TPTP Problem File: ITP010_7.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ITP010_7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 syntactic export of thm_2Ecardinal_2ECARD__NOT__LE.p, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : thm_2Ecardinal_2ECARD__NOT__LE.p [Gau20]
% : HL404501_7.p [TPAP]
% Status : Theorem
% Rating : 0.00 v7.5.0
% Syntax : Number of formulae : 16737 (5790 unt;5973 typ; 0 def)
% Number of atoms : 28699 (14171 equ)
% Maximal formula atoms : 912 ( 1 avg)
% Number of connectives : 19333 (1398 ~; 869 |;6595 &)
% (4848 <=>;5623 =>; 0 <=; 0 <~>)
% Maximal formula depth : 360 ( 6 avg)
% Maximal term depth : 29 ( 2 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 5045 (2946 >;2099 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 1930 (1930 usr; 239 con; 0-8 aty)
% Number of variables : 61058 (42747 !;12883 ?;61058 :)
% (5428 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_THM_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
include('Axioms/ITP001/ITP002_7.ax').
include('Axioms/ITP001/ITP003_7.ax').
include('Axioms/ITP001/ITP004_7.ax').
include('Axioms/ITP001/ITP005_7.ax').
include('Axioms/ITP001/ITP006_7.ax').
include('Axioms/ITP001/ITP007_7.ax').
include('Axioms/ITP001/ITP008_7.ax').
include('Axioms/ITP001/ITP009_7.ax').
include('Axioms/ITP001/ITP010_7.ax').
include('Axioms/ITP001/ITP011_7.ax').
include('Axioms/ITP001/ITP012_7.ax').
include('Axioms/ITP001/ITP013_7.ax').
include('Axioms/ITP001/ITP014_7.ax').
include('Axioms/ITP001/ITP015_7.ax').
include('Axioms/ITP001/ITP016_7.ax').
include('Axioms/ITP001/ITP017_7.ax').
include('Axioms/ITP001/ITP018_7.ax').
include('Axioms/ITP001/ITP019_7.ax').
include('Axioms/ITP001/ITP020_7.ax').
include('Axioms/ITP001/ITP021_7.ax').
include('Axioms/ITP001/ITP022_7.ax').
include('Axioms/ITP001/ITP023_7.ax').
include('Axioms/ITP001/ITP024_7.ax').
include('Axioms/ITP001/ITP025_7.ax').
include('Axioms/ITP001/ITP026_7.ax').
include('Axioms/ITP001/ITP027_7.ax').
include('Axioms/ITP001/ITP028_7.ax').
include('Axioms/ITP001/ITP029_7.ax').
include('Axioms/ITP001/ITP030_7.ax').
include('Axioms/ITP001/ITP031_7.ax').
include('Axioms/ITP001/ITP032_7.ax').
include('Axioms/ITP001/ITP033_7.ax').
include('Axioms/ITP001/ITP034_7.ax').
include('Axioms/ITP001/ITP035_7.ax').
include('Axioms/ITP001/ITP036_7.ax').
include('Axioms/ITP001/ITP037_7.ax').
include('Axioms/ITP001/ITP038_7.ax').
include('Axioms/ITP001/ITP039_7.ax').
include('Axioms/ITP001/ITP040_7.ax').
include('Axioms/ITP001/ITP041_7.ax').
include('Axioms/ITP001/ITP042_7.ax').
include('Axioms/ITP001/ITP043_7.ax').
include('Axioms/ITP001/ITP044_7.ax').
include('Axioms/ITP001/ITP045_7.ax').
include('Axioms/ITP001/ITP046_7.ax').
include('Axioms/ITP001/ITP047_7.ax').
include('Axioms/ITP001/ITP048_7.ax').
include('Axioms/ITP001/ITP049_7.ax').
include('Axioms/ITP001/ITP050_7.ax').
include('Axioms/ITP001/ITP051_7.ax').
include('Axioms/ITP001/ITP052_7.ax').
include('Axioms/ITP001/ITP053_7.ax').
include('Axioms/ITP001/ITP054_7.ax').
include('Axioms/ITP001/ITP055_7.ax').
include('Axioms/ITP001/ITP056_7.ax').
include('Axioms/ITP001/ITP057_7.ax').
include('Axioms/ITP001/ITP058_7.ax').
include('Axioms/ITP001/ITP059_7.ax').
include('Axioms/ITP001/ITP060_7.ax').
include('Axioms/ITP001/ITP061_7.ax').
include('Axioms/ITP001/ITP062_7.ax').
%------------------------------------------------------------------------------
tff(tyop_2Elist_2Elist,type,
tyop_2Elist_2Elist: $tType > $tType ).
tff(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
tff(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: $tType ).
tff(tyop_2Eoption_2Eoption,type,
tyop_2Eoption_2Eoption: $tType > $tType ).
tff(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).
tff(tyop_2Esum_2Esum,type,
tyop_2Esum_2Esum: ( $tType * $tType ) > $tType ).
tff(app_2E2,type,
app_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(p,type,
p: tyop_2Emin_2Ebool > $o ).
tff(combin_i_2E0,type,
combin_i_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(combin_k_2E0,type,
combin_k_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(combin_s_2E0,type,
combin_s_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))) ).
tff(c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Earithmetic_2E_2A_2E0,type,
c_2Earithmetic_2E_2A_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2A_2E2,type,
c_2Earithmetic_2E_2A_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2E_2B_2E0,type,
c_2Earithmetic_2E_2B_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2B_2E2,type,
c_2Earithmetic_2E_2B_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Epair_2E_2C_2E0,type,
c_2Epair_2E_2C_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))) ).
tff(c_2Epair_2E_2C_2E2,type,
c_2Epair_2E_2C_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > tyop_2Epair_2Eprod(A_27a,A_27b) ) ).
tff(c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Enum_2E0_2E0,type,
c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).
tff(c_2Eprim__rec_2E_3C_2E0,type,
c_2Eprim__rec_2E_3C_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Eprim__rec_2E_3C_2E2,type,
c_2Eprim__rec_2E_3C_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(c_2Earithmetic_2E_3C_3D_2E0,type,
c_2Earithmetic_2E_3C_3D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Earithmetic_2E_3C_3D_2E2,type,
c_2Earithmetic_2E_3C_3D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2:
!>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Earithmetic_2E_3E_3D_2E0,type,
c_2Earithmetic_2E_3E_3D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Earithmetic_2E_3E_3D_2E2,type,
c_2Earithmetic_2E_3E_3D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2E_3F_21_2E0,type,
c_2Ebool_2E_3F_21_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_3F_21_2E1,type,
c_2Ebool_2E_3F_21_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2EBIGUNION_2E0,type,
c_2Epred__set_2EBIGUNION_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2EBIGUNION_2E1,type,
c_2Epred__set_2EBIGUNION_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Epred__set_2EBIJ_2E0,type,
c_2Epred__set_2EBIJ_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EBIJ_2E3,type,
c_2Epred__set_2EBIJ_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Earithmetic_2EBIT1_2E0,type,
c_2Earithmetic_2EBIT1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EBIT1_2E1,type,
c_2Earithmetic_2EBIT1_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2EBIT2_2E0,type,
c_2Earithmetic_2EBIT2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EBIT2_2E1,type,
c_2Earithmetic_2EBIT2_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Epred__set_2ECARD_2E0,type,
c_2Epred__set_2ECARD_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum) ).
tff(c_2Epred__set_2ECARD_2E1,type,
c_2Epred__set_2ECARD_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Enum_2Enum ) ).
tff(c_2Ebool_2ECOND_2E0,type,
c_2Ebool_2ECOND_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))) ).
tff(c_2Ebool_2ECOND_2E3,type,
c_2Ebool_2ECOND_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Ebool * A_27a * A_27a ) > A_27a ) ).
tff(c_2Epred__set_2ECROSS_2E0,type,
c_2Epred__set_2ECROSS_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2ECROSS_2E2,type,
c_2Epred__set_2ECROSS_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool) ) ).
tff(c_2Epred__set_2EDELETE_2E0,type,
c_2Epred__set_2EDELETE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EDELETE_2E2,type,
c_2Epred__set_2EDELETE_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * A_27a ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Epred__set_2EDIFF_2E0,type,
c_2Epred__set_2EDIFF_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EDIFF_2E2,type,
c_2Epred__set_2EDIFF_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Epred__set_2EDISJOINT_2E0,type,
c_2Epred__set_2EDISJOINT_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2EDISJOINT_2E2,type,
c_2Epred__set_2EDISJOINT_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2EEMPTY_2E0,type,
c_2Epred__set_2EEMPTY_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).
tff(c_2Earithmetic_2EEXP_2E0,type,
c_2Earithmetic_2EEXP_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2EEXP_2E2,type,
c_2Earithmetic_2EEXP_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(c_2Epred__set_2EFINITE_2E0,type,
c_2Epred__set_2EFINITE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Epred__set_2EFINITE_2E1,type,
c_2Epred__set_2EFINITE_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2EGSPEC_2E0,type,
c_2Epred__set_2EGSPEC_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2EGSPEC_2E1,type,
c_2Epred__set_2EGSPEC_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Ecardinal_2EHAS__SIZE_2E0,type,
c_2Ecardinal_2EHAS__SIZE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Ecardinal_2EHAS__SIZE_2E2,type,
c_2Ecardinal_2EHAS__SIZE_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2EIMAGE_2E0,type,
c_2Epred__set_2EIMAGE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EIMAGE_2E2,type,
c_2Epred__set_2EIMAGE_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) ).
tff(c_2Ebool_2EIN_2E0,type,
c_2Ebool_2EIN_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2EIN_2E2,type,
c_2Ebool_2EIN_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2EINJ_2E0,type,
c_2Epred__set_2EINJ_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EINJ_2E3,type,
c_2Epred__set_2EINJ_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2EINSERT_2E0,type,
c_2Epred__set_2EINSERT_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EINSERT_2E2,type,
c_2Epred__set_2EINSERT_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Epred__set_2EINTER_2E0,type,
c_2Epred__set_2EINTER_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EINTER_2E2,type,
c_2Epred__set_2EINTER_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Ecombin_2EK_2E0,type,
c_2Ecombin_2EK_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(c_2Ecombin_2EK_2E1,type,
c_2Ecombin_2EK_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( A_27a > tyop_2Emin_2Efun(A_27b,A_27a) ) ).
tff(c_2Elist_2ELENGTH_2E0,type,
c_2Elist_2ELENGTH_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum) ).
tff(c_2Elist_2ELENGTH_2E1,type,
c_2Elist_2ELENGTH_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Enum_2Enum ) ).
tff(c_2Elist_2ELIST__TO__SET_2E0,type,
c_2Elist_2ELIST__TO__SET_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Elist_2ELIST__TO__SET_2E1,type,
c_2Elist_2ELIST__TO__SET_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Elist_2ENIL_2E0,type,
c_2Elist_2ENIL_2E0:
!>[A_27a: $tType] : tyop_2Elist_2Elist(A_27a) ).
tff(c_2Eoption_2ENONE_2E0,type,
c_2Eoption_2ENONE_2E0:
!>[A_27a: $tType] : tyop_2Eoption_2Eoption(A_27a) ).
tff(c_2Earithmetic_2ENUMERAL_2E0,type,
c_2Earithmetic_2ENUMERAL_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2ENUMERAL_2E1,type,
c_2Earithmetic_2ENUMERAL_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Epred__set_2EPOW_2E0,type,
c_2Epred__set_2EPOW_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2EPOW_2E1,type,
c_2Epred__set_2EPOW_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ) ).
tff(c_2Eoption_2ESOME_2E0,type,
c_2Eoption_2ESOME_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)) ).
tff(c_2Eoption_2ESOME_2E1,type,
c_2Eoption_2ESOME_2E1:
!>[A_27a: $tType] : ( A_27a > tyop_2Eoption_2Eoption(A_27a) ) ).
tff(c_2Epred__set_2ESUBSET_2E0,type,
c_2Epred__set_2ESUBSET_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2ESUBSET_2E2,type,
c_2Epred__set_2ESUBSET_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Enum_2ESUC_2E0,type,
c_2Enum_2ESUC_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Enum_2ESUC_2E1,type,
c_2Enum_2ESUC_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Epred__set_2ESURJ_2E0,type,
c_2Epred__set_2ESURJ_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2ESURJ_2E3,type,
c_2Epred__set_2ESURJ_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(c_2Eoption_2ETHE_2E0,type,
c_2Eoption_2ETHE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),A_27a) ).
tff(c_2Epair_2EUNCURRY_2E0,type,
c_2Epair_2EUNCURRY_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)) ).
tff(c_2Epair_2EUNCURRY_2E1,type,
c_2Epair_2EUNCURRY_2E1:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c) ) ).
tff(c_2Epred__set_2EUNION_2E0,type,
c_2Epred__set_2EUNION_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EUNION_2E2,type,
c_2Epred__set_2EUNION_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Epred__set_2EUNIV_2E0,type,
c_2Epred__set_2EUNIV_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).
tff(c_2Earithmetic_2EZERO_2E0,type,
c_2Earithmetic_2EZERO_2E0: tyop_2Enum_2Enum ).
tff(c_2Ebool_2E_5C_2F_2E0,type,
c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_5C_2F_2E2,type,
c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Ecardinal_2Ebijns_2E0,type,
c_2Ecardinal_2Ebijns_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)) ).
tff(c_2Ecardinal_2Ebijns_2E1,type,
c_2Ecardinal_2Ebijns_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool) ) ).
tff(c_2Ecardinal_2Ecardeq_2E0,type,
c_2Ecardinal_2Ecardeq_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Ecardinal_2Ecardeq_2E2,type,
c_2Ecardinal_2Ecardeq_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ecardinal_2Ecardgeq_2E0,type,
c_2Ecardinal_2Ecardgeq_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Ecardinal_2Ecardgeq_2E2,type,
c_2Ecardinal_2Ecardgeq_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ecardinal_2Ecardgt_2E0,type,
c_2Ecardinal_2Ecardgt_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Ecardinal_2Ecardgt_2E2,type,
c_2Ecardinal_2Ecardgt_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ecardinal_2Ecardleq_2E0,type,
c_2Ecardinal_2Ecardleq_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Ecardinal_2Ecardleq_2E2,type,
c_2Ecardinal_2Ecardleq_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2Ecount_2E0,type,
c_2Epred__set_2Ecount_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2Ecount_2E1,type,
c_2Epred__set_2Ecount_2E1: tyop_2Enum_2Enum > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).
tff(c_2Epred__set_2Ecountable_2E0,type,
c_2Epred__set_2Ecountable_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Epred__set_2Ecountable_2E1,type,
c_2Epred__set_2Ecountable_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Ecardinal_2Elist_2E0,type,
c_2Ecardinal_2Elist_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Ecardinal_2Elist_2E1,type,
c_2Ecardinal_2Elist_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool) ) ).
tff(c_2Ecombin_2Eo_2E0,type,
c_2Ecombin_2Eo_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b))) ).
tff(c_2Ecombin_2Eo_2E2,type,
c_2Ecombin_2Eo_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27c,A_27b) * tyop_2Emin_2Efun(A_27a,A_27c) ) > tyop_2Emin_2Efun(A_27a,A_27b) ) ).
tff(c_2Ecardinal_2Eset__exp_2E0,type,
c_2Ecardinal_2Eset__exp_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool))) ).
tff(c_2Ecardinal_2Eset__exp_2E2,type,
c_2Ecardinal_2Eset__exp_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool) ) ).
tff(c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(thm_2Eextra_2Dho_2Eeq__ext,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V2x_2E0: A_27a] : app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)
=> ( V0f_2E0 = V1g_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Eboolext,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( ( p(V0_2E0)
<=> p(V1_2E0) )
=> ( V0_2E0 = V1_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Etruth,axiom,
p(c_2Ebool_2ET_2E0) ).
tff(thm_2Eextra_2Dho_2Enotfalse,axiom,
~ p(c_2Ebool_2EF_2E0) ).
tff(thm_2Eextra_2Dho_2Ebool__cases__ax,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
| ( V0t_2E0 = c_2Ebool_2EF_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Ei__thm,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : app_2E2(A_27a,A_27a,combin_i_2E0(A_27a),V0x_2E0) = V0x_2E0 ).
tff(thm_2Eextra_2Dho_2Ek__thm,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),combin_k_2E0(A_27a,A_27b),V0x_2E0),V1y_2E0) = V0x_2E0 ).
tff(thm_2Eextra_2Dho_2Es__thm,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a] : app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),combin_s_2E0(A_27a,A_27b,A_27c),V0f_2E0),V1g_2E0),V2x_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V2x_2E0),app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)) ).
tff(logicdef_2E_2F_5C,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
& p(V1_2E0) ) ) ).
tff(logicdef_2E_5C_2F,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
| p(V1_2E0) ) ) ).
tff(logicdef_2E_7E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(V0_2E0))
<=> ~ p(V0_2E0) ) ).
tff(logicdef_2E_3D_3D_3E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
=> p(V1_2E0) ) ) ).
tff(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0_2E0: A_27a,V1_2E0: A_27a] :
( p(c_2Emin_2E_3D_2E2(A_27a,V0_2E0,V1_2E0))
<=> ( V0_2E0 = V1_2E0 ) ) ).
tff(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(A_27a,V0f_2E0))
<=> ! [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_2E1(A_27a,V0f_2E0))
<=> ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ebool_2E_21_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(A_27a),X0_2E0) ).
tff(arityeq2_2Ec_2Earithmetic_2E_2A_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_2A_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A_2E0,X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_2B_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E0,X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a,X1_2E0: A_27b] : c_2Epair_2E_2C_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Epair_2E_2C_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Ebool] : c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(A_27a,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Emin_2Ebool] : c_2Epair_2E_2C_2E2(A_27b,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(A_27b,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27c: $tType,X0_2E0: A_27c,X1_2E0: tyop_2Emin_2Ebool] : c_2Epair_2E_2C_2E2(A_27c,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool),app_2E2(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(A_27c,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Ebool] : c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27a_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),X1_2E0: tyop_2Emin_2Ebool] : c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27b_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0: tyop_2Emin_2Ebool] : c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Ebool] : c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28A_27c_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),X1_2E0: tyop_2Emin_2Ebool] : c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Emin_2Ebool] : c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Ebool] : c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0: tyop_2Emin_2Ebool] : c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
& p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : c_2Eprim__rec_2E_3C_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_3C_3D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3C_3D_2E0,X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] :
( ( X0_2E0 = X1_2E0 )
<=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
=> p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_3E_3D_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_3E_3D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3E_3D_2E0,X0_2E0),X1_2E0) ).
tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ebool_2E_3F_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ebool_2E_3F_21_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : c_2Ebool_2E_3F_21_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E0(A_27b),X0_2E0) ).
tff(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : c_2Ebool_2E_3F_21_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E0(tyop_2Enum_2Enum),X0_2E0) ).
tff(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : c_2Epred__set_2EBIGUNION_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : c_2Epred__set_2EBIGUNION_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E0(A_27b),X0_2E0) ).
tff(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28A_27a_29_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : c_2Epred__set_2EBIGUNION_2E1(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E0(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),X0_2E0) ).
tff(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Epred__set_2EBIJ_2E3(A_27a,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(A_27a,A_27a),X0_2E0),X1_2E0),X2_2E0) ).
tff(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ).
tff(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2EBIT1_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E0,X0_2E0) ).
tff(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2EBIT2_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E0,X0_2E0) ).
tff(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Epred__set_2ECARD_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : c_2Epred__set_2ECARD_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E0(A_27b),X0_2E0) ).
tff(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] : c_2Epred__set_2ECARD_2E1(tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E0(tyop_2Emin_2Ebool),X0_2E0) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eoption_2Eoption(A_27b),X2_2E0: tyop_2Eoption_2Eoption(A_27b)] : c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27b),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b))),c_2Ebool_2ECOND_2E0(tyop_2Eoption_2Eoption(A_27b)),X0_2E0),X1_2E0),X2_2E0) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27c_29,axiom,
! [A_27c: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eoption_2Eoption(A_27c),X2_2E0: tyop_2Eoption_2Eoption(A_27c)] : c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27c),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27c),tyop_2Eoption_2Eoption(A_27c),app_2E2(tyop_2Eoption_2Eoption(A_27c),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Eoption_2Eoption(A_27c)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Eoption_2Eoption(A_27c))),c_2Ebool_2ECOND_2E0(tyop_2Eoption_2Eoption(A_27c)),X0_2E0),X1_2E0),X2_2E0) ).
tff(arityeq2_2Ec_2Epred__set_2ECROSS_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Epred__set_2ECROSS_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2ECROSS_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epred__set_2ECROSS_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2ECROSS_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epred__set_2ECROSS_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : c_2Epred__set_2ECROSS_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool)),c_2Epred__set_2ECROSS_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epred__set_2ECROSS_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Epred__set_2ECROSS_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2ECROSS_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epred__set_2ECROSS_2E2_2Emono_2EA_27b_20mono_2EA_27d,axiom,
! [A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)] : c_2Epred__set_2ECROSS_2E2(A_27b,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27d),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27d),tyop_2Emin_2Ebool)),c_2Epred__set_2ECROSS_2E0(A_27b,A_27d),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epred__set_2ECROSS_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27b_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)] : c_2Epred__set_2ECROSS_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Ebool)),c_2Epred__set_2ECROSS_2E0(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epred__set_2ECROSS_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Epred__set_2ECROSS_2E2(tyop_2Emin_2Ebool,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2ECROSS_2E0(tyop_2Emin_2Ebool,A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: A_27a] : c_2Epred__set_2EDELETE_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EDELETE_2E0(A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Epred__set_2EDIFF_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EDIFF_2E0(A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Epred__set_2EDISJOINT_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EDISJOINT_2E0(A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : c_2Epred__set_2EDISJOINT_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EDISJOINT_2E0(A_27b),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Earithmetic_2EEXP_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2EEXP_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP_2E0,X0_2E0),X1_2E0) ).
tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Epred__set_2EFINITE_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : c_2Epred__set_2EFINITE_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(A_27b),X0_2E0) ).
tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2EA_27c,axiom,
! [A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : c_2Epred__set_2EFINITE_2E1(A_27c,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(A_27c),X0_2E0) ).
tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] : c_2Epred__set_2EFINITE_2E1(tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(tyop_2Emin_2Ebool),X0_2E0) ).
tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : c_2Epred__set_2EFINITE_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0) ).
tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(tyop_2Enum_2Enum),X0_2E0) ).
tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] : c_2Epred__set_2EFINITE_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) ).
tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool)] : c_2Epred__set_2EFINITE_2E1(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),X0_2E0) ).
tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))] : c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(A_27a,A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27b_20mono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))] : c_2Epred__set_2EGSPEC_2E1(A_27b,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(A_27b,A_27b),X0_2E0) ).
tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28A_27c_29_29_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool))] : c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),A_27c,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),A_27c),X0_2E0) ).
tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0) ).
tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27a_29_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool))] : c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),X0_2E0) ).
tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27b_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27b_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool))] : c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X0_2E0) ).
tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))] : c_2Epred__set_2EGSPEC_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0) ).
tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] : c_2Epred__set_2EGSPEC_2E1(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0) ).
tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27c_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool))] : c_2Epred__set_2EGSPEC_2E1(A_27c,tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(A_27c,tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) ).
tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))] : c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2EHAS__SIZE_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Enum_2Enum] : c_2Ecardinal_2EHAS__SIZE_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ecardinal_2EHAS__SIZE_2E0(A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2EHAS__SIZE_2E2_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X1_2E0: tyop_2Enum_2Enum] : c_2Ecardinal_2EHAS__SIZE_2E2(tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ecardinal_2EHAS__SIZE_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2EHAS__SIZE_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Enum_2Enum] : c_2Ecardinal_2EHAS__SIZE_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ecardinal_2EHAS__SIZE_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Epred__set_2EIMAGE_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Epred__set_2EIMAGE_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28A_27a_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ebool_2EIN_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : c_2Ebool_2EIN_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(A_27b),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27c,axiom,
! [A_27c: $tType,X0_2E0: A_27c,X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : c_2Ebool_2EIN_2E2(A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(A_27c),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ).
tff(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : c_2Epred__set_2EINJ_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EINJ_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ).
tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Epred__set_2EINSERT_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E0(A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : c_2Epred__set_2EINSERT_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E0(A_27b),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] : c_2Epred__set_2EINSERT_2E2(tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27b_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)] : c_2Epred__set_2EINSERT_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] : c_2Epred__set_2EINSERT_2E2(tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epred__set_2EINTER_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Epred__set_2EINTER_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EINTER_2E0(A_27a),X0_2E0),X1_2E0) ).
tff(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Eoption_2Eoption_28A_27b_29_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27b)] : c_2Ecombin_2EK_2E1(tyop_2Eoption_2Eoption(A_27b),A_27a,X0_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Ecombin_2EK_2E0(tyop_2Eoption_2Eoption(A_27b),A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : c_2Elist_2ELENGTH_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : c_2Elist_2ELIST__TO__SET_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2ENUMERAL_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E0,X0_2E0) ).
tff(arityeq1_2Ec_2Epred__set_2EPOW_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Epred__set_2EPOW_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a] : c_2Eoption_2ESOME_2E1(A_27a,X0_2E0) = app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: A_27b] : c_2Eoption_2ESOME_2E1(A_27b,X0_2E0) = app_2E2(A_27b,tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E0(A_27b),X0_2E0) ).
tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27c,axiom,
! [A_27c: $tType,X0_2E0: A_27c] : c_2Eoption_2ESOME_2E1(A_27c,X0_2E0) = app_2E2(A_27c,tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ESOME_2E0(A_27c),X0_2E0) ).
tff(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Epred__set_2ESUBSET_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2ESUBSET_2E0(A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : c_2Epred__set_2ESUBSET_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2ESUBSET_2E0(A_27b),X0_2E0),X1_2E0) ).
tff(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : c_2Enum_2ESUC_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC_2E0,X0_2E0) ).
tff(arityeq3_2Ec_2Epred__set_2ESURJ_2E3_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Epred__set_2ESURJ_2E3(A_27b,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESURJ_2E0(A_27b,A_27a),X0_2E0),X1_2E0),X2_2E0) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27c_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool)))] : c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E0(A_27a,A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool)),X0_2E0) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))] : c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E0(A_27a,A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0) ).
tff(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Epred__set_2EUNION_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EUNION_2E0(A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : c_2Epred__set_2EUNION_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EUNION_2E0(A_27b),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : c_2Epred__set_2EUNION_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2EUNION_2E0(tyop_2Epair_2Eprod(A_27a,A_27a)),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
| p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Ecardinal_2Ebijns_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ebijns_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),c_2Ecardinal_2Ebijns_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Ecardinal_2Ebijns_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ebijns_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),c_2Ecardinal_2Ebijns_2E0(A_27b),X0_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardeq_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2CA_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardeq_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2EA_27a1_20mono_2EA_27a2,axiom,
! [A_27a1: $tType,A_27a2: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardeq_2E2(A_27a1,A_27a2,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(A_27a1,A_27a2),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardeq_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardeq_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2EA_27b1_20mono_2EA_27b2,axiom,
! [A_27b1: $tType,A_27b2: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b1,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b2,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardeq_2E2(A_27b1,A_27b2,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b2,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b2,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(A_27b1,A_27b2),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardeq_2E2(A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(A_27c,A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardeq_2E2(A_27c,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(A_27c,A_27d),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27a_29_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28A_27b_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b))),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27b_29_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Enum_2Enum),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27b_29_29_20mono_2Etyop_2Epair_2Eprod_28A_27b_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27b_29_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28A_27c_29_29_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_2Ctyop_2Eoption_2Eoption_28A_27c_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27c)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27c))),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28A_27c_29_29_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),A_27c),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b1_2Ctyop_2Eoption_2Eoption_28A_27a1_29_29_20mono_2Etyop_2Emin_2Efun_28A_27b2_2Ctyop_2Eoption_2Eoption_28A_27a2_29_29,axiom,
! [A_27a1: $tType,A_27a2: $tType,A_27b1: $tType,A_27b2: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b1,tyop_2Eoption_2Eoption(A_27a1)),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b2,tyop_2Eoption_2Eoption(A_27a2)),tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27b1,tyop_2Eoption_2Eoption(A_27a1)),tyop_2Emin_2Efun(A_27b2,tyop_2Eoption_2Eoption(A_27a2)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b2,tyop_2Eoption_2Eoption(A_27a2)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b1,tyop_2Eoption_2Eoption(A_27a1)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b2,tyop_2Eoption_2Eoption(A_27a2)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Emin_2Efun(A_27b1,tyop_2Eoption_2Eoption(A_27a1)),tyop_2Emin_2Efun(A_27b2,tyop_2Eoption_2Eoption(A_27a2))),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28A_27a_29_29_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28A_27a_29_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardeq_2E2(tyop_2Elist_2Elist(A_27a),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Elist_2Elist(A_27a),A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28A_27a_29_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardeq_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardeq_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardeq_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Epair_2Eprod(A_27a,A_27a),A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardeq_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27d_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27d),tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardeq_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27d),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27d),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27d),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27d)),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardgeq_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardgeq_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardgeq_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardgeq_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardgeq_2E2(tyop_2Enum_2Enum,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardgeq_2E0(tyop_2Enum_2Enum,A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardgt_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardgt_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardgt_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardleq_2E2(A_27a,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(A_27a,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27b_20mono_2EA_27d,axiom,
! [A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(A_27b,A_27d),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(A_27c,A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(A_27c,A_27b),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(A_27c,A_27d),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27d_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardleq_2E2(A_27d,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(A_27d,A_27b),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardleq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardleq_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27d_2Ctyop_2Eoption_2Eoption_28A_27c_29_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28A_27a_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardleq_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardleq_2E2(tyop_2Enum_2Enum,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(tyop_2Enum_2Enum,A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27d_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27d),tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardleq_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27d),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27d),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27d),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27d)),X0_2E0),X1_2E0) ).
tff(arityeq1_2Ec_2Epred__set_2Ecount_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : c_2Epred__set_2Ecount_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E0,X0_2E0) ).
tff(arityeq1_2Ec_2Epred__set_2Ecountable_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Epred__set_2Ecountable_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Epred__set_2Ecountable_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : c_2Epred__set_2Ecountable_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E0(A_27b),X0_2E0) ).
tff(arityeq1_2Ec_2Ecardinal_2Elist_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Elist_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Ecardinal_2Elist_2E0(A_27a),X0_2E0) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),A_27a),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))] : c_2Ecombin_2Eo_2E2(A_27a,A_27a,tyop_2Eoption_2Eoption(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ecombin_2Eo_2E0(A_27a,A_27a,tyop_2Eoption_2Eoption(A_27a)),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Eset__exp_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Eset__exp_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)),c_2Ecardinal_2Eset__exp_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Eset__exp_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Eset__exp_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)),c_2Ecardinal_2Eset__exp_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Eset__exp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Eset__exp_2E2(tyop_2Enum_2Enum,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)),c_2Ecardinal_2Eset__exp_2E0(tyop_2Enum_2Enum,A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Eset__exp_2E2_2Emono_2EA_27b1_20mono_2EA_27a1,axiom,
! [A_27a1: $tType,A_27b1: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b1,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Eset__exp_2E2(A_27b1,A_27a1,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b1,tyop_2Eoption_2Eoption(A_27a1)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b1,tyop_2Eoption_2Eoption(A_27a1)),tyop_2Emin_2Ebool)),c_2Ecardinal_2Eset__exp_2E0(A_27b1,A_27a1),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Eset__exp_2E2_2Emono_2EA_27b2_20mono_2EA_27a2,axiom,
! [A_27a2: $tType,A_27b2: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b2,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Eset__exp_2E2(A_27b2,A_27a2,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b2,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b2,tyop_2Eoption_2Eoption(A_27a2)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b2,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b2,tyop_2Eoption_2Eoption(A_27a2)),tyop_2Emin_2Ebool)),c_2Ecardinal_2Eset__exp_2E0(A_27b2,A_27a2),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Eset__exp_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Eset__exp_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),c_2Ecardinal_2Eset__exp_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Eset__exp_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Eset__exp_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool)),c_2Ecardinal_2Eset__exp_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Eset__exp_2E2_2Emono_2EA_27d_20mono_2EA_27c,axiom,
! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Eset__exp_2E2(A_27d,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool)),c_2Ecardinal_2Eset__exp_2E0(A_27d,A_27c),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Eset__exp_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool)] : c_2Ecardinal_2Eset__exp_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool)),c_2Ecardinal_2Eset__exp_2E0(tyop_2Epair_2Eprod(A_27b,A_27a),A_27c),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Eset__exp_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Eset__exp_2E2(A_27c,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),tyop_2Emin_2Ebool)),c_2Ecardinal_2Eset__exp_2E0(A_27c,A_27d),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Eset__exp_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28A_27c_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Eset__exp_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),tyop_2Emin_2Ebool)),c_2Ecardinal_2Eset__exp_2E0(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ecardinal_2Eset__exp_2E2_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Eset__exp_2E2(A_27a,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),c_2Ecardinal_2Eset__exp_2E0(A_27a,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ).
tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] :
( ~ p(X0_2E0)
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0_2E0)) ) ).
tff(thm_2Ecardinal_2Ecardleq__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s1_2E0,V1s2_2E0))
<=> ? [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V2f_2E0,V0s1_2E0,V1s2_2E0)) ) ).
tff(thm_2Ecardinal_2Ecardeq__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s1_2E0,V1s2_2E0))
<=> ? [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V2f_2E0,V0s1_2E0,V1s2_2E0)) ) ).
tff(thm_2Ecardinal_2EHAS__SIZE,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1n_2E0: tyop_2Enum_2Enum] :
( p(c_2Ecardinal_2EHAS__SIZE_2E2(A_27a,V0s_2E0,V1n_2E0))
<=> ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
& ( c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0) = V1n_2E0 ) ) ) ).
tff(thm_2Ecardinal_2Elist__def,axiom,
! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))] :
( ! [V1l_2E0: tyop_2Elist_2Elist(A_27a),V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F1_2E0,V1l_2E0),V0A_2E0))
<=> ! [V2e_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2e_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0)))
=> p(c_2Ebool_2EIN_2E2(A_27a,V2e_2E0,V0A_2E0)) ) )
=> ( ! [V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),F0_2E0,V0A_2E0),V1l_2E0) = c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V1l_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F1_2E0,V1l_2E0),V0A_2E0))
=> ! [V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Elist_2E1(A_27a,V0A_2E0) = c_2Epred__set_2EGSPEC_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),F0_2E0,V0A_2E0)) ) ) ).
tff(thm_2Ecardinal_2Ebijns__def,axiom,
! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)))] :
( ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F1_2E0,V1f_2E0),V0A_2E0))
<=> ( p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27a,c_2Ecombin_2Eo_2E2(A_27a,A_27a,tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ETHE_2E0(A_27a),V1f_2E0),V0A_2E0,V0A_2E0))
& ! [V2a_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2a_2E0,V0A_2E0))
<=> ? [V3b_2E0: A_27a] : app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27a),V1f_2E0,V2a_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V3b_2E0) ) ) )
=> ( ! [V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))] : app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)),F0_2E0,V0A_2E0),V1f_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool,V1f_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F1_2E0,V1f_2E0),V0A_2E0))
=> ! [V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ebijns_2E1(A_27a,V0A_2E0) = c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)),F0_2E0,V0A_2E0)) ) ) ).
tff(thm_2Ecardinal_2Ecardgeq__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardgeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0) = c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0) ).
tff(thm_2Ecardinal_2Ecardgt__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardgt_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
<=> ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) ) ).
tff(thm_2Ecardinal_2Eset__exp__def,axiom,
! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool))))] :
( ! [V1B_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0A_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))] :
( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),F1_2E0,V1B_2E0),V0A_2E0),V2f_2E0))
<=> ( ! [V3b_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3b_2E0,V1B_2E0))
=> ? [V4a_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V4a_2E0,V0A_2E0))
& ( app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27b),V2f_2E0,V3b_2E0) = c_2Eoption_2ESOME_2E1(A_27b,V4a_2E0) ) ) )
& ! [V5b_2E0: A_27a] :
( ~ p(c_2Ebool_2EIN_2E2(A_27a,V5b_2E0,V1B_2E0))
=> ( app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27b),V2f_2E0,V5b_2E0) = c_2Eoption_2ENONE_2E0(A_27b) ) ) ) )
=> ( ! [V1B_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0A_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))] : app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool))),F0_2E0,V1B_2E0),V0A_2E0),V2f_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool,V2f_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),F1_2E0,V1B_2E0),V0A_2E0),V2f_2E0))
=> ! [V0A_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1B_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Eset__exp_2E2(A_27a,A_27b,V0A_2E0,V1B_2E0) = c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool))),F0_2E0,V1B_2E0),V0A_2E0)) ) ) ).
tff(thm_2Ecardinal_2ECARD__BIGUNION,axiom,
! [A_27a: $tType,A_27b: $tType,V0s1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1k_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V1k_2E0))
& p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),A_27a,V0s1_2E0,V1k_2E0))
& ! [V2e_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2e_2E0,V0s1_2E0))
=> p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V2e_2E0,V1k_2E0)) ) )
=> p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,c_2Epred__set_2EBIGUNION_2E1(A_27b,V0s1_2E0),V1k_2E0)) ) ).
tff(thm_2Ecardinal_2ESET__SUM__CARDEQ__SET,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
=> ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a),V0s_2E0,c_2Epred__set_2ECROSS_2E2(tyop_2Emin_2Ebool,A_27a,c_2Epred__set_2EINSERT_2E2(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0,c_2Epred__set_2EINSERT_2E2(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Emin_2Ebool))),V0s_2E0)))
& ! [V1A_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2B_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EDISJOINT_2E2(A_27b,V1A_2E0,V2B_2E0))
& p(c_2Ecardinal_2Ecardeq_2E2(A_27b,A_27a,V1A_2E0,V0s_2E0))
& p(c_2Ecardinal_2Ecardeq_2E2(A_27b,A_27a,V2B_2E0,V0s_2E0)) )
=> p(c_2Ecardinal_2Ecardeq_2E2(A_27b,A_27a,c_2Epred__set_2EUNION_2E2(A_27b,V1A_2E0,V2B_2E0),V0s_2E0)) ) ) ) ).
tff(thm_2Ecardinal_2ESET__SQUARED__CARDEQ__SET,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
=> p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),A_27a,c_2Epred__set_2ECROSS_2E2(A_27a,A_27a,V0s_2E0,V0s_2E0),V0s_2E0)) ) ).
tff(thm_2Ecardinal_2Eset__binomial2,axiom,
! [A_27a: $tType,V0B_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Epred__set_2ECROSS_2E2(A_27a,A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V1A_2E0,V0B_2E0),c_2Epred__set_2EUNION_2E2(A_27a,V1A_2E0,V0B_2E0)) = c_2Epred__set_2EUNION_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epred__set_2EUNION_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epred__set_2EUNION_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epred__set_2ECROSS_2E2(A_27a,A_27a,V1A_2E0,V1A_2E0),c_2Epred__set_2ECROSS_2E2(A_27a,A_27a,V1A_2E0,V0B_2E0)),c_2Epred__set_2ECROSS_2E2(A_27a,A_27a,V0B_2E0,V1A_2E0)),c_2Epred__set_2ECROSS_2E2(A_27a,A_27a,V0B_2E0,V0B_2E0)) ).
tff(thm_2Ecardinal_2Ecardleq__empty,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27b)))
<=> ( V0x_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) ).
tff(thm_2Ecardinal_2Ecardleq__lt__trans,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
( ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
& ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27b,V2u_2E0,V1t_2E0)) )
=> ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27a,V2u_2E0,V0s_2E0)) ) ).
tff(thm_2Ecardinal_2Ecardlt__leq__trans,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
( ( ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0))
& p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27c,V1t_2E0,V2u_2E0)) )
=> ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27a,V2u_2E0,V0s_2E0)) ) ).
tff(thm_2Ecardinal_2Ecardlt__TRANS,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27b,V1t_2E0,V0s_2E0))
& ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27c,V2u_2E0,V1t_2E0)) )
=> ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V2u_2E0,V0s_2E0)) ) ).
tff(thm_2Ecardinal_2Ecardlt__lenoteq,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0))
<=> ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
& ~ p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) ) ) ).
tff(thm_2Ecardinal_2Ecardlt__REFL,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
~ ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27a,V0s_2E0,V0s_2E0)) ).
tff(thm_2Ecardinal_2Ecardleq__lteq,axiom,
! [A_27a: $tType,A_27b: $tType,V0s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s1_2E0,V1s2_2E0))
<=> ( ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1s2_2E0,V0s1_2E0))
| p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s1_2E0,V1s2_2E0)) ) ) ).
tff(thm_2Ecardinal_2Ecardleq__dichotomy,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
| p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0)) ) ).
tff(thm_2Ecardinal_2Ecountable__cardeq,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
=> ( c_2Epred__set_2Ecountable_2E1(A_27a,V0s_2E0) = c_2Epred__set_2Ecountable_2E1(A_27b,V1t_2E0) ) ) ).
tff(thm_2Ecardinal_2Ecountable__thm,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Epred__set_2Ecountable_2E1(A_27a,V0s_2E0) = c_2Ecardinal_2Ecardleq_2E2(A_27a,tyop_2Enum_2Enum,V0s_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)) ).
tff(thm_2Ecardinal_2EIMAGE__cardleq__rwt,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V1s_2E0,V2t_2E0))
=> p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27c,V0f_2E0,V1s_2E0),V2t_2E0)) ) ).
tff(thm_2Ecardinal_2ESUBSET__CARDLEQ,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0x_2E0,V1y_2E0))
=> p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27a,V0x_2E0,V1y_2E0)) ) ).
tff(thm_2Ecardinal_2ECARDLEQ__CROSS__CONG,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_27_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3t_27_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)] :
( ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1s_27_2E0))
& p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27d,V2t_2E0,V3t_27_2E0)) )
=> p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27d),c_2Epred__set_2ECROSS_2E2(A_27a,A_27c,V0s_2E0,V2t_2E0),c_2Epred__set_2ECROSS_2E2(A_27b,A_27d,V1s_27_2E0,V3t_27_2E0))) ) ).
tff(thm_2Ecardinal_2EIMAGE__cardleq,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0),V1s_2E0)) ).
tff(thm_2Ecardinal_2EINFINITE__UNIV__INF,axiom,
! [A_27a: $tType] : ~ p(c_2Epred__set_2EFINITE_2E1(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),c_2Epred__set_2EUNIV_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)))) ).
tff(thm_2Ecardinal_2ECARDLEQ__FINITE,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27b,V1t_2E0))
& p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) )
=> p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0)) ) ).
tff(thm_2Ecardinal_2ECARDEQ__CARDLEQ,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0t2_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V1t1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V2s2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V3s1_2E0,V2s2_2E0))
& p(c_2Ecardinal_2Ecardeq_2E2(A_27c,A_27d,V1t1_2E0,V0t2_2E0)) )
=> ( c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27c,V3s1_2E0,V1t1_2E0) = c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27d,V2s2_2E0,V0t2_2E0) ) ) ).
tff(thm_2Ecardinal_2ECARDEQ__SUBSET__CARDLEQ,axiom,
! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V1s_2E0,V0t_2E0))
=> p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V1s_2E0,V0t_2E0)) ) ).
tff(thm_2Ecardinal_2ECARDEQ__CROSS__SYM,axiom,
! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,V1s_2E0,V0t_2E0),c_2Epred__set_2ECROSS_2E2(A_27b,A_27a,V0t_2E0,V1s_2E0))) ).
tff(thm_2Ecardinal_2ECARDEQ__CROSS,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0t2_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V1t1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V2s2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V3s1_2E0,V2s2_2E0))
& p(c_2Ecardinal_2Ecardeq_2E2(A_27c,A_27d,V1t1_2E0,V0t2_2E0)) )
=> p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27d),c_2Epred__set_2ECROSS_2E2(A_27a,A_27c,V3s1_2E0,V1t1_2E0),c_2Epred__set_2ECROSS_2E2(A_27b,A_27d,V2s2_2E0,V0t2_2E0))) ) ).
tff(thm_2Ecardinal_2EFINITE__CLE__INFINITE,axiom,
! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
& ~ p(c_2Epred__set_2EFINITE_2E1(A_27b,V0t_2E0)) )
=> p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V1s_2E0,V0t_2E0)) ) ).
tff(thm_2Ecardinal_2EEMPTY__CARDLEQ,axiom,
! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,c_2Epred__set_2EEMPTY_2E0(A_27a),V0t_2E0)) ).
tff(thm_2Ecardinal_2ECARDEQ__INSERT__RWT,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
=> p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,V1s_2E0),V1s_2E0)) ) ).
tff(thm_2Ecardinal_2Ecardeq__INSERT,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,V1s_2E0),V1s_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V1s_2E0))
| ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0)) ) ) ).
tff(thm_2Ecardinal_2ECARDEQ__0,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27b)))
<=> ( V0x_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) )
& ( p(c_2Ecardinal_2Ecardeq_2E2(A_27c,A_27a,c_2Epred__set_2EEMPTY_2E0(A_27c),V0x_2E0))
<=> ( V0x_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) ) ).
tff(thm_2Ecardinal_2ECARDEQ__CARD,axiom,
! [A_27a: $tType,A_27b: $tType,V0s2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V1s1_2E0,V0s2_2E0))
& p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s1_2E0)) )
=> ( c_2Epred__set_2ECARD_2E1(A_27a,V1s1_2E0) = c_2Epred__set_2ECARD_2E1(A_27b,V0s2_2E0) ) ) ).
tff(thm_2Ecardinal_2ECARDEQ__FINITE,axiom,
! [A_27a: $tType,A_27b: $tType,V0s2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V1s1_2E0,V0s2_2E0))
=> ( c_2Epred__set_2EFINITE_2E1(A_27a,V1s1_2E0) = c_2Epred__set_2EFINITE_2E1(A_27b,V0s2_2E0) ) ) ).
tff(thm_2Ecardinal_2Ecardleq__ANTISYM,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
& p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0)) )
=> p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) ) ).
tff(thm_2Ecardinal_2Ecardleq__TRANS,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
( ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
& p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27c,V1t_2E0,V2u_2E0)) )
=> p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27c,V0s_2E0,V2u_2E0)) ) ).
tff(thm_2Ecardinal_2Ecardleq__REFL,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27a,V0s_2E0,V0s_2E0)) ).
tff(thm_2Ecardinal_2Ecardeq__TRANS,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
( ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
& p(c_2Ecardinal_2Ecardeq_2E2(A_27b,A_27c,V1t_2E0,V2u_2E0)) )
=> p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27c,V0s_2E0,V2u_2E0)) ) ).
tff(thm_2Ecardinal_2Ecardeq__SYM,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0) = c_2Ecardinal_2Ecardeq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0) ).
tff(thm_2Ecardinal_2Ecardeq__REFL,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27a,V0s_2E0,V0s_2E0)) ).
tff(thm_2Ecardinal_2ESURJECTIVE__ON__RIGHT__INVERSE,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ! [V3y_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V3y_2E0,V2t_2E0))
=> ? [V4x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V0s_2E0))
& ( app_2E2(A_27a,A_27b,V1f_2E0,V4x_2E0) = V3y_2E0 ) ) )
<=> ? [V5g_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
! [V6y_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V6y_2E0,V2t_2E0))
=> ( p(c_2Ebool_2EIN_2E2(A_27a,app_2E2(A_27b,A_27a,V5g_2E0,V6y_2E0),V0s_2E0))
& ( app_2E2(A_27a,A_27b,V1f_2E0,app_2E2(A_27b,A_27a,V5g_2E0,V6y_2E0)) = V6y_2E0 ) ) ) ) ).
tff(thm_2Ecardinal_2ESURJECTIVE__RIGHT__INVERSE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( ! [V1y_2E0: A_27a] :
? [V2x_2E0: A_27b] : app_2E2(A_27b,A_27a,V0f_2E0,V2x_2E0) = V1y_2E0
<=> ? [V3g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
! [V4y_2E0: A_27a] : app_2E2(A_27b,A_27a,V0f_2E0,app_2E2(A_27a,A_27b,V3g_2E0,V4y_2E0)) = V4y_2E0 ) ).
tff(thm_2Ecardinal_2EFINITE__IMAGE__INJ__GENERAL,axiom,
! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))))] :
( ! [V5x_2E0: A_27a,V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1A_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0,V5x_2E0),V2s_2E0),V0f_2E0),V1A_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,V2s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V5x_2E0),V1A_2E0)) ) )
=> ( ! [V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1A_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5x_2E0: A_27a] : app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0,V2s_2E0),V0f_2E0),V1A_2E0),V5x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V5x_2E0,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0,V5x_2E0),V2s_2E0),V0f_2E0),V1A_2E0))
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1A_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V2s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V4y_2E0,V2s_2E0))
& ( app_2E2(A_27a,A_27b,V0f_2E0,V3x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V4y_2E0) ) )
=> ( V3x_2E0 = V4y_2E0 ) )
& p(c_2Epred__set_2EFINITE_2E1(A_27b,V1A_2E0)) )
=> p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0,V2s_2E0),V0f_2E0),V1A_2E0)))) ) ) ) ).
tff(thm_2Ecardinal_2EFINITE__IMAGE__INJ,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1A_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4x_2E0: A_27a] : app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V1A_2E0),V4x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V4x_2E0,c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V4x_2E0),V1A_2E0))
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1A_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
( ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V3y_2E0) )
=> ( V2x_2E0 = V3y_2E0 ) )
& p(c_2Epred__set_2EFINITE_2E1(A_27b,V1A_2E0)) )
=> p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V1A_2E0)))) ) ) ).
tff(thm_2Ecardinal_2EFINITE__IMAGE__INJ__EQ,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,V1s_2E0))
& ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V3y_2E0) ) )
=> ( V2x_2E0 = V3y_2E0 ) )
=> ( c_2Epred__set_2EFINITE_2E1(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0)) = c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0) ) ) ).
tff(thm_2Ecardinal_2EINFINITE__IMAGE__INJ,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V1x_2E0: A_27a,V2y_2E0: A_27a] :
( ( app_2E2(A_27a,A_27b,V0f_2E0,V1x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V2y_2E0) )
=> ( V1x_2E0 = V2y_2E0 ) )
=> ! [V3s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V3s_2E0))
=> ~ p(c_2Epred__set_2EFINITE_2E1(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V3s_2E0))) ) ) ).
tff(thm_2Ecardinal_2EINFINITE__NONEMPTY,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
=> ( V0s_2E0 != c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) ).
tff(thm_2Ecardinal_2EFINITE__PRODUCT__DEPENDENT,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool))))))] :
( ! [V4x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5y_2E0: A_27b,V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool))),F1_2E0,V4x_2E0),V1s_2E0),V5y_2E0),V2t_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V1s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27b,V5y_2E0,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0,V4x_2E0))) ) )
=> ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4x_2E0: A_27a,V5y_2E0: A_27b] : app_2E2(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool))))),F0_2E0,V0f_2E0),V1s_2E0),V2t_2E0),V4x_2E0),V5y_2E0) = c_2Epair_2E_2C_2E2(A_27c,tyop_2Emin_2Ebool,app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V4x_2E0),V5y_2E0),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool))),F1_2E0,V4x_2E0),V1s_2E0),V5y_2E0),V2t_2E0))
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
& ! [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V1s_2E0))
=> p(c_2Epred__set_2EFINITE_2E1(A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0,V3x_2E0))) ) )
=> p(c_2Epred__set_2EFINITE_2E1(A_27c,c_2Epred__set_2EGSPEC_2E1(A_27c,tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool))))),F0_2E0,V0f_2E0),V1s_2E0),V2t_2E0))))) ) ) ) ).
tff(thm_2Ecardinal_2EFINITE__PRODUCT,axiom,
! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))))] :
( ! [V2x_2E0: A_27a,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3y_2E0: A_27b,V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0,V2x_2E0),V0s_2E0),V3y_2E0),V1t_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27b,V3y_2E0,V1t_2E0)) ) )
=> ( ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2x_2E0: A_27a,V3y_2E0: A_27b] : app_2E2(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0,V0s_2E0),V1t_2E0),V2x_2E0),V3y_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V3y_2E0),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0,V2x_2E0),V0s_2E0),V3y_2E0),V1t_2E0))
=> ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
& p(c_2Epred__set_2EFINITE_2E1(A_27b,V1t_2E0)) )
=> p(c_2Epred__set_2EFINITE_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0,V0s_2E0),V1t_2E0))))) ) ) ) ).
tff(thm_2Ecardinal_2ESURJECTIVE__IMAGE__THM,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)))] :
( ! [V3P_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V4x_2E0: A_27a] : app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V3P_2E0),V0f_2E0),V4x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V4x_2E0,app_2E2(A_27b,tyop_2Emin_2Ebool,V3P_2E0,app_2E2(A_27a,A_27b,V0f_2E0,V4x_2E0)))
=> ( ! [V3P_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5x_2E0: A_27b] : app_2E2(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),F1_2E0,V3P_2E0),V5x_2E0) = c_2Epair_2E_2C_2E2(A_27b,tyop_2Emin_2Ebool,V5x_2E0,app_2E2(A_27b,tyop_2Emin_2Ebool,V3P_2E0,V5x_2E0))
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V1y_2E0: A_27b] :
? [V2x_2E0: A_27a] : app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = V1y_2E0
<=> ! [V3P_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V3P_2E0),V0f_2E0))) = c_2Epred__set_2EGSPEC_2E1(A_27b,A_27b,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),F1_2E0,V3P_2E0)) ) ) ) ).
tff(thm_2Ecardinal_2ESURJECTIVE__ON__IMAGE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1u_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2v_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ! [V3t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESUBSET_2E2(A_27b,V3t_2E0,V2v_2E0))
=> ? [V4s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V4s_2E0,V1u_2E0))
& ( c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V4s_2E0) = V3t_2E0 ) ) )
<=> ! [V5y_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V5y_2E0,V2v_2E0))
=> ? [V6x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V6x_2E0,V1u_2E0))
& ( app_2E2(A_27a,A_27b,V0f_2E0,V6x_2E0) = V5y_2E0 ) ) ) ) ).
tff(thm_2Ecardinal_2ESURJECTIVE__IMAGE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
? [V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V2s_2E0) = V1t_2E0
<=> ! [V3y_2E0: A_27b] :
? [V4x_2E0: A_27a] : app_2E2(A_27a,A_27b,V0f_2E0,V4x_2E0) = V3y_2E0 ) ).
tff(thm_2Ecardinal_2ECARD__LE__INJ,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
& p(c_2Epred__set_2EFINITE_2E1(A_27b,V1t_2E0))
& p(c_2Earithmetic_2E_3C_3D_2E2(c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0),c_2Epred__set_2ECARD_2E1(A_27b,V1t_2E0))) )
=> ? [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( p(c_2Epred__set_2ESUBSET_2E2(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V2f_2E0,V0s_2E0),V1t_2E0))
& ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V0s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V4y_2E0,V0s_2E0))
& ( app_2E2(A_27a,A_27b,V2f_2E0,V3x_2E0) = app_2E2(A_27a,A_27b,V2f_2E0,V4y_2E0) ) )
=> ( V3x_2E0 = V4y_2E0 ) ) ) ) ).
tff(thm_2Ecardinal_2ECARD__IMAGE__INJ,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,V1s_2E0))
& ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V3y_2E0) ) )
=> ( V2x_2E0 = V3y_2E0 ) )
& p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0)) )
=> ( c_2Epred__set_2ECARD_2E1(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0)) = c_2Epred__set_2ECARD_2E1(A_27a,V1s_2E0) ) ) ).
tff(thm_2Ecardinal_2ECARD__IMAGE__LE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
=> p(c_2Earithmetic_2E_3C_3D_2E2(c_2Epred__set_2ECARD_2E1(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0)),c_2Epred__set_2ECARD_2E1(A_27a,V1s_2E0))) ) ).
tff(thm_2Ecardinal_2ESURJECTIVE__IFF__INJECTIVE__GEN,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
& p(c_2Epred__set_2EFINITE_2E1(A_27b,V1t_2E0))
& ( c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0) = c_2Epred__set_2ECARD_2E1(A_27b,V1t_2E0) )
& p(c_2Epred__set_2ESUBSET_2E2(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V2f_2E0,V0s_2E0),V1t_2E0)) )
=> ( ! [V3y_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V3y_2E0,V1t_2E0))
=> ? [V4x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V0s_2E0))
& ( app_2E2(A_27a,A_27b,V2f_2E0,V4x_2E0) = V3y_2E0 ) ) )
<=> ! [V5x_2E0: A_27a,V6y_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,V0s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V6y_2E0,V0s_2E0))
& ( app_2E2(A_27a,A_27b,V2f_2E0,V5x_2E0) = app_2E2(A_27a,A_27b,V2f_2E0,V6y_2E0) ) )
=> ( V5x_2E0 = V6y_2E0 ) ) ) ) ).
tff(thm_2Ecardinal_2ESURJECTIVE__IFF__INJECTIVE,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27a)] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27a,V1f_2E0,V0s_2E0),V0s_2E0)) )
=> ( ! [V2y_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2y_2E0,V0s_2E0))
=> ? [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V0s_2E0))
& ( app_2E2(A_27a,A_27a,V1f_2E0,V3x_2E0) = V2y_2E0 ) ) )
<=> ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V0s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V5y_2E0,V0s_2E0))
& ( app_2E2(A_27a,A_27a,V1f_2E0,V4x_2E0) = app_2E2(A_27a,A_27a,V1f_2E0,V5y_2E0) ) )
=> ( V4x_2E0 = V5y_2E0 ) ) ) ) ).
tff(thm_2Ecardinal_2ECARD__EQ__BIJECTION,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
& p(c_2Epred__set_2EFINITE_2E1(A_27b,V1t_2E0))
& ( c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0) = c_2Epred__set_2ECARD_2E1(A_27b,V1t_2E0) ) )
=> ? [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V0s_2E0))
=> p(c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V2f_2E0,V3x_2E0),V1t_2E0)) )
& ! [V4y_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V4y_2E0,V1t_2E0))
=> ? [V5x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,V0s_2E0))
& ( app_2E2(A_27a,A_27b,V2f_2E0,V5x_2E0) = V4y_2E0 ) ) )
& ! [V6x_2E0: A_27a,V7y_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V6x_2E0,V0s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V7y_2E0,V0s_2E0))
& ( app_2E2(A_27a,A_27b,V2f_2E0,V6x_2E0) = app_2E2(A_27a,A_27b,V2f_2E0,V7y_2E0) ) )
=> ( V6x_2E0 = V7y_2E0 ) ) ) ) ).
tff(thm_2Ecardinal_2ECARD__EQ__BIJECTIONS,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
& p(c_2Epred__set_2EFINITE_2E1(A_27b,V1t_2E0))
& ( c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0) = c_2Epred__set_2ECARD_2E1(A_27b,V1t_2E0) ) )
=> ? [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V3g_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( ! [V4x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V0s_2E0))
=> ( p(c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V2f_2E0,V4x_2E0),V1t_2E0))
& ( app_2E2(A_27b,A_27a,V3g_2E0,app_2E2(A_27a,A_27b,V2f_2E0,V4x_2E0)) = V4x_2E0 ) ) )
& ! [V5y_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V5y_2E0,V1t_2E0))
=> ( p(c_2Ebool_2EIN_2E2(A_27a,app_2E2(A_27b,A_27a,V3g_2E0,V5y_2E0),V0s_2E0))
& ( app_2E2(A_27a,A_27b,V2f_2E0,app_2E2(A_27b,A_27a,V3g_2E0,V5y_2E0)) = V5y_2E0 ) ) ) ) ) ).
tff(thm_2Ecardinal_2ESING__SUBSET,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0: A_27a] : c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V1x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)),V0s_2E0) = c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V0s_2E0) ).
tff(thm_2Ecardinal_2EINJECTIVE__ON__IMAGE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1u_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V2s_2E0,V1u_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V3t_2E0,V1u_2E0))
& ( c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V2s_2E0) = c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V3t_2E0) ) )
=> ( V2s_2E0 = V3t_2E0 ) )
<=> ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V1u_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V5y_2E0,V1u_2E0))
& ( app_2E2(A_27a,A_27b,V0f_2E0,V4x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V5y_2E0) ) )
=> ( V4x_2E0 = V5y_2E0 ) ) ) ).
tff(thm_2Ecardinal_2EINJECTIVE__IMAGE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0) = c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V2t_2E0) )
=> ( V1s_2E0 = V2t_2E0 ) )
<=> ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
( ( app_2E2(A_27a,A_27b,V0f_2E0,V3x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V4y_2E0) )
=> ( V3x_2E0 = V4y_2E0 ) ) ) ).
tff(thm_2Ecardinal_2EFINITE__FINITE__BIGUNION,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))
=> ( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EBIGUNION_2E1(A_27a,V0s_2E0)))
<=> ! [V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0,V0s_2E0))
=> p(c_2Epred__set_2EFINITE_2E1(A_27a,V1t_2E0)) ) ) ) ).
tff(thm_2Ecardinal_2Enum__FINITE,axiom,
! [V0s_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,V0s_2E0))
<=> ? [V1a_2E0: tyop_2Enum_2Enum] :
! [V2x_2E0: tyop_2Enum_2Enum] :
( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V2x_2E0,V0s_2E0))
=> p(c_2Earithmetic_2E_3C_3D_2E2(V2x_2E0,V1a_2E0)) ) ) ).
tff(thm_2Ecardinal_2Enum__FINITE__AVOID,axiom,
! [V0s_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,V0s_2E0))
=> ? [V1a_2E0: tyop_2Enum_2Enum] : ~ p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V1a_2E0,V0s_2E0)) ) ).
tff(thm_2Ecardinal_2Enum__INFINITE,axiom,
~ p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))) ).
tff(thm_2Ecardinal_2EHAS__SIZE__CARD,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1n_2E0: tyop_2Enum_2Enum] :
( p(c_2Ecardinal_2EHAS__SIZE_2E2(A_27a,V0s_2E0,V1n_2E0))
=> ( c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0) = V1n_2E0 ) ) ).
tff(thm_2Ecardinal_2EHAS__SIZE__0,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2EHAS__SIZE_2E2(A_27a,V0s_2E0,c_2Enum_2E0_2E0))
<=> ( V0s_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) ).
tff(thm_2Ecardinal_2EHAS__SIZE__SUC,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1n_2E0: tyop_2Enum_2Enum] :
( p(c_2Ecardinal_2EHAS__SIZE_2E2(A_27a,V0s_2E0,c_2Enum_2ESUC_2E1(V1n_2E0)))
<=> ( ( V0s_2E0 != c_2Epred__set_2EEMPTY_2E0(A_27a) )
& ! [V2a_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2a_2E0,V0s_2E0))
=> p(c_2Ecardinal_2EHAS__SIZE_2E2(A_27a,c_2Epred__set_2EDELETE_2E2(A_27a,V0s_2E0,V2a_2E0),V1n_2E0)) ) ) ) ).
tff(thm_2Ecardinal_2EFINITE__HAS__SIZE,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0) = c_2Ecardinal_2EHAS__SIZE_2E2(A_27a,V0s_2E0,c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0)) ).
tff(thm_2Ecardinal_2EHAS__SIZE__CLAUSES,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Ecardinal_2EHAS__SIZE_2E2(A_27a,V1s_2E0,c_2Enum_2E0_2E0))
<=> ( V1s_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) )
& ( p(c_2Ecardinal_2EHAS__SIZE_2E2(A_27a,V1s_2E0,c_2Enum_2ESUC_2E1(V0n_2E0)))
<=> ? [V2a_2E0: A_27a,V3t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2EHAS__SIZE_2E2(A_27a,V3t_2E0,V0n_2E0))
& ~ p(c_2Ebool_2EIN_2E2(A_27a,V2a_2E0,V3t_2E0))
& ( V1s_2E0 = c_2Epred__set_2EINSERT_2E2(A_27a,V2a_2E0,V3t_2E0) ) ) ) ) ).
tff(thm_2Ecardinal_2ECARD__SUBSET__EQ,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1b_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0a_2E0,V1b_2E0))
& ( c_2Epred__set_2ECARD_2E1(A_27a,V0a_2E0) = c_2Epred__set_2ECARD_2E1(A_27a,V1b_2E0) ) )
=> ( V0a_2E0 = V1b_2E0 ) ) ).
tff(thm_2Ecardinal_2EHAS__SIZE__INDEX,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))))] :
( ! [V1n_2E0: tyop_2Enum_2Enum,V2f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V4x_2E0: A_27a,V5m_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F0_2E0,V1n_2E0),V2f_2E0),V4x_2E0),V5m_2E0))
<=> ( p(c_2Eprim__rec_2E_3C_2E2(V5m_2E0,V1n_2E0))
& ( app_2E2(tyop_2Enum_2Enum,A_27a,V2f_2E0,V5m_2E0) = V4x_2E0 ) ) )
=> ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1n_2E0: tyop_2Enum_2Enum] :
( p(c_2Ecardinal_2EHAS__SIZE_2E2(A_27a,V0s_2E0,V1n_2E0))
=> ? [V2f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] :
( ! [V3m_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V3m_2E0,V1n_2E0))
=> p(c_2Ebool_2EIN_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,A_27a,V2f_2E0,V3m_2E0),V0s_2E0)) )
& ! [V4x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V0s_2E0))
=> p(c_2Ebool_2E_3F_21_2E1(tyop_2Enum_2Enum,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F0_2E0,V1n_2E0),V2f_2E0),V4x_2E0))) ) ) ) ) ).
tff(thm_2Ecardinal_2ECARD__BIGUNION__LE,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))))] :
( ! [V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5x_2E0: A_27a] : app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0,V1t_2E0),V0s_2E0),V5x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0,V5x_2E0),c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,V0s_2E0))
=> ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2m_2E0: tyop_2Enum_2Enum,V3n_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Ecardinal_2EHAS__SIZE_2E2(A_27a,V0s_2E0,V2m_2E0))
& ! [V4x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V0s_2E0))
=> ( p(c_2Epred__set_2EFINITE_2E1(A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0,V4x_2E0)))
& p(c_2Earithmetic_2E_3C_3D_2E2(c_2Epred__set_2ECARD_2E1(A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0,V4x_2E0)),V3n_2E0)) ) ) )
=> p(c_2Earithmetic_2E_3C_3D_2E2(c_2Epred__set_2ECARD_2E1(A_27b,c_2Epred__set_2EBIGUNION_2E1(A_27b,c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0,V1t_2E0),V0s_2E0)))),c_2Earithmetic_2E_2A_2E2(V2m_2E0,V3n_2E0))) ) ) ).
tff(thm_2Ecardinal_2EHAS__SIZE__BOOL,axiom,
p(c_2Ecardinal_2EHAS__SIZE_2E2(tyop_2Emin_2Ebool,c_2Epred__set_2EUNIV_2E0(tyop_2Emin_2Ebool),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))) ).
tff(thm_2Ecardinal_2ECARD__BOOL,axiom,
c_2Epred__set_2ECARD_2E1(tyop_2Emin_2Ebool,c_2Epred__set_2EUNIV_2E0(tyop_2Emin_2Ebool)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)) ).
tff(thm_2Ecardinal_2EFINITE__BOOL,axiom,
p(c_2Epred__set_2EFINITE_2E1(tyop_2Emin_2Ebool,c_2Epred__set_2EUNIV_2E0(tyop_2Emin_2Ebool))) ).
tff(thm_2Ecardinal_2EHAS__SIZE__CART__UNIV,axiom,
! [A_27a: $tType,V0m_2E0: tyop_2Enum_2Enum] :
( p(c_2Ecardinal_2EHAS__SIZE_2E2(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a),V0m_2E0))
=> p(c_2Ecardinal_2EHAS__SIZE_2E2(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a),c_2Earithmetic_2EEXP_2E2(V0m_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ) ).
tff(thm_2Ecardinal_2ECARD__CART__UNIV,axiom,
! [A_27a: $tType] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)))
=> ( c_2Epred__set_2ECARD_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)) = c_2Earithmetic_2EEXP_2E2(c_2Epred__set_2ECARD_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ) ).
tff(thm_2Ecardinal_2EFINITE__CART__UNIV,axiom,
! [A_27a: $tType] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)))
=> p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a))) ) ).
tff(thm_2Ecardinal_2EHAS__SIZE__NUMSEG__LT,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
( ! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] : app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V0n_2E0),V1m_2E0) = c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1m_2E0,c_2Eprim__rec_2E_3C_2E2(V1m_2E0,V0n_2E0))
=> ! [V0n_2E0: tyop_2Enum_2Enum] : p(c_2Ecardinal_2EHAS__SIZE_2E2(tyop_2Enum_2Enum,c_2Epred__set_2EGSPEC_2E1(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V0n_2E0)),V0n_2E0)) ) ).
tff(thm_2Ecardinal_2EFINITE__NUMSEG__LT,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
( ! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] : app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V0n_2E0),V1m_2E0) = c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1m_2E0,c_2Eprim__rec_2E_3C_2E2(V1m_2E0,V0n_2E0))
=> ! [V0n_2E0: tyop_2Enum_2Enum] : p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,c_2Epred__set_2EGSPEC_2E1(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V0n_2E0)))) ) ).
tff(thm_2Ecardinal_2EHAS__SIZE__NUMSEG__LE,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
( ! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] : app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V0n_2E0),V1m_2E0) = c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1m_2E0,c_2Earithmetic_2E_3C_3D_2E2(V1m_2E0,V0n_2E0))
=> ! [V0n_2E0: tyop_2Enum_2Enum] : p(c_2Ecardinal_2EHAS__SIZE_2E2(tyop_2Enum_2Enum,c_2Epred__set_2EGSPEC_2E1(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V0n_2E0)),c_2Earithmetic_2E_2B_2E2(V0n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ) ).
tff(thm_2Ecardinal_2EFINITE__NUMSEG__LE,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
( ! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] : app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V0n_2E0),V1m_2E0) = c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1m_2E0,c_2Earithmetic_2E_3C_3D_2E2(V1m_2E0,V0n_2E0))
=> ! [V0n_2E0: tyop_2Enum_2Enum] : p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,c_2Epred__set_2EGSPEC_2E1(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V0n_2E0)))) ) ).
tff(thm_2Ecardinal_2EINFINITE__DIFF__FINITE,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
& p(c_2Epred__set_2EFINITE_2E1(A_27a,V1t_2E0)) )
=> ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EDIFF_2E2(A_27a,V0s_2E0,V1t_2E0))) ) ).
tff(thm_2Ecardinal_2ELE__CASES,axiom,
! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V0m_2E0,V1n_2E0))
| p(c_2Earithmetic_2E_3C_3D_2E2(V1n_2E0,V0m_2E0)) ) ).
tff(thm_2Ecardinal_2ELT__CASES,axiom,
! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V0m_2E0,V1n_2E0))
| p(c_2Eprim__rec_2E_3C_2E2(V1n_2E0,V0m_2E0))
| ( V0m_2E0 = V1n_2E0 ) ) ).
tff(thm_2Ecardinal_2ELT,axiom,
( ! [V0m_2E0: tyop_2Enum_2Enum] : c_2Eprim__rec_2E_3C_2E2(V0m_2E0,c_2Enum_2E0_2E0) = c_2Ebool_2EF_2E0
& ! [V1m_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V1m_2E0,c_2Enum_2ESUC_2E1(V2n_2E0)))
<=> ( ( V1m_2E0 = V2n_2E0 )
| p(c_2Eprim__rec_2E_3C_2E2(V1m_2E0,V2n_2E0)) ) ) ) ).
tff(thm_2Ecardinal_2ELT__LE,axiom,
! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V0m_2E0,V1n_2E0))
<=> ( p(c_2Earithmetic_2E_3C_3D_2E2(V0m_2E0,V1n_2E0))
& ( V0m_2E0 != V1n_2E0 ) ) ) ).
tff(thm_2Ecardinal_2EGE,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_3E_3D_2E2(V1m_2E0,V0n_2E0) = c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,V1m_2E0) ).
tff(thm_2Ecardinal_2ELE__SUC__LT,axiom,
! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_3C_3D_2E2(c_2Enum_2ESUC_2E1(V0m_2E0),V1n_2E0) = c_2Eprim__rec_2E_3C_2E2(V0m_2E0,V1n_2E0) ).
tff(thm_2Ecardinal_2EEMPTY__set__exp,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0B_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V1A_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ( c_2Ecardinal_2Eset__exp_2E2(A_27a,A_27b,V1A_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) = c_2Epred__set_2EINSERT_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Ecombin_2EK_2E1(tyop_2Eoption_2Eoption(A_27b),A_27a,c_2Eoption_2ENONE_2E0(A_27b)),c_2Epred__set_2EEMPTY_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))) )
& ( ( V0B_2E0 != c_2Epred__set_2EEMPTY_2E0(A_27c) )
=> ( c_2Ecardinal_2Eset__exp_2E2(A_27c,A_27d,c_2Epred__set_2EEMPTY_2E0(A_27d),V0B_2E0) = c_2Epred__set_2EEMPTY_2E0(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d))) ) ) ) ).
tff(thm_2Ecardinal_2EEMPTY__set__exp__CARD,axiom,
! [A_27a: $tType,A_27b: $tType,V0A_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Enum_2Enum,c_2Ecardinal_2Eset__exp_2E2(A_27a,A_27b,V0A_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)),c_2Epred__set_2Ecount_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ).
tff(thm_2Ecardinal_2ESING__set__exp,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))),F3_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),F1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool))))] :
( ! [V1B_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0: A_27b,V3b_2E0: A_27a] : app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),F0_2E0,V1B_2E0),V0x_2E0),V3b_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27b),c_2Ebool_2EIN_2E2(A_27a,V3b_2E0,V1B_2E0),c_2Eoption_2ESOME_2E1(A_27b,V0x_2E0),c_2Eoption_2ENONE_2E0(A_27b))
=> ( ! [V5b_2E0: A_27b,V0x_2E0: A_27b] :
( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),F3_2E0,V5b_2E0),V0x_2E0))
<=> ( V5b_2E0 = V0x_2E0 ) )
=> ( ! [V0x_2E0: A_27b,V4a_2E0: A_27c,V5b_2E0: A_27b] : app_2E2(A_27b,tyop_2Eoption_2Eoption(A_27c),app_2E2(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),F2_2E0,V0x_2E0),V4a_2E0),V5b_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27c),app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),F3_2E0,V5b_2E0),V0x_2E0),c_2Eoption_2ESOME_2E1(A_27c,V4a_2E0),c_2Eoption_2ENONE_2E0(A_27c))
=> ( ! [V0x_2E0: A_27b,V2A_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V4a_2E0: A_27c] : app_2E2(A_27c,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool))),F1_2E0,V0x_2E0),V2A_2E0),V4a_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool,app_2E2(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),F2_2E0,V0x_2E0),V4a_2E0),c_2Ebool_2EIN_2E2(A_27c,V4a_2E0,V2A_2E0))
=> ! [V0x_2E0: A_27b,V1B_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2A_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
( ( c_2Ecardinal_2Eset__exp_2E2(A_27a,A_27b,c_2Epred__set_2EINSERT_2E2(A_27b,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27b)),V1B_2E0) = c_2Epred__set_2EINSERT_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),F0_2E0,V1B_2E0),V0x_2E0),c_2Epred__set_2EEMPTY_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))) )
& ( c_2Ecardinal_2Eset__exp_2E2(A_27b,A_27c,V2A_2E0,c_2Epred__set_2EINSERT_2E2(A_27b,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27b))) = c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),A_27c,app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool))),F1_2E0,V0x_2E0),V2A_2E0)) ) ) ) ) ) ) ).
tff(thm_2Ecardinal_2ESING__set__exp__CARD,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0x_2E0: A_27b,V1B_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2A_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Enum_2Enum,c_2Ecardinal_2Eset__exp_2E2(A_27a,A_27b,c_2Epred__set_2EINSERT_2E2(A_27b,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27b)),V1B_2E0),c_2Epred__set_2Ecount_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))
& p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),A_27c,c_2Ecardinal_2Eset__exp_2E2(A_27b,A_27c,V2A_2E0,c_2Epred__set_2EINSERT_2E2(A_27b,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27b))),V2A_2E0)) ) ).
tff(thm_2Ecardinal_2EPOW__TWO__set__exp,axiom,
! [A_27a: $tType,V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Epred__set_2EPOW_2E1(A_27a,V0A_2E0),c_2Ecardinal_2Eset__exp_2E2(A_27a,tyop_2Enum_2Enum,c_2Epred__set_2Ecount_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),V0A_2E0))) ).
tff(thm_2Ecardinal_2Eset__exp__count,axiom,
! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))))] :
( ! [V2l_2E0: tyop_2Elist_2Elist(A_27a),V0n_2E0: tyop_2Enum_2Enum,V1A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0,V2l_2E0),V0n_2E0),V1A_2E0))
<=> ( ( c_2Elist_2ELENGTH_2E1(A_27a,V2l_2E0) = V0n_2E0 )
& ! [V3e_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3e_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2l_2E0)))
=> p(c_2Ebool_2EIN_2E2(A_27a,V3e_2E0,V1A_2E0)) ) ) )
=> ( ! [V0n_2E0: tyop_2Enum_2Enum,V1A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2l_2E0: tyop_2Elist_2Elist(A_27a)] : app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),F0_2E0,V0n_2E0),V1A_2E0),V2l_2E0) = c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V2l_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0,V2l_2E0),V0n_2E0),V1A_2E0))
=> ! [V0n_2E0: tyop_2Enum_2Enum,V1A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Elist_2Elist(A_27a),c_2Ecardinal_2Eset__exp_2E2(tyop_2Enum_2Enum,A_27a,V1A_2E0,c_2Epred__set_2Ecount_2E1(V0n_2E0)),c_2Epred__set_2EGSPEC_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),F0_2E0,V0n_2E0),V1A_2E0)))) ) ) ).
tff(thm_2Ecardinal_2Eset__exp__card__cong,axiom,
! [A_27a1: $tType,A_27a2: $tType,A_27b1: $tType,A_27b2: $tType,V0b2_2E0: tyop_2Emin_2Efun(A_27b2,tyop_2Emin_2Ebool),V1b1_2E0: tyop_2Emin_2Efun(A_27b1,tyop_2Emin_2Ebool),V2a2_2E0: tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Ebool),V3a1_2E0: tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardeq_2E2(A_27a1,A_27a2,V3a1_2E0,V2a2_2E0))
=> ( p(c_2Ecardinal_2Ecardeq_2E2(A_27b1,A_27b2,V1b1_2E0,V0b2_2E0))
=> p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27b1,tyop_2Eoption_2Eoption(A_27a1)),tyop_2Emin_2Efun(A_27b2,tyop_2Eoption_2Eoption(A_27a2)),c_2Ecardinal_2Eset__exp_2E2(A_27b1,A_27a1,V3a1_2E0,V1b1_2E0),c_2Ecardinal_2Eset__exp_2E2(A_27b2,A_27a2,V2a2_2E0,V0b2_2E0))) ) ) ).
tff(thm_2Ecardinal_2Eset__exp__cardle__cong,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0d_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1c_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V2b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
( ( ( V2b_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) )
=> ( V0d_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27b) ) )
=> ( ( p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27a,V3a_2E0,V2b_2E0))
& p(c_2Ecardinal_2Ecardleq_2E2(A_27d,A_27b,V1c_2E0,V0d_2E0)) )
=> p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),c_2Ecardinal_2Eset__exp_2E2(A_27d,A_27c,V3a_2E0,V1c_2E0),c_2Ecardinal_2Eset__exp_2E2(A_27b,A_27a,V2b_2E0,V0d_2E0))) ) ) ).
tff(thm_2Ecardinal_2Eexp__INSERT__cardeq,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1e_2E0: A_27a,V2A_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ~ p(c_2Ebool_2EIN_2E2(A_27a,V1e_2E0,V0s_2E0))
=> p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Ecardinal_2Eset__exp_2E2(A_27a,A_27b,V2A_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V1e_2E0,V0s_2E0)),c_2Epred__set_2ECROSS_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2A_2E0,c_2Ecardinal_2Eset__exp_2E2(A_27a,A_27b,V2A_2E0,V0s_2E0)))) ) ).
tff(thm_2Ecardinal_2Eexp__count__cardeq,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V1A_2E0))
& p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V0n_2E0)) )
=> p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),A_27a,c_2Ecardinal_2Eset__exp_2E2(tyop_2Enum_2Enum,A_27a,V1A_2E0,c_2Epred__set_2Ecount_2E1(V0n_2E0)),V1A_2E0)) ) ).
tff(thm_2Ecardinal_2EINFINITE__Unum,axiom,
! [A_27a: $tType,V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0A_2E0))
<=> p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Enum_2Enum,A_27a,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),V0A_2E0)) ) ).
tff(thm_2Ecardinal_2Ecardleq__SURJ,axiom,
! [A_27a: $tType,A_27b: $tType,V0B_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V1A_2E0,V0B_2E0))
<=> ( ? [V2f_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : p(c_2Epred__set_2ESURJ_2E3(A_27b,A_27a,V2f_2E0,V0B_2E0,V1A_2E0))
| ( V1A_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) ) ).
tff(thm_2Ecardinal_2EINFINITE__cardleq__INSERT,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27b,V1s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V2A_2E0))
=> ( c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,c_2Epred__set_2EINSERT_2E2(A_27b,V0x_2E0,V1s_2E0),V2A_2E0) = c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1s_2E0,V2A_2E0) ) ) ).
tff(thm_2Ecardinal_2Elist__EMPTY,axiom,
! [A_27a: $tType] : c_2Ecardinal_2Elist_2E1(A_27a,c_2Epred__set_2EEMPTY_2E0(A_27a)) = c_2Epred__set_2EINSERT_2E2(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0(A_27a),c_2Epred__set_2EEMPTY_2E0(tyop_2Elist_2Elist(A_27a))) ).
tff(thm_2Ecardinal_2Elist__SING,axiom,
! [A_27a: $tType,V0e_2E0: A_27a] : p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum,c_2Ecardinal_2Elist_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V0e_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a))),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))) ).
tff(thm_2Ecardinal_2EUNIV__list,axiom,
! [A_27a: $tType] : c_2Epred__set_2EUNIV_2E0(tyop_2Elist_2Elist(A_27a)) = c_2Ecardinal_2Elist_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)) ).
tff(thm_2Ecardinal_2Elist__BIGUNION__EXP,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)))] :
( ! [V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1n_2E0: tyop_2Enum_2Enum] : app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)),F0_2E0,V0A_2E0),V1n_2E0) = c_2Ecardinal_2Eset__exp_2E2(tyop_2Enum_2Enum,A_27a,V0A_2E0,c_2Epred__set_2Ecount_2E1(V1n_2E0))
=> ! [V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),c_2Ecardinal_2Elist_2E1(A_27a,V0A_2E0),c_2Epred__set_2EBIGUNION_2E1(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)),F0_2E0,V0A_2E0),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))))) ) ).
tff(thm_2Ecardinal_2EINFINITE__A__list__BIJ__A,axiom,
! [A_27a: $tType,V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0A_2E0))
=> p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Elist_2Elist(A_27a),A_27a,c_2Ecardinal_2Elist_2E1(A_27a,V0A_2E0),V0A_2E0)) ) ).
tff(thm_2Ecardinal_2Efinite__subsets__bijection,axiom,
! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))] :
( ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F1_2E0,V1s_2E0),V0A_2E0))
<=> ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,V0A_2E0)) ) )
=> ( ! [V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0,V0A_2E0),V1s_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V1s_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F1_2E0,V1s_2E0),V0A_2E0))
=> ! [V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0A_2E0))
=> p(c_2Ecardinal_2Ecardeq_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0A_2E0,c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0,V0A_2E0)))) ) ) ) ).
tff(thm_2Ecardinal_2EFINITE__IMAGE__INJ_27,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,V0s_2E0)) )
=> ( ( app_2E2(A_27a,A_27b,V1f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1f_2E0,V3y_2E0) )
<=> ( V2x_2E0 = V3y_2E0 ) ) )
=> ( c_2Epred__set_2EFINITE_2E1(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V1f_2E0,V0s_2E0)) = c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0) ) ) ).
tff(thm_2Ecardinal_2Ecountable__decomposition,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
=> ? [V1A_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ( c_2Epred__set_2EBIGUNION_2E1(A_27a,V1A_2E0) = V0s_2E0 )
& ! [V2a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2a_2E0,V1A_2E0))
=> ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V2a_2E0))
& p(c_2Epred__set_2Ecountable_2E1(A_27a,V2a_2E0)) ) ) ) ) ).
tff(thm_2Ecardinal_2Edisjoint__countable__decomposition,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
=> ? [V1A_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ( c_2Epred__set_2EBIGUNION_2E1(A_27a,V1A_2E0) = V0s_2E0 )
& ! [V2a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2a_2E0,V1A_2E0))
=> ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V2a_2E0))
& p(c_2Epred__set_2Ecountable_2E1(A_27a,V2a_2E0)) ) )
& ! [V3a1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4a2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a1_2E0,V1A_2E0))
& p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4a2_2E0,V1A_2E0))
& ( V3a1_2E0 != V4a2_2E0 ) )
=> p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V3a1_2E0,V4a2_2E0)) ) ) ) ).
tff(thm_2Ecardinal_2Ecount__cardle,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Enum_2Enum,A_27a,c_2Epred__set_2Ecount_2E1(V0n_2E0),V1A_2E0))
<=> ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1A_2E0))
=> p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Epred__set_2ECARD_2E1(A_27a,V1A_2E0))) ) ) ).
tff(thm_2Ecardinal_2ECANTOR,axiom,
! [A_27a: $tType,V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ~ p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a,c_2Epred__set_2EPOW_2E1(A_27a,V0A_2E0),V0A_2E0)) ).
tff(thm_2Ecardinal_2Ecardlt__cardle,axiom,
! [A_27a: $tType,A_27b: $tType,V0B_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V0B_2E0,V1A_2E0))
=> p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V1A_2E0,V0B_2E0)) ) ).
tff(thm_2Ecardinal_2Eset__exp__product,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0B2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1B1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2A_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27c)),c_2Ecardinal_2Eset__exp_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),c_2Ecardinal_2Eset__exp_2E2(A_27b,A_27c,V2A_2E0,V1B1_2E0),V0B2_2E0),c_2Ecardinal_2Eset__exp_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),A_27c,V2A_2E0,c_2Epred__set_2ECROSS_2E2(A_27b,A_27a,V1B1_2E0,V0B2_2E0)))) ).
tff(thm_2Ecardinal_2ECOUNT__EQ__EMPTY,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] :
( ( c_2Epred__set_2Ecount_2E1(V0n_2E0) = c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum) )
<=> ( V0n_2E0 = c_2Enum_2E0_2E0 ) ) ).
tff(thm_2Ecardinal_2EPOW__EQ__X__EXP__X,axiom,
! [A_27a: $tType,V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0A_2E0))
=> p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Epred__set_2EPOW_2E1(A_27a,V0A_2E0),c_2Ecardinal_2Eset__exp_2E2(A_27a,A_27a,V0A_2E0,V0A_2E0))) ) ).
tff(thm_2Ecardinal_2Ecardeq__bijns__cong,axiom,
! [A_27a: $tType,A_27b: $tType,V0B_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V1A_2E0,V0B_2E0))
=> p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),c_2Ecardinal_2Ebijns_2E1(A_27a,V1A_2E0),c_2Ecardinal_2Ebijns_2E1(A_27b,V0B_2E0))) ) ).
tff(thm_2Ecardinal_2Ebijections__cardeq,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
=> p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecardinal_2Ebijns_2E1(A_27a,V0s_2E0),c_2Epred__set_2EPOW_2E1(A_27a,V0s_2E0))) ) ).
tff(thm_2Ecardinal_2ELEFT__IMP__EXISTS__THM,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Ebool] :
( ( ? [V2x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0))
=> p(V1Q_2E0) )
<=> ! [V3x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0))
=> p(V1Q_2E0) ) ) ).
tff(thm_2Ecardinal_2ELEFT__IMP__FORALL__THM,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Ebool] :
( ( ! [V2x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0))
=> p(V1Q_2E0) )
<=> ? [V3x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0))
=> p(V1Q_2E0) ) ) ).
tff(thm_2Ecardinal_2ERIGHT__IMP__EXISTS__THM,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Ebool,V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(V0P_2E0)
=> ? [V2x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V2x_2E0)) )
<=> ? [V3x_2E0: A_27a] :
( p(V0P_2E0)
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V3x_2E0)) ) ) ).
tff(thm_2Ecardinal_2ERIGHT__IMP__FORALL__THM,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Ebool,V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(V0P_2E0)
=> ! [V2x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V2x_2E0)) )
<=> ! [V3x_2E0: A_27a] :
( p(V0P_2E0)
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V3x_2E0)) ) ) ).
tff(thm_2Ecardinal_2EFINITE__FINITE__BIGUNIONS,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))
=> ( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EBIGUNION_2E1(A_27a,V0s_2E0)))
<=> ! [V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0,V0s_2E0))
=> p(c_2Epred__set_2EFINITE_2E1(A_27a,V1t_2E0)) ) ) ) ).
tff(thm_2Ecardinal_2ECONJ__EQ__IMP,axiom,
! [V0r_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool,V2q_2E0: tyop_2Emin_2Ebool] :
( ( ( p(V1p_2E0)
& p(V2q_2E0) )
=> p(V0r_2E0) )
<=> ( p(V1p_2E0)
=> ( p(V2q_2E0)
=> p(V0r_2E0) ) ) ) ).
tff(thm_2Ecardinal_2EIMP__CONJ__ALT,axiom,
! [V0r_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool,V2q_2E0: tyop_2Emin_2Ebool] :
( ( ( p(V1p_2E0)
& p(V2q_2E0) )
=> p(V0r_2E0) )
<=> ( p(V2q_2E0)
=> ( p(V1p_2E0)
=> p(V0r_2E0) ) ) ) ).
tff(thm_2Ecardinal_2ELT__SUC__LE,axiom,
! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : c_2Eprim__rec_2E_3C_2E2(V0m_2E0,c_2Enum_2ESUC_2E1(V1n_2E0)) = c_2Earithmetic_2E_3C_3D_2E2(V0m_2E0,V1n_2E0) ).
tff(thm_2Ecardinal_2EINJECTIVE__ON__LEFT__INVERSE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,V1s_2E0))
& ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V3y_2E0) ) )
=> ( V2x_2E0 = V3y_2E0 ) )
<=> ? [V4g_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
! [V5x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,V1s_2E0))
=> ( app_2E2(A_27b,A_27a,V4g_2E0,app_2E2(A_27a,A_27b,V0f_2E0,V5x_2E0)) = V5x_2E0 ) ) ) ).
tff(thm_2Ecardinal_2EINJECTIVE__LEFT__INVERSE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V1x_2E0: A_27a,V2y_2E0: A_27a] :
( ( app_2E2(A_27a,A_27b,V0f_2E0,V1x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V2y_2E0) )
=> ( V1x_2E0 = V2y_2E0 ) )
<=> ? [V3g_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
! [V4x_2E0: A_27a] : app_2E2(A_27b,A_27a,V3g_2E0,app_2E2(A_27a,A_27b,V0f_2E0,V4x_2E0)) = V4x_2E0 ) ).
tff(thm_2Ecardinal_2EINTER__ACI,axiom,
! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( c_2Epred__set_2EINTER_2E2(A_27a,V1p_2E0,V2q_2E0) = c_2Epred__set_2EINTER_2E2(A_27a,V2q_2E0,V1p_2E0) )
& ( c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EINTER_2E2(A_27a,V1p_2E0,V2q_2E0),V0r_2E0) = c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EINTER_2E2(A_27a,V1p_2E0,V2q_2E0),V0r_2E0) )
& ( c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EINTER_2E2(A_27a,V1p_2E0,V2q_2E0),V0r_2E0) = c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EINTER_2E2(A_27a,V2q_2E0,V1p_2E0),V0r_2E0) )
& ( c_2Epred__set_2EINTER_2E2(A_27a,V1p_2E0,V1p_2E0) = V1p_2E0 )
& ( c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EINTER_2E2(A_27a,V1p_2E0,V1p_2E0),V2q_2E0) = c_2Epred__set_2EINTER_2E2(A_27a,V1p_2E0,V2q_2E0) ) ) ).
tff(thm_2Ecardinal_2ECONJ__ACI,axiom,
! [V0r_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool,V2q_2E0: tyop_2Emin_2Ebool] :
( ( ( p(V1p_2E0)
& p(V2q_2E0) )
<=> ( p(V2q_2E0)
& p(V1p_2E0) ) )
& ( ( p(V1p_2E0)
& p(V2q_2E0)
& p(V0r_2E0) )
<=> ( p(V1p_2E0)
& p(V2q_2E0)
& p(V0r_2E0) ) )
& ( ( p(V1p_2E0)
& p(V2q_2E0)
& p(V0r_2E0) )
<=> ( p(V2q_2E0)
& p(V1p_2E0)
& p(V0r_2E0) ) )
& ( ( p(V1p_2E0)
& p(V1p_2E0) )
<=> p(V1p_2E0) )
& ( ( p(V1p_2E0)
& p(V1p_2E0)
& p(V2q_2E0) )
<=> ( p(V1p_2E0)
& p(V2q_2E0) ) ) ) ).
tff(thm_2Ecardinal_2EUNION__ACI,axiom,
! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( c_2Epred__set_2EUNION_2E2(A_27a,V1p_2E0,V2q_2E0) = c_2Epred__set_2EUNION_2E2(A_27a,V2q_2E0,V1p_2E0) )
& ( c_2Epred__set_2EUNION_2E2(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V1p_2E0,V2q_2E0),V0r_2E0) = c_2Epred__set_2EUNION_2E2(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V1p_2E0,V2q_2E0),V0r_2E0) )
& ( c_2Epred__set_2EUNION_2E2(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V1p_2E0,V2q_2E0),V0r_2E0) = c_2Epred__set_2EUNION_2E2(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V2q_2E0,V1p_2E0),V0r_2E0) )
& ( c_2Epred__set_2EUNION_2E2(A_27a,V1p_2E0,V1p_2E0) = V1p_2E0 )
& ( c_2Epred__set_2EUNION_2E2(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V1p_2E0,V1p_2E0),V2q_2E0) = c_2Epred__set_2EUNION_2E2(A_27a,V1p_2E0,V2q_2E0) ) ) ).
tff(thm_2Ecardinal_2ELT__NZ,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V0n_2E0))
<=> ( V0n_2E0 != c_2Enum_2E0_2E0 ) ) ).
tff(thm_2Ecardinal_2ELE__1,axiom,
( ! [V0n_2E0: tyop_2Enum_2Enum] :
( ( V0n_2E0 != c_2Enum_2E0_2E0 )
=> p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V0n_2E0)) )
& ! [V1n_2E0: tyop_2Enum_2Enum] :
( ( V1n_2E0 != c_2Enum_2E0_2E0 )
=> p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V1n_2E0)) )
& ! [V2n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V2n_2E0))
=> ( V2n_2E0 != c_2Enum_2E0_2E0 ) )
& ! [V3n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V3n_2E0))
=> p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V3n_2E0)) )
& ! [V4n_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V4n_2E0))
=> p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V4n_2E0)) )
& ! [V5n_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V5n_2E0))
=> ( V5n_2E0 != c_2Enum_2E0_2E0 ) ) ) ).
tff(thm_2Ecardinal_2EOR__EXISTS__THM,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( ? [V2x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0))
| ? [V3x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V3x_2E0)) )
<=> ? [V4x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V4x_2E0))
| p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V4x_2E0)) ) ) ).
tff(thm_2Ecardinal_2EBIJECTIVE__INJECTIVE__SURJECTIVE,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))))] :
( ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V4y_2E0: A_27b,V5x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V1s_2E0),V0f_2E0),V4y_2E0),V5x_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,V1s_2E0))
& ( app_2E2(A_27a,A_27b,V0f_2E0,V5x_2E0) = V4y_2E0 ) ) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ( ! [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V1s_2E0))
=> p(c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V3x_2E0),V2t_2E0)) )
& ! [V4y_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V4y_2E0,V2t_2E0))
=> p(c_2Ebool_2E_3F_21_2E1(A_27a,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V1s_2E0),V0f_2E0),V4y_2E0))) ) )
<=> ( ! [V6x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V6x_2E0,V1s_2E0))
=> p(c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V6x_2E0),V2t_2E0)) )
& ! [V7x_2E0: A_27a,V8y_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V7x_2E0,V1s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V8y_2E0,V1s_2E0))
& ( app_2E2(A_27a,A_27b,V0f_2E0,V7x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V8y_2E0) ) )
=> ( V7x_2E0 = V8y_2E0 ) )
& ! [V9y_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V9y_2E0,V2t_2E0))
=> ? [V10x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V10x_2E0,V1s_2E0))
& ( app_2E2(A_27a,A_27b,V0f_2E0,V10x_2E0) = V9y_2E0 ) ) ) ) ) ) ).
tff(thm_2Ecardinal_2EBIJECTIVE__INVERSES,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))))] :
( ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V4y_2E0: A_27b,V5x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V1s_2E0),V0f_2E0),V4y_2E0),V5x_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,V1s_2E0))
& ( app_2E2(A_27a,A_27b,V0f_2E0,V5x_2E0) = V4y_2E0 ) ) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ( ! [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V1s_2E0))
=> p(c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V3x_2E0),V2t_2E0)) )
& ! [V4y_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V4y_2E0,V2t_2E0))
=> p(c_2Ebool_2E_3F_21_2E1(A_27a,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V1s_2E0),V0f_2E0),V4y_2E0))) ) )
<=> ( ! [V6x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V6x_2E0,V1s_2E0))
=> p(c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V6x_2E0),V2t_2E0)) )
& ? [V7g_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( ! [V8y_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V8y_2E0,V2t_2E0))
=> p(c_2Ebool_2EIN_2E2(A_27a,app_2E2(A_27b,A_27a,V7g_2E0,V8y_2E0),V1s_2E0)) )
& ! [V9y_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V9y_2E0,V2t_2E0))
=> ( app_2E2(A_27a,A_27b,V0f_2E0,app_2E2(A_27b,A_27a,V7g_2E0,V9y_2E0)) = V9y_2E0 ) )
& ! [V10x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V10x_2E0,V1s_2E0))
=> ( app_2E2(A_27b,A_27a,V7g_2E0,app_2E2(A_27a,A_27b,V0f_2E0,V10x_2E0)) = V10x_2E0 ) ) ) ) ) ) ).
tff(thm_2Ecardinal_2Ele__c,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
<=> ? [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V0s_2E0))
=> p(c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V2f_2E0,V3x_2E0),V1t_2E0)) )
& ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V0s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V5y_2E0,V0s_2E0))
& ( app_2E2(A_27a,A_27b,V2f_2E0,V4x_2E0) = app_2E2(A_27a,A_27b,V2f_2E0,V5y_2E0) ) )
=> ( V4x_2E0 = V5y_2E0 ) ) ) ) ).
tff(thm_2Ecardinal_2Elt__c,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0))
<=> ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
& ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0)) ) ) ).
tff(thm_2Ecardinal_2Eeq__c,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))))] :
( ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V4y_2E0: A_27b,V5x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0s_2E0),V2f_2E0),V4y_2E0),V5x_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,V0s_2E0))
& ( app_2E2(A_27a,A_27b,V2f_2E0,V5x_2E0) = V4y_2E0 ) ) )
=> ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
<=> ? [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V0s_2E0))
=> p(c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V2f_2E0,V3x_2E0),V1t_2E0)) )
& ! [V4y_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V4y_2E0,V1t_2E0))
=> p(c_2Ebool_2E_3F_21_2E1(A_27a,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0s_2E0),V2f_2E0),V4y_2E0))) ) ) ) ) ).
tff(thm_2Ecardinal_2Ege__c,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardgeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0) = c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0) ).
tff(thm_2Ecardinal_2Egt__c,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardgt_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
<=> ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) ) ).
tff(thm_2Ecardinal_2ELE__C,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
<=> ? [V2g_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
! [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V0s_2E0))
=> ? [V4y_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V4y_2E0,V1t_2E0))
& ( app_2E2(A_27b,A_27a,V2g_2E0,V4y_2E0) = V3x_2E0 ) ) ) ) ).
tff(thm_2Ecardinal_2EGE__C,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardgeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
<=> ? [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
! [V3y_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V3y_2E0,V1t_2E0))
=> ? [V4x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V0s_2E0))
& ( V3y_2E0 = app_2E2(A_27a,A_27b,V2f_2E0,V4x_2E0) ) ) ) ) ).
tff(thm_2Ecardinal_2ECOUNTABLE,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Epred__set_2Ecountable_2E1(A_27a,V0t_2E0) = c_2Ecardinal_2Ecardgeq_2E2(tyop_2Enum_2Enum,A_27a,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),V0t_2E0) ).
tff(thm_2Ecardinal_2EEQ__C,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))))] :
( ! [V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2R_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V5x_2E0: A_27a,V6y_2E0: A_27b] :
( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F0_2E0,V1t_2E0),V2R_2E0),V5x_2E0),V6y_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27b,V6y_2E0,V1t_2E0))
& p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V2R_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V5x_2E0,V6y_2E0))) ) )
=> ( ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V7y_2E0: A_27b,V8x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0,V0s_2E0),V2R_2E0),V7y_2E0),V8x_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V8x_2E0,V0s_2E0))
& p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V2R_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V8x_2E0,V7y_2E0))) ) )
=> ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
<=> ? [V2R_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] :
( ! [V3x_2E0: A_27a,V4y_2E0: A_27b] :
( p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V2R_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V3x_2E0,V4y_2E0)))
=> ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V0s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27b,V4y_2E0,V1t_2E0)) ) )
& ! [V5x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,V0s_2E0))
=> p(c_2Ebool_2E_3F_21_2E1(A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F0_2E0,V1t_2E0),V2R_2E0),V5x_2E0))) )
& ! [V7y_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V7y_2E0,V1t_2E0))
=> p(c_2Ebool_2E_3F_21_2E1(A_27a,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0,V0s_2E0),V2R_2E0),V7y_2E0))) ) ) ) ) ) ).
tff(thm_2Ecardinal_2ECARD__LE__REFL,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27a,V0s_2E0,V0s_2E0)) ).
tff(thm_2Ecardinal_2ECARD__LE__TRANS,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
( ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
& p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27c,V1t_2E0,V2u_2E0)) )
=> p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27c,V0s_2E0,V2u_2E0)) ) ).
tff(thm_2Ecardinal_2ECARD__LT__REFL,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
~ ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27a,V0s_2E0,V0s_2E0)) ).
tff(thm_2Ecardinal_2ECARD__LET__TRANS,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
( ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
& ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27b,V2u_2E0,V1t_2E0)) )
=> ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27a,V2u_2E0,V0s_2E0)) ) ).
tff(thm_2Ecardinal_2ECARD__LTE__TRANS,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
( ( ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0))
& p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27c,V1t_2E0,V2u_2E0)) )
=> ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27a,V2u_2E0,V0s_2E0)) ) ).
tff(thm_2Ecardinal_2ECARD__LT__TRANS,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
( ( ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0))
& ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27b,V2u_2E0,V1t_2E0)) )
=> ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27a,V2u_2E0,V0s_2E0)) ) ).
tff(thm_2Ecardinal_2ECARD__EQ__REFL,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27a,V0s_2E0,V0s_2E0)) ).
tff(thm_2Ecardinal_2ECARD__EQ__SYM,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0) = c_2Ecardinal_2Ecardeq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0) ).
tff(thm_2Ecardinal_2ECARD__EQ__IMP__LE,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
=> p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) ) ).
tff(thm_2Ecardinal_2ECARD__LT__IMP__LE,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0))
=> p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) ) ).
tff(thm_2Ecardinal_2ECARD__LE__RELATIONAL,axiom,
! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))))] :
( ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V5y_2E0: A_27b] :
( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F1_2E0,V1s_2E0),V0R_2E0),V5y_2E0))
<=> ? [V6x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V6x_2E0,V1s_2E0))
& p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0R_2E0,V6x_2E0),V5y_2E0)) ) )
=> ( ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V5y_2E0: A_27b] : app_2E2(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))),F0_2E0,V1s_2E0),V0R_2E0),V5y_2E0) = c_2Epair_2E_2C_2E2(A_27b,tyop_2Emin_2Ebool,V5y_2E0,app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F1_2E0,V1s_2E0),V0R_2E0),V5y_2E0))
=> ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V2x_2E0: A_27a,V3y_2E0: A_27b,V4y_27_2E0: A_27b] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
& p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0R_2E0,V2x_2E0),V3y_2E0))
& p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0R_2E0,V2x_2E0),V4y_27_2E0)) )
=> ( V3y_2E0 = V4y_27_2E0 ) )
=> p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,c_2Epred__set_2EGSPEC_2E1(A_27b,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))),F0_2E0,V1s_2E0),V0R_2E0)),V1s_2E0)) ) ) ) ).
tff(thm_2Ecardinal_2ECARD__LE__EMPTY,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27b)))
<=> ( V0x_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) ).
tff(thm_2Ecardinal_2ECARD__EQ__EMPTY,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,c_2Epred__set_2EEMPTY_2E0(A_27b)))
<=> ( V0s_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) ).
tff(thm_2Ecardinal_2ECARD__LE__ANTISYM,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
& p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0)) )
<=> p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) ) ).
tff(thm_2Ecardinal_2ECARD__LE__TOTAL,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
| p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0)) ) ).
tff(thm_2Ecardinal_2ECARD__LET__TOTAL,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
| ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) ) ).
tff(thm_2Ecardinal_2ECARD__LTE__TOTAL,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0))
| p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0)) ) ).
tff(thm_2Ecardinal_2ECARD__LT__TOTAL,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
| ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0))
| ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) ) ).
tff(thm_2Ecardinal_2ECARDLEQ__CARD,axiom,
! [A_27a: $tType,A_27b: $tType,V0s2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s1_2E0))
& p(c_2Epred__set_2EFINITE_2E1(A_27b,V0s2_2E0)) )
=> ( c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V1s1_2E0,V0s2_2E0) = c_2Earithmetic_2E_3C_3D_2E2(c_2Epred__set_2ECARD_2E1(A_27a,V1s1_2E0),c_2Epred__set_2ECARD_2E1(A_27b,V0s2_2E0)) ) ) ).
tff(thm_2Ecardinal_2ECARDEQ__CARD__EQN,axiom,
! [A_27a: $tType,A_27b: $tType,V0s2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s1_2E0))
& p(c_2Epred__set_2EFINITE_2E1(A_27b,V0s2_2E0)) )
=> ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V1s1_2E0,V0s2_2E0))
<=> ( c_2Epred__set_2ECARD_2E1(A_27a,V1s1_2E0) = c_2Epred__set_2ECARD_2E1(A_27b,V0s2_2E0) ) ) ) ).
tff(thm_2Ecardinal_2ECARD__CARDEQ__I,axiom,
! [A_27a: $tType,A_27b: $tType,V0s2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s1_2E0))
& p(c_2Epred__set_2EFINITE_2E1(A_27b,V0s2_2E0))
& ( c_2Epred__set_2ECARD_2E1(A_27a,V1s1_2E0) = c_2Epred__set_2ECARD_2E1(A_27b,V0s2_2E0) ) )
=> p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V1s1_2E0,V0s2_2E0)) ) ).
tff(thm_2Ecardinal_2EBIJ__functions__agree,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V0f_2E0,V2s_2E0,V3t_2E0))
& ! [V4x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V2s_2E0))
=> ( app_2E2(A_27a,A_27b,V0f_2E0,V4x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V4x_2E0) ) ) )
=> p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V1g_2E0,V2s_2E0,V3t_2E0)) ) ).
tff(thm_2Ecardinal_2ECARD__NOT__LE,conjecture,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
<=> ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) ) ).
%------------------------------------------------------------------------------