ITP001 Axioms: ITP018_7.ax
%------------------------------------------------------------------------------
% File : ITP018_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 : numeral.ax [Gau19]
% : HL4018_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 212 ( 59 unt; 105 typ; 0 def)
% Number of atoms : 304 ( 243 equ)
% Maximal formula atoms : 40 ( 1 avg)
% Number of connectives : 206 ( 9 ~; 3 |; 143 &)
% ( 28 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 5 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 83 ( 50 >; 33 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 102 ( 102 usr; 40 con; 0-5 aty)
% Number of variables : 362 ( 324 !; 2 ?; 362 :)
% ( 36 !>; 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(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_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Enum_2E0_2E0,type,
c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).
tff(c_2Eprim__rec_2E_3C_2E0,type,
c_2Eprim__rec_2E_3C_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Eprim__rec_2E_3C_2E2,type,
c_2Eprim__rec_2E_3C_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(c_2Earithmetic_2E_3C_3D_2E0,type,
c_2Earithmetic_2E_3C_3D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Earithmetic_2E_3C_3D_2E2,type,
c_2Earithmetic_2E_3C_3D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2:
!>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Earithmetic_2E_3E_2E0,type,
c_2Earithmetic_2E_3E_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Earithmetic_2E_3E_2E2,type,
c_2Earithmetic_2E_3E_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(c_2Earithmetic_2E_3E_3D_2E0,type,
c_2Earithmetic_2E_3E_3D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Earithmetic_2E_3E_3D_2E2,type,
c_2Earithmetic_2E_3E_3D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_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_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_2Earithmetic_2EDIV_2E0,type,
c_2Earithmetic_2EDIV_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2EDIV_2E2,type,
c_2Earithmetic_2EDIV_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2EDIV2_2E0,type,
c_2Earithmetic_2EDIV2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EDIV2_2E1,type,
c_2Earithmetic_2EDIV2_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2EDIVMOD_2E0,type,
c_2Earithmetic_2EDIVMOD_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2EDIVMOD_2E1,type,
c_2Earithmetic_2EDIVMOD_2E1: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EEVEN_2E0,type,
c_2Earithmetic_2EEVEN_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).
tff(c_2Earithmetic_2EEVEN_2E1,type,
c_2Earithmetic_2EEVEN_2E1: tyop_2Enum_2Enum > 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_2Epair_2EFST_2E0,type,
c_2Epair_2EFST_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a) ).
tff(c_2Epair_2EFST_2E1,type,
c_2Epair_2EFST_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epair_2Eprod(A_27a,A_27b) > A_27a ) ).
tff(c_2Earithmetic_2EFUNPOW_2E0,type,
c_2Earithmetic_2EFUNPOW_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))) ).
tff(c_2Earithmetic_2EFUNPOW_2E3,type,
c_2Earithmetic_2EFUNPOW_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27a) * tyop_2Enum_2Enum * A_27a ) > A_27a ) ).
tff(c_2Ebool_2ELET_2E0,type,
c_2Ebool_2ELET_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) ).
tff(c_2Ebool_2ELET_2E2,type,
c_2Ebool_2ELET_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(c_2Earithmetic_2EMAX_2E0,type,
c_2Earithmetic_2EMAX_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2EMAX_2E2,type,
c_2Earithmetic_2EMAX_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2EMIN_2E0,type,
c_2Earithmetic_2EMIN_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2EMIN_2E2,type,
c_2Earithmetic_2EMIN_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2EMOD_2E0,type,
c_2Earithmetic_2EMOD_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2EMOD_2E2,type,
c_2Earithmetic_2EMOD_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
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_2Earithmetic_2EODD_2E0,type,
c_2Earithmetic_2EODD_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).
tff(c_2Earithmetic_2EODD_2E1,type,
c_2Earithmetic_2EODD_2E1: tyop_2Enum_2Enum > tyop_2Emin_2Ebool ).
tff(c_2Eprim__rec_2EPRE_2E0,type,
c_2Eprim__rec_2EPRE_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Eprim__rec_2EPRE_2E1,type,
c_2Eprim__rec_2EPRE_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Epair_2ESND_2E0,type,
c_2Epair_2ESND_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b) ).
tff(c_2Epair_2ESND_2E1,type,
c_2Epair_2ESND_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epair_2Eprod(A_27a,A_27b) > A_27b ) ).
tff(c_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_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_2Enumeral_2Eexactlog_2E0,type,
c_2Enumeral_2Eexactlog_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Enumeral_2Eexactlog_2E1,type,
c_2Enumeral_2Eexactlog_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2Efindq_2E0,type,
c_2Earithmetic_2Efindq_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2Efindq_2E1,type,
c_2Earithmetic_2Efindq_2E1: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) > tyop_2Enum_2Enum ).
tff(c_2Enumeral_2EiBIT__cases_2E0,type,
c_2Enumeral_2EiBIT__cases_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a)))) ).
tff(c_2Enumeral_2EiBIT__cases_2E4,type,
c_2Enumeral_2EiBIT__cases_2E4:
!>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * A_27a * tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a) * tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a) ) > A_27a ) ).
tff(c_2Enumeral_2EiDUB_2E0,type,
c_2Enumeral_2EiDUB_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Enumeral_2EiDUB_2E1,type,
c_2Enumeral_2EiDUB_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Enumeral_2EiSQR_2E0,type,
c_2Enumeral_2EiSQR_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Enumeral_2EiSQR_2E1,type,
c_2Enumeral_2EiSQR_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Enumeral_2EiSUB_2E0,type,
c_2Enumeral_2EiSUB_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))) ).
tff(c_2Enumeral_2EiSUB_2E3,type,
c_2Enumeral_2EiSUB_2E3: ( tyop_2Emin_2Ebool * tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Enumeral_2EiZ_2E0,type,
c_2Enumeral_2EiZ_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Enumeral_2EiZ_2E1,type,
c_2Enumeral_2EiZ_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Enumeral_2EiiSUC_2E0,type,
c_2Enumeral_2EiiSUC_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Enumeral_2EiiSUC_2E1,type,
c_2Enumeral_2EiiSUC_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Enumeral_2Einternal__mult_2E0,type,
c_2Enumeral_2Einternal__mult_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Enumeral_2Einternal__mult_2E2,type,
c_2Enumeral_2Einternal__mult_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Enumeral_2Eonecount_2E0,type,
c_2Enumeral_2Eonecount_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Enumeral_2Eonecount_2E2,type,
c_2Enumeral_2Eonecount_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Enumeral_2Etexp__help_2E0,type,
c_2Enumeral_2Etexp__help_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Enumeral_2Etexp__help_2E2,type,
c_2Enumeral_2Etexp__help_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
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_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Epair_2E_2C_2E0(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_2D_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
& p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3C_3D_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] :
( ( X0_2E0 = X1_2E0 )
<=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
=> p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_3E_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3E_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3E_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_3E_3D_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3E_3D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3E_3D_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_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(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_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X2_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ECOND_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2EDIV_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EDIV_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EDIV2_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EDIV2_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIV2_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EDIVMOD_2E1,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Earithmetic_2EDIVMOD_2E1(X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIVMOD_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EEVEN_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEVEN_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2EEXP_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEXP_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_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_2Epair_2EFST_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Epair_2EFST_2E1(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Epair_2EFST_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq3_2Ec_2Earithmetic_2EFUNPOW_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0: tyop_2Enum_2Enum,X2_2E0: A_27a] : ( c_2Earithmetic_2EFUNPOW_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),c_2Earithmetic_2EFUNPOW_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Enum_2Enum] : ( c_2Ebool_2ELET_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = 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),c_2Ebool_2ELET_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X1_2E0: tyop_2Enum_2Enum] : ( c_2Ebool_2ELET_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ELET_2E0(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2EMAX_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EMAX_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMAX_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2EMIN_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EMIN_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EMIN_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2EMOD_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EMOD_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_2EMOD_2E0,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(arityeq1_2Ec_2Earithmetic_2EODD_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EODD_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Eprim__rec_2EPRE_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2EPRE_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Eprim__rec_2EPRE_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Epair_2ESND_2E1(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Epair_2ESND_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_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_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_2Enumeral_2Eexactlog_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Enumeral_2Eexactlog_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2Eexactlog_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2Efindq_2E1,axiom,
! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Earithmetic_2Efindq_2E1(X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Enum_2Enum,c_2Earithmetic_2Efindq_2E0,X0_2E0) ) ).
tff(arityeq4_2Ec_2Enumeral_2EiBIT__cases_2E4_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: A_27a,X2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X3_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : ( c_2Enumeral_2EiBIT__cases_2E4(A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),A_27a))),c_2Enumeral_2EiBIT__cases_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq4_2Ec_2Enumeral_2EiBIT__cases_2E4_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X3_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Enumeral_2EiBIT__cases_2E4(tyop_2Enum_2Enum,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,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_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,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_2Enum_2Enum)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,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_2Enum_2Enum))),c_2Enumeral_2EiBIT__cases_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq1_2Ec_2Enumeral_2EiDUB_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Enumeral_2EiDUB_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiDUB_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Enumeral_2EiSQR_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Enumeral_2EiSQR_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiSQR_2E0,X0_2E0) ) ).
tff(arityeq3_2Ec_2Enumeral_2EiSUB_2E3,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Enum_2Enum] : ( c_2Enumeral_2EiSUB_2E3(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_2Enumeral_2EiSUB_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Enumeral_2EiZ_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Enumeral_2EiZ_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiZ_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Enumeral_2EiiSUC_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Enumeral_2EiiSUC_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enumeral_2EiiSUC_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Enumeral_2Einternal__mult_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Enumeral_2Einternal__mult_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_2Enumeral_2Einternal__mult_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Enumeral_2Eonecount_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Enumeral_2Eonecount_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_2Enumeral_2Eonecount_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Enumeral_2Etexp__help_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Enumeral_2Etexp__help_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_2Enumeral_2Etexp__help_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] :
( ~ p(X0_2E0)
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0_2E0)) ) ).
tff(thm_2Enumeral_2EiZ,axiom,
! [V0x_2E0: tyop_2Enum_2Enum] : ( c_2Enumeral_2EiZ_2E1(V0x_2E0) = V0x_2E0 ) ).
tff(thm_2Enumeral_2EiiSUC,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Enumeral_2EiiSUC_2E1(V0n_2E0) = c_2Enum_2ESUC_2E1(c_2Enum_2ESUC_2E1(V0n_2E0)) ) ).
tff(thm_2Enumeral_2EiBIT__cases,axiom,
! [A_27a: $tType] :
( ! [V0zf_2E0: A_27a,V1bf1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2bf2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : ( c_2Enumeral_2EiBIT__cases_2E4(A_27a,c_2Earithmetic_2EZERO_2E0,V0zf_2E0,V1bf1_2E0,V2bf2_2E0) = V0zf_2E0 )
& ! [V3n_2E0: tyop_2Enum_2Enum,V4zf_2E0: A_27a,V5bf1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V6bf2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : ( c_2Enumeral_2EiBIT__cases_2E4(A_27a,c_2Earithmetic_2EBIT1_2E1(V3n_2E0),V4zf_2E0,V5bf1_2E0,V6bf2_2E0) = app_2E2(tyop_2Enum_2Enum,A_27a,V5bf1_2E0,V3n_2E0) )
& ! [V7n_2E0: tyop_2Enum_2Enum,V8zf_2E0: A_27a,V9bf1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V10bf2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : ( c_2Enumeral_2EiBIT__cases_2E4(A_27a,c_2Earithmetic_2EBIT2_2E1(V7n_2E0),V8zf_2E0,V9bf1_2E0,V10bf2_2E0) = app_2E2(tyop_2Enum_2Enum,A_27a,V10bf2_2E0,V7n_2E0) ) ) ).
tff(thm_2Enumeral_2EiDUB,axiom,
! [V0x_2E0: tyop_2Enum_2Enum] : ( c_2Enumeral_2EiDUB_2E1(V0x_2E0) = c_2Earithmetic_2E_2B_2E2(V0x_2E0,V0x_2E0) ) ).
tff(thm_2Enumeral_2EiSUB__DEF,axiom,
! [F3_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F4_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F5_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] :
( ! [V10n_2E0: tyop_2Enum_2Enum,V13m_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),F3_2E0,V10n_2E0),V13m_2E0) = c_2Enumeral_2EiDUB_2E1(c_2Enumeral_2EiSUB_2E3(c_2Ebool_2ET_2E0,V10n_2E0,V13m_2E0)) )
=> ( ! [V3n_2E0: tyop_2Enum_2Enum,V5m_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,V3n_2E0),V5m_2E0) = c_2Enumeral_2EiDUB_2E1(c_2Enumeral_2EiSUB_2E3(c_2Ebool_2ET_2E0,V3n_2E0,V5m_2E0)) )
=> ( ! [V3n_2E0: tyop_2Enum_2Enum,V8m_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),F4_2E0,V3n_2E0),V8m_2E0) = c_2Enumeral_2EiDUB_2E1(c_2Enumeral_2EiSUB_2E3(c_2Ebool_2EF_2E0,V3n_2E0,V8m_2E0)) )
=> ( ! [V10n_2E0: tyop_2Enum_2Enum,V12m_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),F1_2E0,V10n_2E0),V12m_2E0) = c_2Earithmetic_2EBIT1_2E1(c_2Enumeral_2EiSUB_2E3(c_2Ebool_2ET_2E0,V10n_2E0,V12m_2E0)) )
=> ( ! [V10n_2E0: tyop_2Enum_2Enum,V15m_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),F5_2E0,V10n_2E0),V15m_2E0) = c_2Earithmetic_2EBIT1_2E1(c_2Enumeral_2EiSUB_2E3(c_2Ebool_2EF_2E0,V10n_2E0,V15m_2E0)) )
=> ( ! [V3n_2E0: tyop_2Enum_2Enum,V6m_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),F2_2E0,V3n_2E0),V6m_2E0) = c_2Earithmetic_2EBIT1_2E1(c_2Enumeral_2EiSUB_2E3(c_2Ebool_2EF_2E0,V3n_2E0,V6m_2E0)) )
=> ( ! [V0b_2E0: tyop_2Emin_2Ebool,V1x_2E0: tyop_2Enum_2Enum] : ( c_2Enumeral_2EiSUB_2E3(V0b_2E0,c_2Earithmetic_2EZERO_2E0,V1x_2E0) = c_2Earithmetic_2EZERO_2E0 )
& ! [V2b_2E0: tyop_2Emin_2Ebool,V3n_2E0: tyop_2Enum_2Enum,V4x_2E0: tyop_2Enum_2Enum] : ( c_2Enumeral_2EiSUB_2E3(V2b_2E0,c_2Earithmetic_2EBIT1_2E1(V3n_2E0),V4x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,V2b_2E0,c_2Enumeral_2EiBIT__cases_2E4(tyop_2Enum_2Enum,V4x_2E0,c_2Earithmetic_2EBIT1_2E1(V3n_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),F0_2E0,V3n_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),F2_2E0,V3n_2E0)),c_2Enumeral_2EiBIT__cases_2E4(tyop_2Enum_2Enum,V4x_2E0,c_2Enumeral_2EiDUB_2E1(V3n_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),F2_2E0,V3n_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),F4_2E0,V3n_2E0))) )
& ! [V9b_2E0: tyop_2Emin_2Ebool,V10n_2E0: tyop_2Enum_2Enum,V11x_2E0: tyop_2Enum_2Enum] : ( c_2Enumeral_2EiSUB_2E3(V9b_2E0,c_2Earithmetic_2EBIT2_2E1(V10n_2E0),V11x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,V9b_2E0,c_2Enumeral_2EiBIT__cases_2E4(tyop_2Enum_2Enum,V11x_2E0,c_2Earithmetic_2EBIT2_2E1(V10n_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),F1_2E0,V10n_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),F3_2E0,V10n_2E0)),c_2Enumeral_2EiBIT__cases_2E4(tyop_2Enum_2Enum,V11x_2E0,c_2Earithmetic_2EBIT1_2E1(V10n_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),F3_2E0,V10n_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),F5_2E0,V10n_2E0))) ) ) ) ) ) ) ) ) ).
tff(thm_2Enumeral_2EiSQR,axiom,
! [V0x_2E0: tyop_2Enum_2Enum] : ( c_2Enumeral_2EiSQR_2E1(V0x_2E0) = c_2Earithmetic_2E_2A_2E2(V0x_2E0,V0x_2E0) ) ).
tff(thm_2Enumeral_2Etexp__help__def,axiom,
( ! [V0acc_2E0: tyop_2Enum_2Enum] : ( c_2Enumeral_2Etexp__help_2E2(c_2Enum_2E0_2E0,V0acc_2E0) = c_2Earithmetic_2EBIT2_2E1(V0acc_2E0) )
& ! [V1n_2E0: tyop_2Enum_2Enum,V2acc_2E0: tyop_2Enum_2Enum] : ( c_2Enumeral_2Etexp__help_2E2(c_2Enum_2ESUC_2E1(V1n_2E0),V2acc_2E0) = c_2Enumeral_2Etexp__help_2E2(V1n_2E0,c_2Earithmetic_2EBIT1_2E1(V2acc_2E0)) ) ) ).
tff(thm_2Enumeral_2Eonecount__def,axiom,
( ! [V0x_2E0: tyop_2Enum_2Enum] : ( c_2Enumeral_2Eonecount_2E2(c_2Earithmetic_2EZERO_2E0,V0x_2E0) = V0x_2E0 )
& ! [V1n_2E0: tyop_2Enum_2Enum,V2x_2E0: tyop_2Enum_2Enum] : ( c_2Enumeral_2Eonecount_2E2(c_2Earithmetic_2EBIT1_2E1(V1n_2E0),V2x_2E0) = c_2Enumeral_2Eonecount_2E2(V1n_2E0,c_2Enum_2ESUC_2E1(V2x_2E0)) )
& ! [V3n_2E0: tyop_2Enum_2Enum,V4x_2E0: tyop_2Enum_2Enum] : ( c_2Enumeral_2Eonecount_2E2(c_2Earithmetic_2EBIT2_2E1(V3n_2E0),V4x_2E0) = c_2Earithmetic_2EZERO_2E0 ) ) ).
tff(thm_2Enumeral_2Eexactlog__def,axiom,
! [F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] :
( ! [V2x_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F1_2E0,V2x_2E0))
<=> ( V2x_2E0 = c_2Earithmetic_2EZERO_2E0 ) )
=> ( ! [V2x_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,F0_2E0,V2x_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F1_2E0,V2x_2E0),c_2Earithmetic_2EZERO_2E0,c_2Earithmetic_2EBIT1_2E1(V2x_2E0)) )
=> ( ( c_2Enumeral_2Eexactlog_2E1(c_2Earithmetic_2EZERO_2E0) = c_2Earithmetic_2EZERO_2E0 )
& ! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Enumeral_2Eexactlog_2E1(c_2Earithmetic_2EBIT1_2E1(V0n_2E0)) = c_2Earithmetic_2EZERO_2E0 )
& ! [V1n_2E0: tyop_2Enum_2Enum] : ( c_2Enumeral_2Eexactlog_2E1(c_2Earithmetic_2EBIT2_2E1(V1n_2E0)) = c_2Ebool_2ELET_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,F0_2E0,c_2Enumeral_2Eonecount_2E2(V1n_2E0,c_2Earithmetic_2EZERO_2E0)) ) ) ) ) ).
tff(thm_2Enumeral_2Einternal__mult__def,axiom,
c_2Enumeral_2Einternal__mult_2E0 = c_2Earithmetic_2E_2A_2E0 ).
tff(thm_2Enumeral_2Enumeral__suc,axiom,
( ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2EZERO_2E0) = c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0) )
& ! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2EBIT1_2E1(V0n_2E0)) = c_2Earithmetic_2EBIT2_2E1(V0n_2E0) )
& ! [V1n_2E0: tyop_2Enum_2Enum] : ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2EBIT2_2E1(V1n_2E0)) = c_2Earithmetic_2EBIT1_2E1(c_2Enum_2ESUC_2E1(V1n_2E0)) ) ) ).
tff(thm_2Enumeral_2Enumeral__distrib,axiom,
( ! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B_2E2(c_2Enum_2E0_2E0,V0n_2E0) = V0n_2E0 )
& ! [V1n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B_2E2(V1n_2E0,c_2Enum_2E0_2E0) = V1n_2E0 )
& ! [V2n_2E0: tyop_2Enum_2Enum,V3m_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(V2n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V3m_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(V2n_2E0,V3m_2E0))) )
& ! [V4n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2A_2E2(c_2Enum_2E0_2E0,V4n_2E0) = c_2Enum_2E0_2E0 )
& ! [V5n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2A_2E2(V5n_2E0,c_2Enum_2E0_2E0) = c_2Enum_2E0_2E0 )
& ! [V6n_2E0: tyop_2Enum_2Enum,V7m_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(V6n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V7m_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2E_2A_2E2(V6n_2E0,V7m_2E0)) )
& ! [V8n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2D_2E2(c_2Enum_2E0_2E0,V8n_2E0) = c_2Enum_2E0_2E0 )
& ! [V9n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2D_2E2(V9n_2E0,c_2Enum_2E0_2E0) = V9n_2E0 )
& ! [V10n_2E0: tyop_2Enum_2Enum,V11m_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(V10n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V11m_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2E_2D_2E2(V10n_2E0,V11m_2E0)) )
& ! [V12n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEXP_2E2(c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V12n_2E0))) = c_2Enum_2E0_2E0 )
& ! [V13n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEXP_2E2(c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V13n_2E0))) = c_2Enum_2E0_2E0 )
& ! [V14n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEXP_2E2(V14n_2E0,c_2Enum_2E0_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) )
& ! [V15n_2E0: tyop_2Enum_2Enum,V16m_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(V15n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V16m_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EEXP_2E2(V15n_2E0,V16m_2E0)) )
& ( c_2Enum_2ESUC_2E1(c_2Enum_2E0_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) )
& ! [V17n_2E0: tyop_2Enum_2Enum] : ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2ENUMERAL_2E1(V17n_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Enum_2ESUC_2E1(V17n_2E0)) )
& ( c_2Eprim__rec_2EPRE_2E1(c_2Enum_2E0_2E0) = c_2Enum_2E0_2E0 )
& ! [V18n_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2EPRE_2E1(c_2Earithmetic_2ENUMERAL_2E1(V18n_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Eprim__rec_2EPRE_2E1(V18n_2E0)) )
& ! [V19n_2E0: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2ENUMERAL_2E1(V19n_2E0) = c_2Enum_2E0_2E0 )
<=> ( V19n_2E0 = c_2Earithmetic_2EZERO_2E0 ) )
& ! [V20n_2E0: tyop_2Enum_2Enum] :
( ( c_2Enum_2E0_2E0 = c_2Earithmetic_2ENUMERAL_2E1(V20n_2E0) )
<=> ( V20n_2E0 = c_2Earithmetic_2EZERO_2E0 ) )
& ! [V21n_2E0: tyop_2Enum_2Enum,V22m_2E0: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2ENUMERAL_2E1(V21n_2E0) = c_2Earithmetic_2ENUMERAL_2E1(V22m_2E0) )
<=> ( V21n_2E0 = V22m_2E0 ) )
& ! [V23n_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(V23n_2E0,c_2Enum_2E0_2E0) = c_2Ebool_2EF_2E0 )
& ! [V24n_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,c_2Earithmetic_2ENUMERAL_2E1(V24n_2E0)) = c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2EZERO_2E0,V24n_2E0) )
& ! [V25n_2E0: tyop_2Enum_2Enum,V26m_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2ENUMERAL_2E1(V25n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V26m_2E0)) = c_2Eprim__rec_2E_3C_2E2(V25n_2E0,V26m_2E0) )
& ! [V27n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3E_2E2(c_2Enum_2E0_2E0,V27n_2E0) = c_2Ebool_2EF_2E0 )
& ! [V28n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3E_2E2(c_2Earithmetic_2ENUMERAL_2E1(V28n_2E0),c_2Enum_2E0_2E0) = c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2EZERO_2E0,V28n_2E0) )
& ! [V29n_2E0: tyop_2Enum_2Enum,V30m_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3E_2E2(c_2Earithmetic_2ENUMERAL_2E1(V29n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V30m_2E0)) = c_2Eprim__rec_2E_3C_2E2(V30m_2E0,V29n_2E0) )
& ! [V31n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D_2E2(c_2Enum_2E0_2E0,V31n_2E0) = c_2Ebool_2ET_2E0 )
& ! [V32n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2ENUMERAL_2E1(V32n_2E0),c_2Enum_2E0_2E0) = c_2Earithmetic_2E_3C_3D_2E2(V32n_2E0,c_2Earithmetic_2EZERO_2E0) )
& ! [V33n_2E0: tyop_2Enum_2Enum,V34m_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2ENUMERAL_2E1(V33n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V34m_2E0)) = c_2Earithmetic_2E_3C_3D_2E2(V33n_2E0,V34m_2E0) )
& ! [V35n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3E_3D_2E2(V35n_2E0,c_2Enum_2E0_2E0) = c_2Ebool_2ET_2E0 )
& ! [V36n_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3E_3D_2E2(c_2Enum_2E0_2E0,V36n_2E0))
<=> ( V36n_2E0 = c_2Enum_2E0_2E0 ) )
& ! [V37n_2E0: tyop_2Enum_2Enum,V38m_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3E_3D_2E2(c_2Earithmetic_2ENUMERAL_2E1(V37n_2E0),c_2Earithmetic_2ENUMERAL_2E1(V38m_2E0)) = c_2Earithmetic_2E_3C_3D_2E2(V38m_2E0,V37n_2E0) )
& ! [V39n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EODD_2E1(c_2Earithmetic_2ENUMERAL_2E1(V39n_2E0)) = c_2Earithmetic_2EODD_2E1(V39n_2E0) )
& ! [V40n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEVEN_2E1(c_2Earithmetic_2ENUMERAL_2E1(V40n_2E0)) = c_2Earithmetic_2EEVEN_2E1(V40n_2E0) )
& ~ p(c_2Earithmetic_2EODD_2E1(c_2Enum_2E0_2E0))
& p(c_2Earithmetic_2EEVEN_2E1(c_2Enum_2E0_2E0)) ) ).
tff(thm_2Enumeral_2Enumeral__iisuc,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] :
( ( c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2EZERO_2E0) = c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0) )
& ( c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2EBIT1_2E1(V0n_2E0)) = c_2Earithmetic_2EBIT1_2E1(c_2Enum_2ESUC_2E1(V0n_2E0)) )
& ( c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2EBIT2_2E1(V0n_2E0)) = c_2Earithmetic_2EBIT2_2E1(c_2Enum_2ESUC_2E1(V0n_2E0)) ) ) ).
tff(thm_2Enumeral_2Enumeral__add,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] :
( ( c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EZERO_2E0,V0n_2E0)) = V0n_2E0 )
& ( c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,c_2Earithmetic_2EZERO_2E0)) = V0n_2E0 )
& ( c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),c_2Earithmetic_2EBIT1_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT2_2E1(c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
& ( c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),c_2Earithmetic_2EBIT2_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT1_2E1(c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
& ( c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT2_2E1(V0n_2E0),c_2Earithmetic_2EBIT1_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT1_2E1(c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
& ( c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT2_2E1(V0n_2E0),c_2Earithmetic_2EBIT2_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT2_2E1(c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
& ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EZERO_2E0,V0n_2E0)) = c_2Enum_2ESUC_2E1(V0n_2E0) )
& ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,c_2Earithmetic_2EZERO_2E0)) = c_2Enum_2ESUC_2E1(V0n_2E0) )
& ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),c_2Earithmetic_2EBIT1_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT1_2E1(c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
& ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),c_2Earithmetic_2EBIT2_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT2_2E1(c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
& ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT2_2E1(V0n_2E0),c_2Earithmetic_2EBIT1_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT2_2E1(c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
& ( c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT2_2E1(V0n_2E0),c_2Earithmetic_2EBIT2_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT1_2E1(c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
& ( c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EZERO_2E0,V0n_2E0)) = c_2Enumeral_2EiiSUC_2E1(V0n_2E0) )
& ( c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,c_2Earithmetic_2EZERO_2E0)) = c_2Enumeral_2EiiSUC_2E1(V0n_2E0) )
& ( c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),c_2Earithmetic_2EBIT1_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT2_2E1(c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
& ( c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),c_2Earithmetic_2EBIT2_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT1_2E1(c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
& ( c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT2_2E1(V0n_2E0),c_2Earithmetic_2EBIT1_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT1_2E1(c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) )
& ( c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2EBIT2_2E1(V0n_2E0),c_2Earithmetic_2EBIT2_2E1(V1m_2E0))) = c_2Earithmetic_2EBIT2_2E1(c_2Enumeral_2EiiSUC_2E1(c_2Earithmetic_2E_2B_2E2(V0n_2E0,V1m_2E0))) ) ) ).
tff(thm_2Enumeral_2Enumeral__eq,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EZERO_2E0 = c_2Earithmetic_2EBIT1_2E1(V0n_2E0) )
<=> p(c_2Ebool_2EF_2E0) )
& ( ( c_2Earithmetic_2EBIT1_2E1(V0n_2E0) = c_2Earithmetic_2EZERO_2E0 )
<=> p(c_2Ebool_2EF_2E0) )
& ( ( c_2Earithmetic_2EZERO_2E0 = c_2Earithmetic_2EBIT2_2E1(V0n_2E0) )
<=> p(c_2Ebool_2EF_2E0) )
& ( ( c_2Earithmetic_2EBIT2_2E1(V0n_2E0) = c_2Earithmetic_2EZERO_2E0 )
<=> p(c_2Ebool_2EF_2E0) )
& ( ( c_2Earithmetic_2EBIT1_2E1(V0n_2E0) = c_2Earithmetic_2EBIT2_2E1(V1m_2E0) )
<=> p(c_2Ebool_2EF_2E0) )
& ( ( c_2Earithmetic_2EBIT2_2E1(V0n_2E0) = c_2Earithmetic_2EBIT1_2E1(V1m_2E0) )
<=> p(c_2Ebool_2EF_2E0) )
& ( ( c_2Earithmetic_2EBIT1_2E1(V0n_2E0) = c_2Earithmetic_2EBIT1_2E1(V1m_2E0) )
<=> ( V0n_2E0 = V1m_2E0 ) )
& ( ( c_2Earithmetic_2EBIT2_2E1(V0n_2E0) = c_2Earithmetic_2EBIT2_2E1(V1m_2E0) )
<=> ( V0n_2E0 = V1m_2E0 ) ) ) ).
tff(thm_2Enumeral_2Enumeral__lt,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2EZERO_2E0,c_2Earithmetic_2EBIT1_2E1(V0n_2E0)) = c_2Ebool_2ET_2E0 )
& ( c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2EZERO_2E0,c_2Earithmetic_2EBIT2_2E1(V0n_2E0)) = c_2Ebool_2ET_2E0 )
& ( c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Earithmetic_2EZERO_2E0) = c_2Ebool_2EF_2E0 )
& ( c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),c_2Earithmetic_2EBIT1_2E1(V1m_2E0)) = c_2Eprim__rec_2E_3C_2E2(V0n_2E0,V1m_2E0) )
& ( c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2EBIT2_2E1(V0n_2E0),c_2Earithmetic_2EBIT2_2E1(V1m_2E0)) = c_2Eprim__rec_2E_3C_2E2(V0n_2E0,V1m_2E0) )
& ( p(c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),c_2Earithmetic_2EBIT2_2E1(V1m_2E0)))
<=> ~ p(c_2Eprim__rec_2E_3C_2E2(V1m_2E0,V0n_2E0)) )
& ( c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2EBIT2_2E1(V0n_2E0),c_2Earithmetic_2EBIT1_2E1(V1m_2E0)) = c_2Eprim__rec_2E_3C_2E2(V0n_2E0,V1m_2E0) ) ) ).
tff(thm_2Enumeral_2Enumeral__lte,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2EZERO_2E0,V0n_2E0) = c_2Ebool_2ET_2E0 )
& ( c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),c_2Earithmetic_2EZERO_2E0) = c_2Ebool_2EF_2E0 )
& ( c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2EBIT2_2E1(V0n_2E0),c_2Earithmetic_2EZERO_2E0) = c_2Ebool_2EF_2E0 )
& ( c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),c_2Earithmetic_2EBIT1_2E1(V1m_2E0)) = c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,V1m_2E0) )
& ( c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),c_2Earithmetic_2EBIT2_2E1(V1m_2E0)) = c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,V1m_2E0) )
& ( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2EBIT2_2E1(V0n_2E0),c_2Earithmetic_2EBIT1_2E1(V1m_2E0)))
<=> ~ p(c_2Earithmetic_2E_3C_3D_2E2(V1m_2E0,V0n_2E0)) )
& ( c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2EBIT2_2E1(V0n_2E0),c_2Earithmetic_2EBIT2_2E1(V1m_2E0)) = c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,V1m_2E0) ) ) ).
tff(thm_2Enumeral_2Enumeral__pre,axiom,
( ( c_2Eprim__rec_2EPRE_2E1(c_2Earithmetic_2EZERO_2E0) = c_2Earithmetic_2EZERO_2E0 )
& ( c_2Eprim__rec_2EPRE_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) = c_2Earithmetic_2EZERO_2E0 )
& ! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2EPRE_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(V0n_2E0))) = c_2Earithmetic_2EBIT2_2E1(c_2Eprim__rec_2EPRE_2E1(c_2Earithmetic_2EBIT1_2E1(V0n_2E0))) )
& ! [V1n_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2EPRE_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(V1n_2E0))) = c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(V1n_2E0)) )
& ! [V2n_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2EPRE_2E1(c_2Earithmetic_2EBIT2_2E1(V2n_2E0)) = c_2Earithmetic_2EBIT1_2E1(V2n_2E0) ) ) ).
tff(thm_2Enumeral_2Ebit__initiality,axiom,
! [A_27a: $tType,V0zf_2E0: A_27a,V1b1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a)),V2b2f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a))] :
? [V3f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] :
( ( app_2E2(tyop_2Enum_2Enum,A_27a,V3f_2E0,c_2Earithmetic_2EZERO_2E0) = V0zf_2E0 )
& ! [V4n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27a,V3f_2E0,c_2Earithmetic_2EBIT1_2E1(V4n_2E0)) = app_2E2(A_27a,A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a),V1b1f_2E0,V4n_2E0),app_2E2(tyop_2Enum_2Enum,A_27a,V3f_2E0,V4n_2E0)) )
& ! [V5n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27a,V3f_2E0,c_2Earithmetic_2EBIT2_2E1(V5n_2E0)) = app_2E2(A_27a,A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27a),V2b2f_2E0,V5n_2E0),app_2E2(tyop_2Enum_2Enum,A_27a,V3f_2E0,V5n_2E0)) ) ) ).
tff(thm_2Enumeral_2Ebit__induction,axiom,
! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Earithmetic_2EZERO_2E0))
& ! [V1n_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,V1n_2E0))
=> p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Earithmetic_2EBIT1_2E1(V1n_2E0))) )
& ! [V2n_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,V2n_2E0))
=> p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Earithmetic_2EBIT2_2E1(V2n_2E0))) ) )
=> ! [V3n_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,V3n_2E0)) ) ).
tff(thm_2Enumeral_2EiSUB__THM,axiom,
! [V0x_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Emin_2Ebool,V2n_2E0: tyop_2Enum_2Enum,V3m_2E0: tyop_2Enum_2Enum] :
( ( c_2Enumeral_2EiSUB_2E3(V1b_2E0,c_2Earithmetic_2EZERO_2E0,V0x_2E0) = c_2Earithmetic_2EZERO_2E0 )
& ( c_2Enumeral_2EiSUB_2E3(c_2Ebool_2ET_2E0,V2n_2E0,c_2Earithmetic_2EZERO_2E0) = V2n_2E0 )
& ( c_2Enumeral_2EiSUB_2E3(c_2Ebool_2EF_2E0,c_2Earithmetic_2EBIT1_2E1(V2n_2E0),c_2Earithmetic_2EZERO_2E0) = c_2Enumeral_2EiDUB_2E1(V2n_2E0) )
& ( c_2Enumeral_2EiSUB_2E3(c_2Ebool_2ET_2E0,c_2Earithmetic_2EBIT1_2E1(V2n_2E0),c_2Earithmetic_2EBIT1_2E1(V3m_2E0)) = c_2Enumeral_2EiDUB_2E1(c_2Enumeral_2EiSUB_2E3(c_2Ebool_2ET_2E0,V2n_2E0,V3m_2E0)) )
& ( c_2Enumeral_2EiSUB_2E3(c_2Ebool_2EF_2E0,c_2Earithmetic_2EBIT1_2E1(V2n_2E0),c_2Earithmetic_2EBIT1_2E1(V3m_2E0)) = c_2Earithmetic_2EBIT1_2E1(c_2Enumeral_2EiSUB_2E3(c_2Ebool_2EF_2E0,V2n_2E0,V3m_2E0)) )
& ( c_2Enumeral_2EiSUB_2E3(c_2Ebool_2ET_2E0,c_2Earithmetic_2EBIT1_2E1(V2n_2E0),c_2Earithmetic_2EBIT2_2E1(V3m_2E0)) = c_2Earithmetic_2EBIT1_2E1(c_2Enumeral_2EiSUB_2E3(c_2Ebool_2EF_2E0,V2n_2E0,V3m_2E0)) )
& ( c_2Enumeral_2EiSUB_2E3(c_2Ebool_2EF_2E0,c_2Earithmetic_2EBIT1_2E1(V2n_2E0),c_2Earithmetic_2EBIT2_2E1(V3m_2E0)) = c_2Enumeral_2EiDUB_2E1(c_2Enumeral_2EiSUB_2E3(c_2Ebool_2EF_2E0,V2n_2E0,V3m_2E0)) )
& ( c_2Enumeral_2EiSUB_2E3(c_2Ebool_2EF_2E0,c_2Earithmetic_2EBIT2_2E1(V2n_2E0),c_2Earithmetic_2EZERO_2E0) = c_2Earithmetic_2EBIT1_2E1(V2n_2E0) )
& ( c_2Enumeral_2EiSUB_2E3(c_2Ebool_2ET_2E0,c_2Earithmetic_2EBIT2_2E1(V2n_2E0),c_2Earithmetic_2EBIT1_2E1(V3m_2E0)) = c_2Earithmetic_2EBIT1_2E1(c_2Enumeral_2EiSUB_2E3(c_2Ebool_2ET_2E0,V2n_2E0,V3m_2E0)) )
& ( c_2Enumeral_2EiSUB_2E3(c_2Ebool_2EF_2E0,c_2Earithmetic_2EBIT2_2E1(V2n_2E0),c_2Earithmetic_2EBIT1_2E1(V3m_2E0)) = c_2Enumeral_2EiDUB_2E1(c_2Enumeral_2EiSUB_2E3(c_2Ebool_2ET_2E0,V2n_2E0,V3m_2E0)) )
& ( c_2Enumeral_2EiSUB_2E3(c_2Ebool_2ET_2E0,c_2Earithmetic_2EBIT2_2E1(V2n_2E0),c_2Earithmetic_2EBIT2_2E1(V3m_2E0)) = c_2Enumeral_2EiDUB_2E1(c_2Enumeral_2EiSUB_2E3(c_2Ebool_2ET_2E0,V2n_2E0,V3m_2E0)) )
& ( c_2Enumeral_2EiSUB_2E3(c_2Ebool_2EF_2E0,c_2Earithmetic_2EBIT2_2E1(V2n_2E0),c_2Earithmetic_2EBIT2_2E1(V3m_2E0)) = c_2Earithmetic_2EBIT1_2E1(c_2Enumeral_2EiSUB_2E3(c_2Ebool_2EF_2E0,V2n_2E0,V3m_2E0)) ) ) ).
tff(thm_2Enumeral_2Enumeral__sub,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2E_2D_2E2(V0n_2E0,V1m_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Eprim__rec_2E_3C_2E2(V1m_2E0,V0n_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Enumeral_2EiSUB_2E3(c_2Ebool_2ET_2E0,V0n_2E0,V1m_2E0)),c_2Enum_2E0_2E0) ) ).
tff(thm_2Enumeral_2EiDUB__removal,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] :
( ( c_2Enumeral_2EiDUB_2E1(c_2Earithmetic_2EBIT1_2E1(V0n_2E0)) = c_2Earithmetic_2EBIT2_2E1(c_2Enumeral_2EiDUB_2E1(V0n_2E0)) )
& ( c_2Enumeral_2EiDUB_2E1(c_2Earithmetic_2EBIT2_2E1(V0n_2E0)) = c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(V0n_2E0)) )
& ( c_2Enumeral_2EiDUB_2E1(c_2Earithmetic_2EZERO_2E0) = c_2Earithmetic_2EZERO_2E0 ) ) ).
tff(thm_2Enumeral_2Enumeral__mult,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2EZERO_2E0,V0n_2E0) = c_2Earithmetic_2EZERO_2E0 )
& ( c_2Earithmetic_2E_2A_2E2(V0n_2E0,c_2Earithmetic_2EZERO_2E0) = c_2Earithmetic_2EZERO_2E0 )
& ( c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),V1m_2E0) = c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(c_2Enumeral_2EiDUB_2E1(c_2Earithmetic_2E_2A_2E2(V0n_2E0,V1m_2E0)),V1m_2E0)) )
& ( c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2EBIT2_2E1(V0n_2E0),V1m_2E0) = c_2Enumeral_2EiDUB_2E1(c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2A_2E2(V0n_2E0,V1m_2E0),V1m_2E0))) ) ) ).
tff(thm_2Enumeral_2Enumeral__exp,axiom,
( ! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEXP_2E2(V0n_2E0,c_2Earithmetic_2EZERO_2E0) = c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0) )
& ! [V1n_2E0: tyop_2Enum_2Enum,V2m_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEXP_2E2(V1n_2E0,c_2Earithmetic_2EBIT1_2E1(V2m_2E0)) = c_2Earithmetic_2E_2A_2E2(V1n_2E0,c_2Enumeral_2EiSQR_2E1(c_2Earithmetic_2EEXP_2E2(V1n_2E0,V2m_2E0))) )
& ! [V3n_2E0: tyop_2Enum_2Enum,V4m_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEXP_2E2(V3n_2E0,c_2Earithmetic_2EBIT2_2E1(V4m_2E0)) = c_2Earithmetic_2E_2A_2E2(c_2Enumeral_2EiSQR_2E1(V3n_2E0),c_2Enumeral_2EiSQR_2E1(c_2Earithmetic_2EEXP_2E2(V3n_2E0,V4m_2E0))) ) ) ).
tff(thm_2Enumeral_2Enumeral__evenodd,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2EEVEN_2E1(c_2Earithmetic_2EZERO_2E0))
& p(c_2Earithmetic_2EEVEN_2E1(c_2Earithmetic_2EBIT2_2E1(V0n_2E0)))
& ~ p(c_2Earithmetic_2EEVEN_2E1(c_2Earithmetic_2EBIT1_2E1(V0n_2E0)))
& ~ p(c_2Earithmetic_2EODD_2E1(c_2Earithmetic_2EZERO_2E0))
& ~ p(c_2Earithmetic_2EODD_2E1(c_2Earithmetic_2EBIT2_2E1(V0n_2E0)))
& p(c_2Earithmetic_2EODD_2E1(c_2Earithmetic_2EBIT1_2E1(V0n_2E0))) ) ).
tff(thm_2Enumeral_2Enumeral__fact,axiom,
( ( c_2Earithmetic_2EFACT_2E1(c_2Enum_2E0_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) )
& ! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EFACT_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V0n_2E0))) = c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V0n_2E0)),c_2Earithmetic_2EFACT_2E1(c_2Eprim__rec_2EPRE_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V0n_2E0))))) )
& ! [V1n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EFACT_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V1n_2E0))) = c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V1n_2E0)),c_2Earithmetic_2EFACT_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V1n_2E0)))) ) ) ).
tff(thm_2Enumeral_2Enumeral__funpow,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1n_2E0: tyop_2Enum_2Enum,V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27a)] :
( ( c_2Earithmetic_2EFUNPOW_2E3(A_27a,V2f_2E0,c_2Enum_2E0_2E0,V0x_2E0) = V0x_2E0 )
& ( c_2Earithmetic_2EFUNPOW_2E3(A_27a,V2f_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V1n_2E0)),V0x_2E0) = c_2Earithmetic_2EFUNPOW_2E3(A_27a,V2f_2E0,c_2Eprim__rec_2EPRE_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V1n_2E0))),app_2E2(A_27a,A_27a,V2f_2E0,V0x_2E0)) )
& ( c_2Earithmetic_2EFUNPOW_2E3(A_27a,V2f_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V1n_2E0)),V0x_2E0) = c_2Earithmetic_2EFUNPOW_2E3(A_27a,V2f_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V1n_2E0)),app_2E2(A_27a,A_27a,V2f_2E0,V0x_2E0)) ) ) ).
tff(thm_2Enumeral_2Enumeral__MIN,axiom,
! [V0y_2E0: tyop_2Enum_2Enum,V1x_2E0: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMIN_2E2(c_2Enum_2E0_2E0,V1x_2E0) = c_2Enum_2E0_2E0 )
& ( c_2Earithmetic_2EMIN_2E2(V1x_2E0,c_2Enum_2E0_2E0) = c_2Enum_2E0_2E0 )
& ( c_2Earithmetic_2EMIN_2E2(c_2Earithmetic_2ENUMERAL_2E1(V1x_2E0),c_2Earithmetic_2ENUMERAL_2E1(V0y_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Eprim__rec_2E_3C_2E2(V1x_2E0,V0y_2E0),V1x_2E0,V0y_2E0)) ) ) ).
tff(thm_2Enumeral_2Enumeral__MAX,axiom,
! [V0y_2E0: tyop_2Enum_2Enum,V1x_2E0: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMAX_2E2(c_2Enum_2E0_2E0,V1x_2E0) = V1x_2E0 )
& ( c_2Earithmetic_2EMAX_2E2(V1x_2E0,c_2Enum_2E0_2E0) = V1x_2E0 )
& ( c_2Earithmetic_2EMAX_2E2(c_2Earithmetic_2ENUMERAL_2E1(V1x_2E0),c_2Earithmetic_2ENUMERAL_2E1(V0y_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Eprim__rec_2E_3C_2E2(V1x_2E0,V0y_2E0),V0y_2E0,V1x_2E0)) ) ) ).
tff(thm_2Enumeral_2Edivmod__POS,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))))] :
( ! [V1a_2E0: tyop_2Enum_2Enum,V0m_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum,V3q_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),F0_2E0,V1a_2E0),V0m_2E0),V2n_2E0),V3q_2E0) = c_2Earithmetic_2EDIVMOD_2E1(c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E2(V1a_2E0,V3q_2E0),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(V0m_2E0,c_2Earithmetic_2E_2A_2E2(V2n_2E0,V3q_2E0)),V2n_2E0))) )
=> ! [V0m_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V2n_2E0))
=> ( c_2Earithmetic_2EDIVMOD_2E1(c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1a_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V0m_2E0,V2n_2E0))) = c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Eprim__rec_2E_3C_2E2(V0m_2E0,V2n_2E0),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V1a_2E0,V0m_2E0),c_2Ebool_2ELET_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),F0_2E0,V1a_2E0),V0m_2E0),V2n_2E0),c_2Earithmetic_2Efindq_2E1(c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V0m_2E0,V2n_2E0))))) ) ) ) ).
tff(thm_2Enumeral_2EDIVMOD__NUMERAL__CALC,axiom,
( ! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EDIV_2E2(V0m_2E0,c_2Earithmetic_2EBIT1_2E1(V1n_2E0)) = c_2Epair_2EFST_2E1(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIVMOD_2E1(c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EZERO_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V0m_2E0,c_2Earithmetic_2EBIT1_2E1(V1n_2E0))))) )
& ! [V2m_2E0: tyop_2Enum_2Enum,V3n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EDIV_2E2(V2m_2E0,c_2Earithmetic_2EBIT2_2E1(V3n_2E0)) = c_2Epair_2EFST_2E1(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIVMOD_2E1(c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EZERO_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V2m_2E0,c_2Earithmetic_2EBIT2_2E1(V3n_2E0))))) )
& ! [V4m_2E0: tyop_2Enum_2Enum,V5n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EMOD_2E2(V4m_2E0,c_2Earithmetic_2EBIT1_2E1(V5n_2E0)) = c_2Epair_2ESND_2E1(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIVMOD_2E1(c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EZERO_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V4m_2E0,c_2Earithmetic_2EBIT1_2E1(V5n_2E0))))) )
& ! [V6m_2E0: tyop_2Enum_2Enum,V7n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EMOD_2E2(V6m_2E0,c_2Earithmetic_2EBIT2_2E1(V7n_2E0)) = c_2Epair_2ESND_2E1(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EDIVMOD_2E1(c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EZERO_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V6m_2E0,c_2Earithmetic_2EBIT2_2E1(V7n_2E0))))) ) ) ).
tff(thm_2Enumeral_2Enumeral__div2,axiom,
( ( c_2Earithmetic_2EDIV2_2E1(c_2Enum_2E0_2E0) = c_2Enum_2E0_2E0 )
& ! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EDIV2_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V0n_2E0))) = c_2Earithmetic_2ENUMERAL_2E1(V0n_2E0) )
& ! [V1n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EDIV2_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V1n_2E0))) = c_2Earithmetic_2ENUMERAL_2E1(c_2Enum_2ESUC_2E1(V1n_2E0)) ) ) ).
tff(thm_2Enumeral_2Etexp__help__thm,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Enum_2Enum] : ( c_2Enumeral_2Etexp__help_2E2(V0n_2E0,V1a_2E0) = c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2E_2B_2E2(V1a_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2B_2E2(V0n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ) ).
tff(thm_2Enumeral_2Etexp__help0,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Enumeral_2Etexp__help_2E2(V0n_2E0,c_2Enum_2E0_2E0) = c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2B_2E2(V0n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) ) ).
tff(thm_2Enumeral_2Enumeral__texp__help,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1acc_2E0: tyop_2Enum_2Enum] :
( ( c_2Enumeral_2Etexp__help_2E2(c_2Earithmetic_2EZERO_2E0,V1acc_2E0) = c_2Earithmetic_2EBIT2_2E1(V1acc_2E0) )
& ( c_2Enumeral_2Etexp__help_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),V1acc_2E0) = c_2Enumeral_2Etexp__help_2E2(c_2Eprim__rec_2EPRE_2E1(c_2Earithmetic_2EBIT1_2E1(V0n_2E0)),c_2Earithmetic_2EBIT1_2E1(V1acc_2E0)) )
& ( c_2Enumeral_2Etexp__help_2E2(c_2Earithmetic_2EBIT2_2E1(V0n_2E0),V1acc_2E0) = c_2Enumeral_2Etexp__help_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),c_2Earithmetic_2EBIT1_2E1(V1acc_2E0)) ) ) ).
tff(thm_2Enumeral_2ETWO__EXP__THM,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Enum_2E0_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) )
& ( c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V0n_2E0))) = c_2Earithmetic_2ENUMERAL_2E1(c_2Enumeral_2Etexp__help_2E2(c_2Eprim__rec_2EPRE_2E1(c_2Earithmetic_2EBIT1_2E1(V0n_2E0)),c_2Earithmetic_2EZERO_2E0)) )
& ( c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V0n_2E0))) = c_2Earithmetic_2ENUMERAL_2E1(c_2Enumeral_2Etexp__help_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),c_2Earithmetic_2EZERO_2E0)) ) ) ).
tff(thm_2Enumeral_2Eonecount__characterisation,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1a_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,c_2Enumeral_2Eonecount_2E2(V0n_2E0,V1a_2E0)))
& p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V0n_2E0)) )
=> ( V0n_2E0 = c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2D_2E2(c_2Enumeral_2Eonecount_2E2(V0n_2E0,V1a_2E0),V1a_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ) ).
tff(thm_2Enumeral_2Eexactlog__characterisation,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] :
( ( c_2Enumeral_2Eexactlog_2E1(V0n_2E0) = c_2Earithmetic_2EBIT1_2E1(V1m_2E0) )
=> ( V0n_2E0 = c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2B_2E2(V1m_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) ) ) ).
tff(thm_2Enumeral_2EDIV2__BIT1,axiom,
! [V0x_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EDIV2_2E1(c_2Earithmetic_2EBIT1_2E1(V0x_2E0)) = V0x_2E0 ) ).
tff(thm_2Enumeral_2Eenumeral__mult,axiom,
! [F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F3_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))),F2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)))] :
( ! [V0y_2E0: tyop_2Enum_2Enum,V1x_2E0: tyop_2Enum_2Enum,V4m_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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F1_2E0,V0y_2E0),V1x_2E0),V4m_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Earithmetic_2EODD_2E1(V4m_2E0),c_2Enumeral_2Etexp__help_2E2(c_2Earithmetic_2EDIV2_2E1(V4m_2E0),c_2Eprim__rec_2EPRE_2E1(c_2Earithmetic_2EBIT1_2E1(V0y_2E0))),c_2Enumeral_2Einternal__mult_2E2(c_2Earithmetic_2EBIT2_2E1(V1x_2E0),c_2Earithmetic_2EBIT1_2E1(V0y_2E0))) )
=> ( ! [V1x_2E0: tyop_2Enum_2Enum,V0y_2E0: tyop_2Enum_2Enum,V3n_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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F0_2E0,V1x_2E0),V0y_2E0),V3n_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Earithmetic_2EODD_2E1(V3n_2E0),c_2Enumeral_2Etexp__help_2E2(c_2Earithmetic_2EDIV2_2E1(V3n_2E0),c_2Eprim__rec_2EPRE_2E1(c_2Earithmetic_2EBIT1_2E1(V1x_2E0))),c_2Enumeral_2Einternal__mult_2E2(c_2Earithmetic_2EBIT1_2E1(V1x_2E0),c_2Earithmetic_2EBIT2_2E1(V0y_2E0))) )
=> ( ! [V5m_2E0: tyop_2Enum_2Enum,V0y_2E0: tyop_2Enum_2Enum,V1x_2E0: tyop_2Enum_2Enum,V6n_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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F3_2E0,V5m_2E0),V0y_2E0),V1x_2E0),V6n_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Earithmetic_2EODD_2E1(V5m_2E0),c_2Enumeral_2Etexp__help_2E2(c_2Earithmetic_2EDIV2_2E1(V5m_2E0),c_2Eprim__rec_2EPRE_2E1(c_2Earithmetic_2EBIT2_2E1(V0y_2E0))),c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Earithmetic_2EODD_2E1(V6n_2E0),c_2Enumeral_2Etexp__help_2E2(c_2Earithmetic_2EDIV2_2E1(V6n_2E0),c_2Eprim__rec_2EPRE_2E1(c_2Earithmetic_2EBIT2_2E1(V1x_2E0))),c_2Enumeral_2Einternal__mult_2E2(c_2Earithmetic_2EBIT2_2E1(V1x_2E0),c_2Earithmetic_2EBIT2_2E1(V0y_2E0)))) )
=> ( ! [V0y_2E0: tyop_2Enum_2Enum,V1x_2E0: tyop_2Enum_2Enum,V5m_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_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F2_2E0,V0y_2E0),V1x_2E0),V5m_2E0) = c_2Ebool_2ELET_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),F3_2E0,V5m_2E0),V0y_2E0),V1x_2E0),c_2Enumeral_2Eexactlog_2E1(c_2Earithmetic_2EBIT2_2E1(V0y_2E0))) )
=> ! [V0y_2E0: tyop_2Enum_2Enum,V1x_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2EZERO_2E0,V2n_2E0) = c_2Earithmetic_2EZERO_2E0 )
& ( c_2Earithmetic_2E_2A_2E2(V2n_2E0,c_2Earithmetic_2EZERO_2E0) = c_2Earithmetic_2EZERO_2E0 )
& ( c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2EBIT1_2E1(V1x_2E0),c_2Earithmetic_2EBIT1_2E1(V0y_2E0)) = c_2Enumeral_2Einternal__mult_2E2(c_2Earithmetic_2EBIT1_2E1(V1x_2E0),c_2Earithmetic_2EBIT1_2E1(V0y_2E0)) )
& ( c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2EBIT1_2E1(V1x_2E0),c_2Earithmetic_2EBIT2_2E1(V0y_2E0)) = c_2Ebool_2ELET_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F0_2E0,V1x_2E0),V0y_2E0),c_2Enumeral_2Eexactlog_2E1(c_2Earithmetic_2EBIT2_2E1(V0y_2E0))) )
& ( c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2EBIT2_2E1(V1x_2E0),c_2Earithmetic_2EBIT1_2E1(V0y_2E0)) = c_2Ebool_2ELET_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F1_2E0,V0y_2E0),V1x_2E0),c_2Enumeral_2Eexactlog_2E1(c_2Earithmetic_2EBIT2_2E1(V1x_2E0))) )
& ( c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2EBIT2_2E1(V1x_2E0),c_2Earithmetic_2EBIT2_2E1(V0y_2E0)) = c_2Ebool_2ELET_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F2_2E0,V0y_2E0),V1x_2E0),c_2Enumeral_2Eexactlog_2E1(c_2Earithmetic_2EBIT2_2E1(V1x_2E0))) ) ) ) ) ) ) ).
tff(thm_2Enumeral_2Einternal__mult__characterisation,axiom,
! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] :
( ( c_2Enumeral_2Einternal__mult_2E2(c_2Earithmetic_2EZERO_2E0,V0n_2E0) = c_2Earithmetic_2EZERO_2E0 )
& ( c_2Enumeral_2Einternal__mult_2E2(V0n_2E0,c_2Earithmetic_2EZERO_2E0) = c_2Earithmetic_2EZERO_2E0 )
& ( c_2Enumeral_2Einternal__mult_2E2(c_2Earithmetic_2EBIT1_2E1(V0n_2E0),V1m_2E0) = c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(c_2Enumeral_2EiDUB_2E1(c_2Enumeral_2Einternal__mult_2E2(V0n_2E0,V1m_2E0)),V1m_2E0)) )
& ( c_2Enumeral_2Einternal__mult_2E2(c_2Earithmetic_2EBIT2_2E1(V0n_2E0),V1m_2E0) = c_2Enumeral_2EiDUB_2E1(c_2Enumeral_2EiZ_2E1(c_2Earithmetic_2E_2B_2E2(c_2Enumeral_2Einternal__mult_2E2(V0n_2E0,V1m_2E0),V1m_2E0))) ) ) ).
%------------------------------------------------------------------------------