ITP001 Axioms: ITP147_7.ax
%------------------------------------------------------------------------------
% File : ITP147_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 : product.ax [Gau19]
% : HL4147_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 264 ( 67 unt; 107 typ; 0 def)
% Number of atoms : 385 ( 211 equ)
% Maximal formula atoms : 15 ( 1 avg)
% Number of connectives : 237 ( 9 ~; 3 |; 67 &)
% ( 25 <=>; 133 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 85 ( 50 >; 35 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 103 ( 103 usr; 30 con; 0-5 aty)
% Number of variables : 712 ( 644 !; 5 ?; 712 :)
% ( 63 !>; 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_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).
tff(tyop_2Erealax_2Ereal,type,
tyop_2Erealax_2Ereal: $tType ).
tff(app_2E2,type,
app_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(p,type,
p: tyop_2Emin_2Ebool > $o ).
tff(combin_i_2E0,type,
combin_i_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(combin_k_2E0,type,
combin_k_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(combin_s_2E0,type,
combin_s_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))) ).
tff(c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Earithmetic_2E_2A_2E0,type,
c_2Earithmetic_2E_2A_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2A_2E2,type,
c_2Earithmetic_2E_2A_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2E_2B_2E0,type,
c_2Earithmetic_2E_2B_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2B_2E2,type,
c_2Earithmetic_2E_2B_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Epair_2E_2C_2E0,type,
c_2Epair_2E_2C_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))) ).
tff(c_2Epair_2E_2C_2E2,type,
c_2Epair_2E_2C_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > tyop_2Epair_2Eprod(A_27a,A_27b) ) ).
tff(c_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_2Eiterate_2E_2E_2E_2E0,type,
c_2Eiterate_2E_2E_2E_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))) ).
tff(c_2Eiterate_2E_2E_2E_2E2,type,
c_2Eiterate_2E_2E_2E_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).
tff(c_2Ereal_2E_2F_2E0,type,
c_2Ereal_2E_2F_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)) ).
tff(c_2Ereal_2E_2F_2E2,type,
c_2Ereal_2E_2F_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal ).
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_2Earithmetic_2EBIT1_2E0,type,
c_2Earithmetic_2EBIT1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EBIT1_2E1,type,
c_2Earithmetic_2EBIT1_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2EBIT2_2E0,type,
c_2Earithmetic_2EBIT2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EBIT2_2E1,type,
c_2Earithmetic_2EBIT2_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Epred__set_2ECARD_2E0,type,
c_2Epred__set_2ECARD_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum) ).
tff(c_2Epred__set_2ECARD_2E1,type,
c_2Epred__set_2ECARD_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Enum_2Enum ) ).
tff(c_2Ebool_2ECOND_2E0,type,
c_2Ebool_2ECOND_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))) ).
tff(c_2Ebool_2ECOND_2E3,type,
c_2Ebool_2ECOND_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Ebool * A_27a * A_27a ) > A_27a ) ).
tff(c_2Epred__set_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_2EDISJOINT_2E0,type,
c_2Epred__set_2EDISJOINT_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2EDISJOINT_2E2,type,
c_2Epred__set_2EDISJOINT_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2EEMPTY_2E0,type,
c_2Epred__set_2EEMPTY_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).
tff(c_2Earithmetic_2EEXP_2E0,type,
c_2Earithmetic_2EEXP_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2EEXP_2E2,type,
c_2Earithmetic_2EEXP_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(c_2Earithmetic_2EFACT_2E0,type,
c_2Earithmetic_2EFACT_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EFACT_2E1,type,
c_2Earithmetic_2EFACT_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Epred__set_2EFINITE_2E0,type,
c_2Epred__set_2EFINITE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Epred__set_2EFINITE_2E1,type,
c_2Epred__set_2EFINITE_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2EGSPEC_2E0,type,
c_2Epred__set_2EGSPEC_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2EGSPEC_2E1,type,
c_2Epred__set_2EGSPEC_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Epred__set_2EIMAGE_2E0,type,
c_2Epred__set_2EIMAGE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EIMAGE_2E2,type,
c_2Epred__set_2EIMAGE_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) ).
tff(c_2Ebool_2EIN_2E0,type,
c_2Ebool_2EIN_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2EIN_2E2,type,
c_2Ebool_2EIN_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2EINSERT_2E0,type,
c_2Epred__set_2EINSERT_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EINSERT_2E2,type,
c_2Epred__set_2EINSERT_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_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_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_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
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_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_2Ereal_2Eabs_2E0,type,
c_2Ereal_2Eabs_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) ).
tff(c_2Ereal_2Eabs_2E1,type,
c_2Ereal_2Eabs_2E1: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
tff(c_2Erealax_2Einv_2E0,type,
c_2Erealax_2Einv_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) ).
tff(c_2Erealax_2Einv_2E1,type,
c_2Erealax_2Einv_2E1: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
tff(c_2Eiterate_2Eiterate_2E0,type,
c_2Eiterate_2Eiterate_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b))) ).
tff(c_2Eiterate_2Eiterate_2E1,type,
c_2Eiterate_2Eiterate_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)) ) ).
tff(c_2Eproduct_2Enproduct_2E0,type,
c_2Eproduct_2Enproduct_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Enum_2Enum)) ).
tff(c_2Eproduct_2Enproduct_2E2,type,
c_2Eproduct_2Enproduct_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,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_2Ereal_2Epow_2E0,type,
c_2Ereal_2Epow_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)) ).
tff(c_2Ereal_2Epow_2E2,type,
c_2Ereal_2Epow_2E2: ( tyop_2Erealax_2Ereal * tyop_2Enum_2Enum ) > tyop_2Erealax_2Ereal ).
tff(c_2Eproduct_2Eproduct_2E0,type,
c_2Eproduct_2Eproduct_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Erealax_2Ereal)) ).
tff(c_2Eproduct_2Eproduct_2E2,type,
c_2Eproduct_2Eproduct_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal) ) > tyop_2Erealax_2Ereal ) ).
tff(c_2Erealax_2Ereal__add_2E0,type,
c_2Erealax_2Ereal__add_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)) ).
tff(c_2Erealax_2Ereal__add_2E2,type,
c_2Erealax_2Ereal__add_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal ).
tff(c_2Erealax_2Ereal__lt_2E0,type,
c_2Erealax_2Ereal__lt_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)) ).
tff(c_2Erealax_2Ereal__lt_2E2,type,
c_2Erealax_2Ereal__lt_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Emin_2Ebool ).
tff(c_2Ereal_2Ereal__lte_2E0,type,
c_2Ereal_2Ereal__lte_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool)) ).
tff(c_2Ereal_2Ereal__lte_2E2,type,
c_2Ereal_2Ereal__lte_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Emin_2Ebool ).
tff(c_2Erealax_2Ereal__mul_2E0,type,
c_2Erealax_2Ereal__mul_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)) ).
tff(c_2Erealax_2Ereal__mul_2E2,type,
c_2Erealax_2Ereal__mul_2E2: ( tyop_2Erealax_2Ereal * tyop_2Erealax_2Ereal ) > tyop_2Erealax_2Ereal ).
tff(c_2Erealax_2Ereal__neg_2E0,type,
c_2Erealax_2Ereal__neg_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) ).
tff(c_2Erealax_2Ereal__neg_2E1,type,
c_2Erealax_2Ereal__neg_2E1: tyop_2Erealax_2Ereal > tyop_2Erealax_2Ereal ).
tff(c_2Ereal_2Ereal__of__num_2E0,type,
c_2Ereal_2Ereal__of__num_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal) ).
tff(c_2Ereal_2Ereal__of__num_2E1,type,
c_2Ereal_2Ereal__of__num_2E1: tyop_2Enum_2Enum > tyop_2Erealax_2Ereal ).
tff(c_2Eiterate_2Esupport_2E0,type,
c_2Eiterate_2Esupport_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),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_2Emin_2Ebool)))) ).
tff(c_2Eiterate_2Esupport_2E3,type,
c_2Eiterate_2Esupport_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)) * tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(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(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_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_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_2Eiterate_2E_2E_2E_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Eiterate_2E_2E_2E_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Eiterate_2E_2E_2E_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ereal_2E_2F_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2E_2F_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ereal_2E_2F_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_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(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_2Erealax_2Ereal,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Erealax_2Ereal,X2_2E0: tyop_2Erealax_2Ereal] : ( c_2Ebool_2ECOND_2E3(tyop_2Erealax_2Ereal,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),c_2Ebool_2ECOND_2E0(tyop_2Erealax_2Ereal),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: A_27a] : ( c_2Epred__set_2EDELETE_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EDELETE_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_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_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_2Earithmetic_2EFACT_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EFACT_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EFACT_2E0,X0_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_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_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(A_27b,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(A_27b,A_27b),X0_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_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_2Epred__set_2EINSERT_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINSERT_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINSERT_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(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(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(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_2EUNION_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EUNION_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
| p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Ereal_2Eabs_2E1,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Eabs_2E1(X0_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Ereal_2Eabs_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Erealax_2Einv_2E1,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Einv_2E1(X0_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Erealax_2Einv_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Eiterate_2Eiterate_2E1_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Eiterate_2Eiterate_2E1(A_27a,tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Enum_2Enum)),c_2Eiterate_2Eiterate_2E0(A_27a,tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eiterate_2Eiterate_2E1_2Emono_2EA_27a_20mono_2Etyop_2Erealax_2Ereal,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal))] : ( c_2Eiterate_2Eiterate_2E1(A_27a,tyop_2Erealax_2Ereal,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Erealax_2Ereal)),c_2Eiterate_2Eiterate_2E0(A_27a,tyop_2Erealax_2Ereal),X0_2E0) ) ).
tff(arityeq2_2Ec_2Eproduct_2Enproduct_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_2Enum_2Enum)] : ( c_2Eproduct_2Enproduct_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Eproduct_2Enproduct_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eproduct_2Enproduct_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_2Enum_2Enum)] : ( c_2Eproduct_2Enproduct_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Eproduct_2Enproduct_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eproduct_2Enproduct_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_2Enum_2Enum)] : ( c_2Eproduct_2Enproduct_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Eproduct_2Enproduct_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Ecombin_2Eo_2E2(A_27a,tyop_2Enum_2Enum,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),c_2Ecombin_2Eo_2E0(A_27a,tyop_2Enum_2Enum,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Erealax_2Ereal_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Erealax_2Ereal),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Ecombin_2Eo_2E2(A_27a,tyop_2Erealax_2Ereal,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal)),c_2Ecombin_2Eo_2E0(A_27a,tyop_2Erealax_2Ereal,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ereal_2Epow_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Enum_2Enum] : ( c_2Ereal_2Epow_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),c_2Ereal_2Epow_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eproduct_2Eproduct_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_2Erealax_2Ereal)] : ( c_2Eproduct_2Eproduct_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Erealax_2Ereal,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Erealax_2Ereal),c_2Eproduct_2Eproduct_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eproduct_2Eproduct_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_2Erealax_2Ereal)] : ( c_2Eproduct_2Eproduct_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Erealax_2Ereal),tyop_2Erealax_2Ereal,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Erealax_2Ereal),tyop_2Erealax_2Ereal),c_2Eproduct_2Eproduct_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eproduct_2Eproduct_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_2Erealax_2Ereal)] : ( c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Erealax_2Ereal,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Erealax_2Ereal),c_2Eproduct_2Eproduct_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erealax_2Ereal__add_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__add_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Ereal__add_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erealax_2Ereal__lt_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__lt_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Erealax_2Ereal__lt_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ereal_2Ereal__lte_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Ereal_2Ereal__lte_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal_2Ereal__lte_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erealax_2Ereal__mul_2E2,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal,X1_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__mul_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Erealax_2Ereal__mul_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Erealax_2Ereal__neg_2E1,axiom,
! [X0_2E0: tyop_2Erealax_2Ereal] : ( c_2Erealax_2Ereal__neg_2E1(X0_2E0) = app_2E2(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__neg_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Ereal_2Ereal__of__num_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Ereal_2Ereal__of__num_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,c_2Ereal_2Ereal__of__num_2E0,X0_2E0) ) ).
tff(arityeq3_2Ec_2Eiterate_2Esupport_2E3_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eiterate_2Esupport_2E3(A_27a,tyop_2Enum_2Enum,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_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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),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))),c_2Eiterate_2Esupport_2E0(A_27a,tyop_2Enum_2Enum),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Eiterate_2Esupport_2E3_2Emono_2EA_27a_20mono_2Etyop_2Erealax_2Ereal,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eiterate_2Esupport_2E3(A_27a,tyop_2Erealax_2Ereal,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_2Erealax_2Ereal),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_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eiterate_2Esupport_2E0(A_27a,tyop_2Erealax_2Ereal),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_2Eproduct_2Eproduct,axiom,
! [A_27a: $tType] : ( c_2Eproduct_2Eproduct_2E0(A_27a) = c_2Eiterate_2Eiterate_2E1(A_27a,tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E0) ) ).
tff(thm_2Eproduct_2Enproduct,axiom,
! [A_27a: $tType] : ( c_2Eproduct_2Enproduct_2E0(A_27a) = c_2Eiterate_2Eiterate_2E1(A_27a,tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E0) ) ).
tff(thm_2Eproduct_2EPRODUCT__DELTA,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(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal)))] :
( ! [V3x_2E0: A_27a,V2a_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,V3x_2E0),V2a_2E0))
<=> ( V3x_2E0 = V2a_2E0 ) )
=> ( ! [V2a_2E0: A_27a,V0b_2E0: tyop_2Erealax_2Ereal,V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal)),F0_2E0,V2a_2E0),V0b_2E0),V3x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Erealax_2Ereal,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F1_2E0,V3x_2E0),V2a_2E0),V0b_2E0,c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) )
=> ! [V0b_2E0: tyop_2Erealax_2Ereal,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2a_2E0: A_27a] : ( c_2Eproduct_2Eproduct_2E2(A_27a,V1s_2E0,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal)),F0_2E0,V2a_2E0),V0b_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Erealax_2Ereal,c_2Ebool_2EIN_2E2(A_27a,V2a_2E0,V1s_2E0),V0b_2E0,c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) ) ) ) ).
tff(thm_2Eproduct_2EPRODUCT__DELETE,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2a_2E0: A_27a] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V2a_2E0,V1s_2E0)) )
=> ( c_2Erealax_2Ereal__mul_2E2(app_2E2(A_27a,tyop_2Erealax_2Ereal,V0f_2E0,V2a_2E0),c_2Eproduct_2Eproduct_2E2(A_27a,c_2Epred__set_2EDELETE_2E2(A_27a,V1s_2E0,V2a_2E0),V0f_2E0)) = c_2Eproduct_2Eproduct_2E2(A_27a,V1s_2E0,V0f_2E0) ) ) ).
tff(thm_2Eproduct_2EPRODUCT__PAIR,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V3i_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),F0_2E0,V0f_2E0),V3i_2E0) = c_2Erealax_2Ereal__mul_2E2(app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V0f_2E0,c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V3i_2E0)),app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V0f_2E0,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V3i_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V1m_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] : ( c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1m_2E0),c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V2n_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0f_2E0) = c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V1m_2E0,V2n_2E0),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),F0_2E0,V0f_2E0)) ) ) ).
tff(thm_2Eproduct_2EPRODUCT__SUPERSET,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V1u_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2v_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1u_2E0,V2v_2E0))
& ! [V3x_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V2v_2E0))
& ~ p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V1u_2E0)) )
=> ( app_2E2(A_27a,tyop_2Erealax_2Ereal,V0f_2E0,V3x_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ) )
=> ( c_2Eproduct_2Eproduct_2E2(A_27a,V2v_2E0,V0f_2E0) = c_2Eproduct_2Eproduct_2E2(A_27a,V1u_2E0,V0f_2E0) ) ) ).
tff(thm_2Eproduct_2EREAL__OF__NUM__NPRODUCT,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Erealax_2Ereal,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),F0_2E0,V0f_2E0),V2x_2E0) = c_2Ereal_2Ereal__of__num_2E1(app_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V2x_2E0)) )
=> ! [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_2Ereal_2Ereal__of__num_2E1(c_2Eproduct_2Enproduct_2E2(A_27a,V1s_2E0,V0f_2E0)) = c_2Eproduct_2Eproduct_2E2(A_27a,V1s_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),F0_2E0,V0f_2E0)) ) ) ) ).
tff(thm_2Eproduct_2EPRODUCT__CLAUSES__RIGHT,axiom,
! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V1m_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V2n_2E0))
& p(c_2Earithmetic_2E_3C_3D_2E2(V1m_2E0,V2n_2E0)) )
=> ( c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V1m_2E0,V2n_2E0),V0f_2E0) = c_2Erealax_2Ereal__mul_2E2(c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V1m_2E0,c_2Earithmetic_2E_2D_2E2(V2n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0f_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V0f_2E0,V2n_2E0)) ) ) ).
tff(thm_2Eproduct_2EPRODUCT__CLAUSES__LEFT,axiom,
! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V1m_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V1m_2E0,V2n_2E0))
=> ( c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V1m_2E0,V2n_2E0),V0f_2E0) = c_2Erealax_2Ereal__mul_2E2(app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V0f_2E0,V1m_2E0),c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(c_2Earithmetic_2E_2B_2E2(V1m_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V2n_2E0),V0f_2E0)) ) ) ).
tff(thm_2Eproduct_2EPRODUCT__CLOSED,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,V0P_2E0,c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))
& ! [V3x_2E0: tyop_2Erealax_2Ereal,V4y_2E0: tyop_2Erealax_2Ereal] :
( ( p(app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0))
& p(app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,V0P_2E0,V4y_2E0)) )
=> p(app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,V0P_2E0,c_2Erealax_2Ereal__mul_2E2(V3x_2E0,V4y_2E0))) )
& ! [V5a_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V5a_2E0,V2s_2E0))
=> p(app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,V0P_2E0,app_2E2(A_27a,tyop_2Erealax_2Ereal,V1f_2E0,V5a_2E0))) ) )
=> p(app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool,V0P_2E0,c_2Eproduct_2Eproduct_2E2(A_27a,V2s_2E0,V1f_2E0))) ) ).
tff(thm_2Eproduct_2EPRODUCT__ABS,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Erealax_2Ereal,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),F0_2E0,V0f_2E0),V2x_2E0) = c_2Ereal_2Eabs_2E1(app_2E2(A_27a,tyop_2Erealax_2Ereal,V0f_2E0,V2x_2E0)) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
=> ( c_2Eproduct_2Eproduct_2E2(A_27a,V1s_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),F0_2E0,V0f_2E0)) = c_2Ereal_2Eabs_2E1(c_2Eproduct_2Eproduct_2E2(A_27a,V1s_2E0,V0f_2E0)) ) ) ) ).
tff(thm_2Eproduct_2EPRODUCT__LE__1,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
& ! [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
=> ( p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0),app_2E2(A_27a,tyop_2Erealax_2Ereal,V0f_2E0,V2x_2E0)))
& p(c_2Ereal_2Ereal__lte_2E2(app_2E2(A_27a,tyop_2Erealax_2Ereal,V0f_2E0,V2x_2E0),c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ) ) )
=> p(c_2Ereal_2Ereal__lte_2E2(c_2Eproduct_2Eproduct_2E2(A_27a,V1s_2E0,V0f_2E0),c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ) ).
tff(thm_2Eproduct_2EPRODUCT__ONE,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal)] :
( ! [V1n_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Erealax_2Ereal,F0_2E0,V1n_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) )
=> ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eproduct_2Eproduct_2E2(A_27a,V0s_2E0,F0_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ) ).
tff(thm_2Eproduct_2EPRODUCT__DIV__NUMSEG,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V1g_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4x_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),F0_2E0,V0f_2E0),V1g_2E0),V4x_2E0) = c_2Ereal_2E_2F_2E2(app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V0f_2E0,V4x_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V1g_2E0,V4x_2E0)) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V1g_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2m_2E0: tyop_2Enum_2Enum,V3n_2E0: tyop_2Enum_2Enum] : ( c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V2m_2E0,V3n_2E0),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),F0_2E0,V0f_2E0),V1g_2E0)) = c_2Ereal_2E_2F_2E2(c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V2m_2E0,V3n_2E0),V0f_2E0),c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V2m_2E0,V3n_2E0),V1g_2E0)) ) ) ).
tff(thm_2Eproduct_2EPRODUCT__DIV,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal)))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Erealax_2Ereal,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal)),F0_2E0,V0f_2E0),V1g_2E0),V3x_2E0) = c_2Ereal_2E_2F_2E2(app_2E2(A_27a,tyop_2Erealax_2Ereal,V0f_2E0,V3x_2E0),app_2E2(A_27a,tyop_2Erealax_2Ereal,V1g_2E0,V3x_2E0)) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V2s_2E0))
=> ( c_2Eproduct_2Eproduct_2E2(A_27a,V2s_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal)),F0_2E0,V0f_2E0),V1g_2E0)) = c_2Ereal_2E_2F_2E2(c_2Eproduct_2Eproduct_2E2(A_27a,V2s_2E0,V0f_2E0),c_2Eproduct_2Eproduct_2E2(A_27a,V2s_2E0,V1g_2E0)) ) ) ) ).
tff(thm_2Eproduct_2EPRODUCT__INV,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Erealax_2Ereal,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),F0_2E0,V0f_2E0),V2x_2E0) = c_2Erealax_2Einv_2E1(app_2E2(A_27a,tyop_2Erealax_2Ereal,V0f_2E0,V2x_2E0)) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
=> ( c_2Eproduct_2Eproduct_2E2(A_27a,V1s_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),F0_2E0,V0f_2E0)) = c_2Erealax_2Einv_2E1(c_2Eproduct_2Eproduct_2E2(A_27a,V1s_2E0,V0f_2E0)) ) ) ) ).
tff(thm_2Eproduct_2EPRODUCT__NEG__NUMSEG__1,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2i_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),F0_2E0,V0f_2E0),V2i_2E0) = c_2Erealax_2Ereal__neg_2E1(app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V0f_2E0,V2i_2E0)) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V1n_2E0: tyop_2Enum_2Enum] : ( c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V1n_2E0),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),F0_2E0,V0f_2E0)) = c_2Erealax_2Ereal__mul_2E2(c_2Ereal_2Epow_2E2(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V1n_2E0),c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V1n_2E0),V0f_2E0)) ) ) ).
tff(thm_2Eproduct_2EPRODUCT__NEG__NUMSEG,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V3i_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),F0_2E0,V0f_2E0),V3i_2E0) = c_2Erealax_2Ereal__neg_2E1(app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V0f_2E0,V3i_2E0)) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V1m_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] : ( c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V1m_2E0,V2n_2E0),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),F0_2E0,V0f_2E0)) = c_2Erealax_2Ereal__mul_2E2(c_2Ereal_2Epow_2E2(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2E_2B_2E2(V2n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V1m_2E0)),c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V1m_2E0,V2n_2E0),V0f_2E0)) ) ) ).
tff(thm_2Eproduct_2EPRODUCT__NEG,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V2i_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Erealax_2Ereal,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),F0_2E0,V0f_2E0),V2i_2E0) = c_2Erealax_2Ereal__neg_2E1(app_2E2(A_27a,tyop_2Erealax_2Ereal,V0f_2E0,V2i_2E0)) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
=> ( c_2Eproduct_2Eproduct_2E2(A_27a,V1s_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),F0_2E0,V0f_2E0)) = c_2Erealax_2Ereal__mul_2E2(c_2Ereal_2Epow_2E2(c_2Erealax_2Ereal__neg_2E1(c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2Epred__set_2ECARD_2E1(A_27a,V1s_2E0)),c_2Eproduct_2Eproduct_2E2(A_27a,V1s_2E0,V0f_2E0)) ) ) ) ).
tff(thm_2Eproduct_2EPRODUCT__CONST__NUMSEG__1,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal))] :
( ! [V0c_2E0: tyop_2Erealax_2Ereal,V2x_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),F0_2E0,V0c_2E0),V2x_2E0) = V0c_2E0 )
=> ! [V0c_2E0: tyop_2Erealax_2Ereal,V1n_2E0: tyop_2Enum_2Enum] : ( c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V1n_2E0),app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),F0_2E0,V0c_2E0)) = c_2Ereal_2Epow_2E2(V0c_2E0,V1n_2E0) ) ) ).
tff(thm_2Eproduct_2EPRODUCT__CONST__NUMSEG,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal))] :
( ! [V0c_2E0: tyop_2Erealax_2Ereal,V3x_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),F0_2E0,V0c_2E0),V3x_2E0) = V0c_2E0 )
=> ! [V0c_2E0: tyop_2Erealax_2Ereal,V1m_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] : ( c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V1m_2E0,V2n_2E0),app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),F0_2E0,V0c_2E0)) = c_2Ereal_2Epow_2E2(V0c_2E0,c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2E_2B_2E2(V2n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V1m_2E0)) ) ) ).
tff(thm_2Eproduct_2EPRODUCT__CONST,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal))] :
( ! [V0c_2E0: tyop_2Erealax_2Ereal,V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Erealax_2Ereal,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),F0_2E0,V0c_2E0),V2x_2E0) = V0c_2E0 )
=> ! [V0c_2E0: tyop_2Erealax_2Ereal,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
=> ( c_2Eproduct_2Eproduct_2E2(A_27a,V1s_2E0,app_2E2(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),F0_2E0,V0c_2E0)) = c_2Ereal_2Epow_2E2(V0c_2E0,c_2Epred__set_2ECARD_2E1(A_27a,V1s_2E0)) ) ) ) ).
tff(thm_2Eproduct_2EPRODUCT__MUL__NUMSEG,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V1g_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V4x_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),F0_2E0,V0f_2E0),V1g_2E0),V4x_2E0) = c_2Erealax_2Ereal__mul_2E2(app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V0f_2E0,V4x_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V1g_2E0,V4x_2E0)) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V1g_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2m_2E0: tyop_2Enum_2Enum,V3n_2E0: tyop_2Enum_2Enum] : ( c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V2m_2E0,V3n_2E0),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),F0_2E0,V0f_2E0),V1g_2E0)) = c_2Erealax_2Ereal__mul_2E2(c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V2m_2E0,V3n_2E0),V0f_2E0),c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V2m_2E0,V3n_2E0),V1g_2E0)) ) ) ).
tff(thm_2Eproduct_2EPRODUCT__MUL,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal)))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Erealax_2Ereal,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal)),F0_2E0,V0f_2E0),V1g_2E0),V3x_2E0) = c_2Erealax_2Ereal__mul_2E2(app_2E2(A_27a,tyop_2Erealax_2Ereal,V0f_2E0,V3x_2E0),app_2E2(A_27a,tyop_2Erealax_2Ereal,V1g_2E0,V3x_2E0)) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V2s_2E0))
=> ( c_2Eproduct_2Eproduct_2E2(A_27a,V2s_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal)),F0_2E0,V0f_2E0),V1g_2E0)) = c_2Erealax_2Ereal__mul_2E2(c_2Eproduct_2Eproduct_2E2(A_27a,V2s_2E0,V0f_2E0),c_2Eproduct_2Eproduct_2E2(A_27a,V2s_2E0,V1g_2E0)) ) ) ) ).
tff(thm_2Eproduct_2EPRODUCT__MUL__GEN,axiom,
! [A_27a: $tType,F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal))),F4_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_2Erealax_2Ereal),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_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),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_2Erealax_2Ereal),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_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V5x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Erealax_2Ereal,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal)),F2_2E0,V0f_2E0),V1g_2E0),V5x_2E0) = c_2Erealax_2Ereal__mul_2E2(app_2E2(A_27a,tyop_2Erealax_2Ereal,V0f_2E0,V5x_2E0),app_2E2(A_27a,tyop_2Erealax_2Ereal,V1g_2E0,V5x_2E0)) )
=> ( ! [V4x_2E0: A_27a,V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal)] :
( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),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_2Erealax_2Ereal),tyop_2Emin_2Ebool)),F4_2E0,V4x_2E0),V2s_2E0),V1g_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V2s_2E0))
& ( app_2E2(A_27a,tyop_2Erealax_2Ereal,V1g_2E0,V4x_2E0) != c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ) )
=> ( ! [V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V4x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),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_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F1_2E0,V2s_2E0),V1g_2E0),V4x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V4x_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),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_2Erealax_2Ereal),tyop_2Emin_2Ebool)),F4_2E0,V4x_2E0),V2s_2E0),V1g_2E0)) )
=> ( ! [V3x_2E0: A_27a,V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal)] :
( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),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_2Erealax_2Ereal),tyop_2Emin_2Ebool)),F3_2E0,V3x_2E0),V2s_2E0),V0f_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V2s_2E0))
& ( app_2E2(A_27a,tyop_2Erealax_2Ereal,V0f_2E0,V3x_2E0) != c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ) )
=> ( ! [V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),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_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V2s_2E0),V0f_2E0),V3x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V3x_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),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_2Erealax_2Ereal),tyop_2Emin_2Ebool)),F3_2E0,V3x_2E0),V2s_2E0),V0f_2E0)) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),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_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V2s_2E0),V0f_2E0))))
& p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),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_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F1_2E0,V2s_2E0),V1g_2E0)))) )
=> ( c_2Eproduct_2Eproduct_2E2(A_27a,V2s_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal)),F2_2E0,V0f_2E0),V1g_2E0)) = c_2Erealax_2Ereal__mul_2E2(c_2Eproduct_2Eproduct_2E2(A_27a,V2s_2E0,V0f_2E0),c_2Eproduct_2Eproduct_2E2(A_27a,V2s_2E0,V1g_2E0)) ) ) ) ) ) ) ) ).
tff(thm_2Eproduct_2EPRODUCT__EQ__1__NUMSEG,axiom,
! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V1m_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] :
( ! [V3i_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Earithmetic_2E_3C_3D_2E2(V1m_2E0,V3i_2E0))
& p(c_2Earithmetic_2E_3C_3D_2E2(V3i_2E0,V2n_2E0)) )
=> ( app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V0f_2E0,V3i_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) )
=> ( c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V1m_2E0,V2n_2E0),V0f_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ) ).
tff(thm_2Eproduct_2EPRODUCT__EQ__1,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),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))
=> ( app_2E2(A_27a,tyop_2Erealax_2Ereal,V0f_2E0,V2x_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) )
=> ( c_2Eproduct_2Eproduct_2E2(A_27a,V1s_2E0,V0f_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ) ).
tff(thm_2Eproduct_2EPRODUCT__LE__NUMSEG,axiom,
! [V0g_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2m_2E0: tyop_2Enum_2Enum,V3n_2E0: tyop_2Enum_2Enum] :
( ! [V4i_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Earithmetic_2E_3C_3D_2E2(V2m_2E0,V4i_2E0))
& p(c_2Earithmetic_2E_3C_3D_2E2(V4i_2E0,V3n_2E0)) )
=> ( p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V1f_2E0,V4i_2E0)))
& p(c_2Ereal_2Ereal__lte_2E2(app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V1f_2E0,V4i_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V0g_2E0,V4i_2E0))) ) )
=> p(c_2Ereal_2Ereal__lte_2E2(c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V2m_2E0,V3n_2E0),V1f_2E0),c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V2m_2E0,V3n_2E0),V0g_2E0))) ) ).
tff(thm_2Eproduct_2EPRODUCT__LE,axiom,
! [A_27a: $tType,V0g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),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_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0),app_2E2(A_27a,tyop_2Erealax_2Ereal,V1f_2E0,V3x_2E0)))
& p(c_2Ereal_2Ereal__lte_2E2(app_2E2(A_27a,tyop_2Erealax_2Ereal,V1f_2E0,V3x_2E0),app_2E2(A_27a,tyop_2Erealax_2Ereal,V0g_2E0,V3x_2E0))) ) ) )
=> p(c_2Ereal_2Ereal__lte_2E2(c_2Eproduct_2Eproduct_2E2(A_27a,V2s_2E0,V1f_2E0),c_2Eproduct_2Eproduct_2E2(A_27a,V2s_2E0,V0g_2E0))) ) ).
tff(thm_2Eproduct_2EPRODUCT__EQ__0__NUMSEG,axiom,
! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V1m_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] :
( ( c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V1m_2E0,V2n_2E0),V0f_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) )
<=> ? [V3x_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V1m_2E0,V3x_2E0))
& p(c_2Earithmetic_2E_3C_3D_2E2(V3x_2E0,V2n_2E0))
& ( app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V0f_2E0,V3x_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) ) ) ) ).
tff(thm_2Eproduct_2EPRODUCT__EQ__0,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
=> ( ( c_2Eproduct_2Eproduct_2E2(A_27a,V1s_2E0,V0f_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) )
<=> ? [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
& ( app_2E2(A_27a,tyop_2Erealax_2Ereal,V0f_2E0,V2x_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0) ) ) ) ) ).
tff(thm_2Eproduct_2EPRODUCT__EQ__NUMSEG,axiom,
! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V1g_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2m_2E0: tyop_2Enum_2Enum,V3n_2E0: tyop_2Enum_2Enum] :
( ! [V4i_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Earithmetic_2E_3C_3D_2E2(V2m_2E0,V4i_2E0))
& p(c_2Earithmetic_2E_3C_3D_2E2(V4i_2E0,V3n_2E0)) )
=> ( app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V0f_2E0,V4i_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V1g_2E0,V4i_2E0) ) )
=> ( c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V2m_2E0,V3n_2E0),V0f_2E0) = c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V2m_2E0,V3n_2E0),V1g_2E0) ) ) ).
tff(thm_2Eproduct_2EPRODUCT__EQ,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V2s_2E0))
=> ( app_2E2(A_27a,tyop_2Erealax_2Ereal,V0f_2E0,V3x_2E0) = app_2E2(A_27a,tyop_2Erealax_2Ereal,V1g_2E0,V3x_2E0) ) )
=> ( c_2Eproduct_2Eproduct_2E2(A_27a,V2s_2E0,V0f_2E0) = c_2Eproduct_2Eproduct_2E2(A_27a,V2s_2E0,V1g_2E0) ) ) ).
tff(thm_2Eproduct_2EPRODUCT__CLAUSES__NUMSEG,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( ! [V1m_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V1m_2E0))
<=> ( V1m_2E0 = c_2Enum_2E0_2E0 ) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)] :
( ! [V1m_2E0: tyop_2Enum_2Enum] : ( c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V1m_2E0,c_2Enum_2E0_2E0),V0f_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Erealax_2Ereal,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V1m_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V0f_2E0,c_2Enum_2E0_2E0),c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) )
& ! [V2m_2E0: tyop_2Enum_2Enum,V3n_2E0: tyop_2Enum_2Enum] : ( c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V2m_2E0,c_2Enum_2ESUC_2E1(V3n_2E0)),V0f_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Erealax_2Ereal,c_2Earithmetic_2E_3C_3D_2E2(V2m_2E0,c_2Enum_2ESUC_2E1(V3n_2E0)),c_2Erealax_2Ereal__mul_2E2(c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V2m_2E0,V3n_2E0),V0f_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V0f_2E0,c_2Enum_2ESUC_2E1(V3n_2E0))),c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V2m_2E0,V3n_2E0),V0f_2E0)) ) ) ) ).
tff(thm_2Eproduct_2EPRODUCT__SING__NUMSEG,axiom,
! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V1n_2E0: tyop_2Enum_2Enum] : ( c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V1n_2E0,V1n_2E0),V0f_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V0f_2E0,V1n_2E0) ) ).
tff(thm_2Eproduct_2EPRODUCT__SING,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V1x_2E0: A_27a] : ( c_2Eproduct_2Eproduct_2E2(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V1x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)),V0f_2E0) = app_2E2(A_27a,tyop_2Erealax_2Ereal,V0f_2E0,V1x_2E0) ) ).
tff(thm_2Eproduct_2EPRODUCT__OFFSET,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)))] :
( ! [V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V3p_2E0: tyop_2Enum_2Enum,V4i_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),F0_2E0,V1f_2E0),V3p_2E0),V4i_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V1f_2E0,c_2Earithmetic_2E_2B_2E2(V4i_2E0,V3p_2E0)) )
=> ! [V0n_2E0: tyop_2Enum_2Enum,V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V2m_2E0: tyop_2Enum_2Enum,V3p_2E0: tyop_2Enum_2Enum] : ( c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(c_2Earithmetic_2E_2B_2E2(V2m_2E0,V3p_2E0),c_2Earithmetic_2E_2B_2E2(V0n_2E0,V3p_2E0)),V1f_2E0) = c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V2m_2E0,V0n_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),F0_2E0,V1f_2E0),V3p_2E0)) ) ) ).
tff(thm_2Eproduct_2EPRODUCT__POS__LT__NUMSEG,axiom,
! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V1m_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] :
( ! [V3x_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Earithmetic_2E_3C_3D_2E2(V1m_2E0,V3x_2E0))
& p(c_2Earithmetic_2E_3C_3D_2E2(V3x_2E0,V2n_2E0)) )
=> p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V0f_2E0,V3x_2E0))) )
=> p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0),c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V1m_2E0,V2n_2E0),V0f_2E0))) ) ).
tff(thm_2Eproduct_2EPRODUCT__POS__LT,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
& ! [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
=> p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0),app_2E2(A_27a,tyop_2Erealax_2Ereal,V0f_2E0,V2x_2E0))) ) )
=> p(c_2Erealax_2Ereal__lt_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0),c_2Eproduct_2Eproduct_2E2(A_27a,V1s_2E0,V0f_2E0))) ) ).
tff(thm_2Eproduct_2EPRODUCT__POS__LE__NUMSEG,axiom,
! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V1m_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] :
( ! [V3x_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Earithmetic_2E_3C_3D_2E2(V1m_2E0,V3x_2E0))
& p(c_2Earithmetic_2E_3C_3D_2E2(V3x_2E0,V2n_2E0)) )
=> p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V0f_2E0,V3x_2E0))) )
=> p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0),c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V1m_2E0,V2n_2E0),V0f_2E0))) ) ).
tff(thm_2Eproduct_2EPRODUCT__POS__LE,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
& ! [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
=> p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0),app_2E2(A_27a,tyop_2Erealax_2Ereal,V0f_2E0,V2x_2E0))) ) )
=> p(c_2Ereal_2Ereal__lte_2E2(c_2Ereal_2Ereal__of__num_2E1(c_2Enum_2E0_2E0),c_2Eproduct_2Eproduct_2E2(A_27a,V1s_2E0,V0f_2E0))) ) ).
tff(thm_2Eproduct_2EPRODUCT__ADD__SPLIT,axiom,
! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V1m_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum,V3p_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V1m_2E0,c_2Earithmetic_2E_2B_2E2(V2n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))
=> ( c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V1m_2E0,c_2Earithmetic_2E_2B_2E2(V2n_2E0,V3p_2E0)),V0f_2E0) = c_2Erealax_2Ereal__mul_2E2(c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V1m_2E0,V2n_2E0),V0f_2E0),c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(c_2Earithmetic_2E_2B_2E2(V2n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2E_2B_2E2(V2n_2E0,V3p_2E0)),V0f_2E0)) ) ) ).
tff(thm_2Eproduct_2EPRODUCT__IMAGE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Erealax_2Ereal),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V2s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V4y_2E0,V2s_2E0))
& ( app_2E2(A_27a,A_27b,V0f_2E0,V3x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V4y_2E0) ) )
=> ( V3x_2E0 = V4y_2E0 ) )
=> ( c_2Eproduct_2Eproduct_2E2(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V2s_2E0),V1g_2E0) = c_2Eproduct_2Eproduct_2E2(A_27a,V2s_2E0,c_2Ecombin_2Eo_2E2(A_27a,tyop_2Erealax_2Ereal,A_27b,V1g_2E0,V0f_2E0)) ) ) ).
tff(thm_2Eproduct_2EPRODUCT__UNION,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),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))
& p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V1s_2E0,V2t_2E0)) )
=> ( c_2Eproduct_2Eproduct_2E2(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,V2t_2E0),V0f_2E0) = c_2Erealax_2Ereal__mul_2E2(c_2Eproduct_2Eproduct_2E2(A_27a,V1s_2E0,V0f_2E0),c_2Eproduct_2Eproduct_2E2(A_27a,V2t_2E0,V0f_2E0)) ) ) ).
tff(thm_2Eproduct_2EPRODUCT__SUPPORT,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eproduct_2Eproduct_2E2(A_27a,c_2Eiterate_2Esupport_2E3(A_27a,tyop_2Erealax_2Ereal,c_2Erealax_2Ereal__mul_2E0,V0f_2E0,V1s_2E0),V0f_2E0) = c_2Eproduct_2Eproduct_2E2(A_27a,V1s_2E0,V0f_2E0) ) ).
tff(thm_2Eproduct_2EPRODUCT__CLAUSES,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal)] : ( c_2Eproduct_2Eproduct_2E2(A_27a,c_2Epred__set_2EEMPTY_2E0(A_27a),V0f_2E0) = c_2Ereal_2Ereal__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) )
& ! [V1x_2E0: A_27b,V2f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Erealax_2Ereal),V3s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27b,V3s_2E0))
=> ( c_2Eproduct_2Eproduct_2E2(A_27b,c_2Epred__set_2EINSERT_2E2(A_27b,V1x_2E0,V3s_2E0),V2f_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Erealax_2Ereal,c_2Ebool_2EIN_2E2(A_27b,V1x_2E0,V3s_2E0),c_2Eproduct_2Eproduct_2E2(A_27b,V3s_2E0,V2f_2E0),c_2Erealax_2Ereal__mul_2E2(app_2E2(A_27b,tyop_2Erealax_2Ereal,V2f_2E0,V1x_2E0),c_2Eproduct_2Eproduct_2E2(A_27b,V3s_2E0,V2f_2E0))) ) ) ) ).
tff(thm_2Eproduct_2EREAL__ADD__AC,axiom,
! [V0p_2E0: tyop_2Erealax_2Ereal,V1n_2E0: tyop_2Erealax_2Ereal,V2m_2E0: tyop_2Erealax_2Ereal] :
( ( c_2Erealax_2Ereal__add_2E2(V2m_2E0,V1n_2E0) = c_2Erealax_2Ereal__add_2E2(V1n_2E0,V2m_2E0) )
& ( c_2Erealax_2Ereal__add_2E2(c_2Erealax_2Ereal__add_2E2(V2m_2E0,V1n_2E0),V0p_2E0) = c_2Erealax_2Ereal__add_2E2(V2m_2E0,c_2Erealax_2Ereal__add_2E2(V1n_2E0,V0p_2E0)) )
& ( c_2Erealax_2Ereal__add_2E2(V2m_2E0,c_2Erealax_2Ereal__add_2E2(V1n_2E0,V0p_2E0)) = c_2Erealax_2Ereal__add_2E2(V1n_2E0,c_2Erealax_2Ereal__add_2E2(V2m_2E0,V0p_2E0)) ) ) ).
tff(thm_2Eproduct_2EMULT__AC,axiom,
! [V0p_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum,V2m_2E0: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A_2E2(V2m_2E0,V1n_2E0) = c_2Earithmetic_2E_2A_2E2(V1n_2E0,V2m_2E0) )
& ( c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2E_2A_2E2(V2m_2E0,V1n_2E0),V0p_2E0) = c_2Earithmetic_2E_2A_2E2(V2m_2E0,c_2Earithmetic_2E_2A_2E2(V1n_2E0,V0p_2E0)) )
& ( c_2Earithmetic_2E_2A_2E2(V2m_2E0,c_2Earithmetic_2E_2A_2E2(V1n_2E0,V0p_2E0)) = c_2Earithmetic_2E_2A_2E2(V1n_2E0,c_2Earithmetic_2E_2A_2E2(V2m_2E0,V0p_2E0)) ) ) ).
tff(thm_2Eproduct_2ENPRODUCT__CLAUSES,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Eproduct_2Enproduct_2E2(A_27a,c_2Epred__set_2EEMPTY_2E0(A_27a),V0f_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) )
& ! [V1x_2E0: A_27b,V2f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V3s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( p(c_2Epred__set_2EFINITE_2E1(A_27b,V3s_2E0))
=> ( c_2Eproduct_2Enproduct_2E2(A_27b,c_2Epred__set_2EINSERT_2E2(A_27b,V1x_2E0,V3s_2E0),V2f_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Ebool_2EIN_2E2(A_27b,V1x_2E0,V3s_2E0),c_2Eproduct_2Enproduct_2E2(A_27b,V3s_2E0,V2f_2E0),c_2Earithmetic_2E_2A_2E2(app_2E2(A_27b,tyop_2Enum_2Enum,V2f_2E0,V1x_2E0),c_2Eproduct_2Enproduct_2E2(A_27b,V3s_2E0,V2f_2E0))) ) ) ) ).
tff(thm_2Eproduct_2ENPRODUCT__SUPPORT,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eproduct_2Enproduct_2E2(A_27a,c_2Eiterate_2Esupport_2E3(A_27a,tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E0,V0f_2E0,V1s_2E0),V0f_2E0) = c_2Eproduct_2Enproduct_2E2(A_27a,V1s_2E0,V0f_2E0) ) ).
tff(thm_2Eproduct_2ENPRODUCT__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))
& p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V1s_2E0,V2t_2E0)) )
=> ( c_2Eproduct_2Enproduct_2E2(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V1s_2E0,V2t_2E0),V0f_2E0) = c_2Earithmetic_2E_2A_2E2(c_2Eproduct_2Enproduct_2E2(A_27a,V1s_2E0,V0f_2E0),c_2Eproduct_2Enproduct_2E2(A_27a,V2t_2E0,V0f_2E0)) ) ) ).
tff(thm_2Eproduct_2ENPRODUCT__IMAGE,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V2s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V4y_2E0,V2s_2E0))
& ( app_2E2(A_27a,A_27b,V0f_2E0,V3x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V4y_2E0) ) )
=> ( V3x_2E0 = V4y_2E0 ) )
=> ( c_2Eproduct_2Enproduct_2E2(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V2s_2E0),V1g_2E0) = c_2Eproduct_2Enproduct_2E2(A_27a,V2s_2E0,c_2Ecombin_2Eo_2E2(A_27a,tyop_2Enum_2Enum,A_27b,V1g_2E0,V0f_2E0)) ) ) ).
tff(thm_2Eproduct_2ENPRODUCT__ADD__SPLIT,axiom,
! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1m_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum,V3p_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V1m_2E0,c_2Earithmetic_2E_2B_2E2(V2n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))
=> ( c_2Eproduct_2Enproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V1m_2E0,c_2Earithmetic_2E_2B_2E2(V2n_2E0,V3p_2E0)),V0f_2E0) = c_2Earithmetic_2E_2A_2E2(c_2Eproduct_2Enproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V1m_2E0,V2n_2E0),V0f_2E0),c_2Eproduct_2Enproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(c_2Earithmetic_2E_2B_2E2(V2n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2E_2B_2E2(V2n_2E0,V3p_2E0)),V0f_2E0)) ) ) ).
tff(thm_2Eproduct_2ENPRODUCT__POS__LT,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))
& ! [V2x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
=> p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,app_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V2x_2E0))) ) )
=> p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,c_2Eproduct_2Enproduct_2E2(A_27a,V1s_2E0,V0f_2E0))) ) ).
tff(thm_2Eproduct_2ENPRODUCT__POS__LT__NUMSEG,axiom,
! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1m_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] :
( ! [V3x_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Earithmetic_2E_3C_3D_2E2(V1m_2E0,V3x_2E0))
& p(c_2Earithmetic_2E_3C_3D_2E2(V3x_2E0,V2n_2E0)) )
=> p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V0f_2E0,V3x_2E0))) )
=> p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,c_2Eproduct_2Enproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V1m_2E0,V2n_2E0),V0f_2E0))) ) ).
tff(thm_2Eproduct_2ENPRODUCT__OFFSET,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))] :
( ! [V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V3p_2E0: tyop_2Enum_2Enum,V4i_2E0: tyop_2Enum_2Enum] : ( 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_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F0_2E0,V1f_2E0),V3p_2E0),V4i_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V1f_2E0,c_2Earithmetic_2E_2B_2E2(V4i_2E0,V3p_2E0)) )
=> ! [V0n_2E0: tyop_2Enum_2Enum,V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2m_2E0: tyop_2Enum_2Enum,V3p_2E0: tyop_2Enum_2Enum] : ( c_2Eproduct_2Enproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(c_2Earithmetic_2E_2B_2E2(V2m_2E0,V3p_2E0),c_2Earithmetic_2E_2B_2E2(V0n_2E0,V3p_2E0)),V1f_2E0) = c_2Eproduct_2Enproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V2m_2E0,V0n_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F0_2E0,V1f_2E0),V3p_2E0)) ) ) ).
tff(thm_2Eproduct_2ENPRODUCT__SING,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1x_2E0: A_27a] : ( c_2Eproduct_2Enproduct_2E2(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V1x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)),V0f_2E0) = app_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V1x_2E0) ) ).
tff(thm_2Eproduct_2ENPRODUCT__SING__NUMSEG,axiom,
! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1n_2E0: tyop_2Enum_2Enum] : ( c_2Eproduct_2Enproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V1n_2E0,V1n_2E0),V0f_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V0f_2E0,V1n_2E0) ) ).
tff(thm_2Eproduct_2ENPRODUCT__CLAUSES__NUMSEG,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( ! [V1m_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V1m_2E0))
<=> ( V1m_2E0 = c_2Enum_2E0_2E0 ) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] :
( ! [V1m_2E0: tyop_2Enum_2Enum] : ( c_2Eproduct_2Enproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V1m_2E0,c_2Enum_2E0_2E0),V0f_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V1m_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V0f_2E0,c_2Enum_2E0_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) )
& ! [V2m_2E0: tyop_2Enum_2Enum,V3n_2E0: tyop_2Enum_2Enum] : ( c_2Eproduct_2Enproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V2m_2E0,c_2Enum_2ESUC_2E1(V3n_2E0)),V0f_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Earithmetic_2E_3C_3D_2E2(V2m_2E0,c_2Enum_2ESUC_2E1(V3n_2E0)),c_2Earithmetic_2E_2A_2E2(c_2Eproduct_2Enproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V2m_2E0,V3n_2E0),V0f_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V0f_2E0,c_2Enum_2ESUC_2E1(V3n_2E0))),c_2Eproduct_2Enproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V2m_2E0,V3n_2E0),V0f_2E0)) ) ) ) ).
tff(thm_2Eproduct_2ENPRODUCT__EQ,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V2s_2E0))
=> ( app_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V3x_2E0) = app_2E2(A_27a,tyop_2Enum_2Enum,V1g_2E0,V3x_2E0) ) )
=> ( c_2Eproduct_2Enproduct_2E2(A_27a,V2s_2E0,V0f_2E0) = c_2Eproduct_2Enproduct_2E2(A_27a,V2s_2E0,V1g_2E0) ) ) ).
tff(thm_2Eproduct_2ENPRODUCT__EQ__NUMSEG,axiom,
! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1g_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2m_2E0: tyop_2Enum_2Enum,V3n_2E0: tyop_2Enum_2Enum] :
( ! [V4i_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Earithmetic_2E_3C_3D_2E2(V2m_2E0,V4i_2E0))
& p(c_2Earithmetic_2E_3C_3D_2E2(V4i_2E0,V3n_2E0)) )
=> ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V0f_2E0,V4i_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V1g_2E0,V4i_2E0) ) )
=> ( c_2Eproduct_2Enproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V2m_2E0,V3n_2E0),V0f_2E0) = c_2Eproduct_2Enproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V2m_2E0,V3n_2E0),V1g_2E0) ) ) ).
tff(thm_2Eproduct_2ENPRODUCT__EQ__0,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_2Eproduct_2Enproduct_2E2(A_27a,V1s_2E0,V0f_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_2Eproduct_2ENPRODUCT__EQ__0__NUMSEG,axiom,
! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1m_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] :
( ( c_2Eproduct_2Enproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V1m_2E0,V2n_2E0),V0f_2E0) = c_2Enum_2E0_2E0 )
<=> ? [V3x_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V1m_2E0,V3x_2E0))
& p(c_2Earithmetic_2E_3C_3D_2E2(V3x_2E0,V2n_2E0))
& ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V0f_2E0,V3x_2E0) = c_2Enum_2E0_2E0 ) ) ) ).
tff(thm_2Eproduct_2ENPRODUCT__LE,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(c_2Enum_2E0_2E0,app_2E2(A_27a,tyop_2Enum_2Enum,V1f_2E0,V3x_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_2Eproduct_2Enproduct_2E2(A_27a,V2s_2E0,V1f_2E0),c_2Eproduct_2Enproduct_2E2(A_27a,V2s_2E0,V0g_2E0))) ) ).
tff(thm_2Eproduct_2ENPRODUCT__LE__NUMSEG,axiom,
! [V0g_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2m_2E0: tyop_2Enum_2Enum,V3n_2E0: tyop_2Enum_2Enum] :
( ! [V4i_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Earithmetic_2E_3C_3D_2E2(V2m_2E0,V4i_2E0))
& p(c_2Earithmetic_2E_3C_3D_2E2(V4i_2E0,V3n_2E0)) )
=> ( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Enum_2E0_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V1f_2E0,V4i_2E0)))
& p(c_2Earithmetic_2E_3C_3D_2E2(app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V1f_2E0,V4i_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V0g_2E0,V4i_2E0))) ) )
=> p(c_2Earithmetic_2E_3C_3D_2E2(c_2Eproduct_2Enproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V2m_2E0,V3n_2E0),V1f_2E0),c_2Eproduct_2Enproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V2m_2E0,V3n_2E0),V0g_2E0))) ) ).
tff(thm_2Eproduct_2ENPRODUCT__EQ__1,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_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
=> ( app_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V2x_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ) )
=> ( c_2Eproduct_2Enproduct_2E2(A_27a,V1s_2E0,V0f_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ) ) ).
tff(thm_2Eproduct_2ENPRODUCT__EQ__1__NUMSEG,axiom,
! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1m_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] :
( ! [V3i_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Earithmetic_2E_3C_3D_2E2(V1m_2E0,V3i_2E0))
& p(c_2Earithmetic_2E_3C_3D_2E2(V3i_2E0,V2n_2E0)) )
=> ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V0f_2E0,V3i_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ) )
=> ( c_2Eproduct_2Enproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V1m_2E0,V2n_2E0),V0f_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ) ) ).
tff(thm_2Eproduct_2ENPRODUCT__MUL__GEN,axiom,
! [A_27a: $tType,F2_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))),F4_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_2Enum_2Enum),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_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),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_2Enum_2Enum),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_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V5x_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)),F2_2E0,V0f_2E0),V1g_2E0),V5x_2E0) = c_2Earithmetic_2E_2A_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V5x_2E0),app_2E2(A_27a,tyop_2Enum_2Enum,V1g_2E0,V5x_2E0)) )
=> ( ! [V4x_2E0: A_27a,V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),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_2Enum_2Enum),tyop_2Emin_2Ebool)),F4_2E0,V4x_2E0),V2s_2E0),V1g_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V2s_2E0))
& ( app_2E2(A_27a,tyop_2Enum_2Enum,V1g_2E0,V4x_2E0) != c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ) ) )
=> ( ! [V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),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_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F1_2E0,V2s_2E0),V1g_2E0),V4x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V4x_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),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_2Enum_2Enum),tyop_2Emin_2Ebool)),F4_2E0,V4x_2E0),V2s_2E0),V1g_2E0)) )
=> ( ! [V3x_2E0: A_27a,V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),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_2Enum_2Enum),tyop_2Emin_2Ebool)),F3_2E0,V3x_2E0),V2s_2E0),V0f_2E0))
<=> ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V2s_2E0))
& ( app_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V3x_2E0) != c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ) ) )
=> ( ! [V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),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_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V2s_2E0),V0f_2E0),V3x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V3x_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),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_2Enum_2Enum),tyop_2Emin_2Ebool)),F3_2E0,V3x_2E0),V2s_2E0),V0f_2E0)) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1g_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,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),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_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V2s_2E0),V0f_2E0))))
& p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),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_2Enum_2Enum),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F1_2E0,V2s_2E0),V1g_2E0)))) )
=> ( c_2Eproduct_2Enproduct_2E2(A_27a,V2s_2E0,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)),F2_2E0,V0f_2E0),V1g_2E0)) = c_2Earithmetic_2E_2A_2E2(c_2Eproduct_2Enproduct_2E2(A_27a,V2s_2E0,V0f_2E0),c_2Eproduct_2Enproduct_2E2(A_27a,V2s_2E0,V1g_2E0)) ) ) ) ) ) ) ) ).
tff(thm_2Eproduct_2ENPRODUCT__MUL,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)))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1g_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,V0f_2E0),V1g_2E0),V3x_2E0) = c_2Earithmetic_2E_2A_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V3x_2E0),app_2E2(A_27a,tyop_2Enum_2Enum,V1g_2E0,V3x_2E0)) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1g_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))
=> ( c_2Eproduct_2Enproduct_2E2(A_27a,V2s_2E0,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,V0f_2E0),V1g_2E0)) = c_2Earithmetic_2E_2A_2E2(c_2Eproduct_2Enproduct_2E2(A_27a,V2s_2E0,V0f_2E0),c_2Eproduct_2Enproduct_2E2(A_27a,V2s_2E0,V1g_2E0)) ) ) ) ).
tff(thm_2Eproduct_2ENPRODUCT__MUL__NUMSEG,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1g_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V4x_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F0_2E0,V0f_2E0),V1g_2E0),V4x_2E0) = c_2Earithmetic_2E_2A_2E2(app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V0f_2E0,V4x_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V1g_2E0,V4x_2E0)) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1g_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V2m_2E0: tyop_2Enum_2Enum,V3n_2E0: tyop_2Enum_2Enum] : ( c_2Eproduct_2Enproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V2m_2E0,V3n_2E0),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F0_2E0,V0f_2E0),V1g_2E0)) = c_2Earithmetic_2E_2A_2E2(c_2Eproduct_2Enproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V2m_2E0,V3n_2E0),V0f_2E0),c_2Eproduct_2Enproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V2m_2E0,V3n_2E0),V1g_2E0)) ) ) ).
tff(thm_2Eproduct_2ENPRODUCT__CONST,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))] :
( ! [V0c_2E0: tyop_2Enum_2Enum,V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),F0_2E0,V0c_2E0),V2x_2E0) = V0c_2E0 )
=> ! [V0c_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_2Eproduct_2Enproduct_2E2(A_27a,V1s_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),F0_2E0,V0c_2E0)) = c_2Earithmetic_2EEXP_2E2(V0c_2E0,c_2Epred__set_2ECARD_2E1(A_27a,V1s_2E0)) ) ) ) ).
tff(thm_2Eproduct_2ENPRODUCT__CONST__NUMSEG,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] :
( ! [V0c_2E0: tyop_2Enum_2Enum,V3x_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),F0_2E0,V0c_2E0),V3x_2E0) = V0c_2E0 )
=> ! [V0c_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] : ( c_2Eproduct_2Enproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V1m_2E0,V2n_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),F0_2E0,V0c_2E0)) = c_2Earithmetic_2EEXP_2E2(V0c_2E0,c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2E_2B_2E2(V2n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V1m_2E0)) ) ) ).
tff(thm_2Eproduct_2ENPRODUCT__CONST__NUMSEG__1,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] :
( ! [V0c_2E0: tyop_2Enum_2Enum,V2x_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),F0_2E0,V0c_2E0),V2x_2E0) = V0c_2E0 )
=> ! [V0c_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : ( c_2Eproduct_2Enproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V1n_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),F0_2E0,V0c_2E0)) = c_2Earithmetic_2EEXP_2E2(V0c_2E0,V1n_2E0) ) ) ).
tff(thm_2Eproduct_2ENPRODUCT__ONE,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] :
( ! [V1n_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Enum_2Enum,F0_2E0,V1n_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) )
=> ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eproduct_2Enproduct_2E2(A_27a,V0s_2E0,F0_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ) ) ).
tff(thm_2Eproduct_2ENPRODUCT__CLOSED,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))
& ! [V3x_2E0: tyop_2Enum_2Enum,V4y_2E0: tyop_2Enum_2Enum] :
( ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0))
& p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,V4y_2E0)) )
=> p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Earithmetic_2E_2A_2E2(V3x_2E0,V4y_2E0))) )
& ! [V5a_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V5a_2E0,V2s_2E0))
=> p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,app_2E2(A_27a,tyop_2Enum_2Enum,V1f_2E0,V5a_2E0))) ) )
=> p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Eproduct_2Enproduct_2E2(A_27a,V2s_2E0,V1f_2E0))) ) ).
tff(thm_2Eproduct_2ENPRODUCT__CLAUSES__LEFT,axiom,
! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1m_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(V1m_2E0,V2n_2E0))
=> ( c_2Eproduct_2Enproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V1m_2E0,V2n_2E0),V0f_2E0) = c_2Earithmetic_2E_2A_2E2(app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V0f_2E0,V1m_2E0),c_2Eproduct_2Enproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(c_2Earithmetic_2E_2B_2E2(V1m_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V2n_2E0),V0f_2E0)) ) ) ).
tff(thm_2Eproduct_2ENPRODUCT__CLAUSES__RIGHT,axiom,
! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1m_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V2n_2E0))
& p(c_2Earithmetic_2E_3C_3D_2E2(V1m_2E0,V2n_2E0)) )
=> ( c_2Eproduct_2Enproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V1m_2E0,V2n_2E0),V0f_2E0) = c_2Earithmetic_2E_2A_2E2(c_2Eproduct_2Enproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V1m_2E0,c_2Earithmetic_2E_2D_2E2(V2n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0f_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V0f_2E0,V2n_2E0)) ) ) ).
tff(thm_2Eproduct_2ENPRODUCT__SUPERSET,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1u_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2v_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1u_2E0,V2v_2E0))
& ! [V3x_2E0: A_27a] :
( ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V2v_2E0))
& ~ p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V1u_2E0)) )
=> ( app_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V3x_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ) ) )
=> ( c_2Eproduct_2Enproduct_2E2(A_27a,V2v_2E0,V0f_2E0) = c_2Eproduct_2Enproduct_2E2(A_27a,V1u_2E0,V0f_2E0) ) ) ).
tff(thm_2Eproduct_2ENPRODUCT__PAIR,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V3i_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),F0_2E0,V0f_2E0),V3i_2E0) = c_2Earithmetic_2E_2A_2E2(app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V0f_2E0,c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V3i_2E0)),app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V0f_2E0,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V3i_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1m_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] : ( c_2Eproduct_2Enproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1m_2E0),c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V2n_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),V0f_2E0) = c_2Eproduct_2Enproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V1m_2E0,V2n_2E0),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),F0_2E0,V0f_2E0)) ) ) ).
tff(thm_2Eproduct_2ENPRODUCT__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),V2a_2E0: A_27a] :
( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
& p(c_2Ebool_2EIN_2E2(A_27a,V2a_2E0,V1s_2E0)) )
=> ( c_2Earithmetic_2E_2A_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V0f_2E0,V2a_2E0),c_2Eproduct_2Enproduct_2E2(A_27a,c_2Epred__set_2EDELETE_2E2(A_27a,V1s_2E0,V2a_2E0),V0f_2E0)) = c_2Eproduct_2Enproduct_2E2(A_27a,V1s_2E0,V0f_2E0) ) ) ).
tff(thm_2Eproduct_2ENPRODUCT__FACT,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] :
( ! [V1m_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,F0_2E0,V1m_2E0) = V1m_2E0 )
=> ! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Eproduct_2Enproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0n_2E0),F0_2E0) = c_2Earithmetic_2EFACT_2E1(V0n_2E0) ) ) ).
tff(thm_2Eproduct_2ENPRODUCT__DELTA,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(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)))] :
( ! [V3x_2E0: A_27a,V2a_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,V3x_2E0),V2a_2E0))
<=> ( V3x_2E0 = V2a_2E0 ) )
=> ( ! [V2a_2E0: A_27a,V0b_2E0: tyop_2Enum_2Enum,V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),F0_2E0,V2a_2E0),V0b_2E0),V3x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F1_2E0,V3x_2E0),V2a_2E0),V0b_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) )
=> ! [V0b_2E0: tyop_2Enum_2Enum,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2a_2E0: A_27a] : ( c_2Eproduct_2Enproduct_2E2(A_27a,V1s_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),F0_2E0,V2a_2E0),V0b_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Ebool_2EIN_2E2(A_27a,V2a_2E0,V1s_2E0),V0b_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ) ) ).
tff(thm_2Eproduct_2Eth,axiom,
! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal)),F4_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27b,tyop_2Erealax_2Ereal)),F3_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))),F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal))] :
( ! [V5f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V10i_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),F1_2E0,V5f_2E0),V10i_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V5f_2E0,V10i_2E0) )
=> ( ! [V11f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Erealax_2Ereal),V16i_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Erealax_2Ereal,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27b,tyop_2Erealax_2Ereal),F4_2E0,V11f_2E0),V16i_2E0) = app_2E2(A_27b,tyop_2Erealax_2Ereal,V11f_2E0,V16i_2E0) )
=> ( ! [V13p_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V17y_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),F3_2E0,V13p_2E0),V17y_2E0) = c_2Epair_2E_2C_2E2(A_27b,tyop_2Emin_2Ebool,V17y_2E0,app_2E2(A_27b,tyop_2Emin_2Ebool,V13p_2E0,V17y_2E0)) )
=> ( ! [V13p_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V15y_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),F2_2E0,V13p_2E0),V15y_2E0) = c_2Epair_2E_2C_2E2(A_27b,tyop_2Emin_2Ebool,V15y_2E0,app_2E2(A_27b,tyop_2Emin_2Ebool,V13p_2E0,V15y_2E0)) )
=> ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V4i_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Erealax_2Ereal,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),F0_2E0,V0f_2E0),V4i_2E0) = app_2E2(A_27a,tyop_2Erealax_2Ereal,V0f_2E0,V4i_2E0) )
=> ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V3x_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V2s_2E0))
=> ( app_2E2(A_27a,tyop_2Erealax_2Ereal,V0f_2E0,V3x_2E0) = app_2E2(A_27a,tyop_2Erealax_2Ereal,V1g_2E0,V3x_2E0) ) )
=> ( c_2Eproduct_2Eproduct_2E2(A_27a,V2s_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27a,tyop_2Erealax_2Ereal),F0_2E0,V0f_2E0)) = c_2Eproduct_2Eproduct_2E2(A_27a,V2s_2E0,V1g_2E0) ) )
& ! [V5f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V6g_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),V7a_2E0: tyop_2Enum_2Enum,V8b_2E0: tyop_2Enum_2Enum] :
( ! [V9i_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Earithmetic_2E_3C_3D_2E2(V7a_2E0,V9i_2E0))
& p(c_2Earithmetic_2E_3C_3D_2E2(V9i_2E0,V8b_2E0)) )
=> ( app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V5f_2E0,V9i_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal,V6g_2E0,V9i_2E0) ) )
=> ( c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V7a_2E0,V8b_2E0),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Erealax_2Ereal),F1_2E0,V5f_2E0)) = c_2Eproduct_2Eproduct_2E2(tyop_2Enum_2Enum,c_2Eiterate_2E_2E_2E_2E2(V7a_2E0,V8b_2E0),V6g_2E0) ) )
& ! [V11f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Erealax_2Ereal),V12g_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Erealax_2Ereal),V13p_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
( ! [V14x_2E0: A_27b] :
( p(app_2E2(A_27b,tyop_2Emin_2Ebool,V13p_2E0,V14x_2E0))
=> ( app_2E2(A_27b,tyop_2Erealax_2Ereal,V11f_2E0,V14x_2E0) = app_2E2(A_27b,tyop_2Erealax_2Ereal,V12g_2E0,V14x_2E0) ) )
=> ( c_2Eproduct_2Eproduct_2E2(A_27b,c_2Epred__set_2EGSPEC_2E1(A_27b,A_27b,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),F2_2E0,V13p_2E0)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Erealax_2Ereal),tyop_2Emin_2Efun(A_27b,tyop_2Erealax_2Ereal),F4_2E0,V11f_2E0)) = c_2Eproduct_2Eproduct_2E2(A_27b,c_2Epred__set_2EGSPEC_2E1(A_27b,A_27b,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),F3_2E0,V13p_2E0)),V12g_2E0) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------