrow_216713899_above,hAPP_A1646126530t_bool(p,I_1)),c),e))) )
            & ( ( hAPP_A376526755di_nat(h,I_1) != n )
             => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),e)),hAPP_A1601437999t_bool(hAPP_f1761571331t_bool(arrow_1481558583_mkbot,hAPP_A1646126530t_bool(p,I_1)),e))) ) ) ) )
    <=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A376526755di_nat(h,I_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
         => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,a),b)),lab)) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A376526755di_nat(h,I_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
         => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,a),b)),lba)) ) ) ) ).

tff(fact_186_inv__f__eq,axiom,
    ! [X_2: arrow_856714788e_indi,Y_2: nat,F: fun_Ar671024215di_nat] :
      ( hBOOL(hAPP_f584385070l_bool(inj_on1960344199di_nat(F),top_to788185952i_bool))
     => ( ( hAPP_A376526755di_nat(F,X_2) = Y_2 )
       => ( hAPP_n1937165849e_indi(hilber1580028780di_nat(top_to788185952i_bool,F),Y_2) = X_2 ) ) ) ).

tff(fact_187_inv__f__eq,axiom,
    ! [X_2: nat,Y_2: nat,F: fun_nat_nat] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool))
     => ( ( hAPP_nat_nat(F,X_2) = Y_2 )
       => ( hAPP_nat_nat(hilber195283148at_nat(top_top_fun_nat_bool,F),Y_2) = X_2 ) ) ) ).

tff(fact_188_inv__f__f,axiom,
    ! [X_2: arrow_856714788e_indi,F: fun_Ar671024215di_nat] :
      ( hBOOL(hAPP_f584385070l_bool(inj_on1960344199di_nat(F),top_to788185952i_bool))
     => ( hAPP_n1937165849e_indi(hilber1580028780di_nat(top_to788185952i_bool,F),hAPP_A376526755di_nat(F,X_2)) = X_2 ) ) ).

tff(fact_189_inv__f__f,axiom,
    ! [X_2: nat,F: fun_nat_nat] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool))
     => ( hAPP_nat_nat(hilber195283148at_nat(top_top_fun_nat_bool,F),hAPP_nat_nat(F,X_2)) = X_2 ) ) ).

tff(fact_190_PiE,axiom,
    ! [X_2: produc472769767le_alt,F: fun_Pr2067565481t_bool,A: fun_Pr2067565481t_bool,B: fun_Pr1780397033l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,F),pi_Pro1238944957t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1178790471t_bool(F,X_2)),hAPP_P1103642805l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A)) ) ) ).

tff(fact_191_PiE,axiom,
    ! [X_2: arrow_856714788e_indi,F: fun_Ar338949104le_alt,A: fun_Ar1809396326i_bool,B: fun_Ar274636406t_bool] :
      ( hBOOL(hAPP_f1754488902l_bool(hAPP_f766019597l_bool(member387840963le_alt,F),pi_Arr1460528004le_alt(A,B)))
     => ( ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A899858958le_alt(F,X_2)),hAPP_A1646126530t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A)) ) ) ).

tff(fact_192_PiE,axiom,
    ! [X_2: bool,F: fun_bo1682907689le_alt,A: fun_bool_bool,B: fun_bo1431306493t_bool] :
      ( hBOOL(hAPP_f1620711039l_bool(hAPP_f334747853l_bool(member684813948le_alt,F),pi_boo7125949le_alt(A,B)))
     => ( ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_b2094455111le_alt(F,X_2)),hAPP_b128655177t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) ) ) ).

tff(fact_193_PiE,axiom,
    ! [X_2: product_unit,F: fun_Pr2090226719le_alt,A: fun_Pr1643180309t_bool,B: fun_Pr1887398791t_bool] :
      ( hBOOL(hAPP_f684683381l_bool(hAPP_f41367117l_bool(member869664626le_alt,F),pi_Pro1820940723le_alt(A,B)))
     => ( ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_P396106045le_alt(F,X_2)),hAPP_P1914371027t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) ) ) ).

tff(fact_194_PiE,axiom,
    ! [X_2: arrow_856714788e_indi,F: fun_Ar624010239t_bool,A: fun_Ar1809396326i_bool,B: fun_Ar1998664965l_bool] :
      ( hBOOL(hAPP_f826064725l_bool(hAPP_f1364091725l_bool(member1124505298t_bool,F),pi_Arr2025169427t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_A2107398813t_bool(F,X_2)),hAPP_A1411662545l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A)) ) ) ).

tff(fact_195_PiE,axiom,
    ! [X_2: bool,F: fun_bo1476023096t_bool,A: fun_bool_bool,B: fun_bo2107365004l_bool] :
      ( hBOOL(hAPP_f1605957262l_bool(hAPP_f1525863565l_bool(member344984203t_bool,F),pi_boo347863884t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_b489616086t_bool(F,X_2)),hAPP_b1078573912l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) ) ) ).

tff(fact_196_PiE,axiom,
    ! [X_2: product_unit,F: fun_Pr1531194158t_bool,A: fun_Pr1643180309t_bool,B: fun_Pr537467670l_bool] :
      ( hBOOL(hAPP_f1851324036l_bool(hAPP_f1974966541l_bool(member364267905t_bool,F),pi_Pro782712642t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_P913627340t_bool(F,X_2)),hAPP_P284783074l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) ) ) ).

tff(fact_197_PiE,axiom,
    ! [X_2: arrow_856714788e_indi,F: fun_Ar286530093t_bool,A: fun_Ar1809396326i_bool,B: fun_Ar1321653811l_bool] :
      ( hBOOL(hAPP_f686820739l_bool(hAPP_f692361165l_bool(member785631232t_bool,F),pi_Arr687740481t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_A1378093259t_bool(F,X_2)),hAPP_A2084592127l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A)) ) ) ).

tff(fact_198_PiE,axiom,
    ! [X_2: bool,F: fun_bo559790694t_bool,A: fun_bool_bool,B: fun_bo1445676730l_bool] :
      ( hBOOL(hAPP_f1211446716l_bool(hAPP_f1134773005l_bool(member1782492345t_bool,F),pi_boo769613946t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_b1029214724t_bool(F,X_2)),hAPP_b1777246598l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) ) ) ).

tff(fact_199_PiE,axiom,
    ! [X_2: product_unit,F: fun_Pr2016729180t_bool,A: fun_Pr1643180309t_bool,B: fun_Pr151242052l_bool] :
      ( hBOOL(hAPP_f2068478898l_bool(hAPP_f1883507597l_bool(member480326063t_bool,F),pi_Pro1533274736t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_P1858715130t_bool(F,X_2)),hAPP_P283873808l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) ) ) ).

tff(fact_200_PiE,axiom,
    ! [X_2: bool,F: fun_bo1431306493t_bool,A: fun_bool_bool,B: fun_bo377688929l_bool] :
      ( hBOOL(hAPP_f398210311l_bool(hAPP_f416878261l_bool(member1133581546t_bool,F),pi_boo1111177555t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_b128655177t_bool(F,X_2)),hAPP_b1272691967l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) ) ) ).

tff(fact_201_PiE,axiom,
    ! [X_2: product_unit,F: fun_Pr1887398791t_bool,A: fun_Pr1643180309t_bool,B: fun_Pr1791323223l_bool] :
      ( hBOOL(hAPP_f1426814865l_bool(hAPP_f1942212041l_bool(member803887220t_bool,F),pi_Pro1290680285t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_P1914371027t_bool(F,X_2)),hAPP_P754918389l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) ) ) ).

tff(fact_202_PiE,axiom,
    ! [X_2: arrow_856714788e_indi,F: fun_Ar671024215di_nat,A: fun_Ar1809396326i_bool,B: fun_Ar603939593t_bool] :
      ( hBOOL(hAPP_f225240161l_bool(hAPP_f677301097l_bool(member1502495556di_nat,F),pi_Arr1233262509di_nat(A,B)))
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A376526755di_nat(F,X_2)),hAPP_A1686943911t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A)) ) ) ).

tff(fact_203_PiE,axiom,
    ! [X_2: bool,F: fun_bool_nat,A: fun_bool_bool,B: fun_bo1570548802t_bool] :
      ( hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,F),pi_bool_nat(A,B)))
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(F,X_2)),hAPP_b1013836512t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) ) ) ).

tff(fact_204_PiE,axiom,
    ! [X_2: product_unit,F: fun_Product_unit_nat,A: fun_Pr1643180309t_bool,B: fun_Pr1029464120t_bool] :
      ( hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,F),pi_Product_unit_nat(A,B)))
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(F,X_2)),hAPP_P32877782t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) ) ) ).

tff(fact_205_PiE,axiom,
    ! [X_2: produc472769767le_alt,F: fun_Pr1509342064e_indi,A: fun_Pr2067565481t_bool,B: fun_Pr895221296i_bool] :
      ( hBOOL(hAPP_f2124588998l_bool(hAPP_f1187850253l_bool(member1558233923e_indi,F),pi_Pro837265796e_indi(A,B)))
     => ( ~ hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_P276596750e_indi(F,X_2)),hAPP_P1859429372i_bool(B,X_2)))
       => ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A)) ) ) ).

tff(fact_206_PiE,axiom,
    ! [X_2: produc472769767le_alt,F: fun_Pr376858015t_unit,A: fun_Pr2067565481t_bool,B: fun_Pr1069395679t_bool] :
      ( hBOOL(hAPP_f1159856629l_bool(hAPP_f1700632141l_bool(member1303779570t_unit,F),pi_Pro346842291t_unit(A,B)))
     => ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1069491261t_unit(F,X_2)),hAPP_P2037731755t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A)) ) ) ).

tff(fact_207_PiE,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu1929591039e_indi,A: fun_fu3835832l_bool,B: fun_fu223278561i_bool] :
      ( hBOOL(hAPP_f665932885l_bool(hAPP_f430646093l_bool(member282602450e_indi,F),pi_fun520512275e_indi(A,B)))
     => ( ~ hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_f602741661e_indi(F,X_2)),hAPP_f391644589i_bool(B,X_2)))
       => ~ hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A)) ) ) ).

tff(fact_208_PiE,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu3835832l_bool,A: fun_fu3835832l_bool,B: fun_fu916327706l_bool] :
      ( hBOOL(hAPP_f1867557646l_bool(hAPP_f1048573069l_bool(member1020280587l_bool,F),pi_fun853738700l_bool(A,B)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f995490902l_bool(F,X_2)),hAPP_f1676084198l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A)) ) ) ).

tff(fact_209_PiE,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu1023022254t_unit,A: fun_fu3835832l_bool,B: fun_fu1734317328t_bool] :
      ( hBOOL(hAPP_f115957764l_bool(hAPP_f1184790797l_bool(member2003579649t_unit,F),pi_fun1644711874t_unit(A,B)))
     => ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f1775626572t_unit(F,X_2)),hAPP_f1438163420t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A)) ) ) ).

tff(fact_210_PiE,axiom,
    ! [X_2: fun_fu2114379172t_bool,F: fun_fu748153389e_indi,A: fun_fu2098777574l_bool,B: fun_fu2109152051i_bool] :
      ( hBOOL(hAPP_f2350467l_bool(hAPP_f1411422157l_bool(member1247254528e_indi,F),pi_fun1807454273e_indi(A,B)))
     => ( ~ hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_f350323403e_indi(F,X_2)),hAPP_f399308031i_bool(B,X_2)))
       => ~ hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A)) ) ) ).

tff(fact_211_PiE,axiom,
    ! [X_2: fun_fu2114379172t_bool,F: fun_fu2098777574l_bool,A: fun_fu2098777574l_bool,B: fun_fu1522163052l_bool] :
      ( hBOOL(hAPP_f2047920444l_bool(hAPP_f59810573l_bool(member1173995577l_bool,F),pi_fun1312540410l_bool(A,B)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1572141188l_bool(F,X_2)),hAPP_f414129720l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A)) ) ) ).

tff(fact_212_PiE,axiom,
    ! [X_2: fun_fu2114379172t_bool,F: fun_fu1480298716t_unit,A: fun_fu2098777574l_bool,B: fun_fu1143287650t_bool] :
      ( hBOOL(hAPP_f92582962l_bool(hAPP_f1494690701l_bool(member2091379247t_unit,F),pi_fun1540376560t_unit(A,B)))
     => ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f1865816954t_unit(F,X_2)),hAPP_f151782958t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A)) ) ) ).

tff(fact_213_PiE,axiom,
    ! [X_2: fun_Pr2067565481t_bool,F: fun_fu562005862e_indi,A: fun_fu638310559l_bool,B: fun_fu2142850746i_bool] :
      ( hBOOL(hAPP_f679138160l_bool(hAPP_f1006969351l_bool(member1220706259e_indi,F),pi_fun1470523330e_indi(A,B)))
     => ( ~ hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_f9587896e_indi(F,X_2)),hAPP_f2010315474i_bool(B,X_2)))
       => ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A)) ) ) ).

tff(fact_214_PiE,axiom,
    ! [X_2: fun_Pr2067565481t_bool,F: fun_fu638310559l_bool,A: fun_fu638310559l_bool,B: fun_fu237781875l_bool] :
      ( hBOOL(hAPP_f1686510249l_bool(hAPP_f1930590713l_bool(member340585612l_bool,F),pi_fun1035089915l_bool(A,B)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f52567537l_bool(F,X_2)),hAPP_f463104139l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A)) ) ) ).

tff(fact_215_PiE,axiom,
    ! [X_2: fun_Pr2067565481t_bool,F: fun_fu665686165t_unit,A: fun_fu638310559l_bool,B: fun_fu643686505t_bool] :
      ( hBOOL(hAPP_f1478188703l_bool(hAPP_f1329172965l_bool(member1729658242t_unit,F),pi_fun177985009t_unit(A,B)))
     => ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f801675751t_unit(F,X_2)),hAPP_f1400551297t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A)) ) ) ).

tff(fact_216_PiE,axiom,
    ! [X_2: nat,F: fun_na699243463e_indi,A: fun_nat_bool,B: fun_na2037635353i_bool] :
      ( hBOOL(hAPP_f736267217l_bool(hAPP_f707406409l_bool(member1530714804e_indi,F),pi_nat646417955e_indi(A,B)))
     => ( ~ hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_n1937165849e_indi(F,X_2)),hAPP_n34002993i_bool(B,X_2)))
       => ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) ) ) ).

tff(fact_217_PiE,axiom,
    ! [X_2: nat,F: fun_nat_bool,A: fun_nat_bool,B: fun_na1469252690l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,F),pi_nat_bool(A,B)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(F,X_2)),hAPP_n1006566506l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) ) ) ).

tff(fact_218_PiE,axiom,
    ! [X_2: nat,F: fun_nat_Product_unit,A: fun_nat_bool,B: fun_na1041622088t_bool] :
      ( hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,F),pi_nat_Product_unit(A,B)))
     => ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(F,X_2)),hAPP_n454528608t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) ) ) ).

tff(fact_219_PiE,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu2114379172t_bool,A: fun_fu3835832l_bool,B: fun_fu1863781882l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,F),pi_fun1746584570t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_f2008608496t_bool(F,X_2)),hAPP_f1915815064l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A)) ) ) ).

tff(fact_220_PiE,axiom,
    ! [X_2: arrow_856714788e_indi,F: fun_Ar274636406t_bool,A: fun_Ar1809396326i_bool,B: fun_Ar1474557608l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,F),pi_Arr959578316t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_A1646126530t_bool(F,X_2)),hAPP_A897398598l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A)) ) ) ).

tff(fact_221_complete__Lin,axiom,
    ! [Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt] :
      ( ( Aa != Ba )
     => ? [X_1: fun_Pr2067565481t_bool] :
          ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_1),arrow_1361987423le_Lin))
          & hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Aa),Ba)),X_1)) ) ) ).

tff(fact_222_Pi__UNIV,axiom,
    ! [A: fun_Pr2067565481t_bool] : ( pi_Pro1238944957t_bool(A,hAPP_f699791347l_bool(cOMBK_138598520le_alt,top_to1647826457l_bool)) = top_to1312956197l_bool ) ).

tff(fact_223_Pi__UNIV,axiom,
    ! [A: fun_fu3835832l_bool] : ( pi_fun1746584570t_bool(A,hAPP_f1104294872l_bool(cOMBK_1701906001t_bool,top_to1312956197l_bool)) = top_to827110112l_bool ) ).

tff(fact_224_Pi__UNIV,axiom,
    ! [A: fun_Ar1809396326i_bool] : ( pi_Arr959578316t_bool(A,hAPP_f1717907078l_bool(cOMBK_1520063231e_indi,top_to1312956197l_bool)) = top_to553140914l_bool ) ).

tff(fact_225_in__below,axiom,
    ! [X_2: arrow_1893660431le_alt,Y_2: arrow_1893660431le_alt,L_3: fun_Pr2067565481t_bool,Aa: arrow_1893660431le_alt,Ba: arrow_1893660431le_alt] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,L_3),arrow_1361987423le_Lin))
       => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Y_2)),arrow_1525312447_below(L_3,Aa,Ba)))
        <=> ( ( X_2 != Y_2 )
            & ( ( Y_2 = Aa )
             => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Ba)),L_3)) )
            & ( ( Y_2 != Aa )
             => ( ( ( X_2 = Aa )
                 => ( ( Y_2 = Ba )
                    | hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,Ba),Y_2)),L_3)) ) )
                & ( ( X_2 != Aa )
                 => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,X_2),Y_2)),L_3)) ) ) ) ) ) ) ) ).

tff(fact_226_order__refl,axiom,
    ! [X_2: fun_fu638310559l_bool] : hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,X_2),X_2)) ).

tff(fact_227_order__refl,axiom,
    ! [X_2: fun_fu2098777574l_bool] : hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,X_2),X_2)) ).

tff(fact_228_order__refl,axiom,
    ! [X_2: fun_fu3835832l_bool] : hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,X_2),X_2)) ).

tff(fact_229_order__refl,axiom,
    ! [X_2: fun_Pr2067565481t_bool] : hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,X_2),X_2)) ).

tff(fact_230_order__refl,axiom,
    ! [X_2: bool] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),X_2)) ).

tff(fact_231_order__refl,axiom,
    ! [X_2: fun_Ar1809396326i_bool] : hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,X_2),X_2)) ).

tff(fact_232_order__refl,axiom,
    ! [X_2: fun_Pr1643180309t_bool] : hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),X_2)) ).

tff(fact_233_order__refl,axiom,
    ! [X_2: fun_Ar331856045t_bool] : hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,X_2),X_2)) ).

tff(fact_234_order__refl,axiom,
    ! [X_20: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_20),X_20)) ).

tff(fact_235_order__refl,axiom,
    ! [X_2: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),X_2)) ).

tff(fact_236__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I,axiom,
    ? [N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_f846027769ol_nat(finite1672073426e_indi,top_to788185952i_bool)))
      & ! [M: nat] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1))
         => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,b),a)),hAPP_f2008608496t_bool(f,hAPP_f480276746t_bool(hAPP_f601594885t_bool(cOMBC_750853729t_bool,hAPP_f1344464862t_bool(hAPP_f1908974253t_bool(cOMBC_156709173t_bool,hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(ord_less_nat),h)),M))),lab)),lba)))) )
      & hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,a),b)),hAPP_f2008608496t_bool(f,hAPP_f480276746t_bool(hAPP_f601594885t_bool(cOMBC_750853729t_bool,hAPP_f1344464862t_bool(hAPP_f1908974253t_bool(cOMBC_156709173t_bool,hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),one_one_nat)))),lab)),lba)))) ) ).

tff(fact_237__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_,axiom,
    ~ ! [N_1: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_f846027769ol_nat(finite1672073426e_indi,top_to788185952i_bool)))
       => ( ! [M: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N_1))
             => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,b),a)),hAPP_f2008608496t_bool(f,hAPP_f480276746t_bool(hAPP_f601594885t_bool(cOMBC_750853729t_bool,hAPP_f1344464862t_bool(hAPP_f1908974253t_bool(cOMBC_156709173t_bool,hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(ord_less_nat),h)),M))),lab)),lba)))) )
         => ~ hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,a),b)),hAPP_f2008608496t_bool(f,hAPP_f480276746t_bool(hAPP_f601594885t_bool(cOMBC_750853729t_bool,hAPP_f1344464862t_bool(hAPP_f1908974253t_bool(cOMBC_156709173t_bool,hAPP_f668886383t_bool(cOMBB_1061985500e_indi(if_fun523439385t_bool),hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,hAPP_f966656047t_bool(cOMBB_1869811296e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),one_one_nat)))),lab)),lba)))) ) ) ).

tff(fact_238_linorder__le__cases,axiom,
    ! [X_19: nat,Y_19: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_19),Y_19))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_19),X_19)) ) ).

tff(fact_239_le__funE,axiom,
    ! [X_2: fun_Pr2067565481t_bool,F: fun_fu638310559l_bool,G: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f52567537l_bool(F,X_2)),hAPP_f52567537l_bool(G,X_2))) ) ).

tff(fact_240_le__funE,axiom,
    ! [X_2: fun_fu2114379172t_bool,F: fun_fu2098777574l_bool,G: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f1572141188l_bool(F,X_2)),hAPP_f1572141188l_bool(G,X_2))) ) ).

tff(fact_241_le__funE,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu3835832l_bool,G: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f995490902l_bool(F,X_2)),hAPP_f995490902l_bool(G,X_2))) ) ).

tff(fact_242_le__funE,axiom,
    ! [X_2: produc472769767le_alt,F: fun_Pr2067565481t_bool,G: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1178790471t_bool(F,X_2)),hAPP_P1178790471t_bool(G,X_2))) ) ).

tff(fact_243_le__funE,axiom,
    ! [X_2: arrow_856714788e_indi,F: fun_Ar1809396326i_bool,G: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A997847300i_bool(F,X_2)),hAPP_A997847300i_bool(G,X_2))) ) ).

tff(fact_244_le__funE,axiom,
    ! [X_2: product_unit,F: fun_Pr1643180309t_bool,G: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(F,X_2)),hAPP_P1676879539t_bool(G,X_2))) ) ).

tff(fact_245_le__funE,axiom,
    ! [X_2: arrow_1893660431le_alt,F: fun_Ar331856045t_bool,G: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,F),G))
     => hBOOL(hAPP_f739344229l_bool(hAPP_f1549168575l_bool(ord_le1779845435t_bool,hAPP_A2063800319t_bool(F,X_2)),hAPP_A2063800319t_bool(G,X_2))) ) ).

tff(fact_246_le__funE,axiom,
    ! [X_2: nat,F: fun_nat_bool,G: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_2)),hAPP_nat_bool(G,X_2))) ) ).

tff(fact_247_xt1_I6_J,axiom,
    ! [Z_2: fun_fu638310559l_bool,Y_2: fun_fu638310559l_bool,X_2: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Z_2),Y_2))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Z_2),X_2)) ) ) ).

tff(fact_248_xt1_I6_J,axiom,
    ! [Z_2: fun_fu2098777574l_bool,Y_2: fun_fu2098777574l_bool,X_2: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Z_2),Y_2))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Z_2),X_2)) ) ) ).

tff(fact_249_xt1_I6_J,axiom,
    ! [Z_2: fun_fu3835832l_bool,Y_2: fun_fu3835832l_bool,X_2: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Z_2),Y_2))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Z_2),X_2)) ) ) ).

tff(fact_250_xt1_I6_J,axiom,
    ! [Z_2: fun_Pr2067565481t_bool,Y_2: fun_Pr2067565481t_bool,X_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Z_2),Y_2))
       => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Z_2),X_2)) ) ) ).

tff(fact_251_xt1_I6_J,axiom,
    ! [Z_2: bool,Y_2: bool,X_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z_2),Y_2))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z_2),X_2)) ) ) ).

tff(fact_252_xt1_I6_J,axiom,
    ! [Z_2: fun_Ar1809396326i_bool,Y_2: fun_Ar1809396326i_bool,X_2: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Z_2),Y_2))
       => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Z_2),X_2)) ) ) ).

tff(fact_253_xt1_I6_J,axiom,
    ! [Z_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool,X_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Z_2),Y_2))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Z_2),X_2)) ) ) ).

tff(fact_254_xt1_I6_J,axiom,
    ! [Z_2: fun_Ar331856045t_bool,Y_2: fun_Ar331856045t_bool,X_2: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Z_2),Y_2))
       => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Z_2),X_2)) ) ) ).

tff(fact_255_xt1_I6_J,axiom,
    ! [Z_7: nat,Y_18: nat,X_18: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_18),X_18))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_7),Y_18))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_7),X_18)) ) ) ).

tff(fact_256_xt1_I6_J,axiom,
    ! [Z_2: fun_nat_bool,Y_2: fun_nat_bool,X_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_2),Y_2))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_2),X_2)) ) ) ).

tff(fact_257_xt1_I5_J,axiom,
    ! [Y_2: fun_fu638310559l_bool,X_2: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,X_2),Y_2))
       => ( X_2 = Y_2 ) ) ) ).

tff(fact_258_xt1_I5_J,axiom,
    ! [Y_2: fun_fu2098777574l_bool,X_2: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,X_2),Y_2))
       => ( X_2 = Y_2 ) ) ) ).

tff(fact_259_xt1_I5_J,axiom,
    ! [Y_2: fun_fu3835832l_bool,X_2: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,X_2),Y_2))
       => ( X_2 = Y_2 ) ) ) ).

tff(fact_260_xt1_I5_J,axiom,
    ! [Y_2: fun_Pr2067565481t_bool,X_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,X_2),Y_2))
       => ( X_2 = Y_2 ) ) ) ).

tff(fact_261_xt1_I5_J,axiom,
    ! [Y_2: bool,X_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
       => ( hBOOL(X_2)
        <=> hBOOL(Y_2) ) ) ) ).

tff(fact_262_xt1_I5_J,axiom,
    ! [Y_2: fun_Ar1809396326i_bool,X_2: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,X_2),Y_2))
       => ( X_2 = Y_2 ) ) ) ).

tff(fact_263_xt1_I5_J,axiom,
    ! [Y_2: fun_Pr1643180309t_bool,X_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
       => ( X_2 = Y_2 ) ) ) ).

tff(fact_264_xt1_I5_J,axiom,
    ! [Y_2: fun_Ar331856045t_bool,X_2: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,X_2),Y_2))
       => ( X_2 = Y_2 ) ) ) ).

tff(fact_265_xt1_I5_J,axiom,
    ! [Y_17: nat,X_17: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_17),X_17))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_17),Y_17))
       => ( X_17 = Y_17 ) ) ) ).

tff(fact_266_xt1_I5_J,axiom,
    ! [Y_2: fun_nat_bool,X_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
       => ( X_2 = Y_2 ) ) ) ).

tff(fact_267_order__trans,axiom,
    ! [Z_2: fun_fu638310559l_bool,X_2: fun_fu638310559l_bool,Y_2: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Y_2),Z_2))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,X_2),Z_2)) ) ) ).

tff(fact_268_order__trans,axiom,
    ! [Z_2: fun_fu2098777574l_bool,X_2: fun_fu2098777574l_bool,Y_2: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Y_2),Z_2))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,X_2),Z_2)) ) ) ).

tff(fact_269_order__trans,axiom,
    ! [Z_2: fun_fu3835832l_bool,X_2: fun_fu3835832l_bool,Y_2: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Y_2),Z_2))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,X_2),Z_2)) ) ) ).

tff(fact_270_order__trans,axiom,
    ! [Z_2: fun_Pr2067565481t_bool,X_2: fun_Pr2067565481t_bool,Y_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Y_2),Z_2))
       => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,X_2),Z_2)) ) ) ).

tff(fact_271_order__trans,axiom,
    ! [Z_2: bool,X_2: bool,Y_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),Z_2))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Z_2)) ) ) ).

tff(fact_272_order__trans,axiom,
    ! [Z_2: fun_Ar1809396326i_bool,X_2: fun_Ar1809396326i_bool,Y_2: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Y_2),Z_2))
       => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,X_2),Z_2)) ) ) ).

tff(fact_273_order__trans,axiom,
    ! [Z_2: fun_Pr1643180309t_bool,X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),Z_2))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Z_2)) ) ) ).

tff(fact_274_order__trans,axiom,
    ! [Z_2: fun_Ar331856045t_bool,X_2: fun_Ar331856045t_bool,Y_2: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Y_2),Z_2))
       => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,X_2),Z_2)) ) ) ).

tff(fact_275_order__trans,axiom,
    ! [Z_6: nat,X_16: nat,Y_16: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_16),Y_16))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_16),Z_6))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_16),Z_6)) ) ) ).

tff(fact_276_order__trans,axiom,
    ! [Z_2: fun_nat_bool,X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),Z_2))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Z_2)) ) ) ).

tff(fact_277_order__antisym,axiom,
    ! [X_2: fun_fu638310559l_bool,Y_2: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Y_2),X_2))
       => ( X_2 = Y_2 ) ) ) ).

tff(fact_278_order__antisym,axiom,
    ! [X_2: fun_fu2098777574l_bool,Y_2: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Y_2),X_2))
       => ( X_2 = Y_2 ) ) ) ).

tff(fact_279_order__antisym,axiom,
    ! [X_2: fun_fu3835832l_bool,Y_2: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Y_2),X_2))
       => ( X_2 = Y_2 ) ) ) ).

tff(fact_280_order__antisym,axiom,
    ! [X_2: fun_Pr2067565481t_bool,Y_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Y_2),X_2))
       => ( X_2 = Y_2 ) ) ) ).

tff(fact_281_order__antisym,axiom,
    ! [X_2: bool,Y_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
       => ( hBOOL(X_2)
        <=> hBOOL(Y_2) ) ) ) ).

tff(fact_282_order__antisym,axiom,
    ! [X_2: fun_Ar1809396326i_bool,Y_2: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Y_2),X_2))
       => ( X_2 = Y_2 ) ) ) ).

tff(fact_283_order__antisym,axiom,
    ! [X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),X_2))
       => ( X_2 = Y_2 ) ) ) ).

tff(fact_284_order__antisym,axiom,
    ! [X_2: fun_Ar331856045t_bool,Y_2: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Y_2),X_2))
       => ( X_2 = Y_2 ) ) ) ).

tff(fact_285_order__antisym,axiom,
    ! [X_15: nat,Y_15: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_15),Y_15))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_15),X_15))
       => ( X_15 = Y_15 ) ) ) ).

tff(fact_286_order__antisym,axiom,
    ! [X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2))
       => ( X_2 = Y_2 ) ) ) ).

tff(fact_287_xt1_I4_J,axiom,
    ! [Ca: fun_fu638310559l_bool,Ba: fun_fu638310559l_bool,Aa: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Ba),Aa))
     => ( ( Ba = Ca )
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Ca),Aa)) ) ) ).

tff(fact_288_xt1_I4_J,axiom,
    ! [Ca: fun_fu2098777574l_bool,Ba: fun_fu2098777574l_bool,Aa: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Ba),Aa))
     => ( ( Ba = Ca )
       => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Ca),Aa)) ) ) ).

tff(fact_289_xt1_I4_J,axiom,
    ! [Ca: fun_fu3835832l_bool,Ba: fun_fu3835832l_bool,Aa: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Ba),Aa))
     => ( ( Ba = Ca )
       => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Ca),Aa)) ) ) ).

tff(fact_290_xt1_I4_J,axiom,
    ! [Ca: fun_Pr2067565481t_bool,Ba: fun_Pr2067565481t_bool,Aa: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Ba),Aa))
     => ( ( Ba = Ca )
       => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Ca),Aa)) ) ) ).

tff(fact_291_xt1_I4_J,axiom,
    ! [Ca: bool,Ba: bool,Aa: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Aa))
     => ( ( hBOOL(Ba)
        <=> hBOOL(Ca) )
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),Aa)) ) ) ).

tff(fact_292_xt1_I4_J,axiom,
    ! [Ca: fun_Ar1809396326i_bool,Ba: fun_Ar1809396326i_bool,Aa: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Ba),Aa))
     => ( ( Ba = Ca )
       => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Ca),Aa)) ) ) ).

tff(fact_293_xt1_I4_J,axiom,
    ! [Ca: fun_Pr1643180309t_bool,Ba: fun_Pr1643180309t_bool,Aa: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Aa))
     => ( ( Ba = Ca )
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ca),Aa)) ) ) ).

tff(fact_294_xt1_I4_J,axiom,
    ! [Ca: fun_Ar331856045t_bool,Ba: fun_Ar331856045t_bool,Aa: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Ba),Aa))
     => ( ( Ba = Ca )
       => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Ca),Aa)) ) ) ).

tff(fact_295_xt1_I4_J,axiom,
    ! [C_20: nat,B_24: nat,A_26: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_24),A_26))
     => ( ( B_24 = C_20 )
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_20),A_26)) ) ) ).

tff(fact_296_xt1_I4_J,axiom,
    ! [Ca: fun_nat_bool,Ba: fun_nat_bool,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
     => ( ( Ba = Ca )
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Aa)) ) ) ).

tff(fact_297_ord__le__eq__trans,axiom,
    ! [Ca: fun_fu638310559l_bool,Aa: fun_fu638310559l_bool,Ba: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Aa),Ba))
     => ( ( Ba = Ca )
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Aa),Ca)) ) ) ).

tff(fact_298_ord__le__eq__trans,axiom,
    ! [Ca: fun_fu2098777574l_bool,Aa: fun_fu2098777574l_bool,Ba: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Aa),Ba))
     => ( ( Ba = Ca )
       => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Aa),Ca)) ) ) ).

tff(fact_299_ord__le__eq__trans,axiom,
    ! [Ca: fun_fu3835832l_bool,Aa: fun_fu3835832l_bool,Ba: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Aa),Ba))
     => ( ( Ba = Ca )
       => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Aa),Ca)) ) ) ).

tff(fact_300_ord__le__eq__trans,axiom,
    ! [Ca: fun_Pr2067565481t_bool,Aa: fun_Pr2067565481t_bool,Ba: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Aa),Ba))
     => ( ( Ba = Ca )
       => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Aa),Ca)) ) ) ).

tff(fact_301_ord__le__eq__trans,axiom,
    ! [Ca: bool,Aa: bool,Ba: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ba))
     => ( ( hBOOL(Ba)
        <=> hBOOL(Ca) )
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ca)) ) ) ).

tff(fact_302_ord__le__eq__trans,axiom,
    ! [Ca: fun_Ar1809396326i_bool,Aa: fun_Ar1809396326i_bool,Ba: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Aa),Ba))
     => ( ( Ba = Ca )
       => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Aa),Ca)) ) ) ).

tff(fact_303_ord__le__eq__trans,axiom,
    ! [Ca: fun_Pr1643180309t_bool,Aa: fun_Pr1643180309t_bool,Ba: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ba))
     => ( ( Ba = Ca )
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ca)) ) ) ).

tff(fact_304_ord__le__eq__trans,axiom,
    ! [Ca: fun_Ar331856045t_bool,Aa: fun_Ar331856045t_bool,Ba: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Aa),Ba))
     => ( ( Ba = Ca )
       => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Aa),Ca)) ) ) ).

tff(fact_305_ord__le__eq__trans,axiom,
    ! [C_19: nat,A_25: nat,B_23: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_25),B_23))
     => ( ( B_23 = C_19 )
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_25),C_19)) ) ) ).

tff(fact_306_ord__le__eq__trans,axiom,
    ! [Ca: fun_nat_bool,Aa: fun_nat_bool,Ba: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
     => ( ( Ba = Ca )
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ca)) ) ) ).

tff(fact_307_xt1_I3_J,axiom,
    ! [Ca: fun_fu638310559l_bool,Aa: fun_fu638310559l_bool,Ba: fun_fu638310559l_bool] :
      ( ( Aa = Ba )
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Ca),Ba))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Ca),Aa)) ) ) ).

tff(fact_308_xt1_I3_J,axiom,
    ! [Ca: fun_fu2098777574l_bool,Aa: fun_fu2098777574l_bool,Ba: fun_fu2098777574l_bool] :
      ( ( Aa = Ba )
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Ca),Ba))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Ca),Aa)) ) ) ).

tff(fact_309_xt1_I3_J,axiom,
    ! [Ca: fun_fu3835832l_bool,Aa: fun_fu3835832l_bool,Ba: fun_fu3835832l_bool] :
      ( ( Aa = Ba )
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Ca),Ba))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Ca),Aa)) ) ) ).

tff(fact_310_xt1_I3_J,axiom,
    ! [Ca: fun_Pr2067565481t_bool,Aa: fun_Pr2067565481t_bool,Ba: fun_Pr2067565481t_bool] :
      ( ( Aa = Ba )
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Ca),Ba))
       => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Ca),Aa)) ) ) ).

tff(fact_311_xt1_I3_J,axiom,
    ! [Ca: bool,Ba: bool,Aa: bool] :
      ( ( hBOOL(Aa)
      <=> hBOOL(Ba) )
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),Ba))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),Aa)) ) ) ).

tff(fact_312_xt1_I3_J,axiom,
    ! [Ca: fun_Ar1809396326i_bool,Aa: fun_Ar1809396326i_bool,Ba: fun_Ar1809396326i_bool] :
      ( ( Aa = Ba )
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Ca),Ba))
       => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Ca),Aa)) ) ) ).

tff(fact_313_xt1_I3_J,axiom,
    ! [Ca: fun_Pr1643180309t_bool,Aa: fun_Pr1643180309t_bool,Ba: fun_Pr1643180309t_bool] :
      ( ( Aa = Ba )
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ca),Ba))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ca),Aa)) ) ) ).

tff(fact_314_xt1_I3_J,axiom,
    ! [Ca: fun_Ar331856045t_bool,Aa: fun_Ar331856045t_bool,Ba: fun_Ar331856045t_bool] :
      ( ( Aa = Ba )
     => ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Ca),Ba))
       => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Ca),Aa)) ) ) ).

tff(fact_315_xt1_I3_J,axiom,
    ! [C_18: nat,A_24: nat,B_22: nat] :
      ( ( A_24 = B_22 )
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_18),B_22))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_18),A_24)) ) ) ).

tff(fact_316_xt1_I3_J,axiom,
    ! [Ca: fun_nat_bool,Aa: fun_nat_bool,Ba: fun_nat_bool] :
      ( ( Aa = Ba )
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Aa)) ) ) ).

tff(fact_317_ord__eq__le__trans,axiom,
    ! [Ca: fun_fu638310559l_bool,Aa: fun_fu638310559l_bool,Ba: fun_fu638310559l_bool] :
      ( ( Aa = Ba )
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Ba),Ca))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Aa),Ca)) ) ) ).

tff(fact_318_ord__eq__le__trans,axiom,
    ! [Ca: fun_fu2098777574l_bool,Aa: fun_fu2098777574l_bool,Ba: fun_fu2098777574l_bool] :
      ( ( Aa = Ba )
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Ba),Ca))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Aa),Ca)) ) ) ).

tff(fact_319_ord__eq__le__trans,axiom,
    ! [Ca: fun_fu3835832l_bool,Aa: fun_fu3835832l_bool,Ba: fun_fu3835832l_bool] :
      ( ( Aa = Ba )
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Ba),Ca))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Aa),Ca)) ) ) ).

tff(fact_320_ord__eq__le__trans,axiom,
    ! [Ca: fun_Pr2067565481t_bool,Aa: fun_Pr2067565481t_bool,Ba: fun_Pr2067565481t_bool] :
      ( ( Aa = Ba )
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Ba),Ca))
       => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Aa),Ca)) ) ) ).

tff(fact_321_ord__eq__le__trans,axiom,
    ! [Ca: bool,Ba: bool,Aa: bool] :
      ( ( hBOOL(Aa)
      <=> hBOOL(Ba) )
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Ca))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ca)) ) ) ).

tff(fact_322_ord__eq__le__trans,axiom,
    ! [Ca: fun_Ar1809396326i_bool,Aa: fun_Ar1809396326i_bool,Ba: fun_Ar1809396326i_bool] :
      ( ( Aa = Ba )
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Ba),Ca))
       => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Aa),Ca)) ) ) ).

tff(fact_323_ord__eq__le__trans,axiom,
    ! [Ca: fun_Pr1643180309t_bool,Aa: fun_Pr1643180309t_bool,Ba: fun_Pr1643180309t_bool] :
      ( ( Aa = Ba )
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Ca))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ca)) ) ) ).

tff(fact_324_ord__eq__le__trans,axiom,
    ! [Ca: fun_Ar331856045t_bool,Aa: fun_Ar331856045t_bool,Ba: fun_Ar331856045t_bool] :
      ( ( Aa = Ba )
     => ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Ba),Ca))
       => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Aa),Ca)) ) ) ).

tff(fact_325_ord__eq__le__trans,axiom,
    ! [C_17: nat,A_23: nat,B_21: nat] :
      ( ( A_23 = B_21 )
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_21),C_17))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_23),C_17)) ) ) ).

tff(fact_326_ord__eq__le__trans,axiom,
    ! [Ca: fun_nat_bool,Aa: fun_nat_bool,Ba: fun_nat_bool] :
      ( ( Aa = Ba )
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ca)) ) ) ).

tff(fact_327_order__antisym__conv,axiom,
    ! [Y_2: fun_fu638310559l_bool,X_2: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,X_2),Y_2))
      <=> ( X_2 = Y_2 ) ) ) ).

tff(fact_328_order__antisym__conv,axiom,
    ! [Y_2: fun_fu2098777574l_bool,X_2: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,X_2),Y_2))
      <=> ( X_2 = Y_2 ) ) ) ).

tff(fact_329_order__antisym__conv,axiom,
    ! [Y_2: fun_fu3835832l_bool,X_2: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,X_2),Y_2))
      <=> ( X_2 = Y_2 ) ) ) ).

tff(fact_330_order__antisym__conv,axiom,
    ! [Y_2: fun_Pr2067565481t_bool,X_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,X_2),Y_2))
      <=> ( X_2 = Y_2 ) ) ) ).

tff(fact_331_order__antisym__conv,axiom,
    ! [Y_2: bool,X_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
      <=> ( hBOOL(X_2)
        <=> hBOOL(Y_2) ) ) ) ).

tff(fact_332_order__antisym__conv,axiom,
    ! [Y_2: fun_Ar1809396326i_bool,X_2: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,X_2),Y_2))
      <=> ( X_2 = Y_2 ) ) ) ).

tff(fact_333_order__antisym__conv,axiom,
    ! [Y_2: fun_Pr1643180309t_bool,X_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
      <=> ( X_2 = Y_2 ) ) ) ).

tff(fact_334_order__antisym__conv,axiom,
    ! [Y_2: fun_Ar331856045t_bool,X_2: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,X_2),Y_2))
      <=> ( X_2 = Y_2 ) ) ) ).

tff(fact_335_order__antisym__conv,axiom,
    ! [Y_2: nat,X_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
      <=> ( X_2 = Y_2 ) ) ) ).

tff(fact_336_order__antisym__conv,axiom,
    ! [Y_2: fun_nat_bool,X_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
      <=> ( X_2 = Y_2 ) ) ) ).

tff(fact_337_le__funD,axiom,
    ! [X_2: fun_Pr2067565481t_bool,F: fun_fu638310559l_bool,G: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f52567537l_bool(F,X_2)),hAPP_f52567537l_bool(G,X_2))) ) ).

tff(fact_338_le__funD,axiom,
    ! [X_2: fun_fu2114379172t_bool,F: fun_fu2098777574l_bool,G: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f1572141188l_bool(F,X_2)),hAPP_f1572141188l_bool(G,X_2))) ) ).

tff(fact_339_le__funD,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu3835832l_bool,G: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f995490902l_bool(F,X_2)),hAPP_f995490902l_bool(G,X_2))) ) ).

tff(fact_340_le__funD,axiom,
    ! [X_2: produc472769767le_alt,F: fun_Pr2067565481t_bool,G: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1178790471t_bool(F,X_2)),hAPP_P1178790471t_bool(G,X_2))) ) ).

tff(fact_341_le__funD,axiom,
    ! [X_2: arrow_856714788e_indi,F: fun_Ar1809396326i_bool,G: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A997847300i_bool(F,X_2)),hAPP_A997847300i_bool(G,X_2))) ) ).

tff(fact_342_le__funD,axiom,
    ! [X_2: product_unit,F: fun_Pr1643180309t_bool,G: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(F,X_2)),hAPP_P1676879539t_bool(G,X_2))) ) ).

tff(fact_343_le__funD,axiom,
    ! [X_2: arrow_1893660431le_alt,F: fun_Ar331856045t_bool,G: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,F),G))
     => hBOOL(hAPP_f739344229l_bool(hAPP_f1549168575l_bool(ord_le1779845435t_bool,hAPP_A2063800319t_bool(F,X_2)),hAPP_A2063800319t_bool(G,X_2))) ) ).

tff(fact_344_le__funD,axiom,
    ! [X_2: nat,F: fun_nat_bool,G: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_2)),hAPP_nat_bool(G,X_2))) ) ).

tff(fact_345_order__eq__refl,axiom,
    ! [X_2: fun_fu638310559l_bool,Y_2: fun_fu638310559l_bool] :
      ( ( X_2 = Y_2 )
     => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,X_2),Y_2)) ) ).

tff(fact_346_order__eq__refl,axiom,
    ! [X_2: fun_fu2098777574l_bool,Y_2: fun_fu2098777574l_bool] :
      ( ( X_2 = Y_2 )
     => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,X_2),Y_2)) ) ).

tff(fact_347_order__eq__refl,axiom,
    ! [X_2: fun_fu3835832l_bool,Y_2: fun_fu3835832l_bool] :
      ( ( X_2 = Y_2 )
     => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,X_2),Y_2)) ) ).

tff(fact_348_order__eq__refl,axiom,
    ! [X_2: fun_Pr2067565481t_bool,Y_2: fun_Pr2067565481t_bool] :
      ( ( X_2 = Y_2 )
     => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,X_2),Y_2)) ) ).

tff(fact_349_order__eq__refl,axiom,
    ! [Y_2: bool,X_2: bool] :
      ( ( hBOOL(X_2)
      <=> hBOOL(Y_2) )
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) ) ).

tff(fact_350_order__eq__refl,axiom,
    ! [X_2: fun_Ar1809396326i_bool,Y_2: fun_Ar1809396326i_bool] :
      ( ( X_2 = Y_2 )
     => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,X_2),Y_2)) ) ).

tff(fact_351_order__eq__refl,axiom,
    ! [X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( ( X_2 = Y_2 )
     => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2)) ) ).

tff(fact_352_order__eq__refl,axiom,
    ! [X_2: fun_Ar331856045t_bool,Y_2: fun_Ar331856045t_bool] :
      ( ( X_2 = Y_2 )
     => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,X_2),Y_2)) ) ).

tff(fact_353_order__eq__refl,axiom,
    ! [X_14: nat,Y_14: nat] :
      ( ( X_14 = Y_14 )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_14),Y_14)) ) ).

tff(fact_354_order__eq__refl,axiom,
    ! [X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( ( X_2 = Y_2 )
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) ) ).

tff(fact_355_order__eq__iff,axiom,
    ! [X_2: fun_fu638310559l_bool,Y_2: fun_fu638310559l_bool] :
      ( ( X_2 = Y_2 )
    <=> ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,X_2),Y_2))
        & hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Y_2),X_2)) ) ) ).

tff(fact_356_order__eq__iff,axiom,
    ! [X_2: fun_fu2098777574l_bool,Y_2: fun_fu2098777574l_bool] :
      ( ( X_2 = Y_2 )
    <=> ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,X_2),Y_2))
        & hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Y_2),X_2)) ) ) ).

tff(fact_357_order__eq__iff,axiom,
    ! [X_2: fun_fu3835832l_bool,Y_2: fun_fu3835832l_bool] :
      ( ( X_2 = Y_2 )
    <=> ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,X_2),Y_2))
        & hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Y_2),X_2)) ) ) ).

tff(fact_358_order__eq__iff,axiom,
    ! [X_2: fun_Pr2067565481t_bool,Y_2: fun_Pr2067565481t_bool] :
      ( ( X_2 = Y_2 )
    <=> ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,X_2),Y_2))
        & hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Y_2),X_2)) ) ) ).

tff(fact_359_order__eq__iff,axiom,
    ! [Y_2: bool,X_2: bool] :
      ( ( hBOOL(X_2)
      <=> hBOOL(Y_2) )
    <=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
        & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2)) ) ) ).

tff(fact_360_order__eq__iff,axiom,
    ! [X_2: fun_Ar1809396326i_bool,Y_2: fun_Ar1809396326i_bool] :
      ( ( X_2 = Y_2 )
    <=> ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,X_2),Y_2))
        & hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Y_2),X_2)) ) ) ).

tff(fact_361_order__eq__iff,axiom,
    ! [X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( ( X_2 = Y_2 )
    <=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
        & hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),X_2)) ) ) ).

tff(fact_362_order__eq__iff,axiom,
    ! [X_2: fun_Ar331856045t_bool,Y_2: fun_Ar331856045t_bool] :
      ( ( X_2 = Y_2 )
    <=> ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,X_2),Y_2))
        & hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Y_2),X_2)) ) ) ).

tff(fact_363_order__eq__iff,axiom,
    ! [X_2: nat,Y_2: nat] :
      ( ( X_2 = Y_2 )
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_2)) ) ) ).

tff(fact_364_order__eq__iff,axiom,
    ! [X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( ( X_2 = Y_2 )
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2)) ) ) ).

tff(fact_365_linorder__linear,axiom,
    ! [X_13: nat,Y_13: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_13),Y_13))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_13),X_13)) ) ).

tff(fact_366_le__fun__def,axiom,
    ! [F: fun_fu638310559l_bool,G: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,F),G))
    <=> ! [X_1: fun_Pr2067565481t_bool] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f52567537l_bool(F,X_1)),hAPP_f52567537l_bool(G,X_1))) ) ).

tff(fact_367_le__fun__def,axiom,
    ! [F: fun_fu2098777574l_bool,G: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,F),G))
    <=> ! [X_1: fun_fu2114379172t_bool] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f1572141188l_bool(F,X_1)),hAPP_f1572141188l_bool(G,X_1))) ) ).

tff(fact_368_le__fun__def,axiom,
    ! [F: fun_fu3835832l_bool,G: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,F),G))
    <=> ! [X_1: fun_Ar274636406t_bool] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f995490902l_bool(F,X_1)),hAPP_f995490902l_bool(G,X_1))) ) ).

tff(fact_369_le__fun__def,axiom,
    ! [F: fun_Pr2067565481t_bool,G: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,F),G))
    <=> ! [X_1: produc472769767le_alt] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1178790471t_bool(F,X_1)),hAPP_P1178790471t_bool(G,X_1))) ) ).

tff(fact_370_le__fun__def,axiom,
    ! [F: fun_Ar1809396326i_bool,G: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,F),G))
    <=> ! [X_1: arrow_856714788e_indi] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A997847300i_bool(F,X_1)),hAPP_A997847300i_bool(G,X_1))) ) ).

tff(fact_371_le__fun__def,axiom,
    ! [F: fun_Pr1643180309t_bool,G: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,F),G))
    <=> ! [X_1: product_unit] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(F,X_1)),hAPP_P1676879539t_bool(G,X_1))) ) ).

tff(fact_372_le__fun__def,axiom,
    ! [F: fun_Ar331856045t_bool,G: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,F),G))
    <=> ! [X_1: arrow_1893660431le_alt] : hBOOL(hAPP_f739344229l_bool(hAPP_f1549168575l_bool(ord_le1779845435t_bool,hAPP_A2063800319t_bool(F,X_1)),hAPP_A2063800319t_bool(G,X_1))) ) ).

tff(fact_373_le__fun__def,axiom,
    ! [F: fun_nat_bool,G: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G))
    <=> ! [X_1: nat] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(G,X_1))) ) ).

tff(fact_374_linorder__not__less,axiom,
    ! [X_2: nat,Y_2: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_2)) ) ).

tff(fact_375_linorder__not__le,axiom,
    ! [X_2: nat,Y_2: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2)) ) ).

tff(fact_376_linorder__le__less__linear,axiom,
    ! [X_12: nat,Y_12: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_12),Y_12))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_12),X_12)) ) ).

tff(fact_377_order__less__le,axiom,
    ! [X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
        & ( X_2 != Y_2 ) ) ) ).

tff(fact_378_order__less__le,axiom,
    ! [X_2: fun_Ar1809396326i_bool,Y_2: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,X_2),Y_2))
        & ( X_2 != Y_2 ) ) ) ).

tff(fact_379_order__less__le,axiom,
    ! [X_2: fun_fu638310559l_bool,Y_2: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,X_2),Y_2))
        & ( X_2 != Y_2 ) ) ) ).

tff(fact_380_order__less__le,axiom,
    ! [X_2: fun_fu2098777574l_bool,Y_2: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,X_2),Y_2))
        & ( X_2 != Y_2 ) ) ) ).

tff(fact_381_order__less__le,axiom,
    ! [X_2: fun_fu3835832l_bool,Y_2: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,X_2),Y_2))
        & ( X_2 != Y_2 ) ) ) ).

tff(fact_382_order__less__le,axiom,
    ! [X_2: fun_Pr2067565481t_bool,Y_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,X_2),Y_2))
        & ( X_2 != Y_2 ) ) ) ).

tff(fact_383_order__less__le,axiom,
    ! [X_2: bool,Y_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
        & ~ ( hBOOL(X_2)
          <=> hBOOL(Y_2) ) ) ) ).

tff(fact_384_order__less__le,axiom,
    ! [X_2: fun_Ar331856045t_bool,Y_2: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,X_2),Y_2))
        & ( X_2 != Y_2 ) ) ) ).

tff(fact_385_order__less__le,axiom,
    ! [X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
        & ( X_2 != Y_2 ) ) ) ).

tff(fact_386_order__less__le,axiom,
    ! [X_2: nat,Y_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
        & ( X_2 != Y_2 ) ) ) ).

tff(fact_387_less__le__not__le,axiom,
    ! [X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
        & ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),X_2)) ) ) ).

tff(fact_388_less__le__not__le,axiom,
    ! [X_2: fun_Ar1809396326i_bool,Y_2: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,X_2),Y_2))
        & ~ hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Y_2),X_2)) ) ) ).

tff(fact_389_less__le__not__le,axiom,
    ! [X_2: fun_fu638310559l_bool,Y_2: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,X_2),Y_2))
        & ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Y_2),X_2)) ) ) ).

tff(fact_390_less__le__not__le,axiom,
    ! [X_2: fun_fu2098777574l_bool,Y_2: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,X_2),Y_2))
        & ~ hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Y_2),X_2)) ) ) ).

tff(fact_391_less__le__not__le,axiom,
    ! [X_2: fun_fu3835832l_bool,Y_2: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,X_2),Y_2))
        & ~ hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Y_2),X_2)) ) ) ).

tff(fact_392_less__le__not__le,axiom,
    ! [X_2: fun_Pr2067565481t_bool,Y_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,X_2),Y_2))
        & ~ hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Y_2),X_2)) ) ) ).

tff(fact_393_less__le__not__le,axiom,
    ! [X_2: bool,Y_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
        & ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2)) ) ) ).

tff(fact_394_less__le__not__le,axiom,
    ! [X_2: fun_Ar331856045t_bool,Y_2: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,X_2),Y_2))
        & ~ hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Y_2),X_2)) ) ) ).

tff(fact_395_less__le__not__le,axiom,
    ! [X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
        & ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2)) ) ) ).

tff(fact_396_less__le__not__le,axiom,
    ! [X_2: nat,Y_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
        & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_2)) ) ) ).

tff(fact_397_order__le__less,axiom,
    ! [X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
        | ( X_2 = Y_2 ) ) ) ).

tff(fact_398_order__le__less,axiom,
    ! [X_2: fun_Ar1809396326i_bool,Y_2: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,X_2),Y_2))
        | ( X_2 = Y_2 ) ) ) ).

tff(fact_399_order__le__less,axiom,
    ! [X_2: fun_fu638310559l_bool,Y_2: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,X_2),Y_2))
        | ( X_2 = Y_2 ) ) ) ).

tff(fact_400_order__le__less,axiom,
    ! [X_2: fun_fu2098777574l_bool,Y_2: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,X_2),Y_2))
        | ( X_2 = Y_2 ) ) ) ).

tff(fact_401_order__le__less,axiom,
    ! [X_2: fun_fu3835832l_bool,Y_2: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,X_2),Y_2))
        | ( X_2 = Y_2 ) ) ) ).

tff(fact_402_order__le__less,axiom,
    ! [X_2: fun_Pr2067565481t_bool,Y_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,X_2),Y_2))
        | ( X_2 = Y_2 ) ) ) ).

tff(fact_403_order__le__less,axiom,
    ! [X_2: bool,Y_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2))
        | ( hBOOL(X_2)
        <=> hBOOL(Y_2) ) ) ) ).

tff(fact_404_order__le__less,axiom,
    ! [X_2: fun_Ar331856045t_bool,Y_2: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,X_2),Y_2))
        | ( X_2 = Y_2 ) ) ) ).

tff(fact_405_order__le__less,axiom,
    ! [X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
        | ( X_2 = Y_2 ) ) ) ).

tff(fact_406_order__le__less,axiom,
    ! [X_2: nat,Y_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
        | ( X_2 = Y_2 ) ) ) ).

tff(fact_407_leI,axiom,
    ! [X_11: nat,Y_11: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_11),Y_11))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_11),X_11)) ) ).

tff(fact_408_not__leE,axiom,
    ! [Y_10: nat,X_10: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_10),X_10))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_10),Y_10)) ) ).

tff(fact_409_linorder__antisym__conv1,axiom,
    ! [X_2: nat,Y_2: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
      <=> ( X_2 = Y_2 ) ) ) ).

tff(fact_410_order__neq__le__trans,axiom,
    ! [Aa: fun_Pr1643180309t_bool,Ba: fun_Pr1643180309t_bool] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ba))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba)) ) ) ).

tff(fact_411_order__neq__le__trans,axiom,
    ! [Aa: fun_Ar1809396326i_bool,Ba: fun_Ar1809396326i_bool] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Aa),Ba))
       => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Aa),Ba)) ) ) ).

tff(fact_412_order__neq__le__trans,axiom,
    ! [Aa: fun_fu638310559l_bool,Ba: fun_fu638310559l_bool] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Aa),Ba))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,Aa),Ba)) ) ) ).

tff(fact_413_order__neq__le__trans,axiom,
    ! [Aa: fun_fu2098777574l_bool,Ba: fun_fu2098777574l_bool] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Aa),Ba))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,Aa),Ba)) ) ) ).

tff(fact_414_order__neq__le__trans,axiom,
    ! [Aa: fun_fu3835832l_bool,Ba: fun_fu3835832l_bool] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Aa),Ba))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,Aa),Ba)) ) ) ).

tff(fact_415_order__neq__le__trans,axiom,
    ! [Aa: fun_Pr2067565481t_bool,Ba: fun_Pr2067565481t_bool] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Aa),Ba))
       => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,Aa),Ba)) ) ) ).

tff(fact_416_order__neq__le__trans,axiom,
    ! [Ba: bool,Aa: bool] :
      ( ~ ( hBOOL(Aa)
        <=> hBOOL(Ba) )
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ba))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),Ba)) ) ) ).

tff(fact_417_order__neq__le__trans,axiom,
    ! [Aa: fun_Ar331856045t_bool,Ba: fun_Ar331856045t_bool] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Aa),Ba))
       => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,Aa),Ba)) ) ) ).

tff(fact_418_order__neq__le__trans,axiom,
    ! [Aa: fun_nat_bool,Ba: fun_nat_bool] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba)) ) ) ).

tff(fact_419_order__neq__le__trans,axiom,
    ! [A_22: nat,B_20: nat] :
      ( ( A_22 != B_20 )
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_22),B_20))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_22),B_20)) ) ) ).

tff(fact_420_xt1_I12_J,axiom,
    ! [Aa: fun_Pr1643180309t_bool,Ba: fun_Pr1643180309t_bool] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Aa))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa)) ) ) ).

tff(fact_421_xt1_I12_J,axiom,
    ! [Aa: fun_Ar1809396326i_bool,Ba: fun_Ar1809396326i_bool] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Ba),Aa))
       => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Ba),Aa)) ) ) ).

tff(fact_422_xt1_I12_J,axiom,
    ! [Aa: fun_fu638310559l_bool,Ba: fun_fu638310559l_bool] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Ba),Aa))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,Ba),Aa)) ) ) ).

tff(fact_423_xt1_I12_J,axiom,
    ! [Aa: fun_fu2098777574l_bool,Ba: fun_fu2098777574l_bool] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Ba),Aa))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,Ba),Aa)) ) ) ).

tff(fact_424_xt1_I12_J,axiom,
    ! [Aa: fun_fu3835832l_bool,Ba: fun_fu3835832l_bool] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Ba),Aa))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,Ba),Aa)) ) ) ).

tff(fact_425_xt1_I12_J,axiom,
    ! [Aa: fun_Pr2067565481t_bool,Ba: fun_Pr2067565481t_bool] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Ba),Aa))
       => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,Ba),Aa)) ) ) ).

tff(fact_426_xt1_I12_J,axiom,
    ! [Ba: bool,Aa: bool] :
      ( ~ ( hBOOL(Aa)
        <=> hBOOL(Ba) )
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Aa))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ba),Aa)) ) ) ).

tff(fact_427_xt1_I12_J,axiom,
    ! [Aa: fun_Ar331856045t_bool,Ba: fun_Ar331856045t_bool] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Ba),Aa))
       => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,Ba),Aa)) ) ) ).

tff(fact_428_xt1_I12_J,axiom,
    ! [Aa: fun_nat_bool,Ba: fun_nat_bool] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa)) ) ) ).

tff(fact_429_xt1_I12_J,axiom,
    ! [A_21: nat,B_19: nat] :
      ( ( A_21 != B_19 )
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_19),A_21))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_19),A_21)) ) ) ).

tff(fact_430_leD,axiom,
    ! [Y_9: nat,X_9: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_9),X_9))
     => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_9),Y_9)) ) ).

tff(fact_431_order__less__imp__le,axiom,
    ! [X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
     => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2)) ) ).

tff(fact_432_order__less__imp__le,axiom,
    ! [X_2: fun_Ar1809396326i_bool,Y_2: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,X_2),Y_2))
     => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,X_2),Y_2)) ) ).

tff(fact_433_order__less__imp__le,axiom,
    ! [X_2: fun_fu638310559l_bool,Y_2: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,X_2),Y_2))
     => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,X_2),Y_2)) ) ).

tff(fact_434_order__less__imp__le,axiom,
    ! [X_2: fun_fu2098777574l_bool,Y_2: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,X_2),Y_2))
     => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,X_2),Y_2)) ) ).

tff(fact_435_order__less__imp__le,axiom,
    ! [X_2: fun_fu3835832l_bool,Y_2: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,X_2),Y_2))
     => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,X_2),Y_2)) ) ).

tff(fact_436_order__less__imp__le,axiom,
    ! [X_2: fun_Pr2067565481t_bool,Y_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,X_2),Y_2))
     => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,X_2),Y_2)) ) ).

tff(fact_437_order__less__imp__le,axiom,
    ! [X_2: bool,Y_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) ) ).

tff(fact_438_order__less__imp__le,axiom,
    ! [X_2: fun_Ar331856045t_bool,Y_2: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,X_2),Y_2))
     => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,X_2),Y_2)) ) ).

tff(fact_439_order__less__imp__le,axiom,
    ! [X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) ) ).

tff(fact_440_order__less__imp__le,axiom,
    ! [X_8: nat,Y_8: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_8),Y_8))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_8),Y_8)) ) ).

tff(fact_441_linorder__antisym__conv2,axiom,
    ! [X_2: nat,Y_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
      <=> ( X_2 = Y_2 ) ) ) ).

tff(fact_442_order__le__imp__less__or__eq,axiom,
    ! [X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
        | ( X_2 = Y_2 ) ) ) ).

tff(fact_443_order__le__imp__less__or__eq,axiom,
    ! [X_2: fun_Ar1809396326i_bool,Y_2: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,X_2),Y_2))
        | ( X_2 = Y_2 ) ) ) ).

tff(fact_444_order__le__imp__less__or__eq,axiom,
    ! [X_2: fun_fu638310559l_bool,Y_2: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,X_2),Y_2))
        | ( X_2 = Y_2 ) ) ) ).

tff(fact_445_order__le__imp__less__or__eq,axiom,
    ! [X_2: fun_fu2098777574l_bool,Y_2: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,X_2),Y_2))
        | ( X_2 = Y_2 ) ) ) ).

tff(fact_446_order__le__imp__less__or__eq,axiom,
    ! [X_2: fun_fu3835832l_bool,Y_2: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,X_2),Y_2))
        | ( X_2 = Y_2 ) ) ) ).

tff(fact_447_order__le__imp__less__or__eq,axiom,
    ! [X_2: fun_Pr2067565481t_bool,Y_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,X_2),Y_2))
        | ( X_2 = Y_2 ) ) ) ).

tff(fact_448_order__le__imp__less__or__eq,axiom,
    ! [X_2: bool,Y_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2))
        | ( hBOOL(X_2)
        <=> hBOOL(Y_2) ) ) ) ).

tff(fact_449_order__le__imp__less__or__eq,axiom,
    ! [X_2: fun_Ar331856045t_bool,Y_2: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,X_2),Y_2))
        | ( X_2 = Y_2 ) ) ) ).

tff(fact_450_order__le__imp__less__or__eq,axiom,
    ! [X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
        | ( X_2 = Y_2 ) ) ) ).

tff(fact_451_order__le__imp__less__or__eq,axiom,
    ! [X_7: nat,Y_7: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_7),Y_7))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_7),Y_7))
        | ( X_7 = Y_7 ) ) ) ).

tff(fact_452_order__le__neq__trans,axiom,
    ! [Aa: fun_Pr1643180309t_bool,Ba: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ba))
     => ( ( Aa != Ba )
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba)) ) ) ).

tff(fact_453_order__le__neq__trans,axiom,
    ! [Aa: fun_Ar1809396326i_bool,Ba: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Aa),Ba))
     => ( ( Aa != Ba )
       => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Aa),Ba)) ) ) ).

tff(fact_454_order__le__neq__trans,axiom,
    ! [Aa: fun_fu638310559l_bool,Ba: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Aa),Ba))
     => ( ( Aa != Ba )
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,Aa),Ba)) ) ) ).

tff(fact_455_order__le__neq__trans,axiom,
    ! [Aa: fun_fu2098777574l_bool,Ba: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Aa),Ba))
     => ( ( Aa != Ba )
       => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,Aa),Ba)) ) ) ).

tff(fact_456_order__le__neq__trans,axiom,
    ! [Aa: fun_fu3835832l_bool,Ba: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Aa),Ba))
     => ( ( Aa != Ba )
       => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,Aa),Ba)) ) ) ).

tff(fact_457_order__le__neq__trans,axiom,
    ! [Aa: fun_Pr2067565481t_bool,Ba: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Aa),Ba))
     => ( ( Aa != Ba )
       => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,Aa),Ba)) ) ) ).

tff(fact_458_order__le__neq__trans,axiom,
    ! [Aa: bool,Ba: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ba))
     => ( ~ ( hBOOL(Aa)
          <=> hBOOL(Ba) )
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),Ba)) ) ) ).

tff(fact_459_order__le__neq__trans,axiom,
    ! [Aa: fun_Ar331856045t_bool,Ba: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Aa),Ba))
     => ( ( Aa != Ba )
       => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,Aa),Ba)) ) ) ).

tff(fact_460_order__le__neq__trans,axiom,
    ! [Aa: fun_nat_bool,Ba: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
     => ( ( Aa != Ba )
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba)) ) ) ).

tff(fact_461_order__le__neq__trans,axiom,
    ! [A_20: nat,B_18: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_20),B_18))
     => ( ( A_20 != B_18 )
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_20),B_18)) ) ) ).

tff(fact_462_xt1_I11_J,axiom,
    ! [Ba: fun_Pr1643180309t_bool,Aa: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Aa))
     => ( ( Aa != Ba )
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa)) ) ) ).

tff(fact_463_xt1_I11_J,axiom,
    ! [Ba: fun_Ar1809396326i_bool,Aa: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Ba),Aa))
     => ( ( Aa != Ba )
       => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Ba),Aa)) ) ) ).

tff(fact_464_xt1_I11_J,axiom,
    ! [Ba: fun_fu638310559l_bool,Aa: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Ba),Aa))
     => ( ( Aa != Ba )
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,Ba),Aa)) ) ) ).

tff(fact_465_xt1_I11_J,axiom,
    ! [Ba: fun_fu2098777574l_bool,Aa: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Ba),Aa))
     => ( ( Aa != Ba )
       => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,Ba),Aa)) ) ) ).

tff(fact_466_xt1_I11_J,axiom,
    ! [Ba: fun_fu3835832l_bool,Aa: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Ba),Aa))
     => ( ( Aa != Ba )
       => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,Ba),Aa)) ) ) ).

tff(fact_467_xt1_I11_J,axiom,
    ! [Ba: fun_Pr2067565481t_bool,Aa: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Ba),Aa))
     => ( ( Aa != Ba )
       => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,Ba),Aa)) ) ) ).

tff(fact_468_xt1_I11_J,axiom,
    ! [Ba: bool,Aa: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Aa))
     => ( ~ ( hBOOL(Aa)
          <=> hBOOL(Ba) )
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ba),Aa)) ) ) ).

tff(fact_469_xt1_I11_J,axiom,
    ! [Ba: fun_Ar331856045t_bool,Aa: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Ba),Aa))
     => ( ( Aa != Ba )
       => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,Ba),Aa)) ) ) ).

tff(fact_470_xt1_I11_J,axiom,
    ! [Ba: fun_nat_bool,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
     => ( ( Aa != Ba )
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa)) ) ) ).

tff(fact_471_xt1_I11_J,axiom,
    ! [B_17: nat,A_19: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_17),A_19))
     => ( ( A_19 != B_17 )
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_17),A_19)) ) ) ).

tff(fact_472_order__less__le__trans,axiom,
    ! [Z_2: fun_Pr1643180309t_bool,X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),Z_2))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Z_2)) ) ) ).

tff(fact_473_order__less__le__trans,axiom,
    ! [Z_2: fun_Ar1809396326i_bool,X_2: fun_Ar1809396326i_bool,Y_2: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Y_2),Z_2))
       => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,X_2),Z_2)) ) ) ).

tff(fact_474_order__less__le__trans,axiom,
    ! [Z_2: fun_fu638310559l_bool,X_2: fun_fu638310559l_bool,Y_2: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Y_2),Z_2))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,X_2),Z_2)) ) ) ).

tff(fact_475_order__less__le__trans,axiom,
    ! [Z_2: fun_fu2098777574l_bool,X_2: fun_fu2098777574l_bool,Y_2: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Y_2),Z_2))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,X_2),Z_2)) ) ) ).

tff(fact_476_order__less__le__trans,axiom,
    ! [Z_2: fun_fu3835832l_bool,X_2: fun_fu3835832l_bool,Y_2: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Y_2),Z_2))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,X_2),Z_2)) ) ) ).

tff(fact_477_order__less__le__trans,axiom,
    ! [Z_2: fun_Pr2067565481t_bool,X_2: fun_Pr2067565481t_bool,Y_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Y_2),Z_2))
       => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,X_2),Z_2)) ) ) ).

tff(fact_478_order__less__le__trans,axiom,
    ! [Z_2: bool,X_2: bool,Y_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),Z_2))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Z_2)) ) ) ).

tff(fact_479_order__less__le__trans,axiom,
    ! [Z_2: fun_Ar331856045t_bool,X_2: fun_Ar331856045t_bool,Y_2: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Y_2),Z_2))
       => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,X_2),Z_2)) ) ) ).

tff(fact_480_order__less__le__trans,axiom,
    ! [Z_2: fun_nat_bool,X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),Z_2))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Z_2)) ) ) ).

tff(fact_481_order__less__le__trans,axiom,
    ! [Z_5: nat,X_6: nat,Y_6: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_6),Y_6))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_6),Z_5))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_6),Z_5)) ) ) ).

tff(fact_482_xt1_I7_J,axiom,
    ! [Z_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool,X_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Z_2),Y_2))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_2),X_2)) ) ) ).

tff(fact_483_xt1_I7_J,axiom,
    ! [Z_2: fun_Ar1809396326i_bool,Y_2: fun_Ar1809396326i_bool,X_2: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Z_2),Y_2))
       => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Z_2),X_2)) ) ) ).

tff(fact_484_xt1_I7_J,axiom,
    ! [Z_2: fun_fu638310559l_bool,Y_2: fun_fu638310559l_bool,X_2: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Z_2),Y_2))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,Z_2),X_2)) ) ) ).

tff(fact_485_xt1_I7_J,axiom,
    ! [Z_2: fun_fu2098777574l_bool,Y_2: fun_fu2098777574l_bool,X_2: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Z_2),Y_2))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,Z_2),X_2)) ) ) ).

tff(fact_486_xt1_I7_J,axiom,
    ! [Z_2: fun_fu3835832l_bool,Y_2: fun_fu3835832l_bool,X_2: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Z_2),Y_2))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,Z_2),X_2)) ) ) ).

tff(fact_487_xt1_I7_J,axiom,
    ! [Z_2: fun_Pr2067565481t_bool,Y_2: fun_Pr2067565481t_bool,X_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Z_2),Y_2))
       => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,Z_2),X_2)) ) ) ).

tff(fact_488_xt1_I7_J,axiom,
    ! [Z_2: bool,Y_2: bool,X_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Y_2),X_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z_2),Y_2))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Z_2),X_2)) ) ) ).

tff(fact_489_xt1_I7_J,axiom,
    ! [Z_2: fun_Ar331856045t_bool,Y_2: fun_Ar331856045t_bool,X_2: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Z_2),Y_2))
       => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,Z_2),X_2)) ) ) ).

tff(fact_490_xt1_I7_J,axiom,
    ! [Z_2: fun_nat_bool,Y_2: fun_nat_bool,X_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_2),Y_2))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_2),X_2)) ) ) ).

tff(fact_491_xt1_I7_J,axiom,
    ! [Z_4: nat,Y_5: nat,X_5: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_5),X_5))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_4),Y_5))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_4),X_5)) ) ) ).

tff(fact_492_order__le__less__trans,axiom,
    ! [Z_2: fun_Pr1643180309t_bool,X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),Z_2))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Z_2)) ) ) ).

tff(fact_493_order__le__less__trans,axiom,
    ! [Z_2: fun_Ar1809396326i_bool,X_2: fun_Ar1809396326i_bool,Y_2: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Y_2),Z_2))
       => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,X_2),Z_2)) ) ) ).

tff(fact_494_order__le__less__trans,axiom,
    ! [Z_2: fun_fu638310559l_bool,X_2: fun_fu638310559l_bool,Y_2: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,Y_2),Z_2))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,X_2),Z_2)) ) ) ).

tff(fact_495_order__le__less__trans,axiom,
    ! [Z_2: fun_fu2098777574l_bool,X_2: fun_fu2098777574l_bool,Y_2: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,Y_2),Z_2))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,X_2),Z_2)) ) ) ).

tff(fact_496_order__le__less__trans,axiom,
    ! [Z_2: fun_fu3835832l_bool,X_2: fun_fu3835832l_bool,Y_2: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,Y_2),Z_2))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,X_2),Z_2)) ) ) ).

tff(fact_497_order__le__less__trans,axiom,
    ! [Z_2: fun_Pr2067565481t_bool,X_2: fun_Pr2067565481t_bool,Y_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,Y_2),Z_2))
       => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,X_2),Z_2)) ) ) ).

tff(fact_498_order__le__less__trans,axiom,
    ! [Z_2: bool,X_2: bool,Y_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Y_2),Z_2))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Z_2)) ) ) ).

tff(fact_499_order__le__less__trans,axiom,
    ! [Z_2: fun_Ar331856045t_bool,X_2: fun_Ar331856045t_bool,Y_2: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,Y_2),Z_2))
       => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,X_2),Z_2)) ) ) ).

tff(fact_500_order__le__less__trans,axiom,
    ! [Z_2: fun_nat_bool,X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),Z_2))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Z_2)) ) ) ).

tff(fact_501_order__le__less__trans,axiom,
    ! [Z_3: nat,X_4: nat,Y_4: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_4),Y_4))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_4),Z_3))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_4),Z_3)) ) ) ).

tff(fact_502_xt1_I8_J,axiom,
    ! [Z_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool,X_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_2),Y_2))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_2),X_2)) ) ) ).

tff(fact_503_xt1_I8_J,axiom,
    ! [Z_2: fun_Ar1809396326i_bool,Y_2: fun_Ar1809396326i_bool,X_2: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Z_2),Y_2))
       => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Z_2),X_2)) ) ) ).

tff(fact_504_xt1_I8_J,axiom,
    ! [Z_2: fun_fu638310559l_bool,Y_2: fun_fu638310559l_bool,X_2: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,Z_2),Y_2))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,Z_2),X_2)) ) ) ).

tff(fact_505_xt1_I8_J,axiom,
    ! [Z_2: fun_fu2098777574l_bool,Y_2: fun_fu2098777574l_bool,X_2: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,Z_2),Y_2))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,Z_2),X_2)) ) ) ).

tff(fact_506_xt1_I8_J,axiom,
    ! [Z_2: fun_fu3835832l_bool,Y_2: fun_fu3835832l_bool,X_2: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,Z_2),Y_2))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,Z_2),X_2)) ) ) ).

tff(fact_507_xt1_I8_J,axiom,
    ! [Z_2: fun_Pr2067565481t_bool,Y_2: fun_Pr2067565481t_bool,X_2: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,Z_2),Y_2))
       => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,Z_2),X_2)) ) ) ).

tff(fact_508_xt1_I8_J,axiom,
    ! [Z_2: bool,Y_2: bool,X_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Z_2),Y_2))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Z_2),X_2)) ) ) ).

tff(fact_509_xt1_I8_J,axiom,
    ! [Z_2: fun_Ar331856045t_bool,Y_2: fun_Ar331856045t_bool,X_2: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,Z_2),Y_2))
       => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,Z_2),X_2)) ) ) ).

tff(fact_510_xt1_I8_J,axiom,
    ! [Z_2: fun_nat_bool,Y_2: fun_nat_bool,X_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_2),Y_2))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_2),X_2)) ) ) ).

tff(fact_511_xt1_I8_J,axiom,
    ! [Z_1: nat,Y_3: nat,X_3: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_3),X_3))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_1),Y_3))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_1),X_3)) ) ) ).

tff(fact_512_top__greatest,axiom,
    ! [Aa: fun_fu638310559l_bool] : hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Aa),top_to1312956197l_bool)) ).

tff(fact_513_top__greatest,axiom,
    ! [Aa: fun_fu3835832l_bool] : hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Aa),top_to553140914l_bool)) ).

tff(fact_514_top__greatest,axiom,
    ! [Aa: fun_fu2098777574l_bool] : hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Aa),top_to827110112l_bool)) ).

tff(fact_515_top__greatest,axiom,
    ! [Aa: bool] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),top_top_bool)) ).

tff(fact_516_top__greatest,axiom,
    ! [Aa: fun_Pr2067565481t_bool] : hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Aa),top_to1138392227t_bool)) ).

tff(fact_517_top__greatest,axiom,
    ! [Aa: fun_Ar331856045t_bool] : hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Aa),top_to951839027t_bool)) ).

tff(fact_518_top__greatest,axiom,
    ! [Aa: fun_Ar1809396326i_bool] : hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Aa),top_to788185952i_bool)) ).

tff(fact_519_top__greatest,axiom,
    ! [Aa: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),top_top_fun_nat_bool)) ).

tff(fact_520_top__greatest,axiom,
    ! [Aa: fun_Pr1643180309t_bool] : hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),top_to1257323279t_bool)) ).

tff(fact_521_top__unique,axiom,
    ! [Aa: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,top_to1312956197l_bool),Aa))
    <=> ( Aa = top_to1312956197l_bool ) ) ).

tff(fact_522_top__unique,axiom,
    ! [Aa: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,top_to553140914l_bool),Aa))
    <=> ( Aa = top_to553140914l_bool ) ) ).

tff(fact_523_top__unique,axiom,
    ! [Aa: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,top_to827110112l_bool),Aa))
    <=> ( Aa = top_to827110112l_bool ) ) ).

tff(fact_524_top__unique,axiom,
    ! [Aa: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),Aa))
    <=> ( hBOOL(Aa)
      <=> hBOOL(top_top_bool) ) ) ).

tff(fact_525_top__unique,axiom,
    ! [Aa: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,top_to1138392227t_bool),Aa))
    <=> ( Aa = top_to1138392227t_bool ) ) ).

tff(fact_526_top__unique,axiom,
    ! [Aa: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,top_to951839027t_bool),Aa))
    <=> ( Aa = top_to951839027t_bool ) ) ).

tff(fact_527_top__unique,axiom,
    ! [Aa: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,top_to788185952i_bool),Aa))
    <=> ( Aa = top_to788185952i_bool ) ) ).

tff(fact_528_top__unique,axiom,
    ! [Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),Aa))
    <=> ( Aa = top_top_fun_nat_bool ) ) ).

tff(fact_529_top__unique,axiom,
    ! [Aa: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),Aa))
    <=> ( Aa = top_to1257323279t_bool ) ) ).

tff(fact_530_top__le,axiom,
    ! [Aa: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,top_to1312956197l_bool),Aa))
     => ( Aa = top_to1312956197l_bool ) ) ).

tff(fact_531_top__le,axiom,
    ! [Aa: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,top_to553140914l_bool),Aa))
     => ( Aa = top_to553140914l_bool ) ) ).

tff(fact_532_top__le,axiom,
    ! [Aa: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,top_to827110112l_bool),Aa))
     => ( Aa = top_to827110112l_bool ) ) ).

tff(fact_533_top__le,axiom,
    ! [Aa: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),Aa))
     => ( hBOOL(Aa)
      <=> hBOOL(top_top_bool) ) ) ).

tff(fact_534_top__le,axiom,
    ! [Aa: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,top_to1138392227t_bool),Aa))
     => ( Aa = top_to1138392227t_bool ) ) ).

tff(fact_535_top__le,axiom,
    ! [Aa: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,top_to951839027t_bool),Aa))
     => ( Aa = top_to951839027t_bool ) ) ).

tff(fact_536_top__le,axiom,
    ! [Aa: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,top_to788185952i_bool),Aa))
     => ( Aa = top_to788185952i_bool ) ) ).

tff(fact_537_top__le,axiom,
    ! [Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),Aa))
     => ( Aa = top_top_fun_nat_bool ) ) ).

tff(fact_538_top__le,axiom,
    ! [Aa: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),Aa))
     => ( Aa = top_to1257323279t_bool ) ) ).

tff(fact_539_inj__on__def,axiom,
    ! [F: fun_Ar671024215di_nat,A: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(inj_on1960344199di_nat(F),A))
    <=> ! [X_1: arrow_856714788e_indi] :
          ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_1),A))
         => ! [Xa: arrow_856714788e_indi] :
              ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,Xa),A))
             => ( ( hAPP_A376526755di_nat(F,X_1) = hAPP_A376526755di_nat(F,Xa) )
               => ( X_1 = Xa ) ) ) ) ) ).

tff(fact_540_inj__on__def,axiom,
    ! [F: fun_nat_nat,A: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
    <=> ! [X_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
         => ! [Xa: nat] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Xa),A))
             => ( ( hAPP_nat_nat(F,X_1) = hAPP_nat_nat(F,Xa) )
               => ( X_1 = Xa ) ) ) ) ) ).

tff(fact_541_inj__on__contraD,axiom,
    ! [X_2: arrow_856714788e_indi,Y_2: arrow_856714788e_indi,F: fun_Ar671024215di_nat,A: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(inj_on1960344199di_nat(F),A))
     => ( ( X_2 != Y_2 )
       => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A))
         => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,Y_2),A))
           => ( hAPP_A376526755di_nat(F,X_2) != hAPP_A376526755di_nat(F,Y_2) ) ) ) ) ) ).

tff(fact_542_inj__on__contraD,axiom,
    ! [X_2: nat,Y_2: nat,F: fun_nat_nat,A: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
     => ( ( X_2 != Y_2 )
       => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
         => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_2),A))
           => ( hAPP_nat_nat(F,X_2) != hAPP_nat_nat(F,Y_2) ) ) ) ) ) ).

tff(fact_543_inj__on__iff,axiom,
    ! [Y_2: arrow_856714788e_indi,X_2: arrow_856714788e_indi,F: fun_Ar671024215di_nat,A: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(inj_on1960344199di_nat(F),A))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A))
       => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,Y_2),A))
         => ( ( hAPP_A376526755di_nat(F,X_2) = hAPP_A376526755di_nat(F,Y_2) )
          <=> ( X_2 = Y_2 ) ) ) ) ) ).

tff(fact_544_inj__on__iff,axiom,
    ! [Y_2: nat,X_2: nat,F: fun_nat_nat,A: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
       => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_2),A))
         => ( ( hAPP_nat_nat(F,X_2) = hAPP_nat_nat(F,Y_2) )
          <=> ( X_2 = Y_2 ) ) ) ) ) ).

tff(fact_545_inj__onD,axiom,
    ! [X_2: arrow_856714788e_indi,Y_2: arrow_856714788e_indi,F: fun_Ar671024215di_nat,A: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(inj_on1960344199di_nat(F),A))
     => ( ( hAPP_A376526755di_nat(F,X_2) = hAPP_A376526755di_nat(F,Y_2) )
       => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A))
         => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,Y_2),A))
           => ( X_2 = Y_2 ) ) ) ) ) ).

tff(fact_546_inj__onD,axiom,
    ! [X_2: nat,Y_2: nat,F: fun_nat_nat,A: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
     => ( ( hAPP_nat_nat(F,X_2) = hAPP_nat_nat(F,Y_2) )
       => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
         => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_2),A))
           => ( X_2 = Y_2 ) ) ) ) ) ).

tff(fact_547_Pi__mem,axiom,
    ! [X_2: produc472769767le_alt,F: fun_Pr2067565481t_bool,A: fun_Pr2067565481t_bool,B: fun_Pr1780397033l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,F),pi_Pro1238944957t_bool(A,B)))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1178790471t_bool(F,X_2)),hAPP_P1103642805l_bool(B,X_2))) ) ) ).

tff(fact_548_Pi__mem,axiom,
    ! [X_2: produc472769767le_alt,F: fun_Pr1509342064e_indi,A: fun_Pr2067565481t_bool,B: fun_Pr895221296i_bool] :
      ( hBOOL(hAPP_f2124588998l_bool(hAPP_f1187850253l_bool(member1558233923e_indi,F),pi_Pro837265796e_indi(A,B)))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A))
       => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_P276596750e_indi(F,X_2)),hAPP_P1859429372i_bool(B,X_2))) ) ) ).

tff(fact_549_Pi__mem,axiom,
    ! [X_2: produc472769767le_alt,F: fun_Pr376858015t_unit,A: fun_Pr2067565481t_bool,B: fun_Pr1069395679t_bool] :
      ( hBOOL(hAPP_f1159856629l_bool(hAPP_f1700632141l_bool(member1303779570t_unit,F),pi_Pro346842291t_unit(A,B)))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1069491261t_unit(F,X_2)),hAPP_P2037731755t_bool(B,X_2))) ) ) ).

tff(fact_550_Pi__mem,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu1929591039e_indi,A: fun_fu3835832l_bool,B: fun_fu223278561i_bool] :
      ( hBOOL(hAPP_f665932885l_bool(hAPP_f430646093l_bool(member282602450e_indi,F),pi_fun520512275e_indi(A,B)))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A))
       => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_f602741661e_indi(F,X_2)),hAPP_f391644589i_bool(B,X_2))) ) ) ).

tff(fact_551_Pi__mem,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu3835832l_bool,A: fun_fu3835832l_bool,B: fun_fu916327706l_bool] :
      ( hBOOL(hAPP_f1867557646l_bool(hAPP_f1048573069l_bool(member1020280587l_bool,F),pi_fun853738700l_bool(A,B)))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f995490902l_bool(F,X_2)),hAPP_f1676084198l_bool(B,X_2))) ) ) ).

tff(fact_552_Pi__mem,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu1023022254t_unit,A: fun_fu3835832l_bool,B: fun_fu1734317328t_bool] :
      ( hBOOL(hAPP_f115957764l_bool(hAPP_f1184790797l_bool(member2003579649t_unit,F),pi_fun1644711874t_unit(A,B)))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f1775626572t_unit(F,X_2)),hAPP_f1438163420t_bool(B,X_2))) ) ) ).

tff(fact_553_Pi__mem,axiom,
    ! [X_2: fun_fu2114379172t_bool,F: fun_fu748153389e_indi,A: fun_fu2098777574l_bool,B: fun_fu2109152051i_bool] :
      ( hBOOL(hAPP_f2350467l_bool(hAPP_f1411422157l_bool(member1247254528e_indi,F),pi_fun1807454273e_indi(A,B)))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A))
       => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_f350323403e_indi(F,X_2)),hAPP_f399308031i_bool(B,X_2))) ) ) ).

tff(fact_554_Pi__mem,axiom,
    ! [X_2: fun_fu2114379172t_bool,F: fun_fu2098777574l_bool,A: fun_fu2098777574l_bool,B: fun_fu1522163052l_bool] :
      ( hBOOL(hAPP_f2047920444l_bool(hAPP_f59810573l_bool(member1173995577l_bool,F),pi_fun1312540410l_bool(A,B)))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1572141188l_bool(F,X_2)),hAPP_f414129720l_bool(B,X_2))) ) ) ).

tff(fact_555_Pi__mem,axiom,
    ! [X_2: fun_fu2114379172t_bool,F: fun_fu1480298716t_unit,A: fun_fu2098777574l_bool,B: fun_fu1143287650t_bool] :
      ( hBOOL(hAPP_f92582962l_bool(hAPP_f1494690701l_bool(member2091379247t_unit,F),pi_fun1540376560t_unit(A,B)))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f1865816954t_unit(F,X_2)),hAPP_f151782958t_bool(B,X_2))) ) ) ).

tff(fact_556_Pi__mem,axiom,
    ! [X_2: fun_Pr2067565481t_bool,F: fun_fu562005862e_indi,A: fun_fu638310559l_bool,B: fun_fu2142850746i_bool] :
      ( hBOOL(hAPP_f679138160l_bool(hAPP_f1006969351l_bool(member1220706259e_indi,F),pi_fun1470523330e_indi(A,B)))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A))
       => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_f9587896e_indi(F,X_2)),hAPP_f2010315474i_bool(B,X_2))) ) ) ).

tff(fact_557_Pi__mem,axiom,
    ! [X_2: fun_Pr2067565481t_bool,F: fun_fu638310559l_bool,A: fun_fu638310559l_bool,B: fun_fu237781875l_bool] :
      ( hBOOL(hAPP_f1686510249l_bool(hAPP_f1930590713l_bool(member340585612l_bool,F),pi_fun1035089915l_bool(A,B)))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f52567537l_bool(F,X_2)),hAPP_f463104139l_bool(B,X_2))) ) ) ).

tff(fact_558_Pi__mem,axiom,
    ! [X_2: fun_Pr2067565481t_bool,F: fun_fu665686165t_unit,A: fun_fu638310559l_bool,B: fun_fu643686505t_bool] :
      ( hBOOL(hAPP_f1478188703l_bool(hAPP_f1329172965l_bool(member1729658242t_unit,F),pi_fun177985009t_unit(A,B)))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f801675751t_unit(F,X_2)),hAPP_f1400551297t_bool(B,X_2))) ) ) ).

tff(fact_559_Pi__mem,axiom,
    ! [X_2: nat,F: fun_na699243463e_indi,A: fun_nat_bool,B: fun_na2037635353i_bool] :
      ( hBOOL(hAPP_f736267217l_bool(hAPP_f707406409l_bool(member1530714804e_indi,F),pi_nat646417955e_indi(A,B)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
       => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_n1937165849e_indi(F,X_2)),hAPP_n34002993i_bool(B,X_2))) ) ) ).

tff(fact_560_Pi__mem,axiom,
    ! [X_2: nat,F: fun_nat_bool,A: fun_nat_bool,B: fun_na1469252690l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,F),pi_nat_bool(A,B)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(F,X_2)),hAPP_n1006566506l_bool(B,X_2))) ) ) ).

tff(fact_561_Pi__mem,axiom,
    ! [X_2: nat,F: fun_nat_Product_unit,A: fun_nat_bool,B: fun_na1041622088t_bool] :
      ( hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,F),pi_nat_Product_unit(A,B)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(F,X_2)),hAPP_n454528608t_bool(B,X_2))) ) ) ).

tff(fact_562_Pi__mem,axiom,
    ! [X_2: arrow_856714788e_indi,F: fun_Ar338949104le_alt,A: fun_Ar1809396326i_bool,B: fun_Ar274636406t_bool] :
      ( hBOOL(hAPP_f1754488902l_bool(hAPP_f766019597l_bool(member387840963le_alt,F),pi_Arr1460528004le_alt(A,B)))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A))
       => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A899858958le_alt(F,X_2)),hAPP_A1646126530t_bool(B,X_2))) ) ) ).

tff(fact_563_Pi__mem,axiom,
    ! [X_2: bool,F: fun_bo1682907689le_alt,A: fun_bool_bool,B: fun_bo1431306493t_bool] :
      ( hBOOL(hAPP_f1620711039l_bool(hAPP_f334747853l_bool(member684813948le_alt,F),pi_boo7125949le_alt(A,B)))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
       => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_b2094455111le_alt(F,X_2)),hAPP_b128655177t_bool(B,X_2))) ) ) ).

tff(fact_564_Pi__mem,axiom,
    ! [X_2: product_unit,F: fun_Pr2090226719le_alt,A: fun_Pr1643180309t_bool,B: fun_Pr1887398791t_bool] :
      ( hBOOL(hAPP_f684683381l_bool(hAPP_f41367117l_bool(member869664626le_alt,F),pi_Pro1820940723le_alt(A,B)))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
       => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_P396106045le_alt(F,X_2)),hAPP_P1914371027t_bool(B,X_2))) ) ) ).

tff(fact_565_Pi__mem,axiom,
    ! [X_2: arrow_856714788e_indi,F: fun_Ar624010239t_bool,A: fun_Ar1809396326i_bool,B: fun_Ar1998664965l_bool] :
      ( hBOOL(hAPP_f826064725l_bool(hAPP_f1364091725l_bool(member1124505298t_bool,F),pi_Arr2025169427t_bool(A,B)))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_A2107398813t_bool(F,X_2)),hAPP_A1411662545l_bool(B,X_2))) ) ) ).

tff(fact_566_Pi__mem,axiom,
    ! [X_2: bool,F: fun_bo1476023096t_bool,A: fun_bool_bool,B: fun_bo2107365004l_bool] :
      ( hBOOL(hAPP_f1605957262l_bool(hAPP_f1525863565l_bool(member344984203t_bool,F),pi_boo347863884t_bool(A,B)))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_b489616086t_bool(F,X_2)),hAPP_b1078573912l_bool(B,X_2))) ) ) ).

tff(fact_567_Pi__mem,axiom,
    ! [X_2: product_unit,F: fun_Pr1531194158t_bool,A: fun_Pr1643180309t_bool,B: fun_Pr537467670l_bool] :
      ( hBOOL(hAPP_f1851324036l_bool(hAPP_f1974966541l_bool(member364267905t_bool,F),pi_Pro782712642t_bool(A,B)))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_P913627340t_bool(F,X_2)),hAPP_P284783074l_bool(B,X_2))) ) ) ).

tff(fact_568_Pi__mem,axiom,
    ! [X_2: arrow_856714788e_indi,F: fun_Ar286530093t_bool,A: fun_Ar1809396326i_bool,B: fun_Ar1321653811l_bool] :
      ( hBOOL(hAPP_f686820739l_bool(hAPP_f692361165l_bool(member785631232t_bool,F),pi_Arr687740481t_bool(A,B)))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_A1378093259t_bool(F,X_2)),hAPP_A2084592127l_bool(B,X_2))) ) ) ).

tff(fact_569_Pi__mem,axiom,
    ! [X_2: bool,F: fun_bo559790694t_bool,A: fun_bool_bool,B: fun_bo1445676730l_bool] :
      ( hBOOL(hAPP_f1211446716l_bool(hAPP_f1134773005l_bool(member1782492345t_bool,F),pi_boo769613946t_bool(A,B)))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_b1029214724t_bool(F,X_2)),hAPP_b1777246598l_bool(B,X_2))) ) ) ).

tff(fact_570_Pi__mem,axiom,
    ! [X_2: product_unit,F: fun_Pr2016729180t_bool,A: fun_Pr1643180309t_bool,B: fun_Pr151242052l_bool] :
      ( hBOOL(hAPP_f2068478898l_bool(hAPP_f1883507597l_bool(member480326063t_bool,F),pi_Pro1533274736t_bool(A,B)))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_P1858715130t_bool(F,X_2)),hAPP_P283873808l_bool(B,X_2))) ) ) ).

tff(fact_571_Pi__mem,axiom,
    ! [X_2: bool,F: fun_bo1431306493t_bool,A: fun_bool_bool,B: fun_bo377688929l_bool] :
      ( hBOOL(hAPP_f398210311l_bool(hAPP_f416878261l_bool(member1133581546t_bool,F),pi_boo1111177555t_bool(A,B)))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_b128655177t_bool(F,X_2)),hAPP_b1272691967l_bool(B,X_2))) ) ) ).

tff(fact_572_Pi__mem,axiom,
    ! [X_2: product_unit,F: fun_Pr1887398791t_bool,A: fun_Pr1643180309t_bool,B: fun_Pr1791323223l_bool] :
      ( hBOOL(hAPP_f1426814865l_bool(hAPP_f1942212041l_bool(member803887220t_bool,F),pi_Pro1290680285t_bool(A,B)))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_P1914371027t_bool(F,X_2)),hAPP_P754918389l_bool(B,X_2))) ) ) ).

tff(fact_573_Pi__mem,axiom,
    ! [X_2: arrow_856714788e_indi,F: fun_Ar671024215di_nat,A: fun_Ar1809396326i_bool,B: fun_Ar603939593t_bool] :
      ( hBOOL(hAPP_f225240161l_bool(hAPP_f677301097l_bool(member1502495556di_nat,F),pi_Arr1233262509di_nat(A,B)))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A376526755di_nat(F,X_2)),hAPP_A1686943911t_bool(B,X_2))) ) ) ).

tff(fact_574_Pi__mem,axiom,
    ! [X_2: bool,F: fun_bool_nat,A: fun_bool_bool,B: fun_bo1570548802t_bool] :
      ( hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,F),pi_bool_nat(A,B)))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(F,X_2)),hAPP_b1013836512t_bool(B,X_2))) ) ) ).

tff(fact_575_Pi__mem,axiom,
    ! [X_2: product_unit,F: fun_Product_unit_nat,A: fun_Pr1643180309t_bool,B: fun_Pr1029464120t_bool] :
      ( hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,F),pi_Product_unit_nat(A,B)))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(F,X_2)),hAPP_P32877782t_bool(B,X_2))) ) ) ).

tff(fact_576_Pi__mem,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu2114379172t_bool,A: fun_fu3835832l_bool,B: fun_fu1863781882l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,F),pi_fun1746584570t_bool(A,B)))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_f2008608496t_bool(F,X_2)),hAPP_f1915815064l_bool(B,X_2))) ) ) ).

tff(fact_577_Pi__mem,axiom,
    ! [X_2: arrow_856714788e_indi,F: fun_Ar274636406t_bool,A: fun_Ar1809396326i_bool,B: fun_Ar1474557608l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,F),pi_Arr959578316t_bool(A,B)))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_A1646126530t_bool(F,X_2)),hAPP_A897398598l_bool(B,X_2))) ) ) ).

tff(fact_578_below__Lin,axiom,
    ! [L_3: fun_Pr2067565481t_bool,X_2: arrow_1893660431le_alt,Y_2: arrow_1893660431le_alt] :
      ( ( X_2 != Y_2 )
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,L_3),arrow_1361987423le_Lin))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,arrow_1525312447_below(L_3,X_2,Y_2)),arrow_1361987423le_Lin)) ) ) ).

tff(fact_579_Prof__def,axiom,
    arrow_5070731e_Prof = pi_Arr959578316t_bool(top_to788185952i_bool,hAPP_f1717907078l_bool(cOMBK_1520063231e_indi,arrow_1361987423le_Lin)) ).

tff(fact_580_inj__on__id2,axiom,
    ! [A: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(cOMBI_nat),A)) ).

tff(fact_581_funcset__mem,axiom,
    ! [X_2: produc472769767le_alt,F: fun_Pr2067565481t_bool,A: fun_Pr2067565481t_bool,B: fun_bool_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,F),pi_Pro1238944957t_bool(A,hAPP_f699791347l_bool(cOMBK_138598520le_alt,B))))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1178790471t_bool(F,X_2)),B)) ) ) ).

tff(fact_582_funcset__mem,axiom,
    ! [X_2: produc472769767le_alt,F: fun_Pr1509342064e_indi,A: fun_Pr2067565481t_bool,B: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f2124588998l_bool(hAPP_f1187850253l_bool(member1558233923e_indi,F),pi_Pro837265796e_indi(A,hAPP_f359069313i_bool(cOMBK_1987648063le_alt,B))))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A))
       => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_P276596750e_indi(F,X_2)),B)) ) ) ).

tff(fact_583_funcset__mem,axiom,
    ! [X_2: produc472769767le_alt,F: fun_Pr376858015t_unit,A: fun_Pr2067565481t_bool,B: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f1159856629l_bool(hAPP_f1700632141l_bool(member1303779570t_unit,F),pi_Pro346842291t_unit(A,hAPP_f723483871t_bool(cOMBK_751896174le_alt,B))))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1069491261t_unit(F,X_2)),B)) ) ) ).

tff(fact_584_funcset__mem,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu1929591039e_indi,A: fun_fu3835832l_bool,B: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f665932885l_bool(hAPP_f430646093l_bool(member282602450e_indi,F),pi_fun520512275e_indi(A,hAPP_f2022065970i_bool(cOMBK_818801614t_bool,B))))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A))
       => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_f602741661e_indi(F,X_2)),B)) ) ) ).

tff(fact_585_funcset__mem,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu3835832l_bool,A: fun_fu3835832l_bool,B: fun_bool_bool] :
      ( hBOOL(hAPP_f1867557646l_bool(hAPP_f1048573069l_bool(member1020280587l_bool,F),pi_fun853738700l_bool(A,hAPP_f1582869284l_bool(cOMBK_542452487t_bool,B))))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f995490902l_bool(F,X_2)),B)) ) ) ).

tff(fact_586_funcset__mem,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu1023022254t_unit,A: fun_fu3835832l_bool,B: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f115957764l_bool(hAPP_f1184790797l_bool(member2003579649t_unit,F),pi_fun1644711874t_unit(A,hAPP_f134177552t_bool(cOMBK_1220673277t_bool,B))))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f1775626572t_unit(F,X_2)),B)) ) ) ).

tff(fact_587_funcset__mem,axiom,
    ! [X_2: fun_fu2114379172t_bool,F: fun_fu748153389e_indi,A: fun_fu2098777574l_bool,B: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f2350467l_bool(hAPP_f1411422157l_bool(member1247254528e_indi,F),pi_fun1807454273e_indi(A,hAPP_f448050564i_bool(cOMBK_443335420t_bool,B))))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A))
       => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_f350323403e_indi(F,X_2)),B)) ) ) ).

tff(fact_588_funcset__mem,axiom,
    ! [X_2: fun_fu2114379172t_bool,F: fun_fu2098777574l_bool,A: fun_fu2098777574l_bool,B: fun_bool_bool] :
      ( hBOOL(hAPP_f2047920444l_bool(hAPP_f59810573l_bool(member1173995577l_bool,F),pi_fun1312540410l_bool(A,hAPP_f1152234870l_bool(cOMBK_1770320693t_bool,B))))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1572141188l_bool(F,X_2)),B)) ) ) ).

tff(fact_589_funcset__mem,axiom,
    ! [X_2: fun_fu2114379172t_bool,F: fun_fu1480298716t_unit,A: fun_fu2098777574l_bool,B: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f92582962l_bool(hAPP_f1494690701l_bool(member2091379247t_unit,F),pi_fun1540376560t_unit(A,hAPP_f1327693154t_bool(cOMBK_1385893163t_bool,B))))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f1865816954t_unit(F,X_2)),B)) ) ) ).

tff(fact_590_funcset__mem,axiom,
    ! [X_2: fun_Pr2067565481t_bool,F: fun_fu562005862e_indi,A: fun_fu638310559l_bool,B: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f679138160l_bool(hAPP_f1006969351l_bool(member1220706259e_indi,F),pi_fun1470523330e_indi(A,hAPP_f1128827177i_bool(cOMBK_814147665t_bool,B))))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A))
       => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_f9587896e_indi(F,X_2)),B)) ) ) ).

tff(fact_591_funcset__mem,axiom,
    ! [X_2: fun_Pr2067565481t_bool,F: fun_fu638310559l_bool,A: fun_fu638310559l_bool,B: fun_bool_bool] :
      ( hBOOL(hAPP_f1686510249l_bool(hAPP_f1930590713l_bool(member340585612l_bool,F),pi_fun1035089915l_bool(A,hAPP_f1713038057l_bool(cOMBK_118864600t_bool,B))))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f52567537l_bool(F,X_2)),B)) ) ) ).

tff(fact_592_funcset__mem,axiom,
    ! [X_2: fun_Pr2067565481t_bool,F: fun_fu665686165t_unit,A: fun_fu638310559l_bool,B: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f1478188703l_bool(hAPP_f1329172965l_bool(member1729658242t_unit,F),pi_fun177985009t_unit(A,hAPP_f168465001t_bool(cOMBK_14887266t_bool,B))))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f801675751t_unit(F,X_2)),B)) ) ) ).

tff(fact_593_funcset__mem,axiom,
    ! [X_2: nat,F: fun_na699243463e_indi,A: fun_nat_bool,B: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f736267217l_bool(hAPP_f707406409l_bool(member1530714804e_indi,F),pi_nat646417955e_indi(A,hAPP_f1549597448i_bool(cOMBK_341987762ol_nat,B))))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
       => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_n1937165849e_indi(F,X_2)),B)) ) ) ).

tff(fact_594_funcset__mem,axiom,
    ! [X_2: nat,F: fun_nat_bool,A: fun_nat_bool,B: fun_bool_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,F),pi_nat_bool(A,hAPP_f1579826888l_bool(cOMBK_623810489ol_nat,B))))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(F,X_2)),B)) ) ) ).

tff(fact_595_funcset__mem,axiom,
    ! [X_2: nat,F: fun_nat_Product_unit,A: fun_nat_bool,B: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,F),pi_nat_Product_unit(A,hAPP_f1539020360t_bool(cOMBK_649751363ol_nat,B))))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(F,X_2)),B)) ) ) ).

tff(fact_596_funcset__mem,axiom,
    ! [X_2: arrow_856714788e_indi,F: fun_Ar338949104le_alt,A: fun_Ar1809396326i_bool,B: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f1754488902l_bool(hAPP_f766019597l_bool(member387840963le_alt,F),pi_Arr1460528004le_alt(A,hAPP_f480276746t_bool(cOMBK_1650320063e_indi,B))))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A))
       => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A899858958le_alt(F,X_2)),B)) ) ) ).

tff(fact_597_funcset__mem,axiom,
    ! [X_2: bool,F: fun_bo1682907689le_alt,A: fun_bool_bool,B: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f1620711039l_bool(hAPP_f334747853l_bool(member684813948le_alt,F),pi_boo7125949le_alt(A,hAPP_f1723896209t_bool(cOMBK_5056120l_bool,B))))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
       => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_b2094455111le_alt(F,X_2)),B)) ) ) ).

tff(fact_598_funcset__mem,axiom,
    ! [X_2: product_unit,F: fun_Pr2090226719le_alt,A: fun_Pr1643180309t_bool,B: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f684683381l_bool(hAPP_f41367117l_bool(member869664626le_alt,F),pi_Pro1820940723le_alt(A,hAPP_f15777819t_bool(cOMBK_681766254t_unit,B))))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
       => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_P396106045le_alt(F,X_2)),B)) ) ) ).

tff(fact_599_funcset__mem,axiom,
    ! [X_2: arrow_856714788e_indi,F: fun_Ar624010239t_bool,A: fun_Ar1809396326i_bool,B: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f826064725l_bool(hAPP_f1364091725l_bool(member1124505298t_bool,F),pi_Arr2025169427t_bool(A,hAPP_f1352816552l_bool(cOMBK_1255579598e_indi,B))))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_A2107398813t_bool(F,X_2)),B)) ) ) ).

tff(fact_600_funcset__mem,axiom,
    ! [X_2: bool,F: fun_bo1476023096t_bool,A: fun_bool_bool,B: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f1605957262l_bool(hAPP_f1525863565l_bool(member344984203t_bool,F),pi_boo347863884t_bool(A,hAPP_f1322579375l_bool(cOMBK_317366791l_bool,B))))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_b489616086t_bool(F,X_2)),B)) ) ) ).

tff(fact_601_funcset__mem,axiom,
    ! [X_2: product_unit,F: fun_Pr1531194158t_bool,A: fun_Pr1643180309t_bool,B: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f1851324036l_bool(hAPP_f1974966541l_bool(member364267905t_bool,F),pi_Pro782712642t_bool(A,hAPP_f1482764601l_bool(cOMBK_708287485t_unit,B))))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_P913627340t_bool(F,X_2)),B)) ) ) ).

tff(fact_602_funcset__mem,axiom,
    ! [X_2: arrow_856714788e_indi,F: fun_Ar286530093t_bool,A: fun_Ar1809396326i_bool,B: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f686820739l_bool(hAPP_f692361165l_bool(member785631232t_bool,F),pi_Arr687740481t_bool(A,hAPP_f258290692l_bool(cOMBK_1514079484e_indi,B))))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_A1378093259t_bool(F,X_2)),B)) ) ) ).

tff(fact_603_funcset__mem,axiom,
    ! [X_2: bool,F: fun_bo559790694t_bool,A: fun_bool_bool,B: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f1211446716l_bool(hAPP_f1134773005l_bool(member1782492345t_bool,F),pi_boo769613946t_bool(A,hAPP_f369767947l_bool(cOMBK_2030738485l_bool,B))))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_b1029214724t_bool(F,X_2)),B)) ) ) ).

tff(fact_604_funcset__mem,axiom,
    ! [X_2: product_unit,F: fun_Pr2016729180t_bool,A: fun_Pr1643180309t_bool,B: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f2068478898l_bool(hAPP_f1883507597l_bool(member480326063t_bool,F),pi_Pro1533274736t_bool(A,hAPP_f956752277l_bool(cOMBK_1075760171t_unit,B))))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_P1858715130t_bool(F,X_2)),B)) ) ) ).

tff(fact_605_funcset__mem,axiom,
    ! [X_2: bool,F: fun_bo1431306493t_bool,A: fun_bool_bool,B: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f398210311l_bool(hAPP_f416878261l_bool(member1133581546t_bool,F),pi_boo1111177555t_bool(A,hAPP_f86272063l_bool(cOMBK_650639032l_bool,B))))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_b128655177t_bool(F,X_2)),B)) ) ) ).

tff(fact_606_funcset__mem,axiom,
    ! [X_2: product_unit,F: fun_Pr1887398791t_bool,A: fun_Pr1643180309t_bool,B: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f1426814865l_bool(hAPP_f1942212041l_bool(member803887220t_bool,F),pi_Pro1290680285t_bool(A,hAPP_f502523701l_bool(cOMBK_1521810862t_unit,B))))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_P1914371027t_bool(F,X_2)),B)) ) ) ).

tff(fact_607_funcset__mem,axiom,
    ! [X_2: arrow_856714788e_indi,F: fun_Ar671024215di_nat,A: fun_Ar1809396326i_bool,B: fun_nat_bool] :
      ( hBOOL(hAPP_f225240161l_bool(hAPP_f677301097l_bool(member1502495556di_nat,F),pi_Arr1233262509di_nat(A,hAPP_f1132083526t_bool(cOMBK_833041760e_indi,B))))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A376526755di_nat(F,X_2)),B)) ) ) ).

tff(fact_608_funcset__mem,axiom,
    ! [X_2: bool,F: fun_bool_nat,A: fun_bool_bool,B: fun_nat_bool] :
      ( hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,F),pi_bool_nat(A,hAPP_f1247925759t_bool(cOMBK_1034797721l_bool,B))))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(F,X_2)),B)) ) ) ).

tff(fact_609_funcset__mem,axiom,
    ! [X_2: product_unit,F: fun_Product_unit_nat,A: fun_Pr1643180309t_bool,B: fun_nat_bool] :
      ( hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,F),pi_Product_unit_nat(A,hAPP_f1212412661t_bool(cOMBK_356206223t_unit,B))))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(F,X_2)),B)) ) ) ).

tff(fact_610_funcset__mem,axiom,
    ! [X_2: fun_Ar274636406t_bool,F: fun_fu2114379172t_bool,A: fun_fu3835832l_bool,B: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,F),pi_fun1746584570t_bool(A,hAPP_f1104294872l_bool(cOMBK_1701906001t_bool,B))))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_f2008608496t_bool(F,X_2)),B)) ) ) ).

tff(fact_611_funcset__mem,axiom,
    ! [X_2: arrow_856714788e_indi,F: fun_Ar274636406t_bool,A: fun_Ar1809396326i_bool,B: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,F),pi_Arr959578316t_bool(A,hAPP_f1717907078l_bool(cOMBK_1520063231e_indi,B))))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_A1646126530t_bool(F,X_2)),B)) ) ) ).

tff(fact_612_inj__eq,axiom,
    ! [X_2: arrow_856714788e_indi,Y_2: arrow_856714788e_indi,F: fun_Ar671024215di_nat] :
      ( hBOOL(hAPP_f584385070l_bool(inj_on1960344199di_nat(F),top_to788185952i_bool))
     => ( ( hAPP_A376526755di_nat(F,X_2) = hAPP_A376526755di_nat(F,Y_2) )
      <=> ( X_2 = Y_2 ) ) ) ).

tff(fact_613_inj__eq,axiom,
    ! [X_2: nat,Y_2: nat,F: fun_nat_nat] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool))
     => ( ( hAPP_nat_nat(F,X_2) = hAPP_nat_nat(F,Y_2) )
      <=> ( X_2 = Y_2 ) ) ) ).

tff(fact_614_injD,axiom,
    ! [X_2: arrow_856714788e_indi,Y_2: arrow_856714788e_indi,F: fun_Ar671024215di_nat] :
      ( hBOOL(hAPP_f584385070l_bool(inj_on1960344199di_nat(F),top_to788185952i_bool))
     => ( ( hAPP_A376526755di_nat(F,X_2) = hAPP_A376526755di_nat(F,Y_2) )
       => ( X_2 = Y_2 ) ) ) ).

tff(fact_615_injD,axiom,
    ! [X_2: nat,Y_2: nat,F: fun_nat_nat] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool))
     => ( ( hAPP_nat_nat(F,X_2) = hAPP_nat_nat(F,Y_2) )
       => ( X_2 = Y_2 ) ) ) ).

tff(fact_616_inv__into__f__f,axiom,
    ! [X_2: arrow_856714788e_indi,F: fun_Ar671024215di_nat,A: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(inj_on1960344199di_nat(F),A))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A))
       => ( hAPP_n1937165849e_indi(hilber1580028780di_nat(A,F),hAPP_A376526755di_nat(F,X_2)) = X_2 ) ) ) ).

tff(fact_617_inv__into__f__f,axiom,
    ! [X_2: nat,F: fun_nat_nat,A: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
       => ( hAPP_nat_nat(hilber195283148at_nat(A,F),hAPP_nat_nat(F,X_2)) = X_2 ) ) ) ).

tff(fact_618_inv__into__f__eq,axiom,
    ! [Y_2: nat,X_2: arrow_856714788e_indi,F: fun_Ar671024215di_nat,A: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(inj_on1960344199di_nat(F),A))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_2),A))
       => ( ( hAPP_A376526755di_nat(F,X_2) = Y_2 )
         => ( hAPP_n1937165849e_indi(hilber1580028780di_nat(A,F),Y_2) = X_2 ) ) ) ) ).

tff(fact_619_inv__into__f__eq,axiom,
    ! [Y_2: nat,X_2: nat,F: fun_nat_nat,A: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
       => ( ( hAPP_nat_nat(F,X_2) = Y_2 )
         => ( hAPP_nat_nat(hilber195283148at_nat(A,F),Y_2) = X_2 ) ) ) ) ).

tff(fact_620_Pi__I,axiom,
    ! [F: fun_Pr1509342064e_indi,B: fun_Pr895221296i_bool,A: fun_Pr2067565481t_bool] :
      ( ! [X_1: produc472769767le_alt] :
          ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_1),A))
         => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_P276596750e_indi(F,X_1)),hAPP_P1859429372i_bool(B,X_1))) )
     => hBOOL(hAPP_f2124588998l_bool(hAPP_f1187850253l_bool(member1558233923e_indi,F),pi_Pro837265796e_indi(A,B))) ) ).

tff(fact_621_Pi__I,axiom,
    ! [F: fun_Pr376858015t_unit,B: fun_Pr1069395679t_bool,A: fun_Pr2067565481t_bool] :
      ( ! [X_1: produc472769767le_alt] :
          ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_1),A))
         => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P1069491261t_unit(F,X_1)),hAPP_P2037731755t_bool(B,X_1))) )
     => hBOOL(hAPP_f1159856629l_bool(hAPP_f1700632141l_bool(member1303779570t_unit,F),pi_Pro346842291t_unit(A,B))) ) ).

tff(fact_622_Pi__I,axiom,
    ! [F: fun_fu1929591039e_indi,B: fun_fu223278561i_bool,A: fun_fu3835832l_bool] :
      ( ! [X_1: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),A))
         => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_f602741661e_indi(F,X_1)),hAPP_f391644589i_bool(B,X_1))) )
     => hBOOL(hAPP_f665932885l_bool(hAPP_f430646093l_bool(member282602450e_indi,F),pi_fun520512275e_indi(A,B))) ) ).

tff(fact_623_Pi__I,axiom,
    ! [F: fun_fu3835832l_bool,B: fun_fu916327706l_bool,A: fun_fu3835832l_bool] :
      ( ! [X_1: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),A))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f995490902l_bool(F,X_1)),hAPP_f1676084198l_bool(B,X_1))) )
     => hBOOL(hAPP_f1867557646l_bool(hAPP_f1048573069l_bool(member1020280587l_bool,F),pi_fun853738700l_bool(A,B))) ) ).

tff(fact_624_Pi__I,axiom,
    ! [F: fun_fu1023022254t_unit,B: fun_fu1734317328t_bool,A: fun_fu3835832l_bool] :
      ( ! [X_1: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),A))
         => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f1775626572t_unit(F,X_1)),hAPP_f1438163420t_bool(B,X_1))) )
     => hBOOL(hAPP_f115957764l_bool(hAPP_f1184790797l_bool(member2003579649t_unit,F),pi_fun1644711874t_unit(A,B))) ) ).

tff(fact_625_Pi__I,axiom,
    ! [F: fun_fu748153389e_indi,B: fun_fu2109152051i_bool,A: fun_fu2098777574l_bool] :
      ( ! [X_1: fun_fu2114379172t_bool] :
          ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_1),A))
         => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_f350323403e_indi(F,X_1)),hAPP_f399308031i_bool(B,X_1))) )
     => hBOOL(hAPP_f2350467l_bool(hAPP_f1411422157l_bool(member1247254528e_indi,F),pi_fun1807454273e_indi(A,B))) ) ).

tff(fact_626_Pi__I,axiom,
    ! [F: fun_fu2098777574l_bool,B: fun_fu1522163052l_bool,A: fun_fu2098777574l_bool] :
      ( ! [X_1: fun_fu2114379172t_bool] :
          ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_1),A))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1572141188l_bool(F,X_1)),hAPP_f414129720l_bool(B,X_1))) )
     => hBOOL(hAPP_f2047920444l_bool(hAPP_f59810573l_bool(member1173995577l_bool,F),pi_fun1312540410l_bool(A,B))) ) ).

tff(fact_627_Pi__I,axiom,
    ! [F: fun_fu1480298716t_unit,B: fun_fu1143287650t_bool,A: fun_fu2098777574l_bool] :
      ( ! [X_1: fun_fu2114379172t_bool] :
          ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_1),A))
         => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f1865816954t_unit(F,X_1)),hAPP_f151782958t_bool(B,X_1))) )
     => hBOOL(hAPP_f92582962l_bool(hAPP_f1494690701l_bool(member2091379247t_unit,F),pi_fun1540376560t_unit(A,B))) ) ).

tff(fact_628_Pi__I,axiom,
    ! [F: fun_fu562005862e_indi,B: fun_fu2142850746i_bool,A: fun_fu638310559l_bool] :
      ( ! [X_1: fun_Pr2067565481t_bool] :
          ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_1),A))
         => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_f9587896e_indi(F,X_1)),hAPP_f2010315474i_bool(B,X_1))) )
     => hBOOL(hAPP_f679138160l_bool(hAPP_f1006969351l_bool(member1220706259e_indi,F),pi_fun1470523330e_indi(A,B))) ) ).

tff(fact_629_Pi__I,axiom,
    ! [F: fun_fu638310559l_bool,B: fun_fu237781875l_bool,A: fun_fu638310559l_bool] :
      ( ! [X_1: fun_Pr2067565481t_bool] :
          ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_1),A))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f52567537l_bool(F,X_1)),hAPP_f463104139l_bool(B,X_1))) )
     => hBOOL(hAPP_f1686510249l_bool(hAPP_f1930590713l_bool(member340585612l_bool,F),pi_fun1035089915l_bool(A,B))) ) ).

tff(fact_630_Pi__I,axiom,
    ! [F: fun_fu665686165t_unit,B: fun_fu643686505t_bool,A: fun_fu638310559l_bool] :
      ( ! [X_1: fun_Pr2067565481t_bool] :
          ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_1),A))
         => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f801675751t_unit(F,X_1)),hAPP_f1400551297t_bool(B,X_1))) )
     => hBOOL(hAPP_f1478188703l_bool(hAPP_f1329172965l_bool(member1729658242t_unit,F),pi_fun177985009t_unit(A,B))) ) ).

tff(fact_631_Pi__I,axiom,
    ! [F: fun_na699243463e_indi,B: fun_na2037635353i_bool,A: fun_nat_bool] :
      ( ! [X_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
         => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,hAPP_n1937165849e_indi(F,X_1)),hAPP_n34002993i_bool(B,X_1))) )
     => hBOOL(hAPP_f736267217l_bool(hAPP_f707406409l_bool(member1530714804e_indi,F),pi_nat646417955e_indi(A,B))) ) ).

tff(fact_632_Pi__I,axiom,
    ! [F: fun_nat_bool,B: fun_na1469252690l_bool,A: fun_nat_bool] :
      ( ! [X_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(F,X_1)),hAPP_n1006566506l_bool(B,X_1))) )
     => hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,F),pi_nat_bool(A,B))) ) ).

tff(fact_633_Pi__I,axiom,
    ! [F: fun_nat_Product_unit,B: fun_na1041622088t_bool,A: fun_nat_bool] :
      ( ! [X_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
         => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(F,X_1)),hAPP_n454528608t_bool(B,X_1))) )
     => hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,F),pi_nat_Product_unit(A,B))) ) ).

tff(fact_634_Pi__I,axiom,
    ! [F: fun_Ar338949104le_alt,B: fun_Ar274636406t_bool,A: fun_Ar1809396326i_bool] :
      ( ! [X_1: arrow_856714788e_indi] :
          ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_1),A))
         => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A899858958le_alt(F,X_1)),hAPP_A1646126530t_bool(B,X_1))) )
     => hBOOL(hAPP_f1754488902l_bool(hAPP_f766019597l_bool(member387840963le_alt,F),pi_Arr1460528004le_alt(A,B))) ) ).

tff(fact_635_Pi__I,axiom,
    ! [F: fun_bo1682907689le_alt,B: fun_bo1431306493t_bool,A: fun_bool_bool] :
      ( ! [X_1: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A))
         => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_b2094455111le_alt(F,X_1)),hAPP_b128655177t_bool(B,X_1))) )
     => hBOOL(hAPP_f1620711039l_bool(hAPP_f334747853l_bool(member684813948le_alt,F),pi_boo7125949le_alt(A,B))) ) ).

tff(fact_636_Pi__I,axiom,
    ! [F: fun_Pr2090226719le_alt,B: fun_Pr1887398791t_bool,A: fun_Pr1643180309t_bool] :
      ( ! [X_1: product_unit] :
          ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_1),A))
         => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_P396106045le_alt(F,X_1)),hAPP_P1914371027t_bool(B,X_1))) )
     => hBOOL(hAPP_f684683381l_bool(hAPP_f41367117l_bool(member869664626le_alt,F),pi_Pro1820940723le_alt(A,B))) ) ).

tff(fact_637_Pi__I,axiom,
    ! [F: fun_Ar624010239t_bool,B: fun_Ar1998664965l_bool,A: fun_Ar1809396326i_bool] :
      ( ! [X_1: arrow_856714788e_indi] :
          ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_1),A))
         => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_A2107398813t_bool(F,X_1)),hAPP_A1411662545l_bool(B,X_1))) )
     => hBOOL(hAPP_f826064725l_bool(hAPP_f1364091725l_bool(member1124505298t_bool,F),pi_Arr2025169427t_bool(A,B))) ) ).

tff(fact_638_Pi__I,axiom,
    ! [F: fun_bo1476023096t_bool,B: fun_bo2107365004l_bool,A: fun_bool_bool] :
      ( ! [X_1: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A))
         => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_b489616086t_bool(F,X_1)),hAPP_b1078573912l_bool(B,X_1))) )
     => hBOOL(hAPP_f1605957262l_bool(hAPP_f1525863565l_bool(member344984203t_bool,F),pi_boo347863884t_bool(A,B))) ) ).

tff(fact_639_Pi__I,axiom,
    ! [F: fun_Pr1531194158t_bool,B: fun_Pr537467670l_bool,A: fun_Pr1643180309t_bool] :
      ( ! [X_1: product_unit] :
          ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_1),A))
         => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,hAPP_P913627340t_bool(F,X_1)),hAPP_P284783074l_bool(B,X_1))) )
     => hBOOL(hAPP_f1851324036l_bool(hAPP_f1974966541l_bool(member364267905t_bool,F),pi_Pro782712642t_bool(A,B))) ) ).

tff(fact_640_Pi__I,axiom,
    ! [F: fun_Ar286530093t_bool,B: fun_Ar1321653811l_bool,A: fun_Ar1809396326i_bool] :
      ( ! [X_1: arrow_856714788e_indi] :
          ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_1),A))
         => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_A1378093259t_bool(F,X_1)),hAPP_A2084592127l_bool(B,X_1))) )
     => hBOOL(hAPP_f686820739l_bool(hAPP_f692361165l_bool(member785631232t_bool,F),pi_Arr687740481t_bool(A,B))) ) ).

tff(fact_641_Pi__I,axiom,
    ! [F: fun_bo559790694t_bool,B: fun_bo1445676730l_bool,A: fun_bool_bool] :
      ( ! [X_1: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A))
         => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_b1029214724t_bool(F,X_1)),hAPP_b1777246598l_bool(B,X_1))) )
     => hBOOL(hAPP_f1211446716l_bool(hAPP_f1134773005l_bool(member1782492345t_bool,F),pi_boo769613946t_bool(A,B))) ) ).

tff(fact_642_Pi__I,axiom,
    ! [F: fun_Pr2016729180t_bool,B: fun_Pr151242052l_bool,A: fun_Pr1643180309t_bool] :
      ( ! [X_1: product_unit] :
          ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_1),A))
         => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,hAPP_P1858715130t_bool(F,X_1)),hAPP_P283873808l_bool(B,X_1))) )
     => hBOOL(hAPP_f2068478898l_bool(hAPP_f1883507597l_bool(member480326063t_bool,F),pi_Pro1533274736t_bool(A,B))) ) ).

tff(fact_643_Pi__I,axiom,
    ! [F: fun_bo1431306493t_bool,B: fun_bo377688929l_bool,A: fun_bool_bool] :
      ( ! [X_1: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A))
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_b128655177t_bool(F,X_1)),hAPP_b1272691967l_bool(B,X_1))) )
     => hBOOL(hAPP_f398210311l_bool(hAPP_f416878261l_bool(member1133581546t_bool,F),pi_boo1111177555t_bool(A,B))) ) ).

tff(fact_644_Pi__I,axiom,
    ! [F: fun_Pr1887398791t_bool,B: fun_Pr1791323223l_bool,A: fun_Pr1643180309t_bool] :
      ( ! [X_1: product_unit] :
          ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_1),A))
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_P1914371027t_bool(F,X_1)),hAPP_P754918389l_bool(B,X_1))) )
     => hBOOL(hAPP_f1426814865l_bool(hAPP_f1942212041l_bool(member803887220t_bool,F),pi_Pro1290680285t_bool(A,B))) ) ).

tff(fact_645_Pi__I,axiom,
    ! [F: fun_Ar671024215di_nat,B: fun_Ar603939593t_bool,A: fun_Ar1809396326i_bool] :
      ( ! [X_1: arrow_856714788e_indi] :
          ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_1),A))
         => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A376526755di_nat(F,X_1)),hAPP_A1686943911t_bool(B,X_1))) )
     => hBOOL(hAPP_f225240161l_bool(hAPP_f677301097l_bool(member1502495556di_nat,F),pi_Arr1233262509di_nat(A,B))) ) ).

tff(fact_646_Pi__I,axiom,
    ! [F: fun_bool_nat,B: fun_bo1570548802t_bool,A: fun_bool_bool] :
      ( ! [X_1: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A))
         => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(F,X_1)),hAPP_b1013836512t_bool(B,X_1))) )
     => hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,F),pi_bool_nat(A,B))) ) ).

tff(fact_647_Pi__I,axiom,
    ! [F: fun_Product_unit_nat,B: fun_Pr1029464120t_bool,A: fun_Pr1643180309t_bool] :
      ( ! [X_1: product_unit] :
          ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_1),A))
         => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(F,X_1)),hAPP_P32877782t_bool(B,X_1))) )
     => hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,F),pi_Product_unit_nat(A,B))) ) ).

tff(fact_648_Pi__I,axiom,
    ! [F: fun_Pr2067565481t_bool,B: fun_Pr1780397033l_bool,A: fun_Pr2067565481t_bool] :
      ( ! [X_1: produc472769767le_alt] :
          ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_1),A))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1178790471t_bool(F,X_1)),hAPP_P1103642805l_bool(B,X_1))) )
     => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,F),pi_Pro1238944957t_bool(A,B))) ) ).

tff(fact_649_Pi__I,axiom,
    ! [F: fun_fu2114379172t_bool,B: fun_fu1863781882l_bool,A: fun_fu3835832l_bool] :
      ( ! [X_1: fun_Ar274636406t_bool] :
          ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_1),A))
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_f2008608496t_bool(F,X_1)),hAPP_f1915815064l_bool(B,X_1))) )
     => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,F),pi_fun1746584570t_bool(A,B))) ) ).

tff(fact_650_Pi__I,axiom,
    ! [F: fun_Ar274636406t_bool,B: fun_Ar1474557608l_bool,A: fun_Ar1809396326i_bool] :
      ( ! [X_1: arrow_856714788e_indi] :
          ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,X_1),A))
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,hAPP_A1646126530t_bool(F,X_1)),hAPP_A897398598l_bool(B,X_1))) )
     => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,F),pi_Arr959578316t_bool(A,B))) ) ).

tff(fact_651_inj__imp__inv__eq,axiom,
    ! [G: fun_na699243463e_indi,F: fun_Ar671024215di_nat] :
      ( hBOOL(hAPP_f584385070l_bool(inj_on1960344199di_nat(F),top_to788185952i_bool))
     => ( ! [X_1: nat] : ( hAPP_A376526755di_nat(F,hAPP_n1937165849e_indi(G,X_1)) = X_1 )
       => ( hilber1580028780di_nat(top_to788185952i_bool,F) = G ) ) ) ).

tff(fact_652_inj__imp__inv__eq,axiom,
    ! [G: fun_nat_nat,F: fun_nat_nat] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool))
     => ( ! [X_1: nat] : ( hAPP_nat_nat(F,hAPP_nat_nat(G,X_1)) = X_1 )
       => ( hilber195283148at_nat(top_top_fun_nat_bool,F) = G ) ) ) ).

tff(fact_653_less__add__one,axiom,
    ! [A_18: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_18),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_18),one_one_nat))) ).

tff(fact_654_add__less__le__mono,axiom,
    ! [C_16: nat,D_3: nat,A_17: nat,B_16: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_17),B_16))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_16),D_3))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_17),C_16)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_16),D_3))) ) ) ).

tff(fact_655_add__le__less__mono,axiom,
    ! [C_15: nat,D_2: nat,A_16: nat,B_15: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_16),B_15))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_15),D_2))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_16),C_15)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_15),D_2))) ) ) ).

tff(fact_656_injI,axiom,
    ! [F: fun_Ar671024215di_nat] :
      ( ! [X_1: arrow_856714788e_indi,Y_1: arrow_856714788e_indi] :
          ( ( hAPP_A376526755di_nat(F,X_1) = hAPP_A376526755di_nat(F,Y_1) )
         => ( X_1 = Y_1 ) )
     => hBOOL(hAPP_f584385070l_bool(inj_on1960344199di_nat(F),top_to788185952i_bool)) ) ).

tff(fact_657_injI,axiom,
    ! [F: fun_nat_nat] :
      ( ! [X_1: nat,Y_1: nat] :
          ( ( hAPP_nat_nat(F,X_1) = hAPP_nat_nat(F,Y_1) )
         => ( X_1 = Y_1 ) )
     => hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool)) ) ).

tff(fact_658_xt5,axiom,
    ! [Ca: fun_nat_bool,F: fun_fu821463397t_bool,Ba: fun_nat_bool,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),hAPP_f800510211t_bool(F,Ba)))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Y_1)),hAPP_f800510211t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f800510211t_bool(F,Aa))) ) ) ) ).

tff(fact_659_xt5,axiom,
    ! [Ca: fun_nat_bool,F: fun_fu988033326t_bool,Ba: fun_Pr1643180309t_bool,Aa: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),hAPP_f543204480t_bool(F,Ba)))
       => ( ! [X_1: fun_Pr1643180309t_bool,Y_1: fun_Pr1643180309t_bool] :
              ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Y_1)),hAPP_f543204480t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f543204480t_bool(F,Aa))) ) ) ) ).

tff(fact_660_xt5,axiom,
    ! [Ca: fun_nat_bool,F: fun_fu1254370943t_bool,Ba: fun_Ar1809396326i_bool,Aa: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Ba),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),hAPP_f622418129t_bool(F,Ba)))
       => ( ! [X_1: fun_Ar1809396326i_bool,Y_1: fun_Ar1809396326i_bool] :
              ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f622418129t_bool(F,Y_1)),hAPP_f622418129t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f622418129t_bool(F,Aa))) ) ) ) ).

tff(fact_661_xt5,axiom,
    ! [Ca: fun_nat_bool,F: fun_nat_fun_nat_bool,Ba: nat,Aa: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),hAPP_n1699378549t_bool(F,Ba)))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Y_1)),hAPP_n1699378549t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_n1699378549t_bool(F,Aa))) ) ) ) ).

tff(fact_662_xt5,axiom,
    ! [Ca: fun_Pr1643180309t_bool,F: fun_na1041622088t_bool,Ba: nat,Aa: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ca),hAPP_n454528608t_bool(F,Ba)))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Y_1)),hAPP_n454528608t_bool(F,X_1))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),hAPP_n454528608t_bool(F,Aa))) ) ) ) ).

tff(fact_663_xt5,axiom,
    ! [Ca: fun_Ar1809396326i_bool,F: fun_na2037635353i_bool,Ba: nat,Aa: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Ca),hAPP_n34002993i_bool(F,Ba)))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,hAPP_n34002993i_bool(F,Y_1)),hAPP_n34002993i_bool(F,X_1))) )
         => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Ca),hAPP_n34002993i_bool(F,Aa))) ) ) ) ).

tff(fact_664_xt5,axiom,
    ! [Ca: fun_fu638310559l_bool,F: fun_na144630978l_bool,Ba: nat,Aa: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Ca),hAPP_n1134275860l_bool(F,Ba)))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,hAPP_n1134275860l_bool(F,Y_1)),hAPP_n1134275860l_bool(F,X_1))) )
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,Ca),hAPP_n1134275860l_bool(F,Aa))) ) ) ) ).

tff(fact_665_xt5,axiom,
    ! [Ca: fun_fu2098777574l_bool,F: fun_na138495129l_bool,Ba: nat,Aa: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Ca),hAPP_n1555388849l_bool(F,Ba)))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,hAPP_n1555388849l_bool(F,Y_1)),hAPP_n1555388849l_bool(F,X_1))) )
         => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,Ca),hAPP_n1555388849l_bool(F,Aa))) ) ) ) ).

tff(fact_666_xt5,axiom,
    ! [Ca: fun_fu3835832l_bool,F: fun_na6909291l_bool,Ba: nat,Aa: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Ca),hAPP_n2125602947l_bool(F,Ba)))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,hAPP_n2125602947l_bool(F,Y_1)),hAPP_n2125602947l_bool(F,X_1))) )
         => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,Ca),hAPP_n2125602947l_bool(F,Aa))) ) ) ) ).

tff(fact_667_xt5,axiom,
    ! [Ca: fun_Pr2067565481t_bool,F: fun_na998785244t_bool,Ba: nat,Aa: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Ca),hAPP_n1161265524t_bool(F,Ba)))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,hAPP_n1161265524t_bool(F,Y_1)),hAPP_n1161265524t_bool(F,X_1))) )
         => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,Ca),hAPP_n1161265524t_bool(F,Aa))) ) ) ) ).

tff(fact_668_xt5,axiom,
    ! [Ca: bool,F: fun_nat_bool,Ba: nat,Aa: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),hAPP_nat_bool(F,Ba)))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Y_1)),hAPP_nat_bool(F,X_1))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ca),hAPP_nat_bool(F,Aa))) ) ) ) ).

tff(fact_669_xt5,axiom,
    ! [Ca: fun_Ar331856045t_bool,F: fun_na300967376t_bool,Ba: nat,Aa: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Aa))
     => ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Ca),hAPP_n1312530466t_bool(F,Ba)))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,hAPP_n1312530466t_bool(F,Y_1)),hAPP_n1312530466t_bool(F,X_1))) )
         => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,Ca),hAPP_n1312530466t_bool(F,Aa))) ) ) ) ).

tff(fact_670_xt5,axiom,
    ! [Ca: nat,F: fun_fun_nat_bool_nat,Ba: fun_nat_bool,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),hAPP_f22106695ol_nat(F,Ba)))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_1),X_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(F,Y_1)),hAPP_f22106695ol_nat(F,X_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f22106695ol_nat(F,Aa))) ) ) ) ).

tff(fact_671_xt5,axiom,
    ! [Ca: nat,F: fun_fu572628082ol_nat,Ba: fun_Pr1643180309t_bool,Aa: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),hAPP_f2030293770ol_nat(F,Ba)))
       => ( ! [X_1: fun_Pr1643180309t_bool,Y_1: fun_Pr1643180309t_bool] :
              ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_1),X_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Y_1)),hAPP_f2030293770ol_nat(F,X_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f2030293770ol_nat(F,Aa))) ) ) ) ).

tff(fact_672_xt5,axiom,
    ! [Ca: nat,F: fun_fu1603738721ol_nat,Ba: fun_Ar1809396326i_bool,Aa: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Ba),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),hAPP_f846027769ol_nat(F,Ba)))
       => ( ! [X_1: fun_Ar1809396326i_bool,Y_1: fun_Ar1809396326i_bool] :
              ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Y_1),X_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f846027769ol_nat(F,Y_1)),hAPP_f846027769ol_nat(F,X_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f846027769ol_nat(F,Aa))) ) ) ) ).

tff(fact_673_xt7,axiom,
    ! [Ca: fun_nat_bool,F: fun_nat_fun_nat_bool,Ba: nat,Aa: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_n1699378549t_bool(F,Ba)))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,Y_1)),hAPP_n1699378549t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_n1699378549t_bool(F,Aa))) ) ) ) ).

tff(fact_674_xt7,axiom,
    ! [Ca: fun_Pr1643180309t_bool,F: fun_na1041622088t_bool,Ba: nat,Aa: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),hAPP_n454528608t_bool(F,Ba)))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(F,Y_1)),hAPP_n454528608t_bool(F,X_1))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),hAPP_n454528608t_bool(F,Aa))) ) ) ) ).

tff(fact_675_xt7,axiom,
    ! [Ca: fun_Ar1809396326i_bool,F: fun_na2037635353i_bool,Ba: nat,Aa: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Ca),hAPP_n34002993i_bool(F,Ba)))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,hAPP_n34002993i_bool(F,Y_1)),hAPP_n34002993i_bool(F,X_1))) )
         => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Ca),hAPP_n34002993i_bool(F,Aa))) ) ) ) ).

tff(fact_676_xt7,axiom,
    ! [Ca: fun_fu638310559l_bool,F: fun_na144630978l_bool,Ba: nat,Aa: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,Ca),hAPP_n1134275860l_bool(F,Ba)))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,hAPP_n1134275860l_bool(F,Y_1)),hAPP_n1134275860l_bool(F,X_1))) )
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,Ca),hAPP_n1134275860l_bool(F,Aa))) ) ) ) ).

tff(fact_677_xt7,axiom,
    ! [Ca: fun_fu2098777574l_bool,F: fun_na138495129l_bool,Ba: nat,Aa: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,Ca),hAPP_n1555388849l_bool(F,Ba)))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,hAPP_n1555388849l_bool(F,Y_1)),hAPP_n1555388849l_bool(F,X_1))) )
         => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,Ca),hAPP_n1555388849l_bool(F,Aa))) ) ) ) ).

tff(fact_678_xt7,axiom,
    ! [Ca: fun_fu3835832l_bool,F: fun_na6909291l_bool,Ba: nat,Aa: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,Ca),hAPP_n2125602947l_bool(F,Ba)))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,hAPP_n2125602947l_bool(F,Y_1)),hAPP_n2125602947l_bool(F,X_1))) )
         => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,Ca),hAPP_n2125602947l_bool(F,Aa))) ) ) ) ).

tff(fact_679_xt7,axiom,
    ! [Ca: fun_Pr2067565481t_bool,F: fun_na998785244t_bool,Ba: nat,Aa: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,Ca),hAPP_n1161265524t_bool(F,Ba)))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,hAPP_n1161265524t_bool(F,Y_1)),hAPP_n1161265524t_bool(F,X_1))) )
         => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,Ca),hAPP_n1161265524t_bool(F,Aa))) ) ) ) ).

tff(fact_680_xt7,axiom,
    ! [Ca: bool,F: fun_nat_bool,Ba: nat,Aa: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ca),hAPP_nat_bool(F,Ba)))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,Y_1)),hAPP_nat_bool(F,X_1))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ca),hAPP_nat_bool(F,Aa))) ) ) ) ).

tff(fact_681_xt7,axiom,
    ! [Ca: fun_Ar331856045t_bool,F: fun_na300967376t_bool,Ba: nat,Aa: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Aa))
     => ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,Ca),hAPP_n1312530466t_bool(F,Ba)))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,hAPP_n1312530466t_bool(F,Y_1)),hAPP_n1312530466t_bool(F,X_1))) )
         => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,Ca),hAPP_n1312530466t_bool(F,Aa))) ) ) ) ).

tff(fact_682_xt7,axiom,
    ! [Ca: fun_nat_bool,F: fun_fu821463397t_bool,Ba: fun_nat_bool,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f800510211t_bool(F,Ba)))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(F,Y_1)),hAPP_f800510211t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f800510211t_bool(F,Aa))) ) ) ) ).

tff(fact_683_xt7,axiom,
    ! [Ca: fun_Pr1643180309t_bool,F: fun_fu1096920966t_bool,Ba: fun_nat_bool,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),hAPP_f1061584978t_bool(F,Ba)))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(F,Y_1)),hAPP_f1061584978t_bool(F,X_1))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),hAPP_f1061584978t_bool(F,Aa))) ) ) ) ).

tff(fact_684_xt7,axiom,
    ! [Ca: fun_Ar1809396326i_bool,F: fun_fu1415967063i_bool,Ba: fun_nat_bool,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Ca),hAPP_f1992344867i_bool(F,Ba)))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,hAPP_f1992344867i_bool(F,Y_1)),hAPP_f1992344867i_bool(F,X_1))) )
         => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Ca),hAPP_f1992344867i_bool(F,Aa))) ) ) ) ).

tff(fact_685_xt7,axiom,
    ! [Ca: fun_fu638310559l_bool,F: fun_fu1182412548l_bool,Ba: fun_nat_bool,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,Ca),hAPP_f229466530l_bool(F,Ba)))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,hAPP_f229466530l_bool(F,Y_1)),hAPP_f229466530l_bool(F,X_1))) )
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,Ca),hAPP_f229466530l_bool(F,Aa))) ) ) ) ).

tff(fact_686_xt7,axiom,
    ! [Ca: fun_fu2098777574l_bool,F: fun_fu1927280855l_bool,Ba: fun_nat_bool,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,Ca),hAPP_f561646243l_bool(F,Ba)))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,hAPP_f561646243l_bool(F,Y_1)),hAPP_f561646243l_bool(F,X_1))) )
         => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,Ca),hAPP_f561646243l_bool(F,Aa))) ) ) ) ).

tff(fact_687_xt7,axiom,
    ! [Ca: fun_fu3835832l_bool,F: fun_fu138597289l_bool,Ba: fun_nat_bool,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,Ca),hAPP_f256405365l_bool(F,Ba)))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,hAPP_f256405365l_bool(F,Y_1)),hAPP_f256405365l_bool(F,X_1))) )
         => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,Ca),hAPP_f256405365l_bool(F,Aa))) ) ) ) ).

tff(fact_688_xt7,axiom,
    ! [Ca: fun_Pr2067565481t_bool,F: fun_fu1778022682t_bool,Ba: fun_nat_bool,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,Ca),hAPP_f1472089702t_bool(F,Ba)))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,hAPP_f1472089702t_bool(F,Y_1)),hAPP_f1472089702t_bool(F,X_1))) )
         => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,Ca),hAPP_f1472089702t_bool(F,Aa))) ) ) ) ).

tff(fact_689_xt7,axiom,
    ! [Ca: bool,F: fun_fu425979586l_bool,Ba: fun_nat_bool,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ca),hAPP_f54304608l_bool(F,Ba)))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(F,Y_1)),hAPP_f54304608l_bool(F,X_1))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ca),hAPP_f54304608l_bool(F,Aa))) ) ) ) ).

tff(fact_690_xt7,axiom,
    ! [Ca: fun_Ar331856045t_bool,F: fun_fu221658642t_bool,Ba: fun_nat_bool,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
     => ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,Ca),hAPP_f1635284656t_bool(F,Ba)))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,hAPP_f1635284656t_bool(F,Y_1)),hAPP_f1635284656t_bool(F,X_1))) )
         => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,Ca),hAPP_f1635284656t_bool(F,Aa))) ) ) ) ).

tff(fact_691_xt7,axiom,
    ! [Ca: fun_nat_bool,F: fun_fu1632756612t_bool,Ba: fun_fu638310559l_bool,Aa: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Ba),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f2063587362t_bool(F,Ba)))
       => ( ! [X_1: fun_fu638310559l_bool,Y_1: fun_fu638310559l_bool] :
              ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2063587362t_bool(F,Y_1)),hAPP_f2063587362t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f2063587362t_bool(F,Aa))) ) ) ) ).

tff(fact_692_xt7,axiom,
    ! [Ca: fun_nat_bool,F: fun_fu309681663t_bool,Ba: fun_fu2098777574l_bool,Aa: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Ba),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f1705385041t_bool(F,Ba)))
       => ( ! [X_1: fun_fu2098777574l_bool,Y_1: fun_fu2098777574l_bool] :
              ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1705385041t_bool(F,Y_1)),hAPP_f1705385041t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f1705385041t_bool(F,Aa))) ) ) ) ).

tff(fact_693_xt7,axiom,
    ! [Ca: fun_nat_bool,F: fun_fu1078872017t_bool,Ba: fun_fu3835832l_bool,Aa: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Ba),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f743717923t_bool(F,Ba)))
       => ( ! [X_1: fun_fu3835832l_bool,Y_1: fun_fu3835832l_bool] :
              ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f743717923t_bool(F,Y_1)),hAPP_f743717923t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f743717923t_bool(F,Aa))) ) ) ) ).

tff(fact_694_xt7,axiom,
    ! [Ca: fun_nat_bool,F: fun_fu477456066t_bool,Ba: fun_Pr2067565481t_bool,Aa: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Ba),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f703394068t_bool(F,Ba)))
       => ( ! [X_1: fun_Pr2067565481t_bool,Y_1: fun_Pr2067565481t_bool] :
              ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f703394068t_bool(F,Y_1)),hAPP_f703394068t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f703394068t_bool(F,Aa))) ) ) ) ).

tff(fact_695_xt7,axiom,
    ! [Ca: fun_nat_bool,F: fun_bo1570548802t_bool,Ba: bool,Aa: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_b1013836512t_bool(F,Ba)))
       => ( ! [X_1: bool,Y_1: bool] :
              ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(F,Y_1)),hAPP_b1013836512t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_b1013836512t_bool(F,Aa))) ) ) ) ).

tff(fact_696_xt7,axiom,
    ! [Ca: fun_nat_bool,F: fun_fu1254370943t_bool,Ba: fun_Ar1809396326i_bool,Aa: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Ba),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f622418129t_bool(F,Ba)))
       => ( ! [X_1: fun_Ar1809396326i_bool,Y_1: fun_Ar1809396326i_bool] :
              ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f622418129t_bool(F,Y_1)),hAPP_f622418129t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f622418129t_bool(F,Aa))) ) ) ) ).

tff(fact_697_xt7,axiom,
    ! [Ca: fun_nat_bool,F: fun_fu988033326t_bool,Ba: fun_Pr1643180309t_bool,Aa: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f543204480t_bool(F,Ba)))
       => ( ! [X_1: fun_Pr1643180309t_bool,Y_1: fun_Pr1643180309t_bool] :
              ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(F,Y_1)),hAPP_f543204480t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f543204480t_bool(F,Aa))) ) ) ) ).

tff(fact_698_xt7,axiom,
    ! [Ca: fun_nat_bool,F: fun_fu1869722514t_bool,Ba: fun_Ar331856045t_bool,Aa: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Ba),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f1691234864t_bool(F,Ba)))
       => ( ! [X_1: fun_Ar331856045t_bool,Y_1: fun_Ar331856045t_bool] :
              ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1691234864t_bool(F,Y_1)),hAPP_f1691234864t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),hAPP_f1691234864t_bool(F,Aa))) ) ) ) ).

tff(fact_699_xt7,axiom,
    ! [Ca: nat,F: fun_fu955147676ol_nat,Ba: fun_fu638310559l_bool,Aa: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Ba),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f1487854056ol_nat(F,Ba)))
       => ( ! [X_1: fun_fu638310559l_bool,Y_1: fun_fu638310559l_bool] :
              ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Y_1),X_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1487854056ol_nat(F,Y_1)),hAPP_f1487854056ol_nat(F,X_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f1487854056ol_nat(F,Aa))) ) ) ) ).

tff(fact_700_xt7,axiom,
    ! [Ca: nat,F: fun_fu859131105ol_nat,Ba: fun_fu2098777574l_bool,Aa: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Ba),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f1049163897ol_nat(F,Ba)))
       => ( ! [X_1: fun_fu2098777574l_bool,Y_1: fun_fu2098777574l_bool] :
              ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Y_1),X_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1049163897ol_nat(F,Y_1)),hAPP_f1049163897ol_nat(F,X_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f1049163897ol_nat(F,Aa))) ) ) ) ).

tff(fact_701_xt7,axiom,
    ! [Ca: nat,F: fun_fu777705871ol_nat,Ba: fun_fu3835832l_bool,Aa: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Ba),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f602722087ol_nat(F,Ba)))
       => ( ! [X_1: fun_fu3835832l_bool,Y_1: fun_fu3835832l_bool] :
              ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Y_1),X_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f602722087ol_nat(F,Y_1)),hAPP_f602722087ol_nat(F,X_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f602722087ol_nat(F,Aa))) ) ) ) ).

tff(fact_702_xt7,axiom,
    ! [Ca: nat,F: fun_fu841105374ol_nat,Ba: fun_Pr2067565481t_bool,Aa: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Ba),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f1842225014ol_nat(F,Ba)))
       => ( ! [X_1: fun_Pr2067565481t_bool,Y_1: fun_Pr2067565481t_bool] :
              ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Y_1),X_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1842225014ol_nat(F,Y_1)),hAPP_f1842225014ol_nat(F,X_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f1842225014ol_nat(F,Aa))) ) ) ) ).

tff(fact_703_xt7,axiom,
    ! [Ca: nat,F: fun_bool_nat,Ba: bool,Aa: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_bool_nat(F,Ba)))
       => ( ! [X_1: bool,Y_1: bool] :
              ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_1),X_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(F,Y_1)),hAPP_bool_nat(F,X_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_bool_nat(F,Aa))) ) ) ) ).

tff(fact_704_xt7,axiom,
    ! [Ca: nat,F: fun_fu1603738721ol_nat,Ba: fun_Ar1809396326i_bool,Aa: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Ba),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f846027769ol_nat(F,Ba)))
       => ( ! [X_1: fun_Ar1809396326i_bool,Y_1: fun_Ar1809396326i_bool] :
              ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Y_1),X_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f846027769ol_nat(F,Y_1)),hAPP_f846027769ol_nat(F,X_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f846027769ol_nat(F,Aa))) ) ) ) ).

tff(fact_705_xt7,axiom,
    ! [Ca: nat,F: fun_fu572628082ol_nat,Ba: fun_Pr1643180309t_bool,Aa: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f2030293770ol_nat(F,Ba)))
       => ( ! [X_1: fun_Pr1643180309t_bool,Y_1: fun_Pr1643180309t_bool] :
              ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_1),X_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(F,Y_1)),hAPP_f2030293770ol_nat(F,X_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f2030293770ol_nat(F,Aa))) ) ) ) ).

tff(fact_706_xt7,axiom,
    ! [Ca: nat,F: fun_fu1677555470ol_nat,Ba: fun_Ar331856045t_bool,Aa: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Ba),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f1403773274ol_nat(F,Ba)))
       => ( ! [X_1: fun_Ar331856045t_bool,Y_1: fun_Ar331856045t_bool] :
              ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Y_1),X_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1403773274ol_nat(F,Y_1)),hAPP_f1403773274ol_nat(F,X_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),hAPP_f1403773274ol_nat(F,Aa))) ) ) ) ).

tff(fact_707_less__fun__def,axiom,
    ! [F: fun_Pr1643180309t_bool,G: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,F),G))
    <=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,F),G))
        & ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,G),F)) ) ) ).

tff(fact_708_less__fun__def,axiom,
    ! [F: fun_Ar1809396326i_bool,G: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,F),G))
    <=> ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,F),G))
        & ~ hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,G),F)) ) ) ).

tff(fact_709_less__fun__def,axiom,
    ! [F: fun_fu638310559l_bool,G: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,F),G))
    <=> ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,F),G))
        & ~ hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,G),F)) ) ) ).

tff(fact_710_less__fun__def,axiom,
    ! [F: fun_fu2098777574l_bool,G: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,F),G))
    <=> ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,F),G))
        & ~ hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,G),F)) ) ) ).

tff(fact_711_less__fun__def,axiom,
    ! [F: fun_fu3835832l_bool,G: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,F),G))
    <=> ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,F),G))
        & ~ hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,G),F)) ) ) ).

tff(fact_712_less__fun__def,axiom,
    ! [F: fun_Pr2067565481t_bool,G: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,F),G))
    <=> ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,F),G))
        & ~ hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,G),F)) ) ) ).

tff(fact_713_less__fun__def,axiom,
    ! [F: fun_Ar331856045t_bool,G: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,F),G))
    <=> ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,F),G))
        & ~ hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,G),F)) ) ) ).

tff(fact_714_less__fun__def,axiom,
    ! [F: fun_nat_bool,G: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,F),G))
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G))
        & ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,G),F)) ) ) ).

tff(fact_715_Pi__anti__mono,axiom,
    ! [B: fun_Pr1780397033l_bool,A_15: fun_Pr2067565481t_bool,A: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,A_15),A))
     => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,pi_Pro1238944957t_bool(A,B)),pi_Pro1238944957t_bool(A_15,B))) ) ).

tff(fact_716_Pi__anti__mono,axiom,
    ! [B: fun_fu1863781882l_bool,A_15: fun_fu3835832l_bool,A: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,A_15),A))
     => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,pi_fun1746584570t_bool(A,B)),pi_fun1746584570t_bool(A_15,B))) ) ).

tff(fact_717_Pi__anti__mono,axiom,
    ! [B: fun_Ar1474557608l_bool,A_15: fun_Ar1809396326i_bool,A: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,A_15),A))
     => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,pi_Arr959578316t_bool(A,B)),pi_Arr959578316t_bool(A_15,B))) ) ).

tff(fact_718_pred__subset__eq2,axiom,
    ! [R_1: fun_Pr2067565481t_bool,S_1: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,hAPP_f449303873t_bool(hAPP_f1081591777t_bool(cOMBC_557453916t_bool,hAPP_f105674721t_bool(cOMBB_652885079le_alt(cOMBC_395465908l_bool),hAPP_f184584489l_bool(cOMBB_1575576719le_alt(cOMBB_1660064607le_alt(member1333168212le_alt)),produc1590937303le_alt))),R_1)),hAPP_f449303873t_bool(hAPP_f1081591777t_bool(cOMBC_557453916t_bool,hAPP_f105674721t_bool(cOMBB_652885079le_alt(cOMBC_395465908l_bool),hAPP_f184584489l_bool(cOMBB_1575576719le_alt(cOMBB_1660064607le_alt(member1333168212le_alt)),produc1590937303le_alt))),S_1)))
    <=> hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,R_1),S_1)) ) ).

tff(fact_719_subset__UNIV,axiom,
    ! [A: fun_fu638310559l_bool] : hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,A),top_to1312956197l_bool)) ).

tff(fact_720_subset__UNIV,axiom,
    ! [A: fun_fu3835832l_bool] : hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,A),top_to553140914l_bool)) ).

tff(fact_721_subset__UNIV,axiom,
    ! [A: fun_fu2098777574l_bool] : hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,A),top_to827110112l_bool)) ).

tff(fact_722_subset__UNIV,axiom,
    ! [A: fun_Pr2067565481t_bool] : hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,A),top_to1138392227t_bool)) ).

tff(fact_723_subset__UNIV,axiom,
    ! [A: fun_Ar1809396326i_bool] : hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,A),top_to788185952i_bool)) ).

tff(fact_724_subset__UNIV,axiom,
    ! [A: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),top_top_fun_nat_bool)) ).

tff(fact_725_subset__UNIV,axiom,
    ! [A: fun_Pr1643180309t_bool] : hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),top_to1257323279t_bool)) ).

tff(fact_726_subset__inj__on,axiom,
    ! [A: fun_Ar1809396326i_bool,F: fun_Ar671024215di_nat,B: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(inj_on1960344199di_nat(F),B))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,A),B))
       => hBOOL(hAPP_f584385070l_bool(inj_on1960344199di_nat(F),A)) ) ) ).

tff(fact_727_subset__inj__on,axiom,
    ! [A: fun_nat_bool,F: fun_nat_nat,B: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
       => hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A)) ) ) ).

tff(fact_728_add__right__imp__eq,axiom,
    ! [B_14: nat,A_14: nat,C_14: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_14),A_14) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_14),A_14) )
     => ( B_14 = C_14 ) ) ).

tff(fact_729_add__imp__eq,axiom,
    ! [A_13: nat,B_13: nat,C_13: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_13),B_13) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_13),C_13) )
     => ( B_13 = C_13 ) ) ).

tff(fact_730_add__left__imp__eq,axiom,
    ! [A_12: nat,B_12: nat,C_12: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_12),B_12) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_12),C_12) )
     => ( B_12 = C_12 ) ) ).

tff(fact_731_add__right__cancel,axiom,
    ! [Ba: nat,Aa: nat,Ca: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),Aa) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Aa) )
    <=> ( Ba = Ca ) ) ).

tff(fact_732_add__left__cancel,axiom,
    ! [Aa: nat,Ba: nat,Ca: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),Ba) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),Ca) )
    <=> ( Ba = Ca ) ) ).

tff(fact_733_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
    ! [A_11: nat,B_11: nat,C_11: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_11),B_11)),C_11) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_11),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_11),C_11)) ) ).

tff(fact_734_one__reorient,axiom,
    ! [X_2: nat] :
      ( ( one_one_nat = X_2 )
    <=> ( X_2 = one_one_nat ) ) ).

tff(fact_735_add__le__imp__le__left,axiom,
    ! [C_10: nat,A_10: nat,B_10: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_10),A_10)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_10),B_10)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_10),B_10)) ) ).

tff(fact_736_add__le__imp__le__right,axiom,
    ! [A_9: nat,C_9: nat,B_9: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_9),C_9)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_9),C_9)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_9),B_9)) ) ).

tff(fact_737_add__mono,axiom,
    ! [C_8: nat,D_1: nat,A_8: nat,B_8: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_8),B_8))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_8),D_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_8),C_8)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_8),D_1))) ) ) ).

tff(fact_738_add__left__mono,axiom,
    ! [C_7: nat,A_7: nat,B_7: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_7),B_7))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_7),A_7)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_7),B_7))) ) ).

tff(fact_739_add__right__mono,axiom,
    ! [C_6: nat,A_6: nat,B_6: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_6),B_6))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_6),C_6)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_6),C_6))) ) ).

tff(fact_740_add__le__cancel__left,axiom,
    ! [Ca: nat,Aa: nat,Ba: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Aa)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Ba)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba)) ) ).

tff(fact_741_add__le__cancel__right,axiom,
    ! [Aa: nat,Ca: nat,Ba: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),Ca)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),Ca)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba)) ) ).

tff(fact_742_add__less__imp__less__left,axiom,
    ! [C_5: nat,A_5: nat,B_5: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_5),A_5)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_5),B_5)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_5),B_5)) ) ).

tff(fact_743_add__less__imp__less__right,axiom,
    ! [A_4: nat,C_4: nat,B_4: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_4),C_4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_4),C_4)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_4),B_4)) ) ).

tff(fact_744_add__strict__mono,axiom,
    ! [C_3: nat,D: nat,A_3: nat,B_3: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_3),B_3))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_3),D))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_3),C_3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_3),D))) ) ) ).

tff(fact_745_add__strict__left__mono,axiom,
    ! [C_2: nat,A_2: nat,B_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_2),B_2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_2),A_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_2),B_2))) ) ).

tff(fact_746_add__strict__right__mono,axiom,
    ! [C_1: nat,A_1: nat,B_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_1),B_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_1),C_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_1),C_1))) ) ).

tff(fact_747_add__less__cancel__left,axiom,
    ! [Ca: nat,Aa: nat,Ba: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Aa)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Ba)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)) ) ).

tff(fact_748_add__less__cancel__right,axiom,
    ! [Aa: nat,Ca: nat,Ba: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),Ca)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),Ca)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)) ) ).

tff(fact_749_le__funI,axiom,
    ! [F: fun_fu638310559l_bool,G: fun_fu638310559l_bool] :
      ( ! [X_1: fun_Pr2067565481t_bool] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f52567537l_bool(F,X_1)),hAPP_f52567537l_bool(G,X_1)))
     => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,F),G)) ) ).

tff(fact_750_le__funI,axiom,
    ! [F: fun_fu2098777574l_bool,G: fun_fu2098777574l_bool] :
      ( ! [X_1: fun_fu2114379172t_bool] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f1572141188l_bool(F,X_1)),hAPP_f1572141188l_bool(G,X_1)))
     => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,F),G)) ) ).

tff(fact_751_le__funI,axiom,
    ! [F: fun_fu3835832l_bool,G: fun_fu3835832l_bool] :
      ( ! [X_1: fun_Ar274636406t_bool] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f995490902l_bool(F,X_1)),hAPP_f995490902l_bool(G,X_1)))
     => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,F),G)) ) ).

tff(fact_752_le__funI,axiom,
    ! [F: fun_Pr2067565481t_bool,G: fun_Pr2067565481t_bool] :
      ( ! [X_1: produc472769767le_alt] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1178790471t_bool(F,X_1)),hAPP_P1178790471t_bool(G,X_1)))
     => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,F),G)) ) ).

tff(fact_753_le__funI,axiom,
    ! [F: fun_Ar1809396326i_bool,G: fun_Ar1809396326i_bool] :
      ( ! [X_1: arrow_856714788e_indi] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_A997847300i_bool(F,X_1)),hAPP_A997847300i_bool(G,X_1)))
     => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,F),G)) ) ).

tff(fact_754_le__funI,axiom,
    ! [F: fun_Pr1643180309t_bool,G: fun_Pr1643180309t_bool] :
      ( ! [X_1: product_unit] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_P1676879539t_bool(F,X_1)),hAPP_P1676879539t_bool(G,X_1)))
     => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,F),G)) ) ).

tff(fact_755_le__funI,axiom,
    ! [F: fun_Ar331856045t_bool,G: fun_Ar331856045t_bool] :
      ( ! [X_1: arrow_1893660431le_alt] : hBOOL(hAPP_f739344229l_bool(hAPP_f1549168575l_bool(ord_le1779845435t_bool,hAPP_A2063800319t_bool(F,X_1)),hAPP_A2063800319t_bool(G,X_1)))
     => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,F),G)) ) ).

tff(fact_756_le__funI,axiom,
    ! [F: fun_nat_bool,G: fun_nat_bool] :
      ( ! [X_1: nat] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(G,X_1)))
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G)) ) ).

tff(fact_757_xt6,axiom,
    ! [Ca: fun_nat_bool,F: fun_fu821463397t_bool,Ba: fun_nat_bool,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),Ba))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Y_1)),hAPP_f800510211t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_758_xt6,axiom,
    ! [Ca: fun_Pr1643180309t_bool,F: fun_fu988033326t_bool,Ba: fun_Pr1643180309t_bool,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),Ba))
       => ( ! [X_1: fun_Pr1643180309t_bool,Y_1: fun_Pr1643180309t_bool] :
              ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Y_1)),hAPP_f543204480t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_759_xt6,axiom,
    ! [Ca: fun_Ar1809396326i_bool,F: fun_fu1254370943t_bool,Ba: fun_Ar1809396326i_bool,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f622418129t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Ca),Ba))
       => ( ! [X_1: fun_Ar1809396326i_bool,Y_1: fun_Ar1809396326i_bool] :
              ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f622418129t_bool(F,Y_1)),hAPP_f622418129t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f622418129t_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_760_xt6,axiom,
    ! [Ca: nat,F: fun_nat_fun_nat_bool,Ba: nat,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Y_1)),hAPP_n1699378549t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_761_xt6,axiom,
    ! [Ca: nat,F: fun_na1041622088t_bool,Ba: nat,Aa: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Y_1)),hAPP_n454528608t_bool(F,X_1))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_762_xt6,axiom,
    ! [Ca: nat,F: fun_na2037635353i_bool,Ba: nat,Aa: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,hAPP_n34002993i_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,hAPP_n34002993i_bool(F,Y_1)),hAPP_n34002993i_bool(F,X_1))) )
         => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,hAPP_n34002993i_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_763_xt6,axiom,
    ! [Ca: nat,F: fun_na144630978l_bool,Ba: nat,Aa: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,hAPP_n1134275860l_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,hAPP_n1134275860l_bool(F,Y_1)),hAPP_n1134275860l_bool(F,X_1))) )
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,hAPP_n1134275860l_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_764_xt6,axiom,
    ! [Ca: nat,F: fun_na138495129l_bool,Ba: nat,Aa: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,hAPP_n1555388849l_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,hAPP_n1555388849l_bool(F,Y_1)),hAPP_n1555388849l_bool(F,X_1))) )
         => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,hAPP_n1555388849l_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_765_xt6,axiom,
    ! [Ca: nat,F: fun_na6909291l_bool,Ba: nat,Aa: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,hAPP_n2125602947l_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,hAPP_n2125602947l_bool(F,Y_1)),hAPP_n2125602947l_bool(F,X_1))) )
         => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,hAPP_n2125602947l_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_766_xt6,axiom,
    ! [Ca: nat,F: fun_na998785244t_bool,Ba: nat,Aa: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,hAPP_n1161265524t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,hAPP_n1161265524t_bool(F,Y_1)),hAPP_n1161265524t_bool(F,X_1))) )
         => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,hAPP_n1161265524t_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_767_xt6,axiom,
    ! [Ca: nat,F: fun_nat_bool,Ba: nat,Aa: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Y_1)),hAPP_nat_bool(F,X_1))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_768_xt6,axiom,
    ! [Ca: nat,F: fun_na300967376t_bool,Ba: nat,Aa: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,hAPP_n1312530466t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ca),Ba))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_1))
             => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,hAPP_n1312530466t_bool(F,Y_1)),hAPP_n1312530466t_bool(F,X_1))) )
         => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,hAPP_n1312530466t_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_769_xt6,axiom,
    ! [Ca: fun_nat_bool,F: fun_fun_nat_bool_nat,Ba: fun_nat_bool,Aa: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(F,Ba)),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),Ba))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_1),X_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(F,Y_1)),hAPP_f22106695ol_nat(F,X_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(F,Ca)),Aa)) ) ) ) ).

tff(fact_770_xt6,axiom,
    ! [Ca: fun_Pr1643180309t_bool,F: fun_fu572628082ol_nat,Ba: fun_Pr1643180309t_bool,Aa: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(F,Ba)),Aa))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),Ba))
       => ( ! [X_1: fun_Pr1643180309t_bool,Y_1: fun_Pr1643180309t_bool] :
              ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_1),X_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Y_1)),hAPP_f2030293770ol_nat(F,X_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Ca)),Aa)) ) ) ) ).

tff(fact_771_xt6,axiom,
    ! [Ca: fun_Ar1809396326i_bool,F: fun_fu1603738721ol_nat,Ba: fun_Ar1809396326i_bool,Aa: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f846027769ol_nat(F,Ba)),Aa))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Ca),Ba))
       => ( ! [X_1: fun_Ar1809396326i_bool,Y_1: fun_Ar1809396326i_bool] :
              ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Y_1),X_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f846027769ol_nat(F,Y_1)),hAPP_f846027769ol_nat(F,X_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f846027769ol_nat(F,Ca)),Aa)) ) ) ) ).

tff(fact_772_xt4,axiom,
    ! [Ca: nat,F: fun_nat_fun_nat_bool,Ba: nat,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,Y_1)),hAPP_n1699378549t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_773_xt4,axiom,
    ! [Ca: nat,F: fun_na1041622088t_bool,Ba: nat,Aa: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(F,Y_1)),hAPP_n454528608t_bool(F,X_1))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_774_xt4,axiom,
    ! [Ca: nat,F: fun_na2037635353i_bool,Ba: nat,Aa: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,hAPP_n34002993i_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,hAPP_n34002993i_bool(F,Y_1)),hAPP_n34002993i_bool(F,X_1))) )
         => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,hAPP_n34002993i_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_775_xt4,axiom,
    ! [Ca: nat,F: fun_na144630978l_bool,Ba: nat,Aa: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,hAPP_n1134275860l_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,hAPP_n1134275860l_bool(F,Y_1)),hAPP_n1134275860l_bool(F,X_1))) )
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,hAPP_n1134275860l_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_776_xt4,axiom,
    ! [Ca: nat,F: fun_na138495129l_bool,Ba: nat,Aa: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,hAPP_n1555388849l_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,hAPP_n1555388849l_bool(F,Y_1)),hAPP_n1555388849l_bool(F,X_1))) )
         => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,hAPP_n1555388849l_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_777_xt4,axiom,
    ! [Ca: nat,F: fun_na6909291l_bool,Ba: nat,Aa: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,hAPP_n2125602947l_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,hAPP_n2125602947l_bool(F,Y_1)),hAPP_n2125602947l_bool(F,X_1))) )
         => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,hAPP_n2125602947l_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_778_xt4,axiom,
    ! [Ca: nat,F: fun_na998785244t_bool,Ba: nat,Aa: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,hAPP_n1161265524t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,hAPP_n1161265524t_bool(F,Y_1)),hAPP_n1161265524t_bool(F,X_1))) )
         => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,hAPP_n1161265524t_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_779_xt4,axiom,
    ! [Ca: nat,F: fun_nat_bool,Ba: nat,Aa: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,Y_1)),hAPP_nat_bool(F,X_1))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_780_xt4,axiom,
    ! [Ca: nat,F: fun_na300967376t_bool,Ba: nat,Aa: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,hAPP_n1312530466t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ca),Ba))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
             => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,hAPP_n1312530466t_bool(F,Y_1)),hAPP_n1312530466t_bool(F,X_1))) )
         => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,hAPP_n1312530466t_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_781_xt4,axiom,
    ! [Ca: fun_nat_bool,F: fun_fu821463397t_bool,Ba: fun_nat_bool,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(F,Y_1)),hAPP_f800510211t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_782_xt4,axiom,
    ! [Ca: fun_nat_bool,F: fun_fu1096920966t_bool,Ba: fun_nat_bool,Aa: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(F,Y_1)),hAPP_f1061584978t_bool(F,X_1))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_783_xt4,axiom,
    ! [Ca: fun_nat_bool,F: fun_fu1415967063i_bool,Ba: fun_nat_bool,Aa: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,hAPP_f1992344867i_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,hAPP_f1992344867i_bool(F,Y_1)),hAPP_f1992344867i_bool(F,X_1))) )
         => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,hAPP_f1992344867i_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_784_xt4,axiom,
    ! [Ca: fun_nat_bool,F: fun_fu1182412548l_bool,Ba: fun_nat_bool,Aa: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,hAPP_f229466530l_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,hAPP_f229466530l_bool(F,Y_1)),hAPP_f229466530l_bool(F,X_1))) )
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,hAPP_f229466530l_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_785_xt4,axiom,
    ! [Ca: fun_nat_bool,F: fun_fu1927280855l_bool,Ba: fun_nat_bool,Aa: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,hAPP_f561646243l_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,hAPP_f561646243l_bool(F,Y_1)),hAPP_f561646243l_bool(F,X_1))) )
         => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,hAPP_f561646243l_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_786_xt4,axiom,
    ! [Ca: fun_nat_bool,F: fun_fu138597289l_bool,Ba: fun_nat_bool,Aa: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,hAPP_f256405365l_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,hAPP_f256405365l_bool(F,Y_1)),hAPP_f256405365l_bool(F,X_1))) )
         => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,hAPP_f256405365l_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_787_xt4,axiom,
    ! [Ca: fun_nat_bool,F: fun_fu1778022682t_bool,Ba: fun_nat_bool,Aa: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,hAPP_f1472089702t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,hAPP_f1472089702t_bool(F,Y_1)),hAPP_f1472089702t_bool(F,X_1))) )
         => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,hAPP_f1472089702t_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_788_xt4,axiom,
    ! [Ca: fun_nat_bool,F: fun_fu425979586l_bool,Ba: fun_nat_bool,Aa: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(F,Y_1)),hAPP_f54304608l_bool(F,X_1))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_789_xt4,axiom,
    ! [Ca: fun_nat_bool,F: fun_fu221658642t_bool,Ba: fun_nat_bool,Aa: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,hAPP_f1635284656t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
             => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,hAPP_f1635284656t_bool(F,Y_1)),hAPP_f1635284656t_bool(F,X_1))) )
         => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,hAPP_f1635284656t_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_790_xt4,axiom,
    ! [Ca: fun_fu638310559l_bool,F: fun_fu1632756612t_bool,Ba: fun_fu638310559l_bool,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2063587362t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Ca),Ba))
       => ( ! [X_1: fun_fu638310559l_bool,Y_1: fun_fu638310559l_bool] :
              ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2063587362t_bool(F,Y_1)),hAPP_f2063587362t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2063587362t_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_791_xt4,axiom,
    ! [Ca: fun_fu2098777574l_bool,F: fun_fu309681663t_bool,Ba: fun_fu2098777574l_bool,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1705385041t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Ca),Ba))
       => ( ! [X_1: fun_fu2098777574l_bool,Y_1: fun_fu2098777574l_bool] :
              ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1705385041t_bool(F,Y_1)),hAPP_f1705385041t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1705385041t_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_792_xt4,axiom,
    ! [Ca: fun_fu3835832l_bool,F: fun_fu1078872017t_bool,Ba: fun_fu3835832l_bool,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f743717923t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Ca),Ba))
       => ( ! [X_1: fun_fu3835832l_bool,Y_1: fun_fu3835832l_bool] :
              ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f743717923t_bool(F,Y_1)),hAPP_f743717923t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f743717923t_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_793_xt4,axiom,
    ! [Ca: fun_Pr2067565481t_bool,F: fun_fu477456066t_bool,Ba: fun_Pr2067565481t_bool,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f703394068t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Ca),Ba))
       => ( ! [X_1: fun_Pr2067565481t_bool,Y_1: fun_Pr2067565481t_bool] :
              ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f703394068t_bool(F,Y_1)),hAPP_f703394068t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f703394068t_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_794_xt4,axiom,
    ! [Ca: bool,F: fun_bo1570548802t_bool,Ba: bool,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),Ba))
       => ( ! [X_1: bool,Y_1: bool] :
              ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(F,Y_1)),hAPP_b1013836512t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_795_xt4,axiom,
    ! [Ca: fun_Ar1809396326i_bool,F: fun_fu1254370943t_bool,Ba: fun_Ar1809396326i_bool,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f622418129t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Ca),Ba))
       => ( ! [X_1: fun_Ar1809396326i_bool,Y_1: fun_Ar1809396326i_bool] :
              ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f622418129t_bool(F,Y_1)),hAPP_f622418129t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f622418129t_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_796_xt4,axiom,
    ! [Ca: fun_Pr1643180309t_bool,F: fun_fu988033326t_bool,Ba: fun_Pr1643180309t_bool,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ca),Ba))
       => ( ! [X_1: fun_Pr1643180309t_bool,Y_1: fun_Pr1643180309t_bool] :
              ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(F,Y_1)),hAPP_f543204480t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_797_xt4,axiom,
    ! [Ca: fun_Ar331856045t_bool,F: fun_fu1869722514t_bool,Ba: fun_Ar331856045t_bool,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1691234864t_bool(F,Ba)),Aa))
     => ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Ca),Ba))
       => ( ! [X_1: fun_Ar331856045t_bool,Y_1: fun_Ar331856045t_bool] :
              ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Y_1),X_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1691234864t_bool(F,Y_1)),hAPP_f1691234864t_bool(F,X_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1691234864t_bool(F,Ca)),Aa)) ) ) ) ).

tff(fact_798_xt4,axiom,
    ! [Ca: fun_fu638310559l_bool,F: fun_fu955147676ol_nat,Ba: fun_fu638310559l_bool,Aa: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1487854056ol_nat(F,Ba)),Aa))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Ca),Ba))
       => ( ! [X_1: fun_fu638310559l_bool,Y_1: fun_fu638310559l_bool] :
              ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Y_1),X_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1487854056ol_nat(F,Y_1)),hAPP_f1487854056ol_nat(F,X_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1487854056ol_nat(F,Ca)),Aa)) ) ) ) ).

tff(fact_799_xt4,axiom,
    ! [Ca: fun_fu2098777574l_bool,F: fun_fu859131105ol_nat,Ba: fun_fu2098777574l_bool,Aa: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1049163897ol_nat(F,Ba)),Aa))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Ca),Ba))
       => ( ! [X_1: fun_fu2098777574l_bool,Y_1: fun_fu2098777574l_bool] :
              ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Y_1),X_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1049163897ol_nat(F,Y_1)),hAPP_f1049163897ol_nat(F,X_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1049163897ol_nat(F,Ca)),Aa)) ) ) ) ).

tff(fact_800_xt4,axiom,
    ! [Ca: fun_fu3835832l_bool,F: fun_fu777705871ol_nat,Ba: fun_fu3835832l_bool,Aa: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f602722087ol_nat(F,Ba)),Aa))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Ca),Ba))
       => ( ! [X_1: fun_fu3835832l_bool,Y_1: fun_fu3835832l_bool] :
              ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Y_1),X_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f602722087ol_nat(F,Y_1)),hAPP_f602722087ol_nat(F,X_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f602722087ol_nat(F,Ca)),Aa)) ) ) ) ).

tff(fact_801_xt4,axiom,
    ! [Ca: fun_Pr2067565481t_bool,F: fun_fu841105374ol_nat,Ba: fun_Pr2067565481t_bool,Aa: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1842225014ol_nat(F,Ba)),Aa))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Ca),Ba))
       => ( ! [X_1: fun_Pr2067565481t_bool,Y_1: fun_Pr2067565481t_bool] :
              ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Y_1),X_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1842225014ol_nat(F,Y_1)),hAPP_f1842225014ol_nat(F,X_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1842225014ol_nat(F,Ca)),Aa)) ) ) ) ).

tff(fact_802_xt4,axiom,
    ! [Ca: bool,F: fun_bool_nat,Ba: bool,Aa: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(F,Ba)),Aa))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),Ba))
       => ( ! [X_1: bool,Y_1: bool] :
              ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_1),X_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(F,Y_1)),hAPP_bool_nat(F,X_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(F,Ca)),Aa)) ) ) ) ).

tff(fact_803_xt4,axiom,
    ! [Ca: fun_Ar1809396326i_bool,F: fun_fu1603738721ol_nat,Ba: fun_Ar1809396326i_bool,Aa: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f846027769ol_nat(F,Ba)),Aa))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Ca),Ba))
       => ( ! [X_1: fun_Ar1809396326i_bool,Y_1: fun_Ar1809396326i_bool] :
              ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Y_1),X_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f846027769ol_nat(F,Y_1)),hAPP_f846027769ol_nat(F,X_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f846027769ol_nat(F,Ca)),Aa)) ) ) ) ).

tff(fact_804_xt4,axiom,
    ! [Ca: fun_Pr1643180309t_bool,F: fun_fu572628082ol_nat,Ba: fun_Pr1643180309t_bool,Aa: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Ba)),Aa))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ca),Ba))
       => ( ! [X_1: fun_Pr1643180309t_bool,Y_1: fun_Pr1643180309t_bool] :
              ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_1),X_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(F,Y_1)),hAPP_f2030293770ol_nat(F,X_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Ca)),Aa)) ) ) ) ).

tff(fact_805_xt4,axiom,
    ! [Ca: fun_Ar331856045t_bool,F: fun_fu1677555470ol_nat,Ba: fun_Ar331856045t_bool,Aa: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1403773274ol_nat(F,Ba)),Aa))
     => ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Ca),Ba))
       => ( ! [X_1: fun_Ar331856045t_bool,Y_1: fun_Ar331856045t_bool] :
              ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Y_1),X_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1403773274ol_nat(F,Y_1)),hAPP_f1403773274ol_nat(F,X_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1403773274ol_nat(F,Ca)),Aa)) ) ) ) ).

tff(fact_806_order__le__less__subst1,axiom,
    ! [Ca: fun_nat_bool,Aa: fun_nat_bool,F: fun_fu821463397t_bool,Ba: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),hAPP_f800510211t_bool(F,Ba)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Ca))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,X_1)),hAPP_f800510211t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f800510211t_bool(F,Ca))) ) ) ) ).

tff(fact_807_order__le__less__subst1,axiom,
    ! [Ca: fun_Pr1643180309t_bool,Aa: fun_nat_bool,F: fun_fu988033326t_bool,Ba: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),hAPP_f543204480t_bool(F,Ba)))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Ca))
       => ( ! [X_1: fun_Pr1643180309t_bool,Y_1: fun_Pr1643180309t_bool] :
              ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,X_1)),hAPP_f543204480t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f543204480t_bool(F,Ca))) ) ) ) ).

tff(fact_808_order__le__less__subst1,axiom,
    ! [Ca: fun_Ar1809396326i_bool,Aa: fun_nat_bool,F: fun_fu1254370943t_bool,Ba: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),hAPP_f622418129t_bool(F,Ba)))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Ba),Ca))
       => ( ! [X_1: fun_Ar1809396326i_bool,Y_1: fun_Ar1809396326i_bool] :
              ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f622418129t_bool(F,X_1)),hAPP_f622418129t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f622418129t_bool(F,Ca))) ) ) ) ).

tff(fact_809_order__le__less__subst1,axiom,
    ! [Ca: nat,Aa: fun_nat_bool,F: fun_nat_fun_nat_bool,Ba: nat] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),hAPP_n1699378549t_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,X_1)),hAPP_n1699378549t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_n1699378549t_bool(F,Ca))) ) ) ) ).

tff(fact_810_order__le__less__subst1,axiom,
    ! [Ca: nat,Aa: fun_Pr1643180309t_bool,F: fun_na1041622088t_bool,Ba: nat] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),hAPP_n454528608t_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,X_1)),hAPP_n454528608t_bool(F,Y_1))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),hAPP_n454528608t_bool(F,Ca))) ) ) ) ).

tff(fact_811_order__le__less__subst1,axiom,
    ! [Ca: nat,Aa: fun_Ar1809396326i_bool,F: fun_na2037635353i_bool,Ba: nat] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Aa),hAPP_n34002993i_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,hAPP_n34002993i_bool(F,X_1)),hAPP_n34002993i_bool(F,Y_1))) )
         => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Aa),hAPP_n34002993i_bool(F,Ca))) ) ) ) ).

tff(fact_812_order__le__less__subst1,axiom,
    ! [Ca: nat,Aa: fun_fu638310559l_bool,F: fun_na144630978l_bool,Ba: nat] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Aa),hAPP_n1134275860l_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,hAPP_n1134275860l_bool(F,X_1)),hAPP_n1134275860l_bool(F,Y_1))) )
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,Aa),hAPP_n1134275860l_bool(F,Ca))) ) ) ) ).

tff(fact_813_order__le__less__subst1,axiom,
    ! [Ca: nat,Aa: fun_fu2098777574l_bool,F: fun_na138495129l_bool,Ba: nat] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Aa),hAPP_n1555388849l_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,hAPP_n1555388849l_bool(F,X_1)),hAPP_n1555388849l_bool(F,Y_1))) )
         => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,Aa),hAPP_n1555388849l_bool(F,Ca))) ) ) ) ).

tff(fact_814_order__le__less__subst1,axiom,
    ! [Ca: nat,Aa: fun_fu3835832l_bool,F: fun_na6909291l_bool,Ba: nat] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Aa),hAPP_n2125602947l_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,hAPP_n2125602947l_bool(F,X_1)),hAPP_n2125602947l_bool(F,Y_1))) )
         => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,Aa),hAPP_n2125602947l_bool(F,Ca))) ) ) ) ).

tff(fact_815_order__le__less__subst1,axiom,
    ! [Ca: nat,Aa: fun_Pr2067565481t_bool,F: fun_na998785244t_bool,Ba: nat] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Aa),hAPP_n1161265524t_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,hAPP_n1161265524t_bool(F,X_1)),hAPP_n1161265524t_bool(F,Y_1))) )
         => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,Aa),hAPP_n1161265524t_bool(F,Ca))) ) ) ) ).

tff(fact_816_order__le__less__subst1,axiom,
    ! [Ca: nat,Aa: bool,F: fun_nat_bool,Ba: nat] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),hAPP_nat_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(F,Y_1))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),hAPP_nat_bool(F,Ca))) ) ) ) ).

tff(fact_817_order__le__less__subst1,axiom,
    ! [Ca: nat,Aa: fun_Ar331856045t_bool,F: fun_na300967376t_bool,Ba: nat] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Aa),hAPP_n1312530466t_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Ba),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,hAPP_n1312530466t_bool(F,X_1)),hAPP_n1312530466t_bool(F,Y_1))) )
         => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,Aa),hAPP_n1312530466t_bool(F,Ca))) ) ) ) ).

tff(fact_818_order__le__less__subst1,axiom,
    ! [Ca: fun_nat_bool,Aa: nat,F: fun_fun_nat_bool_nat,Ba: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),hAPP_f22106695ol_nat(F,Ba)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Ca))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Y_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(F,X_1)),hAPP_f22106695ol_nat(F,Y_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f22106695ol_nat(F,Ca))) ) ) ) ).

tff(fact_819_order__le__less__subst1,axiom,
    ! [Ca: fun_Pr1643180309t_bool,Aa: nat,F: fun_fu572628082ol_nat,Ba: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),hAPP_f2030293770ol_nat(F,Ba)))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Ca))
       => ( ! [X_1: fun_Pr1643180309t_bool,Y_1: fun_Pr1643180309t_bool] :
              ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_1),Y_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,X_1)),hAPP_f2030293770ol_nat(F,Y_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f2030293770ol_nat(F,Ca))) ) ) ) ).

tff(fact_820_order__le__less__subst1,axiom,
    ! [Ca: fun_Ar1809396326i_bool,Aa: nat,F: fun_fu1603738721ol_nat,Ba: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),hAPP_f846027769ol_nat(F,Ba)))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Ba),Ca))
       => ( ! [X_1: fun_Ar1809396326i_bool,Y_1: fun_Ar1809396326i_bool] :
              ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,X_1),Y_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f846027769ol_nat(F,X_1)),hAPP_f846027769ol_nat(F,Y_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f846027769ol_nat(F,Ca))) ) ) ) ).

tff(fact_821_order__less__le__subst1,axiom,
    ! [Ca: nat,Aa: fun_nat_bool,F: fun_nat_fun_nat_bool,Ba: nat] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_n1699378549t_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,X_1)),hAPP_n1699378549t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_n1699378549t_bool(F,Ca))) ) ) ) ).

tff(fact_822_order__less__le__subst1,axiom,
    ! [Ca: nat,Aa: fun_Pr1643180309t_bool,F: fun_na1041622088t_bool,Ba: nat] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),hAPP_n454528608t_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(F,X_1)),hAPP_n454528608t_bool(F,Y_1))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),hAPP_n454528608t_bool(F,Ca))) ) ) ) ).

tff(fact_823_order__less__le__subst1,axiom,
    ! [Ca: nat,Aa: fun_Ar1809396326i_bool,F: fun_na2037635353i_bool,Ba: nat] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Aa),hAPP_n34002993i_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,hAPP_n34002993i_bool(F,X_1)),hAPP_n34002993i_bool(F,Y_1))) )
         => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Aa),hAPP_n34002993i_bool(F,Ca))) ) ) ) ).

tff(fact_824_order__less__le__subst1,axiom,
    ! [Ca: nat,Aa: fun_fu638310559l_bool,F: fun_na144630978l_bool,Ba: nat] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,Aa),hAPP_n1134275860l_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,hAPP_n1134275860l_bool(F,X_1)),hAPP_n1134275860l_bool(F,Y_1))) )
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,Aa),hAPP_n1134275860l_bool(F,Ca))) ) ) ) ).

tff(fact_825_order__less__le__subst1,axiom,
    ! [Ca: nat,Aa: fun_fu2098777574l_bool,F: fun_na138495129l_bool,Ba: nat] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,Aa),hAPP_n1555388849l_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,hAPP_n1555388849l_bool(F,X_1)),hAPP_n1555388849l_bool(F,Y_1))) )
         => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,Aa),hAPP_n1555388849l_bool(F,Ca))) ) ) ) ).

tff(fact_826_order__less__le__subst1,axiom,
    ! [Ca: nat,Aa: fun_fu3835832l_bool,F: fun_na6909291l_bool,Ba: nat] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,Aa),hAPP_n2125602947l_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,hAPP_n2125602947l_bool(F,X_1)),hAPP_n2125602947l_bool(F,Y_1))) )
         => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,Aa),hAPP_n2125602947l_bool(F,Ca))) ) ) ) ).

tff(fact_827_order__less__le__subst1,axiom,
    ! [Ca: nat,Aa: fun_Pr2067565481t_bool,F: fun_na998785244t_bool,Ba: nat] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,Aa),hAPP_n1161265524t_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,hAPP_n1161265524t_bool(F,X_1)),hAPP_n1161265524t_bool(F,Y_1))) )
         => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,Aa),hAPP_n1161265524t_bool(F,Ca))) ) ) ) ).

tff(fact_828_order__less__le__subst1,axiom,
    ! [Ca: nat,Aa: bool,F: fun_nat_bool,Ba: nat] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),hAPP_nat_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(F,Y_1))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),hAPP_nat_bool(F,Ca))) ) ) ) ).

tff(fact_829_order__less__le__subst1,axiom,
    ! [Ca: nat,Aa: fun_Ar331856045t_bool,F: fun_na300967376t_bool,Ba: nat] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,Aa),hAPP_n1312530466t_bool(F,Ba)))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Ba),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,hAPP_n1312530466t_bool(F,X_1)),hAPP_n1312530466t_bool(F,Y_1))) )
         => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,Aa),hAPP_n1312530466t_bool(F,Ca))) ) ) ) ).

tff(fact_830_order__less__le__subst1,axiom,
    ! [Ca: fun_nat_bool,Aa: fun_nat_bool,F: fun_fu821463397t_bool,Ba: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f800510211t_bool(F,Ba)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(F,X_1)),hAPP_f800510211t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f800510211t_bool(F,Ca))) ) ) ) ).

tff(fact_831_order__less__le__subst1,axiom,
    ! [Ca: fun_nat_bool,Aa: fun_Pr1643180309t_bool,F: fun_fu1096920966t_bool,Ba: fun_nat_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),hAPP_f1061584978t_bool(F,Ba)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(F,X_1)),hAPP_f1061584978t_bool(F,Y_1))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),hAPP_f1061584978t_bool(F,Ca))) ) ) ) ).

tff(fact_832_order__less__le__subst1,axiom,
    ! [Ca: fun_nat_bool,Aa: fun_Ar1809396326i_bool,F: fun_fu1415967063i_bool,Ba: fun_nat_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Aa),hAPP_f1992344867i_bool(F,Ba)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,hAPP_f1992344867i_bool(F,X_1)),hAPP_f1992344867i_bool(F,Y_1))) )
         => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Aa),hAPP_f1992344867i_bool(F,Ca))) ) ) ) ).

tff(fact_833_order__less__le__subst1,axiom,
    ! [Ca: fun_nat_bool,Aa: fun_fu638310559l_bool,F: fun_fu1182412548l_bool,Ba: fun_nat_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,Aa),hAPP_f229466530l_bool(F,Ba)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,hAPP_f229466530l_bool(F,X_1)),hAPP_f229466530l_bool(F,Y_1))) )
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,Aa),hAPP_f229466530l_bool(F,Ca))) ) ) ) ).

tff(fact_834_order__less__le__subst1,axiom,
    ! [Ca: fun_nat_bool,Aa: fun_fu2098777574l_bool,F: fun_fu1927280855l_bool,Ba: fun_nat_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,Aa),hAPP_f561646243l_bool(F,Ba)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,hAPP_f561646243l_bool(F,X_1)),hAPP_f561646243l_bool(F,Y_1))) )
         => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,Aa),hAPP_f561646243l_bool(F,Ca))) ) ) ) ).

tff(fact_835_order__less__le__subst1,axiom,
    ! [Ca: fun_nat_bool,Aa: fun_fu3835832l_bool,F: fun_fu138597289l_bool,Ba: fun_nat_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,Aa),hAPP_f256405365l_bool(F,Ba)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,hAPP_f256405365l_bool(F,X_1)),hAPP_f256405365l_bool(F,Y_1))) )
         => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,Aa),hAPP_f256405365l_bool(F,Ca))) ) ) ) ).

tff(fact_836_order__less__le__subst1,axiom,
    ! [Ca: fun_nat_bool,Aa: fun_Pr2067565481t_bool,F: fun_fu1778022682t_bool,Ba: fun_nat_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,Aa),hAPP_f1472089702t_bool(F,Ba)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,hAPP_f1472089702t_bool(F,X_1)),hAPP_f1472089702t_bool(F,Y_1))) )
         => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,Aa),hAPP_f1472089702t_bool(F,Ca))) ) ) ) ).

tff(fact_837_order__less__le__subst1,axiom,
    ! [Ca: fun_nat_bool,Aa: bool,F: fun_fu425979586l_bool,Ba: fun_nat_bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),hAPP_f54304608l_bool(F,Ba)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(F,X_1)),hAPP_f54304608l_bool(F,Y_1))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),hAPP_f54304608l_bool(F,Ca))) ) ) ) ).

tff(fact_838_order__less__le__subst1,axiom,
    ! [Ca: fun_nat_bool,Aa: fun_Ar331856045t_bool,F: fun_fu221658642t_bool,Ba: fun_nat_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,Aa),hAPP_f1635284656t_bool(F,Ba)))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,hAPP_f1635284656t_bool(F,X_1)),hAPP_f1635284656t_bool(F,Y_1))) )
         => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,Aa),hAPP_f1635284656t_bool(F,Ca))) ) ) ) ).

tff(fact_839_order__less__le__subst1,axiom,
    ! [Ca: fun_fu638310559l_bool,Aa: fun_nat_bool,F: fun_fu1632756612t_bool,Ba: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f2063587362t_bool(F,Ba)))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Ba),Ca))
       => ( ! [X_1: fun_fu638310559l_bool,Y_1: fun_fu638310559l_bool] :
              ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2063587362t_bool(F,X_1)),hAPP_f2063587362t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f2063587362t_bool(F,Ca))) ) ) ) ).

tff(fact_840_order__less__le__subst1,axiom,
    ! [Ca: fun_fu2098777574l_bool,Aa: fun_nat_bool,F: fun_fu309681663t_bool,Ba: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f1705385041t_bool(F,Ba)))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Ba),Ca))
       => ( ! [X_1: fun_fu2098777574l_bool,Y_1: fun_fu2098777574l_bool] :
              ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1705385041t_bool(F,X_1)),hAPP_f1705385041t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f1705385041t_bool(F,Ca))) ) ) ) ).

tff(fact_841_order__less__le__subst1,axiom,
    ! [Ca: fun_fu3835832l_bool,Aa: fun_nat_bool,F: fun_fu1078872017t_bool,Ba: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f743717923t_bool(F,Ba)))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Ba),Ca))
       => ( ! [X_1: fun_fu3835832l_bool,Y_1: fun_fu3835832l_bool] :
              ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f743717923t_bool(F,X_1)),hAPP_f743717923t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f743717923t_bool(F,Ca))) ) ) ) ).

tff(fact_842_order__less__le__subst1,axiom,
    ! [Ca: fun_Pr2067565481t_bool,Aa: fun_nat_bool,F: fun_fu477456066t_bool,Ba: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f703394068t_bool(F,Ba)))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Ba),Ca))
       => ( ! [X_1: fun_Pr2067565481t_bool,Y_1: fun_Pr2067565481t_bool] :
              ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f703394068t_bool(F,X_1)),hAPP_f703394068t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f703394068t_bool(F,Ca))) ) ) ) ).

tff(fact_843_order__less__le__subst1,axiom,
    ! [Ca: bool,Aa: fun_nat_bool,F: fun_bo1570548802t_bool,Ba: bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_b1013836512t_bool(F,Ba)))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Ca))
       => ( ! [X_1: bool,Y_1: bool] :
              ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(F,X_1)),hAPP_b1013836512t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_b1013836512t_bool(F,Ca))) ) ) ) ).

tff(fact_844_order__less__le__subst1,axiom,
    ! [Ca: fun_Ar1809396326i_bool,Aa: fun_nat_bool,F: fun_fu1254370943t_bool,Ba: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f622418129t_bool(F,Ba)))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Ba),Ca))
       => ( ! [X_1: fun_Ar1809396326i_bool,Y_1: fun_Ar1809396326i_bool] :
              ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f622418129t_bool(F,X_1)),hAPP_f622418129t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f622418129t_bool(F,Ca))) ) ) ) ).

tff(fact_845_order__less__le__subst1,axiom,
    ! [Ca: fun_Pr1643180309t_bool,Aa: fun_nat_bool,F: fun_fu988033326t_bool,Ba: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f543204480t_bool(F,Ba)))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Ca))
       => ( ! [X_1: fun_Pr1643180309t_bool,Y_1: fun_Pr1643180309t_bool] :
              ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(F,X_1)),hAPP_f543204480t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f543204480t_bool(F,Ca))) ) ) ) ).

tff(fact_846_order__less__le__subst1,axiom,
    ! [Ca: fun_Ar331856045t_bool,Aa: fun_nat_bool,F: fun_fu1869722514t_bool,Ba: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f1691234864t_bool(F,Ba)))
     => ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Ba),Ca))
       => ( ! [X_1: fun_Ar331856045t_bool,Y_1: fun_Ar331856045t_bool] :
              ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1691234864t_bool(F,X_1)),hAPP_f1691234864t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),hAPP_f1691234864t_bool(F,Ca))) ) ) ) ).

tff(fact_847_order__less__le__subst1,axiom,
    ! [Ca: fun_fu638310559l_bool,Aa: nat,F: fun_fu955147676ol_nat,Ba: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f1487854056ol_nat(F,Ba)))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Ba),Ca))
       => ( ! [X_1: fun_fu638310559l_bool,Y_1: fun_fu638310559l_bool] :
              ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,X_1),Y_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1487854056ol_nat(F,X_1)),hAPP_f1487854056ol_nat(F,Y_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f1487854056ol_nat(F,Ca))) ) ) ) ).

tff(fact_848_order__less__le__subst1,axiom,
    ! [Ca: fun_fu2098777574l_bool,Aa: nat,F: fun_fu859131105ol_nat,Ba: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f1049163897ol_nat(F,Ba)))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Ba),Ca))
       => ( ! [X_1: fun_fu2098777574l_bool,Y_1: fun_fu2098777574l_bool] :
              ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,X_1),Y_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1049163897ol_nat(F,X_1)),hAPP_f1049163897ol_nat(F,Y_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f1049163897ol_nat(F,Ca))) ) ) ) ).

tff(fact_849_order__less__le__subst1,axiom,
    ! [Ca: fun_fu3835832l_bool,Aa: nat,F: fun_fu777705871ol_nat,Ba: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f602722087ol_nat(F,Ba)))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Ba),Ca))
       => ( ! [X_1: fun_fu3835832l_bool,Y_1: fun_fu3835832l_bool] :
              ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,X_1),Y_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f602722087ol_nat(F,X_1)),hAPP_f602722087ol_nat(F,Y_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f602722087ol_nat(F,Ca))) ) ) ) ).

tff(fact_850_order__less__le__subst1,axiom,
    ! [Ca: fun_Pr2067565481t_bool,Aa: nat,F: fun_fu841105374ol_nat,Ba: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f1842225014ol_nat(F,Ba)))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Ba),Ca))
       => ( ! [X_1: fun_Pr2067565481t_bool,Y_1: fun_Pr2067565481t_bool] :
              ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,X_1),Y_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1842225014ol_nat(F,X_1)),hAPP_f1842225014ol_nat(F,Y_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f1842225014ol_nat(F,Ca))) ) ) ) ).

tff(fact_851_order__less__le__subst1,axiom,
    ! [Ca: bool,Aa: nat,F: fun_bool_nat,Ba: bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_bool_nat(F,Ba)))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Ca))
       => ( ! [X_1: bool,Y_1: bool] :
              ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(F,X_1)),hAPP_bool_nat(F,Y_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_bool_nat(F,Ca))) ) ) ) ).

tff(fact_852_order__less__le__subst1,axiom,
    ! [Ca: fun_Ar1809396326i_bool,Aa: nat,F: fun_fu1603738721ol_nat,Ba: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f846027769ol_nat(F,Ba)))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Ba),Ca))
       => ( ! [X_1: fun_Ar1809396326i_bool,Y_1: fun_Ar1809396326i_bool] :
              ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,X_1),Y_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f846027769ol_nat(F,X_1)),hAPP_f846027769ol_nat(F,Y_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f846027769ol_nat(F,Ca))) ) ) ) ).

tff(fact_853_order__less__le__subst1,axiom,
    ! [Ca: fun_Pr1643180309t_bool,Aa: nat,F: fun_fu572628082ol_nat,Ba: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f2030293770ol_nat(F,Ba)))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Ca))
       => ( ! [X_1: fun_Pr1643180309t_bool,Y_1: fun_Pr1643180309t_bool] :
              ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_1),Y_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(F,X_1)),hAPP_f2030293770ol_nat(F,Y_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f2030293770ol_nat(F,Ca))) ) ) ) ).

tff(fact_854_order__less__le__subst1,axiom,
    ! [Ca: fun_Ar331856045t_bool,Aa: nat,F: fun_fu1677555470ol_nat,Ba: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f1403773274ol_nat(F,Ba)))
     => ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Ba),Ca))
       => ( ! [X_1: fun_Ar331856045t_bool,Y_1: fun_Ar331856045t_bool] :
              ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,X_1),Y_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1403773274ol_nat(F,X_1)),hAPP_f1403773274ol_nat(F,Y_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),hAPP_f1403773274ol_nat(F,Ca))) ) ) ) ).

tff(fact_855_order__le__less__subst2,axiom,
    ! [F: fun_nat_fun_nat_bool,Ca: fun_nat_bool,Aa: nat,Ba: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Ba)),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,X_1)),hAPP_n1699378549t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_856_order__le__less__subst2,axiom,
    ! [F: fun_na1041622088t_bool,Ca: fun_Pr1643180309t_bool,Aa: nat,Ba: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Ba)),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(F,X_1)),hAPP_n454528608t_bool(F,Y_1))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_857_order__le__less__subst2,axiom,
    ! [F: fun_na2037635353i_bool,Ca: fun_Ar1809396326i_bool,Aa: nat,Ba: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,hAPP_n34002993i_bool(F,Ba)),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,hAPP_n34002993i_bool(F,X_1)),hAPP_n34002993i_bool(F,Y_1))) )
         => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,hAPP_n34002993i_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_858_order__le__less__subst2,axiom,
    ! [F: fun_na144630978l_bool,Ca: fun_fu638310559l_bool,Aa: nat,Ba: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,hAPP_n1134275860l_bool(F,Ba)),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,hAPP_n1134275860l_bool(F,X_1)),hAPP_n1134275860l_bool(F,Y_1))) )
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,hAPP_n1134275860l_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_859_order__le__less__subst2,axiom,
    ! [F: fun_na138495129l_bool,Ca: fun_fu2098777574l_bool,Aa: nat,Ba: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,hAPP_n1555388849l_bool(F,Ba)),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,hAPP_n1555388849l_bool(F,X_1)),hAPP_n1555388849l_bool(F,Y_1))) )
         => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,hAPP_n1555388849l_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_860_order__le__less__subst2,axiom,
    ! [F: fun_na6909291l_bool,Ca: fun_fu3835832l_bool,Aa: nat,Ba: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,hAPP_n2125602947l_bool(F,Ba)),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,hAPP_n2125602947l_bool(F,X_1)),hAPP_n2125602947l_bool(F,Y_1))) )
         => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,hAPP_n2125602947l_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_861_order__le__less__subst2,axiom,
    ! [F: fun_na998785244t_bool,Ca: fun_Pr2067565481t_bool,Aa: nat,Ba: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,hAPP_n1161265524t_bool(F,Ba)),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,hAPP_n1161265524t_bool(F,X_1)),hAPP_n1161265524t_bool(F,Y_1))) )
         => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,hAPP_n1161265524t_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_862_order__le__less__subst2,axiom,
    ! [F: fun_nat_bool,Ca: bool,Aa: nat,Ba: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Ba)),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(F,Y_1))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_863_order__le__less__subst2,axiom,
    ! [F: fun_na300967376t_bool,Ca: fun_Ar331856045t_bool,Aa: nat,Ba: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba))
     => ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,hAPP_n1312530466t_bool(F,Ba)),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
             => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,hAPP_n1312530466t_bool(F,X_1)),hAPP_n1312530466t_bool(F,Y_1))) )
         => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,hAPP_n1312530466t_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_864_order__le__less__subst2,axiom,
    ! [F: fun_fu821463397t_bool,Ca: fun_nat_bool,Aa: fun_nat_bool,Ba: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Ba)),Ca))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(F,X_1)),hAPP_f800510211t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_865_order__le__less__subst2,axiom,
    ! [F: fun_fu1096920966t_bool,Ca: fun_Pr1643180309t_bool,Aa: fun_nat_bool,Ba: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(F,Ba)),Ca))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f1061584978t_bool(F,X_1)),hAPP_f1061584978t_bool(F,Y_1))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_f1061584978t_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_866_order__le__less__subst2,axiom,
    ! [F: fun_fu1415967063i_bool,Ca: fun_Ar1809396326i_bool,Aa: fun_nat_bool,Ba: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,hAPP_f1992344867i_bool(F,Ba)),Ca))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,hAPP_f1992344867i_bool(F,X_1)),hAPP_f1992344867i_bool(F,Y_1))) )
         => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,hAPP_f1992344867i_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_867_order__le__less__subst2,axiom,
    ! [F: fun_fu1182412548l_bool,Ca: fun_fu638310559l_bool,Aa: fun_nat_bool,Ba: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,hAPP_f229466530l_bool(F,Ba)),Ca))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,hAPP_f229466530l_bool(F,X_1)),hAPP_f229466530l_bool(F,Y_1))) )
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,hAPP_f229466530l_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_868_order__le__less__subst2,axiom,
    ! [F: fun_fu1927280855l_bool,Ca: fun_fu2098777574l_bool,Aa: fun_nat_bool,Ba: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,hAPP_f561646243l_bool(F,Ba)),Ca))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,hAPP_f561646243l_bool(F,X_1)),hAPP_f561646243l_bool(F,Y_1))) )
         => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,hAPP_f561646243l_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_869_order__le__less__subst2,axiom,
    ! [F: fun_fu138597289l_bool,Ca: fun_fu3835832l_bool,Aa: fun_nat_bool,Ba: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,hAPP_f256405365l_bool(F,Ba)),Ca))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,hAPP_f256405365l_bool(F,X_1)),hAPP_f256405365l_bool(F,Y_1))) )
         => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,hAPP_f256405365l_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_870_order__le__less__subst2,axiom,
    ! [F: fun_fu1778022682t_bool,Ca: fun_Pr2067565481t_bool,Aa: fun_nat_bool,Ba: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,hAPP_f1472089702t_bool(F,Ba)),Ca))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,hAPP_f1472089702t_bool(F,X_1)),hAPP_f1472089702t_bool(F,Y_1))) )
         => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,hAPP_f1472089702t_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_871_order__le__less__subst2,axiom,
    ! [F: fun_fu425979586l_bool,Ca: bool,Aa: fun_nat_bool,Ba: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(F,Ba)),Ca))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_f54304608l_bool(F,X_1)),hAPP_f54304608l_bool(F,Y_1))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_f54304608l_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_872_order__le__less__subst2,axiom,
    ! [F: fun_fu221658642t_bool,Ca: fun_Ar331856045t_bool,Aa: fun_nat_bool,Ba: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
     => ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,hAPP_f1635284656t_bool(F,Ba)),Ca))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
             => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,hAPP_f1635284656t_bool(F,X_1)),hAPP_f1635284656t_bool(F,Y_1))) )
         => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,hAPP_f1635284656t_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_873_order__le__less__subst2,axiom,
    ! [F: fun_fu1632756612t_bool,Ca: fun_nat_bool,Aa: fun_fu638310559l_bool,Ba: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Aa),Ba))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2063587362t_bool(F,Ba)),Ca))
       => ( ! [X_1: fun_fu638310559l_bool,Y_1: fun_fu638310559l_bool] :
              ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f2063587362t_bool(F,X_1)),hAPP_f2063587362t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f2063587362t_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_874_order__le__less__subst2,axiom,
    ! [F: fun_fu309681663t_bool,Ca: fun_nat_bool,Aa: fun_fu2098777574l_bool,Ba: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Aa),Ba))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1705385041t_bool(F,Ba)),Ca))
       => ( ! [X_1: fun_fu2098777574l_bool,Y_1: fun_fu2098777574l_bool] :
              ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1705385041t_bool(F,X_1)),hAPP_f1705385041t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1705385041t_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_875_order__le__less__subst2,axiom,
    ! [F: fun_fu1078872017t_bool,Ca: fun_nat_bool,Aa: fun_fu3835832l_bool,Ba: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Aa),Ba))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f743717923t_bool(F,Ba)),Ca))
       => ( ! [X_1: fun_fu3835832l_bool,Y_1: fun_fu3835832l_bool] :
              ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f743717923t_bool(F,X_1)),hAPP_f743717923t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f743717923t_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_876_order__le__less__subst2,axiom,
    ! [F: fun_fu477456066t_bool,Ca: fun_nat_bool,Aa: fun_Pr2067565481t_bool,Ba: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Aa),Ba))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f703394068t_bool(F,Ba)),Ca))
       => ( ! [X_1: fun_Pr2067565481t_bool,Y_1: fun_Pr2067565481t_bool] :
              ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f703394068t_bool(F,X_1)),hAPP_f703394068t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f703394068t_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_877_order__le__less__subst2,axiom,
    ! [F: fun_bo1570548802t_bool,Ca: fun_nat_bool,Aa: bool,Ba: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ba))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(F,Ba)),Ca))
       => ( ! [X_1: bool,Y_1: bool] :
              ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_b1013836512t_bool(F,X_1)),hAPP_b1013836512t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_b1013836512t_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_878_order__le__less__subst2,axiom,
    ! [F: fun_fu1254370943t_bool,Ca: fun_nat_bool,Aa: fun_Ar1809396326i_bool,Ba: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Aa),Ba))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f622418129t_bool(F,Ba)),Ca))
       => ( ! [X_1: fun_Ar1809396326i_bool,Y_1: fun_Ar1809396326i_bool] :
              ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f622418129t_bool(F,X_1)),hAPP_f622418129t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f622418129t_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_879_order__le__less__subst2,axiom,
    ! [F: fun_fu988033326t_bool,Ca: fun_nat_bool,Aa: fun_Pr1643180309t_bool,Ba: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ba))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Ba)),Ca))
       => ( ! [X_1: fun_Pr1643180309t_bool,Y_1: fun_Pr1643180309t_bool] :
              ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(F,X_1)),hAPP_f543204480t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_880_order__le__less__subst2,axiom,
    ! [F: fun_fu1869722514t_bool,Ca: fun_nat_bool,Aa: fun_Ar331856045t_bool,Ba: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Aa),Ba))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1691234864t_bool(F,Ba)),Ca))
       => ( ! [X_1: fun_Ar331856045t_bool,Y_1: fun_Ar331856045t_bool] :
              ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f1691234864t_bool(F,X_1)),hAPP_f1691234864t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f1691234864t_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_881_order__le__less__subst2,axiom,
    ! [F: fun_fu955147676ol_nat,Ca: nat,Aa: fun_fu638310559l_bool,Ba: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,Aa),Ba))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1487854056ol_nat(F,Ba)),Ca))
       => ( ! [X_1: fun_fu638310559l_bool,Y_1: fun_fu638310559l_bool] :
              ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,X_1),Y_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1487854056ol_nat(F,X_1)),hAPP_f1487854056ol_nat(F,Y_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1487854056ol_nat(F,Aa)),Ca)) ) ) ) ).

tff(fact_882_order__le__less__subst2,axiom,
    ! [F: fun_fu859131105ol_nat,Ca: nat,Aa: fun_fu2098777574l_bool,Ba: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,Aa),Ba))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1049163897ol_nat(F,Ba)),Ca))
       => ( ! [X_1: fun_fu2098777574l_bool,Y_1: fun_fu2098777574l_bool] :
              ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,X_1),Y_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1049163897ol_nat(F,X_1)),hAPP_f1049163897ol_nat(F,Y_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1049163897ol_nat(F,Aa)),Ca)) ) ) ) ).

tff(fact_883_order__le__less__subst2,axiom,
    ! [F: fun_fu777705871ol_nat,Ca: nat,Aa: fun_fu3835832l_bool,Ba: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,Aa),Ba))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f602722087ol_nat(F,Ba)),Ca))
       => ( ! [X_1: fun_fu3835832l_bool,Y_1: fun_fu3835832l_bool] :
              ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,X_1),Y_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f602722087ol_nat(F,X_1)),hAPP_f602722087ol_nat(F,Y_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f602722087ol_nat(F,Aa)),Ca)) ) ) ) ).

tff(fact_884_order__le__less__subst2,axiom,
    ! [F: fun_fu841105374ol_nat,Ca: nat,Aa: fun_Pr2067565481t_bool,Ba: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,Aa),Ba))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1842225014ol_nat(F,Ba)),Ca))
       => ( ! [X_1: fun_Pr2067565481t_bool,Y_1: fun_Pr2067565481t_bool] :
              ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,X_1),Y_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1842225014ol_nat(F,X_1)),hAPP_f1842225014ol_nat(F,Y_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1842225014ol_nat(F,Aa)),Ca)) ) ) ) ).

tff(fact_885_order__le__less__subst2,axiom,
    ! [F: fun_bool_nat,Ca: nat,Aa: bool,Ba: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ba))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(F,Ba)),Ca))
       => ( ! [X_1: bool,Y_1: bool] :
              ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_1),Y_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_bool_nat(F,X_1)),hAPP_bool_nat(F,Y_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_bool_nat(F,Aa)),Ca)) ) ) ) ).

tff(fact_886_order__le__less__subst2,axiom,
    ! [F: fun_fu1603738721ol_nat,Ca: nat,Aa: fun_Ar1809396326i_bool,Ba: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,Aa),Ba))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f846027769ol_nat(F,Ba)),Ca))
       => ( ! [X_1: fun_Ar1809396326i_bool,Y_1: fun_Ar1809396326i_bool] :
              ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,X_1),Y_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f846027769ol_nat(F,X_1)),hAPP_f846027769ol_nat(F,Y_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f846027769ol_nat(F,Aa)),Ca)) ) ) ) ).

tff(fact_887_order__le__less__subst2,axiom,
    ! [F: fun_fu572628082ol_nat,Ca: nat,Aa: fun_Pr1643180309t_bool,Ba: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ba))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Ba)),Ca))
       => ( ! [X_1: fun_Pr1643180309t_bool,Y_1: fun_Pr1643180309t_bool] :
              ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_1),Y_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(F,X_1)),hAPP_f2030293770ol_nat(F,Y_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Aa)),Ca)) ) ) ) ).

tff(fact_888_order__le__less__subst2,axiom,
    ! [F: fun_fu1677555470ol_nat,Ca: nat,Aa: fun_Ar331856045t_bool,Ba: fun_Ar331856045t_bool] :
      ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,Aa),Ba))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1403773274ol_nat(F,Ba)),Ca))
       => ( ! [X_1: fun_Ar331856045t_bool,Y_1: fun_Ar331856045t_bool] :
              ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,X_1),Y_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f1403773274ol_nat(F,X_1)),hAPP_f1403773274ol_nat(F,Y_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f1403773274ol_nat(F,Aa)),Ca)) ) ) ) ).

tff(fact_889_order__less__le__subst2,axiom,
    ! [F: fun_fu821463397t_bool,Ca: fun_nat_bool,Aa: fun_nat_bool,Ba: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(F,Ba)),Ca))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,X_1)),hAPP_f800510211t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f800510211t_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_890_order__less__le__subst2,axiom,
    ! [F: fun_fu988033326t_bool,Ca: fun_nat_bool,Aa: fun_Pr1643180309t_bool,Ba: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f543204480t_bool(F,Ba)),Ca))
       => ( ! [X_1: fun_Pr1643180309t_bool,Y_1: fun_Pr1643180309t_bool] :
              ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,X_1)),hAPP_f543204480t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f543204480t_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_891_order__less__le__subst2,axiom,
    ! [F: fun_fu1254370943t_bool,Ca: fun_nat_bool,Aa: fun_Ar1809396326i_bool,Ba: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Aa),Ba))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f622418129t_bool(F,Ba)),Ca))
       => ( ! [X_1: fun_Ar1809396326i_bool,Y_1: fun_Ar1809396326i_bool] :
              ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f622418129t_bool(F,X_1)),hAPP_f622418129t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_f622418129t_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_892_order__less__le__subst2,axiom,
    ! [F: fun_nat_fun_nat_bool,Ca: fun_nat_bool,Aa: nat,Ba: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,Ba)),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,X_1)),hAPP_n1699378549t_bool(F,Y_1))) )
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,hAPP_n1699378549t_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_893_order__less__le__subst2,axiom,
    ! [F: fun_na1041622088t_bool,Ca: fun_Pr1643180309t_bool,Aa: nat,Ba: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_n454528608t_bool(F,Ba)),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,X_1)),hAPP_n454528608t_bool(F,Y_1))) )
         => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,hAPP_n454528608t_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_894_order__less__le__subst2,axiom,
    ! [F: fun_na2037635353i_bool,Ca: fun_Ar1809396326i_bool,Aa: nat,Ba: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,hAPP_n34002993i_bool(F,Ba)),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,hAPP_n34002993i_bool(F,X_1)),hAPP_n34002993i_bool(F,Y_1))) )
         => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,hAPP_n34002993i_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_895_order__less__le__subst2,axiom,
    ! [F: fun_na144630978l_bool,Ca: fun_fu638310559l_bool,Aa: nat,Ba: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,hAPP_n1134275860l_bool(F,Ba)),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,hAPP_n1134275860l_bool(F,X_1)),hAPP_n1134275860l_bool(F,Y_1))) )
         => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,hAPP_n1134275860l_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_896_order__less__le__subst2,axiom,
    ! [F: fun_na138495129l_bool,Ca: fun_fu2098777574l_bool,Aa: nat,Ba: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,hAPP_n1555388849l_bool(F,Ba)),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,hAPP_n1555388849l_bool(F,X_1)),hAPP_n1555388849l_bool(F,Y_1))) )
         => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,hAPP_n1555388849l_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_897_order__less__le__subst2,axiom,
    ! [F: fun_na6909291l_bool,Ca: fun_fu3835832l_bool,Aa: nat,Ba: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,hAPP_n2125602947l_bool(F,Ba)),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,hAPP_n2125602947l_bool(F,X_1)),hAPP_n2125602947l_bool(F,Y_1))) )
         => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,hAPP_n2125602947l_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_898_order__less__le__subst2,axiom,
    ! [F: fun_na998785244t_bool,Ca: fun_Pr2067565481t_bool,Aa: nat,Ba: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,hAPP_n1161265524t_bool(F,Ba)),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,hAPP_n1161265524t_bool(F,X_1)),hAPP_n1161265524t_bool(F,Y_1))) )
         => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,hAPP_n1161265524t_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_899_order__less__le__subst2,axiom,
    ! [F: fun_nat_bool,Ca: bool,Aa: nat,Ba: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,Ba)),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(F,Y_1))) )
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,hAPP_nat_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_900_order__less__le__subst2,axiom,
    ! [F: fun_na300967376t_bool,Ca: fun_Ar331856045t_bool,Aa: nat,Ba: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba))
     => ( hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le172225251t_bool,hAPP_n1312530466t_bool(F,Ba)),Ca))
       => ( ! [X_1: nat,Y_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
             => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,hAPP_n1312530466t_bool(F,X_1)),hAPP_n1312530466t_bool(F,Y_1))) )
         => hBOOL(hAPP_f1452856589l_bool(hAPP_f1055587775l_bool(ord_le19409623t_bool,hAPP_n1312530466t_bool(F,Aa)),Ca)) ) ) ) ).

tff(fact_901_order__less__le__subst2,axiom,
    ! [F: fun_fun_nat_bool_nat,Ca: nat,Aa: fun_nat_bool,Ba: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(F,Ba)),Ca))
       => ( ! [X_1: fun_nat_bool,Y_1: fun_nat_bool] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_1),Y_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(F,X_1)),hAPP_f22106695ol_nat(F,Y_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f22106695ol_nat(F,Aa)),Ca)) ) ) ) ).

tff(fact_902_order__less__le__subst2,axiom,
    ! [F: fun_fu572628082ol_nat,Ca: nat,Aa: fun_Pr1643180309t_bool,Ba: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2030293770ol_nat(F,Ba)),Ca))
       => ( ! [X_1: fun_Pr1643180309t_bool,Y_1: fun_Pr1643180309t_bool] :
              ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_1),Y_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,X_1)),hAPP_f2030293770ol_nat(F,Y_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f2030293770ol_nat(F,Aa)),Ca)) ) ) ) ).

tff(fact_903_order__less__le__subst2,axiom,
    ! [F: fun_fu1603738721ol_nat,Ca: nat,Aa: fun_Ar1809396326i_bool,Ba: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,Aa),Ba))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f846027769ol_nat(F,Ba)),Ca))
       => ( ! [X_1: fun_Ar1809396326i_bool,Y_1: fun_Ar1809396326i_bool] :
              ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,X_1),Y_1))
             => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f846027769ol_nat(F,X_1)),hAPP_f846027769ol_nat(F,Y_1))) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_f846027769ol_nat(F,Aa)),Ca)) ) ) ) ).

tff(fact_904_add__leE,axiom,
    ! [M_2: nat,K_2: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_2)),N))
     => ~ ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N))
         => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N)) ) ) ).

tff(fact_905_equalityI,axiom,
    ! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,A),B))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,B),A))
       => ( A = B ) ) ) ).

tff(fact_906_equalityI,axiom,
    ! [A: fun_fu2098777574l_bool,B: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,A),B))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,B),A))
       => ( A = B ) ) ) ).

tff(fact_907_equalityI,axiom,
    ! [A: fun_fu3835832l_bool,B: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,A),B))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,B),A))
       => ( A = B ) ) ) ).

tff(fact_908_equalityI,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,A),B))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,B),A))
       => ( A = B ) ) ) ).

tff(fact_909_equalityI,axiom,
    ! [A: fun_Ar1809396326i_bool,B: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,A),B))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,B),A))
       => ( A = B ) ) ) ).

tff(fact_910_equalityI,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,B),A))
       => ( A = B ) ) ) ).

tff(fact_911_equalityI,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A))
       => ( A = B ) ) ) ).

tff(fact_912_subsetD,axiom,
    ! [Ca: arrow_856714788e_indi,A: fun_Ar1809396326i_bool,B: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,A),B))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,Ca),A))
       => hBOOL(hAPP_f584385070l_bool(hAPP_A1597696899l_bool(member1479139729e_indi,Ca),B)) ) ) ).

tff(fact_913_subsetD,axiom,
    ! [Ca: bool,A: fun_bool_bool,B: fun_bool_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A),B))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Ca),A))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Ca),B)) ) ) ).

tff(fact_914_subsetD,axiom,
    ! [Ca: product_unit,A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,Ca),A))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,Ca),B)) ) ) ).

tff(fact_915_subsetD,axiom,
    ! [Ca: produc472769767le_alt,A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,A),B))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,Ca),A))
       => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,Ca),B)) ) ) ).

tff(fact_916_subsetD,axiom,
    ! [Ca: fun_Ar274636406t_bool,A: fun_fu3835832l_bool,B: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,A),B))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,Ca),A))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,Ca),B)) ) ) ).

tff(fact_917_subsetD,axiom,
    ! [Ca: fun_fu2114379172t_bool,A: fun_fu2098777574l_bool,B: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,A),B))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,Ca),A))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,Ca),B)) ) ) ).

tff(fact_918_subsetD,axiom,
    ! [Ca: fun_Pr2067565481t_bool,A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,A),B))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,Ca),A))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,Ca),B)) ) ) ).

tff(fact_919_subsetD,axiom,
    ! [Ca: nat,A: fun_nat_bool,B: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B)) ) ) ).

tff(fact_920_psubset__eq,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B))
    <=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B))
        & ( A != B ) ) ) ).

tff(fact_921_psubset__eq,axiom,
    ! [A: fun_Ar1809396326i_bool,B: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,A),B))
    <=> ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,A),B))
        & ( A != B ) ) ) ).

tff(fact_922_psubset__eq,axiom,
    ! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,A),B))
    <=> ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,A),B))
        & ( A != B ) ) ) ).

tff(fact_923_psubset__eq,axiom,
    ! [A: fun_fu2098777574l_bool,B: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,A),B))
    <=> ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,A),B))
        & ( A != B ) ) ) ).

tff(fact_924_psubset__eq,axiom,
    ! [A: fun_fu3835832l_bool,B: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,A),B))
    <=> ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,A),B))
        & ( A != B ) ) ) ).

tff(fact_925_psubset__eq,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,A),B))
    <=> ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,A),B))
        & ( A != B ) ) ) ).

tff(fact_926_psubset__eq,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B))
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
        & ( A != B ) ) ) ).

tff(fact_927_subset__iff__psubset__eq,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B))
    <=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B))
        | ( A = B ) ) ) ).

tff(fact_928_subset__iff__psubset__eq,axiom,
    ! [A: fun_Ar1809396326i_bool,B: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,A),B))
    <=> ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,A),B))
        | ( A = B ) ) ) ).

tff(fact_929_subset__iff__psubset__eq,axiom,
    ! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,A),B))
    <=> ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,A),B))
        | ( A = B ) ) ) ).

tff(fact_930_subset__iff__psubset__eq,axiom,
    ! [A: fun_fu2098777574l_bool,B: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,A),B))
    <=> ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,A),B))
        | ( A = B ) ) ) ).

tff(fact_931_subset__iff__psubset__eq,axiom,
    ! [A: fun_fu3835832l_bool,B: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,A),B))
    <=> ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,A),B))
        | ( A = B ) ) ) ).

tff(fact_932_subset__iff__psubset__eq,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,A),B))
    <=> ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,A),B))
        | ( A = B ) ) ) ).

tff(fact_933_subset__iff__psubset__eq,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B))
        | ( A = B ) ) ) ).

tff(fact_934_psubset__imp__subset,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B))
     => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B)) ) ).

tff(fact_935_psubset__imp__subset,axiom,
    ! [A: fun_Ar1809396326i_bool,B: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,A),B))
     => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,A),B)) ) ).

tff(fact_936_psubset__imp__subset,axiom,
    ! [A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,A),B))
     => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,A),B)) ) ).

tff(fact_937_psubset__imp__subset,axiom,
    ! [A: fun_fu2098777574l_bool,B: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,A),B))
     => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,A),B)) ) ).

tff(fact_938_psubset__imp__subset,axiom,
    ! [A: fun_fu3835832l_bool,B: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,A),B))
     => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,A),B)) ) ).

tff(fact_939_psubset__imp__subset,axiom,
    ! [A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,A),B))
     => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,A),B)) ) ).

tff(fact_940_psubset__imp__subset,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B))
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ) ).

tff(fact_941_psubset__subset__trans,axiom,
    ! [C: fun_Pr1643180309t_bool,A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,B),C))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),C)) ) ) ).

tff(fact_942_psubset__subset__trans,axiom,
    ! [C: fun_Ar1809396326i_bool,A: fun_Ar1809396326i_bool,B: fun_Ar1809396326i_bool] :
      ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,A),B))
     => ( hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le1609180592i_bool,B),C))
       => hBOOL(hAPP_f584385070l_bool(hAPP_f731870893l_bool(ord_le225487548i_bool,A),C)) ) ) ).

tff(fact_943_psubset__subset__trans,axiom,
    ! [C: fun_fu638310559l_bool,A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,A),B))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,B),C))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,A),C)) ) ) ).

tff(fact_944_psubset__subset__trans,axiom,
    ! [C: fun_fu2098777574l_bool,A: fun_fu2098777574l_bool,B: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,A),B))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,B),C))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,A),C)) ) ) ).

tff(fact_945_psubset__subset__trans,axiom,
    ! [C: fun_fu3835832l_bool,A: fun_fu3835832l_bool,B: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,A),B))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,B),C))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,A),C)) ) ) ).

tff(fact_946_psubset__subset__trans,axiom,
    ! [C: fun_Pr2067565481t_bool,A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,A),B))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,B),C))
       => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,A),C)) ) ) ).

tff(fact_947_psubset__subset__trans,axiom,
    ! [C: fun_nat_bool,A: fun_nat_bool,B: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),C))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),C)) ) ) ).

tff(fact_948_subset__psubset__trans,axiom,
    ! [C: fun_fu638310559l_bool,A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,A),B))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,B),C))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1727358153l_bool,A),C)) ) ) ).

tff(fact_949_subset__psubset__trans,axiom,
    ! [C: fun_fu2098777574l_bool,A: fun_fu2098777574l_bool,B: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,A),B))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,B),C))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le119247420l_bool,A),C)) ) ) ).

tff(fact_950_subset__psubset__trans,axiom,
    ! [C: fun_fu3835832l_bool,A: fun_fu3835832l_bool,B: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,A),B))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,B),C))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1959568910l_bool,A),C)) ) ) ).

tff(fact_951_subset__psubset__trans,axiom,
    ! [C: fun_Pr2067565481t_bool,A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,A),B))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,B),C))
       => hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1478665215t_bool,A),C)) ) ) ).

tff(fact_952_subset__psubset__trans,axiom,
    ! [C: fun_nat_bool,A: fun_nat_bool,B: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,B),C))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),C)) ) ) ).

tff(fact_953_equalityE,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( A = B )
     => ~ ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
         => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)) ) ) ).

tff(fact_954_subset__trans,axiom,
    ! [C: fun_nat_bool,A: fun_nat_bool,B: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),C))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),C)) ) ) ).

tff(fact_955_set__mp,axiom,
    ! [X_2: nat,A: fun_nat_bool,B: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B)) ) ) ).

tff(fact_956_set__mp,axiom,
    ! [X_2: fun_Pr2067565481t_bool,A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,A),B))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),B)) ) ) ).

tff(fact_957_set__mp,axiom,
    ! [X_2: fun_fu2114379172t_bool,A: fun_fu2098777574l_bool,B: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,A),B))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),B)) ) ) ).

tff(fact_958_set__mp,axiom,
    ! [X_2: fun_Ar274636406t_bool,A: fun_fu3835832l_bool,B: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,A),B))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),B)) ) ) ).

tff(fact_959_set__mp,axiom,
    ! [X_2: produc472769767le_alt,A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,A),B))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A))
       => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),B)) ) ) ).

tff(fact_960_set__rev__mp,axiom,
    ! [B: fun_nat_bool,X_2: nat,A: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B)) ) ) ).

tff(fact_961_set__rev__mp,axiom,
    ! [B: fun_fu638310559l_bool,X_2: fun_Pr2067565481t_bool,A: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,A),B))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),B)) ) ) ).

tff(fact_962_set__rev__mp,axiom,
    ! [B: fun_fu2098777574l_bool,X_2: fun_fu2114379172t_bool,A: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,A),B))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),B)) ) ) ).

tff(fact_963_set__rev__mp,axiom,
    ! [B: fun_fu3835832l_bool,X_2: fun_Ar274636406t_bool,A: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,A),B))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),B)) ) ) ).

tff(fact_964_set__rev__mp,axiom,
    ! [B: fun_Pr2067565481t_bool,X_2: produc472769767le_alt,A: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,A),B))
       => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),B)) ) ) ).

tff(fact_965_predicate1D,axiom,
    ! [X_2: nat,Pa: fun_nat_bool,Q_1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Pa),Q_1))
     => ( hBOOL(hAPP_nat_bool(Pa,X_2))
       => hBOOL(hAPP_nat_bool(Q_1,X_2)) ) ) ).

tff(fact_966_in__mono,axiom,
    ! [X_2: nat,A: fun_nat_bool,B: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B)) ) ) ).

tff(fact_967_in__mono,axiom,
    ! [X_2: fun_Pr2067565481t_bool,A: fun_fu638310559l_bool,B: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,A),B))
     => ( hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),A))
       => hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,X_2),B)) ) ) ).

tff(fact_968_in__mono,axiom,
    ! [X_2: fun_fu2114379172t_bool,A: fun_fu2098777574l_bool,B: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,A),B))
     => ( hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),A))
       => hBOOL(hAPP_f975209902l_bool(hAPP_f1714503811l_bool(member173038353t_bool,X_2),B)) ) ) ).

tff(fact_969_in__mono,axiom,
    ! [X_2: fun_Ar274636406t_bool,A: fun_fu3835832l_bool,B: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,A),B))
     => ( hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),A))
       => hBOOL(hAPP_f73423488l_bool(hAPP_f1225332775l_bool(member933336803t_bool,X_2),B)) ) ) ).

tff(fact_970_in__mono,axiom,
    ! [X_2: produc472769767le_alt,A: fun_Pr2067565481t_bool,B: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,A),B))
     => ( hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),A))
       => hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,X_2),B)) ) ) ).

tff(fact_971_equalityD2,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( A = B )
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)) ) ).

tff(fact_972_equalityD1,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( A = B )
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ) ).

tff(fact_973_rev__predicate1D,axiom,
    ! [Q_1: fun_nat_bool,Pa: fun_nat_bool,X_2: nat] :
      ( hBOOL(hAPP_nat_bool(Pa,X_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Pa),Q_1))
       => hBOOL(hAPP_nat_bool(Q_1,X_2)) ) ) ).

tff(fact_974_set__eq__subset,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( A = B )
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)) ) ) ).

tff(fact_975_subset__refl,axiom,
    ! [A: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),A)) ).

tff(fact_976_pred__subset__eq,axiom,
    ! [R_1: fun_nat_bool,S_1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),R_1)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),S_1)))
    <=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,R_1),S_1)) ) ).

tff(fact_977_pred__subset__eq,axiom,
    ! [R_1: fun_fu638310559l_bool,S_1: fun_fu638310559l_bool] :
      ( hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,hAPP_f1060563265l_bool(hAPP_f1776355587l_bool(cOMBC_2133093654l_bool,member1069471740t_bool),R_1)),hAPP_f1060563265l_bool(hAPP_f1776355587l_bool(cOMBC_2133093654l_bool,member1069471740t_bool),S_1)))
    <=> hBOOL(hAPP_f182583295l_bool(hAPP_f1722316607l_bool(ord_le1545885909l_bool,R_1),S_1)) ) ).

tff(fact_978_pred__subset__eq,axiom,
    ! [R_1: fun_fu2098777574l_bool,S_1: fun_fu2098777574l_bool] :
      ( hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,hAPP_f1181604821l_bool(hAPP_f1169241965l_bool(cOMBC_1209358050l_bool,member173038353t_bool),R_1)),hAPP_f1181604821l_bool(hAPP_f1169241965l_bool(cOMBC_1209358050l_bool,member173038353t_bool),S_1)))
    <=> hBOOL(hAPP_f975209902l_bool(hAPP_f916323245l_bool(ord_le1121695024l_bool,R_1),S_1)) ) ).

tff(fact_979_pred__subset__eq,axiom,
    ! [R_1: fun_fu3835832l_bool,S_1: fun_fu3835832l_bool] :
      ( hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,hAPP_f819682389l_bool(hAPP_f1760776521l_bool(cOMBC_514203746l_bool,member933336803t_bool),R_1)),hAPP_f819682389l_bool(hAPP_f1760776521l_bool(cOMBC_514203746l_bool,member933336803t_bool),S_1)))
    <=> hBOOL(hAPP_f73423488l_bool(hAPP_f585353809l_bool(ord_le1099920642l_bool,R_1),S_1)) ) ).

tff(fact_980_pred__subset__eq,axiom,
    ! [R_1: fun_Pr2067565481t_bool,S_1: fun_Pr2067565481t_bool] :
      ( hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,hAPP_f1356305429t_bool(hAPP_f1033183015t_bool(cOMBC_593569186l_bool,member1333168212le_alt),R_1)),hAPP_f1356305429t_bool(hAPP_f1033183015t_bool(cOMBC_593569186l_bool,member1333168212le_alt),S_1)))
    <=> hBOOL(hAPP_f52567537l_bool(hAPP_f930900275l_bool(ord_le1577377523t_bool,R_1),S_1)) ) ).

tff(fact_981_less__not__refl,axiom,
    ! [N: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N)) ).

tff(fact_982_nat__neq__iff,axiom,
    ! [M_1: nat,Na: nat] :
      ( ( M_1 != Na )
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1)) ) ) ).

tff(fact_983_linorder__neqE__nat,axiom,
    ! [X: nat,Y: nat] :
      ( ( X != Y )
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y),X)) ) ) ).

tff(fact_984_less__irrefl__nat,axiom,
    ! [N: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N)) ).

tff(fact_985_less__not__refl2,axiom,
    ! [N: nat,M_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M_2))
     => ( M_2 != N ) ) ).

tff(fact_986_less__not__refl3,axiom,
    ! [S: nat,T: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T))
     => ( S != T ) ) ).

tff(fact_987_nat__less__cases,axiom,
    ! [Pa: fun_nat_fun_nat_bool,M_1: nat,Na: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1)) )
     => ( ( ( M_1 = Na )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1)) )
       => ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1))
           => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1)) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_1)) ) ) ) ).

tff(fact_988_nat__add__commute,axiom,
    ! [M_2: nat,N: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M_2) ) ).

tff(fact_989_nat__add__left__commute,axiom,
    ! [X: nat,Y: nat,Z: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X),Z)) ) ).

tff(fact_990_nat__add__assoc,axiom,
    ! [M_2: nat,N: nat,K_2: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N)),K_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),K_2)) ) ).

tff(fact_991_nat__add__left__cancel,axiom,
    ! [K: nat,M_1: nat,Na: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na) )
    <=> ( M_1 = Na ) ) ).

tff(fact_992_nat__add__right__cancel,axiom,
    ! [M_1: nat,K: nat,Na: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Na),K) )
    <=> ( M_1 = Na ) ) ).

tff(fact_993_le__refl,axiom,
    ! [N: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),N)) ).

tff(fact_994_nat__le__linear,axiom,
    ! [M_2: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M_2)) ) ).

tff(fact_995_eq__imp__le,axiom,
    ! [M_2: nat,N: nat] :
      ( ( M_2 = N )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N)) ) ).

tff(fact_996_le__trans,axiom,
    ! [K_2: nat,I_2: nat,J_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),K_2))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),K_2)) ) ) ).

tff(fact_997_le__antisym,axiom,
    ! [M_2: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M_2))
       => ( M_2 = N ) ) ) ).

tff(fact_998_inj__on__add__nat,axiom,
    ! [K: nat,N_2: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),K)),N_2)) ).

tff(fact_999_not__add__less1,axiom,
    ! [I_2: nat,J_1: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),J_1)),I_2)) ).

tff(fact_1000_not__add__less2,axiom,
    ! [J_1: nat,I_2: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),I_2)),I_2)) ).

tff(fact_1001_nat__add__left__cancel__less,axiom,
    ! [K: nat,M_1: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ).

tff(fact_1002_trans__less__add1,axiom,
    ! [M_2: nat,I_2: nat,J_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),M_2))) ) ).

tff(fact_1003_trans__less__add2,axiom,
    ! [M_2: nat,I_2: nat,J_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),J_1))) ) ).

tff(fact_1004_add__less__mono1,axiom,
    ! [K_2: nat,I_2: nat,J_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),K_2))) ) ).

tff(fact_1005_add__less__mono,axiom,
    ! [K_2: nat,L_1: nat,I_2: nat,J_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_2),L_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),L_1))) ) ) ).

tff(fact_1006_less__add__eq__less,axiom,
    ! [M_2: nat,N: nat,K_2: nat,L_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_2),L_1))
     => ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),L_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_2),N) )
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) ) ) ).

tff(fact_1007_add__lessD1,axiom,
    ! [I_2: nat,J_1: nat,K_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),J_1)),K_2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),K_2)) ) ).

tff(fact_1008_nat__less__le,axiom,
    ! [M_1: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
        & ( M_1 != Na ) ) ) ).

tff(fact_1009_le__eq__less__or__eq,axiom,
    ! [M_1: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
        | ( M_1 = Na ) ) ) ).

tff(fact_1010_less__imp__le__nat,axiom,
    ! [M_2: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N)) ) ).

tff(fact_1011_le__neq__implies__less,axiom,
    ! [M_2: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N))
     => ( ( M_2 != N )
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) ) ) ).

tff(fact_1012_less__or__eq__imp__le,axiom,
    ! [M_2: nat,N: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
        | ( M_2 = N ) )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N)) ) ).

tff(fact_1013_le__add2,axiom,
    ! [N: nat,M_2: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N))) ).

tff(fact_1014_le__add1,axiom,
    ! [N: nat,M_2: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M_2))) ).

tff(fact_1015_le__iff__add,axiom,
    ! [M_1: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
    <=> ? [K_1: nat] : ( Na = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1) ) ) ).

tff(fact_1016_nat__add__left__cancel__le,axiom,
    ! [K: nat,M_1: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) ).

tff(fact_1017_trans__le__add1,axiom,
    ! [M_2: nat,I_2: nat,J_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),M_2))) ) ).

tff(fact_1018_trans__le__add2,axiom,
    ! [M_2: nat,I_2: nat,J_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),J_1))) ) ).

tff(fact_1019_add__le__mono1,axiom,
    ! [K_2: nat,I_2: nat,J_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),K_2))) ) ).

tff(fact_1020_add__le__mono,axiom,
    ! [K_2: nat,L_1: nat,I_2: nat,J_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),L_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_1),L_1))) ) ) ).

tff(fact_1021_add__leD2,axiom,
    ! [M_2: nat,K_2: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_2)),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),N)) ) ).

tff(fact_1022_add__leD1,axiom,
    ! [M_2: nat,K_2: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_2)),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N)) ) ).

tff(fact_1023_mono__nat__linear__lb,axiom,
    ! [M_1: nat,K: nat,F: fun_nat_nat] :
      ( ! [M: nat,N_1: nat] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N_1))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,M)),hAPP_nat_nat(F,N_1))) )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(F,M_1)),K)),hAPP_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K)))) ) ).

tff(fact_1024_less__mono__imp__le__mono,axiom,
    ! [I: nat,J: nat,F: fun_nat_nat] :
      ( ! [I_1: nat,J_2: nat] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J_2))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,I_1)),hAPP_nat_nat(F,J_2))) )
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,I)),hAPP_nat_nat(F,J))) ) ) ).

tff(fact_1025_termination__basic__simps_I3_J,axiom,
    ! [Z: nat,X: nat,Y: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Y))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))) ) ).

tff(fact_1026_termination__basic__simps_I4_J,axiom,
    ! [Y: nat,X: nat,Z: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Z))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))) ) ).

tff(fact_1027_termination__basic__simps_I5_J,axiom,
    ! [X: nat,Y: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Y)) ) ).

tff(fact_1028_termination__basic__simps_I2_J,axiom,
    ! [Y: nat,X: nat,Z: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Z))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))) ) ).

tff(fact_1029_termination__basic__simps_I1_J,axiom,
    ! [Z: nat,X: nat,Y: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))) ) ).

tff(fact_1030_linear__alt,axiom,
    ? [L_2: fun_Pr2067565481t_bool] : hBOOL(hAPP_f182583295l_bool(hAPP_f1482930381l_bool(member1069471740t_bool,L_2),arrow_1361987423le_Lin)) ).

tff(fact_1031_finite__indi,axiom,
    hBOOL(hAPP_f584385070l_bool(finite92092049e_indi,top_to788185952i_bool)) ).

tff(fact_1032_finite__Collect__le__nat,axiom,
    ! [K: nat] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),K)))) ).

tff(fact_1033_finite__Collect__less__nat,axiom,
    ! [K: nat] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),K)))) ).

tff(fact_1034_infinite__UNIV__nat,axiom,
    ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,top_top_fun_nat_bool)) ).

tff(fact_1035_card__UNIV__unit,axiom,
    hAPP_f2030293770ol_nat(finite1949902593t_unit,top_to1257323279t_bool) = one_one_nat ).

tff(fact_1036_card__Collect__less__nat,axiom,
    ! [Na: nat] : ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),Na))) = Na ) ).

tff(fact_1037_finite__M__bounded__by__nat,axiom,
    ! [Pa: fun_nat_bool,I: nat] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),Pa)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),I))))) ).

tff(fact_1038_finite__nat__set__iff__bounded__le,axiom,
    ! [N_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_2))
    <=> ? [M: nat] :
        ! [X_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_2))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),M)) ) ) ).

tff(fact_1039_finite__nat__set__iff__bounded,axiom,
    ! [N_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_2))
    <=> ? [M: nat] :
        ! [X_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_2))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),M)) ) ) ).

tff(fact_1040_finite__less__ub,axiom,
    ! [U: nat,F: fun_nat_nat] :
      ( ! [N_1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(F,N_1)))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,hAPP_f618557131t_bool(cOMBB_800536526ol_nat(ord_less_eq_nat),F)),U)))) ) ).

tff(fact_1041_bounded__nat__set__is__finite,axiom,
    ! [Na: nat,N_2: fun_nat_bool] :
      ( ! [X_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_2))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Na)) )
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_2)) ) ).

tff(fact_1042_less__zeroE,axiom,
    ! [N: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat)) ).

tff(fact_1043_le0,axiom,
    ! [N: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N)) ).

tff(fact_1044_not__less0,axiom,
    ! [N: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat)) ).

tff(fact_1045_neq0__conv,axiom,
    ! [Na: nat] :
      ( ( Na != zero_zero_nat )
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na)) ) ).

tff(fact_1046_less__nat__zero__code,axiom,
    ! [N: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat)) ).

tff(fact_1047_gr__implies__not0,axiom,
    ! [M_2: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
     => ( N != zero_zero_nat ) ) ).

tff(fact_1048_gr0I,axiom,
    ! [N: nat] :
      ( ( N != zero_zero_nat )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) ) ).

tff(fact_1049_plus__nat_Oadd__0,axiom,
    ! [N: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),N) = N ) ).

tff(fact_1050_Nat_Oadd__0__right,axiom,
    ! [M_2: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),zero_zero_nat) = M_2 ) ).

tff(fact_1051_add__is__0,axiom,
    ! [M_1: nat,Na: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),Na) = zero_zero_nat )
    <=> ( ( M_1 = zero_zero_nat )
        & ( Na = zero_zero_nat ) ) ) ).

tff(fact_1052_add__eq__self__zero,axiom,
    ! [M_2: nat,N: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N) = M_2 )
     => ( N = zero_zero_nat ) ) ).

tff(fact_1053_le__0__eq,axiom,
    ! [Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),zero_zero_nat))
    <=> ( Na = zero_zero_nat ) ) ).

tff(fact_1054_less__eq__nat_Osimps_I1_J,axiom,
    ! [N: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N)) ).

tff(fact_1055_add__gr__0,axiom,
    ! [M_1: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),Na)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M_1))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na)) ) ) ).

tff(fact_1056_ex__least__nat__less,axiom,
    ! [Na: nat,Pa: fun_nat_bool] :
      ( ~ hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
     => ( hBOOL(hAPP_nat_bool(Pa,Na))
       => ? [K_1: nat] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_1),Na))
            & ! [I_1: nat] :
                ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),K_1))
               => ~ hBOOL(hAPP_nat_bool(Pa,I_1)) )
            & hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),one_one_nat))) ) ) ) ).

tff(fact_1057_ex__least__nat__le,axiom,
    ! [Na: nat,Pa: fun_nat_bool] :
      ( ~ hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
     => ( hBOOL(hAPP_nat_bool(Pa,Na))
       => ? [K_1: nat] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),Na))
            & ! [I_1: nat] :
                ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),K_1))
               => ~ hBOOL(hAPP_nat_bool(Pa,I_1)) )
            & hBOOL(hAPP_nat_bool(Pa,K_1)) ) ) ) ).

tff(fact_1058_less__imp__add__positive,axiom,
    ! [I_2: nat,J_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1))
     => ? [K_1: nat] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1))
          & ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K_1) = J_1 ) ) ) ).

tff(fact_1059_lessI,axiom,
    ! [N: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,N))) ).

tff(fact_1060_Suc__mono,axiom,
    ! [M_2: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),hAPP_nat_nat(suc,N))) ) ).

tff(fact_1061_zero__less__Suc,axiom,
    ! [N: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,N))) ).

tff(fact_1062_Suc__inject,axiom,
    ! [X: nat,Y: nat] :
      ( ( hAPP_nat_nat(suc,X) = hAPP_nat_nat(suc,Y) )
     => ( X = Y ) ) ).

tff(fact_1063_nat_Oinject,axiom,
    ! [Nat_5: nat,Nat_4: nat] :
      ( ( hAPP_nat_nat(suc,Nat_5) = hAPP_nat_nat(suc,Nat_4) )
    <=> ( Nat_5 = Nat_4 ) ) ).

tff(fact_1064_Suc__n__not__n,axiom,
    ! [N: nat] : ( hAPP_nat_nat(suc,N) != N ) ).

tff(fact_1065_n__not__Suc__n,axiom,
    ! [N: nat] : ( N != hAPP_nat_nat(suc,N) ) ).

tff(fact_1066_Suc__neq__Zero,axiom,
    ! [M_2: nat] : ( hAPP_nat_nat(suc,M_2) != zero_zero_nat ) ).

tff(fact_1067_Zero__neq__Suc,axiom,
    ! [M_2: nat] : ( zero_zero_nat != hAPP_nat_nat(suc,M_2) ) ).

tff(fact_1068_nat_Osimps_I3_J,axiom,
    ! [Nat_3: nat] : ( hAPP_nat_nat(suc,Nat_3) != zero_zero_nat ) ).

tff(fact_1069_Suc__not__Zero,axiom,
    ! [M_2: nat] : ( hAPP_nat_nat(suc,M_2) != zero_zero_nat ) ).

tff(fact_1070_nat_Osimps_I2_J,axiom,
    ! [Nat_2: nat] : ( zero_zero_nat != hAPP_nat_nat(suc,Nat_2) ) ).

tff(fact_1071_Zero__not__Suc,axiom,
    ! [M_2: nat] : ( zero_zero_nat != hAPP_nat_nat(suc,M_2) ) ).

tff(fact_1072_Suc__less__SucD,axiom,
    ! [M_2: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),hAPP_nat_nat(suc,N)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) ) ).

tff(fact_1073_Suc__lessD,axiom,
    ! [M_2: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) ) ).

tff(fact_1074_less__SucE,axiom,
    ! [M_2: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N)))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
       => ( M_2 = N ) ) ) ).

tff(fact_1075_less__trans__Suc,axiom,
    ! [K_2: nat,I_2: nat,J_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_1),K_2))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I_2)),K_2)) ) ) ).

tff(fact_1076_Suc__lessI,axiom,
    ! [M_2: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
     => ( ( hAPP_nat_nat(suc,M_2) != N )
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),N)) ) ) ).

tff(fact_1077_less__SucI,axiom,
    ! [M_2: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N))) ) ).

tff(fact_1078_less__antisym,axiom,
    ! [N: nat,M_2: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,M_2)))
       => ( M_2 = N ) ) ) ).

tff(fact_1079_not__less__less__Suc__eq,axiom,
    ! [Na: nat,M_1: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_1)))
      <=> ( Na = M_1 ) ) ) ).

tff(fact_1080_Suc__less__eq,axiom,
    ! [M_1: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ).

tff(fact_1081_less__Suc__eq,axiom,
    ! [M_1: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,Na)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
        | ( M_1 = Na ) ) ) ).

tff(fact_1082_not__less__eq,axiom,
    ! [M_1: nat,Na: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_1))) ) ).

tff(fact_1083_add__Suc__shift,axiom,
    ! [M_2: nat,N: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_2)),N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(suc,N)) ) ).

tff(fact_1084_add__Suc,axiom,
    ! [M_2: nat,N: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_2)),N) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N)) ) ).

tff(fact_1085_add__Suc__right,axiom,
    ! [M_2: nat,N: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N)) ) ).

tff(fact_1086_Suc__leD,axiom,
    ! [M_2: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N)) ) ).

tff(fact_1087_le__SucE,axiom,
    ! [M_2: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N)))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N))
       => ( M_2 = hAPP_nat_nat(suc,N) ) ) ) ).

tff(fact_1088_le__SucI,axiom,
    ! [M_2: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N))) ) ).

tff(fact_1089_Suc__le__mono,axiom,
    ! [Na: nat,M_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),hAPP_nat_nat(suc,M_1)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),M_1)) ) ).

tff(fact_1090_le__Suc__eq,axiom,
    ! [M_1: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(suc,Na)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
        | ( M_1 = hAPP_nat_nat(suc,Na) ) ) ) ).

tff(fact_1091_not__less__eq__eq,axiom,
    ! [M_1: nat,Na: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_1)) ) ).

tff(fact_1092_Suc__n__not__le__n,axiom,
    ! [N: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),N)) ).

tff(fact_1093_inj__Suc,axiom,
    ! [N_2: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(suc),N_2)) ).

tff(fact_1094_gr0__conv__Suc,axiom,
    ! [Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na))
    <=> ? [M: nat] : ( Na = hAPP_nat_nat(suc,M) ) ) ).

tff(fact_1095_less__Suc0,axiom,
    ! [Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,zero_zero_nat)))
    <=> ( Na = zero_zero_nat ) ) ).

tff(fact_1096_less__Suc__eq__0__disj,axiom,
    ! [M_1: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,Na)))
    <=> ( ( M_1 = zero_zero_nat )
        | ? [J_2: nat] :
            ( ( M_1 = hAPP_nat_nat(suc,J_2) )
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_2),Na)) ) ) ) ).

tff(fact_1097_add__is__1,axiom,
    ! [M_1: nat,Na: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),Na) = hAPP_nat_nat(suc,zero_zero_nat) )
    <=> ( ( ( M_1 = hAPP_nat_nat(suc,zero_zero_nat) )
          & ( Na = zero_zero_nat ) )
        | ( ( M_1 = zero_zero_nat )
          & ( Na = hAPP_nat_nat(suc,zero_zero_nat) ) ) ) ) ).

tff(fact_1098_one__is__add,axiom,
    ! [M_1: nat,Na: nat] :
      ( ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),Na) )
    <=> ( ( ( M_1 = hAPP_nat_nat(suc,zero_zero_nat) )
          & ( Na = zero_zero_nat ) )
        | ( ( M_1 = zero_zero_nat )
          & ( Na = hAPP_nat_nat(suc,zero_zero_nat) ) ) ) ) ).

tff(fact_1099_less__add__Suc1,axiom,
    ! [I_2: nat,M_2: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),M_2)))) ).

tff(fact_1100_less__add__Suc2,axiom,
    ! [I_2: nat,M_2: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),I_2)))) ).

tff(fact_1101_less__iff__Suc__add,axiom,
    ! [M_1: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na))
    <=> ? [K_1: nat] : ( Na = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1)) ) ) ).

tff(fact_1102_less__eq__Suc__le,axiom,
    ! [Na: nat,M_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_1))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_1)) ) ).

tff(fact_1103_less__Suc__eq__le,axiom,
    ! [M_1: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) ).

tff(fact_1104_Suc__le__eq,axiom,
    ! [M_1: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),Na))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ).

tff(fact_1105_le__imp__less__Suc,axiom,
    ! [M_2: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N))) ) ).

tff(fact_1106_Suc__leI,axiom,
    ! [M_2: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N)) ) ).

tff(fact_1107_le__less__Suc__eq,axiom,
    ! [M_1: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_1)))
      <=> ( Na = M_1 ) ) ) ).

tff(fact_1108_Suc__le__lessD,axiom,
    ! [M_2: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N)) ) ).

tff(fact_1109_One__nat__def,axiom,
    one_one_nat = hAPP_nat_nat(suc,zero_zero_nat) ).

tff(fact_1110_less__eq__Suc__le__raw,axiom,
    ! [X_1: nat] : ( hAPP_n1699378549t_bool(ord_less_nat,X_1) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X_1)) ) ).

tff(fact_1111_card__Collect__le__nat,axiom,
    ! [Na: nat] : ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),Na))) = hAPP_nat_nat(suc,Na) ) ).

tff(fact_1112_card__less__Suc,axiom,
    ! [I: nat,M_4: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_4))
     => ( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(member_nat),suc)),M_4))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),I))))) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),M_4))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,I))))) ) ) ).

tff(fact_1113_card__less,axiom,
    ! [I: nat,M_4: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_4))
     => ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),M_4))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,I))))) != zero_zero_nat ) ) ).

tff(fact_1114_card__less__Suc2,axiom,
    ! [I: nat,M_4: fun_nat_bool] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_4))
     => ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(member_nat),suc)),M_4))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),I)))) = hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(collect_nat,hAPP_f800510211t_bool(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),M_4))),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,I))))) ) ) ).

tff(fact_1115_inc__induct,axiom,
    ! [Pa: fun_nat_bool,I: nat,J: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J))
     => ( hBOOL(hAPP_nat_bool(Pa,J))
       => ( ! [I_1: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J))
             => ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,I_1)))
               => hBOOL(hAPP_nat_bool(Pa,I_1)) ) )
         => hBOOL(hAPP_nat_bool(Pa,I)) ) ) ) ).

tff(fact_1116_less__imp__Suc__add,axiom,
    ! [M_2: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N))
     => ? [K_1: nat] : ( N = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_1)) ) ) ).

tff(fact_1117_gr0__implies__Suc,axiom,
    ! [N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N))
     => ? [M: nat] : ( N = hAPP_nat_nat(suc,M) ) ) ).

tff(fact_1118_Suc__eq__plus1,axiom,
    ! [N: nat] : ( hAPP_nat_nat(suc,N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat) ) ).

tff(fact_1119_Suc__eq__plus1__left,axiom,
    ! [N: nat] : ( hAPP_nat_nat(suc,N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N) ) ).

tff(fact_1120_Suc__le__D,axiom,
    ! [N: nat,M_3: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),M_3))
     => ? [M: nat] : ( M_3 = hAPP_nat_nat(suc,M) ) ) ).

tff(fact_1121_lessE,axiom,
    ! [I_2: nat,K_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),K_2))
     => ( ( K_2 != hAPP_nat_nat(suc,I_2) )
       => ~ ! [J_2: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_2))
             => ( K_2 != hAPP_nat_nat(suc,J_2) ) ) ) ) ).

tff(fact_1122_Suc__lessE,axiom,
    ! [I_2: nat,K_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I_2)),K_2))
     => ~ ! [J_2: nat] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_2))
           => ( K_2 != hAPP_nat_nat(suc,J_2) ) ) ) ).

tff(fact_1123_not0__implies__Suc,axiom,
    ! [N: nat] :
      ( ( N != zero_zero_nat )
     => ? [M: nat] : ( N = hAPP_nat_nat(suc,M) ) ) ).

tff(fact_1124_nat_Oexhaust,axiom,
    ! [Y: nat] :
      ( ( Y != zero_zero_nat )
     => ~ ! [Nat_1: nat] : ( Y != hAPP_nat_nat(suc,Nat_1) ) ) ).

tff(fact_1125_zero__induct,axiom,
    ! [Pa: fun_nat_bool,K: nat] :
      ( hBOOL(hAPP_nat_bool(Pa,K))
     => ( ! [N_1: nat] :
            ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_1)))
           => hBOOL(hAPP_nat_bool(Pa,N_1)) )
       => hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) ) ) ).

tff(fact_1126_nat__induct,axiom,
    ! [Na: nat,Pa: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
     => ( ! [N_1: nat] :
            ( hBOOL(hAPP_nat_bool(Pa,N_1))
           => hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_1))) )
       => hBOOL(hAPP_nat_bool(Pa,Na)) ) ) ).

tff(fact_1127_surjh,axiom,
    hAPP_f622418129t_bool(image_1465793779di_nat(h),top_to788185952i_bool) = hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),hAPP_f846027769ol_nat(finite1672073426e_indi,top_to788185952i_bool)) ).

tff(fact_1128_finite__atLeastLessThan,axiom,
    ! [L: nat,U: nat] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_at4362885an_nat(L),U))) ).

tff(fact_1129__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_12,axiom,
    ~ ! [H: fun_Ar671024215di_nat] :
        ( hBOOL(hAPP_f584385070l_bool(inj_on1960344199di_nat(H),top_to788185952i_bool))
       => ( hAPP_f622418129t_bool(image_1465793779di_nat(H),top_to788185952i_bool) != hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),hAPP_f846027769ol_nat(finite1672073426e_indi,top_to788185952i_bool)) ) ) ).

tff(fact_1130_subset__card__intvl__is__intvl,axiom,
    ! [A: fun_nat_bool,K: nat] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_n1699378549t_bool(ord_at4362885an_nat(K),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),hAPP_f22106695ol_nat(finite_card_nat,A)))))
     => ( A = hAPP_n1699378549t_bool(ord_at4362885an_nat(K),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),hAPP_f22106695ol_nat(finite_card_nat,A))) ) ) ).

tff(fact_1131_image__Suc__atLeastLessThan,axiom,
    ! [I: nat,J: nat] : ( hAPP_f800510211t_bool(image_nat_nat(suc),hAPP_n1699378549t_bool(ord_at4362885an_nat(I),J)) = hAPP_n1699378549t_bool(ord_at4362885an_nat(hAPP_nat_nat(suc,I)),hAPP_nat_nat(suc,J)) ) ).

tff(fact_1132_image__add__atLeastLessThan,axiom,
    ! [K: nat,I: nat,J: nat] : ( hAPP_f800510211t_bool(image_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),K)),hAPP_n1699378549t_bool(ord_at4362885an_nat(I),J)) = hAPP_n1699378549t_bool(ord_at4362885an_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K)) ) ).

tff(fact_1133_all__nat__less__eq,axiom,
    ! [Pa: fun_nat_bool,Na: nat] :
      ( ! [M: nat] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))
         => hBOOL(hAPP_nat_bool(Pa,M)) )
    <=> ! [X_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),Na)))
         => hBOOL(hAPP_nat_bool(Pa,X_1)) ) ) ).

tff(fact_1134_ex__nat__less__eq,axiom,
    ! [Pa: fun_nat_bool,Na: nat] :
      ( ? [M: nat] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))
          & hBOOL(hAPP_nat_bool(Pa,M)) )
    <=> ? [X_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),Na)))
          & hBOOL(hAPP_nat_bool(Pa,X_1)) ) ) ).

tff(fact_1135_greaterThan__0,axiom,
    hAPP_n1699378549t_bool(ord_greaterThan_nat,zero_zero_nat) = hAPP_f800510211t_bool(image_nat_nat(suc),top_top_fun_nat_bool) ).

tff(fact_1136_less__eq__nat_Osimps_I2_J,axiom,
    ! [M_1: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),Na))
    <=> hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(nat_case_bool(fFalse),hAPP_n1699378549t_bool(ord_less_eq_nat,M_1)),Na)) ) ).

tff(fact_1137_finite__greaterThanAtMost,axiom,
    ! [L: nat,U: nat] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_gr375877188st_nat(L),U))) ).

tff(fact_1138_finite__greaterThanLessThan,axiom,
    ! [L: nat,U: nat] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_gr660468384an_nat(L),U))) ).

tff(fact_1139_atLeastSucLessThan__greaterThanLessThan,axiom,
    ! [L: nat,U: nat] : ( hAPP_n1699378549t_bool(ord_at4362885an_nat(hAPP_nat_nat(suc,L)),U) = hAPP_n1699378549t_bool(ord_gr660468384an_nat(L),U) ) ).

tff(fact_1140_le__square,axiom,
    ! [M_2: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(times_times_nat(M_2),M_2))) ).

tff(fact_1141_le__cube,axiom,
    ! [M_2: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(times_times_nat(M_2),hAPP_nat_nat(times_times_nat(M_2),M_2)))) ).

tff(fact_1142_mult__le__mono1,axiom,
    ! [K_2: nat,I_2: nat,J_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(I_2),K_2)),hAPP_nat_nat(times_times_nat(J_1),K_2))) ) ).

tff(fact_1143_mult__le__mono2,axiom,
    ! [K_2: nat,I_2: nat,J_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(K_2),I_2)),hAPP_nat_nat(times_times_nat(K_2),J_1))) ) ).

tff(fact_1144_mult__le__mono,axiom,
    ! [K_2: nat,L_1: nat,I_2: nat,J_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),L_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(I_2),K_2)),hAPP_nat_nat(times_times_nat(J_1),L_1))) ) ) ).

tff(fact_1145_nat__mult__eq__1__iff,axiom,
    ! [M_1: nat,Na: nat] :
      ( ( hAPP_nat_nat(times_times_nat(M_1),Na) = one_one_nat )
    <=> ( ( M_1 = one_one_nat )
        & ( Na = one_one_nat ) ) ) ).

tff(fact_1146_nat__mult__1__right,axiom,
    ! [N: nat] : ( hAPP_nat_nat(times_times_nat(N),one_one_nat) = N ) ).

tff(fact_1147_nat__1__eq__mult__iff,axiom,
    ! [M_1: nat,Na: nat] :
      ( ( one_one_nat = hAPP_nat_nat(times_times_nat(M_1),Na) )
    <=> ( ( M_1 = one_one_nat )
        & ( Na = one_one_nat ) ) ) ).

tff(fact_1148_nat__mult__1,axiom,
    ! [N: nat] : ( hAPP_nat_nat(times_times_nat(one_one_nat),N) = N ) ).

tff(fact_1149_add__mult__distrib,axiom,
    ! [M_2: nat,N: nat,K_2: nat] : ( hAPP_nat_nat(times_times_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N)),K_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(M_2),K_2)),hAPP_nat_nat(times_times_nat(N),K_2)) ) ).

tff(fact_1150_add__mult__distrib2,axiom,
    ! [K_2: nat,M_2: nat,N: nat] : ( hAPP_nat_nat(times_times_nat(K_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(K_2),M_2)),hAPP_nat_nat(times_times_nat(K_2),N)) ) ).

tff(fact_1151_Suc__mult__cancel1,axiom,
    ! [K: nat,M_1: nat,Na: nat] :
      ( ( hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K)),M_1) = hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K)),Na) )
    <=> ( M_1 = Na ) ) ).

tff(fact_1152_mult__cancel2,axiom,
    ! [M_1: nat,K: nat,Na: nat] :
      ( ( hAPP_nat_nat(times_times_nat(M_1),K) = hAPP_nat_nat(times_times_nat(Na),K) )
    <=> ( ( M_1 = Na )
        | ( K = zero_zero_nat ) ) ) ).

tff(fact_1153_mult__cancel1,axiom,
    ! [K: nat,M_1: nat,Na: nat] :
      ( ( hAPP_nat_nat(times_times_nat(K),M_1) = hAPP_nat_nat(times_times_nat(K),Na) )
    <=> ( ( M_1 = Na )
        | ( K = zero_zero_nat ) ) ) ).

tff(fact_1154_mult__is__0,axiom,
    ! [M_1: nat,Na: nat] :
      ( ( hAPP_nat_nat(times_times_nat(M_1),Na) = zero_zero_nat )
    <=> ( ( M_1 = zero_zero_nat )
        | ( Na = zero_zero_nat ) ) ) ).

tff(fact_1155_mult__0__right,axiom,
    ! [M_2: nat] : ( hAPP_nat_nat(times_times_nat(M_2),zero_zero_nat) = zero_zero_nat ) ).

tff(fact_1156_mult__0,axiom,
    ! [N: nat] : ( hAPP_nat_nat(times_times_nat(zero_zero_nat),N) = zero_zero_nat ) ).

tff(fact_1157_mult__eq__1__iff,axiom,
    ! [M_1: nat,Na: nat] :
      ( ( hAPP_nat_nat(times_times_nat(M_1),Na) = hAPP_nat_nat(suc,zero_zero_nat) )
    <=> ( ( M_1 = hAPP_nat_nat(suc,zero_zero_nat) )
        & ( Na = hAPP_nat_nat(suc,zero_zero_nat) ) ) ) ).

tff(fact_1158_mult__less__mono2,axiom,
    ! [K_2: nat,I_2: nat,J_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_2))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(K_2),I_2)),hAPP_nat_nat(times_times_nat(K_2),J_1))) ) ) ).

tff(fact_1159_mult__less__mono1,axiom,
    ! [K_2: nat,I_2: nat,J_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_2))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(I_2),K_2)),hAPP_nat_nat(times_times_nat(J_1),K_2))) ) ) ).

tff(fact_1160_mult__less__cancel2,axiom,
    ! [M_1: nat,K: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(M_1),K)),hAPP_nat_nat(times_times_nat(Na),K)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ) ).

tff(fact_1161_mult__less__cancel1,axiom,
    ! [K: nat,M_1: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(K),M_1)),hAPP_nat_nat(times_times_nat(K),Na)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ) ).

tff(fact_1162_nat__0__less__mult__iff,axiom,
    ! [M_1: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(times_times_nat(M_1),Na)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M_1))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na)) ) ) ).

tff(fact_1163_Suc__mult__less__cancel1,axiom,
    ! [K: nat,M_1: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K)),M_1)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K)),Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ).

tff(fact_1164_mult__Suc__right,axiom,
    ! [M_2: nat,N: nat] : ( hAPP_nat_nat(times_times_nat(M_2),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(times_times_nat(M_2),N)) ) ).

tff(fact_1165_mult__Suc,axiom,
    ! [M_2: nat,N: nat] : ( hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,M_2)),N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),hAPP_nat_nat(times_times_nat(M_2),N)) ) ).

tff(fact_1166_Suc__mult__le__cancel1,axiom,
    ! [K: nat,M_1: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K)),M_1)),hAPP_nat_nat(times_times_nat(hAPP_nat_nat(suc,K)),Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) ).

tff(fact_1167_mult__eq__self__implies__10,axiom,
    ! [M_2: nat,N: nat] :
      ( ( M_2 = hAPP_nat_nat(times_times_nat(M_2),N) )
     => ( ( N = one_one_nat )
        | ( M_2 = zero_zero_nat ) ) ) ).

tff(fact_1168_n__less__m__mult__n,axiom,
    ! [M_2: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_2))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(times_times_nat(M_2),N))) ) ) ).

tff(fact_1169_n__less__n__mult__m,axiom,
    ! [M_2: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_2))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(times_times_nat(N),M_2))) ) ) ).

tff(fact_1170_one__less__mult,axiom,
    ! [M_2: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_2))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(times_times_nat(M_2),N))) ) ) ).

tff(fact_1171_one__le__mult__iff,axiom,
    ! [M_1: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(times_times_nat(M_1),Na)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_1))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),Na)) ) ) ).

tff(fact_1172_mult__le__cancel2,axiom,
    ! [M_1: nat,K: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(M_1),K)),hAPP_nat_nat(times_times_nat(Na),K)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) ) ).

tff(fact_1173_mult__le__cancel1,axiom,
    ! [K: nat,M_1: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(K),M_1)),hAPP_nat_nat(times_times_nat(K),Na)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) ) ).

tff(fact_1174_nat__mult__commute,axiom,
    ! [M_2: nat,N: nat] : ( hAPP_nat_nat(times_times_nat(M_2),N) = hAPP_nat_nat(times_times_nat(N),M_2) ) ).

tff(fact_1175_nat__mult__assoc,axiom,
    ! [M_2: nat,N: nat,K_2: nat] : ( hAPP_nat_nat(times_times_nat(hAPP_nat_nat(times_times_nat(M_2),N)),K_2) = hAPP_nat_nat(times_times_nat(M_2),hAPP_nat_nat(times_times_nat(N),K_2)) ) ).

tff(fact_1176_nat__mult__le__cancel1,axiom,
    ! [M_1: nat,Na: nat,K: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(times_times_nat(K),M_1)),hAPP_nat_nat(times_times_nat(K),Na)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),Na)) ) ) ).

tff(fact_1177_nat__mult__less__cancel1,axiom,
    ! [M_1: nat,Na: nat,K: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(times_times_nat(K),M_1)),hAPP_nat_nat(times_times_nat(K),Na)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),Na)) ) ) ).

tff(fact_1178_nat__mult__eq__cancel1,axiom,
    ! [M_1: nat,Na: nat,K: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
     => ( ( hAPP_nat_nat(times_times_nat(K),M_1) = hAPP_nat_nat(times_times_nat(K),Na) )
      <=> ( M_1 = Na ) ) ) ).

tff(fact_1179_nat__mult__eq__cancel__disj,axiom,
    ! [K: nat,M_1: nat,Na: nat] :
      ( ( hAPP_nat_nat(times_times_nat(K),M_1) = hAPP_nat_nat(times_times_nat(K),Na) )
    <=> ( ( K = zero_zero_nat )
        | ( M_1 = Na ) ) ) ).

tff(fact_1180_left__add__mult__distrib,axiom,
    ! [I_2: nat,U_1: nat,J_1: nat,K_2: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(I_2),U_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(J_1),U_1)),K_2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(times_times_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),J_1)),U_1)),K_2) ) ).

tff(fact_1181_nat_Osize_I2_J,axiom,
    ! [Nat: nat] : ( hAPP_nat_nat(nat_size,hAPP_nat_nat(suc,Nat)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(nat_size,Nat)),hAPP_nat_nat(suc,zero_zero_nat)) ) ).

tff(fact_1182_nat_Osize_I1_J,axiom,
    hAPP_nat_nat(nat_size,zero_zero_nat) = zero_zero_nat ).

tff(fact_1183_nat_Osize_I4_J,axiom,
    ! [Nat: nat] : ( hAPP_nat_nat(size_size_nat,hAPP_nat_nat(suc,Nat)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(size_size_nat,Nat)),hAPP_nat_nat(suc,zero_zero_nat)) ) ).

tff(fact_1184_nat__size,axiom,
    ! [N: nat] : ( hAPP_nat_nat(size_size_nat,N) = N ) ).

tff(fact_1185_nat_Osize_I3_J,axiom,
    hAPP_nat_nat(size_size_nat,zero_zero_nat) = zero_zero_nat ).

tff(fact_1186_weak__decr__stable,axiom,
    ! [F: fun_nat_nat] :
      ( ! [I_1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,hAPP_nat_nat(suc,I_1))),hAPP_nat_nat(F,I_1)))
     => ? [I_1: nat] :
        ! [K_1: nat] : ( hAPP_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)) = hAPP_nat_nat(F,I_1) ) ) ).

tff(fact_1187_bool_Osize_I1_J,axiom,
    hAPP_bool_nat(bool_size,fTrue) = zero_zero_nat ).

tff(fact_1188_bool_Osize_I2_J,axiom,
    hAPP_bool_nat(bool_size,fFalse) = zero_zero_nat ).

tff(fact_1189_finite__atLeastAtMost,axiom,
    ! [L: nat,U: nat] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_at238088361st_nat(L),U))) ).

tff(fact_1190_atLeastLessThanSuc__atLeastAtMost,axiom,
    ! [L: nat,U: nat] : ( hAPP_n1699378549t_bool(ord_at4362885an_nat(L),hAPP_nat_nat(suc,U)) = hAPP_n1699378549t_bool(ord_at238088361st_nat(L),U) ) ).

tff(fact_1191_ex__nat__less,axiom,
    ! [Pa: fun_nat_bool,Na: nat] :
      ( ? [M: nat] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na))
          & hBOOL(hAPP_nat_bool(Pa,M)) )
    <=> ? [X_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),Na)))
          & hBOOL(hAPP_nat_bool(Pa,X_1)) ) ) ).

tff(fact_1192_all__nat__less,axiom,
    ! [Pa: fun_nat_bool,Na: nat] :
      ( ! [M: nat] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na))
         => hBOOL(hAPP_nat_bool(Pa,M)) )
    <=> ! [X_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),Na)))
         => hBOOL(hAPP_nat_bool(Pa,X_1)) ) ) ).

tff(fact_1193_image__Suc__atLeastAtMost,axiom,
    ! [I: nat,J: nat] : ( hAPP_f800510211t_bool(image_nat_nat(suc),hAPP_n1699378549t_bool(ord_at238088361st_nat(I),J)) = hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(suc,I)),hAPP_nat_nat(suc,J)) ) ).

tff(fact_1194_atLeastSucAtMost__greaterThanAtMost,axiom,
    ! [L: nat,U: nat] : ( hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(suc,L)),U) = hAPP_n1699378549t_bool(ord_gr375877188st_nat(L),U) ) ).

tff(fact_1195_image__add__atLeastAtMost,axiom,
    ! [K: nat,I: nat,J: nat] : ( hAPP_f800510211t_bool(image_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),K)),hAPP_n1699378549t_bool(ord_at238088361st_nat(I),J)) = hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K)) ) ).

tff(fact_1196_atLeastLessThan__add__Un,axiom,
    ! [K: nat,I: nat,J: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J))
     => ( hAPP_n1699378549t_bool(ord_at4362885an_nat(I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K)) = hAPP_f800510211t_bool(semila465093516t_bool(hAPP_n1699378549t_bool(ord_at4362885an_nat(I),J)),hAPP_n1699378549t_bool(ord_at4362885an_nat(J),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K))) ) ) ).

tff(fact_1197_atLeast__0,axiom,
    hAPP_n1699378549t_bool(ord_atLeast_nat,zero_zero_nat) = top_top_fun_nat_bool ).

tff(fact_1198_atLeast__Suc__greaterThan,axiom,
    ! [K: nat] : ( hAPP_n1699378549t_bool(ord_atLeast_nat,hAPP_nat_nat(suc,K)) = hAPP_n1699378549t_bool(ord_greaterThan_nat,K) ) ).

tff(fact_1199_setsum__shift__lb__Suc0__0,axiom,
    ! [K: nat,F: fun_nat_nat] :
      ( ( hAPP_nat_nat(F,zero_zero_nat) = zero_zero_nat )
     => ( hAPP_f22106695ol_nat(big_co387207925at_nat(F),hAPP_n1699378549t_bool(ord_at238088361st_nat(hAPP_nat_nat(suc,zero_zero_nat)),K)) = hAPP_f22106695ol_nat(big_co387207925at_nat(F),hAPP_n1699378549t_bool(ord_at238088361st_nat(zero_zero_nat),K)) ) ) ).

%----Helper facts (78)
tff(help_fTrue_1_1_U,axiom,
    hBOOL(fTrue) ).

tff(help_fTrue_1_1_T,axiom,
    ! [P: bool] :
      ( ( P = fTrue )
      | ( P = fFalse ) ) ).

tff(help_fconj_1_1_U,axiom,
    ! [Q: bool,P: bool] :
      ( ~ hBOOL(P)
      | ~ hBOOL(Q)
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) ) ).

tff(help_fconj_2_1_U,axiom,
    ! [P: bool,Q: bool] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q))
      | hBOOL(P) ) ).

tff(help_fconj_3_1_U,axiom,
    ! [P: bool,Q: bool] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q))
      | hBOOL(Q) ) ).

tff(help_fFalse_1_1_U,axiom,
    ~ hBOOL(fFalse) ).

tff(help_fFalse_1_1_T,axiom,
    ! [P: bool] :
      ( ( P = fTrue )
      | ( P = fFalse ) ) ).

tff(help_COMBI_1_1_COMBI_000tc__Nat__Onat_U,axiom,
    ! [P: nat] : ( hAPP_nat_nat(cOMBI_nat,P) = P ) ).

tff(help_fequal_1_1_fequal_000tc__Nat__Onat_T,axiom,
    ! [X: nat,Y: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__Nat__Onat_T,axiom,
    ! [X: nat,Y: nat] :
      ( ( X != Y )
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y)) ) ).

tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U,axiom,
    ! [P: bool,Q: nat] : ( hAPP_nat_bool(hAPP_b1013836512t_bool(cOMBK_bool_nat,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Product____Type__Ounit_U,axiom,
    ! [P: bool,Q: product_unit] : ( hAPP_P1676879539t_bool(hAPP_b1096750261t_bool(cOMBK_790042732t_unit,P),Q) = P ) ).

tff(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Nat__Onat_U,axiom,
    ! [P: fun_nat_fun_nat_nat,Q: nat,R: nat] : ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,P),Q),R) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(P,R),Q) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U,axiom,
    ! [P: fun_nat_fun_nat_bool,Q: nat,R: nat] : ( hAPP_nat_bool(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,P),Q),R) = hAPP_nat_bool(hAPP_n1699378549t_bool(P,R),Q) ) ).

tff(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
    ! [P: fun_na1469252690l_bool,Q: fun_nat_bool,R: nat] : ( hAPP_nat_bool(hAPP_f800510211t_bool(cOMBS_nat_bool_bool(P),Q),R) = hAPP_bool_bool(hAPP_n1006566506l_bool(P,R),hAPP_nat_bool(Q,R)) ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__Nat__On,axiom,
    ! [P: fun_bool_bool,Q: nat] : ( hAPP_n1006566506l_bool(hAPP_f1579826888l_bool(cOMBK_623810489ol_nat,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo,axiom,
    ! [P: fun_nat_bool,Q: bool] : ( hAPP_b1013836512t_bool(hAPP_f1247925759t_bool(cOMBK_1034797721l_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____eff,axiom,
    ! [P: bool,Q: arrow_856714788e_indi] : ( hAPP_A997847300i_bool(hAPP_b549570054i_bool(cOMBK_561380029e_indi,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Product_,axiom,
    ! [P: fun_nat_bool,Q: product_unit] : ( hAPP_P32877782t_bool(hAPP_f1212412661t_bool(cOMBK_356206223t_unit,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00,axiom,
    ! [P: fun_Pr1643180309t_bool,Q: nat] : ( hAPP_n454528608t_bool(hAPP_f1539020360t_bool(cOMBK_649751363ol_nat,P),Q) = P ) ).

tff(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
    ! [P: fun_nat_fun_nat_bool,Q: fun_nat_nat,R: nat] : ( hAPP_n1699378549t_bool(hAPP_f618557131t_bool(cOMBB_800536526ol_nat(P),Q),R) = hAPP_n1699378549t_bool(P,hAPP_nat_nat(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
    ! [P: fun_na1436237685l_bool,Q: fun_nat_bool,R: nat] : ( hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,P),Q),R) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(P,R),Q) ) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo,axiom,
    ! [P: fun_bo1549164019l_bool,Q: fun_nat_bool,R: nat] : ( hAPP_n1006566506l_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_nat_bool(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000,axiom,
    ! [P: fun_Ar603939593t_bool,Q: nat,R: arrow_856714788e_indi] : ( hAPP_A997847300i_bool(hAPP_n34002993i_bool(hAPP_f721434149i_bool(cOMBC_722552198t_bool,P),Q),R) = hAPP_nat_bool(hAPP_A1686943911t_bool(P,R),Q) ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__,axiom,
    ! [P: fun_Ar1809396326i_bool,Q: nat] : ( hAPP_n34002993i_bool(hAPP_f1549597448i_bool(cOMBK_341987762ol_nat,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Arrow___,axiom,
    ! [P: fun_nat_bool,Q: arrow_856714788e_indi] : ( hAPP_A1686943911t_bool(hAPP_f1132083526t_bool(cOMBK_833041760e_indi,P),Q) = P ) ).

tff(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HO,axiom,
    ! [P: fun_na1436237685l_bool,Q: fun_nat_nat,R: nat] : ( hAPP_n215258509l_bool(hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(P),Q),R) = hAPP_n215258509l_bool(P,hAPP_nat_nat(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__401,axiom,
    ! [P: fun_nat_fun_nat_bool,Q: fun_Ar671024215di_nat,R: arrow_856714788e_indi] : ( hAPP_A1686943911t_bool(hAPP_f966656047t_bool(cOMBB_1869811296e_indi(P),Q),R) = hAPP_n1699378549t_bool(P,hAPP_A376526755di_nat(Q,R)) ) ).

tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabe,axiom,
    ! [P: bool,Q: produc472769767le_alt] : ( hAPP_P1178790471t_bool(hAPP_b128655177t_bool(cOMBK_198697344le_alt,P),Q) = P ) ).

tff(help_If_1_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiq,axiom,
    ! [X: fun_Pr2067565481t_bool,Y: fun_Pr2067565481t_bool] : ( hAPP_f1356305429t_bool(hAPP_f1299954409t_bool(hAPP_b35146737t_bool(if_fun523439385t_bool,fTrue),X),Y) = X ) ).

tff(help_If_2_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiq,axiom,
    ! [X: fun_Pr2067565481t_bool,Y: fun_Pr2067565481t_bool] : ( hAPP_f1356305429t_bool(hAPP_f1299954409t_bool(hAPP_b35146737t_bool(if_fun523439385t_bool,fFalse),X),Y) = Y ) ).

tff(help_If_3_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____effngqiq,axiom,
    ! [P: bool] :
      ( ( P = fTrue )
      | ( P = fFalse ) ) ).

tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order_,axiom,
    ! [P: bool,Q: fun_Pr2067565481t_bool] : ( hAPP_f52567537l_bool(hAPP_b1272691967l_bool(cOMBK_81143760t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__prod_It,axiom,
    ! [P: fun_bool_bool,Q: produc472769767le_alt] : ( hAPP_P1103642805l_bool(hAPP_f699791347l_bool(cOMBK_138598520le_alt,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef,axiom,
    ! [P: fun_Pr2067565481t_bool,Q: bool] : ( hAPP_b128655177t_bool(hAPP_f1723896209t_bool(cOMBK_5056120l_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_402,axiom,
    ! [P: fun_Pr1643180309t_bool,Q: produc472769767le_alt] : ( hAPP_P2037731755t_bool(hAPP_f723483871t_bool(cOMBK_751896174le_alt,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_403,axiom,
    ! [P: fun_Pr2067565481t_bool,Q: product_unit] : ( hAPP_P1914371027t_bool(hAPP_f15777819t_bool(cOMBK_681766254t_unit,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc,axiom,
    ! [P: fun_bool_bool,Q: fun_Pr2067565481t_bool] : ( hAPP_f463104139l_bool(hAPP_f1713038057l_bool(cOMBK_118864600t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe,axiom,
    ! [P: fun_fu638310559l_bool,Q: bool] : ( hAPP_b1272691967l_bool(hAPP_f86272063l_bool(cOMBK_650639032l_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs___404,axiom,
    ! [P: fun_Ar1809396326i_bool,Q: produc472769767le_alt] : ( hAPP_P1859429372i_bool(hAPP_f359069313i_bool(cOMBK_1987648063le_alt,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_405,axiom,
    ! [P: fun_Pr2067565481t_bool,Q: arrow_856714788e_indi] : ( hAPP_A1646126530t_bool(hAPP_f480276746t_bool(cOMBK_1650320063e_indi,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_406,axiom,
    ! [P: fun_Pr1643180309t_bool,Q: fun_Pr2067565481t_bool] : ( hAPP_f1400551297t_bool(hAPP_f168465001t_bool(cOMBK_14887266t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_407,axiom,
    ! [P: fun_fu638310559l_bool,Q: product_unit] : ( hAPP_P754918389l_bool(hAPP_f502523701l_bool(cOMBK_1521810862t_unit,P),Q) = P ) ).

tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000t,axiom,
    ! [P: fun_Ar339057223l_bool,Q: fun_Pr2067565481t_bool,R: arrow_1893660431le_alt] : ( hAPP_A1748732503t_bool(hAPP_f234621849t_bool(hAPP_f1689397393t_bool(cOMBC_395465908l_bool,P),Q),R) = hAPP_f52567537l_bool(hAPP_A442239897l_bool(P,R),Q) ) ).

tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabel,axiom,
    ! [P: bool,Q: fun_Ar274636406t_bool] : ( hAPP_f995490902l_bool(hAPP_b1078573912l_bool(cOMBK_445086735t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs___408,axiom,
    ! [P: fun_Ar1809396326i_bool,Q: fun_Pr2067565481t_bool] : ( hAPP_f2010315474i_bool(hAPP_f1128827177i_bool(cOMBK_814147665t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_409,axiom,
    ! [P: fun_fu638310559l_bool,Q: arrow_856714788e_indi] : ( hAPP_A897398598l_bool(hAPP_f1717907078l_bool(cOMBK_1520063231e_indi,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_410,axiom,
    ! [P: fun_bool_bool,Q: fun_Ar274636406t_bool] : ( hAPP_f1676084198l_bool(hAPP_f1582869284l_bool(cOMBK_542452487t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____eff,axiom,
    ! [P: fun_fu3835832l_bool,Q: bool] : ( hAPP_b1078573912l_bool(hAPP_f1322579375l_bool(cOMBK_317366791l_bool,P),Q) = P ) ).

tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000_411,axiom,
    ! [P: fun_Ar64685412t_bool,Q: arrow_1893660431le_alt,R: arrow_856714788e_indi] : ( hAPP_A1646126530t_bool(hAPP_A425126512t_bool(hAPP_f1631649925t_bool(cOMBC_1417338747t_bool,P),Q),R) = hAPP_A1601437999t_bool(hAPP_A1309733808t_bool(P,R),Q) ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_412,axiom,
    ! [P: fun_Pr1643180309t_bool,Q: fun_Ar274636406t_bool] : ( hAPP_f1438163420t_bool(hAPP_f134177552t_bool(cOMBK_1220673277t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____eff_413,axiom,
    ! [P: fun_fu3835832l_bool,Q: product_unit] : ( hAPP_P284783074l_bool(hAPP_f1482764601l_bool(cOMBK_708287485t_unit,P),Q) = P ) ).

tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oalt_000t_414,axiom,
    ! [P: fun_Ar636018671t_bool,Q: fun_Pr2067565481t_bool,R: arrow_1893660431le_alt] : ( hAPP_A2063800319t_bool(hAPP_f449303873t_bool(hAPP_f1081591777t_bool(cOMBC_557453916t_bool,P),Q),R) = hAPP_f234621849t_bool(hAPP_A656921921t_bool(P,R),Q) ) ).

tff(help_COMBC_1_1_COMBC_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs_,axiom,
    ! [P: fun_Pr1085078251l_bool,Q: fun_Pr2067565481t_bool,R: produc472769767le_alt] : ( hAPP_P1178790471t_bool(hAPP_f1356305429t_bool(hAPP_f1033183015t_bool(cOMBC_593569186l_bool,P),Q),R) = hAPP_f52567537l_bool(hAPP_P38525833l_bool(P,R),Q) ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs___415,axiom,
    ! [P: fun_Ar1809396326i_bool,Q: fun_Ar274636406t_bool] : ( hAPP_f391644589i_bool(hAPP_f2022065970i_bool(cOMBK_818801614t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____eff_416,axiom,
    ! [P: fun_fu3835832l_bool,Q: arrow_856714788e_indi] : ( hAPP_A1411662545l_bool(hAPP_f1352816552l_bool(cOMBK_1255579598e_indi,P),Q) = P ) ).

tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000_417,axiom,
    ! [P: fun_Ar290235730t_bool,Q: arrow_1893660431le_alt,R: arrow_856714788e_indi] : ( hAPP_A1309733808t_bool(hAPP_A1889513822t_bool(hAPP_f2102110817t_bool(cOMBC_1486904681t_bool,P),Q),R) = hAPP_A1058422557t_bool(hAPP_A38124190t_bool(P,R),Q) ) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef,axiom,
    ! [P: fun_fu864675765l_bool,Q: fun_fu638310559l_bool,R: fun_Pr2067565481t_bool] : ( hAPP_f52567537l_bool(hAPP_f1060563265l_bool(hAPP_f1776355587l_bool(cOMBC_2133093654l_bool,P),Q),R) = hAPP_f182583295l_bool(hAPP_f1482930381l_bool(P,R),Q) ) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__Arrow____Order____Mirabelle____effngqiqbs_,axiom,
    ! [P: fun_Pr1085078251l_bool,Q: fun_Ar245737999le_alt,R: arrow_1893660431le_alt] : ( hAPP_A442239897l_bool(hAPP_f1536341593l_bool(cOMBB_1660064607le_alt(P),Q),R) = hAPP_P38525833l_bool(P,hAPP_A1299015393le_alt(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000_418,axiom,
    ! [P: fun_Ar516759882t_bool,Q: fun_Pr2067565481t_bool,R: arrow_856714788e_indi] : ( hAPP_A1646126530t_bool(hAPP_f480276746t_bool(hAPP_f601594885t_bool(cOMBC_750853729t_bool,P),Q),R) = hAPP_f1356305429t_bool(hAPP_A834130326t_bool(P,R),Q) ) ).

tff(help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000,axiom,
    ! [P: fun_Ar516759882t_bool,Q: fun_Ar274636406t_bool,R: arrow_856714788e_indi] : ( hAPP_A1646126530t_bool(hAPP_f1302887663t_bool(cOMBS_1181656689t_bool(P),Q),R) = hAPP_f1356305429t_bool(hAPP_A834130326t_bool(P,R),hAPP_A1646126530t_bool(Q,R)) ) ).

tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order__,axiom,
    ! [P: bool,Q: fun_fu2114379172t_bool] : ( hAPP_f1572141188l_bool(hAPP_b1777246598l_bool(cOMBK_1279003709t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_419,axiom,
    ! [P: fun_fu638310559l_bool,Q: fun_Ar274636406t_bool] : ( hAPP_f1915815064l_bool(hAPP_f1104294872l_bool(cOMBK_1701906001t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_420,axiom,
    ! [P: fun_bool_bool,Q: fun_fu2114379172t_bool] : ( hAPP_f414129720l_bool(hAPP_f1152234870l_bool(cOMBK_1770320693t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel,axiom,
    ! [P: fun_fu2098777574l_bool,Q: bool] : ( hAPP_b1777246598l_bool(hAPP_f369767947l_bool(cOMBK_2030738485l_bool,P),Q) = P ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef,axiom,
    ! [P: fun_fu1679793515t_bool,Q: fun_Ar274636406t_bool,R: arrow_856714788e_indi] : ( hAPP_A1309733808t_bool(hAPP_f831214557t_bool(cOMBB_80760910e_indi(P),Q),R) = hAPP_f1761571331t_bool(P,hAPP_A1646126530t_bool(Q,R)) ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_421,axiom,
    ! [P: fun_Pr1643180309t_bool,Q: fun_fu2114379172t_bool] : ( hAPP_f151782958t_bool(hAPP_f1327693154t_bool(cOMBK_1385893163t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_422,axiom,
    ! [P: fun_fu2098777574l_bool,Q: product_unit] : ( hAPP_P283873808l_bool(hAPP_f956752277l_bool(cOMBK_1075760171t_unit,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs___423,axiom,
    ! [P: fun_Ar1809396326i_bool,Q: fun_fu2114379172t_bool] : ( hAPP_f399308031i_bool(hAPP_f448050564i_bool(cOMBK_443335420t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_424,axiom,
    ! [P: fun_fu2098777574l_bool,Q: arrow_856714788e_indi] : ( hAPP_A2084592127l_bool(hAPP_f258290692l_bool(cOMBK_1514079484e_indi,P),Q) = P ) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__,axiom,
    ! [P: fun_fu361117961l_bool,Q: fun_fu3835832l_bool,R: fun_Ar274636406t_bool] : ( hAPP_f995490902l_bool(hAPP_f819682389l_bool(hAPP_f1760776521l_bool(cOMBC_514203746l_bool,P),Q),R) = hAPP_f73423488l_bool(hAPP_f1225332775l_bool(P,R),Q) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs__,axiom,
    ! [P: fun_fu1572237755l_bool,Q: fun_Ar2121501495le_alt,R: arrow_1893660431le_alt] : ( hAPP_A1608658241l_bool(hAPP_f184584489l_bool(cOMBB_1575576719le_alt(P),Q),R) = hAPP_f1536341593l_bool(P,hAPP_A1146194953le_alt(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ef_425,axiom,
    ! [P: fun_fu1287834969t_bool,Q: fun_Ar274636406t_bool,R: arrow_856714788e_indi] : ( hAPP_A38124190t_bool(hAPP_f1751344075t_bool(cOMBB_1876517692e_indi(P),Q),R) = hAPP_f1550387441t_bool(P,hAPP_A1646126530t_bool(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000_426,axiom,
    ! [P: fun_Ar535288606t_bool,Q: fun_Pr2067565481t_bool,R: arrow_856714788e_indi] : ( hAPP_A834130326t_bool(hAPP_f1344464862t_bool(hAPP_f1908974253t_bool(cOMBC_156709173t_bool,P),Q),R) = hAPP_f1299954409t_bool(hAPP_A1395684458t_bool(P,R),Q) ) ).

tff(help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____effngqiqbs__Oindi_000_427,axiom,
    ! [P: fun_Ar535288606t_bool,Q: fun_Ar274636406t_bool,R: arrow_856714788e_indi] : ( hAPP_A834130326t_bool(hAPP_f1001205955t_bool(cOMBS_1925466437t_bool(P),Q),R) = hAPP_f1299954409t_bool(hAPP_A1395684458t_bool(P,R),hAPP_A1646126530t_bool(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____effngqiqbs___428,axiom,
    ! [P: fun_fu696673523t_bool,Q: fun_Ar1995913199l_bool,R: arrow_1893660431le_alt] : ( hAPP_A656921921t_bool(hAPP_f105674721t_bool(cOMBB_652885079le_alt(P),Q),R) = hAPP_f1689397393t_bool(P,hAPP_A1608658241l_bool(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow_,axiom,
    ! [P: fun_bo1945492389t_bool,Q: fun_Ar1809396326i_bool,R: arrow_856714788e_indi] : ( hAPP_A1395684458t_bool(hAPP_f668886383t_bool(cOMBB_1061985500e_indi(P),Q),R) = hAPP_b35146737t_bool(P,hAPP_A997847300i_bool(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____eff,axiom,
    ! [P: fun_fu1383920485l_bool,Q: fun_fu2098777574l_bool,R: fun_fu2114379172t_bool] : ( hAPP_f1572141188l_bool(hAPP_f1181604821l_bool(hAPP_f1169241965l_bool(cOMBC_1209358050l_bool,P),Q),R) = hAPP_f975209902l_bool(hAPP_f1714503811l_bool(P,R),Q) ) ).

%----Conjectures (1)
% tff(conj_0,conjecture,
%     hBOOL(hAPP_f52567537l_bool(hAPP_P38525833l_bool(member1333168212le_alt,hAPP_A1299015393le_alt(hAPP_A1146194953le_alt(produc1590937303le_alt,c),d)),hAPP_f2008608496t_bool(f,p))) ).

%------------------------------------------------------------------------------