ITP001 Axioms: ITP027_7.ax
%------------------------------------------------------------------------------
% File : ITP027_7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : pred_set.ax [Gau19]
% : HL4027_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 1105 ( 432 unt; 245 typ; 0 def)
% Number of atoms : 1792 ( 787 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 1042 ( 110 ~; 34 |; 278 &)
% ( 201 <=>; 419 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 236 ( 132 >; 104 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 242 ( 242 usr; 34 con; 0-6 aty)
% Number of variables : 3481 (3156 !; 82 ?;3481 :)
% ( 243 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
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_2E1,type,
c_2Earithmetic_2E_2B_2E1: 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_2Earithmetic_2E_2D_2E0,type,
c_2Earithmetic_2E_2D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2D_2E2,type,
c_2Earithmetic_2E_2D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
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_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_2Emin_2E_40_2E0,type,
c_2Emin_2E_40_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a) ).
tff(c_2Emin_2E_40_2E1,type,
c_2Emin_2E_40_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > A_27a ) ).
tff(c_2Earithmetic_2EABS__DIFF_2E0,type,
c_2Earithmetic_2EABS__DIFF_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2EABS__DIFF_2E2,type,
c_2Earithmetic_2EABS__DIFF_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Ebool_2EARB_2E0,type,
c_2Ebool_2EARB_2E0:
!>[A_27a: $tType] : A_27a ).
tff(c_2Epred__set_2EBIGINTER_2E0,type,
c_2Epred__set_2EBIGINTER_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_2EBIGINTER_2E1,type,
c_2Epred__set_2EBIGINTER_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_2EBIGINTER_2E2,type,
c_2Epred__set_2EBIGINTER_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) * A_27a ) > 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_2EBIGUNION_2E2,type,
c_2Epred__set_2EBIGUNION_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) * 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_2Epred__set_2ECHOICE_2E0,type,
c_2Epred__set_2ECHOICE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a) ).
tff(c_2Epred__set_2ECHOICE_2E1,type,
c_2Epred__set_2ECHOICE_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > A_27a ) ).
tff(c_2Epred__set_2ECOMPL_2E0,type,
c_2Epred__set_2ECOMPL_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2ECOMPL_2E1,type,
c_2Epred__set_2ECOMPL_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Epred__set_2ECOMPL_2E2,type,
c_2Epred__set_2ECOMPL_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * A_27a ) > tyop_2Emin_2Ebool ) ).
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_2ECROSS_2E3,type,
c_2Epred__set_2ECROSS_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) * 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_2EDELETE_2E3,type,
c_2Epred__set_2EDELETE_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2EDFUNSET_2E0,type,
c_2Epred__set_2EDFUNSET_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_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EDFUNSET_2E2,type,
c_2Epred__set_2EDFUNSET_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) ) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool) ) ).
tff(c_2Epred__set_2EDFUNSET_2E3,type,
c_2Epred__set_2EDFUNSET_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,A_27b) ) > 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_2EDIFF_2E3,type,
c_2Epred__set_2EDIFF_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * 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_2Earithmetic_2EDIV_2E0,type,
c_2Earithmetic_2EDIV_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2EDIV_2E2,type,
c_2Earithmetic_2EDIV_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
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_2Epred__set_2EEMPTY_2E1,type,
c_2Epred__set_2EEMPTY_2E1:
!>[A_27a: $tType] : ( A_27a > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2EEMPTY__REL_2E0,type,
c_2Erelation_2EEMPTY__REL_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,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_2Epair_2EFST_2E0,type,
c_2Epair_2EFST_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a) ).
tff(c_2Epair_2EFST_2E1,type,
c_2Epair_2EFST_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epair_2Eprod(A_27a,A_27b) > A_27a ) ).
tff(c_2Earithmetic_2EFUNPOW_2E0,type,
c_2Earithmetic_2EFUNPOW_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))) ).
tff(c_2Earithmetic_2EFUNPOW_2E3,type,
c_2Earithmetic_2EFUNPOW_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27a) * tyop_2Enum_2Enum * A_27a ) > A_27a ) ).
tff(c_2Epred__set_2EFUNSET_2E0,type,
c_2Epred__set_2EFUNSET_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_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EFUNSET_2E2,type,
c_2Epred__set_2EFUNSET_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_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool) ) ).
tff(c_2Epred__set_2EFUNSET_2E3,type,
c_2Epred__set_2EFUNSET_2E3:
!>[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(A_27a,A_27b) ) > 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_2Epred__set_2EGSPEC_2E2,type,
c_2Epred__set_2EGSPEC_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)) * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ecombin_2EI_2E0,type,
c_2Ecombin_2EI_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
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_2E1,type,
c_2Epred__set_2EIMAGE_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( 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_2Epred__set_2EIMAGE_2E3,type,
c_2Epred__set_2EIMAGE_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * 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_2Esum_2EINL_2E0,type,
c_2Esum_2EINL_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)) ).
tff(c_2Esum_2EINL_2E1,type,
c_2Esum_2EINL_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( A_27a > tyop_2Esum_2Esum(A_27a,A_27b) ) ).
tff(c_2Esum_2EINR_2E0,type,
c_2Esum_2EINR_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)) ).
tff(c_2Esum_2EINR_2E1,type,
c_2Esum_2EINR_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( A_27b > tyop_2Esum_2Esum(A_27a,A_27b) ) ).
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_2E1,type,
c_2Epred__set_2EINSERT_2E1:
!>[A_27a: $tType] : ( 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_2EINSERT_2E3,type,
c_2Epred__set_2EINSERT_2E3:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * 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_2Epred__set_2EINTER_2E3,type,
c_2Epred__set_2EINTER_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2EITSET_2E0,type,
c_2Epred__set_2EITSET_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27b))) ).
tff(c_2Epred__set_2EITSET_2E3,type,
c_2Epred__set_2EITSET_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * A_27b ) > A_27b ) ).
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_2Ewhile_2ELEAST_2E0,type,
c_2Ewhile_2ELEAST_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum) ).
tff(c_2Ebool_2ELET_2E0,type,
c_2Ebool_2ELET_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) ).
tff(c_2Ebool_2ELET_2E2,type,
c_2Ebool_2ELET_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(c_2Epred__set_2ELINV_2E0,type,
c_2Epred__set_2ELINV_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,A_27a))) ).
tff(c_2Epred__set_2ELINV_2E2,type,
c_2Epred__set_2ELINV_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,A_27a) ) ).
tff(c_2Epred__set_2ELINV_2E3,type,
c_2Epred__set_2ELINV_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * A_27b ) > A_27a ) ).
tff(c_2Epred__set_2ELINV__OPT_2E0,type,
c_2Epred__set_2ELINV__OPT_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_2Eoption_2Eoption(A_27a)))) ).
tff(c_2Epred__set_2ELINV__OPT_2E2,type,
c_2Epred__set_2ELINV__OPT_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_2Eoption_2Eoption(A_27a)) ) ).
tff(c_2Epred__set_2ELINV__OPT_2E3,type,
c_2Epred__set_2ELINV__OPT_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * A_27b ) > tyop_2Eoption_2Eoption(A_27a) ) ).
tff(c_2Earithmetic_2EMAX_2E0,type,
c_2Earithmetic_2EMAX_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2EMAX_2E2,type,
c_2Earithmetic_2EMAX_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Epred__set_2EMAX__SET_2E0,type,
c_2Epred__set_2EMAX__SET_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum) ).
tff(c_2Epred__set_2EMAX__SET_2E1,type,
c_2Epred__set_2EMAX__SET_2E1: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2EMIN_2E0,type,
c_2Earithmetic_2EMIN_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2EMIN_2E2,type,
c_2Earithmetic_2EMIN_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Epred__set_2EMIN__SET_2E0,type,
c_2Epred__set_2EMIN__SET_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum) ).
tff(c_2Epred__set_2EMIN__SET_2E1,type,
c_2Epred__set_2EMIN__SET_2E1: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) > tyop_2Enum_2Enum ).
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_2Eprim__rec_2EPRE_2E0,type,
c_2Eprim__rec_2EPRE_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Eprim__rec_2EPRE_2E1,type,
c_2Eprim__rec_2EPRE_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Epred__set_2EPREIMAGE_2E0,type,
c_2Epred__set_2EPREIMAGE_2E0:
!>[A_27a: $tType,A_27b: $tType] : 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_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EPREIMAGE_2E1,type,
c_2Epred__set_2EPREIMAGE_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,A_27b) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(c_2Epred__set_2EPREIMAGE_2E2,type,
c_2Epred__set_2EPREIMAGE_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Epred__set_2EPREIMAGE_2E3,type,
c_2Epred__set_2EPREIMAGE_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2EPROD__IMAGE_2E0,type,
c_2Epred__set_2EPROD__IMAGE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum)) ).
tff(c_2Epred__set_2EPROD__IMAGE_2E1,type,
c_2Epred__set_2EPROD__IMAGE_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum) ) ).
tff(c_2Epred__set_2EPROD__IMAGE_2E2,type,
c_2Epred__set_2EPROD__IMAGE_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Enum_2Enum ) ).
tff(c_2Epred__set_2EPROD__SET_2E0,type,
c_2Epred__set_2EPROD__SET_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum) ).
tff(c_2Epred__set_2EPROD__SET_2E1,type,
c_2Epred__set_2EPROD__SET_2E1: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) > tyop_2Enum_2Enum ).
tff(c_2Epred__set_2EPSUBSET_2E0,type,
c_2Epred__set_2EPSUBSET_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_2EPSUBSET_2E2,type,
c_2Epred__set_2EPSUBSET_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_2EREL__RESTRICT_2E0,type,
c_2Epred__set_2EREL__RESTRICT_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)))) ).
tff(c_2Epred__set_2EREL__RESTRICT_2E2,type,
c_2Epred__set_2EREL__RESTRICT_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * 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_2EREL__RESTRICT_2E4,type,
c_2Epred__set_2EREL__RESTRICT_2E4:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2EREST_2E0,type,
c_2Epred__set_2EREST_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2EREST_2E1,type,
c_2Epred__set_2EREST_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Epred__set_2EREST_2E2,type,
c_2Epred__set_2EREST_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2ERINV_2E0,type,
c_2Epred__set_2ERINV_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,A_27a))) ).
tff(c_2Epred__set_2ERINV_2E3,type,
c_2Epred__set_2ERINV_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * A_27b ) > A_27a ) ).
tff(c_2Erelation_2ERSUBSET_2E0,type,
c_2Erelation_2ERSUBSET_2E0:
!>[A_27a: $tType,A_27b: $tType] : 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_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)) ).
tff(c_2Erelation_2ERSUBSET_2E2,type,
c_2Erelation_2ERSUBSET_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2ERTC_2E0,type,
c_2Erelation_2ERTC_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Erelation_2ERTC_2E3,type,
c_2Erelation_2ERTC_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2ESING_2E0,type,
c_2Epred__set_2ESING_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Epred__set_2ESING_2E1,type,
c_2Epred__set_2ESING_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Epair_2ESND_2E0,type,
c_2Epair_2ESND_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b) ).
tff(c_2Epair_2ESND_2E1,type,
c_2Epair_2ESND_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epair_2Eprod(A_27a,A_27b) > A_27b ) ).
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_2ESUM__IMAGE_2E0,type,
c_2Epred__set_2ESUM__IMAGE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum)) ).
tff(c_2Epred__set_2ESUM__IMAGE_2E1,type,
c_2Epred__set_2ESUM__IMAGE_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum) ) ).
tff(c_2Epred__set_2ESUM__IMAGE_2E2,type,
c_2Epred__set_2ESUM__IMAGE_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Enum_2Enum ) ).
tff(c_2Epred__set_2ESUM__SET_2E0,type,
c_2Epred__set_2ESUM__SET_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum) ).
tff(c_2Epred__set_2ESUM__SET_2E1,type,
c_2Epred__set_2ESUM__SET_2E1: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) > 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_2Erelation_2EStrongOrder_2E0,type,
c_2Erelation_2EStrongOrder_2E0:
!>[A_27g: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2EStrongOrder_2E1,type,
c_2Erelation_2EStrongOrder_2E1:
!>[A_27g: $tType] : ( tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Efun(A_27g,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(c_2Erelation_2ETC_2E0,type,
c_2Erelation_2ETC_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Erelation_2ETC_2E1,type,
c_2Erelation_2ETC_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,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_2Eoption_2ETHE_2E1,type,
c_2Eoption_2ETHE_2E1:
!>[A_27a: $tType] : ( 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_2EUNION_2E3,type,
c_2Epred__set_2EUNION_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * 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_2Epred__set_2EUNIV_2E1,type,
c_2Epred__set_2EUNIV_2E1:
!>[A_27a: $tType] : ( A_27a > tyop_2Emin_2Ebool ) ).
tff(c_2Ecombin_2EUPDATE_2E0,type,
c_2Ecombin_2EUPDATE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)))) ).
tff(c_2Ecombin_2EUPDATE_2E3,type,
c_2Ecombin_2EUPDATE_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b * tyop_2Emin_2Efun(A_27a,A_27b) ) > tyop_2Emin_2Efun(A_27a,A_27b) ) ).
tff(c_2Erelation_2EWF_2E0,type,
c_2Erelation_2EWF_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2EWF_2E1,type,
c_2Erelation_2EWF_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > 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_2Epred__set_2Echooser_2E0,type,
c_2Epred__set_2Echooser_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)) ).
tff(c_2Epred__set_2Echooser_2E2,type,
c_2Epred__set_2Echooser_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Enum_2Enum ) > A_27a ) ).
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_2Ecount_2E2,type,
c_2Epred__set_2Ecount_2E2: ( tyop_2Enum_2Enum * 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_2Epred__set_2Eenumerate_2E0,type,
c_2Epred__set_2Eenumerate_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)) ).
tff(c_2Epred__set_2Eenumerate_2E1,type,
c_2Epred__set_2Eenumerate_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a) ) ).
tff(c_2Epred__set_2Eequiv__on_2E0,type,
c_2Epred__set_2Eequiv__on_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,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_2Eequiv__on_2E2,type,
c_2Epred__set_2Eequiv__on_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2Einv_2E0,type,
c_2Erelation_2Einv_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Erelation_2Einv_2E1,type,
c_2Erelation_2Einv_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(c_2Erelation_2Eirreflexive_2E0,type,
c_2Erelation_2Eirreflexive_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2Eirreflexive_2E1,type,
c_2Erelation_2Eirreflexive_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2Eis__measure__maximal_2E0,type,
c_2Epred__set_2Eis__measure__maximal_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2Eis__measure__maximal_2E3,type,
c_2Epred__set_2Eis__measure__maximal_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Enumpair_2Enfst_2E0,type,
c_2Enumpair_2Enfst_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Enumpair_2Enfst_2E1,type,
c_2Enumpair_2Enfst_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Enumpair_2Enpair_2E0,type,
c_2Enumpair_2Enpair_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Enumpair_2Enpair_2E2,type,
c_2Enumpair_2Enpair_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Enumpair_2Ensnd_2E0,type,
c_2Enumpair_2Ensnd_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Enumpair_2Ensnd_2E1,type,
c_2Enumpair_2Ensnd_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Epred__set_2Enum__to__pair_2E0,type,
c_2Epred__set_2Enum__to__pair_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Epred__set_2Enum__to__pair_2E1,type,
c_2Epred__set_2Enum__to__pair_2E1: tyop_2Enum_2Enum > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
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_2Ecombin_2Eo_2E3,type,
c_2Ecombin_2Eo_2E3:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27c,A_27b) * tyop_2Emin_2Efun(A_27a,A_27c) * A_27a ) > A_27b ) ).
tff(c_2Epred__set_2Epair__to__num_2E0,type,
c_2Epred__set_2Epair__to__num_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum) ).
tff(c_2Epred__set_2Epair__to__num_2E1,type,
c_2Epred__set_2Epair__to__num_2E1: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) > tyop_2Enum_2Enum ).
tff(c_2Epred__set_2Epairwise_2E0,type,
c_2Epred__set_2Epairwise_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,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_2Epairwise_2E2,type,
c_2Epred__set_2Epairwise_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2Epartition_2E0,type,
c_2Epred__set_2Epartition_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,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_2Emin_2Ebool),tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2Epartition_2E2,type,
c_2Epred__set_2Epartition_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * 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_2Eschroeder__close_2E0,type,
c_2Epred__set_2Eschroeder__close_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(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))) ).
tff(c_2Epred__set_2Eschroeder__close_2E2,type,
c_2Epred__set_2Eschroeder__close_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27a) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Epred__set_2Eschroeder__close_2E3,type,
c_2Epred__set_2Eschroeder__close_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27a) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * A_27a ) > 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(arityeq1_2Ec_2Earithmetic_2E_2B_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E0,X0_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_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] : ( c_2Epair_2E_2C_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27a)),c_2Epair_2E_2C_2E0(A_27a,A_27a),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_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_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_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27a),X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Epair_2Eprod(A_27a,A_27a),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_2Earithmetic_2E_2D_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2D_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_2D_2E0,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(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_2Emin_2E_40_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a,c_2Emin_2E_40_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Emin_2E_40_2E0(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X0_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2EABS__DIFF_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EABS__DIFF_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_2EABS__DIFF_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EBIGINTER_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_2EBIGINTER_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_2EBIGINTER_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EBIGINTER_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0: A_27a] : ( c_2Epred__set_2EBIGINTER_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,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_2EBIGINTER_2E0(A_27a),X0_2E0),X1_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(arityeq2_2Ec_2Epred__set_2EBIGUNION_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0: A_27a] : ( c_2Epred__set_2EBIGUNION_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,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),X1_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(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(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_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),X2_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIJ_2E3(A_27a,A_27c,X0_2E0,X1_2E0,X2_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),app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(A_27a,A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2EBIJ_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_2EBIJ_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_2EBIJ_2E0(A_27b,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIJ_2E3(A_27b,A_27c,X0_2E0,X1_2E0,X2_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),app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(A_27b,A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIJ_2E3(A_27c,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_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(A_27c,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIJ_2E3(tyop_2Enum_2Enum,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(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(tyop_2Enum_2Enum,A_27a),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_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_2ECARD_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_2Enum_2Enum,c_2Epred__set_2ECARD_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECARD_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2ECARD_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_2ECARD_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_2Enum_2Enum,c_2Epred__set_2ECARD_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2ECHOICE_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECHOICE_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a,c_2Epred__set_2ECHOICE_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2ECOMPL_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECOMPL_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2ECOMPL_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_2ECOMPL_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2ECOMPL_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECOMPL_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E0(A_27b),X0_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: A_27b,X2_2E0: A_27b] : ( c_2Ebool_2ECOND_2E3(A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27b,A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),c_2Ebool_2ECOND_2E0(A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0,X2_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)),app_2E2(tyop_2Emin_2Ebool,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))),c_2Ebool_2ECOND_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0,X1_2E0,X2_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)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(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_2Ebool_2ECOND_2E0(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(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_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),c_2Ebool_2ECOND_2E0(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ECOND_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eoption_2Eoption(A_27a),X2_2E0: tyop_2Eoption_2Eoption(A_27a)] : ( c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),c_2Ebool_2ECOND_2E0(tyop_2Eoption_2Eoption(A_27a)),X0_2E0),X1_2E0),X2_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(arityeq3_2Ec_2Epred__set_2ECROSS_2E3_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),X2_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( c_2Epred__set_2ECROSS_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,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),X2_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2ECROSS_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_2Epred__set_2ECROSS_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),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_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool)),c_2Epred__set_2ECROSS_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2ECROSS_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_2Epred__set_2ECROSS_2E2(A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),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_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2ECROSS_2E0(A_27c,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(arityeq3_2Ec_2Epred__set_2EDELETE_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: A_27a,X2_2E0: A_27a] : ( c_2Epred__set_2EDELETE_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,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),X2_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: A_27b] : ( c_2Epred__set_2EDELETE_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EDELETE_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Enum_2Enum] : ( c_2Epred__set_2EDELETE_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(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_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epred__set_2EDELETE_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EDFUNSET_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_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EDFUNSET_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,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(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EDFUNSET_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2EDFUNSET_2E3_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_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X2_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Epred__set_2EDFUNSET_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),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,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(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EDFUNSET_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_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(arityeq3_2Ec_2Epred__set_2EDIFF_2E3_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),X2_2E0: A_27a] : ( c_2Epred__set_2EDIFF_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,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),X2_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EDIFF_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_2EDIFF_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_2EDIFF_2E0(A_27b),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_2EDIV_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EDIV_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_2EDIV_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EEMPTY_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a] : ( c_2Epred__set_2EEMPTY_2E1(A_27a,X0_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,c_2Epred__set_2EEMPTY_2E0(A_27a),X0_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_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_2Epair_2EFST_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( c_2Epair_2EFST_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq3_2Ec_2Earithmetic_2EFUNPOW_2E3_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_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Earithmetic_2EFUNPOW_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Earithmetic_2EFUNPOW_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EFUNSET_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_2EFUNSET_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,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,A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2EFUNSET_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EFUNSET_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_2EFUNSET_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(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_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EFUNSET_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2EFUNSET_2E3_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),X2_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Epred__set_2EFUNSET_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),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_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,A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EFUNSET_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_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_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(A_27b,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(A_27b,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(A_27a,A_27a),A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2EGSPEC_2E0(tyop_2Epair_2Eprod(A_27a,A_27a),A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,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),A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,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),A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EGSPEC_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X1_2E0: A_27a] : ( c_2Epred__set_2EGSPEC_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(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),A_27b,X0_2E0) = app_2E2(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_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),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_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(A_27a,tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(A_27a,tyop_2Enum_2Enum),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_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(arityeq1_2Ec_2Epred__set_2EIMAGE_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27a)] : ( c_2Epred__set_2EIMAGE_2E1(A_27a,A_27a,X0_2E0) = 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) ) ).
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(arityeq1_2Ec_2Epred__set_2EIMAGE_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Epred__set_2EIMAGE_2E1(A_27a,A_27b,X0_2E0) = 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) ) ).
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(arityeq3_2Ec_2Epred__set_2EIMAGE_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: A_27b] : ( c_2Epred__set_2EIMAGE_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27b,tyop_2Emin_2Ebool,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),X2_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_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = 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,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_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27a,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(A_27a,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27a,tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_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)] : ( c_2Epred__set_2EIMAGE_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,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(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = 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,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_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27b_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27b,tyop_2Eoption_2Eoption(A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(A_27b,tyop_2Eoption_2Eoption(A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27b,tyop_2Epair_2Eprod(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_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),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_2EIMAGE_2E0(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27b_20mono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27b,tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(A_27c,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_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_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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_2Efun(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_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_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,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_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,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_2Efun(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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(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_2Epred__set_2EIMAGE_2E0(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Enum_2Enum,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(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(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(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,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(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),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_2Etyop_2Emin_2Efun_28A_27a_2CA_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Emin_2Efun(A_27a,A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Emin_2Efun(A_27a,A_27b)),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_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(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_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_2Ebool,app_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Epair_2Eprod(A_27a,A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Esum_2Esum(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27b_2CA_27a_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Esum_2Esum(A_27b,A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Esum_2Esum(A_27b,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Esum_2Esum(A_27b,A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2EINJ_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_2EINJ_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_2EINJ_2E0(A_27a,A_27a),X0_2E0),X1_2E0),X2_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(arityeq3_2Ec_2Epred__set_2EINJ_2E3_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),X2_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINJ_2E3(A_27a,A_27c,X0_2E0,X1_2E0,X2_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),app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EINJ_2E0(A_27a,A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINJ_2E3(A_27a,tyop_2Enum_2Enum,X0_2E0,X1_2E0,X2_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),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EINJ_2E0(A_27a,tyop_2Enum_2Enum),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27b_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(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINJ_2E3(A_27a,tyop_2Eoption_2Eoption(A_27b),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EINJ_2E0(A_27a,tyop_2Eoption_2Eoption(A_27b)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27a_20mono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINJ_2E3(A_27a,tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EINJ_2E0(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27a_20mono_2Etyop_2Esum_2Esum_28A_27b_2CA_27a_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,A_27a)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINJ_2E3(A_27a,tyop_2Esum_2Esum(A_27b,A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,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_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EINJ_2E0(A_27a,tyop_2Esum_2Esum(A_27b,A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2EINJ_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_2EINJ_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_2EINJ_2E0(A_27b,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINJ_2E3(A_27b,A_27c,X0_2E0,X1_2E0,X2_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),app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EINJ_2E0(A_27b,A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINJ_2E3(tyop_2Enum_2Enum,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(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EINJ_2E0(tyop_2Enum_2Enum,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a] : ( c_2Esum_2EINL_2E1(A_27a,A_27b,X0_2E0) = app_2E2(A_27a,tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a] : ( c_2Esum_2EINR_2E1(A_27b,A_27a,X0_2E0) = app_2E2(A_27a,tyop_2Esum_2Esum(A_27b,A_27a),c_2Esum_2EINR_2E0(A_27b,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EINSERT_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a] : ( c_2Epred__set_2EINSERT_2E1(A_27a,X0_2E0) = 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) ) ).
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(arityeq3_2Ec_2Epred__set_2EINSERT_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: A_27a] : ( c_2Epred__set_2EINSERT_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,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),X2_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_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_2Epred__set_2EINSERT_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_2Efun(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(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_2EINSERT_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINSERT_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINSERT_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(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_2EINSERT_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),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(arityeq3_2Ec_2Epred__set_2EINTER_2E3_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),X2_2E0: A_27a] : ( c_2Epred__set_2EINTER_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,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),X2_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EINTER_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_2EINTER_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_2EINTER_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EINTER_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINTER_2E2(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EINTER_2E0(tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EINTER_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINTER_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epred__set_2EINTER_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2EITSET_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: A_27b] : ( c_2Epred__set_2EITSET_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27b,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27b)),c_2Epred__set_2EITSET_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2EITSET_2E3_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Enum_2Enum] : ( c_2Epred__set_2EITSET_2E3(A_27a,tyop_2Enum_2Enum,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epred__set_2EITSET_2E0(A_27a,tyop_2Enum_2Enum),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a] : ( c_2Ecombin_2EK_2E1(A_27a,A_27b,X0_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),c_2Ecombin_2EK_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Emin_2Ebool_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool] : ( c_2Ecombin_2EK_2E1(tyop_2Emin_2Ebool,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E0(tyop_2Emin_2Ebool,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2EK_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_27b,tyop_2Emin_2Ebool)] : ( c_2Ecombin_2EK_2E1(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Ecombin_2EK_2E0(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(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)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Ebool_2ELET_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),X0_2E0,X1_2E0) = 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),app_2E2(tyop_2Emin_2Efun(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)),tyop_2Emin_2Efun(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_2Ebool_2ELET_2E0(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)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Enum_2Enum] : ( c_2Ebool_2ELET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Ebool_2ELET_2E0(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2ELINV_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_2ELINV_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27a),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,A_27a)),c_2Epred__set_2ELINV_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2ELINV_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: A_27b] : ( c_2Epred__set_2ELINV_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27b,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27a),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,A_27a)),c_2Epred__set_2ELINV_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2ELINV__OPT_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: A_27b] : ( c_2Epred__set_2ELINV__OPT_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27b,tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),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_2Eoption_2Eoption(A_27a))),c_2Epred__set_2ELINV__OPT_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2ELINV__OPT_2E2_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)] : ( c_2Epred__set_2ELINV__OPT_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Epred__set_2ELINV__OPT_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2EMAX_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EMAX_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_2EMAX_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EMAX__SET_2E1,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EMAX__SET_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2EMIN_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EMIN_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_2EMIN_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EMIN__SET_2E1,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EMIN__SET_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E0,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_2Eprim__rec_2EPRE_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2EPRE_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EPREIMAGE_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27a)] : ( c_2Epred__set_2EPREIMAGE_2E1(A_27a,A_27a,X0_2E0) = 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_2EPREIMAGE_2E0(A_27a,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EPREIMAGE_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Epred__set_2EPREIMAGE_2E1(A_27a,A_27b,X0_2E0) = 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_2Emin_2Ebool)),c_2Epred__set_2EPREIMAGE_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EPREIMAGE_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_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(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_2Emin_2Ebool)),c_2Epred__set_2EPREIMAGE_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2EPREIMAGE_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_27b,tyop_2Emin_2Ebool),X2_2E0: A_27a] : ( c_2Epred__set_2EPREIMAGE_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(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_2Emin_2Ebool)),c_2Epred__set_2EPREIMAGE_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EPREIMAGE_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_27c,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EPREIMAGE_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EPREIMAGE_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EPREIMAGE_2E2(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EPREIMAGE_2E0(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EPREIMAGE_2E2_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_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EPREIMAGE_2E2(A_27b,A_27a,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_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EPREIMAGE_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EPREIMAGE_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EPREIMAGE_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EPREIMAGE_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EPROD__IMAGE_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EPROD__IMAGE_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2EPROD__IMAGE_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EPROD__IMAGE_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Epred__set_2EPROD__IMAGE_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2EPROD__IMAGE_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EPROD__SET_2E1,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EPROD__SET_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum,c_2Epred__set_2EPROD__SET_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EPSUBSET_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_2EPSUBSET_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_2EPSUBSET_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EREL__RESTRICT_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EREL__RESTRICT_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EREL__RESTRICT_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq4_2Ec_2Epred__set_2EREL__RESTRICT_2E4_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: A_27a,X3_2E0: A_27a] : ( c_2Epred__set_2EREL__RESTRICT_2E4(A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,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)),app_2E2(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Epred__set_2EREL__RESTRICT_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EREST_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EREST_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EREST_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_2EREST_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2ERINV_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: A_27b] : ( c_2Epred__set_2ERINV_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27b,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,A_27a),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,A_27a)),c_2Epred__set_2ERINV_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2ERSUBSET_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ERSUBSET_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Erelation_2ERSUBSET_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Erelation_2ERTC_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: A_27a,X2_2E0: A_27a] : ( c_2Erelation_2ERTC_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ERTC_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2ESING_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESING_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2ESING_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( c_2Epair_2ESND_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b,c_2Epair_2ESND_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epair_2ESND_2E1(A_27b,tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epair_2ESND_2E0(A_27b,tyop_2Emin_2Ebool),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(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(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_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),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUBSET_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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2ESUBSET_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUBSET_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_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2ESUBSET_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_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),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUBSET_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),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_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2ESUBSET_2E0(tyop_2Epair_2Eprod(A_27a,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(arityeq2_2Ec_2Epred__set_2ESUM__IMAGE_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2ESUM__IMAGE_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2ESUM__IMAGE_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUM__IMAGE_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2ESUM__IMAGE_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2ESUM__IMAGE_2E2_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_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUM__IMAGE_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_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2ESUM__IMAGE_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2ESUM__IMAGE_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Epred__set_2ESUM__IMAGE_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2ESUM__IMAGE_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2ESUM__SET_2E1,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUM__SET_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum,c_2Epred__set_2ESUM__SET_2E0,X0_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2ESURJ_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_2ESURJ_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_2ESURJ_2E0(A_27a,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2ESURJ_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_2ESURJ_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_2ESURJ_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2ESURJ_2E3_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),X2_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESURJ_2E3(A_27a,A_27c,X0_2E0,X1_2E0,X2_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),app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESURJ_2E0(A_27a,A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2ESURJ_2E3_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_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESURJ_2E3(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0,X2_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),app_2E2(tyop_2Emin_2Efun(A_27a,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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESURJ_2E0(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0),X2_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(arityeq3_2Ec_2Epred__set_2ESURJ_2E3_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESURJ_2E3(A_27b,A_27c,X0_2E0,X1_2E0,X2_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),app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESURJ_2E0(A_27b,A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2ESURJ_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESURJ_2E3(tyop_2Enum_2Enum,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(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESURJ_2E0(tyop_2Enum_2Enum,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EStrongOrder_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EStrongOrder_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EStrongOrder_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2ETC_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2ETC_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2ETC_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27a)] : ( c_2Eoption_2ETHE_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27a),A_27a,c_2Eoption_2ETHE_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epair_2EUNCURRY_2E0(A_27a,A_27b,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(arityeq3_2Ec_2Epred__set_2EUNION_2E3_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),X2_2E0: A_27a] : ( c_2Epred__set_2EUNION_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,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),X2_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_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),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_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_2Efun(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(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_2EUNION_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epred__set_2EUNION_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EUNION_2E2_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),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),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_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EUNION_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EUNION_2E0(tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EUNIV_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a] : ( c_2Epred__set_2EUNIV_2E1(A_27a,X0_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,c_2Epred__set_2EUNIV_2E0(A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Ecombin_2EUPDATE_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a,X1_2E0: A_27b,X2_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2EUPDATE_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWF_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E0(A_27a),X0_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(arityeq2_2Ec_2Epred__set_2Echooser_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Enum_2Enum] : ( c_2Epred__set_2Echooser_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Epred__set_2Echooser_2E0(A_27a),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(arityeq2_2Ec_2Epred__set_2Ecount_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Epred__set_2Ecount_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_2Epred__set_2Ecount_2E0,X0_2E0),X1_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_2Epred__set_2Ecountable_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_2Ecountable_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_2Ecountable_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2Ecountable_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2Ecountable_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2Ecountable_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_2Ecountable_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_2Ecountable_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2Ecountable_2E1_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2Ecountable_2E1(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E0(tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2Eenumerate_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2Eenumerate_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Epred__set_2Eenumerate_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2Eequiv__on_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2Eequiv__on_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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Eequiv__on_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Einv_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Einv_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Erelation_2Einv_2E0(A_27a,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2Eirreflexive_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2Eirreflexive_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2Eirreflexive_2E0(A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2Eis__measure__maximal_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: A_27a] : ( c_2Epred__set_2Eis__measure__maximal_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,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_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2Eis__measure__maximal_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Enumpair_2Enfst_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Enumpair_2Enfst_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Enfst_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Enumpair_2Enpair_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Enumpair_2Enpair_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_2Enumpair_2Enpair_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Enumpair_2Ensnd_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Enumpair_2Ensnd_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Ensnd_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2Enum__to__pair_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Epred__set_2Enum__to__pair_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2Enum__to__pair_2E0,X0_2E0) ) ).
tff(arityeq3_2Ec_2Ecombin_2Eo_2E3_2Emono_2EA_27b_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27b,A_27a),X2_2E0: A_27b] : ( c_2Ecombin_2Eo_2E3(A_27b,A_27b,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27b,A_27b,app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,A_27b)),c_2Ecombin_2Eo_2E0(A_27b,A_27b,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] : ( c_2Ecombin_2Eo_2E2(A_27c,A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),c_2Ecombin_2Eo_2E0(A_27c,A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27a)] : ( c_2Ecombin_2Eo_2E2(A_27a,tyop_2Enum_2Enum,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),c_2Ecombin_2Eo_2E0(A_27a,tyop_2Enum_2Enum,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : ( c_2Ecombin_2Eo_2E2(A_27b,tyop_2Enum_2Enum,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum)),c_2Ecombin_2Eo_2E0(A_27b,tyop_2Enum_2Enum,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Ecombin_2Eo_2E3_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0: A_27a] : ( c_2Ecombin_2Eo_2E3(A_27a,A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ecombin_2Eo_2E0(A_27a,A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Ecombin_2Eo_2E2(A_27a,A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),c_2Ecombin_2Eo_2E0(A_27a,A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_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,A_27b)] : ( c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Ebool,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(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_2Emin_2Ebool)),c_2Ecombin_2Eo_2E0(A_27a,tyop_2Emin_2Ebool,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),A_27a),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))] : ( c_2Ecombin_2Eo_2E2(A_27b,A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,A_27a)),c_2Ecombin_2Eo_2E0(A_27b,A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))] : ( c_2Ecombin_2Eo_2E2(A_27b,tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E0(A_27b,tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c))] : ( c_2Ecombin_2Eo_2E2(A_27a,A_27b,tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2Eo_2E0(A_27a,A_27b,tyop_2Epair_2Eprod(A_27b,A_27c)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27c),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c))] : ( c_2Ecombin_2Eo_2E2(A_27a,A_27c,tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Efun(A_27a,A_27c)),c_2Ecombin_2Eo_2E0(A_27a,A_27c,tyop_2Epair_2Eprod(A_27b,A_27c)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2Epair__to__num_2E1,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Epred__set_2Epair__to__num_2E1(X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Epred__set_2Epair__to__num_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2Epairwise_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2Epairwise_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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2Epairwise_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2Epartition_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2Epartition_2E2(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_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,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_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2Epartition_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2Eschroeder__close_2E2_2Emono_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_2Eschroeder__close_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,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2Eschroeder__close_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Epred__set_2Eschroeder__close_2E3_2Emono_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: A_27a] : ( c_2Epred__set_2Eschroeder__close_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,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_2Eschroeder__close_2E0(A_27a),X0_2E0),X1_2E0),X2_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_2Epred__set_2EGSPECIFICATION,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),V1v_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V1v_2E0,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27b,V0f_2E0)))
<=> ? [V2x_2E0: A_27b] : ( c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V1v_2E0,c_2Ebool_2ET_2E0) = app_2E2(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),V0f_2E0,V2x_2E0) ) ) ).
tff(thm_2Epred__set_2EEMPTY__DEF,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( c_2Epred__set_2EEMPTY_2E1(A_27a,V0x_2E0) = c_2Ebool_2EF_2E0 ) ).
tff(thm_2Epred__set_2EUNIV__DEF,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( c_2Epred__set_2EUNIV_2E1(A_27a,V0x_2E0) = c_2Ebool_2ET_2E0 ) ).
tff(thm_2Epred__set_2ESUBSET__DEF,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_2ESUBSET_2E2(A_27a,V0s_2E0,V1t_2E0))
<=> ! [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0))
=> p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1t_2E0)) ) ) ).
tff(thm_2Epred__set_2EPSUBSET__DEF,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_2EPSUBSET_2E2(A_27a,V0s_2E0,V1t_2E0))
<=> ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s_2E0,V1t_2E0))
& ( V0s_2E0 != V1t_2E0 ) ) ) ).
tff(thm_2Epred__set_2EUNION__DEF,axiom,
! [A_27a: $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,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_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
( ! [V2x_2E0: A_27a,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_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),app_2E2(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)),F1_2E0,V2x_2E0),V0s_2E0),V1t_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0))
| p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1t_2E0)) ) )
=> ( ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,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,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0s_2E0),V1t_2E0),V2x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V2x_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(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)),F1_2E0,V2x_2E0),V0s_2E0),V1t_2E0)) )
=> ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(A_27a,V0s_2E0,V1t_2E0) = c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,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,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0s_2E0),V1t_2E0)) ) ) ) ).
tff(thm_2Epred__set_2EINTER__DEF,axiom,
! [A_27a: $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,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_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
( ! [V2x_2E0: A_27a,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_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),app_2E2(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)),F1_2E0,V2x_2E0),V0s_2E0),V1t_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1t_2E0)) ) )
=> ( ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,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,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0s_2E0),V1t_2E0),V2x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V2x_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(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)),F1_2E0,V2x_2E0),V0s_2E0),V1t_2E0)) )
=> ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINTER_2E2(A_27a,V0s_2E0,V1t_2E0) = c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,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,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0s_2E0),V1t_2E0)) ) ) ) ).
tff(thm_2Epred__set_2EDISJOINT__DEF,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_2EDISJOINT_2E2(A_27a,V0s_2E0,V1t_2E0))
<=> ( c_2Epred__set_2EINTER_2E2(A_27a,V0s_2E0,V1t_2E0) = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) ).
tff(thm_2Epred__set_2EDIFF__DEF,axiom,
! [A_27a: $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,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_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
( ! [V2x_2E0: A_27a,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_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),app_2E2(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)),F1_2E0,V2x_2E0),V0s_2E0),V1t_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0))
& ~ p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1t_2E0)) ) )
=> ( ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,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,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0s_2E0),V1t_2E0),V2x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V2x_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(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)),F1_2E0,V2x_2E0),V0s_2E0),V1t_2E0)) )
=> ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EDIFF_2E2(A_27a,V0s_2E0,V1t_2E0) = c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,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,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0s_2E0),V1t_2E0)) ) ) ) ).
tff(thm_2Epred__set_2EINSERT__DEF,axiom,
! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
( ! [V2y_2E0: A_27a,V0x_2E0: A_27a,V1s_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(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0,V2y_2E0),V0x_2E0),V1s_2E0))
<=> ( ( V2y_2E0 = V0x_2E0 )
| p(c_2Ebool_2EIN_2E2(A_27a,V2y_2E0,V1s_2E0)) ) )
=> ( ! [V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0x_2E0),V1s_2E0),V2y_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V2y_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),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0,V2y_2E0),V0x_2E0),V1s_2E0)) )
=> ! [V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,V1s_2E0) = c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0x_2E0),V1s_2E0)) ) ) ) ).
tff(thm_2Epred__set_2EDELETE__DEF,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0: A_27a] : ( c_2Epred__set_2EDELETE_2E2(A_27a,V0s_2E0,V1x_2E0) = c_2Epred__set_2EDIFF_2E2(A_27a,V0s_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V1x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a))) ) ).
tff(thm_2Epred__set_2ECHOICE__DEF,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( V0s_2E0 != c_2Epred__set_2EEMPTY_2E0(A_27a) )
=> p(c_2Ebool_2EIN_2E2(A_27a,c_2Epred__set_2ECHOICE_2E1(A_27a,V0s_2E0),V0s_2E0)) ) ).
tff(thm_2Epred__set_2EREST__DEF,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EREST_2E1(A_27a,V0s_2E0) = c_2Epred__set_2EDELETE_2E2(A_27a,V0s_2E0,c_2Epred__set_2ECHOICE_2E1(A_27a,V0s_2E0)) ) ).
tff(thm_2Epred__set_2ESING__DEF,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESING_2E1(A_27a,V0s_2E0))
<=> ? [V1x_2E0: A_27a] : ( V0s_2E0 = c_2Epred__set_2EINSERT_2E2(A_27a,V1x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) ) ) ).
tff(thm_2Epred__set_2EIMAGE__DEF,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_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V1s_2E0),V2x_2E0) = c_2Epair_2E_2C_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0),c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0)) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_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_2EGSPEC_2E1(A_27b,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V1s_2E0)) ) ) ).
tff(thm_2Epred__set_2EINJ__DEF,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_27b,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V2t_2E0))
<=> ( ! [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)) )
& ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V1s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V5y_2E0,V1s_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_2Epred__set_2ESURJ__DEF,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_27b,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESURJ_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V2t_2E0))
<=> ( ! [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)) )
& ! [V4x_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V4x_2E0,V2t_2E0))
=> ? [V5y_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V5y_2E0,V1s_2E0))
& ( app_2E2(A_27a,A_27b,V0f_2E0,V5y_2E0) = V4x_2E0 ) ) ) ) ) ).
tff(thm_2Epred__set_2EBIJ__DEF,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_27b,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V2t_2E0))
<=> ( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V2t_2E0))
& p(c_2Epred__set_2ESURJ_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V2t_2E0)) ) ) ).
tff(thm_2Epred__set_2EFUNSET,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( p(c_2Epred__set_2EFUNSET_2E3(A_27a,A_27b,V0P_2E0,V1Q_2E0,V2x_2E0))
<=> ! [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V0P_2E0))
=> p(c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V2x_2E0,V3x_2E0),V1Q_2E0)) ) ) ).
tff(thm_2Epred__set_2EDFUNSET,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2x_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( p(c_2Epred__set_2EDFUNSET_2E3(A_27a,A_27b,V0P_2E0,V1Q_2E0,V2x_2E0))
<=> ! [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V0P_2E0))
=> p(c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V2x_2E0,V3x_2E0),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1Q_2E0,V3x_2E0))) ) ) ).
tff(thm_2Epred__set_2Eschroeder__close__def,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27a),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] :
( p(c_2Epred__set_2Eschroeder__close_2E3(A_27a,V0f_2E0,V1s_2E0,V2x_2E0))
<=> ? [V3n_2E0: tyop_2Enum_2Enum] : p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Earithmetic_2EFUNPOW_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E1(A_27a,A_27a,V0f_2E0),V3n_2E0,V1s_2E0))) ) ).
tff(thm_2Epred__set_2ELINV__OPT__def,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),V2y_2E0: A_27b,V3x_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),V2y_2E0),V3x_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V1s_2E0))
& ( app_2E2(A_27a,A_27b,V0f_2E0,V3x_2E0) = V2y_2E0 ) ) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2y_2E0: A_27b] : ( c_2Epred__set_2ELINV__OPT_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V2y_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2EIN_2E2(A_27b,V2y_2E0,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0)),c_2Eoption_2ESOME_2E1(A_27a,c_2Emin_2E_40_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),V2y_2E0))),c_2Eoption_2ENONE_2E0(A_27a)) ) ) ).
tff(thm_2Epred__set_2ELINV__LO,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),V2y_2E0: A_27b] : ( c_2Epred__set_2ELINV_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V2y_2E0) = c_2Eoption_2ETHE_2E1(A_27a,c_2Epred__set_2ELINV__OPT_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V2y_2E0)) ) ).
tff(thm_2Epred__set_2ERINV__LO,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),V2y_2E0: A_27b] : ( c_2Epred__set_2ERINV_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V2y_2E0) = c_2Eoption_2ETHE_2E1(A_27a,c_2Epred__set_2ELINV__OPT_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V2y_2E0)) ) ).
tff(thm_2Epred__set_2EFINITE__DEF,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
<=> ! [V1P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V1P_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)))
& ! [V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V1P_2E0,V2s_2E0))
=> ! [V3e_2E0: A_27a] : p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V1P_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V3e_2E0,V2s_2E0))) ) )
=> p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V1P_2E0,V0s_2E0)) ) ) ).
tff(thm_2Epred__set_2EREL__RESTRICT__DEF,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a,V3y_2E0: A_27a] :
( p(c_2Epred__set_2EREL__RESTRICT_2E4(A_27a,V0R_2E0,V1s_2E0,V2x_2E0,V3y_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,V1s_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2x_2E0),V3y_2E0)) ) ) ).
tff(thm_2Epred__set_2ECARD__DEF,axiom,
! [A_27a: $tType] :
( ( c_2Epred__set_2ECARD_2E1(A_27a,c_2Epred__set_2EEMPTY_2E0(A_27a)) = c_2Enum_2E0_2E0 )
& ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
=> ! [V1x_2E0: A_27a] : ( c_2Epred__set_2ECARD_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V1x_2E0,V0s_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V0s_2E0),c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0),c_2Enum_2ESUC_2E1(c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0))) ) ) ) ).
tff(thm_2Epred__set_2Ecount__def,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] : ( c_2Epred__set_2Ecount_2E1(V0n_2E0) = 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_2Epred__set_2EBIGUNION,axiom,
! [A_27a: $tType,F1_2E0: 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)),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F1_2E0,V0P_2E0),V1x_2E0))
<=> ? [V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0,V0P_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V2s_2E0)) ) )
=> ( ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0P_2E0),V1x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V1x_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F1_2E0,V0P_2E0),V1x_2E0)) )
=> ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIGUNION_2E1(A_27a,V0P_2E0) = c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0P_2E0)) ) ) ) ).
tff(thm_2Epred__set_2EBIGINTER,axiom,
! [A_27a: $tType,F1_2E0: 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)),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F1_2E0,V0P_2E0),V1x_2E0))
<=> ! [V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0,V0P_2E0))
=> p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V2s_2E0)) ) )
=> ( ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0P_2E0),V1x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V1x_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F1_2E0,V0P_2E0),V1x_2E0)) )
=> ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIGINTER_2E1(A_27a,V0P_2E0) = c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0P_2E0)) ) ) ) ).
tff(thm_2Epred__set_2ECROSS__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(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))),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_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))))] :
( ! [V2p_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_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,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(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)),F1_2E0,V2p_2E0),V0P_2E0),V1Q_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,c_2Epair_2EFST_2E1(A_27a,A_27b,V2p_2E0),V0P_2E0))
& p(c_2Ebool_2EIN_2E2(A_27b,c_2Epair_2ESND_2E1(A_27a,A_27b,V2p_2E0),V1Q_2E0)) ) )
=> ( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2p_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( app_2E2(tyop_2Epair_2Eprod(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(tyop_2Epair_2Eprod(A_27a,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(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),F0_2E0,V0P_2E0),V1Q_2E0),V2p_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V2p_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_2Epair_2Eprod(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)),F1_2E0,V2p_2E0),V0P_2E0),V1Q_2E0)) )
=> ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,V0P_2E0,V1Q_2E0) = c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(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)),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_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),F0_2E0,V0P_2E0),V1Q_2E0)) ) ) ) ).
tff(thm_2Epred__set_2ECOMPL__DEF,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECOMPL_2E1(A_27a,V0P_2E0) = c_2Epred__set_2EDIFF_2E2(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a),V0P_2E0) ) ).
tff(thm_2Epred__set_2ESUM__IMAGE__DEF,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2e_2E0: A_27a,V3acc_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F0_2E0,V0f_2E0),V2e_2E0),V3acc_2E0) = c_2Earithmetic_2E_2B_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V2e_2E0),V3acc_2E0) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,V0f_2E0,V1s_2E0) = c_2Epred__set_2EITSET_2E3(A_27a,tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F0_2E0,V0f_2E0),V1s_2E0,c_2Enum_2E0_2E0) ) ) ).
tff(thm_2Epred__set_2ESUM__SET__DEF,axiom,
c_2Epred__set_2ESUM__SET_2E0 = c_2Epred__set_2ESUM__IMAGE_2E1(tyop_2Enum_2Enum,c_2Ecombin_2EI_2E0(tyop_2Enum_2Enum)) ).
tff(thm_2Epred__set_2EPROD__IMAGE__DEF,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2e_2E0: A_27a,V3acc_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F0_2E0,V0f_2E0),V2e_2E0),V3acc_2E0) = c_2Earithmetic_2E_2A_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V2e_2E0),V3acc_2E0) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EPROD__IMAGE_2E2(A_27a,V0f_2E0,V1s_2E0) = c_2Epred__set_2EITSET_2E3(A_27a,tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F0_2E0,V0f_2E0),V1s_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ) ).
tff(thm_2Epred__set_2EPROD__SET__DEF,axiom,
c_2Epred__set_2EPROD__SET_2E0 = c_2Epred__set_2EPROD__IMAGE_2E1(tyop_2Enum_2Enum,c_2Ecombin_2EI_2E0(tyop_2Enum_2Enum)) ).
tff(thm_2Epred__set_2EMAX__SET__DEF,axiom,
! [V0s_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,V0s_2E0))
=> ( ( ( V0s_2E0 != c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum) )
=> ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,c_2Epred__set_2EMAX__SET_2E1(V0s_2E0),V0s_2E0))
& ! [V1y_2E0: tyop_2Enum_2Enum] :
( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V1y_2E0,V0s_2E0))
=> p(c_2Earithmetic_2E_3C_3D_2E2(V1y_2E0,c_2Epred__set_2EMAX__SET_2E1(V0s_2E0))) ) ) )
& ( ( V0s_2E0 = c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum) )
=> ( c_2Epred__set_2EMAX__SET_2E1(V0s_2E0) = c_2Enum_2E0_2E0 ) ) ) ) ).
tff(thm_2Epred__set_2EMIN__SET__DEF,axiom,
c_2Epred__set_2EMIN__SET_2E0 = c_2Ewhile_2ELEAST_2E0 ).
tff(thm_2Epred__set_2EPOW__DEF,axiom,
! [A_27a: $tType,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)))] :
( ! [V0set_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,V0set_2E0),V1s_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V1s_2E0,c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,V0set_2E0)) )
=> ! [V0set_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EPOW_2E1(A_27a,V0set_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,V0set_2E0)) ) ) ).
tff(thm_2Epred__set_2Eequiv__on__def,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2Eequiv__on_2E2(A_27a,V0R_2E0,V1s_2E0))
<=> ( ! [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2x_2E0),V2x_2E0)) )
& ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V1s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V4y_2E0,V1s_2E0)) )
=> ( app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V3x_2E0),V4y_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V4y_2E0),V3x_2E0) ) )
& ! [V5x_2E0: A_27a,V6y_2E0: A_27a,V7z_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,V1s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V6y_2E0,V1s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V7z_2E0,V1s_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V5x_2E0),V6y_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V6y_2E0),V7z_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V5x_2E0),V7z_2E0)) ) ) ) ).
tff(thm_2Epred__set_2Epartition__def,axiom,
! [A_27a: $tType,F3_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,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))),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_2Efun(tyop_2Emin_2Efun(A_27a,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_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))))] :
( ! [V4y_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,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_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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F3_2E0,V4y_2E0),V1s_2E0),V0R_2E0),V3x_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V4y_2E0,V1s_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V3x_2E0),V4y_2E0)) ) )
=> ( ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3x_2E0: A_27a,V4y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,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,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F2_2E0,V1s_2E0),V0R_2E0),V3x_2E0),V4y_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V4y_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,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_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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F3_2E0,V4y_2E0),V1s_2E0),V0R_2E0),V3x_2E0)) )
=> ( ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(app_2E2(tyop_2Emin_2Efun(A_27a,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_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_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),F1_2E0,V1s_2E0),V2t_2E0),V0R_2E0))
<=> ? [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V1s_2E0))
& ( V2t_2E0 = c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,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,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F2_2E0,V1s_2E0),V0R_2E0),V3x_2E0)) ) ) )
=> ( ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2t_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_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)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,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,V1s_2E0),V0R_2E0),V2t_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V2t_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,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_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_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),F1_2E0,V1s_2E0),V2t_2E0),V0R_2E0)) )
=> ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2Epartition_2E2(A_27a,V0R_2E0,V1s_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_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)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,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,V1s_2E0),V0R_2E0)) ) ) ) ) ) ).
tff(thm_2Epred__set_2Epairwise__def,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2Epairwise_2E2(A_27a,V0P_2E0,V1s_2E0))
<=> ! [V2e1_2E0: A_27a,V3e2_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V2e1_2E0,V1s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V3e2_2E0,V1s_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0,V2e1_2E0),V3e2_2E0)) ) ) ).
tff(thm_2Epred__set_2Echooser__def,axiom,
! [A_27a: $tType] :
( ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2Echooser_2E2(A_27a,V0s_2E0,c_2Enum_2E0_2E0) = c_2Epred__set_2ECHOICE_2E1(A_27a,V0s_2E0) )
& ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2n_2E0: tyop_2Enum_2Enum] : ( c_2Epred__set_2Echooser_2E2(A_27a,V1s_2E0,c_2Enum_2ESUC_2E1(V2n_2E0)) = c_2Epred__set_2Echooser_2E2(A_27a,c_2Epred__set_2EREST_2E1(A_27a,V1s_2E0),V2n_2E0) ) ) ).
tff(thm_2Epred__set_2Ecountable__def,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2Ecountable_2E1(A_27a,V0s_2E0))
<=> ? [V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : p(c_2Epred__set_2EINJ_2E3(A_27a,tyop_2Enum_2Enum,V1f_2E0,V0s_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))) ) ).
tff(thm_2Epred__set_2Enum__to__pair__def,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Epred__set_2Enum__to__pair_2E1(V0n_2E0) = c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumpair_2Enfst_2E1(V0n_2E0),c_2Enumpair_2Ensnd_2E1(V0n_2E0)) ) ).
tff(thm_2Epred__set_2Epair__to__num__def,axiom,
! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : ( c_2Epred__set_2Epair__to__num_2E1(c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V0m_2E0,V1n_2E0)) = c_2Enumpair_2Enpair_2E2(V0m_2E0,V1n_2E0) ) ).
tff(thm_2Epred__set_2Eenumerate__def,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool))] :
( ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : ( app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),F0_2E0,V0s_2E0),V1f_2E0) = c_2Epred__set_2EBIJ_2E3(tyop_2Enum_2Enum,A_27a,V1f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),V0s_2E0) )
=> ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2Eenumerate_2E1(A_27a,V0s_2E0) = c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),F0_2E0,V0s_2E0)) ) ) ).
tff(thm_2Epred__set_2EPREIMAGE__def,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),V1s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2x_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),V1s_2E0),V2x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V2x_2E0,c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0),V1s_2E0)) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0) = 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),V1s_2E0)) ) ) ).
tff(thm_2Epred__set_2Eis__measure__maximal__def,axiom,
! [A_27a: $tType,V0m_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] :
( p(c_2Epred__set_2Eis__measure__maximal_2E3(A_27a,V0m_2E0,V1s_2E0,V2x_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
& ! [V3y_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,V1s_2E0))
=> p(c_2Earithmetic_2E_3C_3D_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V0m_2E0,V3y_2E0),app_2E2(A_27a,tyop_2Enum_2Enum,V0m_2E0,V2x_2E0))) ) ) ) ).
tff(thm_2Epred__set_2ESPECIFICATION,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0: A_27a] : ( c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V0P_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V1x_2E0) ) ).
tff(thm_2Epred__set_2EIN__APP,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V1P_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V0x_2E0) ) ).
tff(thm_2Epred__set_2EIN__ABS,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V1P_2E0),V2x_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V2x_2E0) )
=> ! [V0x_2E0: A_27a,V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V1P_2E0)) = app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V0x_2E0) ) ) ).
tff(thm_2Epred__set_2EEXTENSION,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( V0s_2E0 = V1t_2E0 )
<=> ! [V2x_2E0: A_27a] : ( c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0) = c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1t_2E0) ) ) ).
tff(thm_2Epred__set_2ENOT__EQUAL__SETS,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( V0s_2E0 != V1t_2E0 )
<=> ? [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1t_2E0))
<=> ~ p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0)) ) ) ).
tff(thm_2Epred__set_2ENUM__SET__WOP,axiom,
! [V0s_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( ? [V1n_2E0: tyop_2Enum_2Enum] : p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V1n_2E0,V0s_2E0))
<=> ? [V2n_2E0: tyop_2Enum_2Enum] :
( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V2n_2E0,V0s_2E0))
& ! [V3m_2E0: tyop_2Enum_2Enum] :
( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V3m_2E0,V0s_2E0))
=> p(c_2Earithmetic_2E_3C_3D_2E2(V2n_2E0,V3m_2E0)) ) ) ) ).
tff(thm_2Epred__set_2EGSPECIFICATION__applied,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),V1v_2E0: A_27a] :
( p(c_2Epred__set_2EGSPEC_2E2(A_27a,A_27b,V0f_2E0,V1v_2E0))
<=> ? [V2x_2E0: A_27b] : ( c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V1v_2E0,c_2Ebool_2ET_2E0) = app_2E2(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),V0f_2E0,V2x_2E0) ) ) ).
tff(thm_2Epred__set_2EGSPEC__ETA,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0P_2E0),V1x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V1x_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V1x_2E0)) )
=> ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0P_2E0)) = V0P_2E0 ) ) ).
tff(thm_2Epred__set_2EGSPEC__PAIR__ETA,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(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))))] :
( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2y_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_27a,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,V0P_2E0),V1x_2E0),V2y_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,V1x_2E0,V2y_2E0),app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0,V1x_2E0),V2y_2E0)) )
=> ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( 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_27a,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,V0P_2E0))) = c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Emin_2Ebool,V0P_2E0) ) ) ).
tff(thm_2Epred__set_2EIN__GSPEC__IFF,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V1P_2E0),V2x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V2x_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V2x_2E0)) )
=> ! [V0y_2E0: A_27a,V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(A_27a,V0y_2E0,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V1P_2E0))) = app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V0y_2E0) ) ) ).
tff(thm_2Epred__set_2EPAIR__IN__GSPEC__IFF,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(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))))] :
( ! [V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3x_2E0: A_27a,V4y_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_27a,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,V2P_2E0),V3x_2E0),V4y_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,V3x_2E0,V4y_2E0),app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2P_2E0,V3x_2E0),V4y_2E0)) )
=> ! [V0y_2E0: A_27b,V1x_2E0: A_27a,V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V0y_2E0),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_27a,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,V2P_2E0)))) = app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2P_2E0,V1x_2E0),V0y_2E0) ) ) ).
tff(thm_2Epred__set_2EIN__GSPEC,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_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V3P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V3P_2E0),V4x_2E0) = c_2Epair_2E_2C_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,A_27b,V0f_2E0,V4x_2E0),app_2E2(A_27a,tyop_2Emin_2Ebool,V3P_2E0,V4x_2E0)) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1y_2E0: A_27a,V2x_2E0: A_27b,V3P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V3P_2E0,V1y_2E0))
& ( V2x_2E0 = app_2E2(A_27a,A_27b,V0f_2E0,V1y_2E0) ) )
=> p(c_2Ebool_2EIN_2E2(A_27b,V2x_2E0,c_2Epred__set_2EGSPEC_2E1(A_27b,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(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_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V3P_2E0)))) ) ) ).
tff(thm_2Epred__set_2EPAIR__IN__GSPEC__1,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))))] :
( ! [V0x_2E0: A_27b,V3P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4y_2E0: A_27a] : ( app_2E2(A_27a,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(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),F0_2E0,V0x_2E0),V3P_2E0),V4y_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,V4y_2E0,V0x_2E0),app_2E2(A_27a,tyop_2Emin_2Ebool,V3P_2E0,V4y_2E0)) )
=> ! [V0x_2E0: A_27b,V1b_2E0: A_27b,V2a_2E0: A_27a,V3P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V2a_2E0,V1b_2E0),c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),F0_2E0,V0x_2E0),V3P_2E0))))
<=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V3P_2E0,V2a_2E0))
& ( V1b_2E0 = V0x_2E0 ) ) ) ) ).
tff(thm_2Epred__set_2EPAIR__IN__GSPEC__2,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))))] :
( ! [V0x_2E0: A_27a,V3P_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4y_2E0: A_27b] : ( app_2E2(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_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),F0_2E0,V0x_2E0),V3P_2E0),V4y_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,V0x_2E0,V4y_2E0),app_2E2(A_27b,tyop_2Emin_2Ebool,V3P_2E0,V4y_2E0)) )
=> ! [V0x_2E0: A_27a,V1b_2E0: A_27b,V2a_2E0: A_27a,V3P_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V2a_2E0,V1b_2E0),c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),F0_2E0,V0x_2E0),V3P_2E0))))
<=> ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,V3P_2E0,V1b_2E0))
& ( V2a_2E0 = V0x_2E0 ) ) ) ) ).
tff(thm_2Epred__set_2EPAIR__IN__GSPEC__same,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))] :
( ! [V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),F0_2E0,V2P_2E0),V3x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool,c_2Epair_2E_2C_2E2(A_27a,A_27a,V3x_2E0,V3x_2E0),app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V3x_2E0)) )
=> ! [V0b_2E0: A_27a,V1a_2E0: A_27a,V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(A_27a,A_27a,V1a_2E0,V0b_2E0),c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(A_27a,A_27a),A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),F0_2E0,V2P_2E0))))
<=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V2P_2E0,V1a_2E0))
& ( V1a_2E0 = V0b_2E0 ) ) ) ) ).
tff(thm_2Epred__set_2ESET__MINIMUM,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1M_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
( ? [V2x_2E0: A_27a] : p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0))
<=> ? [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V0s_2E0))
& ! [V4y_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V4y_2E0,V0s_2E0))
=> p(c_2Earithmetic_2E_3C_3D_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V1M_2E0,V3x_2E0),app_2E2(A_27a,tyop_2Enum_2Enum,V1M_2E0,V4y_2E0))) ) ) ) ).
tff(thm_2Epred__set_2ENOT__IN__EMPTY,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ~ p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a))) ).
tff(thm_2Epred__set_2EMEMBER__NOT__EMPTY,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ? [V1x_2E0: A_27a] : p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V0s_2E0))
<=> ( V0s_2E0 != c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) ).
tff(thm_2Epred__set_2EEMPTY__applied,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( c_2Epred__set_2EEMPTY_2E1(A_27a,V0x_2E0) = c_2Ebool_2EF_2E0 ) ).
tff(thm_2Epred__set_2EIN__UNIV,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Epred__set_2EUNIV_2E0(A_27a))) ).
tff(thm_2Epred__set_2EUNIV__applied,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : p(c_2Epred__set_2EUNIV_2E1(A_27a,V0x_2E0)) ).
tff(thm_2Epred__set_2EUNIV__NOT__EMPTY,axiom,
! [A_27a: $tType] : ( c_2Epred__set_2EUNIV_2E0(A_27a) != c_2Epred__set_2EEMPTY_2E0(A_27a) ) ).
tff(thm_2Epred__set_2EEMPTY__NOT__UNIV,axiom,
! [A_27a: $tType] : ( c_2Epred__set_2EEMPTY_2E0(A_27a) != c_2Epred__set_2EUNIV_2E0(A_27a) ) ).
tff(thm_2Epred__set_2EEQ__UNIV,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V1x_2E0: A_27a] : p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V0s_2E0))
<=> ( V0s_2E0 = c_2Epred__set_2EUNIV_2E0(A_27a) ) ) ).
tff(thm_2Epred__set_2EIN__EQ__UNIV__IMP,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( V0s_2E0 = c_2Epred__set_2EUNIV_2E0(A_27a) )
=> ! [V1v_2E0: A_27a] : p(c_2Ebool_2EIN_2E2(A_27a,V1v_2E0,V0s_2E0)) ) ).
tff(thm_2Epred__set_2ESUBSET__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)] :
( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0P_2E0,V1Q_2E0))
=> ! [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0P_2E0))
=> p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1Q_2E0)) ) ) ).
tff(thm_2Epred__set_2ESUBSET__applied,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_2ESUBSET_2E2(A_27a,V0s_2E0,V1t_2E0))
<=> ! [V2x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0s_2E0,V2x_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1t_2E0,V2x_2E0)) ) ) ).
tff(thm_2Epred__set_2ESUBSET__TRANS,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s_2E0,V1t_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1t_2E0,V2u_2E0)) )
=> p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s_2E0,V2u_2E0)) ) ).
tff(thm_2Epred__set_2ESUBSET__REFL,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s_2E0,V0s_2E0)) ).
tff(thm_2Epred__set_2ESUBSET__ANTISYM,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_2ESUBSET_2E2(A_27a,V0s_2E0,V1t_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1t_2E0,V0s_2E0)) )
=> ( V0s_2E0 = V1t_2E0 ) ) ).
tff(thm_2Epred__set_2EEMPTY__SUBSET,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Epred__set_2EEMPTY_2E0(A_27a),V0s_2E0)) ).
tff(thm_2Epred__set_2ESUBSET__EMPTY,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)))
<=> ( V0s_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) ).
tff(thm_2Epred__set_2ESUBSET__UNIV,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s_2E0,c_2Epred__set_2EUNIV_2E0(A_27a))) ).
tff(thm_2Epred__set_2EUNIV__SUBSET,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a),V0s_2E0))
<=> ( V0s_2E0 = c_2Epred__set_2EUNIV_2E0(A_27a) ) ) ).
tff(thm_2Epred__set_2EEQ__SUBSET__SUBSET,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( V0s_2E0 = V1t_2E0 )
=> ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s_2E0,V1t_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1t_2E0,V0s_2E0)) ) ) ).
tff(thm_2Epred__set_2ESUBSET__SUBSET__EQ,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_2ESUBSET_2E2(A_27a,V0s_2E0,V1t_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1t_2E0,V0s_2E0)) )
<=> ( V0s_2E0 = V1t_2E0 ) ) ).
tff(thm_2Epred__set_2ESUBSET__ADD,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1n_2E0: tyop_2Enum_2Enum,V2d_2E0: tyop_2Enum_2Enum] :
( ! [V3n_2E0: tyop_2Enum_2Enum] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0,V3n_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0,c_2Enum_2ESUC_2E1(V3n_2E0))))
=> p(c_2Epred__set_2ESUBSET_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0,V1n_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0,c_2Earithmetic_2E_2B_2E2(V1n_2E0,V2d_2E0)))) ) ).
tff(thm_2Epred__set_2EK__SUBSET,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Emin_2Ebool,V1y_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Ecombin_2EK_2E1(tyop_2Emin_2Ebool,A_27a,V0x_2E0),V1y_2E0))
<=> ( ~ p(V0x_2E0)
| p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a),V1y_2E0)) ) ) ).
tff(thm_2Epred__set_2ESUBSET__K,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0: tyop_2Emin_2Ebool] :
( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0x_2E0,c_2Ecombin_2EK_2E1(tyop_2Emin_2Ebool,A_27a,V1y_2E0)))
<=> ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)))
| p(V1y_2E0) ) ) ).
tff(thm_2Epred__set_2EPSUBSET__TRANS,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EPSUBSET_2E2(A_27a,V0s_2E0,V1t_2E0))
& p(c_2Epred__set_2EPSUBSET_2E2(A_27a,V1t_2E0,V2u_2E0)) )
=> p(c_2Epred__set_2EPSUBSET_2E2(A_27a,V0s_2E0,V2u_2E0)) ) ).
tff(thm_2Epred__set_2EPSUBSET__IRREFL,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ~ p(c_2Epred__set_2EPSUBSET_2E2(A_27a,V0s_2E0,V0s_2E0)) ).
tff(thm_2Epred__set_2ENOT__PSUBSET__EMPTY,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ~ p(c_2Epred__set_2EPSUBSET_2E2(A_27a,V0s_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a))) ).
tff(thm_2Epred__set_2ENOT__UNIV__PSUBSET,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ~ p(c_2Epred__set_2EPSUBSET_2E2(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a),V0s_2E0)) ).
tff(thm_2Epred__set_2EPSUBSET__UNIV,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EPSUBSET_2E2(A_27a,V0s_2E0,c_2Epred__set_2EUNIV_2E0(A_27a)))
<=> ? [V1x_2E0: A_27a] : ~ p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V0s_2E0)) ) ).
tff(thm_2Epred__set_2EIN__UNION,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Epred__set_2EUNION_2E2(A_27a,V0s_2E0,V1t_2E0)))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0))
| p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1t_2E0)) ) ) ).
tff(thm_2Epred__set_2EUNION__applied,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] :
( p(c_2Epred__set_2EUNION_2E3(A_27a,V0s_2E0,V1t_2E0,V2x_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0))
| p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1t_2E0)) ) ) ).
tff(thm_2Epred__set_2EUNION__ASSOC,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(A_27a,V0s_2E0,c_2Epred__set_2EUNION_2E2(A_27a,V1t_2E0,V2u_2E0)) = c_2Epred__set_2EUNION_2E2(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V0s_2E0,V1t_2E0),V2u_2E0) ) ).
tff(thm_2Epred__set_2EUNION__IDEMPOT,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(A_27a,V0s_2E0,V0s_2E0) = V0s_2E0 ) ).
tff(thm_2Epred__set_2EUNION__COMM,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(A_27a,V0s_2E0,V1t_2E0) = c_2Epred__set_2EUNION_2E2(A_27a,V1t_2E0,V0s_2E0) ) ).
tff(thm_2Epred__set_2ESUBSET__UNION,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_2ESUBSET_2E2(A_27a,V0s_2E0,c_2Epred__set_2EUNION_2E2(A_27a,V0s_2E0,V1t_2E0)))
& ! [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,c_2Epred__set_2EUNION_2E2(A_27a,V3t_2E0,V2s_2E0))) ) ).
tff(thm_2Epred__set_2EUNION__SUBSET,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V0s_2E0,V1t_2E0),V2u_2E0))
<=> ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s_2E0,V2u_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1t_2E0,V2u_2E0)) ) ) ).
tff(thm_2Epred__set_2ESUBSET__UNION__ABSORPTION,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_2ESUBSET_2E2(A_27a,V0s_2E0,V1t_2E0))
<=> ( c_2Epred__set_2EUNION_2E2(A_27a,V0s_2E0,V1t_2E0) = V1t_2E0 ) ) ).
tff(thm_2Epred__set_2EUNION__EMPTY,axiom,
! [A_27a: $tType] :
( ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(A_27a,c_2Epred__set_2EEMPTY_2E0(A_27a),V0s_2E0) = V0s_2E0 )
& ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) = V1s_2E0 ) ) ).
tff(thm_2Epred__set_2EUNION__UNIV,axiom,
! [A_27a: $tType] :
( ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a),V0s_2E0) = c_2Epred__set_2EUNIV_2E0(A_27a) )
& ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,c_2Epred__set_2EUNIV_2E0(A_27a)) = c_2Epred__set_2EUNIV_2E0(A_27a) ) ) ).
tff(thm_2Epred__set_2EEMPTY__UNION,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( c_2Epred__set_2EUNION_2E2(A_27a,V0s_2E0,V1t_2E0) = c_2Epred__set_2EEMPTY_2E0(A_27a) )
<=> ( ( V0s_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) )
& ( V1t_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) ) ).
tff(thm_2Epred__set_2EFORALL__IN__UNION,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,V2t_2E0)))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0)) )
<=> ( ! [V4x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V1s_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V4x_2E0)) )
& ! [V5x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,V2t_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V5x_2E0)) ) ) ) ).
tff(thm_2Epred__set_2EIN__INTER,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Epred__set_2EINTER_2E2(A_27a,V0s_2E0,V1t_2E0)))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1t_2E0)) ) ) ).
tff(thm_2Epred__set_2EINTER__applied,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] :
( p(c_2Epred__set_2EINTER_2E3(A_27a,V0s_2E0,V1t_2E0,V2x_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1t_2E0)) ) ) ).
tff(thm_2Epred__set_2EINTER__ASSOC,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINTER_2E2(A_27a,V0s_2E0,c_2Epred__set_2EINTER_2E2(A_27a,V1t_2E0,V2u_2E0)) = c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EINTER_2E2(A_27a,V0s_2E0,V1t_2E0),V2u_2E0) ) ).
tff(thm_2Epred__set_2EINTER__IDEMPOT,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINTER_2E2(A_27a,V0s_2E0,V0s_2E0) = V0s_2E0 ) ).
tff(thm_2Epred__set_2EINTER__COMM,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINTER_2E2(A_27a,V0s_2E0,V1t_2E0) = c_2Epred__set_2EINTER_2E2(A_27a,V1t_2E0,V0s_2E0) ) ).
tff(thm_2Epred__set_2EINTER__SUBSET,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_2ESUBSET_2E2(A_27a,c_2Epred__set_2EINTER_2E2(A_27a,V0s_2E0,V1t_2E0),V0s_2E0))
& ! [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,c_2Epred__set_2EINTER_2E2(A_27a,V3t_2E0,V2s_2E0),V2s_2E0)) ) ).
tff(thm_2Epred__set_2ESUBSET__INTER,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s_2E0,c_2Epred__set_2EINTER_2E2(A_27a,V1t_2E0,V2u_2E0)))
<=> ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s_2E0,V1t_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s_2E0,V2u_2E0)) ) ) ).
tff(thm_2Epred__set_2ESUBSET__INTER__ABSORPTION,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_2ESUBSET_2E2(A_27a,V0s_2E0,V1t_2E0))
<=> ( c_2Epred__set_2EINTER_2E2(A_27a,V0s_2E0,V1t_2E0) = V0s_2E0 ) ) ).
tff(thm_2Epred__set_2ESUBSET__INTER1,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_2ESUBSET_2E2(A_27a,V0s_2E0,V1t_2E0))
=> ( c_2Epred__set_2EINTER_2E2(A_27a,V0s_2E0,V1t_2E0) = V0s_2E0 ) ) ).
tff(thm_2Epred__set_2ESUBSET__INTER2,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_2ESUBSET_2E2(A_27a,V0s_2E0,V1t_2E0))
=> ( c_2Epred__set_2EINTER_2E2(A_27a,V1t_2E0,V0s_2E0) = V0s_2E0 ) ) ).
tff(thm_2Epred__set_2EINTER__EMPTY,axiom,
! [A_27a: $tType] :
( ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EEMPTY_2E0(A_27a),V0s_2E0) = c_2Epred__set_2EEMPTY_2E0(A_27a) )
& ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINTER_2E2(A_27a,V1s_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) ).
tff(thm_2Epred__set_2EINTER__UNIV,axiom,
! [A_27a: $tType] :
( ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a),V0s_2E0) = V0s_2E0 )
& ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINTER_2E2(A_27a,V1s_2E0,c_2Epred__set_2EUNIV_2E0(A_27a)) = V1s_2E0 ) ) ).
tff(thm_2Epred__set_2EUNION__OVER__INTER,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINTER_2E2(A_27a,V0s_2E0,c_2Epred__set_2EUNION_2E2(A_27a,V1t_2E0,V2u_2E0)) = c_2Epred__set_2EUNION_2E2(A_27a,c_2Epred__set_2EINTER_2E2(A_27a,V0s_2E0,V1t_2E0),c_2Epred__set_2EINTER_2E2(A_27a,V0s_2E0,V2u_2E0)) ) ).
tff(thm_2Epred__set_2EINTER__OVER__UNION,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(A_27a,V0s_2E0,c_2Epred__set_2EINTER_2E2(A_27a,V1t_2E0,V2u_2E0)) = c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V0s_2E0,V1t_2E0),c_2Epred__set_2EUNION_2E2(A_27a,V0s_2E0,V2u_2E0)) ) ).
tff(thm_2Epred__set_2EIN__DISJOINT,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_2EDISJOINT_2E2(A_27a,V0s_2E0,V1t_2E0))
<=> ~ ? [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1t_2E0)) ) ) ).
tff(thm_2Epred__set_2EDISJOINT__SYM,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EDISJOINT_2E2(A_27a,V0s_2E0,V1t_2E0) = c_2Epred__set_2EDISJOINT_2E2(A_27a,V1t_2E0,V0s_2E0) ) ).
tff(thm_2Epred__set_2EDISJOINT__ALT,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_2EDISJOINT_2E2(A_27a,V0s_2E0,V1t_2E0))
<=> ! [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0))
=> ~ p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1t_2E0)) ) ) ).
tff(thm_2Epred__set_2EDISJOINT__EMPTY,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EDISJOINT_2E2(A_27a,c_2Epred__set_2EEMPTY_2E0(A_27a),V0s_2E0))
& p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V0s_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a))) ) ).
tff(thm_2Epred__set_2EDISJOINT__EMPTY__REFL,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( V0s_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) )
<=> p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V0s_2E0,V0s_2E0)) ) ).
tff(thm_2Epred__set_2EDISJOINT__EMPTY__REFL__RWT,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V0s_2E0,V0s_2E0))
<=> ( V0s_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) ).
tff(thm_2Epred__set_2EDISJOINT__UNION,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EDISJOINT_2E2(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V0s_2E0,V1t_2E0),V2u_2E0))
<=> ( p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V0s_2E0,V2u_2E0))
& p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V1t_2E0,V2u_2E0)) ) ) ).
tff(thm_2Epred__set_2EDISJOINT__UNION__BOTH,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EDISJOINT_2E2(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V0s_2E0,V1t_2E0),V2u_2E0))
<=> ( p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V0s_2E0,V2u_2E0))
& p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V1t_2E0,V2u_2E0)) ) )
& ( p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V2u_2E0,c_2Epred__set_2EUNION_2E2(A_27a,V0s_2E0,V1t_2E0)))
<=> ( p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V0s_2E0,V2u_2E0))
& p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V1t_2E0,V2u_2E0)) ) ) ) ).
tff(thm_2Epred__set_2EDISJOINT__SUBSET,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V0s_2E0,V1t_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V2u_2E0,V1t_2E0)) )
=> p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V0s_2E0,V2u_2E0)) ) ).
tff(thm_2Epred__set_2EIN__DIFF,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Epred__set_2EDIFF_2E2(A_27a,V0s_2E0,V1t_2E0)))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0))
& ~ p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1t_2E0)) ) ) ).
tff(thm_2Epred__set_2EDIFF__applied,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] :
( p(c_2Epred__set_2EDIFF_2E3(A_27a,V0s_2E0,V1t_2E0,V2x_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0))
& ~ p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1t_2E0)) ) ) ).
tff(thm_2Epred__set_2EDIFF__EMPTY,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EDIFF_2E2(A_27a,V0s_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) = V0s_2E0 ) ).
tff(thm_2Epred__set_2EEMPTY__DIFF,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EDIFF_2E2(A_27a,c_2Epred__set_2EEMPTY_2E0(A_27a),V0s_2E0) = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ).
tff(thm_2Epred__set_2EDIFF__UNIV,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EDIFF_2E2(A_27a,V0s_2E0,c_2Epred__set_2EUNIV_2E0(A_27a)) = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ).
tff(thm_2Epred__set_2EDIFF__DIFF,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EDIFF_2E2(A_27a,c_2Epred__set_2EDIFF_2E2(A_27a,V0s_2E0,V1t_2E0),V1t_2E0) = c_2Epred__set_2EDIFF_2E2(A_27a,V0s_2E0,V1t_2E0) ) ).
tff(thm_2Epred__set_2EDIFF__EQ__EMPTY,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EDIFF_2E2(A_27a,V0s_2E0,V0s_2E0) = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ).
tff(thm_2Epred__set_2EDIFF__SUBSET,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_2ESUBSET_2E2(A_27a,c_2Epred__set_2EDIFF_2E2(A_27a,V0s_2E0,V1t_2E0),V0s_2E0)) ).
tff(thm_2Epred__set_2EUNION__DIFF,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,V0t_2E0))
=> ( ( c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,c_2Epred__set_2EDIFF_2E2(A_27a,V0t_2E0,V1s_2E0)) = V0t_2E0 )
& ( c_2Epred__set_2EUNION_2E2(A_27a,c_2Epred__set_2EDIFF_2E2(A_27a,V0t_2E0,V1s_2E0),V1s_2E0) = V0t_2E0 ) ) ) ).
tff(thm_2Epred__set_2EDIFF__DIFF__SUBSET,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_2ESUBSET_2E2(A_27a,V1t_2E0,V0s_2E0))
=> ( c_2Epred__set_2EDIFF_2E2(A_27a,V0s_2E0,c_2Epred__set_2EDIFF_2E2(A_27a,V0s_2E0,V1t_2E0)) = V1t_2E0 ) ) ).
tff(thm_2Epred__set_2EDIFF__UNION,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2z_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EDIFF_2E2(A_27a,V0x_2E0,c_2Epred__set_2EUNION_2E2(A_27a,V1y_2E0,V2z_2E0)) = c_2Epred__set_2EDIFF_2E2(A_27a,c_2Epred__set_2EDIFF_2E2(A_27a,V0x_2E0,V1y_2E0),V2z_2E0) ) ).
tff(thm_2Epred__set_2EDIFF__COMM,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2z_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EDIFF_2E2(A_27a,c_2Epred__set_2EDIFF_2E2(A_27a,V0x_2E0,V1y_2E0),V2z_2E0) = c_2Epred__set_2EDIFF_2E2(A_27a,c_2Epred__set_2EDIFF_2E2(A_27a,V0x_2E0,V2z_2E0),V1y_2E0) ) ).
tff(thm_2Epred__set_2EDIFF__SAME__UNION,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( c_2Epred__set_2EDIFF_2E2(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V0x_2E0,V1y_2E0),V0x_2E0) = c_2Epred__set_2EDIFF_2E2(A_27a,V1y_2E0,V0x_2E0) )
& ( c_2Epred__set_2EDIFF_2E2(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V0x_2E0,V1y_2E0),V1y_2E0) = c_2Epred__set_2EDIFF_2E2(A_27a,V0x_2E0,V1y_2E0) ) ) ).
tff(thm_2Epred__set_2EDIFF__INTER,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EDIFF_2E2(A_27a,V0s_2E0,V1t_2E0),V2g_2E0) = c_2Epred__set_2EDIFF_2E2(A_27a,c_2Epred__set_2EINTER_2E2(A_27a,V0s_2E0,V2g_2E0),V1t_2E0) ) ).
tff(thm_2Epred__set_2EDIFF__INTER2,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EDIFF_2E2(A_27a,V0s_2E0,c_2Epred__set_2EINTER_2E2(A_27a,V1t_2E0,V0s_2E0)) = c_2Epred__set_2EDIFF_2E2(A_27a,V0s_2E0,V1t_2E0) ) ).
tff(thm_2Epred__set_2EDISJOINT__DIFF,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_2EDISJOINT_2E2(A_27a,V1t_2E0,c_2Epred__set_2EDIFF_2E2(A_27a,V0s_2E0,V1t_2E0)))
& p(c_2Epred__set_2EDISJOINT_2E2(A_27a,c_2Epred__set_2EDIFF_2E2(A_27a,V0s_2E0,V1t_2E0),V1t_2E0)) ) ).
tff(thm_2Epred__set_2EDISJOINT__DIFFS,axiom,
! [A_27a: $tType,V0g_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2m_2E0: tyop_2Enum_2Enum,V3n_2E0: tyop_2Enum_2Enum] :
( ( ! [V4n_2E0: tyop_2Enum_2Enum] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,V4n_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,c_2Enum_2ESUC_2E1(V4n_2E0))))
& ! [V5n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0g_2E0,V5n_2E0) = c_2Epred__set_2EDIFF_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,c_2Enum_2ESUC_2E1(V5n_2E0)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,V5n_2E0)) )
& ( V2m_2E0 != V3n_2E0 ) )
=> p(c_2Epred__set_2EDISJOINT_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0g_2E0,V2m_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0g_2E0,V3n_2E0))) ) ).
tff(thm_2Epred__set_2EIN__INSERT,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1y_2E0: A_27a,V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V1y_2E0,V2s_2E0)))
<=> ( ( V0x_2E0 = V1y_2E0 )
| p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V2s_2E0)) ) ) ).
tff(thm_2Epred__set_2EINSERT__applied,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1y_2E0: A_27a,V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EINSERT_2E3(A_27a,V1y_2E0,V2s_2E0,V0x_2E0))
<=> ( ( V0x_2E0 = V1y_2E0 )
| p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V2s_2E0)) ) ) ).
tff(thm_2Epred__set_2ECOMPONENT,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,V1s_2E0))) ).
tff(thm_2Epred__set_2ESET__CASES,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( V0s_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) )
| ? [V1x_2E0: A_27a,V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( V0s_2E0 = c_2Epred__set_2EINSERT_2E2(A_27a,V1x_2E0,V2t_2E0) )
& ~ p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V2t_2E0)) ) ) ).
tff(thm_2Epred__set_2EDECOMPOSITION,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V0s_2E0))
<=> ? [V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( V0s_2E0 = c_2Epred__set_2EINSERT_2E2(A_27a,V1x_2E0,V2t_2E0) )
& ~ p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V2t_2E0)) ) ) ).
tff(thm_2Epred__set_2EABSORPTION,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V1s_2E0))
<=> ( c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,V1s_2E0) = V1s_2E0 ) ) ).
tff(thm_2Epred__set_2EABSORPTION__RWT,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V1s_2E0))
=> ( c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,V1s_2E0) = V1s_2E0 ) ) ).
tff(thm_2Epred__set_2EINSERT__INSERT,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,V1s_2E0)) = c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,V1s_2E0) ) ).
tff(thm_2Epred__set_2EINSERT__COMM,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1y_2E0: A_27a,V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V1y_2E0,V2s_2E0)) = c_2Epred__set_2EINSERT_2E2(A_27a,V1y_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,V2s_2E0)) ) ).
tff(thm_2Epred__set_2EINSERT__UNIV,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,c_2Epred__set_2EUNIV_2E0(A_27a)) = c_2Epred__set_2EUNIV_2E0(A_27a) ) ).
tff(thm_2Epred__set_2ENOT__INSERT__EMPTY,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,V1s_2E0) != c_2Epred__set_2EEMPTY_2E0(A_27a) ) ).
tff(thm_2Epred__set_2ENOT__EMPTY__INSERT,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EEMPTY_2E0(A_27a) != c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,V1s_2E0) ) ).
tff(thm_2Epred__set_2EINSERT__UNION,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,V1s_2E0),V2t_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V2t_2E0),c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,V2t_2E0),c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,V2t_2E0))) ) ).
tff(thm_2Epred__set_2EINSERT__UNION__EQ,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,V1s_2E0),V2t_2E0) = c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,V2t_2E0)) ) ).
tff(thm_2Epred__set_2EINSERT__INTER,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,V1s_2E0),V2t_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V2t_2E0),c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,c_2Epred__set_2EINTER_2E2(A_27a,V1s_2E0,V2t_2E0)),c_2Epred__set_2EINTER_2E2(A_27a,V1s_2E0,V2t_2E0)) ) ).
tff(thm_2Epred__set_2EDISJOINT__INSERT,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EDISJOINT_2E2(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,V1s_2E0),V2t_2E0))
<=> ( p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V1s_2E0,V2t_2E0))
& ~ p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V2t_2E0)) ) ) ).
tff(thm_2Epred__set_2EDISJOINT__INSERT_27,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V2t_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,V1s_2E0)))
<=> ( p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V2t_2E0,V1s_2E0))
& ~ p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V2t_2E0)) ) ) ).
tff(thm_2Epred__set_2EINSERT__SUBSET,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,V1s_2E0),V2t_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V2t_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,V2t_2E0)) ) ) ).
tff(thm_2Epred__set_2ESUBSET__INSERT,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ~ p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V1s_2E0))
=> ! [V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,V2t_2E0)) = c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,V2t_2E0) ) ) ).
tff(thm_2Epred__set_2EINSERT__DIFF,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] : ( c_2Epred__set_2EDIFF_2E2(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V2x_2E0,V0s_2E0),V1t_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1t_2E0),c_2Epred__set_2EDIFF_2E2(A_27a,V0s_2E0,V1t_2E0),c_2Epred__set_2EINSERT_2E2(A_27a,V2x_2E0,c_2Epred__set_2EDIFF_2E2(A_27a,V0s_2E0,V1t_2E0))) ) ).
tff(thm_2Epred__set_2EUNIV__BOOL,axiom,
c_2Epred__set_2EUNIV_2E0(tyop_2Emin_2Ebool) = 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))) ).
tff(thm_2Epred__set_2EFORALL__IN__INSERT,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1a_2E0: A_27a,V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V1a_2E0,V2s_2E0)))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0)) )
<=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V1a_2E0))
& ! [V4x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V2s_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V4x_2E0)) ) ) ) ).
tff(thm_2Epred__set_2EEXISTS__IN__INSERT,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1a_2E0: A_27a,V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ? [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V1a_2E0,V2s_2E0)))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0)) )
<=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V1a_2E0))
| ? [V4x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V2s_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V4x_2E0)) ) ) ) ).
tff(thm_2Epred__set_2EIN__DELETE,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0: A_27a,V2y_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Epred__set_2EDELETE_2E2(A_27a,V0s_2E0,V2y_2E0)))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V0s_2E0))
& ( V1x_2E0 != V2y_2E0 ) ) ) ).
tff(thm_2Epred__set_2EDELETE__applied,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0: A_27a,V2y_2E0: A_27a] :
( p(c_2Epred__set_2EDELETE_2E3(A_27a,V0s_2E0,V2y_2E0,V1x_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V0s_2E0))
& ( V1x_2E0 != V2y_2E0 ) ) ) ).
tff(thm_2Epred__set_2EDELETE__NON__ELEMENT,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ~ p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V1s_2E0))
<=> ( c_2Epred__set_2EDELETE_2E2(A_27a,V1s_2E0,V0x_2E0) = V1s_2E0 ) ) ).
tff(thm_2Epred__set_2EDELETE__NON__ELEMENT__RWT,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0: A_27a] :
( ~ p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V0s_2E0))
=> ( c_2Epred__set_2EDELETE_2E2(A_27a,V0s_2E0,V1x_2E0) = V0s_2E0 ) ) ).
tff(thm_2Epred__set_2EIN__DELETE__EQ,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0: A_27a,V2x_27_2E0: A_27a] :
( ( c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V0s_2E0) = c_2Ebool_2EIN_2E2(A_27a,V2x_27_2E0,V0s_2E0) )
<=> ( c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Epred__set_2EDELETE_2E2(A_27a,V0s_2E0,V2x_27_2E0)) = c_2Ebool_2EIN_2E2(A_27a,V2x_27_2E0,c_2Epred__set_2EDELETE_2E2(A_27a,V0s_2E0,V1x_2E0)) ) ) ).
tff(thm_2Epred__set_2EEMPTY__DELETE,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( c_2Epred__set_2EDELETE_2E2(A_27a,c_2Epred__set_2EEMPTY_2E0(A_27a),V0x_2E0) = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ).
tff(thm_2Epred__set_2EELT__IN__DELETE,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ~ p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Epred__set_2EDELETE_2E2(A_27a,V1s_2E0,V0x_2E0))) ).
tff(thm_2Epred__set_2EDELETE__DELETE,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EDELETE_2E2(A_27a,c_2Epred__set_2EDELETE_2E2(A_27a,V1s_2E0,V0x_2E0),V0x_2E0) = c_2Epred__set_2EDELETE_2E2(A_27a,V1s_2E0,V0x_2E0) ) ).
tff(thm_2Epred__set_2EDELETE__COMM,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1y_2E0: A_27a,V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EDELETE_2E2(A_27a,c_2Epred__set_2EDELETE_2E2(A_27a,V2s_2E0,V0x_2E0),V1y_2E0) = c_2Epred__set_2EDELETE_2E2(A_27a,c_2Epred__set_2EDELETE_2E2(A_27a,V2s_2E0,V1y_2E0),V0x_2E0) ) ).
tff(thm_2Epred__set_2EDELETE__SUBSET,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Epred__set_2EDELETE_2E2(A_27a,V1s_2E0,V0x_2E0),V1s_2E0)) ).
tff(thm_2Epred__set_2ESUBSET__DELETE,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,c_2Epred__set_2EDELETE_2E2(A_27a,V2t_2E0,V0x_2E0)))
<=> ( ~ p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V1s_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,V2t_2E0)) ) ) ).
tff(thm_2Epred__set_2ESUBSET__INSERT__DELETE,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,V2t_2E0)) = c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Epred__set_2EDELETE_2E2(A_27a,V1s_2E0,V0x_2E0),V2t_2E0) ) ).
tff(thm_2Epred__set_2ESUBSET__OF__INSERT,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,V1s_2E0))) ).
tff(thm_2Epred__set_2EDIFF__INSERT,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] : ( c_2Epred__set_2EDIFF_2E2(A_27a,V0s_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V2x_2E0,V1t_2E0)) = c_2Epred__set_2EDIFF_2E2(A_27a,c_2Epred__set_2EDELETE_2E2(A_27a,V0s_2E0,V2x_2E0),V1t_2E0) ) ).
tff(thm_2Epred__set_2EPSUBSET__INSERT__SUBSET,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_2EPSUBSET_2E2(A_27a,V0s_2E0,V1t_2E0))
<=> ? [V2x_2E0: A_27a] :
( ~ p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V2x_2E0,V0s_2E0),V1t_2E0)) ) ) ).
tff(thm_2Epred__set_2EPSUBSET__MEMBER,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_2EPSUBSET_2E2(A_27a,V0s_2E0,V1t_2E0))
<=> ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s_2E0,V1t_2E0))
& ? [V2y_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2y_2E0,V1t_2E0))
& ~ p(c_2Ebool_2EIN_2E2(A_27a,V2y_2E0,V0s_2E0)) ) ) ) ).
tff(thm_2Epred__set_2EDELETE__INSERT,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V0x_2E0: A_27a,V1y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0x_2E0),V1y_2E0))
<=> ( V0x_2E0 = V1y_2E0 ) )
=> ! [V0x_2E0: A_27a,V1y_2E0: A_27a,V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EDELETE_2E2(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,V2s_2E0),V1y_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0x_2E0),V1y_2E0),c_2Epred__set_2EDELETE_2E2(A_27a,V2s_2E0,V1y_2E0),c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,c_2Epred__set_2EDELETE_2E2(A_27a,V2s_2E0,V1y_2E0))) ) ) ).
tff(thm_2Epred__set_2EINSERT__DELETE,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V1s_2E0))
=> ( c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,c_2Epred__set_2EDELETE_2E2(A_27a,V1s_2E0,V0x_2E0)) = V1s_2E0 ) ) ).
tff(thm_2Epred__set_2EDELETE__INTER,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] : ( c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EDELETE_2E2(A_27a,V0s_2E0,V2x_2E0),V1t_2E0) = c_2Epred__set_2EDELETE_2E2(A_27a,c_2Epred__set_2EINTER_2E2(A_27a,V0s_2E0,V1t_2E0),V2x_2E0) ) ).
tff(thm_2Epred__set_2EDISJOINT__DELETE__SYM,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] : ( c_2Epred__set_2EDISJOINT_2E2(A_27a,c_2Epred__set_2EDELETE_2E2(A_27a,V0s_2E0,V2x_2E0),V1t_2E0) = c_2Epred__set_2EDISJOINT_2E2(A_27a,c_2Epred__set_2EDELETE_2E2(A_27a,V1t_2E0,V2x_2E0),V0s_2E0) ) ).
tff(thm_2Epred__set_2EIN__REST,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Epred__set_2EREST_2E1(A_27a,V1s_2E0)))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V1s_2E0))
& ( V0x_2E0 != c_2Epred__set_2ECHOICE_2E1(A_27a,V1s_2E0) ) ) ) ).
tff(thm_2Epred__set_2EREST__applied,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EREST_2E2(A_27a,V1s_2E0,V0x_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V1s_2E0))
& ( V0x_2E0 != c_2Epred__set_2ECHOICE_2E1(A_27a,V1s_2E0) ) ) ) ).
tff(thm_2Epred__set_2ECHOICE__NOT__IN__REST,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ~ p(c_2Ebool_2EIN_2E2(A_27a,c_2Epred__set_2ECHOICE_2E1(A_27a,V0s_2E0),c_2Epred__set_2EREST_2E1(A_27a,V0s_2E0))) ).
tff(thm_2Epred__set_2ECHOICE__INSERT__REST,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( V0s_2E0 != c_2Epred__set_2EEMPTY_2E0(A_27a) )
=> ( c_2Epred__set_2EINSERT_2E2(A_27a,c_2Epred__set_2ECHOICE_2E1(A_27a,V0s_2E0),c_2Epred__set_2EREST_2E1(A_27a,V0s_2E0)) = V0s_2E0 ) ) ).
tff(thm_2Epred__set_2EREST__SUBSET,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Epred__set_2EREST_2E1(A_27a,V0s_2E0),V0s_2E0)) ).
tff(thm_2Epred__set_2EREST__PSUBSET,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( V0s_2E0 != c_2Epred__set_2EEMPTY_2E0(A_27a) )
=> p(c_2Epred__set_2EPSUBSET_2E2(A_27a,c_2Epred__set_2EREST_2E1(A_27a,V0s_2E0),V0s_2E0)) ) ).
tff(thm_2Epred__set_2ESING,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : p(c_2Epred__set_2ESING_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)))) ).
tff(thm_2Epred__set_2ESING__EMPTY,axiom,
! [A_27a: $tType] : ( c_2Epred__set_2ESING_2E1(A_27a,c_2Epred__set_2EEMPTY_2E0(A_27a)) = c_2Ebool_2EF_2E0 ) ).
tff(thm_2Epred__set_2ESING__INSERT,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESING_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,V1s_2E0)))
<=> ( ( V1s_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) )
| ( V1s_2E0 = c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) ) ) ) ).
tff(thm_2Epred__set_2ESING__UNION,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESING_2E1(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,V0t_2E0)))
<=> ( ( p(c_2Epred__set_2ESING_2E1(A_27a,V1s_2E0))
& ( V0t_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) )
| ( p(c_2Epred__set_2ESING_2E1(A_27a,V0t_2E0))
& ( V1s_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) )
| ( p(c_2Epred__set_2ESING_2E1(A_27a,V1s_2E0))
& p(c_2Epred__set_2ESING_2E1(A_27a,V0t_2E0))
& ( V1s_2E0 = V0t_2E0 ) ) ) ) ).
tff(thm_2Epred__set_2EIN__SING,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1y_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V1y_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a))))
<=> ( V0x_2E0 = V1y_2E0 ) ) ).
tff(thm_2Epred__set_2ESING__applied,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1y_2E0: A_27a] :
( p(c_2Epred__set_2EINSERT_2E3(A_27a,V1y_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a),V0x_2E0))
<=> ( V0x_2E0 = V1y_2E0 ) ) ).
tff(thm_2Epred__set_2ENOT__SING__EMPTY,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) != c_2Epred__set_2EEMPTY_2E0(A_27a) ) ).
tff(thm_2Epred__set_2ENOT__EMPTY__SING,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( c_2Epred__set_2EEMPTY_2E0(A_27a) != c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) ) ).
tff(thm_2Epred__set_2EEQUAL__SING,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1y_2E0: A_27a] :
( ( c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) = c_2Epred__set_2EINSERT_2E2(A_27a,V1y_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) )
<=> ( V0x_2E0 = V1y_2E0 ) ) ).
tff(thm_2Epred__set_2EDISJOINT__SING__EMPTY,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : p(c_2Epred__set_2EDISJOINT_2E2(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)),c_2Epred__set_2EEMPTY_2E0(A_27a))) ).
tff(thm_2Epred__set_2EINSERT__SING__UNION,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0: A_27a] : ( c_2Epred__set_2EINSERT_2E2(A_27a,V1x_2E0,V0s_2E0) = c_2Epred__set_2EUNION_2E2(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V1x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)),V0s_2E0) ) ).
tff(thm_2Epred__set_2ESING__DELETE,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( c_2Epred__set_2EDELETE_2E2(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)),V0x_2E0) = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ).
tff(thm_2Epred__set_2EDELETE__EQ__SING,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V0s_2E0))
=> ( ( c_2Epred__set_2EDELETE_2E2(A_27a,V0s_2E0,V1x_2E0) = c_2Epred__set_2EEMPTY_2E0(A_27a) )
<=> ( V0s_2E0 = c_2Epred__set_2EINSERT_2E2(A_27a,V1x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) ) ) ) ).
tff(thm_2Epred__set_2ECHOICE__SING,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( c_2Epred__set_2ECHOICE_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a))) = V0x_2E0 ) ).
tff(thm_2Epred__set_2EREST__SING,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( c_2Epred__set_2EREST_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a))) = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ).
tff(thm_2Epred__set_2ESING__IFF__EMPTY__REST,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESING_2E1(A_27a,V0s_2E0))
<=> ( ( V0s_2E0 != c_2Epred__set_2EEMPTY_2E0(A_27a) )
& ( c_2Epred__set_2EREST_2E1(A_27a,V0s_2E0) = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) ) ).
tff(thm_2Epred__set_2EIN__IMAGE,axiom,
! [A_27a: $tType,A_27b: $tType,V0y_2E0: A_27b,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( p(c_2Ebool_2EIN_2E2(A_27b,V0y_2E0,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V2f_2E0,V1s_2E0)))
<=> ? [V3x_2E0: A_27a] :
( ( V0y_2E0 = app_2E2(A_27a,A_27b,V2f_2E0,V3x_2E0) )
& p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V1s_2E0)) ) ) ).
tff(thm_2Epred__set_2EIMAGE__applied,axiom,
! [A_27a: $tType,A_27b: $tType,V0y_2E0: A_27b,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( p(c_2Epred__set_2EIMAGE_2E3(A_27a,A_27b,V2f_2E0,V1s_2E0,V0y_2E0))
<=> ? [V3x_2E0: A_27a] :
( ( V0y_2E0 = app_2E2(A_27a,A_27b,V2f_2E0,V3x_2E0) )
& p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V1s_2E0)) ) ) ).
tff(thm_2Epred__set_2EIMAGE__IN,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V1s_2E0))
=> ! [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : p(c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V2f_2E0,V0x_2E0),c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V2f_2E0,V1s_2E0))) ) ).
tff(thm_2Epred__set_2EIMAGE__EMPTY,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) = c_2Epred__set_2EEMPTY_2E0(A_27b) ) ).
tff(thm_2Epred__set_2EIMAGE__ID,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,A_27a)] :
( ! [V1x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,F0_2E0,V1x_2E0) = V1x_2E0 )
=> ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27a,A_27a,F0_2E0,V0s_2E0) = V0s_2E0 ) ) ).
tff(thm_2Epred__set_2EIMAGE__I,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27a,A_27a,c_2Ecombin_2EI_2E0(A_27a),V0s_2E0) = V0s_2E0 ) ).
tff(thm_2Epred__set_2EIMAGE__II,axiom,
! [A_27a: $tType] : ( c_2Epred__set_2EIMAGE_2E1(A_27a,A_27a,c_2Ecombin_2EI_2E0(A_27a)) = c_2Ecombin_2EI_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(thm_2Epred__set_2EIMAGE__COMPOSE,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27b,A_27c),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27a,A_27c,c_2Ecombin_2Eo_2E2(A_27a,A_27c,A_27b,V0f_2E0,V1g_2E0),V2s_2E0) = c_2Epred__set_2EIMAGE_2E2(A_27b,A_27c,V0f_2E0,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V1g_2E0,V2s_2E0)) ) ).
tff(thm_2Epred__set_2EIMAGE__INSERT,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1x_2E0: A_27a,V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V1x_2E0,V2s_2E0)) = c_2Epred__set_2EINSERT_2E2(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V1x_2E0),c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V2s_2E0)) ) ).
tff(thm_2Epred__set_2EIMAGE__EQ__EMPTY,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)] :
( ( c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V1f_2E0,V0s_2E0) = c_2Epred__set_2EEMPTY_2E0(A_27b) )
<=> ( V0s_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) ).
tff(thm_2Epred__set_2EIMAGE__DELETE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1x_2E0: A_27a,V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ~ p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V2s_2E0))
=> ( c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EDELETE_2E2(A_27a,V2s_2E0,V1x_2E0)) = c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V2s_2E0) ) ) ).
tff(thm_2Epred__set_2EIMAGE__UNION,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,c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,V2t_2E0)) = c_2Epred__set_2EUNION_2E2(A_27b,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)) ) ).
tff(thm_2Epred__set_2EIMAGE__SUBSET,axiom,
! [A_27a: $tType,A_27b: $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_2ESUBSET_2E2(A_27a,V0s_2E0,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),c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V2f_2E0,V1t_2E0))) ) ).
tff(thm_2Epred__set_2EIMAGE__INTER,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)] : p(c_2Epred__set_2ESUBSET_2E2(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EINTER_2E2(A_27a,V1s_2E0,V2t_2E0)),c_2Epred__set_2EINTER_2E2(A_27b,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)))) ).
tff(thm_2Epred__set_2EIMAGE__11,axiom,
! [A_27a: $tType,A_27b: $tType,V0s2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
( ( app_2E2(A_27a,A_27b,V2f_2E0,V3x_2E0) = app_2E2(A_27a,A_27b,V2f_2E0,V4y_2E0) )
<=> ( V3x_2E0 = V4y_2E0 ) )
=> ( ( c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V2f_2E0,V1s1_2E0) = c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V2f_2E0,V0s2_2E0) )
<=> ( V1s1_2E0 = V0s2_2E0 ) ) ) ).
tff(thm_2Epred__set_2EDISJOINT__IMAGE,axiom,
! [A_27a: $tType,A_27b: $tType,V0s2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
( ( app_2E2(A_27a,A_27b,V2f_2E0,V3x_2E0) = app_2E2(A_27a,A_27b,V2f_2E0,V4y_2E0) )
<=> ( V3x_2E0 = V4y_2E0 ) )
=> ( c_2Epred__set_2EDISJOINT_2E2(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V2f_2E0,V1s1_2E0),c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V2f_2E0,V0s2_2E0)) = c_2Epred__set_2EDISJOINT_2E2(A_27a,V1s1_2E0,V0s2_2E0) ) ) ).
tff(thm_2Epred__set_2EIMAGE__CONG,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),V2f_27_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V3s_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( ( V1s_2E0 = V3s_27_2E0 )
& ! [V4x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V3s_27_2E0))
=> ( app_2E2(A_27a,A_27b,V0f_2E0,V4x_2E0) = app_2E2(A_27a,A_27b,V2f_27_2E0,V4x_2E0) ) ) )
=> ( c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0) = c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V2f_27_2E0,V3s_27_2E0) ) ) ).
tff(thm_2Epred__set_2EGSPEC__IMAGE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(A_27a,A_27b,V0f_2E0) = c_2Epred__set_2EIMAGE_2E2(A_27b,A_27a,c_2Ecombin_2Eo_2E2(A_27b,A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2EFST_2E0(A_27a,tyop_2Emin_2Ebool),V0f_2E0),c_2Ecombin_2Eo_2E2(A_27b,tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2ESND_2E0(A_27a,tyop_2Emin_2Ebool),V0f_2E0)) ) ).
tff(thm_2Epred__set_2EIMAGE__IMAGE,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27c,A_27a),V2s_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EIMAGE_2E2(A_27c,A_27a,V1g_2E0,V2s_2E0)) = c_2Epred__set_2EIMAGE_2E2(A_27c,A_27b,c_2Ecombin_2Eo_2E2(A_27c,A_27b,A_27a,V0f_2E0,V1g_2E0),V2s_2E0) ) ).
tff(thm_2Epred__set_2EFORALL__IN__IMAGE,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27b,A_27a),V2s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ! [V3y_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,c_2Epred__set_2EIMAGE_2E2(A_27b,A_27a,V1f_2E0,V2s_2E0)))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3y_2E0)) )
<=> ! [V4x_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V4x_2E0,V2s_2E0))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,app_2E2(A_27b,A_27a,V1f_2E0,V4x_2E0))) ) ) ).
tff(thm_2Epred__set_2EEXISTS__IN__IMAGE,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27b,A_27a),V2s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ? [V3y_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,c_2Epred__set_2EIMAGE_2E2(A_27b,A_27a,V1f_2E0,V2s_2E0)))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3y_2E0)) )
<=> ? [V4x_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V4x_2E0,V2s_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,app_2E2(A_27b,A_27a,V1f_2E0,V4x_2E0))) ) ) ).
tff(thm_2Epred__set_2EINJ__IFF,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),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V2f_2E0,V1s_2E0,V0t_2E0))
<=> ( ! [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,V2f_2E0,V3x_2E0),V0t_2E0)) )
& ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V1s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V5y_2E0,V1s_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_2Epred__set_2EINJ__ID,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,A_27a)] :
( ! [V1x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,F0_2E0,V1x_2E0) = V1x_2E0 )
=> ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Epred__set_2EINJ_2E3(A_27a,A_27a,F0_2E0,V0s_2E0,V0s_2E0)) ) ).
tff(thm_2Epred__set_2EINJ__COMPOSE,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27b,A_27c),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4u_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V0f_2E0,V2s_2E0,V3t_2E0))
& p(c_2Epred__set_2EINJ_2E3(A_27b,A_27c,V1g_2E0,V3t_2E0,V4u_2E0)) )
=> p(c_2Epred__set_2EINJ_2E3(A_27a,A_27c,c_2Ecombin_2Eo_2E2(A_27a,A_27c,A_27b,V1g_2E0,V0f_2E0),V2s_2E0,V4u_2E0)) ) ).
tff(thm_2Epred__set_2EINJ__EMPTY,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V1s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a),V1s_2E0))
& ! [V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V0f_2E0,V2s_2E0,c_2Epred__set_2EEMPTY_2E0(A_27b)))
<=> ( V2s_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) ) ).
tff(thm_2Epred__set_2EINJ__DELETE,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_2EINJ_2E3(A_27a,A_27b,V2f_2E0,V0s_2E0,V1t_2E0))
=> ! [V3e_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3e_2E0,V0s_2E0))
=> p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V2f_2E0,c_2Epred__set_2EDELETE_2E2(A_27a,V0s_2E0,V3e_2E0),c_2Epred__set_2EDELETE_2E2(A_27b,V1t_2E0,app_2E2(A_27a,A_27b,V2f_2E0,V3e_2E0)))) ) ) ).
tff(thm_2Epred__set_2EINJ__INSERT,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1x_2E0: A_27a,V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V1x_2E0,V2s_2E0),V3t_2E0))
<=> ( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V0f_2E0,V2s_2E0,V3t_2E0))
& p(c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V1x_2E0),V3t_2E0))
& ! [V4y_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V4y_2E0,V2s_2E0))
& ( app_2E2(A_27a,A_27b,V0f_2E0,V1x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V4y_2E0) ) )
=> ( V1x_2E0 = V4y_2E0 ) ) ) ) ).
tff(thm_2Epred__set_2EINJ__EXTEND,axiom,
! [A_27a: $tType,A_27b: $tType,V0y_2E0: A_27b,V1x_2E0: A_27a,V2t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4b_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V4b_2E0,V3s_2E0,V2t_2E0))
& ~ p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V3s_2E0))
& ~ p(c_2Ebool_2EIN_2E2(A_27b,V0y_2E0,V2t_2E0)) )
=> p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,c_2Ecombin_2EUPDATE_2E3(A_27a,A_27b,V1x_2E0,V0y_2E0,V4b_2E0),c_2Epred__set_2EINSERT_2E2(A_27a,V1x_2E0,V3s_2E0),c_2Epred__set_2EINSERT_2E2(A_27b,V0y_2E0,V2t_2E0))) ) ).
tff(thm_2Epred__set_2EINJ__SUBSET,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_27b,tyop_2Emin_2Ebool),V3s0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4t0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V2t_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V3s0_2E0,V1s_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(A_27b,V2t_2E0,V4t0_2E0)) )
=> p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V0f_2E0,V3s0_2E0,V4t0_2E0)) ) ).
tff(thm_2Epred__set_2EINJ__IMAGE,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),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V2f_2E0,V1s_2E0,V0t_2E0))
=> p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V2f_2E0,V1s_2E0,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V2f_2E0,V1s_2E0))) ) ).
tff(thm_2Epred__set_2EINJ__IMAGE__SUBSET,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),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V2f_2E0,V1s_2E0,V0t_2E0))
=> p(c_2Epred__set_2ESUBSET_2E2(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V2f_2E0,V1s_2E0),V0t_2E0)) ) ).
tff(thm_2Epred__set_2ESURJ__ID,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,A_27a)] :
( ! [V1x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,F0_2E0,V1x_2E0) = V1x_2E0 )
=> ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Epred__set_2ESURJ_2E3(A_27a,A_27a,F0_2E0,V0s_2E0,V0s_2E0)) ) ).
tff(thm_2Epred__set_2ESURJ__COMPOSE,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27b,A_27c),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4u_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2ESURJ_2E3(A_27a,A_27b,V0f_2E0,V2s_2E0,V3t_2E0))
& p(c_2Epred__set_2ESURJ_2E3(A_27b,A_27c,V1g_2E0,V3t_2E0,V4u_2E0)) )
=> p(c_2Epred__set_2ESURJ_2E3(A_27a,A_27c,c_2Ecombin_2Eo_2E2(A_27a,A_27c,A_27b,V1g_2E0,V0f_2E0),V2s_2E0,V4u_2E0)) ) ).
tff(thm_2Epred__set_2ESURJ__EMPTY,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V1s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESURJ_2E3(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a),V1s_2E0))
<=> ( V1s_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27b) ) )
& ! [V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESURJ_2E3(A_27a,A_27b,V0f_2E0,V2s_2E0,c_2Epred__set_2EEMPTY_2E0(A_27b)))
<=> ( V2s_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) ) ).
tff(thm_2Epred__set_2EIMAGE__SURJ,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_27b,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESURJ_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V2t_2E0))
<=> ( c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0) = V2t_2E0 ) ) ).
tff(thm_2Epred__set_2ESURJ__IMAGE,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)] : p(c_2Epred__set_2ESURJ_2E3(A_27a,A_27b,V1f_2E0,V0s_2E0,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V1f_2E0,V0s_2E0))) ).
tff(thm_2Epred__set_2ESURJ__IMP__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)] :
( ? [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : p(c_2Epred__set_2ESURJ_2E3(A_27a,A_27b,V2f_2E0,V0s_2E0,V1t_2E0))
=> ? [V3g_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : p(c_2Epred__set_2EINJ_2E3(A_27b,A_27a,V3g_2E0,V1t_2E0,V0s_2E0)) ) ).
tff(thm_2Epred__set_2EBIJ__ID,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,A_27a)] :
( ! [V1x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,F0_2E0,V1x_2E0) = V1x_2E0 )
=> ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27a,F0_2E0,V0s_2E0,V0s_2E0)) ) ).
tff(thm_2Epred__set_2EBIJ__IMP__11,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EUNIV_2E0(A_27a),c_2Epred__set_2EUNIV_2E0(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 ) ) ) ).
tff(thm_2Epred__set_2EBIJ__EMPTY,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V1s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a),V1s_2E0))
<=> ( V1s_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27b) ) )
& ! [V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V0f_2E0,V2s_2E0,c_2Epred__set_2EEMPTY_2E0(A_27b)))
<=> ( V2s_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) ) ).
tff(thm_2Epred__set_2EBIJ__COMPOSE,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27b,A_27c),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4u_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V0f_2E0,V2s_2E0,V3t_2E0))
& p(c_2Epred__set_2EBIJ_2E3(A_27b,A_27c,V1g_2E0,V3t_2E0,V4u_2E0)) )
=> p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27c,c_2Ecombin_2Eo_2E2(A_27a,A_27c,A_27b,V1g_2E0,V0f_2E0),V2s_2E0,V4u_2E0)) ) ).
tff(thm_2Epred__set_2EBIJ__DELETE,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_2EBIJ_2E3(A_27a,A_27b,V2f_2E0,V0s_2E0,V1t_2E0))
=> ! [V3e_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3e_2E0,V0s_2E0))
=> p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V2f_2E0,c_2Epred__set_2EDELETE_2E2(A_27a,V0s_2E0,V3e_2E0),c_2Epred__set_2EDELETE_2E2(A_27b,V1t_2E0,app_2E2(A_27a,A_27b,V2f_2E0,V3e_2E0)))) ) ) ).
tff(thm_2Epred__set_2EINJ__IMAGE__BIJ,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)] : p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V1f_2E0,V0s_2E0,V2t_2E0))
=> p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V1f_2E0,V0s_2E0,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V1f_2E0,V0s_2E0))) ) ).
tff(thm_2Epred__set_2EINJ__BIJ__SUBSET,axiom,
! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s0_2E0,V2s_2E0))
& p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V3f_2E0,V2s_2E0,V0t_2E0)) )
=> p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V3f_2E0,V1s0_2E0,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V3f_2E0,V1s0_2E0))) ) ).
tff(thm_2Epred__set_2EBIJ__SYM__IMP,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_2EBIJ_2E3(A_27a,A_27b,V2f_2E0,V0s_2E0,V1t_2E0))
=> ? [V3g_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : p(c_2Epred__set_2EBIJ_2E3(A_27b,A_27a,V3g_2E0,V1t_2E0,V0s_2E0)) ) ).
tff(thm_2Epred__set_2EBIJ__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)] :
( ? [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V2f_2E0,V0s_2E0,V1t_2E0))
<=> ? [V3g_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : p(c_2Epred__set_2EBIJ_2E3(A_27b,A_27a,V3g_2E0,V1t_2E0,V0s_2E0)) ) ).
tff(thm_2Epred__set_2EBIJ__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_27c,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ( ? [V3f_2E0: tyop_2Emin_2Efun(A_27a,A_27c)] : p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27c,V3f_2E0,V0s_2E0,V1t_2E0))
& ? [V4g_2E0: tyop_2Emin_2Efun(A_27c,A_27b)] : p(c_2Epred__set_2EBIJ_2E3(A_27c,A_27b,V4g_2E0,V1t_2E0,V2u_2E0)) )
=> ? [V5h_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V5h_2E0,V0s_2E0,V2u_2E0)) ) ).
tff(thm_2Epred__set_2EBIJ__INV,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_27b,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V2t_2E0))
=> ? [V3g_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Epred__set_2EBIJ_2E3(A_27b,A_27a,V3g_2E0,V2t_2E0,V1s_2E0))
& ! [V4x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V1s_2E0))
=> ( c_2Ecombin_2Eo_2E3(A_27a,A_27a,A_27b,V3g_2E0,V0f_2E0,V4x_2E0) = V4x_2E0 ) )
& ! [V5x_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V5x_2E0,V2t_2E0))
=> ( c_2Ecombin_2Eo_2E3(A_27b,A_27b,A_27a,V0f_2E0,V3g_2E0,V5x_2E0) = V5x_2E0 ) ) ) ) ).
tff(thm_2Epred__set_2EIN__FUNSET,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0,c_2Epred__set_2EFUNSET_2E2(A_27a,A_27b,V1P_2E0,V2Q_2E0)))
<=> ! [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V1P_2E0))
=> p(c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V3x_2E0),V2Q_2E0)) ) ) ).
tff(thm_2Epred__set_2EFUNSET__applied,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFUNSET_2E3(A_27a,A_27b,V1P_2E0,V2Q_2E0,V0f_2E0))
<=> ! [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V1P_2E0))
=> p(c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V3x_2E0),V2Q_2E0)) ) ) ).
tff(thm_2Epred__set_2EIN__DFUNSET,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0,c_2Epred__set_2EDFUNSET_2E2(A_27a,A_27b,V1P_2E0,V2Q_2E0)))
<=> ! [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V1P_2E0))
=> p(c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V3x_2E0),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0,V3x_2E0))) ) ) ).
tff(thm_2Epred__set_2EDFUNSET__applied,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( p(c_2Epred__set_2EDFUNSET_2E3(A_27a,A_27b,V1P_2E0,V2Q_2E0,V0f_2E0))
<=> ! [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V1P_2E0))
=> p(c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V3x_2E0),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2Q_2E0,V3x_2E0))) ) ) ).
tff(thm_2Epred__set_2EFUNSET__THM,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),V3x_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0,c_2Epred__set_2EFUNSET_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)))
& 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)) ) ).
tff(thm_2Epred__set_2EUNIV__FUNSET__UNIV,axiom,
! [A_27a: $tType,A_27b: $tType] : ( c_2Epred__set_2EFUNSET_2E2(A_27a,A_27b,c_2Epred__set_2EUNIV_2E0(A_27a),c_2Epred__set_2EUNIV_2E0(A_27b)) = c_2Epred__set_2EUNIV_2E0(tyop_2Emin_2Efun(A_27a,A_27b)) ) ).
tff(thm_2Epred__set_2EFUNSET__DFUNSET,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFUNSET_2E2(A_27a,A_27b,V0x_2E0,V1y_2E0) = c_2Epred__set_2EDFUNSET_2E2(A_27a,A_27b,V0x_2E0,c_2Ecombin_2EK_2E1(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),A_27a,V1y_2E0)) ) ).
tff(thm_2Epred__set_2EEMPTY__FUNSET,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFUNSET_2E2(A_27a,A_27b,c_2Epred__set_2EEMPTY_2E0(A_27a),V0s_2E0) = c_2Epred__set_2EUNIV_2E0(tyop_2Emin_2Efun(A_27a,A_27b)) ) ).
tff(thm_2Epred__set_2EFUNSET__EMPTY,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)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0,c_2Epred__set_2EFUNSET_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_2Epred__set_2EFUNSET__INTER,axiom,
! [A_27a: $tType,A_27b: $tType,V0a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1b_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2c_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFUNSET_2E2(A_27a,A_27b,V0a_2E0,c_2Epred__set_2EINTER_2E2(A_27b,V1b_2E0,V2c_2E0)) = c_2Epred__set_2EINTER_2E2(tyop_2Emin_2Efun(A_27a,A_27b),c_2Epred__set_2EFUNSET_2E2(A_27a,A_27b,V0a_2E0,V1b_2E0),c_2Epred__set_2EFUNSET_2E2(A_27a,A_27b,V0a_2E0,V2c_2E0)) ) ).
tff(thm_2Epred__set_2ESCHROEDER__CLOSE,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27a),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Epred__set_2Eschroeder__close_2E2(A_27a,V1f_2E0,V2s_2E0)))
<=> ? [V3n_2E0: tyop_2Enum_2Enum] : p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Earithmetic_2EFUNPOW_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E1(A_27a,A_27a,V1f_2E0),V3n_2E0,V2s_2E0))) ) ).
tff(thm_2Epred__set_2ESCHROEDER__CLOSED,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27a),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27a,V0f_2E0,c_2Epred__set_2Eschroeder__close_2E2(A_27a,V0f_2E0,V1s_2E0)),c_2Epred__set_2Eschroeder__close_2E2(A_27a,V0f_2E0,V1s_2E0))) ).
tff(thm_2Epred__set_2ESCHROEDER__CLOSE__SUBSET,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27a),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,c_2Epred__set_2Eschroeder__close_2E2(A_27a,V0f_2E0,V1s_2E0))) ).
tff(thm_2Epred__set_2ESCHROEDER__CLOSE__SET,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27a),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0,c_2Epred__set_2EFUNSET_2E2(A_27a,A_27a,V1s_2E0,V1s_2E0)))
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V2t_2E0,V1s_2E0)) )
=> p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Epred__set_2Eschroeder__close_2E2(A_27a,V0f_2E0,V2t_2E0),V1s_2E0)) ) ).
tff(thm_2Epred__set_2ESCHROEDER__BERNSTEIN__AUTO,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_2ESUBSET_2E2(A_27a,V1t_2E0,V0s_2E0))
& ? [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27a)] : p(c_2Epred__set_2EINJ_2E3(A_27a,A_27a,V2f_2E0,V0s_2E0,V1t_2E0)) )
=> ? [V3g_2E0: tyop_2Emin_2Efun(A_27a,A_27a)] : p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27a,V3g_2E0,V0s_2E0,V1t_2E0)) ) ).
tff(thm_2Epred__set_2ESCHROEDER__BERNSTEIN,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_2EINJ_2E3(A_27a,A_27b,V2f_2E0,V0s_2E0,V1t_2E0))
& ? [V3g_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : p(c_2Epred__set_2EINJ_2E3(A_27b,A_27a,V3g_2E0,V1t_2E0,V0s_2E0)) )
=> ? [V4h_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V4h_2E0,V0s_2E0,V1t_2E0)) ) ).
tff(thm_2Epred__set_2EBIJ__INJ__SURJ,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_2EINJ_2E3(A_27a,A_27b,V2f_2E0,V0s_2E0,V1t_2E0))
& ? [V3g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : p(c_2Epred__set_2ESURJ_2E3(A_27a,A_27b,V3g_2E0,V0s_2E0,V1t_2E0)) )
=> ? [V4h_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V4h_2E0,V0s_2E0,V1t_2E0)) ) ).
tff(thm_2Epred__set_2EBIJ__ALT,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))))] :
( ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3y_2E0: A_27b,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V4x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,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,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V1s_2E0),V3y_2E0),V0f_2E0),V4x_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V1s_2E0))
& ( V3y_2E0 = app_2E2(A_27a,A_27b,V0f_2E0,V4x_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)] :
( p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V2t_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0,c_2Epred__set_2EFUNSET_2E2(A_27a,A_27b,V1s_2E0,V2t_2E0)))
& ! [V3y_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V3y_2E0,V2t_2E0))
=> p(c_2Ebool_2E_3F_21_2E1(A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,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,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V1s_2E0),V3y_2E0),V0f_2E0))) ) ) ) ) ).
tff(thm_2Epred__set_2EBIJ__INSERT__IMP,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1e_2E0: A_27a,V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ( ~ p(c_2Ebool_2EIN_2E2(A_27a,V1e_2E0,V2s_2E0))
& p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V1e_2E0,V2s_2E0),V3t_2E0)) )
=> ? [V4u_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ( c_2Epred__set_2EINSERT_2E2(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V1e_2E0),V4u_2E0) = V3t_2E0 )
& ~ p(c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V1e_2E0),V4u_2E0))
& p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V0f_2E0,V2s_2E0,V4u_2E0)) ) ) ).
tff(thm_2Epred__set_2EBIJ__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_27b,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V2t_2E0))
=> ( V2t_2E0 = c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0) ) ) ).
tff(thm_2Epred__set_2ELINV__OPT__THM,axiom,
! [A_27a: $tType,A_27b: $tType,V0y_2E0: A_27b,V1x_2E0: A_27a,V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ( c_2Epred__set_2ELINV__OPT_2E3(A_27a,A_27b,V3f_2E0,V2s_2E0,V0y_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V1x_2E0) )
=> ( p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V2s_2E0))
& ( app_2E2(A_27a,A_27b,V3f_2E0,V1x_2E0) = V0y_2E0 ) ) ) ).
tff(thm_2Epred__set_2EINJ__LINV__OPT__IMAGE,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : p(c_2Epred__set_2EINJ_2E3(A_27a,tyop_2Eoption_2Eoption(A_27b),c_2Epred__set_2ELINV__OPT_2E2(A_27b,A_27a,V1f_2E0,V0s_2E0),c_2Epred__set_2EIMAGE_2E2(A_27b,A_27a,V1f_2E0,V0s_2E0),c_2Epred__set_2EIMAGE_2E2(A_27b,tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E0(A_27b),V0s_2E0))) ).
tff(thm_2Epred__set_2EINJ__LINV__OPT,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),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V2f_2E0,V1s_2E0,V0t_2E0))
=> ! [V3x_2E0: A_27a,V4y_2E0: A_27b] :
( ( c_2Epred__set_2ELINV__OPT_2E3(A_27a,A_27b,V2f_2E0,V1s_2E0,V4y_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V3x_2E0) )
<=> ( ( V4y_2E0 = app_2E2(A_27a,A_27b,V2f_2E0,V3x_2E0) )
& p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V1s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27b,V4y_2E0,V0t_2E0)) ) ) ) ).
tff(thm_2Epred__set_2ELINV__DEF,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_27b,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V2t_2E0))
=> ! [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V1s_2E0))
=> ( c_2Epred__set_2ELINV_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,app_2E2(A_27a,A_27b,V0f_2E0,V3x_2E0)) = V3x_2E0 ) ) ) ).
tff(thm_2Epred__set_2EBIJ__LINV__INV,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_27b,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V2t_2E0))
=> ! [V3x_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V3x_2E0,V2t_2E0))
=> ( app_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2ELINV_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V3x_2E0)) = V3x_2E0 ) ) ) ).
tff(thm_2Epred__set_2EBIJ__LINV__BIJ,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_27b,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V2t_2E0))
=> p(c_2Epred__set_2EBIJ_2E3(A_27b,A_27a,c_2Epred__set_2ELINV_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0),V2t_2E0,V1s_2E0)) ) ).
tff(thm_2Epred__set_2EBIJ__IFF__INV,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_27b,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V2t_2E0))
<=> ( ! [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)) )
& ? [V4g_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( ! [V5x_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V5x_2E0,V2t_2E0))
=> p(c_2Ebool_2EIN_2E2(A_27a,app_2E2(A_27b,A_27a,V4g_2E0,V5x_2E0),V1s_2E0)) )
& ! [V6x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V6x_2E0,V1s_2E0))
=> ( app_2E2(A_27b,A_27a,V4g_2E0,app_2E2(A_27a,A_27b,V0f_2E0,V6x_2E0)) = V6x_2E0 ) )
& ! [V7x_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V7x_2E0,V2t_2E0))
=> ( app_2E2(A_27a,A_27b,V0f_2E0,app_2E2(A_27b,A_27a,V4g_2E0,V7x_2E0)) = V7x_2E0 ) ) ) ) ) ).
tff(thm_2Epred__set_2EBIJ__INSERT,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1e_2E0: A_27a,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,c_2Epred__set_2EINSERT_2E2(A_27a,V1e_2E0,V2s_2E0),V3t_2E0))
<=> ( ( ~ p(c_2Ebool_2EIN_2E2(A_27a,V1e_2E0,V2s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V1e_2E0),V3t_2E0))
& p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V0f_2E0,V2s_2E0,c_2Epred__set_2EDELETE_2E2(A_27b,V3t_2E0,app_2E2(A_27a,A_27b,V0f_2E0,V1e_2E0)))) )
| ( p(c_2Ebool_2EIN_2E2(A_27a,V1e_2E0,V2s_2E0))
& p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V0f_2E0,V2s_2E0,V3t_2E0)) ) ) ) ).
tff(thm_2Epred__set_2ERINV__DEF,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_27b,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESURJ_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V2t_2E0))
=> ! [V3x_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V3x_2E0,V2t_2E0))
=> ( app_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2ERINV_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V3x_2E0)) = V3x_2E0 ) ) ) ).
tff(thm_2Epred__set_2ESURJ__INJ__INV,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),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( p(c_2Epred__set_2ESURJ_2E3(A_27a,A_27b,V2f_2E0,V1s_2E0,V0t_2E0))
=> ? [V3g_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Epred__set_2EINJ_2E3(A_27b,A_27a,V3g_2E0,V0t_2E0,V1s_2E0))
& ! [V4y_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V4y_2E0,V0t_2E0))
=> ( app_2E2(A_27a,A_27b,V2f_2E0,app_2E2(A_27b,A_27a,V3g_2E0,V4y_2E0)) = V4y_2E0 ) ) ) ) ).
tff(thm_2Epred__set_2EFINITE__EMPTY,axiom,
! [A_27a: $tType] : p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EEMPTY_2E0(A_27a))) ).
tff(thm_2Epred__set_2EFINITE__INDUCT,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)))
& ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
& p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V1s_2E0)) )
=> ! [V2e_2E0: A_27a] :
( ~ p(c_2Ebool_2EIN_2E2(A_27a,V2e_2E0,V1s_2E0))
=> p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V2e_2E0,V1s_2E0))) ) ) )
=> ! [V3s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V3s_2E0))
=> p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V3s_2E0)) ) ) ).
tff(thm_2Epred__set_2EFINITE__INSERT,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,V1s_2E0)) = c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0) ) ).
tff(thm_2Epred__set_2EFINITE__DELETE,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EDELETE_2E2(A_27a,V1s_2E0,V0x_2E0)) = c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0) ) ).
tff(thm_2Epred__set_2EFINITE__REST,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_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EREST_2E1(A_27a,V0s_2E0))) ) ).
tff(thm_2Epred__set_2EFINITE__REST__EQ,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EREST_2E1(A_27a,V0s_2E0)) = c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0) ) ).
tff(thm_2Epred__set_2EFINITE__UNION,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,c_2Epred__set_2EUNION_2E2(A_27a,V0s_2E0,V1t_2E0)))
<=> ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
& p(c_2Epred__set_2EFINITE_2E1(A_27a,V1t_2E0)) ) ) ).
tff(thm_2Epred__set_2EINTER__FINITE,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
=> ! [V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EINTER_2E2(A_27a,V0s_2E0,V1t_2E0))) ) ).
tff(thm_2Epred__set_2ESUBSET__FINITE,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
=> ! [V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1t_2E0,V0s_2E0))
=> p(c_2Epred__set_2EFINITE_2E1(A_27a,V1t_2E0)) ) ) ).
tff(thm_2Epred__set_2ESUBSET__FINITE__I,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_2ESUBSET_2E2(A_27a,V1t_2E0,V0s_2E0)) )
=> p(c_2Epred__set_2EFINITE_2E1(A_27a,V1t_2E0)) ) ).
tff(thm_2Epred__set_2EPSUBSET__FINITE,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
=> ! [V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EPSUBSET_2E2(A_27a,V1t_2E0,V0s_2E0))
=> p(c_2Epred__set_2EFINITE_2E1(A_27a,V1t_2E0)) ) ) ).
tff(thm_2Epred__set_2EFINITE__DIFF,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
=> ! [V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EDIFF_2E2(A_27a,V0s_2E0,V1t_2E0))) ) ).
tff(thm_2Epred__set_2EFINITE__DIFF__down,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EDIFF_2E2(A_27a,V0P_2E0,V1Q_2E0)))
& p(c_2Epred__set_2EFINITE_2E1(A_27a,V1Q_2E0)) )
=> p(c_2Epred__set_2EFINITE_2E1(A_27a,V0P_2E0)) ) ).
tff(thm_2Epred__set_2EFINITE__SING,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)))) ).
tff(thm_2Epred__set_2ESING__FINITE,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESING_2E1(A_27a,V0s_2E0))
=> p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0)) ) ).
tff(thm_2Epred__set_2EIMAGE__FINITE,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))
=> ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : p(c_2Epred__set_2EFINITE_2E1(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V1f_2E0,V0s_2E0))) ) ).
tff(thm_2Epred__set_2EFINITELY__INJECTIVE__IMAGE__FINITE,axiom,
! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
( ! [V1x_2E0: A_27b,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V1x_2E0),V0f_2E0),V2y_2E0))
<=> ( V1x_2E0 = app_2E2(A_27a,A_27b,V0f_2E0,V2y_2E0) ) )
=> ( ! [V1x_2E0: A_27b,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2y_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(A_27b,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,V1x_2E0),V0f_2E0),V2y_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V2y_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V1x_2E0),V0f_2E0),V2y_2E0)) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V1x_2E0: A_27b] : p(c_2Epred__set_2EFINITE_2E1(A_27a,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(A_27b,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,V1x_2E0),V0f_2E0))))
=> ! [V3s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V3s_2E0)) = c_2Epred__set_2EFINITE_2E1(A_27a,V3s_2E0) ) ) ) ) ).
tff(thm_2Epred__set_2EINJECTIVE__IMAGE__FINITE,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)] : ( c_2Epred__set_2EFINITE_2E1(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V3s_2E0)) = c_2Epred__set_2EFINITE_2E1(A_27a,V3s_2E0) ) ) ).
tff(thm_2Epred__set_2EFINITE__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),V2t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V2t_2E0))
& p(c_2Epred__set_2EFINITE_2E1(A_27b,V2t_2E0)) )
=> p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0)) ) ).
tff(thm_2Epred__set_2EREL__RESTRICT__EMPTY,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EREL__RESTRICT_2E2(A_27a,V0R_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) = c_2Erelation_2EEMPTY__REL_2E0(A_27a) ) ).
tff(thm_2Epred__set_2EREL__RESTRICT__SUBSET,axiom,
! [A_27a: $tType,V0s2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s1_2E0,V0s2_2E0))
=> p(c_2Erelation_2ERSUBSET_2E2(A_27a,A_27a,c_2Epred__set_2EREL__RESTRICT_2E2(A_27a,V2R_2E0,V1s1_2E0),c_2Epred__set_2EREL__RESTRICT_2E2(A_27a,V2R_2E0,V0s2_2E0))) ) ).
tff(thm_2Epred__set_2ECARD__EMPTY,axiom,
! [A_27a: $tType] : ( c_2Epred__set_2ECARD_2E1(A_27a,c_2Epred__set_2EEMPTY_2E0(A_27a)) = c_2Enum_2E0_2E0 ) ).
tff(thm_2Epred__set_2ECARD__INSERT,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
=> ! [V1x_2E0: A_27a] : ( c_2Epred__set_2ECARD_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V1x_2E0,V0s_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V0s_2E0),c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0),c_2Enum_2ESUC_2E1(c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0))) ) ) ).
tff(thm_2Epred__set_2ECARD__EQ__0,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
=> ( ( c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0) = c_2Enum_2E0_2E0 )
<=> ( V0s_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) ) ).
tff(thm_2Epred__set_2ECARD__DELETE,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
=> ! [V1x_2E0: A_27a] : ( c_2Epred__set_2ECARD_2E1(A_27a,c_2Epred__set_2EDELETE_2E2(A_27a,V0s_2E0,V1x_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V0s_2E0),c_2Earithmetic_2E_2D_2E2(c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0)) ) ) ).
tff(thm_2Epred__set_2ECARD__INTER__LESS__EQ,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
=> ! [V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Earithmetic_2E_3C_3D_2E2(c_2Epred__set_2ECARD_2E1(A_27a,c_2Epred__set_2EINTER_2E2(A_27a,V0s_2E0,V1t_2E0)),c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0))) ) ).
tff(thm_2Epred__set_2ECARD__UNION,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
=> ! [V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1t_2E0))
=> ( c_2Earithmetic_2E_2B_2E2(c_2Epred__set_2ECARD_2E1(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V0s_2E0,V1t_2E0)),c_2Epred__set_2ECARD_2E1(A_27a,c_2Epred__set_2EINTER_2E2(A_27a,V0s_2E0,V1t_2E0))) = c_2Earithmetic_2E_2B_2E2(c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0),c_2Epred__set_2ECARD_2E1(A_27a,V1t_2E0)) ) ) ) ).
tff(thm_2Epred__set_2ECARD__UNION__EQN,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)) )
=> ( c_2Epred__set_2ECARD_2E1(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V0s_2E0,V1t_2E0)) = c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2E_2B_2E2(c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0),c_2Epred__set_2ECARD_2E1(A_27a,V1t_2E0)),c_2Epred__set_2ECARD_2E1(A_27a,c_2Epred__set_2EINTER_2E2(A_27a,V0s_2E0,V1t_2E0))) ) ) ).
tff(thm_2Epred__set_2ECARD__SUBSET,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
=> ! [V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1t_2E0,V0s_2E0))
=> p(c_2Earithmetic_2E_3C_3D_2E2(c_2Epred__set_2ECARD_2E1(A_27a,V1t_2E0),c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0))) ) ) ).
tff(thm_2Epred__set_2ECARD__PSUBSET,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
=> ! [V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EPSUBSET_2E2(A_27a,V1t_2E0,V0s_2E0))
=> p(c_2Eprim__rec_2E_3C_2E2(c_2Epred__set_2ECARD_2E1(A_27a,V1t_2E0),c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0))) ) ) ).
tff(thm_2Epred__set_2ESUBSET__EQ__CARD,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
=> ! [V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1t_2E0))
& ( c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0) = c_2Epred__set_2ECARD_2E1(A_27a,V1t_2E0) )
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s_2E0,V1t_2E0)) )
=> ( V0s_2E0 = V1t_2E0 ) ) ) ).
tff(thm_2Epred__set_2ECARD__SING,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( c_2Epred__set_2ECARD_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a))) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ) ).
tff(thm_2Epred__set_2ESING__IFF__CARD1,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESING_2E1(A_27a,V0s_2E0))
<=> ( ( c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) )
& p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0)) ) ) ).
tff(thm_2Epred__set_2ECARD__DIFF,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0t_2E0))
=> ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
=> ( c_2Epred__set_2ECARD_2E1(A_27a,c_2Epred__set_2EDIFF_2E2(A_27a,V1s_2E0,V0t_2E0)) = c_2Earithmetic_2E_2D_2E2(c_2Epred__set_2ECARD_2E1(A_27a,V1s_2E0),c_2Epred__set_2ECARD_2E1(A_27a,c_2Epred__set_2EINTER_2E2(A_27a,V1s_2E0,V0t_2E0))) ) ) ) ).
tff(thm_2Epred__set_2ECARD__DIFF__EQN,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
=> ( c_2Epred__set_2ECARD_2E1(A_27a,c_2Epred__set_2EDIFF_2E2(A_27a,V1s_2E0,V0t_2E0)) = c_2Earithmetic_2E_2D_2E2(c_2Epred__set_2ECARD_2E1(A_27a,V1s_2E0),c_2Epred__set_2ECARD_2E1(A_27a,c_2Epred__set_2EINTER_2E2(A_27a,V1s_2E0,V0t_2E0))) ) ) ).
tff(thm_2Epred__set_2ELESS__CARD__DIFF,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0t_2E0))
=> ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
=> ( p(c_2Eprim__rec_2E_3C_2E2(c_2Epred__set_2ECARD_2E1(A_27a,V0t_2E0),c_2Epred__set_2ECARD_2E1(A_27a,V1s_2E0)))
=> p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,c_2Epred__set_2ECARD_2E1(A_27a,c_2Epred__set_2EDIFF_2E2(A_27a,V1s_2E0,V0t_2E0)))) ) ) ) ).
tff(thm_2Epred__set_2EBIJ__FINITE,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_27b,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V2t_2E0))
& p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0)) )
=> p(c_2Epred__set_2EFINITE_2E1(A_27b,V2t_2E0)) ) ).
tff(thm_2Epred__set_2EBIJ__FINITE__SUBSET,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EBIJ_2E3(tyop_2Enum_2Enum,A_27a,V0f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),V1s_2E0))
& p(c_2Epred__set_2EFINITE_2E1(A_27a,V2t_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V2t_2E0,V1s_2E0)) )
=> ? [V3N_2E0: tyop_2Enum_2Enum] :
! [V4n_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V3N_2E0,V4n_2E0))
=> ~ p(c_2Ebool_2EIN_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,A_27a,V0f_2E0,V4n_2E0),V2t_2E0)) ) ) ).
tff(thm_2Epred__set_2EFINITE__BIJ,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_27b,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
& p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V2t_2E0)) )
=> ( p(c_2Epred__set_2EFINITE_2E1(A_27b,V2t_2E0))
& ( c_2Epred__set_2ECARD_2E1(A_27a,V1s_2E0) = c_2Epred__set_2ECARD_2E1(A_27b,V2t_2E0) ) ) ) ).
tff(thm_2Epred__set_2EFINITE__BIJ__CARD,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_27b,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
& p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V2t_2E0)) )
=> ( c_2Epred__set_2ECARD_2E1(A_27a,V1s_2E0) = c_2Epred__set_2ECARD_2E1(A_27b,V2t_2E0) ) ) ).
tff(thm_2Epred__set_2EFINITE__BIJ__CARD__EQ,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))
=> ! [V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ( p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V2f_2E0,V0S_2E0,V1t_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) ) ) ) ).
tff(thm_2Epred__set_2ECARD__INJ__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)] :
( ( ! [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_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_2Epred__set_2ECARD__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)] :
( 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_2Epred__set_2ESURJ__CARD,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))
=> ! [V2t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESURJ_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V2t_2E0))
=> ( p(c_2Epred__set_2EFINITE_2E1(A_27b,V2t_2E0))
& p(c_2Earithmetic_2E_3C_3D_2E2(c_2Epred__set_2ECARD_2E1(A_27b,V2t_2E0),c_2Epred__set_2ECARD_2E1(A_27a,V1s_2E0))) ) ) ) ).
tff(thm_2Epred__set_2EFINITE__SURJ,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),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
& p(c_2Epred__set_2ESURJ_2E3(A_27a,A_27b,V2f_2E0,V1s_2E0,V0t_2E0)) )
=> p(c_2Epred__set_2EFINITE_2E1(A_27b,V0t_2E0)) ) ).
tff(thm_2Epred__set_2EFINITE__SURJ__BIJ,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),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
& p(c_2Epred__set_2ESURJ_2E3(A_27a,A_27b,V2f_2E0,V1s_2E0,V0t_2E0))
& ( c_2Epred__set_2ECARD_2E1(A_27b,V0t_2E0) = c_2Epred__set_2ECARD_2E1(A_27a,V1s_2E0) ) )
=> p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V2f_2E0,V1s_2E0,V0t_2E0)) ) ).
tff(thm_2Epred__set_2EFINITE__COMPLETE__INDUCTION,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ! [V1x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V2y_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EPSUBSET_2E2(A_27a,V2y_2E0,V1x_2E0))
=> p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V2y_2E0)) )
=> ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1x_2E0))
=> p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V1x_2E0)) ) )
=> ! [V3x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V3x_2E0))
=> p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0)) ) ) ).
tff(thm_2Epred__set_2EINJ__CARD__IMAGE,axiom,
! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V2s_2E0))
=> ( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V1f_2E0,V2s_2E0,V0t_2E0))
=> ( c_2Epred__set_2ECARD_2E1(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V1f_2E0,V2s_2E0)) = c_2Epred__set_2ECARD_2E1(A_27a,V2s_2E0) ) ) ) ).
tff(thm_2Epred__set_2EINJ__CARD,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_27b,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V2t_2E0))
& p(c_2Epred__set_2EFINITE_2E1(A_27b,V2t_2E0)) )
=> p(c_2Earithmetic_2E_3C_3D_2E2(c_2Epred__set_2ECARD_2E1(A_27a,V1s_2E0),c_2Epred__set_2ECARD_2E1(A_27b,V2t_2E0))) ) ).
tff(thm_2Epred__set_2EPHP,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_27b,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27b,V2t_2E0))
& p(c_2Eprim__rec_2E_3C_2E2(c_2Epred__set_2ECARD_2E1(A_27b,V2t_2E0),c_2Epred__set_2ECARD_2E1(A_27a,V1s_2E0))) )
=> ~ p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V2t_2E0)) ) ).
tff(thm_2Epred__set_2EINJ__CARD__IMAGE__EQ,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),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V2f_2E0,V1s_2E0,V0t_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,V2f_2E0,V1s_2E0)) = c_2Epred__set_2ECARD_2E1(A_27a,V1s_2E0) ) ) ) ).
tff(thm_2Epred__set_2EIN__COUNT,axiom,
! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : ( c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V0m_2E0,c_2Epred__set_2Ecount_2E1(V1n_2E0)) = c_2Eprim__rec_2E_3C_2E2(V0m_2E0,V1n_2E0) ) ).
tff(thm_2Epred__set_2ECOUNT__applied,axiom,
! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : ( c_2Epred__set_2Ecount_2E2(V1n_2E0,V0m_2E0) = c_2Eprim__rec_2E_3C_2E2(V0m_2E0,V1n_2E0) ) ).
tff(thm_2Epred__set_2ECOUNT__ZERO,axiom,
c_2Epred__set_2Ecount_2E1(c_2Enum_2E0_2E0) = c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum) ).
tff(thm_2Epred__set_2ECOUNT__SUC,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Epred__set_2Ecount_2E1(c_2Enum_2ESUC_2E1(V0n_2E0)) = c_2Epred__set_2EINSERT_2E2(tyop_2Enum_2Enum,V0n_2E0,c_2Epred__set_2Ecount_2E1(V0n_2E0)) ) ).
tff(thm_2Epred__set_2EFINITE__COUNT,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] : p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,c_2Epred__set_2Ecount_2E1(V0n_2E0))) ).
tff(thm_2Epred__set_2ECARD__COUNT,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Epred__set_2ECARD_2E1(tyop_2Enum_2Enum,c_2Epred__set_2Ecount_2E1(V0n_2E0)) = V0n_2E0 ) ).
tff(thm_2Epred__set_2ECOUNT__11,axiom,
! [V0n2_2E0: tyop_2Enum_2Enum,V1n1_2E0: tyop_2Enum_2Enum] :
( ( c_2Epred__set_2Ecount_2E1(V1n1_2E0) = c_2Epred__set_2Ecount_2E1(V0n2_2E0) )
<=> ( V1n1_2E0 = V0n2_2E0 ) ) ).
tff(thm_2Epred__set_2ENOT__IN__FINITE,axiom,
! [A_27a: $tType] :
( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)))
<=> ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
=> ? [V1x_2E0: A_27a] : ~ p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V0s_2E0)) ) ) ).
tff(thm_2Epred__set_2EINFINITE__INHAB,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0P_2E0))
=> ? [V1x_2E0: A_27a] : p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V0P_2E0)) ) ).
tff(thm_2Epred__set_2EIMAGE__11__INFINITE,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_2Epred__set_2EINFINITE__SUBSET,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
=> ! [V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s_2E0,V1t_2E0))
=> ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V1t_2E0)) ) ) ).
tff(thm_2Epred__set_2EIN__INFINITE__NOT__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)) )
=> ? [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0))
& ~ p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1t_2E0)) ) ) ).
tff(thm_2Epred__set_2EINFINITE__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),V2t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V2t_2E0))
& ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0)) )
=> ~ p(c_2Epred__set_2EFINITE_2E1(A_27b,V2t_2E0)) ) ).
tff(thm_2Epred__set_2EINFINITE__INJ__NOT__SURJ,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
<=> ? [V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27a)] :
( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27a,V1f_2E0,V0s_2E0,V0s_2E0))
& ~ p(c_2Epred__set_2ESURJ_2E3(A_27a,A_27a,V1f_2E0,V0s_2E0,V0s_2E0)) ) ) ).
tff(thm_2Epred__set_2EINFINITE__UNIV,axiom,
! [A_27a: $tType] :
( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)))
<=> ? [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27a)] :
( ! [V1x_2E0: A_27a,V2y_2E0: A_27a] :
( ( app_2E2(A_27a,A_27a,V0f_2E0,V1x_2E0) = app_2E2(A_27a,A_27a,V0f_2E0,V2y_2E0) )
=> ( V1x_2E0 = V2y_2E0 ) )
& ? [V3y_2E0: A_27a] :
! [V4x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,V0f_2E0,V4x_2E0) != V3y_2E0 ) ) ) ).
tff(thm_2Epred__set_2EINFINITE__NUM__UNIV,axiom,
~ p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))) ).
tff(thm_2Epred__set_2EFINITE__PSUBSET__INFINITE,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
<=> ! [V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1t_2E0))
=> ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1t_2E0,V0s_2E0))
=> p(c_2Epred__set_2EPSUBSET_2E2(A_27a,V1t_2E0,V0s_2E0)) ) ) ) ).
tff(thm_2Epred__set_2EFINITE__PSUBSET__UNIV,axiom,
! [A_27a: $tType] :
( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)))
<=> ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
=> p(c_2Epred__set_2EPSUBSET_2E2(A_27a,V0s_2E0,c_2Epred__set_2EUNIV_2E0(A_27a))) ) ) ).
tff(thm_2Epred__set_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)) )
=> ( c_2Epred__set_2EDIFF_2E2(A_27a,V0s_2E0,V1t_2E0) != c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) ).
tff(thm_2Epred__set_2EFINITE__BIJ__COUNT__EQ,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
<=> ? [V1c_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2n_2E0: tyop_2Enum_2Enum] : p(c_2Epred__set_2EBIJ_2E3(tyop_2Enum_2Enum,A_27a,V1c_2E0,c_2Epred__set_2Ecount_2E1(V2n_2E0),V0s_2E0)) ) ).
tff(thm_2Epred__set_2EFINITE__BIJ__COUNT,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
=> ? [V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2b_2E0: tyop_2Enum_2Enum] : p(c_2Epred__set_2EBIJ_2E3(tyop_2Enum_2Enum,A_27a,V1f_2E0,c_2Epred__set_2Ecount_2E1(V2b_2E0),V0s_2E0)) ) ).
tff(thm_2Epred__set_2EFINITE__ISO__NUM,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
( ! [V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V1f_2E0),V0s_2E0),V4n_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,A_27a,V1f_2E0,V4n_2E0),c_2Eprim__rec_2E_3C_2E2(V4n_2E0,c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0))) )
=> ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
=> ? [V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] :
( ! [V2n_2E0: tyop_2Enum_2Enum,V3m_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Eprim__rec_2E_3C_2E2(V2n_2E0,c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0)))
& p(c_2Eprim__rec_2E_3C_2E2(V3m_2E0,c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0))) )
=> ( ( app_2E2(tyop_2Enum_2Enum,A_27a,V1f_2E0,V2n_2E0) = app_2E2(tyop_2Enum_2Enum,A_27a,V1f_2E0,V3m_2E0) )
=> ( V2n_2E0 = V3m_2E0 ) ) )
& ( V0s_2E0 = c_2Epred__set_2EGSPEC_2E1(A_27a,tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V1f_2E0),V0s_2E0)) ) ) ) ) ).
tff(thm_2Epred__set_2EFINITE__WEAK__ENUMERATE,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
<=> ? [V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2b_2E0: tyop_2Enum_2Enum] :
! [V3e_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3e_2E0,V0s_2E0))
<=> ? [V4n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V4n_2E0,V2b_2E0))
& ( V3e_2E0 = app_2E2(tyop_2Enum_2Enum,A_27a,V1f_2E0,V4n_2E0) ) ) ) ) ).
tff(thm_2Epred__set_2EFINITE__WF__noloops,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
=> ( c_2Erelation_2EWF_2E1(A_27a,c_2Epred__set_2EREL__RESTRICT_2E2(A_27a,V0R_2E0,V1s_2E0)) = c_2Erelation_2Eirreflexive_2E1(A_27a,c_2Erelation_2ETC_2E1(A_27a,c_2Epred__set_2EREL__RESTRICT_2E2(A_27a,V0R_2E0,V1s_2E0))) ) ) ).
tff(thm_2Epred__set_2EFINITE__StrongOrder__WF,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,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_2Erelation_2EStrongOrder_2E1(A_27a,c_2Epred__set_2EREL__RESTRICT_2E2(A_27a,V0R_2E0,V1s_2E0))) )
=> p(c_2Erelation_2EWF_2E1(A_27a,c_2Epred__set_2EREL__RESTRICT_2E2(A_27a,V0R_2E0,V1s_2E0))) ) ).
tff(thm_2Epred__set_2EIN__BIGUNION,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1sos_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Epred__set_2EBIGUNION_2E1(A_27a,V1sos_2E0)))
<=> ? [V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V2s_2E0))
& p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0,V1sos_2E0)) ) ) ).
tff(thm_2Epred__set_2EBIGUNION__applied,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1sos_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EBIGUNION_2E2(A_27a,V1sos_2E0,V0x_2E0))
<=> ? [V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V2s_2E0))
& p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0,V1sos_2E0)) ) ) ).
tff(thm_2Epred__set_2EIN__BIGUNION__IMAGE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2y_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V2y_2E0,c_2Epred__set_2EBIGUNION_2E1(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0f_2E0,V1s_2E0))))
<=> ? [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V1s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27b,V2y_2E0,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0f_2E0,V3x_2E0))) ) ) ).
tff(thm_2Epred__set_2EBIGUNION__EMPTY,axiom,
! [A_27a: $tType] : ( c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EEMPTY_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ).
tff(thm_2Epred__set_2EBIGUNION__EQ__EMPTY,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ( ( c_2Epred__set_2EBIGUNION_2E1(A_27a,V0P_2E0) = c_2Epred__set_2EEMPTY_2E0(A_27a) )
<=> ( ( V0P_2E0 = c_2Epred__set_2EEMPTY_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) )
| ( V0P_2E0 = c_2Epred__set_2EINSERT_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0(A_27a),c_2Epred__set_2EEMPTY_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ) ) )
& ( ( c_2Epred__set_2EEMPTY_2E0(A_27a) = c_2Epred__set_2EBIGUNION_2E1(A_27a,V0P_2E0) )
<=> ( ( V0P_2E0 = c_2Epred__set_2EEMPTY_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) )
| ( V0P_2E0 = c_2Epred__set_2EINSERT_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0(A_27a),c_2Epred__set_2EEMPTY_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ) ) ) ) ).
tff(thm_2Epred__set_2EBIGUNION__SING,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))) = V0x_2E0 ) ).
tff(thm_2Epred__set_2EBIGUNION__PAIR,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0,c_2Epred__set_2EINSERT_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))))) = c_2Epred__set_2EUNION_2E2(A_27a,V0s_2E0,V1t_2E0) ) ).
tff(thm_2Epred__set_2EBIGUNION__UNION,axiom,
! [A_27a: $tType,V0s1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EUNION_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0,V1s2_2E0)) = c_2Epred__set_2EUNION_2E2(A_27a,c_2Epred__set_2EBIGUNION_2E1(A_27a,V0s1_2E0),c_2Epred__set_2EBIGUNION_2E1(A_27a,V1s2_2E0)) ) ).
tff(thm_2Epred__set_2EDISJOINT__BIGUNION,axiom,
! [A_27a: $tType] :
( ! [V0s_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EDISJOINT_2E2(A_27a,c_2Epred__set_2EBIGUNION_2E1(A_27a,V0s_2E0),V1t_2E0))
<=> ! [V2s_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_27_2E0,V0s_2E0))
=> p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V2s_27_2E0,V1t_2E0)) ) )
& ! [V3s_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V4t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V4t_2E0,c_2Epred__set_2EBIGUNION_2E1(A_27a,V3s_2E0)))
<=> ! [V5s_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5s_27_2E0,V3s_2E0))
=> p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V4t_2E0,V5s_27_2E0)) ) ) ) ).
tff(thm_2Epred__set_2EBIGUNION__INSERT,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0,V1P_2E0)) = c_2Epred__set_2EUNION_2E2(A_27a,V0s_2E0,c_2Epred__set_2EBIGUNION_2E1(A_27a,V1P_2E0)) ) ).
tff(thm_2Epred__set_2EBIGUNION__SUBSET,axiom,
! [A_27a: $tType,V0X_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Epred__set_2EBIGUNION_2E1(A_27a,V1P_2E0),V0X_2E0))
<=> ! [V2Y_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Y_2E0,V1P_2E0))
=> p(c_2Epred__set_2ESUBSET_2E2(A_27a,V2Y_2E0,V0X_2E0)) ) ) ).
tff(thm_2Epred__set_2EBIGUNION__IMAGE__UNIV,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1N_2E0: tyop_2Enum_2Enum] :
( ! [V2n_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V1N_2E0,V2n_2E0))
=> ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0,V2n_2E0) = c_2Epred__set_2EEMPTY_2E0(A_27a) ) )
=> ( c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))) = c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0,c_2Epred__set_2Ecount_2E1(V1N_2E0))) ) ) ).
tff(thm_2Epred__set_2EFINITE__BIGUNION,axiom,
! [A_27a: $tType,V0P_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),V0P_2E0))
& ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,V0P_2E0))
=> p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0)) ) )
=> p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EBIGUNION_2E1(A_27a,V0P_2E0))) ) ).
tff(thm_2Epred__set_2EFINITE__BIGUNION__EQ,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EBIGUNION_2E1(A_27a,V0P_2E0)))
<=> ( p(c_2Epred__set_2EFINITE_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))
& ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,V0P_2E0))
=> p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0)) ) ) ) ).
tff(thm_2Epred__set_2ESUBSET__BIGUNION__I,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0,V1P_2E0))
=> p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0x_2E0,c_2Epred__set_2EBIGUNION_2E1(A_27a,V1P_2E0))) ) ).
tff(thm_2Epred__set_2ECARD__BIGUNION__SAME__SIZED__SETS,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1s_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),V1s_2E0))
& ! [V2e_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2e_2E0,V1s_2E0))
=> ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V2e_2E0))
& ( c_2Epred__set_2ECARD_2E1(A_27a,V2e_2E0) = V0n_2E0 ) ) )
& ! [V3e1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4e2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3e1_2E0,V1s_2E0))
& p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4e2_2E0,V1s_2E0))
& ( V3e1_2E0 != V4e2_2E0 ) )
=> p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V3e1_2E0,V4e2_2E0)) ) )
=> ( c_2Epred__set_2ECARD_2E1(A_27a,c_2Epred__set_2EBIGUNION_2E1(A_27a,V1s_2E0)) = c_2Earithmetic_2E_2A_2E2(c_2Epred__set_2ECARD_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0),V0n_2E0) ) ) ).
tff(thm_2Epred__set_2EDISJOINT__COUNT,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V1m_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] :
( ( V1m_2E0 != V2n_2E0 )
=> p(c_2Epred__set_2EDISJOINT_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0,V1m_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0,V2n_2E0))) )
=> ! [V3n_2E0: tyop_2Enum_2Enum] : p(c_2Epred__set_2EDISJOINT_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0,V3n_2E0),c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0,c_2Epred__set_2Ecount_2E1(V3n_2E0))))) ) ).
tff(thm_2Epred__set_2EFORALL__IN__BIGUNION,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ! [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Epred__set_2EBIGUNION_2E1(A_27a,V1s_2E0)))
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0)) )
<=> ! [V3t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4x_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0,V1s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V3t_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V4x_2E0)) ) ) ).
tff(thm_2Epred__set_2EIN__BIGINTER,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1B_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Epred__set_2EBIGINTER_2E1(A_27a,V1B_2E0)))
<=> ! [V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0,V1B_2E0))
=> p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V2P_2E0)) ) ) ).
tff(thm_2Epred__set_2EBIGINTER__applied,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1B_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EBIGINTER_2E2(A_27a,V1B_2E0,V0x_2E0))
<=> ! [V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0,V1B_2E0))
=> p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V2P_2E0)) ) ) ).
tff(thm_2Epred__set_2EIN__BIGINTER__IMAGE,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V2s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Epred__set_2EBIGINTER_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,V2s_2E0))))
<=> ! [V3y_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V3y_2E0,V2s_2E0))
=> p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,V3y_2E0))) ) ) ).
tff(thm_2Epred__set_2EBIGINTER__INSERT,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1B_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIGINTER_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0,V1B_2E0)) = c_2Epred__set_2EINTER_2E2(A_27a,V0P_2E0,c_2Epred__set_2EBIGINTER_2E1(A_27a,V1B_2E0)) ) ).
tff(thm_2Epred__set_2EBIGINTER__EMPTY,axiom,
! [A_27a: $tType] : ( c_2Epred__set_2EBIGINTER_2E1(A_27a,c_2Epred__set_2EEMPTY_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) = c_2Epred__set_2EUNIV_2E0(A_27a) ) ).
tff(thm_2Epred__set_2EBIGINTER__INTER,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIGINTER_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0,c_2Epred__set_2EINSERT_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))))) = c_2Epred__set_2EINTER_2E2(A_27a,V0P_2E0,V1Q_2E0) ) ).
tff(thm_2Epred__set_2EBIGINTER__SING,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIGINTER_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))) = V0P_2E0 ) ).
tff(thm_2Epred__set_2ESUBSET__BIGINTER,axiom,
! [A_27a: $tType,V0X_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0X_2E0,c_2Epred__set_2EBIGINTER_2E1(A_27a,V1P_2E0)))
<=> ! [V2Y_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Y_2E0,V1P_2E0))
=> p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0X_2E0,V2Y_2E0)) ) ) ).
tff(thm_2Epred__set_2EDISJOINT__BIGINTER,axiom,
! [A_27a: $tType,V0X_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Y_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Y_2E0,V2P_2E0))
& p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V1Y_2E0,V0X_2E0)) )
=> ( p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V0X_2E0,c_2Epred__set_2EBIGINTER_2E1(A_27a,V2P_2E0)))
& p(c_2Epred__set_2EDISJOINT_2E2(A_27a,c_2Epred__set_2EBIGINTER_2E1(A_27a,V2P_2E0),V0X_2E0)) ) ) ).
tff(thm_2Epred__set_2EBIGINTER__UNION,axiom,
! [A_27a: $tType,V0s1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1s2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIGINTER_2E1(A_27a,c_2Epred__set_2EUNION_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s1_2E0,V1s2_2E0)) = c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EBIGINTER_2E1(A_27a,V0s1_2E0),c_2Epred__set_2EBIGINTER_2E1(A_27a,V1s2_2E0)) ) ).
tff(thm_2Epred__set_2EBIGINTER__SUBSET,axiom,
! [A_27a: $tType,V0sp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ( ! [V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0,V1s_2E0))
=> p(c_2Epred__set_2ESUBSET_2E2(A_27a,V2t_2E0,V0sp_2E0)) )
& ( V1s_2E0 != c_2Epred__set_2EEMPTY_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) )
=> p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Epred__set_2EBIGINTER_2E1(A_27a,V1s_2E0),V0sp_2E0)) ) ).
tff(thm_2Epred__set_2EDIFF__BIGINTER1,axiom,
! [A_27a: $tType,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_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V0sp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0: 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_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)),F0_2E0,V0sp_2E0),V2u_2E0) = c_2Epred__set_2EDIFF_2E2(A_27a,V0sp_2E0,V2u_2E0) )
=> ! [V0sp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EDIFF_2E2(A_27a,V0sp_2E0,c_2Epred__set_2EBIGINTER_2E1(A_27a,V1s_2E0)) = c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_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)),F0_2E0,V0sp_2E0),V1s_2E0)) ) ) ).
tff(thm_2Epred__set_2EDIFF__BIGINTER,axiom,
! [A_27a: $tType,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_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V0sp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3u_2E0: 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_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)),F0_2E0,V0sp_2E0),V3u_2E0) = c_2Epred__set_2EDIFF_2E2(A_27a,V0sp_2E0,V3u_2E0) )
=> ! [V0sp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ( ! [V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0,V1s_2E0))
=> p(c_2Epred__set_2ESUBSET_2E2(A_27a,V2t_2E0,V0sp_2E0)) )
& ( V1s_2E0 != c_2Epred__set_2EEMPTY_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) )
=> ( c_2Epred__set_2EBIGINTER_2E1(A_27a,V1s_2E0) = c_2Epred__set_2EDIFF_2E2(A_27a,V0sp_2E0,c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_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)),F0_2E0,V0sp_2E0),V1s_2E0))) ) ) ) ).
tff(thm_2Epred__set_2EFINITE__BIGINTER,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ? [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0,V0P_2E0))
& p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0)) )
=> p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EBIGINTER_2E1(A_27a,V0P_2E0))) ) ).
tff(thm_2Epred__set_2EIN__CROSS,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V2x_2E0,c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,V0P_2E0,V1Q_2E0)))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,c_2Epair_2EFST_2E1(A_27a,A_27b,V2x_2E0),V0P_2E0))
& p(c_2Ebool_2EIN_2E2(A_27b,c_2Epair_2ESND_2E1(A_27a,A_27b,V2x_2E0),V1Q_2E0)) ) ) ).
tff(thm_2Epred__set_2ECROSS__applied,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2x_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] :
( p(c_2Epred__set_2ECROSS_2E3(A_27a,A_27b,V0P_2E0,V1Q_2E0,V2x_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,c_2Epair_2EFST_2E1(A_27a,A_27b,V2x_2E0),V0P_2E0))
& p(c_2Ebool_2EIN_2E2(A_27b,c_2Epair_2ESND_2E1(A_27a,A_27b,V2x_2E0),V1Q_2E0)) ) ) ).
tff(thm_2Epred__set_2ECROSS__EMPTY,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,V0P_2E0,c_2Epred__set_2EEMPTY_2E0(A_27b)) = c_2Epred__set_2EEMPTY_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)) )
& ( c_2Epred__set_2ECROSS_2E2(A_27c,A_27a,c_2Epred__set_2EEMPTY_2E0(A_27c),V0P_2E0) = c_2Epred__set_2EEMPTY_2E0(tyop_2Epair_2Eprod(A_27c,A_27a)) ) ) ).
tff(thm_2Epred__set_2ECROSS__EMPTY__EQN,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)] :
( ( c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,V1s_2E0,V0t_2E0) = c_2Epred__set_2EEMPTY_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)) )
<=> ( ( V1s_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) )
| ( V0t_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27b) ) ) ) ).
tff(thm_2Epred__set_2ECROSS__INSERT__LEFT,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2x_2E0: A_27a] : ( c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,c_2Epred__set_2EINSERT_2E2(A_27a,V2x_2E0,V0P_2E0),V1Q_2E0) = c_2Epred__set_2EUNION_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,c_2Epred__set_2EINSERT_2E2(A_27a,V2x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)),V1Q_2E0),c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,V0P_2E0,V1Q_2E0)) ) ).
tff(thm_2Epred__set_2ECROSS__INSERT__RIGHT,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2x_2E0: A_27b] : ( c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,V0P_2E0,c_2Epred__set_2EINSERT_2E2(A_27b,V2x_2E0,V1Q_2E0)) = c_2Epred__set_2EUNION_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,V0P_2E0,c_2Epred__set_2EINSERT_2E2(A_27b,V2x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27b))),c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,V0P_2E0,V1Q_2E0)) ) ).
tff(thm_2Epred__set_2EFINITE__CROSS,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0P_2E0))
& p(c_2Epred__set_2EFINITE_2E1(A_27b,V1Q_2E0)) )
=> p(c_2Epred__set_2EFINITE_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,V0P_2E0,V1Q_2E0))) ) ).
tff(thm_2Epred__set_2ECROSS__SINGS,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : ( c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)),c_2Epred__set_2EINSERT_2E2(A_27b,V1y_2E0,c_2Epred__set_2EEMPTY_2E0(A_27b))) = c_2Epred__set_2EINSERT_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V0x_2E0,V1y_2E0),c_2Epred__set_2EEMPTY_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))) ) ).
tff(thm_2Epred__set_2ECARD__SING__CROSS,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1P_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27b,V1P_2E0))
=> ( c_2Epred__set_2ECARD_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)),V1P_2E0)) = c_2Epred__set_2ECARD_2E1(A_27b,V1P_2E0) ) ) ).
tff(thm_2Epred__set_2ECARD__CROSS,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0P_2E0))
& p(c_2Epred__set_2EFINITE_2E1(A_27b,V1Q_2E0)) )
=> ( c_2Epred__set_2ECARD_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,V0P_2E0,V1Q_2E0)) = c_2Earithmetic_2E_2A_2E2(c_2Epred__set_2ECARD_2E1(A_27a,V0P_2E0),c_2Epred__set_2ECARD_2E1(A_27b,V1Q_2E0)) ) ) ).
tff(thm_2Epred__set_2ECROSS__SUBSET,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2P0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3Q0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESUBSET_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,V2P0_2E0,V3Q0_2E0),c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,V0P_2E0,V1Q_2E0)))
<=> ( ( V2P0_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) )
| ( V3Q0_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27b) )
| ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V2P0_2E0,V0P_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(A_27b,V3Q0_2E0,V1Q_2E0)) ) ) ) ).
tff(thm_2Epred__set_2EFINITE__CROSS__EQ,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,V0P_2E0,V1Q_2E0)))
<=> ( ( V0P_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) )
| ( V1Q_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27b) )
| ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0P_2E0))
& p(c_2Epred__set_2EFINITE_2E1(A_27b,V1Q_2E0)) ) ) ) ).
tff(thm_2Epred__set_2ECROSS__UNIV,axiom,
! [A_27a: $tType,A_27b: $tType] : ( c_2Epred__set_2EUNIV_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)) = c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,c_2Epred__set_2EUNIV_2E0(A_27a),c_2Epred__set_2EUNIV_2E0(A_27b)) ) ).
tff(thm_2Epred__set_2EINFINITE__PAIR__UNIV,axiom,
! [A_27a: $tType,A_27b: $tType] :
( p(c_2Epred__set_2EFINITE_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epred__set_2EUNIV_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))))
<=> ( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)))
& p(c_2Epred__set_2EFINITE_2E1(A_27b,c_2Epred__set_2EUNIV_2E0(A_27b))) ) ) ).
tff(thm_2Epred__set_2ESUM__UNIV,axiom,
! [A_27a: $tType,A_27b: $tType] : ( c_2Epred__set_2EUNIV_2E0(tyop_2Esum_2Esum(A_27a,A_27b)) = c_2Epred__set_2EUNION_2E2(tyop_2Esum_2Esum(A_27a,A_27b),c_2Epred__set_2EIMAGE_2E2(A_27a,tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E0(A_27a,A_27b),c_2Epred__set_2EUNIV_2E0(A_27a)),c_2Epred__set_2EIMAGE_2E2(A_27b,tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E0(A_27a,A_27b),c_2Epred__set_2EUNIV_2E0(A_27b))) ) ).
tff(thm_2Epred__set_2EINJ__INL,axiom,
! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
=> p(c_2Ebool_2EIN_2E2(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(A_27a,A_27b,V2x_2E0),V0t_2E0)) )
=> p(c_2Epred__set_2EINJ_2E3(A_27a,tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E0(A_27a,A_27b),V1s_2E0,V0t_2E0)) ) ).
tff(thm_2Epred__set_2EINJ__INR,axiom,
! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
=> p(c_2Ebool_2EIN_2E2(tyop_2Esum_2Esum(A_27b,A_27a),c_2Esum_2EINR_2E1(A_27b,A_27a,V2x_2E0),V0t_2E0)) )
=> p(c_2Epred__set_2EINJ_2E3(A_27a,tyop_2Esum_2Esum(A_27b,A_27a),c_2Esum_2EINR_2E0(A_27b,A_27a),V1s_2E0,V0t_2E0)) ) ).
tff(thm_2Epred__set_2EIN__COMPL,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Epred__set_2ECOMPL_2E1(A_27a,V1s_2E0)))
<=> ~ p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V1s_2E0)) ) ).
tff(thm_2Epred__set_2ECOMPL__applied,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ECOMPL_2E2(A_27a,V1s_2E0,V0x_2E0))
<=> ~ p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V1s_2E0)) ) ).
tff(thm_2Epred__set_2ECOMPL__COMPL,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECOMPL_2E1(A_27a,c_2Epred__set_2ECOMPL_2E1(A_27a,V0s_2E0)) = V0s_2E0 ) ).
tff(thm_2Epred__set_2ECOMPL__CLAUSES,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2ECOMPL_2E1(A_27a,V0s_2E0),V0s_2E0) = c_2Epred__set_2EEMPTY_2E0(A_27a) )
& ( c_2Epred__set_2EUNION_2E2(A_27a,c_2Epred__set_2ECOMPL_2E1(A_27a,V0s_2E0),V0s_2E0) = c_2Epred__set_2EUNIV_2E0(A_27a) ) ) ).
tff(thm_2Epred__set_2ECOMPL__SPLITS,axiom,
! [A_27a: $tType,V0p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(A_27a,c_2Epred__set_2EINTER_2E2(A_27a,V0p_2E0,V1q_2E0),c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2ECOMPL_2E1(A_27a,V0p_2E0),V1q_2E0)) = V1q_2E0 ) ).
tff(thm_2Epred__set_2EINTER__UNION__COMPL,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINTER_2E2(A_27a,V0s_2E0,V1t_2E0) = c_2Epred__set_2ECOMPL_2E1(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,c_2Epred__set_2ECOMPL_2E1(A_27a,V0s_2E0),c_2Epred__set_2ECOMPL_2E1(A_27a,V1t_2E0))) ) ).
tff(thm_2Epred__set_2ECOMPL__EMPTY,axiom,
! [A_27a: $tType] : ( c_2Epred__set_2ECOMPL_2E1(A_27a,c_2Epred__set_2EEMPTY_2E0(A_27a)) = c_2Epred__set_2EUNIV_2E0(A_27a) ) ).
tff(thm_2Epred__set_2ECOMPL__INTER,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( c_2Epred__set_2EINTER_2E2(A_27a,V0x_2E0,c_2Epred__set_2ECOMPL_2E1(A_27a,V0x_2E0)) = c_2Epred__set_2EEMPTY_2E0(A_27a) )
& ( c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2ECOMPL_2E1(A_27a,V0x_2E0),V0x_2E0) = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) ).
tff(thm_2Epred__set_2ECOMPL__UNION,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECOMPL_2E1(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,V0t_2E0)) = c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2ECOMPL_2E1(A_27a,V1s_2E0),c_2Epred__set_2ECOMPL_2E1(A_27a,V0t_2E0)) ) ).
tff(thm_2Epred__set_2EITSET__ind,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( ! [V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3b_2E0: A_27b] :
( ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V2s_2E0))
& ( V2s_2E0 != c_2Epred__set_2EEMPTY_2E0(A_27a) ) )
=> p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0,c_2Epred__set_2EREST_2E1(A_27a,V2s_2E0)),app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0,c_2Epred__set_2ECHOICE_2E1(A_27a,V2s_2E0)),V3b_2E0))) )
=> p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0,V2s_2E0),V3b_2E0)) )
=> ! [V4v_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5v1_2E0: A_27b] : p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0,V4v_2E0),V5v1_2E0)) ) ).
tff(thm_2Epred__set_2EITSET__def,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,F0_2E0,V0s_2E0))
<=> ( V0s_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) )
=> ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V2b_2E0: A_27b] : ( c_2Epred__set_2EITSET_2E3(A_27a,A_27b,V1f_2E0,V0s_2E0,V2b_2E0) = c_2Ebool_2ECOND_2E3(A_27b,c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0),c_2Ebool_2ECOND_2E3(A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,F0_2E0,V0s_2E0),V2b_2E0,c_2Epred__set_2EITSET_2E3(A_27a,A_27b,V1f_2E0,c_2Epred__set_2EREST_2E1(A_27a,V0s_2E0),app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V1f_2E0,c_2Epred__set_2ECHOICE_2E1(A_27a,V0s_2E0)),V2b_2E0))),c_2Ebool_2EARB_2E0(A_27b)) ) ) ).
tff(thm_2Epred__set_2EITSET__IND,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
( ! [V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3b_2E0: A_27b] :
( ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V2s_2E0))
& ( V2s_2E0 != c_2Epred__set_2EEMPTY_2E0(A_27a) ) )
=> p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0,c_2Epred__set_2EREST_2E1(A_27a,V2s_2E0)),app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0,c_2Epred__set_2ECHOICE_2E1(A_27a,V2s_2E0)),V3b_2E0))) )
=> p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0,V2s_2E0),V3b_2E0)) )
=> ! [V4v_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5v1_2E0: A_27b] : p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0,V4v_2E0),V5v1_2E0)) ) ).
tff(thm_2Epred__set_2EITSET__THM,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,F0_2E0,V0s_2E0))
<=> ( V0s_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) )
=> ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V2b_2E0: A_27b] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
=> ( c_2Epred__set_2EITSET_2E3(A_27a,A_27b,V1f_2E0,V0s_2E0,V2b_2E0) = c_2Ebool_2ECOND_2E3(A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,F0_2E0,V0s_2E0),V2b_2E0,c_2Epred__set_2EITSET_2E3(A_27a,A_27b,V1f_2E0,c_2Epred__set_2EREST_2E1(A_27a,V0s_2E0),app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V1f_2E0,c_2Epred__set_2ECHOICE_2E1(A_27a,V0s_2E0)),V2b_2E0))) ) ) ) ).
tff(thm_2Epred__set_2EITSET__EMPTY,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1b_2E0: A_27b] : ( c_2Epred__set_2EITSET_2E3(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a),V1b_2E0) = V1b_2E0 ) ).
tff(thm_2Epred__set_2EITSET__INSERT,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))
=> ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V2x_2E0: A_27a,V3b_2E0: A_27b] : ( c_2Epred__set_2EITSET_2E3(A_27a,A_27b,V1f_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V2x_2E0,V0s_2E0),V3b_2E0) = c_2Epred__set_2EITSET_2E3(A_27a,A_27b,V1f_2E0,c_2Epred__set_2EREST_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V2x_2E0,V0s_2E0)),app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V1f_2E0,c_2Epred__set_2ECHOICE_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V2x_2E0,V0s_2E0))),V3b_2E0)) ) ) ).
tff(thm_2Epred__set_2ECOMMUTING__ITSET__INSERT,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( ! [V2x_2E0: A_27a,V3y_2E0: A_27a,V4z_2E0: A_27b] : ( app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0,V2x_2E0),app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0,V3y_2E0),V4z_2E0)) = app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0,V3y_2E0),app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0,V2x_2E0),V4z_2E0)) )
& p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0)) )
=> ! [V5x_2E0: A_27a,V6b_2E0: A_27b] : ( c_2Epred__set_2EITSET_2E3(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V5x_2E0,V1s_2E0),V6b_2E0) = c_2Epred__set_2EITSET_2E3(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EDELETE_2E2(A_27a,V1s_2E0,V5x_2E0),app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0,V5x_2E0),V6b_2E0)) ) ) ).
tff(thm_2Epred__set_2ECOMMUTING__ITSET__RECURSES,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V1e_2E0: A_27a,V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3b_2E0: A_27b] :
( ( ! [V4x_2E0: A_27a,V5y_2E0: A_27a,V6z_2E0: A_27b] : ( app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0,V4x_2E0),app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0,V5y_2E0),V6z_2E0)) = app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0,V5y_2E0),app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0,V4x_2E0),V6z_2E0)) )
& p(c_2Epred__set_2EFINITE_2E1(A_27a,V2s_2E0)) )
=> ( c_2Epred__set_2EITSET_2E3(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V1e_2E0,V2s_2E0),V3b_2E0) = app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0,V1e_2E0),c_2Epred__set_2EITSET_2E3(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EDELETE_2E2(A_27a,V2s_2E0,V1e_2E0),V3b_2E0)) ) ) ).
tff(thm_2Epred__set_2ESUM__IMAGE__THM,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
( ( c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,V0f_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) = c_2Enum_2E0_2E0 )
& ! [V1e_2E0: A_27a,V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V2s_2E0))
=> ( c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,V0f_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V1e_2E0,V2s_2E0)) = c_2Earithmetic_2E_2B_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V1e_2E0),c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,V0f_2E0,c_2Epred__set_2EDELETE_2E2(A_27a,V2s_2E0,V1e_2E0))) ) ) ) ).
tff(thm_2Epred__set_2ESUM__IMAGE__SING,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1e_2E0: A_27a] : ( c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,V0f_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V1e_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a))) = app_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V1e_2E0) ) ).
tff(thm_2Epred__set_2ESUM__IMAGE__SUBSET__LE,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V2t_2E0,V1s_2E0)) )
=> p(c_2Earithmetic_2E_3C_3D_2E2(c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,V0f_2E0,V2t_2E0),c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,V0f_2E0,V1s_2E0))) ) ).
tff(thm_2Epred__set_2ESUM__IMAGE__IN__LE,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2e_2E0: A_27a] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V2e_2E0,V1s_2E0)) )
=> p(c_2Earithmetic_2E_3C_3D_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V2e_2E0),c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,V0f_2E0,V1s_2E0))) ) ).
tff(thm_2Epred__set_2ESUM__IMAGE__DELETE,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
=> ! [V2e_2E0: A_27a] : ( c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,V0f_2E0,c_2Epred__set_2EDELETE_2E2(A_27a,V1s_2E0,V2e_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Ebool_2EIN_2E2(A_27a,V2e_2E0,V1s_2E0),c_2Earithmetic_2E_2D_2E2(c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,V0f_2E0,V1s_2E0),app_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V2e_2E0)),c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,V0f_2E0,V1s_2E0)) ) ) ).
tff(thm_2Epred__set_2ESUM__IMAGE__UNION,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_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_27a,V2t_2E0)) )
=> ( c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,V0f_2E0,c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,V2t_2E0)) = c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2E_2B_2E2(c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,V0f_2E0,V1s_2E0),c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,V0f_2E0,V2t_2E0)),c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,V0f_2E0,c_2Epred__set_2EINTER_2E2(A_27a,V1s_2E0,V2t_2E0))) ) ) ).
tff(thm_2Epred__set_2ESUM__IMAGE__lower__bound,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
=> ! [V2n_2E0: tyop_2Enum_2Enum] :
( ! [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V1s_2E0))
=> p(c_2Earithmetic_2E_3C_3D_2E2(V2n_2E0,app_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V3x_2E0))) )
=> p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2E_2A_2E2(c_2Epred__set_2ECARD_2E1(A_27a,V1s_2E0),V2n_2E0),c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,V0f_2E0,V1s_2E0))) ) ) ).
tff(thm_2Epred__set_2ESUM__IMAGE__upper__bound,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
=> ! [V2n_2E0: tyop_2Enum_2Enum] :
( ! [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V1s_2E0))
=> p(c_2Earithmetic_2E_3C_3D_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V3x_2E0),V2n_2E0)) )
=> p(c_2Earithmetic_2E_3C_3D_2E2(c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,V0f_2E0,V1s_2E0),c_2Earithmetic_2E_2A_2E2(c_2Epred__set_2ECARD_2E1(A_27a,V1s_2E0),V2n_2E0))) ) ) ).
tff(thm_2Epred__set_2ESUM__SAME__IMAGE,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0P_2E0))
=> ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2p_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V2p_2E0,V0P_2E0))
& ! [V3q_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3q_2E0,V0P_2E0))
=> ( app_2E2(A_27a,tyop_2Enum_2Enum,V1f_2E0,V2p_2E0) = app_2E2(A_27a,tyop_2Enum_2Enum,V1f_2E0,V3q_2E0) ) ) )
=> ( c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,V1f_2E0,V0P_2E0) = c_2Earithmetic_2E_2A_2E2(c_2Epred__set_2ECARD_2E1(A_27a,V0P_2E0),app_2E2(A_27a,tyop_2Enum_2Enum,V1f_2E0,V2p_2E0)) ) ) ) ).
tff(thm_2Epred__set_2ESUM__IMAGE__CONG,axiom,
! [A_27a: $tType,V0s2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3f1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
( ( ( V1s1_2E0 = V0s2_2E0 )
& ! [V4x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V0s2_2E0))
=> ( app_2E2(A_27a,tyop_2Enum_2Enum,V3f1_2E0,V4x_2E0) = app_2E2(A_27a,tyop_2Enum_2Enum,V2f2_2E0,V4x_2E0) ) ) )
=> ( c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,V3f1_2E0,V1s1_2E0) = c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,V2f2_2E0,V0s2_2E0) ) ) ).
tff(thm_2Epred__set_2ESUM__IMAGE__ZERO,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
=> ( ( c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,V0f_2E0,V1s_2E0) = c_2Enum_2E0_2E0 )
<=> ! [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
=> ( app_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V2x_2E0) = c_2Enum_2E0_2E0 ) ) ) ) ).
tff(thm_2Epred__set_2EABS__DIFF__SUM__IMAGE,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)))] :
( ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),F0_2E0,V1f_2E0),V0g_2E0),V3x_2E0) = c_2Earithmetic_2EABS__DIFF_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V1f_2E0,V3x_2E0),app_2E2(A_27a,tyop_2Enum_2Enum,V0g_2E0,V3x_2E0)) )
=> ! [V0g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V2s_2E0))
=> p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2EABS__DIFF_2E2(c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,V1f_2E0,V2s_2E0),c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,V0g_2E0,V2s_2E0)),c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),F0_2E0,V1f_2E0),V0g_2E0),V2s_2E0))) ) ) ).
tff(thm_2Epred__set_2ESUM__IMAGE__MONO__LESS__EQ,axiom,
! [A_27a: $tType,V0g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V2s_2E0))
=> ( ! [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V2s_2E0))
=> p(c_2Earithmetic_2E_3C_3D_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V1f_2E0,V3x_2E0),app_2E2(A_27a,tyop_2Enum_2Enum,V0g_2E0,V3x_2E0))) )
=> p(c_2Earithmetic_2E_3C_3D_2E2(c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,V1f_2E0,V2s_2E0),c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,V0g_2E0,V2s_2E0))) ) ) ).
tff(thm_2Epred__set_2ESUM__IMAGE__MONO__LESS,axiom,
! [A_27a: $tType,V0g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V2s_2E0))
=> ( ( ? [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V2s_2E0))
& p(c_2Eprim__rec_2E_3C_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V1f_2E0,V3x_2E0),app_2E2(A_27a,tyop_2Enum_2Enum,V0g_2E0,V3x_2E0))) )
& ! [V4x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V2s_2E0))
=> p(c_2Earithmetic_2E_3C_3D_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V1f_2E0,V4x_2E0),app_2E2(A_27a,tyop_2Enum_2Enum,V0g_2E0,V4x_2E0))) ) )
=> p(c_2Eprim__rec_2E_3C_2E2(c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,V1f_2E0,V2s_2E0),c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,V0g_2E0,V2s_2E0))) ) ) ).
tff(thm_2Epred__set_2ESUM__IMAGE__INJ__o,axiom,
! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27b,V0s_2E0))
=> ! [V1g_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Epred__set_2EINJ_2E3(A_27b,A_27a,V1g_2E0,V0s_2E0,c_2Epred__set_2EUNIV_2E0(A_27a)))
=> ! [V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,V2f_2E0,c_2Epred__set_2EIMAGE_2E2(A_27b,A_27a,V1g_2E0,V0s_2E0)) = c_2Epred__set_2ESUM__IMAGE_2E2(A_27b,c_2Ecombin_2Eo_2E2(A_27b,tyop_2Enum_2Enum,A_27a,V2f_2E0,V1g_2E0),V0s_2E0) ) ) ) ).
tff(thm_2Epred__set_2ESUM__IMAGE__PERMUTES,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
=> ! [V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27a)] :
( p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27a,V1g_2E0,V0s_2E0,V0s_2E0))
=> ! [V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,c_2Ecombin_2Eo_2E2(A_27a,tyop_2Enum_2Enum,A_27a,V2f_2E0,V1g_2E0),V0s_2E0) = c_2Epred__set_2ESUM__IMAGE_2E2(A_27a,V2f_2E0,V0s_2E0) ) ) ) ).
tff(thm_2Epred__set_2ESUM__SET__THM,axiom,
( ( c_2Epred__set_2ESUM__SET_2E1(c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum)) = c_2Enum_2E0_2E0 )
& ! [V0x_2E0: tyop_2Enum_2Enum,V1s_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,V1s_2E0))
=> ( c_2Epred__set_2ESUM__SET_2E1(c_2Epred__set_2EINSERT_2E2(tyop_2Enum_2Enum,V0x_2E0,V1s_2E0)) = c_2Earithmetic_2E_2B_2E2(V0x_2E0,c_2Epred__set_2ESUM__SET_2E1(c_2Epred__set_2EDELETE_2E2(tyop_2Enum_2Enum,V1s_2E0,V0x_2E0))) ) ) ) ).
tff(thm_2Epred__set_2ESUM__SET__EMPTY,axiom,
c_2Epred__set_2ESUM__SET_2E1(c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum)) = c_2Enum_2E0_2E0 ).
tff(thm_2Epred__set_2ESUM__SET__SING,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Epred__set_2ESUM__SET_2E1(c_2Epred__set_2EINSERT_2E2(tyop_2Enum_2Enum,V0n_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum))) = V0n_2E0 ) ).
tff(thm_2Epred__set_2ESUM__SET__SUBSET__LE,axiom,
! [V0s_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,V1t_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(tyop_2Enum_2Enum,V0s_2E0,V1t_2E0)) )
=> p(c_2Earithmetic_2E_3C_3D_2E2(c_2Epred__set_2ESUM__SET_2E1(V0s_2E0),c_2Epred__set_2ESUM__SET_2E1(V1t_2E0))) ) ).
tff(thm_2Epred__set_2ESUM__SET__IN__LE,axiom,
! [V0x_2E0: tyop_2Enum_2Enum,V1s_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,V1s_2E0))
& p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V0x_2E0,V1s_2E0)) )
=> p(c_2Earithmetic_2E_3C_3D_2E2(V0x_2E0,c_2Epred__set_2ESUM__SET_2E1(V1s_2E0))) ) ).
tff(thm_2Epred__set_2ESUM__SET__DELETE,axiom,
! [V0s_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,V0s_2E0))
=> ! [V1e_2E0: tyop_2Enum_2Enum] : ( c_2Epred__set_2ESUM__SET_2E1(c_2Epred__set_2EDELETE_2E2(tyop_2Enum_2Enum,V0s_2E0,V1e_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V1e_2E0,V0s_2E0),c_2Earithmetic_2E_2D_2E2(c_2Epred__set_2ESUM__SET_2E1(V0s_2E0),V1e_2E0),c_2Epred__set_2ESUM__SET_2E1(V0s_2E0)) ) ) ).
tff(thm_2Epred__set_2ESUM__SET__UNION,axiom,
! [V0s_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,V0s_2E0))
& p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,V1t_2E0)) )
=> ( c_2Epred__set_2ESUM__SET_2E1(c_2Epred__set_2EUNION_2E2(tyop_2Enum_2Enum,V0s_2E0,V1t_2E0)) = c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2E_2B_2E2(c_2Epred__set_2ESUM__SET_2E1(V0s_2E0),c_2Epred__set_2ESUM__SET_2E1(V1t_2E0)),c_2Epred__set_2ESUM__SET_2E1(c_2Epred__set_2EINTER_2E2(tyop_2Enum_2Enum,V0s_2E0,V1t_2E0))) ) ) ).
tff(thm_2Epred__set_2EPROD__IMAGE__THM,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
( ( c_2Epred__set_2EPROD__IMAGE_2E2(A_27a,V0f_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) )
& ! [V1e_2E0: A_27a,V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V2s_2E0))
=> ( c_2Epred__set_2EPROD__IMAGE_2E2(A_27a,V0f_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V1e_2E0,V2s_2E0)) = c_2Earithmetic_2E_2A_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V1e_2E0),c_2Epred__set_2EPROD__IMAGE_2E2(A_27a,V0f_2E0,c_2Epred__set_2EDELETE_2E2(A_27a,V2s_2E0,V1e_2E0))) ) ) ) ).
tff(thm_2Epred__set_2EPROD__SET__THM,axiom,
( ( c_2Epred__set_2EPROD__SET_2E1(c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) )
& ! [V0x_2E0: tyop_2Enum_2Enum,V1s_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,V1s_2E0))
=> ( c_2Epred__set_2EPROD__SET_2E1(c_2Epred__set_2EINSERT_2E2(tyop_2Enum_2Enum,V0x_2E0,V1s_2E0)) = c_2Earithmetic_2E_2A_2E2(V0x_2E0,c_2Epred__set_2EPROD__SET_2E1(c_2Epred__set_2EDELETE_2E2(tyop_2Enum_2Enum,V1s_2E0,V0x_2E0))) ) ) ) ).
tff(thm_2Epred__set_2EPROD__SET__EMPTY,axiom,
c_2Epred__set_2EPROD__SET_2E1(c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ).
tff(thm_2Epred__set_2EPROD__SET__IMAGE__REDUCTION,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] :
( ( p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,c_2Epred__set_2EIMAGE_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V1s_2E0)))
& ~ p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,app_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V2x_2E0),c_2Epred__set_2EIMAGE_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V1s_2E0))) )
=> ( c_2Epred__set_2EPROD__SET_2E1(c_2Epred__set_2EIMAGE_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V2x_2E0,V1s_2E0))) = c_2Earithmetic_2E_2A_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V2x_2E0),c_2Epred__set_2EPROD__SET_2E1(c_2Epred__set_2EIMAGE_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V1s_2E0))) ) ) ).
tff(thm_2Epred__set_2EMAX__SET__THM,axiom,
( ( c_2Epred__set_2EMAX__SET_2E1(c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum)) = c_2Enum_2E0_2E0 )
& ! [V0e_2E0: tyop_2Enum_2Enum,V1s_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,V1s_2E0))
=> ( c_2Epred__set_2EMAX__SET_2E1(c_2Epred__set_2EINSERT_2E2(tyop_2Enum_2Enum,V0e_2E0,V1s_2E0)) = c_2Earithmetic_2EMAX_2E2(V0e_2E0,c_2Epred__set_2EMAX__SET_2E1(V1s_2E0)) ) ) ) ).
tff(thm_2Epred__set_2EMAX__SET__REWRITES,axiom,
! [V0e_2E0: tyop_2Enum_2Enum] :
( ( c_2Epred__set_2EMAX__SET_2E1(c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum)) = c_2Enum_2E0_2E0 )
& ( c_2Epred__set_2EMAX__SET_2E1(c_2Epred__set_2EINSERT_2E2(tyop_2Enum_2Enum,V0e_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum))) = V0e_2E0 ) ) ).
tff(thm_2Epred__set_2EMAX__SET__ELIM,axiom,
! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,V0P_2E0))
& ( ( V0P_2E0 = c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum) )
=> p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1Q_2E0,c_2Enum_2E0_2E0)) )
& ! [V2x_2E0: tyop_2Enum_2Enum] :
( ( ! [V3y_2E0: tyop_2Enum_2Enum] :
( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V3y_2E0,V0P_2E0))
=> p(c_2Earithmetic_2E_3C_3D_2E2(V3y_2E0,V2x_2E0)) )
& p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V2x_2E0,V0P_2E0)) )
=> p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1Q_2E0,V2x_2E0)) ) )
=> p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1Q_2E0,c_2Epred__set_2EMAX__SET_2E1(V0P_2E0))) ) ).
tff(thm_2Epred__set_2EMIN__SET__ELIM,axiom,
! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( ( ( V0P_2E0 != c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum) )
& ! [V2x_2E0: tyop_2Enum_2Enum] :
( ( ! [V3y_2E0: tyop_2Enum_2Enum] :
( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V3y_2E0,V0P_2E0))
=> p(c_2Earithmetic_2E_3C_3D_2E2(V2x_2E0,V3y_2E0)) )
& p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V2x_2E0,V0P_2E0)) )
=> p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1Q_2E0,V2x_2E0)) ) )
=> p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1Q_2E0,c_2Epred__set_2EMIN__SET_2E1(V0P_2E0))) ) ).
tff(thm_2Epred__set_2EMIN__SET__THM,axiom,
( ! [V0e_2E0: tyop_2Enum_2Enum] : ( c_2Epred__set_2EMIN__SET_2E1(c_2Epred__set_2EINSERT_2E2(tyop_2Enum_2Enum,V0e_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum))) = V0e_2E0 )
& ! [V1s_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2e1_2E0: tyop_2Enum_2Enum,V3e2_2E0: tyop_2Enum_2Enum] : ( c_2Epred__set_2EMIN__SET_2E1(c_2Epred__set_2EINSERT_2E2(tyop_2Enum_2Enum,V2e1_2E0,c_2Epred__set_2EINSERT_2E2(tyop_2Enum_2Enum,V3e2_2E0,V1s_2E0))) = c_2Earithmetic_2EMIN_2E2(V2e1_2E0,c_2Epred__set_2EMIN__SET_2E1(c_2Epred__set_2EINSERT_2E2(tyop_2Enum_2Enum,V3e2_2E0,V1s_2E0))) ) ) ).
tff(thm_2Epred__set_2EMIN__SET__LEM,axiom,
! [V0s_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( ( V0s_2E0 != c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum) )
=> ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,c_2Epred__set_2EMIN__SET_2E1(V0s_2E0),V0s_2E0))
& ! [V1x_2E0: tyop_2Enum_2Enum] :
( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V1x_2E0,V0s_2E0))
=> p(c_2Earithmetic_2E_3C_3D_2E2(c_2Epred__set_2EMIN__SET_2E1(V0s_2E0),V1x_2E0)) ) ) ) ).
tff(thm_2Epred__set_2ESUBSET__MIN__SET,axiom,
! [A_27a: $tType,V0I_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1J_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2n_2E0: A_27a] :
( ( ( V0I_2E0 != c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum) )
& ( V1J_2E0 != c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum) )
& p(c_2Epred__set_2ESUBSET_2E2(tyop_2Enum_2Enum,V0I_2E0,V1J_2E0)) )
=> p(c_2Earithmetic_2E_3C_3D_2E2(c_2Epred__set_2EMIN__SET_2E1(V1J_2E0),c_2Epred__set_2EMIN__SET_2E1(V0I_2E0))) ) ).
tff(thm_2Epred__set_2ESUBSET__MAX__SET,axiom,
! [V0I_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1J_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,V0I_2E0))
& p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,V1J_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(tyop_2Enum_2Enum,V0I_2E0,V1J_2E0)) )
=> p(c_2Earithmetic_2E_3C_3D_2E2(c_2Epred__set_2EMAX__SET_2E1(V0I_2E0),c_2Epred__set_2EMAX__SET_2E1(V1J_2E0))) ) ).
tff(thm_2Epred__set_2EMIN__SET__LEQ__MAX__SET,axiom,
! [V0s_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( ( ( V0s_2E0 != c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum) )
& p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,V0s_2E0)) )
=> p(c_2Earithmetic_2E_3C_3D_2E2(c_2Epred__set_2EMIN__SET_2E1(V0s_2E0),c_2Epred__set_2EMAX__SET_2E1(V0s_2E0))) ) ).
tff(thm_2Epred__set_2EMIN__SET__UNION,axiom,
! [V0A_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1B_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,V0A_2E0))
& p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,V1B_2E0))
& ( V0A_2E0 != c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum) )
& ( V1B_2E0 != c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum) ) )
=> ( c_2Epred__set_2EMIN__SET_2E1(c_2Epred__set_2EUNION_2E2(tyop_2Enum_2Enum,V0A_2E0,V1B_2E0)) = c_2Earithmetic_2EMIN_2E2(c_2Epred__set_2EMIN__SET_2E1(V0A_2E0),c_2Epred__set_2EMIN__SET_2E1(V1B_2E0)) ) ) ).
tff(thm_2Epred__set_2EMAX__SET__UNION,axiom,
! [V0A_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1B_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,V0A_2E0))
& p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,V1B_2E0)) )
=> ( c_2Epred__set_2EMAX__SET_2E1(c_2Epred__set_2EUNION_2E2(tyop_2Enum_2Enum,V0A_2E0,V1B_2E0)) = c_2Earithmetic_2EMAX_2E2(c_2Epred__set_2EMAX__SET_2E1(V0A_2E0),c_2Epred__set_2EMAX__SET_2E1(V1B_2E0)) ) ) ).
tff(thm_2Epred__set_2EIN__POW,axiom,
! [A_27a: $tType,V0set_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1e_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1e_2E0,c_2Epred__set_2EPOW_2E1(A_27a,V0set_2E0)) = c_2Epred__set_2ESUBSET_2E2(A_27a,V1e_2E0,V0set_2E0) ) ).
tff(thm_2Epred__set_2EUNIV__FUN__TO__BOOL,axiom,
! [A_27a: $tType] : ( c_2Epred__set_2EUNIV_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) = c_2Epred__set_2EPOW_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)) ) ).
tff(thm_2Epred__set_2ESUBSET__POW,axiom,
! [A_27a: $tType,V0s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s1_2E0,V1s2_2E0))
=> p(c_2Epred__set_2ESUBSET_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(A_27a,V0s1_2E0),c_2Epred__set_2EPOW_2E1(A_27a,V1s2_2E0))) ) ).
tff(thm_2Epred__set_2ESUBSET__INSERT__RIGHT,axiom,
! [A_27a: $tType,V0e_2E0: A_27a,V1s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s1_2E0,V2s2_2E0))
=> p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s1_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V0e_2E0,V2s2_2E0))) ) ).
tff(thm_2Epred__set_2ESUBSET__DELETE__BOTH,axiom,
! [A_27a: $tType,V0s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] :
( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s1_2E0,V1s2_2E0))
=> p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Epred__set_2EDELETE_2E2(A_27a,V0s1_2E0,V2x_2E0),c_2Epred__set_2EDELETE_2E2(A_27a,V1s2_2E0,V2x_2E0))) ) ).
tff(thm_2Epred__set_2EPOW__EMPTY,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EPOW_2E1(A_27a,V0s_2E0) != c_2Epred__set_2EEMPTY_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(thm_2Epred__set_2EPOW__INSERT,axiom,
! [A_27a: $tType,V0e_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EPOW_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V0e_2E0,V1s_2E0)) = c_2Epred__set_2EUNION_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E1(A_27a,V0e_2E0),c_2Epred__set_2EPOW_2E1(A_27a,V1s_2E0)),c_2Epred__set_2EPOW_2E1(A_27a,V1s_2E0)) ) ).
tff(thm_2Epred__set_2EPOW__EQNS,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(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)))] :
( ! [V0e_2E0: A_27a,V2ps_2E0: tyop_2Emin_2Efun(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),app_2E2(A_27a,tyop_2Emin_2Efun(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)),F0_2E0,V0e_2E0),V2ps_2E0) = c_2Epred__set_2EUNION_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E1(A_27a,V0e_2E0),V2ps_2E0),V2ps_2E0) )
=> ( ( c_2Epred__set_2EPOW_2E1(A_27a,c_2Epred__set_2EEMPTY_2E0(A_27a)) = c_2Epred__set_2EINSERT_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0(A_27a),c_2Epred__set_2EEMPTY_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) )
& ! [V0e_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EPOW_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V0e_2E0,V1s_2E0)) = c_2Ebool_2ELET_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),app_2E2(A_27a,tyop_2Emin_2Efun(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)),F0_2E0,V0e_2E0),c_2Epred__set_2EPOW_2E1(A_27a,V1s_2E0)) ) ) ) ).
tff(thm_2Epred__set_2EFINITE__POW,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_2Epred__set_2EFINITE_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(A_27a,V0s_2E0))) ) ).
tff(thm_2Epred__set_2ECARD__POW,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
=> ( c_2Epred__set_2ECARD_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(A_27a,V0s_2E0)) = c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0)) ) ) ).
tff(thm_2Epred__set_2EGSPEC__F,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))] :
( ! [V0x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V0x_2E0,c_2Ebool_2EF_2E0) )
=> ( c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,F0_2E0) = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) ).
tff(thm_2Epred__set_2EGSPEC__T,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))] :
( ! [V0x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V0x_2E0,c_2Ebool_2ET_2E0) )
=> ( c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,F0_2E0) = c_2Epred__set_2EUNIV_2E0(A_27a) ) ) ).
tff(thm_2Epred__set_2EGSPEC__ID,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V0y_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0y_2E0),V1x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V1x_2E0,c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V0y_2E0)) )
=> ! [V0y_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0y_2E0)) = V0y_2E0 ) ) ).
tff(thm_2Epred__set_2EGSPEC__EQ,axiom,
! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V1x_2E0: A_27a,V0y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F1_2E0,V1x_2E0),V0y_2E0))
<=> ( V1x_2E0 = V0y_2E0 ) )
=> ( ! [V0y_2E0: A_27a,V1x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0y_2E0),V1x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V1x_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F1_2E0,V1x_2E0),V0y_2E0)) )
=> ! [V0y_2E0: A_27a] : ( c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0y_2E0)) = c_2Epred__set_2EINSERT_2E2(A_27a,V0y_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) ) ) ) ).
tff(thm_2Epred__set_2EGSPEC__EQ2,axiom,
! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V0y_2E0: A_27a,V1x_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F1_2E0,V0y_2E0),V1x_2E0))
<=> ( V0y_2E0 = V1x_2E0 ) )
=> ( ! [V0y_2E0: A_27a,V1x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0y_2E0),V1x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V1x_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F1_2E0,V0y_2E0),V1x_2E0)) )
=> ! [V0y_2E0: A_27a] : ( c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0y_2E0)) = c_2Epred__set_2EINSERT_2E2(A_27a,V0y_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) ) ) ) ).
tff(thm_2Epred__set_2EGSPEC__F__COND,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))] :
( ! [V1x_2E0: A_27a] : ~ p(c_2Epair_2ESND_2E1(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),V0f_2E0,V1x_2E0)))
=> ( c_2Epred__set_2EGSPEC_2E1(A_27b,A_27a,V0f_2E0) = c_2Epred__set_2EEMPTY_2E0(A_27b) ) ) ).
tff(thm_2Epred__set_2EGSPEC__AND,axiom,
! [A_27a: $tType,F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(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_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a,V1Q_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(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F2_2E0,V0P_2E0),V2x_2E0),V1Q_2E0))
<=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V2x_2E0)) ) )
=> ( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,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,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0P_2E0),V1Q_2E0),V2x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V2x_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),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F2_2E0,V0P_2E0),V2x_2E0),V1Q_2E0)) )
=> ( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V0P_2E0),V3x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V3x_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0)) )
=> ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,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,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0P_2E0),V1Q_2E0)) = c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V0P_2E0)),c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V1Q_2E0))) ) ) ) ) ).
tff(thm_2Epred__set_2EGSPEC__OR,axiom,
! [A_27a: $tType,F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(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_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))] :
( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a,V1Q_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(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F2_2E0,V0P_2E0),V2x_2E0),V1Q_2E0))
<=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0))
| p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V2x_2E0)) ) )
=> ( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,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,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0P_2E0),V1Q_2E0),V2x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V2x_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),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F2_2E0,V0P_2E0),V2x_2E0),V1Q_2E0)) )
=> ( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V0P_2E0),V3x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V3x_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0)) )
=> ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,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,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0P_2E0),V1Q_2E0)) = c_2Epred__set_2EUNION_2E2(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V0P_2E0)),c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V1Q_2E0))) ) ) ) ) ).
tff(thm_2Epred__set_2EBIGUNION__partition,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Epred__set_2Eequiv__on_2E2(A_27a,V1R_2E0,V0s_2E0))
=> ( c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2Epartition_2E2(A_27a,V1R_2E0,V0s_2E0)) = V0s_2E0 ) ) ).
tff(thm_2Epred__set_2EEMPTY__NOT__IN__partition,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Epred__set_2Eequiv__on_2E2(A_27a,V1R_2E0,V0s_2E0))
=> ~ p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0(A_27a),c_2Epred__set_2Epartition_2E2(A_27a,V1R_2E0,V0s_2E0))) ) ).
tff(thm_2Epred__set_2Epartition__elements__disjoint,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Epred__set_2Eequiv__on_2E2(A_27a,V1R_2E0,V0s_2E0))
=> ! [V2t1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t1_2E0,c_2Epred__set_2Epartition_2E2(A_27a,V1R_2E0,V0s_2E0)))
& p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t2_2E0,c_2Epred__set_2Epartition_2E2(A_27a,V1R_2E0,V0s_2E0)))
& ( V2t1_2E0 != V3t2_2E0 ) )
=> p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V2t1_2E0,V3t2_2E0)) ) ) ).
tff(thm_2Epred__set_2Epartition__elements__interrelate,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Epred__set_2Eequiv__on_2E2(A_27a,V1R_2E0,V0s_2E0))
=> ! [V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0,c_2Epred__set_2Epartition_2E2(A_27a,V1R_2E0,V0s_2E0)))
=> ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V2t_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V4y_2E0,V2t_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0,V3x_2E0),V4y_2E0)) ) ) ) ).
tff(thm_2Epred__set_2Epartition__SUBSET,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0,c_2Epred__set_2Epartition_2E2(A_27a,V0R_2E0,V1s_2E0)))
=> p(c_2Epred__set_2ESUBSET_2E2(A_27a,V2t_2E0,V1s_2E0)) ) ).
tff(thm_2Epred__set_2EFINITE__partition,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,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(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2Epartition_2E2(A_27a,V0R_2E0,V1s_2E0)))
& ! [V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0,c_2Epred__set_2Epartition_2E2(A_27a,V0R_2E0,V1s_2E0)))
=> p(c_2Epred__set_2EFINITE_2E1(A_27a,V2t_2E0)) ) ) ) ).
tff(thm_2Epred__set_2Epartition__CARD,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2Eequiv__on_2E2(A_27a,V0R_2E0,V1s_2E0))
& p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0)) )
=> ( c_2Epred__set_2ECARD_2E1(A_27a,V1s_2E0) = c_2Epred__set_2ESUM__IMAGE_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECARD_2E0(A_27a),c_2Epred__set_2Epartition_2E2(A_27a,V0R_2E0,V1s_2E0)) ) ) ).
tff(thm_2Epred__set_2Epairwise__UNION,axiom,
! [A_27a: $tType,V0s2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Epred__set_2Epairwise_2E2(A_27a,V2R_2E0,c_2Epred__set_2EUNION_2E2(A_27a,V1s1_2E0,V0s2_2E0)))
<=> ( p(c_2Epred__set_2Epairwise_2E2(A_27a,V2R_2E0,V1s1_2E0))
& p(c_2Epred__set_2Epairwise_2E2(A_27a,V2R_2E0,V0s2_2E0))
& ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V1s1_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V4y_2E0,V0s2_2E0)) )
=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0,V3x_2E0),V4y_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0,V4y_2E0),V3x_2E0)) ) ) ) ) ).
tff(thm_2Epred__set_2Epairwise__SUBSET,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2Epairwise_2E2(A_27a,V0R_2E0,V2t_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,V2t_2E0)) )
=> p(c_2Epred__set_2Epairwise_2E2(A_27a,V0R_2E0,V1s_2E0)) ) ).
tff(thm_2Epred__set_2EKoenigsLemma,axiom,
! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
( ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3x_2E0: A_27a,V4y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F1_2E0,V0R_2E0),V3x_2E0),V4y_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V4y_2E0,c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V3x_2E0,V4y_2E0)) )
=> ( ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0R_2E0),V1x_2E0),V2y_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V2y_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V2y_2E0)) )
=> ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V1x_2E0: A_27a] : p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0R_2E0),V1x_2E0))))
=> ! [V3x_2E0: A_27a] :
( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F1_2E0,V0R_2E0),V3x_2E0))))
=> ? [V5f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] :
( ( app_2E2(tyop_2Enum_2Enum,A_27a,V5f_2E0,c_2Enum_2E0_2E0) = V3x_2E0 )
& ! [V6n_2E0: tyop_2Enum_2Enum] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,app_2E2(tyop_2Enum_2Enum,A_27a,V5f_2E0,V6n_2E0)),app_2E2(tyop_2Enum_2Enum,A_27a,V5f_2E0,c_2Enum_2ESUC_2E1(V6n_2E0)))) ) ) ) ) ) ).
tff(thm_2Epred__set_2EKoenigsLemma__WF,axiom,
! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
( ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V3x_2E0: A_27a,V4y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F1_2E0,V0R_2E0),V3x_2E0),V4y_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V4y_2E0,c_2Erelation_2ERTC_2E3(A_27a,V0R_2E0,V3x_2E0,V4y_2E0)) )
=> ( ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1x_2E0: A_27a,V2y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0R_2E0),V1x_2E0),V2y_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V2y_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V2y_2E0)) )
=> ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ( ! [V1x_2E0: A_27a] : p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0R_2E0),V1x_2E0))))
& p(c_2Erelation_2EWF_2E1(A_27a,c_2Erelation_2Einv_2E1(A_27a,A_27a,V0R_2E0))) )
=> ! [V3x_2E0: A_27a] : p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F1_2E0,V0R_2E0),V3x_2E0)))) ) ) ) ).
tff(thm_2Epred__set_2ESET__EQ__SUBSET,axiom,
! [A_27a: $tType,V0s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( V0s1_2E0 = V1s2_2E0 )
<=> ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s1_2E0,V1s2_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s2_2E0,V0s1_2E0)) ) ) ).
tff(thm_2Epred__set_2EPSUBSET__EQN,axiom,
! [A_27a: $tType,V0s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EPSUBSET_2E2(A_27a,V0s1_2E0,V1s2_2E0))
<=> ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s1_2E0,V1s2_2E0))
& ~ p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s2_2E0,V0s1_2E0)) ) ) ).
tff(thm_2Epred__set_2EPSUBSET__SUBSET__TRANS,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EPSUBSET_2E2(A_27a,V0s_2E0,V1t_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1t_2E0,V2u_2E0)) )
=> p(c_2Epred__set_2EPSUBSET_2E2(A_27a,V0s_2E0,V2u_2E0)) ) ).
tff(thm_2Epred__set_2ESUBSET__PSUBSET__TRANS,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s_2E0,V1t_2E0))
& p(c_2Epred__set_2EPSUBSET_2E2(A_27a,V1t_2E0,V2u_2E0)) )
=> p(c_2Epred__set_2EPSUBSET_2E2(A_27a,V0s_2E0,V2u_2E0)) ) ).
tff(thm_2Epred__set_2ECROSS__EQNS,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)))] :
( ! [V0a_2E0: A_27a,V3y_2E0: A_27b] : ( 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)),F0_2E0,V0a_2E0),V3y_2E0) = c_2Epair_2E_2C_2E2(A_27a,A_27b,V0a_2E0,V3y_2E0) )
=> ! [V0a_2E0: A_27a,V1s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ( c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,c_2Epred__set_2EEMPTY_2E0(A_27a),V2s2_2E0) = c_2Epred__set_2EEMPTY_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)) )
& ( c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,c_2Epred__set_2EINSERT_2E2(A_27a,V0a_2E0,V1s1_2E0),V2s2_2E0) = c_2Epred__set_2EUNION_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epred__set_2EIMAGE_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)),F0_2E0,V0a_2E0),V2s2_2E0),c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,V1s1_2E0,V2s2_2E0)) ) ) ) ).
tff(thm_2Epred__set_2Ecount__EQN,axiom,
! [F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( ! [V1p_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0,V1p_2E0) = c_2Epred__set_2EINSERT_2E2(tyop_2Enum_2Enum,V1p_2E0,c_2Epred__set_2Ecount_2E1(V1p_2E0)) )
=> ( ! [V0n_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V0n_2E0))
<=> ( V0n_2E0 = c_2Enum_2E0_2E0 ) )
=> ! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Epred__set_2Ecount_2E1(V0n_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V0n_2E0),c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum),c_2Ebool_2ELET_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0,c_2Eprim__rec_2EPRE_2E1(V0n_2E0))) ) ) ) ).
tff(thm_2Epred__set_2EUNIQUE__MEMBER__SING,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V1s_2E0))
& ! [V2y_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2y_2E0,V1s_2E0))
=> ( V0x_2E0 = V2y_2E0 ) ) )
<=> ( V1s_2E0 = c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) ) ) ).
tff(thm_2Epred__set_2Einj__surj,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_27b,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V2t_2E0))
=> ( ( V1s_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) )
| ? [V3f_27_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : p(c_2Epred__set_2ESURJ_2E3(A_27b,A_27a,V3f_27_2E0,V2t_2E0,V1s_2E0)) ) ) ).
tff(thm_2Epred__set_2Einfinite__rest,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_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EREST_2E1(A_27a,V0s_2E0))) ) ).
tff(thm_2Epred__set_2Echooser__def__compute,axiom,
! [A_27a: $tType] :
( ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2Echooser_2E2(A_27a,V0s_2E0,c_2Enum_2E0_2E0) = c_2Epred__set_2ECHOICE_2E1(A_27a,V0s_2E0) )
& ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2n_2E0: tyop_2Enum_2Enum] : ( c_2Epred__set_2Echooser_2E2(A_27a,V1s_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V2n_2E0))) = c_2Epred__set_2Echooser_2E2(A_27a,c_2Epred__set_2EREST_2E1(A_27a,V1s_2E0),c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V2n_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) )
& ! [V3s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4n_2E0: tyop_2Enum_2Enum] : ( c_2Epred__set_2Echooser_2E2(A_27a,V3s_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V4n_2E0))) = c_2Epred__set_2Echooser_2E2(A_27a,c_2Epred__set_2EREST_2E1(A_27a,V3s_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V4n_2E0))) ) ) ).
tff(thm_2Epred__set_2Einfinite__num__inj,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
<=> ? [V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : p(c_2Epred__set_2EINJ_2E3(tyop_2Enum_2Enum,A_27a,V1f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),V0s_2E0)) ) ).
tff(thm_2Epred__set_2Ecountable__image__nats,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : p(c_2Epred__set_2Ecountable_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,A_27a,V0f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))) ).
tff(thm_2Epred__set_2Ecountable__surj,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2Ecountable_2E1(A_27a,V0s_2E0))
<=> ( ( V0s_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) )
| ? [V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : p(c_2Epred__set_2ESURJ_2E3(tyop_2Enum_2Enum,A_27a,V1f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),V0s_2E0)) ) ) ).
tff(thm_2Epred__set_2Enum__countable,axiom,
p(c_2Epred__set_2Ecountable_2E1(tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))) ).
tff(thm_2Epred__set_2Esubset__countable,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_2Ecountable_2E1(A_27a,V0s_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1t_2E0,V0s_2E0)) )
=> p(c_2Epred__set_2Ecountable_2E1(A_27a,V1t_2E0)) ) ).
tff(thm_2Epred__set_2Eimage__countable,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_2Ecountable_2E1(A_27a,V1s_2E0))
=> p(c_2Epred__set_2Ecountable_2E1(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0))) ) ).
tff(thm_2Epred__set_2ECOUNTABLE__ALT,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2Ecountable_2E1(A_27a,V0s_2E0))
<=> ? [V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] :
! [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0))
=> ? [V3n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27a,V1f_2E0,V3n_2E0) = V2x_2E0 ) ) ) ).
tff(thm_2Epred__set_2ECOUNTABLE__SUBSET,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_2ESUBSET_2E2(A_27a,V0s_2E0,V1t_2E0))
& p(c_2Epred__set_2Ecountable_2E1(A_27a,V1t_2E0)) )
=> p(c_2Epred__set_2Ecountable_2E1(A_27a,V0s_2E0)) ) ).
tff(thm_2Epred__set_2Efinite__countable,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_2Epred__set_2Ecountable_2E1(A_27a,V0s_2E0)) ) ).
tff(thm_2Epred__set_2ECOUNTABLE__COUNT,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] : p(c_2Epred__set_2Ecountable_2E1(tyop_2Enum_2Enum,c_2Epred__set_2Ecount_2E1(V0n_2E0))) ).
tff(thm_2Epred__set_2ECOUNTABLE__NUM,axiom,
! [V0s_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : p(c_2Epred__set_2Ecountable_2E1(tyop_2Enum_2Enum,V0s_2E0)) ).
tff(thm_2Epred__set_2ECOUNTABLE__IMAGE__NUM,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1s_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : p(c_2Epred__set_2Ecountable_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,A_27a,V0f_2E0,V1s_2E0))) ).
tff(thm_2Epred__set_2Epair__to__num__formula,axiom,
! [V0x_2E0: tyop_2Enum_2Enum,V1y_2E0: tyop_2Enum_2Enum] : ( c_2Epred__set_2Epair__to__num_2E1(c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V0x_2E0,V1y_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2B_2E2(V0x_2E0,V1y_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2E_2B_2E2(V0x_2E0,V1y_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),V1y_2E0) ) ).
tff(thm_2Epred__set_2Epair__to__num__inv,axiom,
( ! [V0x_2E0: tyop_2Enum_2Enum] : ( c_2Epred__set_2Epair__to__num_2E1(c_2Epred__set_2Enum__to__pair_2E1(V0x_2E0)) = V0x_2E0 )
& ! [V1x_2E0: tyop_2Enum_2Enum,V2y_2E0: tyop_2Enum_2Enum] : ( c_2Epred__set_2Enum__to__pair_2E1(c_2Epred__set_2Epair__to__num_2E1(c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V1x_2E0,V2y_2E0))) = c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V1x_2E0,V2y_2E0) ) ) ).
tff(thm_2Epred__set_2Ecross__countable,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_2Ecountable_2E1(A_27a,V0s_2E0))
& p(c_2Epred__set_2Ecountable_2E1(A_27b,V1t_2E0)) )
=> p(c_2Epred__set_2Ecountable_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))) ) ).
tff(thm_2Epred__set_2Einter__countable,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_2Ecountable_2E1(A_27a,V0s_2E0))
| p(c_2Epred__set_2Ecountable_2E1(A_27a,V1t_2E0)) )
=> p(c_2Epred__set_2Ecountable_2E1(A_27a,c_2Epred__set_2EINTER_2E2(A_27a,V0s_2E0,V1t_2E0))) ) ).
tff(thm_2Epred__set_2Einj__countable,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_27b,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2Ecountable_2E1(A_27b,V2t_2E0))
& p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V2t_2E0)) )
=> p(c_2Epred__set_2Ecountable_2E1(A_27a,V1s_2E0)) ) ).
tff(thm_2Epred__set_2Ebigunion__countable,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2Ecountable_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))
& ! [V1x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0,V0s_2E0))
=> p(c_2Epred__set_2Ecountable_2E1(A_27a,V1x_2E0)) ) )
=> p(c_2Epred__set_2Ecountable_2E1(A_27a,c_2Epred__set_2EBIGUNION_2E1(A_27a,V0s_2E0))) ) ).
tff(thm_2Epred__set_2Eunion__countable,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_2Ecountable_2E1(A_27a,V0s_2E0))
& p(c_2Epred__set_2Ecountable_2E1(A_27a,V1t_2E0)) )
=> p(c_2Epred__set_2Ecountable_2E1(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V0s_2E0,V1t_2E0))) ) ).
tff(thm_2Epred__set_2Eunion__countable__IFF,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2Ecountable_2E1(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,V0t_2E0)))
<=> ( p(c_2Epred__set_2Ecountable_2E1(A_27a,V1s_2E0))
& p(c_2Epred__set_2Ecountable_2E1(A_27a,V0t_2E0)) ) ) ).
tff(thm_2Epred__set_2Einj__image__countable__IFF,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)] :
( p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V1f_2E0,V0s_2E0,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V1f_2E0,V0s_2E0)))
=> ( c_2Epred__set_2Ecountable_2E1(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V1f_2E0,V0s_2E0)) = c_2Epred__set_2Ecountable_2E1(A_27a,V0s_2E0) ) ) ).
tff(thm_2Epred__set_2Epow__no__surj,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
~ ? [V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : p(c_2Epred__set_2ESURJ_2E3(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0,V0s_2E0,c_2Epred__set_2EPOW_2E1(A_27a,V0s_2E0))) ).
tff(thm_2Epred__set_2Einfinite__pow__uncountable,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_2Epred__set_2Ecountable_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E1(A_27a,V0s_2E0))) ) ).
tff(thm_2Epred__set_2Ecountable__Usum,axiom,
! [A_27a: $tType,A_27b: $tType] :
( p(c_2Epred__set_2Ecountable_2E1(tyop_2Esum_2Esum(A_27a,A_27b),c_2Epred__set_2EUNIV_2E0(tyop_2Esum_2Esum(A_27a,A_27b))))
<=> ( p(c_2Epred__set_2Ecountable_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)))
& p(c_2Epred__set_2Ecountable_2E1(A_27b,c_2Epred__set_2EUNIV_2E0(A_27b))) ) ) ).
tff(thm_2Epred__set_2Ecountable__EMPTY,axiom,
! [A_27a: $tType] : p(c_2Epred__set_2Ecountable_2E1(A_27a,c_2Epred__set_2EEMPTY_2E0(A_27a))) ).
tff(thm_2Epred__set_2Ecountable__INSERT,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2Ecountable_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,V1s_2E0)) = c_2Epred__set_2Ecountable_2E1(A_27a,V1s_2E0) ) ).
tff(thm_2Epred__set_2Ecross__countable__IFF,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_2Ecountable_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,V1s_2E0,V0t_2E0)))
<=> ( ( V1s_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) )
| ( V0t_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27b) )
| ( p(c_2Epred__set_2Ecountable_2E1(A_27a,V1s_2E0))
& p(c_2Epred__set_2Ecountable_2E1(A_27b,V0t_2E0)) ) ) ) ).
tff(thm_2Epred__set_2Ecountable__Uprod,axiom,
! [A_27a: $tType,A_27b: $tType] :
( p(c_2Epred__set_2Ecountable_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epred__set_2EUNIV_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))))
<=> ( p(c_2Epred__set_2Ecountable_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)))
& p(c_2Epred__set_2Ecountable_2E1(A_27b,c_2Epred__set_2EUNIV_2E0(A_27b))) ) ) ).
tff(thm_2Epred__set_2EEXPLICIT__ENUMERATE__MONO,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Earithmetic_2EFUNPOW_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E0(A_27a),V0n_2E0,V1s_2E0),V1s_2E0)) ).
tff(thm_2Epred__set_2EEXPLICIT__ENUMERATE__NOT__EMPTY,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
=> ( c_2Earithmetic_2EFUNPOW_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E0(A_27a),V0n_2E0,V1s_2E0) != c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) ).
tff(thm_2Epred__set_2EINFINITE__EXPLICIT__ENUMERATE,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))] :
( ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),F0_2E0,V0s_2E0),V1n_2E0) = c_2Epred__set_2ECHOICE_2E1(A_27a,c_2Earithmetic_2EFUNPOW_2E3(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E0(A_27a),V1n_2E0,V0s_2E0)) )
=> ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
=> p(c_2Epred__set_2EINJ_2E3(tyop_2Enum_2Enum,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),F0_2E0,V0s_2E0),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),V0s_2E0)) ) ) ).
tff(thm_2Epred__set_2EBIJ__NUM__COUNTABLE,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ? [V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : p(c_2Epred__set_2EBIJ_2E3(tyop_2Enum_2Enum,A_27a,V1f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),V0s_2E0))
=> p(c_2Epred__set_2Ecountable_2E1(A_27a,V0s_2E0)) ) ).
tff(thm_2Epred__set_2EENUMERATE,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ? [V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : p(c_2Epred__set_2EBIJ_2E3(tyop_2Enum_2Enum,A_27a,V1f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),V0s_2E0))
<=> p(c_2Epred__set_2EBIJ_2E3(tyop_2Enum_2Enum,A_27a,c_2Epred__set_2Eenumerate_2E1(A_27a,V0s_2E0),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),V0s_2E0)) ) ).
tff(thm_2Epred__set_2ECOUNTABLE__ALT__BIJ,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2Ecountable_2E1(A_27a,V0s_2E0))
<=> ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
| p(c_2Epred__set_2EBIJ_2E3(tyop_2Enum_2Enum,A_27a,c_2Epred__set_2Eenumerate_2E1(A_27a,V0s_2E0),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),V0s_2E0)) ) ) ).
tff(thm_2Epred__set_2ECOUNTABLE__ENUM,axiom,
! [A_27a: $tType,V0c_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2Ecountable_2E1(A_27a,V0c_2E0))
<=> ( ( V0c_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) )
| ? [V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : ( V0c_2E0 = c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,A_27a,V1f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)) ) ) ) ).
tff(thm_2Epred__set_2EIMAGE__BIGUNION,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1M_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EBIGUNION_2E1(A_27a,V1M_2E0)) = c_2Epred__set_2EBIGUNION_2E1(A_27b,c_2Epred__set_2EIMAGE_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E1(A_27a,A_27b,V0f_2E0),V1M_2E0)) ) ).
tff(thm_2Epred__set_2ESUBSET__DIFF,axiom,
! [A_27a: $tType,V0s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s1_2E0,c_2Epred__set_2EDIFF_2E2(A_27a,V1s2_2E0,V2s3_2E0)))
<=> ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s1_2E0,V1s2_2E0))
& p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V0s1_2E0,V2s3_2E0)) ) ) ).
tff(thm_2Epred__set_2EINTER__SUBSET__EQN,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_2EINTER_2E2(A_27a,V1A_2E0,V0B_2E0) = V1A_2E0 )
<=> p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1A_2E0,V0B_2E0)) )
& ( ( c_2Epred__set_2EINTER_2E2(A_27a,V1A_2E0,V0B_2E0) = V0B_2E0 )
<=> p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0B_2E0,V1A_2E0)) ) ) ).
tff(thm_2Epred__set_2EPSUBSET__SING,axiom,
! [A_27a: $tType,V0s_2E0: A_27a,V1x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EPSUBSET_2E2(A_27a,V1x_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V0s_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a))))
<=> ( V1x_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) ).
tff(thm_2Epred__set_2EINTER__UNION,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_2EINTER_2E2(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V1A_2E0,V0B_2E0),V1A_2E0) = V1A_2E0 )
& ( c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V0B_2E0,V1A_2E0),V1A_2E0) = V1A_2E0 )
& ( c_2Epred__set_2EINTER_2E2(A_27a,V1A_2E0,c_2Epred__set_2EUNION_2E2(A_27a,V1A_2E0,V0B_2E0)) = V1A_2E0 )
& ( c_2Epred__set_2EINTER_2E2(A_27a,V1A_2E0,c_2Epred__set_2EUNION_2E2(A_27a,V0B_2E0,V1A_2E0)) = V1A_2E0 ) ) ).
tff(thm_2Epred__set_2EUNION__DELETE,axiom,
! [A_27a: $tType,V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1B_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] : ( c_2Epred__set_2EDELETE_2E2(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V0A_2E0,V1B_2E0),V2x_2E0) = c_2Epred__set_2EUNION_2E2(A_27a,c_2Epred__set_2EDELETE_2E2(A_27a,V0A_2E0,V2x_2E0),c_2Epred__set_2EDELETE_2E2(A_27a,V1B_2E0,V2x_2E0)) ) ).
tff(thm_2Epred__set_2EDELETE__SUBSET__INSERT,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1e_2E0: A_27a,V2s2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Epred__set_2EDELETE_2E2(A_27a,V0s_2E0,V1e_2E0),V2s2_2E0) = c_2Epred__set_2ESUBSET_2E2(A_27a,V0s_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V1e_2E0,V2s2_2E0)) ) ).
tff(thm_2Epred__set_2EIN__INSERT__EXPAND,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1y_2E0: A_27a,V2P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V1y_2E0,V2P_2E0)))
<=> ( ( V0x_2E0 = V1y_2E0 )
| ( ( V0x_2E0 != V1y_2E0 )
& p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V2P_2E0)) ) ) ) ).
tff(thm_2Epred__set_2EFINITE__INTER,axiom,
! [A_27a: $tType,V0s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s1_2E0))
| p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s2_2E0)) )
=> p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EINTER_2E2(A_27a,V0s1_2E0,V1s2_2E0))) ) ).
tff(thm_2Epred__set_2EINSERT__EQ__SING,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0: A_27a,V2y_2E0: A_27a] :
( ( c_2Epred__set_2EINSERT_2E2(A_27a,V1x_2E0,V0s_2E0) = c_2Epred__set_2EINSERT_2E2(A_27a,V2y_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) )
<=> ( ( V1x_2E0 = V2y_2E0 )
& p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V2y_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)))) ) ) ).
tff(thm_2Epred__set_2ECARD__UNION__LE,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Emin_2Efun(A_27a,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_27a,V0t_2E0)) )
=> p(c_2Earithmetic_2E_3C_3D_2E2(c_2Epred__set_2ECARD_2E1(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,V0t_2E0)),c_2Earithmetic_2E_2B_2E2(c_2Epred__set_2ECARD_2E1(A_27a,V1s_2E0),c_2Epred__set_2ECARD_2E1(A_27a,V0t_2E0)))) ) ).
tff(thm_2Epred__set_2EIMAGE__SUBSET__gen,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),V2u_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,V2u_2E0))
& p(c_2Epred__set_2ESUBSET_2E2(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V2u_2E0),V3t_2E0)) )
=> p(c_2Epred__set_2ESUBSET_2E2(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0),V3t_2E0)) ) ).
tff(thm_2Epred__set_2ECARD__REST,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) ) )
=> ( c_2Epred__set_2ECARD_2E1(A_27a,c_2Epred__set_2EREST_2E1(A_27a,V0s_2E0)) = c_2Earithmetic_2E_2D_2E2(c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ) ).
tff(thm_2Epred__set_2ESUBSET__DIFF__EMPTY,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( c_2Epred__set_2EDIFF_2E2(A_27a,V0s_2E0,V1t_2E0) = c_2Epred__set_2EEMPTY_2E0(A_27a) )
<=> p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s_2E0,V1t_2E0)) ) ).
tff(thm_2Epred__set_2EDIFF__INTER__SUBSET,axiom,
! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0r_2E0,V1s_2E0))
=> ( c_2Epred__set_2EDIFF_2E2(A_27a,V0r_2E0,c_2Epred__set_2EINTER_2E2(A_27a,V1s_2E0,V2t_2E0)) = c_2Epred__set_2EDIFF_2E2(A_27a,V0r_2E0,V2t_2E0) ) ) ).
tff(thm_2Epred__set_2EUNION__DIFF__2,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(A_27a,V0s_2E0,c_2Epred__set_2EDIFF_2E2(A_27a,V0s_2E0,V1t_2E0)) = V0s_2E0 ) ).
tff(thm_2Epred__set_2Ecount__add,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] : ( c_2Epred__set_2Ecount_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0)) = c_2Epred__set_2EUNION_2E2(tyop_2Enum_2Enum,c_2Epred__set_2Ecount_2E1(V0n_2E0),c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E1(V0n_2E0),c_2Epred__set_2Ecount_2E1(V1m_2E0))) ) ).
tff(thm_2Epred__set_2EIMAGE__EQ__SING,axiom,
! [A_27a: $tType,A_27b: $tType,V0z_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2f_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( ( c_2Epred__set_2EIMAGE_2E2(A_27b,A_27a,V2f_2E0,V1s_2E0) = c_2Epred__set_2EINSERT_2E2(A_27a,V0z_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) )
<=> ( ( V1s_2E0 != c_2Epred__set_2EEMPTY_2E0(A_27b) )
& ! [V3x_2E0: A_27b] :
( p(c_2Ebool_2EIN_2E2(A_27b,V3x_2E0,V1s_2E0))
=> ( app_2E2(A_27b,A_27a,V2f_2E0,V3x_2E0) = V0z_2E0 ) ) ) ) ).
tff(thm_2Epred__set_2Ecount__add1,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Epred__set_2Ecount_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) = c_2Epred__set_2EINSERT_2E2(tyop_2Enum_2Enum,V0n_2E0,c_2Epred__set_2Ecount_2E1(V0n_2E0)) ) ).
tff(thm_2Epred__set_2Ecompl__insert,axiom,
! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0: A_27a] : ( c_2Epred__set_2ECOMPL_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V1x_2E0,V0s_2E0)) = c_2Epred__set_2EDELETE_2E2(A_27a,c_2Epred__set_2ECOMPL_2E1(A_27a,V0s_2E0),V1x_2E0) ) ).
tff(thm_2Epred__set_2Ein__max__set,axiom,
! [V0s_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,V0s_2E0))
=> ! [V1x_2E0: tyop_2Enum_2Enum] :
( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V1x_2E0,V0s_2E0))
=> p(c_2Earithmetic_2E_3C_3D_2E2(V1x_2E0,c_2Epred__set_2EMAX__SET_2E1(V0s_2E0))) ) ) ).
tff(thm_2Epred__set_2EPREIMAGE__ALT,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0) = c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Ebool,A_27b,V1s_2E0,V0f_2E0) ) ).
tff(thm_2Epred__set_2EIN__PREIMAGE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2x_2E0: A_27a] : ( c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0)) = c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0),V1s_2E0) ) ).
tff(thm_2Epred__set_2EPREIMAGE__applied,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2x_2E0: A_27a] : ( c_2Epred__set_2EPREIMAGE_2E3(A_27a,A_27b,V0f_2E0,V1s_2E0,V2x_2E0) = c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0),V1s_2E0) ) ).
tff(thm_2Epred__set_2EPREIMAGE__EMPTY,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EEMPTY_2E0(A_27b)) = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ).
tff(thm_2Epred__set_2EPREIMAGE__UNIV,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EUNIV_2E0(A_27b)) = c_2Epred__set_2EUNIV_2E0(A_27a) ) ).
tff(thm_2Epred__set_2EPREIMAGE__COMPL,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2ECOMPL_2E1(A_27b,V1s_2E0)) = c_2Epred__set_2ECOMPL_2E1(A_27a,c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0)) ) ).
tff(thm_2Epred__set_2EPREIMAGE__UNION,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EUNION_2E2(A_27b,V1s_2E0,V2t_2E0)) = c_2Epred__set_2EUNION_2E2(A_27a,c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0),c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V0f_2E0,V2t_2E0)) ) ).
tff(thm_2Epred__set_2EPREIMAGE__INTER,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EINTER_2E2(A_27b,V1s_2E0,V2t_2E0)) = c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0),c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V0f_2E0,V2t_2E0)) ) ).
tff(thm_2Epred__set_2EPREIMAGE__BIGUNION,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EBIGUNION_2E1(A_27b,V1s_2E0)) = c_2Epred__set_2EBIGUNION_2E1(A_27a,c_2Epred__set_2EIMAGE_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EPREIMAGE_2E1(A_27a,A_27b,V0f_2E0),V1s_2E0)) ) ).
tff(thm_2Epred__set_2EPREIMAGE__COMP,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27b,A_27c),V2s_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EPREIMAGE_2E2(A_27b,A_27c,V1g_2E0,V2s_2E0)) = c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27c,c_2Ecombin_2Eo_2E2(A_27a,A_27c,A_27b,V1g_2E0,V0f_2E0),V2s_2E0) ) ).
tff(thm_2Epred__set_2EPREIMAGE__DIFF,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EDIFF_2E2(A_27b,V1s_2E0,V2t_2E0)) = c_2Epred__set_2EDIFF_2E2(A_27a,c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0),c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V0f_2E0,V2t_2E0)) ) ).
tff(thm_2Epred__set_2EPREIMAGE__I,axiom,
! [A_27a: $tType] : ( c_2Epred__set_2EPREIMAGE_2E1(A_27a,A_27a,c_2Ecombin_2EI_2E0(A_27a)) = c_2Ecombin_2EI_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ) ).
tff(thm_2Epred__set_2EPREIMAGE__K,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EPREIMAGE_2E2(A_27b,A_27a,c_2Ecombin_2EK_2E1(A_27a,A_27b,V0x_2E0),V1s_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V1s_2E0),c_2Epred__set_2EUNIV_2E0(A_27b),c_2Epred__set_2EEMPTY_2E0(A_27b)) ) ).
tff(thm_2Epred__set_2EPREIMAGE__DISJOINT,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EDISJOINT_2E2(A_27b,V1s_2E0,V2t_2E0))
=> p(c_2Epred__set_2EDISJOINT_2E2(A_27a,c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0),c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V0f_2E0,V2t_2E0))) ) ).
tff(thm_2Epred__set_2EPREIMAGE__SUBSET,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2ESUBSET_2E2(A_27b,V1s_2E0,V2t_2E0))
=> p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0),c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V0f_2E0,V2t_2E0))) ) ).
tff(thm_2Epred__set_2EPREIMAGE__CROSS,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),V1a_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2b_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EPREIMAGE_2E2(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c),V0f_2E0,c_2Epred__set_2ECROSS_2E2(A_27b,A_27c,V1a_2E0,V2b_2E0)) = c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,c_2Ecombin_2Eo_2E2(A_27a,A_27b,tyop_2Epair_2Eprod(A_27b,A_27c),c_2Epair_2EFST_2E0(A_27b,A_27c),V0f_2E0),V1a_2E0),c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27c,c_2Ecombin_2Eo_2E2(A_27a,A_27c,tyop_2Epair_2Eprod(A_27b,A_27c),c_2Epair_2ESND_2E0(A_27b,A_27c),V0f_2E0),V2b_2E0)) ) ).
tff(thm_2Epred__set_2EPREIMAGE__COMPL__INTER,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),V2sp_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2ECOMPL_2E1(A_27b,V1t_2E0)),V2sp_2E0) = c_2Epred__set_2EDIFF_2E2(A_27a,V2sp_2E0,c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1t_2E0)) ) ).
tff(thm_2Epred__set_2EPREIMAGE__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)] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0)))) ).
tff(thm_2Epred__set_2EIMAGE__PREIMAGE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : p(c_2Epred__set_2ESUBSET_2E2(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EPREIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0)),V1s_2E0)) ).
tff(thm_2Epred__set_2EFINITE__is__measure__maximal,axiom,
! [A_27a: $tType,V0m_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
& ( V1s_2E0 != c_2Epred__set_2EEMPTY_2E0(A_27a) ) )
=> ? [V2x_2E0: A_27a] : p(c_2Epred__set_2Eis__measure__maximal_2E3(A_27a,V0m_2E0,V1s_2E0,V2x_2E0)) ) ).
tff(thm_2Epred__set_2Eis__measure__maximal__SING,axiom,
! [A_27a: $tType,V0y_2E0: A_27a,V1x_2E0: A_27a,V2m_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
( p(c_2Epred__set_2Eis__measure__maximal_2E3(A_27a,V2m_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V1x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)),V0y_2E0))
<=> ( V0y_2E0 = V1x_2E0 ) ) ).
tff(thm_2Epred__set_2Eis__measure__maximal__INSERT,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2m_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3e_2E0: A_27a,V4y_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V1s_2E0))
& p(c_2Eprim__rec_2E_3C_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V2m_2E0,V3e_2E0),app_2E2(A_27a,tyop_2Enum_2Enum,V2m_2E0,V0x_2E0))) )
=> ( c_2Epred__set_2Eis__measure__maximal_2E3(A_27a,V2m_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V3e_2E0,V1s_2E0),V4y_2E0) = c_2Epred__set_2Eis__measure__maximal_2E3(A_27a,V2m_2E0,V1s_2E0,V4y_2E0) ) ) ).
%------------------------------------------------------------------------------