TPTP Problem File: ITP015_7.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ITP015_7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 syntactic export of thm_2Einteger__word_2Ei2w__0.p, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : thm_2Einteger__word_2Ei2w__0.p [Gau20]
% : HL407001_7.p [TPAP]
% Status : Theorem
% Rating : 0.00 v7.5.0
% Syntax : Number of formulae : 30576 (10939 unt;11540 typ; 0 def)
% Number of atoms : 46051 (24024 equ)
% Maximal formula atoms : 912 ( 1 avg)
% Number of connectives : 29367 (2352 ~;1392 |;10361 &)
% (6681 <=>;8581 =>; 0 <=; 0 <~>)
% Maximal formula depth : 360 ( 6 avg)
% Maximal term depth : 130 ( 2 avg)
% Number of types : 13 ( 12 usr)
% Number of type conns : 9770 (5627 >;4143 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 3443 (3443 usr; 426 con; 0-10 aty)
% Number of variables : 99122 (74824 !;13736 ?;99122 :)
% (10562 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_THM_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
include('Axioms/ITP001/ITP002_7.ax').
include('Axioms/ITP001/ITP003_7.ax').
include('Axioms/ITP001/ITP004_7.ax').
include('Axioms/ITP001/ITP005_7.ax').
include('Axioms/ITP001/ITP006_7.ax').
include('Axioms/ITP001/ITP007_7.ax').
include('Axioms/ITP001/ITP008_7.ax').
include('Axioms/ITP001/ITP009_7.ax').
include('Axioms/ITP001/ITP010_7.ax').
include('Axioms/ITP001/ITP011_7.ax').
include('Axioms/ITP001/ITP012_7.ax').
include('Axioms/ITP001/ITP013_7.ax').
include('Axioms/ITP001/ITP014_7.ax').
include('Axioms/ITP001/ITP015_7.ax').
include('Axioms/ITP001/ITP016_7.ax').
include('Axioms/ITP001/ITP017_7.ax').
include('Axioms/ITP001/ITP018_7.ax').
include('Axioms/ITP001/ITP019_7.ax').
include('Axioms/ITP001/ITP020_7.ax').
include('Axioms/ITP001/ITP021_7.ax').
include('Axioms/ITP001/ITP022_7.ax').
include('Axioms/ITP001/ITP023_7.ax').
include('Axioms/ITP001/ITP024_7.ax').
include('Axioms/ITP001/ITP025_7.ax').
include('Axioms/ITP001/ITP026_7.ax').
include('Axioms/ITP001/ITP027_7.ax').
include('Axioms/ITP001/ITP028_7.ax').
include('Axioms/ITP001/ITP029_7.ax').
include('Axioms/ITP001/ITP030_7.ax').
include('Axioms/ITP001/ITP031_7.ax').
include('Axioms/ITP001/ITP032_7.ax').
include('Axioms/ITP001/ITP033_7.ax').
include('Axioms/ITP001/ITP034_7.ax').
include('Axioms/ITP001/ITP035_7.ax').
include('Axioms/ITP001/ITP036_7.ax').
include('Axioms/ITP001/ITP037_7.ax').
include('Axioms/ITP001/ITP038_7.ax').
include('Axioms/ITP001/ITP039_7.ax').
include('Axioms/ITP001/ITP040_7.ax').
include('Axioms/ITP001/ITP041_7.ax').
include('Axioms/ITP001/ITP042_7.ax').
include('Axioms/ITP001/ITP043_7.ax').
include('Axioms/ITP001/ITP044_7.ax').
include('Axioms/ITP001/ITP045_7.ax').
include('Axioms/ITP001/ITP046_7.ax').
include('Axioms/ITP001/ITP047_7.ax').
include('Axioms/ITP001/ITP048_7.ax').
include('Axioms/ITP001/ITP049_7.ax').
include('Axioms/ITP001/ITP050_7.ax').
include('Axioms/ITP001/ITP051_7.ax').
include('Axioms/ITP001/ITP052_7.ax').
include('Axioms/ITP001/ITP053_7.ax').
include('Axioms/ITP001/ITP054_7.ax').
include('Axioms/ITP001/ITP055_7.ax').
include('Axioms/ITP001/ITP056_7.ax').
include('Axioms/ITP001/ITP057_7.ax').
include('Axioms/ITP001/ITP058_7.ax').
include('Axioms/ITP001/ITP059_7.ax').
include('Axioms/ITP001/ITP060_7.ax').
include('Axioms/ITP001/ITP061_7.ax').
include('Axioms/ITP001/ITP062_7.ax').
include('Axioms/ITP001/ITP063_7.ax').
include('Axioms/ITP001/ITP064_7.ax').
include('Axioms/ITP001/ITP065_7.ax').
include('Axioms/ITP001/ITP066_7.ax').
include('Axioms/ITP001/ITP067_7.ax').
include('Axioms/ITP001/ITP068_7.ax').
include('Axioms/ITP001/ITP069_7.ax').
include('Axioms/ITP001/ITP070_7.ax').
include('Axioms/ITP001/ITP071_7.ax').
include('Axioms/ITP001/ITP072_7.ax').
include('Axioms/ITP001/ITP073_7.ax').
include('Axioms/ITP001/ITP074_7.ax').
include('Axioms/ITP001/ITP075_7.ax').
include('Axioms/ITP001/ITP076_7.ax').
include('Axioms/ITP001/ITP077_7.ax').
include('Axioms/ITP001/ITP078_7.ax').
include('Axioms/ITP001/ITP079_7.ax').
include('Axioms/ITP001/ITP080_7.ax').
include('Axioms/ITP001/ITP081_7.ax').
include('Axioms/ITP001/ITP082_7.ax').
include('Axioms/ITP001/ITP083_7.ax').
include('Axioms/ITP001/ITP084_7.ax').
include('Axioms/ITP001/ITP085_7.ax').
include('Axioms/ITP001/ITP086_7.ax').
include('Axioms/ITP001/ITP087_7.ax').
include('Axioms/ITP001/ITP088_7.ax').
include('Axioms/ITP001/ITP089_7.ax').
include('Axioms/ITP001/ITP090_7.ax').
include('Axioms/ITP001/ITP091_7.ax').
include('Axioms/ITP001/ITP092_7.ax').
include('Axioms/ITP001/ITP093_7.ax').
include('Axioms/ITP001/ITP094_7.ax').
include('Axioms/ITP001/ITP095_7.ax').
include('Axioms/ITP001/ITP096_7.ax').
include('Axioms/ITP001/ITP097_7.ax').
include('Axioms/ITP001/ITP098_7.ax').
include('Axioms/ITP001/ITP099_7.ax').
include('Axioms/ITP001/ITP100_7.ax').
include('Axioms/ITP001/ITP101_7.ax').
include('Axioms/ITP001/ITP102_7.ax').
include('Axioms/ITP001/ITP103_7.ax').
include('Axioms/ITP001/ITP104_7.ax').
include('Axioms/ITP001/ITP105_7.ax').
include('Axioms/ITP001/ITP106_7.ax').
include('Axioms/ITP001/ITP107_7.ax').
include('Axioms/ITP001/ITP108_7.ax').
include('Axioms/ITP001/ITP109_7.ax').
%------------------------------------------------------------------------------
tff(tyop_2Ebool_2Eitself,type,
tyop_2Ebool_2Eitself: $tType > $tType ).
tff(tyop_2Efcp_2Ecart,type,
tyop_2Efcp_2Ecart: ( $tType * $tType ) > $tType ).
tff(tyop_2Einteger_2Eint,type,
tyop_2Einteger_2Eint: $tType ).
tff(tyop_2Elist_2Elist,type,
tyop_2Elist_2Elist: $tType > $tType ).
tff(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
tff(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: $tType ).
tff(tyop_2Estring_2Echar,type,
tyop_2Estring_2Echar: $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_2D_2E0,type,
c_2Earithmetic_2E_2D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2D_2E2,type,
c_2Earithmetic_2E_2D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Enum_2E0_2E0,type,
c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).
tff(c_2Eprim__rec_2E_3C_2E0,type,
c_2Eprim__rec_2E_3C_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Eprim__rec_2E_3C_2E2,type,
c_2Eprim__rec_2E_3C_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(c_2Earithmetic_2E_3C_3D_2E0,type,
c_2Earithmetic_2E_3C_3D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Earithmetic_2E_3C_3D_2E2,type,
c_2Earithmetic_2E_3C_3D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2:
!>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_40_2E0,type,
c_2Emin_2E_40_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a) ).
tff(c_2Emin_2E_40_2E1,type,
c_2Emin_2E_40_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > A_27a ) ).
tff(c_2Einteger_2EABS_2E0,type,
c_2Einteger_2EABS_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint) ).
tff(c_2Einteger_2EABS_2E1,type,
c_2Einteger_2EABS_2E1: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).
tff(c_2Elist_2EAPPEND_2E0,type,
c_2Elist_2EAPPEND_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Elist_2EAPPEND_2E2,type,
c_2Elist_2EAPPEND_2E2:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
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_2Estring_2ECHR_2E0,type,
c_2Estring_2ECHR_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar) ).
tff(c_2Estring_2ECHR_2E1,type,
c_2Estring_2ECHR_2E1: tyop_2Enum_2Enum > tyop_2Estring_2Echar ).
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_2Elist_2ECONS_2E0,type,
c_2Elist_2ECONS_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Elist_2ECONS_2E2,type,
c_2Elist_2ECONS_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
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_2Ecombin_2EI_2E0,type,
c_2Ecombin_2EI_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(c_2Ecombin_2EI_2E1,type,
c_2Ecombin_2EI_2E1:
!>[A_27a: $tType] : ( A_27a > A_27a ) ).
tff(c_2Einteger__word_2EINT__MAX_2E0,type,
c_2Einteger__word_2EINT__MAX_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Einteger_2Eint) ).
tff(c_2Einteger__word_2EINT__MAX_2E1,type,
c_2Einteger__word_2EINT__MAX_2E1:
!>[A_27a: $tType] : ( tyop_2Ebool_2Eitself(A_27a) > tyop_2Einteger_2Eint ) ).
tff(c_2Ewords_2EINT__MAX_2E0,type,
c_2Ewords_2EINT__MAX_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Enum_2Enum) ).
tff(c_2Ewords_2EINT__MAX_2E1,type,
c_2Ewords_2EINT__MAX_2E1:
!>[A_27a: $tType] : ( tyop_2Ebool_2Eitself(A_27a) > tyop_2Enum_2Enum ) ).
tff(c_2Einteger__word_2EINT__MIN_2E0,type,
c_2Einteger__word_2EINT__MIN_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Einteger_2Eint) ).
tff(c_2Einteger__word_2EINT__MIN_2E1,type,
c_2Einteger__word_2EINT__MIN_2E1:
!>[A_27a: $tType] : ( tyop_2Ebool_2Eitself(A_27a) > tyop_2Einteger_2Eint ) ).
tff(c_2Ewords_2EINT__MIN_2E0,type,
c_2Ewords_2EINT__MIN_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Enum_2Enum) ).
tff(c_2Ewords_2EINT__MIN_2E1,type,
c_2Ewords_2EINT__MIN_2E1:
!>[A_27a: $tType] : ( tyop_2Ebool_2Eitself(A_27a) > 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_2Elist_2ENIL_2E0,type,
c_2Elist_2ENIL_2E0:
!>[A_27a: $tType] : tyop_2Elist_2Elist(A_27a) ).
tff(c_2Earithmetic_2ENUMERAL_2E0,type,
c_2Earithmetic_2ENUMERAL_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2ENUMERAL_2E1,type,
c_2Earithmetic_2ENUMERAL_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Einteger_2ENum_2E0,type,
c_2Einteger_2ENum_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Enum_2Enum) ).
tff(c_2Einteger_2ENum_2E1,type,
c_2Einteger_2ENum_2E1: tyop_2Einteger_2Eint > tyop_2Enum_2Enum ).
tff(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(c_2Einteger__word_2EUINT__MAX_2E0,type,
c_2Einteger__word_2EUINT__MAX_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Einteger_2Eint) ).
tff(c_2Einteger__word_2EUINT__MAX_2E1,type,
c_2Einteger__word_2EUINT__MAX_2E1:
!>[A_27a: $tType] : ( tyop_2Ebool_2Eitself(A_27a) > tyop_2Einteger_2Eint ) ).
tff(c_2Ewords_2EUINT__MAX_2E0,type,
c_2Ewords_2EUINT__MAX_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Enum_2Enum) ).
tff(c_2Ewords_2EUINT__MAX_2E1,type,
c_2Ewords_2EUINT__MAX_2E1:
!>[A_27a: $tType] : ( tyop_2Ebool_2Eitself(A_27a) > tyop_2Enum_2Enum ) ).
tff(c_2Erelation_2EWF_2E0,type,
c_2Erelation_2EWF_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2EWF_2E1,type,
c_2Erelation_2EWF_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2EWFREC_2E0,type,
c_2Erelation_2EWFREC_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b))) ).
tff(c_2Erelation_2EWFREC_2E2,type,
c_2Erelation_2EWFREC_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) ) > tyop_2Emin_2Efun(A_27a,A_27b) ) ).
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_2Efcp_2Edimindex_2E0,type,
c_2Efcp_2Edimindex_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Enum_2Enum) ).
tff(c_2Efcp_2Edimindex_2E1,type,
c_2Efcp_2Edimindex_2E1:
!>[A_27a: $tType] : ( tyop_2Ebool_2Eitself(A_27a) > tyop_2Enum_2Enum ) ).
tff(c_2Ewords_2Edimword_2E0,type,
c_2Ewords_2Edimword_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Enum_2Enum) ).
tff(c_2Ewords_2Edimword_2E1,type,
c_2Ewords_2Edimword_2E1:
!>[A_27a: $tType] : ( tyop_2Ebool_2Eitself(A_27a) > tyop_2Enum_2Enum ) ).
tff(c_2Einteger__word_2EfromString_2E0,type,
c_2Einteger__word_2EfromString_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint) ).
tff(c_2Einteger__word_2EfromString_2E1,type,
c_2Einteger__word_2EfromString_2E1: tyop_2Elist_2Elist(tyop_2Estring_2Echar) > tyop_2Einteger_2Eint ).
tff(c_2Einteger__word_2Ei2w_2E0,type,
c_2Einteger__word_2Ei2w_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)) ).
tff(c_2Einteger__word_2Ei2w_2E1,type,
c_2Einteger__word_2Ei2w_2E1:
!>[A_27a: $tType] : ( tyop_2Einteger_2Eint > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) ).
tff(c_2Einteger_2Eint__add_2E0,type,
c_2Einteger_2Eint__add_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)) ).
tff(c_2Einteger_2Eint__add_2E2,type,
c_2Einteger_2Eint__add_2E2: ( tyop_2Einteger_2Eint * tyop_2Einteger_2Eint ) > tyop_2Einteger_2Eint ).
tff(c_2Einteger_2Eint__div_2E0,type,
c_2Einteger_2Eint__div_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)) ).
tff(c_2Einteger_2Eint__div_2E2,type,
c_2Einteger_2Eint__div_2E2: ( tyop_2Einteger_2Eint * tyop_2Einteger_2Eint ) > tyop_2Einteger_2Eint ).
tff(c_2Einteger_2Eint__exp_2E0,type,
c_2Einteger_2Eint__exp_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Einteger_2Eint)) ).
tff(c_2Einteger_2Eint__exp_2E2,type,
c_2Einteger_2Eint__exp_2E2: ( tyop_2Einteger_2Eint * tyop_2Enum_2Enum ) > tyop_2Einteger_2Eint ).
tff(c_2Einteger_2Eint__ge_2E0,type,
c_2Einteger_2Eint__ge_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)) ).
tff(c_2Einteger_2Eint__ge_2E2,type,
c_2Einteger_2Eint__ge_2E2: ( tyop_2Einteger_2Eint * tyop_2Einteger_2Eint ) > tyop_2Emin_2Ebool ).
tff(c_2Einteger_2Eint__gt_2E0,type,
c_2Einteger_2Eint__gt_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)) ).
tff(c_2Einteger_2Eint__gt_2E2,type,
c_2Einteger_2Eint__gt_2E2: ( tyop_2Einteger_2Eint * tyop_2Einteger_2Eint ) > tyop_2Emin_2Ebool ).
tff(c_2Einteger_2Eint__le_2E0,type,
c_2Einteger_2Eint__le_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)) ).
tff(c_2Einteger_2Eint__le_2E2,type,
c_2Einteger_2Eint__le_2E2: ( tyop_2Einteger_2Eint * tyop_2Einteger_2Eint ) > tyop_2Emin_2Ebool ).
tff(c_2Einteger_2Eint__lt_2E0,type,
c_2Einteger_2Eint__lt_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)) ).
tff(c_2Einteger_2Eint__lt_2E2,type,
c_2Einteger_2Eint__lt_2E2: ( tyop_2Einteger_2Eint * tyop_2Einteger_2Eint ) > tyop_2Emin_2Ebool ).
tff(c_2Einteger_2Eint__mod_2E0,type,
c_2Einteger_2Eint__mod_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)) ).
tff(c_2Einteger_2Eint__mod_2E2,type,
c_2Einteger_2Eint__mod_2E2: ( tyop_2Einteger_2Eint * tyop_2Einteger_2Eint ) > tyop_2Einteger_2Eint ).
tff(c_2Einteger_2Eint__mul_2E0,type,
c_2Einteger_2Eint__mul_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)) ).
tff(c_2Einteger_2Eint__mul_2E2,type,
c_2Einteger_2Eint__mul_2E2: ( tyop_2Einteger_2Eint * tyop_2Einteger_2Eint ) > tyop_2Einteger_2Eint ).
tff(c_2Einteger_2Eint__neg_2E0,type,
c_2Einteger_2Eint__neg_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint) ).
tff(c_2Einteger_2Eint__neg_2E1,type,
c_2Einteger_2Eint__neg_2E1: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).
tff(c_2Einteger_2Eint__of__num_2E0,type,
c_2Einteger_2Eint__of__num_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Einteger_2Eint) ).
tff(c_2Einteger_2Eint__of__num_2E1,type,
c_2Einteger_2Eint__of__num_2E1: tyop_2Enum_2Enum > tyop_2Einteger_2Eint ).
tff(c_2Einteger_2Eint__sub_2E0,type,
c_2Einteger_2Eint__sub_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)) ).
tff(c_2Einteger_2Eint__sub_2E2,type,
c_2Einteger_2Eint__sub_2E2: ( tyop_2Einteger_2Eint * tyop_2Einteger_2Eint ) > tyop_2Einteger_2Eint ).
tff(c_2Elist_2Elist__CASE_2E0,type,
c_2Elist_2Elist__CASE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),A_27b))) ).
tff(c_2Elist_2Elist__CASE_2E3,type,
c_2Elist_2Elist__CASE_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * A_27b * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)) ) > A_27b ) ).
tff(c_2Ebool_2Eliteral__case_2E0,type,
c_2Ebool_2Eliteral__case_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_2Eliteral__case_2E2,type,
c_2Ebool_2Eliteral__case_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(c_2Ewords_2En2w_2E0,type,
c_2Ewords_2En2w_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)) ).
tff(c_2Ewords_2En2w_2E1,type,
c_2Ewords_2En2w_2E1:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) ).
tff(c_2EASCIInumbers_2Enum__from__dec__string_2E0,type,
c_2EASCIInumbers_2Enum__from__dec__string_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum) ).
tff(c_2EASCIInumbers_2Enum__from__dec__string_2E1,type,
c_2EASCIInumbers_2Enum__from__dec__string_2E1: tyop_2Elist_2Elist(tyop_2Estring_2Echar) > tyop_2Enum_2Enum ).
tff(c_2EASCIInumbers_2Enum__to__dec__string_2E0,type,
c_2EASCIInumbers_2Enum__to__dec__string_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)) ).
tff(c_2EASCIInumbers_2Enum__to__dec__string_2E1,type,
c_2EASCIInumbers_2Enum__to__dec__string_2E1: tyop_2Enum_2Enum > tyop_2Elist_2Elist(tyop_2Estring_2Echar) ).
tff(c_2Einteger__word_2Esaturate__i2sw_2E0,type,
c_2Einteger__word_2Esaturate__i2sw_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)) ).
tff(c_2Einteger__word_2Esaturate__i2sw_2E1,type,
c_2Einteger__word_2Esaturate__i2sw_2E1:
!>[A_27a: $tType] : ( tyop_2Einteger_2Eint > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) ).
tff(c_2Einteger__word_2Esaturate__i2w_2E0,type,
c_2Einteger__word_2Esaturate__i2w_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)) ).
tff(c_2Einteger__word_2Esaturate__i2w_2E1,type,
c_2Einteger__word_2Esaturate__i2w_2E1:
!>[A_27a: $tType] : ( tyop_2Einteger_2Eint > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) ).
tff(c_2Einteger__word_2Esaturate__sw2sw_2E0,type,
c_2Einteger__word_2Esaturate__sw2sw_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)) ).
tff(c_2Einteger__word_2Esaturate__sw2sw_2E1,type,
c_2Einteger__word_2Esaturate__sw2sw_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b) ) ).
tff(c_2Einteger__word_2Esaturate__sw2w_2E0,type,
c_2Einteger__word_2Esaturate__sw2w_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)) ).
tff(c_2Einteger__word_2Esaturate__sw2w_2E1,type,
c_2Einteger__word_2Esaturate__sw2w_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b) ) ).
tff(c_2Einteger__word_2Esaturate__w2sw_2E0,type,
c_2Einteger__word_2Esaturate__w2sw_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)) ).
tff(c_2Einteger__word_2Esaturate__w2sw_2E1,type,
c_2Einteger__word_2Esaturate__w2sw_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b) ) ).
tff(c_2Einteger__word_2Esigned__saturate__add_2E0,type,
c_2Einteger__word_2Esigned__saturate__add_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a))) ).
tff(c_2Einteger__word_2Esigned__saturate__add_2E2,type,
c_2Einteger__word_2Esigned__saturate__add_2E2:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) * tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) ).
tff(c_2Einteger__word_2Esigned__saturate__sub_2E0,type,
c_2Einteger__word_2Esigned__saturate__sub_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a))) ).
tff(c_2Einteger__word_2Esigned__saturate__sub_2E2,type,
c_2Einteger__word_2Esigned__saturate__sub_2E2:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) * tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) ).
tff(c_2Ewords_2Esw2sw_2E0,type,
c_2Ewords_2Esw2sw_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)) ).
tff(c_2Ewords_2Esw2sw_2E1,type,
c_2Ewords_2Esw2sw_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b) ) ).
tff(c_2Ebool_2Ethe__value_2E0,type,
c_2Ebool_2Ethe__value_2E0:
!>[A_27a: $tType] : tyop_2Ebool_2Eitself(A_27a) ).
tff(c_2Einteger__word_2EtoString_2E0,type,
c_2Einteger__word_2EtoString_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Elist_2Elist(tyop_2Estring_2Echar)) ).
tff(c_2Einteger__word_2EtoString_2E1,type,
c_2Einteger__word_2EtoString_2E1: tyop_2Einteger_2Eint > tyop_2Elist_2Elist(tyop_2Estring_2Echar) ).
tff(c_2Einteger__word_2Ew2i_2E0,type,
c_2Einteger__word_2Ew2i_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Einteger_2Eint) ).
tff(c_2Einteger__word_2Ew2i_2E1,type,
c_2Einteger__word_2Ew2i_2E1:
!>[A_27a: $tType] : ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) > tyop_2Einteger_2Eint ) ).
tff(c_2Ewords_2Ew2n_2E0,type,
c_2Ewords_2Ew2n_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Enum_2Enum) ).
tff(c_2Ewords_2Ew2n_2E1,type,
c_2Ewords_2Ew2n_2E1:
!>[A_27a: $tType] : ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) > tyop_2Enum_2Enum ) ).
tff(c_2Ewords_2Ew2w_2E0,type,
c_2Ewords_2Ew2w_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)) ).
tff(c_2Ewords_2Ew2w_2E1,type,
c_2Ewords_2Ew2w_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b) ) ).
tff(c_2Ewords_2Eword__2comp_2E0,type,
c_2Ewords_2Eword__2comp_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)) ).
tff(c_2Ewords_2Eword__2comp_2E1,type,
c_2Ewords_2Eword__2comp_2E1:
!>[A_27a: $tType] : ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) ).
tff(c_2Ewords_2Eword__H_2E0,type,
c_2Ewords_2Eword__H_2E0:
!>[A_27a: $tType] : tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ).
tff(c_2Ewords_2Eword__L_2E0,type,
c_2Ewords_2Eword__L_2E0:
!>[A_27a: $tType] : tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ).
tff(c_2Ewords_2Eword__T_2E0,type,
c_2Ewords_2Eword__T_2E0:
!>[A_27a: $tType] : tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ).
tff(c_2Ewords_2Eword__abs_2E0,type,
c_2Ewords_2Eword__abs_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)) ).
tff(c_2Ewords_2Eword__abs_2E1,type,
c_2Ewords_2Eword__abs_2E1:
!>[A_27a: $tType] : ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) ).
tff(c_2Ewords_2Eword__add_2E0,type,
c_2Ewords_2Eword__add_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a))) ).
tff(c_2Ewords_2Eword__add_2E2,type,
c_2Ewords_2Eword__add_2E2:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) * tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) ).
tff(c_2Ewords_2Eword__asr_2E0,type,
c_2Ewords_2Eword__asr_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a))) ).
tff(c_2Ewords_2Eword__asr_2E2,type,
c_2Ewords_2Eword__asr_2E2:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) * tyop_2Enum_2Enum ) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) ).
tff(c_2Ewords_2Eword__ge_2E0,type,
c_2Ewords_2Eword__ge_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Ewords_2Eword__ge_2E2,type,
c_2Ewords_2Eword__ge_2E2:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) * tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ewords_2Eword__gt_2E0,type,
c_2Ewords_2Eword__gt_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Ewords_2Eword__gt_2E2,type,
c_2Ewords_2Eword__gt_2E2:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) * tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ewords_2Eword__le_2E0,type,
c_2Ewords_2Eword__le_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Ewords_2Eword__le_2E2,type,
c_2Ewords_2Eword__le_2E2:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) * tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ewords_2Eword__lt_2E0,type,
c_2Ewords_2Eword__lt_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Ewords_2Eword__lt_2E2,type,
c_2Ewords_2Eword__lt_2E2:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) * tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ewords_2Eword__msb_2E0,type,
c_2Ewords_2Eword__msb_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool) ).
tff(c_2Ewords_2Eword__msb_2E1,type,
c_2Ewords_2Eword__msb_2E1:
!>[A_27a: $tType] : ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) > tyop_2Emin_2Ebool ) ).
tff(c_2Ewords_2Eword__mul_2E0,type,
c_2Ewords_2Eword__mul_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a))) ).
tff(c_2Ewords_2Eword__mul_2E2,type,
c_2Ewords_2Eword__mul_2E2:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) * tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) ).
tff(c_2Einteger__word_2Eword__sdiv_2E0,type,
c_2Einteger__word_2Eword__sdiv_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a))) ).
tff(c_2Einteger__word_2Eword__sdiv_2E2,type,
c_2Einteger__word_2Eword__sdiv_2E2:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) * tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) ).
tff(c_2Einteger__word_2Eword__smod_2E0,type,
c_2Einteger__word_2Eword__smod_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a))) ).
tff(c_2Einteger__word_2Eword__smod_2E2,type,
c_2Einteger__word_2Eword__smod_2E2:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) * tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) ).
tff(c_2Ewords_2Eword__sub_2E0,type,
c_2Ewords_2Eword__sub_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a))) ).
tff(c_2Ewords_2Eword__sub_2E2,type,
c_2Ewords_2Eword__sub_2E2:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) * tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) ).
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_2D_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_2D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D_2E0,X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
& p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : c_2Eprim__rec_2E_3C_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : c_2Earithmetic_2E_3C_3D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3C_3D_2E0,X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] :
( ( X0_2E0 = X1_2E0 )
<=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
=> p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : c_2Ebool_2E_3F_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] : c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E0(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool))),X0_2E0) ).
tff(arityeq1_2Ec_2Einteger_2EABS_2E1,axiom,
! [X0_2E0: tyop_2Einteger_2Eint] : c_2Einteger_2EABS_2E1(X0_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2EABS_2E0,X0_2E0) ).
tff(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Estring_2Echar,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : c_2Elist_2EAPPEND_2E2(tyop_2Estring_2Echar,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Elist_2EAPPEND_2E0(tyop_2Estring_2Echar),X0_2E0),X1_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_2Estring_2ECHR_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : c_2Estring_2ECHR_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Estring_2Echar,c_2Estring_2ECHR_2E0,X0_2E0) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X2_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Ebool_2ECOND_2E3(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a))),c_2Ebool_2ECOND_2E0(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),X0_2E0),X1_2E0),X2_2E0) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Einteger_2Eint,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Einteger_2Eint,X2_2E0: tyop_2Einteger_2Eint] : c_2Ebool_2ECOND_2E3(tyop_2Einteger_2Eint,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),c_2Ebool_2ECOND_2E0(tyop_2Einteger_2Eint),X0_2E0),X1_2E0),X2_2E0) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar),X2_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Ebool_2ECOND_2E0(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X0_2E0),X1_2E0),X2_2E0) ).
tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Estring_2Echar,axiom,
! [X0_2E0: tyop_2Estring_2Echar,X1_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : c_2Elist_2ECONS_2E2(tyop_2Estring_2Echar,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Elist_2ECONS_2E0(tyop_2Estring_2Echar),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_2Ecombin_2EI_2E1_2Emono_2Etyop_2Einteger_2Eint,axiom,
! [X0_2E0: tyop_2Einteger_2Eint] : c_2Ecombin_2EI_2E1(tyop_2Einteger_2Eint,X0_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Ecombin_2EI_2E0(tyop_2Einteger_2Eint),X0_2E0) ).
tff(arityeq1_2Ec_2Einteger__word_2EINT__MAX_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Ebool_2Eitself(A_27a)] : c_2Einteger__word_2EINT__MAX_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(A_27a),tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MAX_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Einteger__word_2EINT__MAX_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Ebool_2Eitself(A_27b)] : c_2Einteger__word_2EINT__MAX_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(A_27b),tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MAX_2E0(A_27b),X0_2E0) ).
tff(arityeq1_2Ec_2Ewords_2EINT__MAX_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Ebool_2Eitself(A_27a)] : c_2Ewords_2EINT__MAX_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(A_27a),tyop_2Enum_2Enum,c_2Ewords_2EINT__MAX_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Einteger__word_2EINT__MIN_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Ebool_2Eitself(A_27a)] : c_2Einteger__word_2EINT__MIN_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(A_27a),tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MIN_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Einteger__word_2EINT__MIN_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Ebool_2Eitself(A_27b)] : c_2Einteger__word_2EINT__MIN_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(A_27b),tyop_2Einteger_2Eint,c_2Einteger__word_2EINT__MIN_2E0(A_27b),X0_2E0) ).
tff(arityeq1_2Ec_2Ewords_2EINT__MIN_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Ebool_2Eitself(A_27a)] : c_2Ewords_2EINT__MIN_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(A_27a),tyop_2Enum_2Enum,c_2Ewords_2EINT__MIN_2E0(A_27a),X0_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_2Einteger_2ENum_2E1,axiom,
! [X0_2E0: tyop_2Einteger_2Eint] : c_2Einteger_2ENum_2E1(X0_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Enum_2Enum,c_2Einteger_2ENum_2E0,X0_2E0) ).
tff(arityeq1_2Ec_2Einteger__word_2EUINT__MAX_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Ebool_2Eitself(A_27a)] : c_2Einteger__word_2EUINT__MAX_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(A_27a),tyop_2Einteger_2Eint,c_2Einteger__word_2EUINT__MAX_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Ewords_2EUINT__MAX_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Ebool_2Eitself(A_27a)] : c_2Ewords_2EUINT__MAX_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(A_27a),tyop_2Enum_2Enum,c_2Ewords_2EUINT__MAX_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool))] : c_2Erelation_2EWF_2E1(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E0(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X0_2E0) ).
tff(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_20mono_2Etyop_2Einteger_2Eint,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint))] : c_2Erelation_2EWFREC_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint)),c_2Erelation_2EWFREC_2E0(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint),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_2Efcp_2Edimindex_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Ebool_2Eitself(A_27a)] : c_2Efcp_2Edimindex_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(A_27a),tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Efcp_2Edimindex_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Ebool_2Eitself(A_27b)] : c_2Efcp_2Edimindex_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(A_27b),tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E0(A_27b),X0_2E0) ).
tff(arityeq1_2Ec_2Efcp_2Edimindex_2E1_2Emono_2EA_27c,axiom,
! [A_27c: $tType,X0_2E0: tyop_2Ebool_2Eitself(A_27c)] : c_2Efcp_2Edimindex_2E1(A_27c,X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(A_27c),tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E0(A_27c),X0_2E0) ).
tff(arityeq1_2Ec_2Ewords_2Edimword_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Ebool_2Eitself(A_27a)] : c_2Ewords_2Edimword_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Ebool_2Eitself(A_27a),tyop_2Enum_2Enum,c_2Ewords_2Edimword_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Einteger__word_2EfromString_2E1,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : c_2Einteger__word_2EfromString_2E1(X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint,c_2Einteger__word_2EfromString_2E0,X0_2E0) ).
tff(arityeq1_2Ec_2Einteger__word_2Ei2w_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Einteger_2Eint] : c_2Einteger__word_2Ei2w_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Ei2w_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Einteger__word_2Ei2w_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Einteger_2Eint] : c_2Einteger__word_2Ei2w_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Einteger__word_2Ei2w_2E0(A_27b),X0_2E0) ).
tff(arityeq2_2Ec_2Einteger_2Eint__add_2E2,axiom,
! [X0_2E0: tyop_2Einteger_2Eint,X1_2E0: tyop_2Einteger_2Eint] : c_2Einteger_2Eint__add_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),c_2Einteger_2Eint__add_2E0,X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Einteger_2Eint__div_2E2,axiom,
! [X0_2E0: tyop_2Einteger_2Eint,X1_2E0: tyop_2Einteger_2Eint] : c_2Einteger_2Eint__div_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),c_2Einteger_2Eint__div_2E0,X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Einteger_2Eint__exp_2E2,axiom,
! [X0_2E0: tyop_2Einteger_2Eint,X1_2E0: tyop_2Enum_2Enum] : c_2Einteger_2Eint__exp_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Einteger_2Eint),c_2Einteger_2Eint__exp_2E0,X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Einteger_2Eint__ge_2E2,axiom,
! [X0_2E0: tyop_2Einteger_2Eint,X1_2E0: tyop_2Einteger_2Eint] : c_2Einteger_2Eint__ge_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__ge_2E0,X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Einteger_2Eint__gt_2E2,axiom,
! [X0_2E0: tyop_2Einteger_2Eint,X1_2E0: tyop_2Einteger_2Eint] : c_2Einteger_2Eint__gt_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__gt_2E0,X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Einteger_2Eint__le_2E2,axiom,
! [X0_2E0: tyop_2Einteger_2Eint,X1_2E0: tyop_2Einteger_2Eint] : c_2Einteger_2Eint__le_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__le_2E0,X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Einteger_2Eint__lt_2E2,axiom,
! [X0_2E0: tyop_2Einteger_2Eint,X1_2E0: tyop_2Einteger_2Eint] : c_2Einteger_2Eint__lt_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Einteger_2Eint__mod_2E2,axiom,
! [X0_2E0: tyop_2Einteger_2Eint,X1_2E0: tyop_2Einteger_2Eint] : c_2Einteger_2Eint__mod_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),c_2Einteger_2Eint__mod_2E0,X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Einteger_2Eint__mul_2E2,axiom,
! [X0_2E0: tyop_2Einteger_2Eint,X1_2E0: tyop_2Einteger_2Eint] : c_2Einteger_2Eint__mul_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),c_2Einteger_2Eint__mul_2E0,X0_2E0),X1_2E0) ).
tff(arityeq1_2Ec_2Einteger_2Eint__neg_2E1,axiom,
! [X0_2E0: tyop_2Einteger_2Eint] : c_2Einteger_2Eint__neg_2E1(X0_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E0,X0_2E0) ).
tff(arityeq1_2Ec_2Einteger_2Eint__of__num_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : c_2Einteger_2Eint__of__num_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0_2E0) ).
tff(arityeq2_2Ec_2Einteger_2Eint__sub_2E2,axiom,
! [X0_2E0: tyop_2Einteger_2Eint,X1_2E0: tyop_2Einteger_2Eint] : c_2Einteger_2Eint__sub_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),c_2Einteger_2Eint__sub_2E0,X0_2E0),X1_2E0) ).
tff(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Einteger_2Eint,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0: tyop_2Einteger_2Eint,X2_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint))] : c_2Elist_2Elist__CASE_2E3(tyop_2Estring_2Echar,tyop_2Einteger_2Eint,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint)),tyop_2Einteger_2Eint,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint)),tyop_2Einteger_2Eint),app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint)),tyop_2Einteger_2Eint)),c_2Elist_2Elist__CASE_2E0(tyop_2Estring_2Echar,tyop_2Einteger_2Eint),X0_2E0),X1_2E0),X2_2E0) ).
tff(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Einteger_2Eint,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Einteger_2Eint),X1_2E0: tyop_2Estring_2Echar] : c_2Ebool_2Eliteral__case_2E2(tyop_2Estring_2Echar,tyop_2Einteger_2Eint,X0_2E0,X1_2E0) = app_2E2(tyop_2Estring_2Echar,tyop_2Einteger_2Eint,app_2E2(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Einteger_2Eint),tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Einteger_2Eint),c_2Ebool_2Eliteral__case_2E0(tyop_2Estring_2Echar,tyop_2Einteger_2Eint),X0_2E0),X1_2E0) ).
tff(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum] : c_2Ewords_2En2w_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2EASCIInumbers_2Enum__from__dec__string_2E1,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : c_2EASCIInumbers_2Enum__from__dec__string_2E1(X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum,c_2EASCIInumbers_2Enum__from__dec__string_2E0,X0_2E0) ).
tff(arityeq1_2Ec_2EASCIInumbers_2Enum__to__dec__string_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : c_2EASCIInumbers_2Enum__to__dec__string_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2EASCIInumbers_2Enum__to__dec__string_2E0,X0_2E0) ).
tff(arityeq1_2Ec_2Einteger__word_2Esaturate__i2sw_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Einteger_2Eint] : c_2Einteger__word_2Esaturate__i2sw_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Esaturate__i2sw_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Einteger__word_2Esaturate__i2sw_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Einteger_2Eint] : c_2Einteger__word_2Esaturate__i2sw_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Einteger__word_2Esaturate__i2sw_2E0(A_27b),X0_2E0) ).
tff(arityeq1_2Ec_2Einteger__word_2Esaturate__i2w_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Einteger_2Eint] : c_2Einteger__word_2Esaturate__i2w_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger__word_2Esaturate__i2w_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Einteger__word_2Esaturate__i2w_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Einteger_2Eint] : c_2Einteger__word_2Esaturate__i2w_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Einteger__word_2Esaturate__i2w_2E0(A_27b),X0_2E0) ).
tff(arityeq1_2Ec_2Einteger__word_2Esaturate__sw2sw_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Einteger__word_2Esaturate__sw2sw_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Einteger__word_2Esaturate__sw2sw_2E0(A_27a,A_27b),X0_2E0) ).
tff(arityeq1_2Ec_2Einteger__word_2Esaturate__sw2w_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Einteger__word_2Esaturate__sw2w_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Einteger__word_2Esaturate__sw2w_2E0(A_27a,A_27b),X0_2E0) ).
tff(arityeq1_2Ec_2Einteger__word_2Esaturate__w2sw_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Einteger__word_2Esaturate__w2sw_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Einteger__word_2Esaturate__w2sw_2E0(A_27a,A_27b),X0_2E0) ).
tff(arityeq2_2Ec_2Einteger__word_2Esigned__saturate__add_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Einteger__word_2Esigned__saturate__add_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Einteger__word_2Esigned__saturate__add_2E0(A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Einteger__word_2Esigned__saturate__sub_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Einteger__word_2Esigned__saturate__sub_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Einteger__word_2Esigned__saturate__sub_2E0(A_27a),X0_2E0),X1_2E0) ).
tff(arityeq1_2Ec_2Ewords_2Esw2sw_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Ewords_2Esw2sw_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),c_2Ewords_2Esw2sw_2E0(A_27a,A_27b),X0_2E0) ).
tff(arityeq1_2Ec_2Ewords_2Esw2sw_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Ewords_2Esw2sw_2E1(A_27a,A_27c,X0_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),c_2Ewords_2Esw2sw_2E0(A_27a,A_27c),X0_2E0) ).
tff(arityeq1_2Ec_2Ewords_2Esw2sw_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)] : c_2Ewords_2Esw2sw_2E1(A_27b,A_27a,X0_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Esw2sw_2E0(A_27b,A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Ewords_2Esw2sw_2E1_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)] : c_2Ewords_2Esw2sw_2E1(A_27b,A_27c,X0_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27c),c_2Ewords_2Esw2sw_2E0(A_27b,A_27c),X0_2E0) ).
tff(arityeq1_2Ec_2Einteger__word_2EtoString_2E1,axiom,
! [X0_2E0: tyop_2Einteger_2Eint] : c_2Einteger__word_2EtoString_2E1(X0_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Einteger__word_2EtoString_2E0,X0_2E0) ).
tff(arityeq1_2Ec_2Einteger__word_2Ew2i_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Einteger__word_2Ew2i_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Einteger__word_2Ew2i_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)] : c_2Einteger__word_2Ew2i_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Einteger_2Eint,c_2Einteger__word_2Ew2i_2E0(A_27b),X0_2E0) ).
tff(arityeq1_2Ec_2Ewords_2Ew2n_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Ewords_2Ew2n_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Enum_2Enum,c_2Ewords_2Ew2n_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Ewords_2Ew2w_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)] : c_2Ewords_2Ew2w_2E1(A_27b,A_27a,X0_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Ew2w_2E0(A_27b,A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Ewords_2Eword__2comp_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__2comp_2E0(A_27a),X0_2E0) ).
tff(arityeq1_2Ec_2Ewords_2Eword__abs_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Ewords_2Eword__abs_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__abs_2E0(A_27a),X0_2E0) ).
tff(arityeq2_2Ec_2Ewords_2Eword__add_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Ewords_2Eword__add_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Ewords_2Eword__add_2E0(A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ewords_2Eword__asr_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0: tyop_2Enum_2Enum] : c_2Ewords_2Eword__asr_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Ewords_2Eword__asr_2E0(A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ewords_2Eword__ge_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Ewords_2Eword__ge_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),c_2Ewords_2Eword__ge_2E0(A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ewords_2Eword__gt_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Ewords_2Eword__gt_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),c_2Ewords_2Eword__gt_2E0(A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ewords_2Eword__le_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Ewords_2Eword__le_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),c_2Ewords_2Eword__le_2E0(A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ewords_2Eword__lt_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Ewords_2Eword__lt_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),c_2Ewords_2Eword__lt_2E0(A_27a),X0_2E0),X1_2E0) ).
tff(arityeq1_2Ec_2Ewords_2Eword__msb_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Ewords_2Eword__msb_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool,c_2Ewords_2Eword__msb_2E0(A_27a),X0_2E0) ).
tff(arityeq2_2Ec_2Ewords_2Eword__mul_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Ewords_2Eword__mul_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Ewords_2Eword__mul_2E0(A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Einteger__word_2Eword__sdiv_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Einteger__word_2Eword__sdiv_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Einteger__word_2Eword__sdiv_2E0(A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Einteger__word_2Eword__smod_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Einteger__word_2Eword__smod_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Einteger__word_2Eword__smod_2E0(A_27a),X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ewords_2Eword__sub_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Ewords_2Eword__sub_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Ewords_2Eword__sub_2E0(A_27a),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_2Einteger__word_2EtoString__def,axiom,
! [V0i_2E0: tyop_2Einteger_2Eint] : c_2Einteger__word_2EtoString_2E1(V0i_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Einteger_2Eint__lt_2E2(V0i_2E0,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)),c_2Elist_2EAPPEND_2E2(tyop_2Estring_2Echar,c_2Elist_2ECONS_2E2(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))),c_2Elist_2ENIL_2E0(tyop_2Estring_2Echar)),c_2EASCIInumbers_2Enum__to__dec__string_2E1(c_2Einteger_2ENum_2E1(c_2Einteger_2Eint__neg_2E1(V0i_2E0)))),c_2EASCIInumbers_2Enum__to__dec__string_2E1(c_2Einteger_2ENum_2E1(V0i_2E0))) ).
tff(thm_2Einteger__word_2EfromString__primitive__def,axiom,
! [F4_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F5_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F3_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Einteger_2Eint)),F2_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint)),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint)),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] :
( ! [V5v4_2E0: tyop_2Estring_2Echar] :
( p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F4_2E0,V5v4_2E0))
<=> ( V5v4_2E0 = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))) ) )
=> ( ! [V5v4_2E0: tyop_2Estring_2Echar] :
( p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F5_2E0,V5v4_2E0))
<=> ( V5v4_2E0 = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))) ) )
=> ( ! [V4t_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar),V5v4_2E0: tyop_2Estring_2Echar] : app_2E2(tyop_2Estring_2Echar,tyop_2Einteger_2Eint,app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Einteger_2Eint),F3_2E0,V4t_2E0),V5v4_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Einteger_2Eint,app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F4_2E0,V5v4_2E0),c_2Ecombin_2EI_2E1(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2EASCIInumbers_2Enum__from__dec__string_2E1(V4t_2E0)))),c_2Ebool_2ECOND_2E3(tyop_2Einteger_2Eint,app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F5_2E0,V5v4_2E0),c_2Ecombin_2EI_2E1(tyop_2Einteger_2Eint,c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2EASCIInumbers_2Enum__from__dec__string_2E1(V4t_2E0)))),c_2Ecombin_2EI_2E1(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(c_2EASCIInumbers_2Enum__from__dec__string_2E1(c_2Elist_2ECONS_2E2(tyop_2Estring_2Echar,V5v4_2E0,V4t_2E0))))))
=> ( ! [V3v2_2E0: tyop_2Estring_2Echar,V4t_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint,app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint),F2_2E0,V3v2_2E0),V4t_2E0) = c_2Ebool_2Eliteral__case_2E2(tyop_2Estring_2Echar,tyop_2Einteger_2Eint,app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Einteger_2Eint),F3_2E0,V4t_2E0),V3v2_2E0)
=> ( ! [V1fromString_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint),V2a_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint,app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint),F1_2E0,V1fromString_2E0),V2a_2E0) = c_2Elist_2Elist__CASE_2E3(tyop_2Estring_2Echar,tyop_2Einteger_2Eint,V2a_2E0,c_2Ecombin_2EI_2E1(tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E1(c_2EASCIInumbers_2Enum__from__dec__string_2E1(c_2Elist_2ENIL_2E0(tyop_2Estring_2Echar)))),F2_2E0)
=> ( ! [V0R_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool))] : app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,F0_2E0,V0R_2E0) = c_2Erelation_2EWF_2E1(tyop_2Elist_2Elist(tyop_2Estring_2Echar),V0R_2E0)
=> ( c_2Einteger__word_2EfromString_2E0 = c_2Erelation_2EWFREC_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Einteger_2Eint,c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),F0_2E0),F1_2E0) ) ) ) ) ) ) ) ).
tff(thm_2Einteger__word_2Ei2w__def,axiom,
! [A_27a: $tType,V0i_2E0: tyop_2Einteger_2Eint] : c_2Einteger__word_2Ei2w_2E1(A_27a,V0i_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger_2Eint__lt_2E2(V0i_2E0,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)),c_2Ewords_2Eword__2comp_2E1(A_27a,c_2Ewords_2En2w_2E1(A_27a,c_2Einteger_2ENum_2E1(c_2Einteger_2Eint__neg_2E1(V0i_2E0)))),c_2Ewords_2En2w_2E1(A_27a,c_2Einteger_2ENum_2E1(V0i_2E0))) ).
tff(thm_2Einteger__word_2Ew2i__def,axiom,
! [A_27a: $tType,V0w_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Einteger__word_2Ew2i_2E1(A_27a,V0w_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Einteger_2Eint,c_2Ewords_2Eword__msb_2E1(A_27a,V0w_2E0),c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Ewords_2Ew2n_2E1(A_27a,c_2Ewords_2Eword__2comp_2E1(A_27a,V0w_2E0)))),c_2Einteger_2Eint__of__num_2E1(c_2Ewords_2Ew2n_2E1(A_27a,V0w_2E0))) ).
tff(thm_2Einteger__word_2EUINT__MAX__def,axiom,
! [A_27a: $tType] : c_2Einteger__word_2EUINT__MAX_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)) = c_2Einteger_2Eint__sub_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Ewords_2Edimword_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a))),c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) ).
tff(thm_2Einteger__word_2EINT__MAX__def,axiom,
! [A_27a: $tType] : c_2Einteger__word_2EINT__MAX_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)) = c_2Einteger_2Eint__sub_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Ewords_2EINT__MIN_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a))),c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) ).
tff(thm_2Einteger__word_2EINT__MIN__def,axiom,
! [A_27a: $tType] : c_2Einteger__word_2EINT__MIN_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)) = c_2Einteger_2Eint__sub_2E2(c_2Einteger_2Eint__neg_2E1(c_2Einteger__word_2EINT__MAX_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a))),c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) ).
tff(thm_2Einteger__word_2Esaturate__i2w__def,axiom,
! [A_27a: $tType,V0i_2E0: tyop_2Einteger_2Eint] : c_2Einteger__word_2Esaturate__i2w_2E1(A_27a,V0i_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger_2Eint__le_2E2(c_2Einteger__word_2EUINT__MAX_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)),V0i_2E0),c_2Ewords_2Eword__T_2E0(A_27a),c_2Ebool_2ECOND_2E3(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger_2Eint__lt_2E2(V0i_2E0,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)),c_2Ewords_2En2w_2E1(A_27a,c_2Enum_2E0_2E0),c_2Ewords_2En2w_2E1(A_27a,c_2Einteger_2ENum_2E1(V0i_2E0)))) ).
tff(thm_2Einteger__word_2Esaturate__i2sw__def,axiom,
! [A_27a: $tType,V0i_2E0: tyop_2Einteger_2Eint] : c_2Einteger__word_2Esaturate__i2sw_2E1(A_27a,V0i_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger_2Eint__le_2E2(c_2Einteger__word_2EINT__MAX_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)),V0i_2E0),c_2Ewords_2Eword__H_2E0(A_27a),c_2Ebool_2ECOND_2E3(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Einteger_2Eint__le_2E2(V0i_2E0,c_2Einteger__word_2EINT__MIN_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a))),c_2Ewords_2Eword__L_2E0(A_27a),c_2Einteger__word_2Ei2w_2E1(A_27a,V0i_2E0))) ).
tff(thm_2Einteger__word_2Esaturate__sw2sw__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0w_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Einteger__word_2Esaturate__sw2sw_2E1(A_27a,A_27b,V0w_2E0) = c_2Einteger__word_2Esaturate__i2sw_2E1(A_27b,c_2Einteger__word_2Ew2i_2E1(A_27a,V0w_2E0)) ).
tff(thm_2Einteger__word_2Esaturate__w2sw__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0w_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Einteger__word_2Esaturate__w2sw_2E1(A_27a,A_27b,V0w_2E0) = c_2Einteger__word_2Esaturate__i2sw_2E1(A_27b,c_2Einteger_2Eint__of__num_2E1(c_2Ewords_2Ew2n_2E1(A_27a,V0w_2E0))) ).
tff(thm_2Einteger__word_2Esaturate__sw2w__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0w_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Einteger__word_2Esaturate__sw2w_2E1(A_27a,A_27b,V0w_2E0) = c_2Einteger__word_2Esaturate__i2w_2E1(A_27b,c_2Einteger__word_2Ew2i_2E1(A_27a,V0w_2E0)) ).
tff(thm_2Einteger__word_2Esigned__saturate__add__def,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Einteger__word_2Esigned__saturate__add_2E2(A_27a,V0a_2E0,V1b_2E0) = c_2Einteger__word_2Esaturate__i2sw_2E1(A_27a,c_2Einteger_2Eint__add_2E2(c_2Einteger__word_2Ew2i_2E1(A_27a,V0a_2E0),c_2Einteger__word_2Ew2i_2E1(A_27a,V1b_2E0))) ).
tff(thm_2Einteger__word_2Esigned__saturate__sub__def,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Einteger__word_2Esigned__saturate__sub_2E2(A_27a,V0a_2E0,V1b_2E0) = c_2Einteger__word_2Esaturate__i2sw_2E1(A_27a,c_2Einteger_2Eint__sub_2E2(c_2Einteger__word_2Ew2i_2E1(A_27a,V0a_2E0),c_2Einteger__word_2Ew2i_2E1(A_27a,V1b_2E0))) ).
tff(thm_2Einteger__word_2Eword__sdiv__def,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Einteger__word_2Eword__sdiv_2E2(A_27a,V0a_2E0,V1b_2E0) = c_2Einteger__word_2Ei2w_2E1(A_27a,c_2Einteger_2Eint__div_2E2(c_2Einteger__word_2Ew2i_2E1(A_27a,V0a_2E0),c_2Einteger__word_2Ew2i_2E1(A_27a,V1b_2E0))) ).
tff(thm_2Einteger__word_2Eword__smod__def,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Einteger__word_2Eword__smod_2E2(A_27a,V0a_2E0,V1b_2E0) = c_2Einteger__word_2Ei2w_2E1(A_27a,c_2Einteger_2Eint__mod_2E2(c_2Einteger__word_2Ew2i_2E1(A_27a,V0a_2E0),c_2Einteger__word_2Ew2i_2E1(A_27a,V1b_2E0))) ).
tff(thm_2Einteger__word_2EfromString__ind,axiom,
! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)] :
( ( ! [V1t_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2ECONS_2E2(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))),V1t_2E0)))
& ! [V2t_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2ECONS_2E2(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))),V2t_2E0)))
& p(app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2ENIL_2E0(tyop_2Estring_2Echar)))
& ! [V3v4_2E0: tyop_2Estring_2Echar,V4v1_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2ECONS_2E2(tyop_2Estring_2Echar,V3v4_2E0,V4v1_2E0))) )
=> ! [V5v_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool,V0P_2E0,V5v_2E0)) ) ).
tff(thm_2Einteger__word_2EfromString__def,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool),F1_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Emin_2Ebool)] :
( ! [V0v4_2E0: tyop_2Estring_2Echar] :
( p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F0_2E0,V0v4_2E0))
<=> ( V0v4_2E0 = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))) ) )
=> ( ! [V0v4_2E0: tyop_2Estring_2Echar] :
( p(app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F1_2E0,V0v4_2E0))
<=> ( V0v4_2E0 = c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))) ) )
=> ! [V0v4_2E0: tyop_2Estring_2Echar,V1v1_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2t_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] :
( ( c_2Einteger__word_2EfromString_2E1(c_2Elist_2ECONS_2E2(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))))),V2t_2E0)) = c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2EASCIInumbers_2Enum__from__dec__string_2E1(V2t_2E0))) )
& ( c_2Einteger__word_2EfromString_2E1(c_2Elist_2ECONS_2E2(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))),V2t_2E0)) = c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2EASCIInumbers_2Enum__from__dec__string_2E1(V2t_2E0))) )
& ( c_2Einteger__word_2EfromString_2E1(c_2Elist_2ENIL_2E0(tyop_2Estring_2Echar)) = c_2Einteger_2Eint__of__num_2E1(c_2EASCIInumbers_2Enum__from__dec__string_2E1(c_2Elist_2ENIL_2E0(tyop_2Estring_2Echar))) )
& ( c_2Einteger__word_2EfromString_2E1(c_2Elist_2ECONS_2E2(tyop_2Estring_2Echar,V0v4_2E0,V1v1_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Einteger_2Eint,app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F0_2E0,V0v4_2E0),c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2EASCIInumbers_2Enum__from__dec__string_2E1(V1v1_2E0))),c_2Ebool_2ECOND_2E3(tyop_2Einteger_2Eint,app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Ebool,F1_2E0,V0v4_2E0),c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2EASCIInumbers_2Enum__from__dec__string_2E1(V1v1_2E0))),c_2Einteger_2Eint__of__num_2E1(c_2EASCIInumbers_2Enum__from__dec__string_2E1(c_2Elist_2ECONS_2E2(tyop_2Estring_2Echar,V0v4_2E0,V1v1_2E0))))) ) ) ) ) ).
tff(thm_2Einteger__word_2EONE__LE__TWOEXP,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] : p(c_2Earithmetic_2E_3C_3D_2E2(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)),V0n_2E0))) ).
tff(thm_2Einteger__word_2Ew2i__w2n__pos,axiom,
! [A_27a: $tType,V0w_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1n_2E0: tyop_2Enum_2Enum] :
( ( ~ p(c_2Ewords_2Eword__msb_2E1(A_27a,V0w_2E0))
& p(c_2Einteger_2Eint__lt_2E2(c_2Einteger__word_2Ew2i_2E1(A_27a,V0w_2E0),c_2Einteger_2Eint__of__num_2E1(V1n_2E0))) )
=> p(c_2Eprim__rec_2E_3C_2E2(c_2Ewords_2Ew2n_2E1(A_27a,V0w_2E0),V1n_2E0)) ) ).
tff(thm_2Einteger__word_2Ew2i__n2w__pos,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum] :
( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Ewords_2EINT__MIN_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a))))
=> ( c_2Einteger__word_2Ew2i_2E1(A_27a,c_2Ewords_2En2w_2E1(A_27a,V0n_2E0)) = c_2Einteger_2Eint__of__num_2E1(V0n_2E0) ) ) ).
tff(thm_2Einteger__word_2Ew2i__n2w__neg,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Ewords_2EINT__MIN_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)),V0n_2E0))
& p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Ewords_2Edimword_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)))) )
=> ( c_2Einteger__word_2Ew2i_2E1(A_27a,c_2Ewords_2En2w_2E1(A_27a,V0n_2E0)) = c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2E_2D_2E2(c_2Ewords_2Edimword_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)),V0n_2E0))) ) ) ).
tff(thm_2Einteger__word_2Ei2w__w2i,axiom,
! [A_27a: $tType,V0w_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Einteger__word_2Ei2w_2E1(A_27a,c_2Einteger__word_2Ew2i_2E1(A_27a,V0w_2E0)) = V0w_2E0 ).
tff(thm_2Einteger__word_2Ew2i__i2w,axiom,
! [A_27a: $tType,V0i_2E0: tyop_2Einteger_2Eint] :
( ( p(c_2Einteger_2Eint__le_2E2(c_2Einteger__word_2EINT__MIN_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)),V0i_2E0))
& p(c_2Einteger_2Eint__le_2E2(V0i_2E0,c_2Einteger__word_2EINT__MAX_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)))) )
=> ( c_2Einteger__word_2Ew2i_2E1(A_27a,c_2Einteger__word_2Ei2w_2E1(A_27a,V0i_2E0)) = V0i_2E0 ) ) ).
tff(thm_2Einteger__word_2Eword__msb__i2w,axiom,
! [A_27a: $tType,V0i_2E0: tyop_2Einteger_2Eint] : c_2Ewords_2Eword__msb_2E1(A_27a,c_2Einteger__word_2Ei2w_2E1(A_27a,V0i_2E0)) = c_2Einteger_2Eint__le_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Ewords_2EINT__MIN_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a))),c_2Einteger_2Eint__mod_2E2(V0i_2E0,c_2Einteger_2Eint__of__num_2E1(c_2Ewords_2Edimword_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a))))) ).
tff(thm_2Einteger__word_2Ew2i__11,axiom,
! [A_27a: $tType,V0v_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1w_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] :
( ( c_2Einteger__word_2Ew2i_2E1(A_27a,V0v_2E0) = c_2Einteger__word_2Ew2i_2E1(A_27a,V1w_2E0) )
<=> ( V0v_2E0 = V1w_2E0 ) ) ).
tff(thm_2Einteger__word_2Eint__word__nchotomy,axiom,
! [A_27a: $tType,V0w_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] :
? [V1i_2E0: tyop_2Einteger_2Eint] : V0w_2E0 = c_2Einteger__word_2Ei2w_2E1(A_27a,V1i_2E0) ).
tff(thm_2Einteger__word_2Ew2i__le,axiom,
! [A_27a: $tType,V0w_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : p(c_2Einteger_2Eint__le_2E2(c_2Einteger__word_2Ew2i_2E1(A_27a,V0w_2E0),c_2Einteger__word_2EINT__MAX_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)))) ).
tff(thm_2Einteger__word_2Ew2i__ge,axiom,
! [A_27a: $tType,V0w_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : p(c_2Einteger_2Eint__le_2E2(c_2Einteger__word_2EINT__MIN_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)),c_2Einteger__word_2Ew2i_2E1(A_27a,V0w_2E0))) ).
tff(thm_2Einteger__word_2Eranged__int__word__nchotomy,axiom,
! [A_27a: $tType,V0w_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] :
? [V1i_2E0: tyop_2Einteger_2Eint] :
( ( V0w_2E0 = c_2Einteger__word_2Ei2w_2E1(A_27a,V1i_2E0) )
& p(c_2Einteger_2Eint__le_2E2(c_2Einteger__word_2EINT__MIN_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)),V1i_2E0))
& p(c_2Einteger_2Eint__le_2E2(V1i_2E0,c_2Einteger__word_2EINT__MAX_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)))) ) ).
tff(thm_2Einteger__word_2Esw2sw__i2w,axiom,
! [A_27a: $tType,A_27b: $tType,V0j_2E0: tyop_2Einteger_2Eint] :
( ( p(c_2Einteger_2Eint__le_2E2(c_2Einteger__word_2EINT__MIN_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b)),V0j_2E0))
& p(c_2Einteger_2Eint__le_2E2(V0j_2E0,c_2Einteger__word_2EINT__MAX_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b))))
& p(c_2Earithmetic_2E_3C_3D_2E2(c_2Efcp_2Edimindex_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b)),c_2Efcp_2Edimindex_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)))) )
=> ( c_2Ewords_2Esw2sw_2E1(A_27b,A_27a,c_2Einteger__word_2Ei2w_2E1(A_27b,V0j_2E0)) = c_2Einteger__word_2Ei2w_2E1(A_27a,V0j_2E0) ) ) ).
tff(thm_2Einteger__word_2Ew2w__i2w,axiom,
! [A_27a: $tType,A_27b: $tType,V0i_2E0: tyop_2Einteger_2Eint] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Efcp_2Edimindex_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)),c_2Efcp_2Edimindex_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b))))
=> ( c_2Ewords_2Ew2w_2E1(A_27b,A_27a,c_2Einteger__word_2Ei2w_2E1(A_27b,V0i_2E0)) = c_2Einteger__word_2Ei2w_2E1(A_27a,V0i_2E0) ) ) ).
tff(thm_2Einteger__word_2EWORD__LTi,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Ewords_2Eword__lt_2E2(A_27a,V0a_2E0,V1b_2E0) = c_2Einteger_2Eint__lt_2E2(c_2Einteger__word_2Ew2i_2E1(A_27a,V0a_2E0),c_2Einteger__word_2Ew2i_2E1(A_27a,V1b_2E0)) ).
tff(thm_2Einteger__word_2EWORD__GTi,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Ewords_2Eword__gt_2E2(A_27a,V0a_2E0,V1b_2E0) = c_2Einteger_2Eint__gt_2E2(c_2Einteger__word_2Ew2i_2E1(A_27a,V0a_2E0),c_2Einteger__word_2Ew2i_2E1(A_27a,V1b_2E0)) ).
tff(thm_2Einteger__word_2EWORD__LEi,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Ewords_2Eword__le_2E2(A_27a,V0a_2E0,V1b_2E0) = c_2Einteger_2Eint__le_2E2(c_2Einteger__word_2Ew2i_2E1(A_27a,V0a_2E0),c_2Einteger__word_2Ew2i_2E1(A_27a,V1b_2E0)) ).
tff(thm_2Einteger__word_2EWORD__GEi,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Ewords_2Eword__ge_2E2(A_27a,V0a_2E0,V1b_2E0) = c_2Einteger_2Eint__ge_2E2(c_2Einteger__word_2Ew2i_2E1(A_27a,V0a_2E0),c_2Einteger__word_2Ew2i_2E1(A_27a,V1b_2E0)) ).
tff(thm_2Einteger__word_2Eword__add__i2w__w2n,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Einteger__word_2Ei2w_2E1(A_27a,c_2Einteger_2Eint__add_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Ewords_2Ew2n_2E1(A_27a,V0a_2E0)),c_2Einteger_2Eint__of__num_2E1(c_2Ewords_2Ew2n_2E1(A_27a,V1b_2E0)))) = c_2Ewords_2Eword__add_2E2(A_27a,V0a_2E0,V1b_2E0) ).
tff(thm_2Einteger__word_2Eword__add__i2w,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Einteger__word_2Ei2w_2E1(A_27a,c_2Einteger_2Eint__add_2E2(c_2Einteger__word_2Ew2i_2E1(A_27a,V0a_2E0),c_2Einteger__word_2Ew2i_2E1(A_27a,V1b_2E0))) = c_2Ewords_2Eword__add_2E2(A_27a,V0a_2E0,V1b_2E0) ).
tff(thm_2Einteger__word_2Eword__sub__i2w__w2n,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Einteger__word_2Ei2w_2E1(A_27a,c_2Einteger_2Eint__sub_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Ewords_2Ew2n_2E1(A_27a,V0a_2E0)),c_2Einteger_2Eint__of__num_2E1(c_2Ewords_2Ew2n_2E1(A_27a,V1b_2E0)))) = c_2Ewords_2Eword__sub_2E2(A_27a,V0a_2E0,V1b_2E0) ).
tff(thm_2Einteger__word_2Eword__sub__i2w,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Einteger__word_2Ei2w_2E1(A_27a,c_2Einteger_2Eint__sub_2E2(c_2Einteger__word_2Ew2i_2E1(A_27a,V0a_2E0),c_2Einteger__word_2Ew2i_2E1(A_27a,V1b_2E0))) = c_2Ewords_2Eword__sub_2E2(A_27a,V0a_2E0,V1b_2E0) ).
tff(thm_2Einteger__word_2Eword__mul__i2w__w2n,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Einteger__word_2Ei2w_2E1(A_27a,c_2Einteger_2Eint__mul_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Ewords_2Ew2n_2E1(A_27a,V0a_2E0)),c_2Einteger_2Eint__of__num_2E1(c_2Ewords_2Ew2n_2E1(A_27a,V1b_2E0)))) = c_2Ewords_2Eword__mul_2E2(A_27a,V0a_2E0,V1b_2E0) ).
tff(thm_2Einteger__word_2Eword__mul__i2w,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Einteger__word_2Ei2w_2E1(A_27a,c_2Einteger_2Eint__mul_2E2(c_2Einteger__word_2Ew2i_2E1(A_27a,V0a_2E0),c_2Einteger__word_2Ew2i_2E1(A_27a,V1b_2E0))) = c_2Ewords_2Eword__mul_2E2(A_27a,V0a_2E0,V1b_2E0) ).
tff(thm_2Einteger__word_2Eword__i2w__add,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Einteger_2Eint,V1b_2E0: tyop_2Einteger_2Eint] : c_2Ewords_2Eword__add_2E2(A_27a,c_2Einteger__word_2Ei2w_2E1(A_27a,V0a_2E0),c_2Einteger__word_2Ei2w_2E1(A_27a,V1b_2E0)) = c_2Einteger__word_2Ei2w_2E1(A_27a,c_2Einteger_2Eint__add_2E2(V0a_2E0,V1b_2E0)) ).
tff(thm_2Einteger__word_2Eword__i2w__mul,axiom,
! [A_27a: $tType,V0a_2E0: tyop_2Einteger_2Eint,V1b_2E0: tyop_2Einteger_2Eint] : c_2Ewords_2Eword__mul_2E2(A_27a,c_2Einteger__word_2Ei2w_2E1(A_27a,V0a_2E0),c_2Einteger__word_2Ei2w_2E1(A_27a,V1b_2E0)) = c_2Einteger__word_2Ei2w_2E1(A_27a,c_2Einteger_2Eint__mul_2E2(V0a_2E0,V1b_2E0)) ).
tff(thm_2Einteger__word_2EMULT__MINUS__ONE,axiom,
! [A_27a: $tType,V0i_2E0: tyop_2Einteger_2Eint] : c_2Ewords_2Eword__mul_2E2(A_27a,c_2Ewords_2Eword__2comp_2E1(A_27a,c_2Ewords_2En2w_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2Einteger__word_2Ei2w_2E1(A_27a,V0i_2E0)) = c_2Einteger__word_2Ei2w_2E1(A_27a,c_2Einteger_2Eint__neg_2E1(V0i_2E0)) ).
tff(thm_2Einteger__word_2Eword__0__w2i,axiom,
! [A_27a: $tType] : c_2Einteger__word_2Ew2i_2E1(A_27a,c_2Ewords_2En2w_2E1(A_27a,c_2Enum_2E0_2E0)) = c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0) ).
tff(thm_2Einteger__word_2Ew2i__eq__0,axiom,
! [A_27a: $tType,V0w_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] :
( ( c_2Einteger__word_2Ew2i_2E1(A_27a,V0w_2E0) = c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0) )
<=> ( V0w_2E0 = c_2Ewords_2En2w_2E1(A_27a,c_2Enum_2E0_2E0) ) ) ).
tff(thm_2Einteger__word_2Ei2w__DIV,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1i_2E0: tyop_2Einteger_2Eint] :
( ( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Efcp_2Edimindex_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a))))
& p(c_2Einteger_2Eint__le_2E2(c_2Einteger__word_2EINT__MIN_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)),V1i_2E0))
& p(c_2Einteger_2Eint__le_2E2(V1i_2E0,c_2Einteger__word_2EINT__MAX_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)))) )
=> ( c_2Einteger__word_2Ei2w_2E1(A_27a,c_2Einteger_2Eint__div_2E2(V1i_2E0,c_2Einteger_2Eint__exp_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),V0n_2E0))) = c_2Ewords_2Eword__asr_2E2(A_27a,c_2Einteger__word_2Ei2w_2E1(A_27a,V1i_2E0),V0n_2E0) ) ) ).
tff(thm_2Einteger__word_2EINT__MIN__MONOTONIC,axiom,
! [A_27a: $tType,A_27b: $tType] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Efcp_2Edimindex_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)),c_2Efcp_2Edimindex_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b))))
=> p(c_2Einteger_2Eint__le_2E2(c_2Einteger__word_2EINT__MIN_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b)),c_2Einteger__word_2EINT__MIN_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)))) ) ).
tff(thm_2Einteger__word_2EINT__MAX__MONOTONIC,axiom,
! [A_27a: $tType,A_27b: $tType] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Efcp_2Edimindex_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)),c_2Efcp_2Edimindex_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b))))
=> p(c_2Einteger_2Eint__le_2E2(c_2Einteger__word_2EINT__MAX_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)),c_2Einteger__word_2EINT__MAX_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b)))) ) ).
tff(thm_2Einteger__word_2Ew2i__sw2sw__bounds,axiom,
! [A_27a: $tType,A_27b: $tType,V0w_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] :
( p(c_2Einteger_2Eint__le_2E2(c_2Einteger__word_2EINT__MIN_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)),c_2Einteger__word_2Ew2i_2E1(A_27b,c_2Ewords_2Esw2sw_2E1(A_27a,A_27b,V0w_2E0))))
& p(c_2Einteger_2Eint__le_2E2(c_2Einteger__word_2Ew2i_2E1(A_27b,c_2Ewords_2Esw2sw_2E1(A_27a,A_27b,V0w_2E0)),c_2Einteger__word_2EINT__MAX_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)))) ) ).
tff(thm_2Einteger__word_2Ew2i__i2w__id,axiom,
! [A_27a: $tType,A_27b: $tType,V0i_2E0: tyop_2Einteger_2Eint] :
( ( p(c_2Einteger_2Eint__le_2E2(c_2Einteger__word_2EINT__MIN_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)),V0i_2E0))
& p(c_2Einteger_2Eint__le_2E2(V0i_2E0,c_2Einteger__word_2EINT__MAX_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a))))
& p(c_2Earithmetic_2E_3C_3D_2E2(c_2Efcp_2Edimindex_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b)),c_2Efcp_2Edimindex_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)))) )
=> ( ( V0i_2E0 = c_2Einteger__word_2Ew2i_2E1(A_27b,c_2Einteger__word_2Ei2w_2E1(A_27b,V0i_2E0)) )
<=> ( c_2Einteger__word_2Ei2w_2E1(A_27a,V0i_2E0) = c_2Ewords_2Esw2sw_2E1(A_27b,A_27a,c_2Einteger__word_2Ei2w_2E1(A_27b,V0i_2E0)) ) ) ) ).
tff(thm_2Einteger__word_2Ew2i__11__lift,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0a_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1b_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)] :
( ( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Efcp_2Edimindex_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)),c_2Efcp_2Edimindex_2E1(A_27c,c_2Ebool_2Ethe__value_2E0(A_27c))))
& p(c_2Earithmetic_2E_3C_3D_2E2(c_2Efcp_2Edimindex_2E1(A_27b,c_2Ebool_2Ethe__value_2E0(A_27b)),c_2Efcp_2Edimindex_2E1(A_27c,c_2Ebool_2Ethe__value_2E0(A_27c)))) )
=> ( ( c_2Einteger__word_2Ew2i_2E1(A_27a,V0a_2E0) = c_2Einteger__word_2Ew2i_2E1(A_27b,V1b_2E0) )
<=> ( c_2Ewords_2Esw2sw_2E1(A_27a,A_27c,V0a_2E0) = c_2Ewords_2Esw2sw_2E1(A_27b,A_27c,V1b_2E0) ) ) ) ).
tff(thm_2Einteger__word_2Ew2i__n2w__mod,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Ewords_2Edimword_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a))))
& p(c_2Earithmetic_2E_3C_3D_2E2(V1m_2E0,c_2Efcp_2Edimindex_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)))) )
=> ( c_2Einteger_2ENum_2E1(c_2Einteger_2Eint__mod_2E2(c_2Einteger__word_2Ew2i_2E1(A_27a,c_2Ewords_2En2w_2E1(A_27a,V0n_2E0)),c_2Einteger_2Eint__exp_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),V1m_2E0))) = c_2Earithmetic_2EMOD_2E2(V0n_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V1m_2E0)) ) ) ).
tff(thm_2Einteger__word_2Eword__abs__w2i,axiom,
! [A_27a: $tType,V0w_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Ewords_2Eword__abs_2E1(A_27a,V0w_2E0) = c_2Ewords_2En2w_2E1(A_27a,c_2Einteger_2ENum_2E1(c_2Einteger_2EABS_2E1(c_2Einteger__word_2Ew2i_2E1(A_27a,V0w_2E0)))) ).
tff(thm_2Einteger__word_2Eword__abs__i2w,axiom,
! [A_27a: $tType,V0i_2E0: tyop_2Einteger_2Eint] :
( ( p(c_2Einteger_2Eint__le_2E2(c_2Einteger__word_2EINT__MIN_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)),V0i_2E0))
& p(c_2Einteger_2Eint__le_2E2(V0i_2E0,c_2Einteger__word_2EINT__MAX_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)))) )
=> ( c_2Ewords_2Eword__abs_2E1(A_27a,c_2Einteger__word_2Ei2w_2E1(A_27a,V0i_2E0)) = c_2Ewords_2En2w_2E1(A_27a,c_2Einteger_2ENum_2E1(c_2Einteger_2EABS_2E1(V0i_2E0))) ) ) ).
tff(thm_2Einteger__word_2EINT__MIN,axiom,
! [A_27a: $tType] : c_2Einteger__word_2EINT__MIN_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)) = c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Ewords_2EINT__MIN_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)))) ).
tff(thm_2Einteger__word_2EINT__MAX,axiom,
! [A_27a: $tType] : c_2Einteger__word_2EINT__MAX_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)) = c_2Einteger_2Eint__of__num_2E1(c_2Ewords_2EINT__MAX_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a))) ).
tff(thm_2Einteger__word_2EUINT__MAX,axiom,
! [A_27a: $tType] : c_2Einteger__word_2EUINT__MAX_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)) = c_2Einteger_2Eint__of__num_2E1(c_2Ewords_2EUINT__MAX_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a))) ).
tff(thm_2Einteger__word_2EINT__BOUND__ORDER,axiom,
! [A_27a: $tType] :
( p(c_2Einteger_2Eint__lt_2E2(c_2Einteger__word_2EINT__MIN_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)),c_2Einteger__word_2EINT__MAX_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a))))
& p(c_2Einteger_2Eint__lt_2E2(c_2Einteger__word_2EINT__MAX_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)),c_2Einteger__word_2EUINT__MAX_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a))))
& p(c_2Einteger_2Eint__lt_2E2(c_2Einteger__word_2EUINT__MAX_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)),c_2Einteger_2Eint__of__num_2E1(c_2Ewords_2Edimword_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a))))) ) ).
tff(thm_2Einteger__word_2EINT__ZERO__LT__INT__MIN,axiom,
! [A_27a: $tType] : p(c_2Einteger_2Eint__lt_2E2(c_2Einteger__word_2EINT__MIN_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)),c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0))) ).
tff(thm_2Einteger__word_2EINT__ZERO__LT__INT__MAX,axiom,
! [A_27a: $tType] :
( p(c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Efcp_2Edimindex_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a))))
=> p(c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0),c_2Einteger__word_2EINT__MAX_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)))) ) ).
tff(thm_2Einteger__word_2EINT__ZERO__LE__INT__MAX,axiom,
! [A_27a: $tType] : p(c_2Einteger_2Eint__le_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0),c_2Einteger__word_2EINT__MAX_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)))) ).
tff(thm_2Einteger__word_2EINT__ZERO__LT__UINT__MAX,axiom,
! [A_27a: $tType] : p(c_2Einteger_2Eint__lt_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0),c_2Einteger__word_2EUINT__MAX_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)))) ).
tff(thm_2Einteger__word_2Ew2i__1,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Ebool] :
( ( p(F0_2E0)
<=> ( c_2Efcp_2Edimindex_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ) )
=> ( c_2Einteger__word_2Ew2i_2E1(A_27a,c_2Ewords_2En2w_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) = c_2Ebool_2ECOND_2E3(tyop_2Einteger_2Eint,F0_2E0,c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) ) ) ).
tff(thm_2Einteger__word_2Ew2i__INT__MINw,axiom,
! [A_27a: $tType] : c_2Einteger__word_2Ew2i_2E1(A_27a,c_2Ewords_2Eword__L_2E0(A_27a)) = c_2Einteger__word_2EINT__MIN_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)) ).
tff(thm_2Einteger__word_2Ew2i__UINT__MAXw,axiom,
! [A_27a: $tType] : c_2Einteger__word_2Ew2i_2E1(A_27a,c_2Ewords_2Eword__T_2E0(A_27a)) = c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) ).
tff(thm_2Einteger__word_2Ew2i__INT__MAXw,axiom,
! [A_27a: $tType] : c_2Einteger__word_2Ew2i_2E1(A_27a,c_2Ewords_2Eword__H_2E0(A_27a)) = c_2Einteger__word_2EINT__MAX_2E1(A_27a,c_2Ebool_2Ethe__value_2E0(A_27a)) ).
tff(thm_2Einteger__word_2Ew2i__minus__1,axiom,
! [A_27a: $tType] : c_2Einteger__word_2Ew2i_2E1(A_27a,c_2Ewords_2Eword__2comp_2E1(A_27a,c_2Ewords_2En2w_2E1(A_27a,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) = c_2Einteger_2Eint__neg_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) ).
tff(thm_2Einteger__word_2Ew2i__lt__0,axiom,
! [A_27a: $tType,V0w_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : c_2Einteger_2Eint__lt_2E2(c_2Einteger__word_2Ew2i_2E1(A_27a,V0w_2E0),c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) = c_2Ewords_2Eword__lt_2E2(A_27a,V0w_2E0,c_2Ewords_2En2w_2E1(A_27a,c_2Enum_2E0_2E0)) ).
tff(thm_2Einteger__word_2Ew2i__neg,axiom,
! [A_27a: $tType,V0w_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] :
( ( V0w_2E0 != c_2Ewords_2Eword__L_2E0(A_27a) )
=> ( c_2Einteger__word_2Ew2i_2E1(A_27a,c_2Ewords_2Eword__2comp_2E1(A_27a,V0w_2E0)) = c_2Einteger_2Eint__neg_2E1(c_2Einteger__word_2Ew2i_2E1(A_27a,V0w_2E0)) ) ) ).
tff(thm_2Einteger__word_2Ei2w__0,conjecture,
! [A_27a: $tType] : c_2Einteger__word_2Ei2w_2E1(A_27a,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) = c_2Ewords_2En2w_2E1(A_27a,c_2Enum_2E0_2E0) ).
%------------------------------------------------------------------------------