ITP001 Axioms: ITP110^5.ax
%------------------------------------------------------------------------------
% File : ITP110^5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 set theory export, 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 : integer_word^2.ax [Gau20]
% : HL4110^5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 133 ( 31 unt; 17 typ; 0 def)
% Number of atoms : 2539 ( 90 equ; 0 cnn)
% Maximal formula atoms : 68 ( 19 avg)
% Number of connectives : 3465 ( 12 ~; 0 |; 26 &;3313 @)
% ( 20 <=>; 94 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg;3313 nst)
% Number of types : 1 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 122 ( 121 usr; 106 con; 0-2 aty)
% Number of variables : 246 ( 8 ^ 236 !; 2 ?; 246 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tp_c_2Einteger__word_2EINT__MAX,type,
c_2Einteger__word_2EINT__MAX: del > $i ).
thf(mem_c_2Einteger__word_2EINT__MAX,axiom,
! [A_27a: del] : ( mem @ ( c_2Einteger__word_2EINT__MAX @ A_27a ) @ ( arr @ ( ty_2Ebool_2Eitself @ A_27a ) @ ty_2Einteger_2Eint ) ) ).
thf(tp_c_2Einteger__word_2EINT__MIN,type,
c_2Einteger__word_2EINT__MIN: del > $i ).
thf(mem_c_2Einteger__word_2EINT__MIN,axiom,
! [A_27a: del] : ( mem @ ( c_2Einteger__word_2EINT__MIN @ A_27a ) @ ( arr @ ( ty_2Ebool_2Eitself @ A_27a ) @ ty_2Einteger_2Eint ) ) ).
thf(tp_c_2Einteger__word_2EUINT__MAX,type,
c_2Einteger__word_2EUINT__MAX: del > $i ).
thf(mem_c_2Einteger__word_2EUINT__MAX,axiom,
! [A_27a: del] : ( mem @ ( c_2Einteger__word_2EUINT__MAX @ A_27a ) @ ( arr @ ( ty_2Ebool_2Eitself @ A_27a ) @ ty_2Einteger_2Eint ) ) ).
thf(tp_c_2Einteger__word_2EfromString,type,
c_2Einteger__word_2EfromString: $i ).
thf(mem_c_2Einteger__word_2EfromString,axiom,
mem @ c_2Einteger__word_2EfromString @ ( arr @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ty_2Einteger_2Eint ) ).
thf(stp_fo_c_2Einteger__word_2EfromString,type,
fo__c_2Einteger__word_2EfromString: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar > tp__ty_2Einteger_2Eint ).
thf(stp_eq_fo_c_2Einteger__word_2EfromString,axiom,
! [X0: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar] :
( ( inj__ty_2Einteger_2Eint @ ( fo__c_2Einteger__word_2EfromString @ X0 ) )
= ( ap @ c_2Einteger__word_2EfromString @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ X0 ) ) ) ).
thf(tp_c_2Einteger__word_2Ei2w,type,
c_2Einteger__word_2Ei2w: del > $i ).
thf(mem_c_2Einteger__word_2Ei2w,axiom,
! [A_27a: del] : ( mem @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( arr @ ty_2Einteger_2Eint @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ).
thf(tp_c_2Einteger__word_2Esaturate__i2sw,type,
c_2Einteger__word_2Esaturate__i2sw: del > $i ).
thf(mem_c_2Einteger__word_2Esaturate__i2sw,axiom,
! [A_27a: del] : ( mem @ ( c_2Einteger__word_2Esaturate__i2sw @ A_27a ) @ ( arr @ ty_2Einteger_2Eint @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ).
thf(tp_c_2Einteger__word_2Esaturate__i2w,type,
c_2Einteger__word_2Esaturate__i2w: del > $i ).
thf(mem_c_2Einteger__word_2Esaturate__i2w,axiom,
! [A_27a: del] : ( mem @ ( c_2Einteger__word_2Esaturate__i2w @ A_27a ) @ ( arr @ ty_2Einteger_2Eint @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ).
thf(tp_c_2Einteger__word_2Esaturate__sw2sw,type,
c_2Einteger__word_2Esaturate__sw2sw: del > del > $i ).
thf(mem_c_2Einteger__word_2Esaturate__sw2sw,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Einteger__word_2Esaturate__sw2sw @ A_27a @ A_27b ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) ) ) ).
thf(tp_c_2Einteger__word_2Esaturate__sw2w,type,
c_2Einteger__word_2Esaturate__sw2w: del > del > $i ).
thf(mem_c_2Einteger__word_2Esaturate__sw2w,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Einteger__word_2Esaturate__sw2w @ A_27a @ A_27b ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) ) ) ).
thf(tp_c_2Einteger__word_2Esaturate__w2sw,type,
c_2Einteger__word_2Esaturate__w2sw: del > del > $i ).
thf(mem_c_2Einteger__word_2Esaturate__w2sw,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Einteger__word_2Esaturate__w2sw @ A_27a @ A_27b ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) ) ) ).
thf(tp_c_2Einteger__word_2Esigned__saturate__add,type,
c_2Einteger__word_2Esigned__saturate__add: del > $i ).
thf(mem_c_2Einteger__word_2Esigned__saturate__add,axiom,
! [A_27a: del] : ( mem @ ( c_2Einteger__word_2Esigned__saturate__add @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Einteger__word_2Esigned__saturate__sub,type,
c_2Einteger__word_2Esigned__saturate__sub: del > $i ).
thf(mem_c_2Einteger__word_2Esigned__saturate__sub,axiom,
! [A_27a: del] : ( mem @ ( c_2Einteger__word_2Esigned__saturate__sub @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Einteger__word_2EtoString,type,
c_2Einteger__word_2EtoString: $i ).
thf(mem_c_2Einteger__word_2EtoString,axiom,
mem @ c_2Einteger__word_2EtoString @ ( arr @ ty_2Einteger_2Eint @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) ).
thf(tp_c_2Einteger__word_2Ew2i,type,
c_2Einteger__word_2Ew2i: del > $i ).
thf(mem_c_2Einteger__word_2Ew2i,axiom,
! [A_27a: del] : ( mem @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ty_2Einteger_2Eint ) ) ).
thf(tp_c_2Einteger__word_2Eword__sdiv,type,
c_2Einteger__word_2Eword__sdiv: del > $i ).
thf(mem_c_2Einteger__word_2Eword__sdiv,axiom,
! [A_27a: del] : ( mem @ ( c_2Einteger__word_2Eword__sdiv @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Einteger__word_2Eword__smod,type,
c_2Einteger__word_2Eword__smod: del > $i ).
thf(mem_c_2Einteger__word_2Eword__smod,axiom,
! [A_27a: del] : ( mem @ ( c_2Einteger__word_2Eword__smod @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(ax_thm_2Einteger__word_2EtoString__def,axiom,
! [V0i: tp__ty_2Einteger_2Eint] :
( ( surj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ ( ap @ c_2Einteger__word_2EtoString @ ( inj__ty_2Einteger_2Eint @ V0i ) ) )
= ( surj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( inj__ty_2Einteger_2Eint @ V0i ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ty_2Estring_2Echar ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Estring_2Echar ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( c_2Elist_2ENIL @ ty_2Estring_2Echar ) ) ) @ ( ap @ c_2EASCIInumbers_2Enum__to__dec__string @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V0i ) ) ) ) ) ) @ ( ap @ c_2EASCIInumbers_2Enum__to__dec__string @ ( ap @ c_2Einteger_2ENum @ ( inj__ty_2Einteger_2Eint @ V0i ) ) ) ) ) ) ).
thf(ax_thm_2Einteger__word_2EfromString__primitive__def,axiom,
( c_2Einteger__word_2EfromString
= ( ap
@ ( ap @ ( c_2Erelation_2EWFREC @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ty_2Einteger_2Eint )
@ ( ap @ ( c_2Emin_2E_40 @ ( arr @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ( arr @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ bool ) ) )
@ ( lam @ ( arr @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ( arr @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ bool ) )
@ ^ [V0R: $i] : ( ap @ ( c_2Erelation_2EWF @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) @ V0R ) ) ) )
@ ( lam @ ( arr @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ty_2Einteger_2Eint )
@ ^ [V1fromString: $i] :
( lam @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar )
@ ^ [V2a: $i] :
( ap @ ( ap @ ( ap @ ( c_2Elist_2Elist__CASE @ ty_2Estring_2Echar @ ty_2Einteger_2Eint ) @ V2a ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Einteger_2Eint ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2EASCIInumbers_2Enum__from__dec__string @ ( c_2Elist_2ENIL @ ty_2Estring_2Echar ) ) ) ) )
@ ( lam @ ty_2Estring_2Echar
@ ^ [V3v2: $i] :
( lam @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar )
@ ^ [V4t: $i] :
( ap
@ ( ap @ ( c_2Ebool_2Eliteral__case @ ty_2Estring_2Echar @ ty_2Einteger_2Eint )
@ ( lam @ ty_2Estring_2Echar
@ ^ [V5v4: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Einteger_2Eint ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Estring_2Echar ) @ V5v4 ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Einteger_2Eint ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2EASCIInumbers_2Enum__from__dec__string @ V4t ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Einteger_2Eint ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Estring_2Echar ) @ V5v4 ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Einteger_2Eint ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2EASCIInumbers_2Enum__from__dec__string @ V4t ) ) ) ) ) @ ( ap @ ( c_2Ecombin_2EI @ ty_2Einteger_2Eint ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2EASCIInumbers_2Enum__from__dec__string @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Estring_2Echar ) @ V5v4 ) @ V4t ) ) ) ) ) ) ) )
@ V3v2 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2EfromString__ind,axiom,
! [V0P: $i] :
( ( mem @ V0P @ ( arr @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ bool ) )
=> ( ( ! [V1t: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar] : ( p @ ( ap @ V0P @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Estring_2Echar ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V1t ) ) ) )
& ! [V2t: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar] : ( p @ ( ap @ V0P @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Estring_2Echar ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V2t ) ) ) )
& ( p @ ( ap @ V0P @ ( c_2Elist_2ENIL @ ty_2Estring_2Echar ) ) )
& ! [V3v4: tp__ty_2Estring_2Echar,V4v1: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar] : ( p @ ( ap @ V0P @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Estring_2Echar ) @ ( inj__ty_2Estring_2Echar @ V3v4 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V4v1 ) ) ) ) )
=> ! [V5v: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar] : ( p @ ( ap @ V0P @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V5v ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2EfromString__def,axiom,
! [V0t: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar,V1v4: tp__ty_2Estring_2Echar,V2v1: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar] :
( ( ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger__word_2EfromString @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Estring_2Echar ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V0t ) ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2EASCIInumbers_2Enum__from__dec__string @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V0t ) ) ) ) ) )
& ( ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger__word_2EfromString @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Estring_2Echar ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V0t ) ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2EASCIInumbers_2Enum__from__dec__string @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V0t ) ) ) ) ) )
& ( ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger__word_2EfromString @ ( c_2Elist_2ENIL @ ty_2Estring_2Echar ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2EASCIInumbers_2Enum__from__dec__string @ ( c_2Elist_2ENIL @ ty_2Estring_2Echar ) ) ) ) )
& ( ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger__word_2EfromString @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Estring_2Echar ) @ ( inj__ty_2Estring_2Echar @ V1v4 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V2v1 ) ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Einteger_2Eint ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Estring_2Echar ) @ ( inj__ty_2Estring_2Echar @ V1v4 ) ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2EASCIInumbers_2Enum__from__dec__string @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V2v1 ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Einteger_2Eint ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Estring_2Echar ) @ ( inj__ty_2Estring_2Echar @ V1v4 ) ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2EASCIInumbers_2Enum__from__dec__string @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V2v1 ) ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2EASCIInumbers_2Enum__from__dec__string @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Estring_2Echar ) @ ( inj__ty_2Estring_2Echar @ V1v4 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V2v1 ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Einteger__word_2Ei2w__def,axiom,
! [A_27a: del,V0i: tp__ty_2Einteger_2Eint] :
( ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( inj__ty_2Einteger_2Eint @ V0i ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( inj__ty_2Einteger_2Eint @ V0i ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V0i ) ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Einteger_2ENum @ ( inj__ty_2Einteger_2Eint @ V0i ) ) ) ) ) ).
thf(ax_thm_2Einteger__word_2Ew2i__def,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0w ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Einteger_2Eint ) @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0w ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0w ) ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0w ) ) ) ) ) ) ).
thf(ax_thm_2Einteger__word_2EUINT__MAX__def,axiom,
! [A_27a: del] :
( ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2EUINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(ax_thm_2Einteger__word_2EINT__MAX__def,axiom,
! [A_27a: del] :
( ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2EINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ ( c_2Ewords_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(ax_thm_2Einteger__word_2EINT__MIN__def,axiom,
! [A_27a: del] :
( ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ ( c_2Einteger__word_2EINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(ax_thm_2Einteger__word_2Esaturate__i2w__def,axiom,
! [A_27a: del,V0i: tp__ty_2Einteger_2Eint] :
( ( ap @ ( c_2Einteger__word_2Esaturate__i2w @ A_27a ) @ ( inj__ty_2Einteger_2Eint @ V0i ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( c_2Einteger__word_2EUINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0i ) ) ) @ ( c_2Ewords_2Eword__T @ A_27a ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( inj__ty_2Einteger_2Eint @ V0i ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Einteger_2ENum @ ( inj__ty_2Einteger_2Eint @ V0i ) ) ) ) ) ) ).
thf(ax_thm_2Einteger__word_2Esaturate__i2sw__def,axiom,
! [A_27a: del,V0i: tp__ty_2Einteger_2Eint] :
( ( ap @ ( c_2Einteger__word_2Esaturate__i2sw @ A_27a ) @ ( inj__ty_2Einteger_2Eint @ V0i ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( c_2Einteger__word_2EINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0i ) ) ) @ ( c_2Ewords_2Eword__H @ A_27a ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V0i ) ) @ ( ap @ ( c_2Einteger__word_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) @ ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( inj__ty_2Einteger_2Eint @ V0i ) ) ) ) ) ).
thf(ax_thm_2Einteger__word_2Esaturate__sw2sw__def,axiom,
! [A_27a: del,A_27b: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Einteger__word_2Esaturate__sw2sw @ A_27a @ A_27b ) @ V0w )
= ( ap @ ( c_2Einteger__word_2Esaturate__i2sw @ A_27b ) @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0w ) ) ) ) ).
thf(ax_thm_2Einteger__word_2Esaturate__w2sw__def,axiom,
! [A_27a: del,A_27b: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Einteger__word_2Esaturate__w2sw @ A_27a @ A_27b ) @ V0w )
= ( ap @ ( c_2Einteger__word_2Esaturate__i2sw @ A_27b ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0w ) ) ) ) ) ).
thf(ax_thm_2Einteger__word_2Esaturate__sw2w__def,axiom,
! [A_27a: del,A_27b: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Einteger__word_2Esaturate__sw2w @ A_27a @ A_27b ) @ V0w )
= ( ap @ ( c_2Einteger__word_2Esaturate__i2w @ A_27b ) @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0w ) ) ) ) ).
thf(ax_thm_2Einteger__word_2Esigned__saturate__add__def,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Einteger__word_2Esigned__saturate__add @ A_27a ) @ V0a ) @ V1b )
= ( ap @ ( c_2Einteger__word_2Esaturate__i2sw @ A_27a ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V1b ) ) ) ) ) ) ).
thf(ax_thm_2Einteger__word_2Esigned__saturate__sub__def,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Einteger__word_2Esigned__saturate__sub @ A_27a ) @ V0a ) @ V1b )
= ( ap @ ( c_2Einteger__word_2Esaturate__i2sw @ A_27a ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V1b ) ) ) ) ) ) ).
thf(ax_thm_2Einteger__word_2Eword__sdiv__def,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Einteger__word_2Eword__sdiv @ A_27a ) @ V0a ) @ V1b )
= ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( ap @ ( ap @ c_2Einteger_2Eint__div @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V1b ) ) ) ) ) ) ).
thf(ax_thm_2Einteger__word_2Eword__smod__def,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Einteger__word_2Eword__smod @ A_27a ) @ V0a ) @ V1b )
= ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mod @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V1b ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2EONE__LE__TWOEXP,axiom,
! [V0n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Ew2i__w2n__pos,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( ~ ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0w ) )
& ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0w ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) )
=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0w ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Ew2i__n2w__pos,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Ewords_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
=> ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Ew2i__n2w__neg,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Ewords_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) )
=> ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Ei2w__w2i,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0w ) )
= V0w ) ) ).
thf(conj_thm_2Einteger__word_2Ew2i__i2w,axiom,
! [A_27a: del,V0i: tp__ty_2Einteger_2Eint] :
( ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( c_2Einteger__word_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0i ) ) )
& ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V0i ) ) @ ( ap @ ( c_2Einteger__word_2EINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) )
=> ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( inj__ty_2Einteger_2Eint @ V0i ) ) ) )
= V0i ) ) ).
thf(conj_thm_2Einteger__word_2Eword__msb__i2w,axiom,
! [A_27a: del,V0i: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( inj__ty_2Einteger_2Eint @ V0i ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ ( c_2Ewords_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mod @ ( inj__ty_2Einteger_2Eint @ V0i ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Ew2i__11,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0v ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V1w ) ) )
<=> ( V0v = V1w ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Eint__word__nchotomy,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ? [V1i: tp__ty_2Einteger_2Eint] :
( V0w
= ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( inj__ty_2Einteger_2Eint @ V1i ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Ew2i__le,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0w ) ) @ ( ap @ ( c_2Einteger__word_2EINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Ew2i__ge,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( c_2Einteger__word_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0w ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Eranged__int__word__nchotomy,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ? [V1i: tp__ty_2Einteger_2Eint] :
( ( V0w
= ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( inj__ty_2Einteger_2Eint @ V1i ) ) )
& ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( c_2Einteger__word_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1i ) ) )
& ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V1i ) ) @ ( ap @ ( c_2Einteger__word_2EINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Esw2sw__i2w,axiom,
! [A_27a: del,A_27b: del,V0j: tp__ty_2Einteger_2Eint] :
( ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( c_2Einteger__word_2EINT__MIN @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0j ) ) )
& ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V0j ) ) @ ( ap @ ( c_2Einteger__word_2EINT__MAX @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) )
=> ( ( ap @ ( c_2Ewords_2Esw2sw @ A_27b @ A_27a ) @ ( ap @ ( c_2Einteger__word_2Ei2w @ A_27b ) @ ( inj__ty_2Einteger_2Eint @ V0j ) ) )
= ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( inj__ty_2Einteger_2Eint @ V0j ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Ew2w__i2w,axiom,
! [A_27a: del,A_27b: del,V0i: tp__ty_2Einteger_2Eint] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) )
=> ( ( ap @ ( c_2Ewords_2Ew2w @ A_27b @ A_27a ) @ ( ap @ ( c_2Einteger__word_2Ei2w @ A_27b ) @ ( inj__ty_2Einteger_2Eint @ V0i ) ) )
= ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( inj__ty_2Einteger_2Eint @ V0i ) ) ) ) ).
thf(conj_thm_2Einteger__word_2EWORD__LTi,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V0a ) @ V1b ) )
<=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V1b ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2EWORD__GTi,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__gt @ A_27a ) @ V0a ) @ V1b ) )
<=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__gt @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V1b ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2EWORD__LEi,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ V0a ) @ V1b ) )
<=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V1b ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2EWORD__GEi,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ge @ A_27a ) @ V0a ) @ V1b ) )
<=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__ge @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V1b ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Eword__add__i2w__w2n,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0a ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1b ) ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0a ) @ V1b ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Eword__add__i2w,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V1b ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0a ) @ V1b ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Eword__sub__i2w__w2n,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0a ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1b ) ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0a ) @ V1b ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Eword__sub__i2w,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V1b ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0a ) @ V1b ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Eword__mul__i2w__w2n,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0a ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1b ) ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V0a ) @ V1b ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Eword__mul__i2w,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V1b ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V0a ) @ V1b ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Eword__i2w__add,axiom,
! [A_27a: del,V0a: tp__ty_2Einteger_2Eint,V1b: tp__ty_2Einteger_2Eint] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( inj__ty_2Einteger_2Eint @ V0a ) ) ) @ ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( inj__ty_2Einteger_2Eint @ V1b ) ) )
= ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( inj__ty_2Einteger_2Eint @ V0a ) ) @ ( inj__ty_2Einteger_2Eint @ V1b ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Eword__i2w__mul,axiom,
! [A_27a: del,V0a: tp__ty_2Einteger_2Eint,V1b: tp__ty_2Einteger_2Eint] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( inj__ty_2Einteger_2Eint @ V0a ) ) ) @ ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( inj__ty_2Einteger_2Eint @ V1b ) ) )
= ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( ap @ ( ap @ c_2Einteger_2Eint__mul @ ( inj__ty_2Einteger_2Eint @ V0a ) ) @ ( inj__ty_2Einteger_2Eint @ V1b ) ) ) ) ).
thf(conj_thm_2Einteger__word_2EMULT__MINUS__ONE,axiom,
! [A_27a: del,V0i: tp__ty_2Einteger_2Eint] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( inj__ty_2Einteger_2Eint @ V0i ) ) )
= ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( ap @ c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V0i ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Eword__0__w2i,axiom,
! [A_27a: del] :
( ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Ew2i__eq__0,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0w ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
<=> ( V0w
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Ei2w__DIV,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1i: tp__ty_2Einteger_2Eint] :
( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( c_2Einteger__word_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__ty_2Einteger_2Eint @ V1i ) ) )
& ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V1i ) ) @ ( ap @ ( c_2Einteger__word_2EINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) )
=> ( ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( ap @ ( ap @ c_2Einteger_2Eint__div @ ( inj__ty_2Einteger_2Eint @ V1i ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__exp @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__asr @ A_27a ) @ ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( inj__ty_2Einteger_2Eint @ V1i ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
thf(conj_thm_2Einteger__word_2EINT__MIN__MONOTONIC,axiom,
! [A_27a: del,A_27b: del] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) )
=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( c_2Einteger__word_2EINT__MIN @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( ap @ ( c_2Einteger__word_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2EINT__MAX__MONOTONIC,axiom,
! [A_27a: del,A_27b: del] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) )
=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( c_2Einteger__word_2EINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Einteger__word_2EINT__MAX @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Ew2i__sw2sw__bounds,axiom,
! [A_27a: del,A_27b: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( c_2Einteger__word_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27b ) @ ( ap @ ( c_2Ewords_2Esw2sw @ A_27a @ A_27b ) @ V0w ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27b ) @ ( ap @ ( c_2Ewords_2Esw2sw @ A_27a @ A_27b ) @ V0w ) ) ) @ ( ap @ ( c_2Einteger__word_2EINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Ew2i__i2w__id,axiom,
! [A_27a: del,A_27b: del,V0i: tp__ty_2Einteger_2Eint] :
( ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( c_2Einteger__word_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0i ) ) )
& ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V0i ) ) @ ( ap @ ( c_2Einteger__word_2EINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) )
=> ( ( V0i
= ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27b ) @ ( ap @ ( c_2Einteger__word_2Ei2w @ A_27b ) @ ( inj__ty_2Einteger_2Eint @ V0i ) ) ) ) )
<=> ( ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( inj__ty_2Einteger_2Eint @ V0i ) )
= ( ap @ ( c_2Ewords_2Esw2sw @ A_27b @ A_27a ) @ ( ap @ ( c_2Einteger__word_2Ei2w @ A_27b ) @ ( inj__ty_2Einteger_2Eint @ V0i ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Ew2i__11__lift,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) )
=> ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27c ) @ ( c_2Ebool_2Ethe__value @ A_27c ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27c ) @ ( c_2Ebool_2Ethe__value @ A_27c ) ) ) ) )
=> ( ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0a ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27b ) @ V1b ) ) )
<=> ( ( ap @ ( c_2Ewords_2Esw2sw @ A_27a @ A_27c ) @ V0a )
= ( ap @ ( c_2Ewords_2Esw2sw @ A_27b @ A_27c ) @ V1b ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Ew2i__n2w__mod,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Einteger_2ENum @ ( ap @ ( ap @ c_2Einteger_2Eint__mod @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__exp @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Eword__abs__w2i,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Eword__abs @ A_27a ) @ V0w )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2EABS @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0w ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Eword__abs__i2w,axiom,
! [A_27a: del,V0i: tp__ty_2Einteger_2Eint] :
( ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( c_2Einteger__word_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0i ) ) )
& ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V0i ) ) @ ( ap @ ( c_2Einteger__word_2EINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) )
=> ( ( ap @ ( c_2Ewords_2Eword__abs @ A_27a ) @ ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( inj__ty_2Einteger_2Eint @ V0i ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Einteger_2ENum @ ( ap @ c_2Einteger_2EABS @ ( inj__ty_2Einteger_2Eint @ V0i ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2EINT__MIN,axiom,
! [A_27a: del] :
( ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ ( c_2Ewords_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2EINT__MAX,axiom,
! [A_27a: del] :
( ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2EINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ ( c_2Ewords_2EINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2EUINT__MAX,axiom,
! [A_27a: del] :
( ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2EUINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ ( c_2Ewords_2EUINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2EINT__BOUND__ORDER,axiom,
! [A_27a: del] :
( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ ( c_2Einteger__word_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Einteger__word_2EINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ ( c_2Einteger__word_2EINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Einteger__word_2EUINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ ( c_2Einteger__word_2EUINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2EINT__ZERO__LT__INT__MIN,axiom,
! [A_27a: del] : ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ ( c_2Einteger__word_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ).
thf(conj_thm_2Einteger__word_2EINT__ZERO__LT__INT__MAX,axiom,
! [A_27a: del] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Einteger__word_2EINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2EINT__ZERO__LE__INT__MAX,axiom,
! [A_27a: del] : ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Einteger__word_2EINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).
thf(conj_thm_2Einteger__word_2EINT__ZERO__LT__UINT__MAX,axiom,
! [A_27a: del] : ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Einteger__word_2EUINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Ew2i__1,axiom,
! [A_27a: del] :
( ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Einteger_2Eint ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Ew2i__INT__MINw,axiom,
! [A_27a: del] :
( ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Ew2i__UINT__MAXw,axiom,
! [A_27a: del] :
( ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ ( c_2Ewords_2Eword__T @ A_27a ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Ew2i__INT__MAXw,axiom,
! [A_27a: del] :
( ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ ( c_2Ewords_2Eword__H @ A_27a ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2EINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Ew2i__minus__1,axiom,
! [A_27a: del] :
( ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Ew2i__lt__0,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0w ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V0w ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Ew2i__neg,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( V0w
!= ( c_2Ewords_2Eword__L @ A_27a ) )
=> ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0w ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0w ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Ei2w__0,axiom,
! [A_27a: del] :
( ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ).
thf(conj_thm_2Einteger__word_2Ei2w__minus__1,axiom,
! [A_27a: del] :
( ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
= ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Ei2w__INT__MIN,axiom,
! [A_27a: del] :
( ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( ap @ ( c_2Einteger__word_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
= ( c_2Ewords_2Eword__L @ A_27a ) ) ).
thf(conj_thm_2Einteger__word_2Ei2w__INT__MAX,axiom,
! [A_27a: del] :
( ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( ap @ ( c_2Einteger__word_2EINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
= ( c_2Ewords_2Eword__H @ A_27a ) ) ).
thf(conj_thm_2Einteger__word_2Ei2w__UINT__MAX,axiom,
! [A_27a: del] :
( ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( ap @ ( c_2Einteger__word_2EUINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
= ( c_2Ewords_2Eword__T @ A_27a ) ) ).
thf(conj_thm_2Einteger__word_2Eword__msb__i2w__lt__0,axiom,
! [A_27a: del,V0i: tp__ty_2Einteger_2Eint] :
( ( ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( ap @ ( c_2Einteger__word_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__ty_2Einteger_2Eint @ V0i ) ) )
& ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__le @ ( inj__ty_2Einteger_2Eint @ V0i ) ) @ ( ap @ ( c_2Einteger__word_2EINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) )
=> ( ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( inj__ty_2Einteger_2Eint @ V0i ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( inj__ty_2Einteger_2Eint @ V0i ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Ei2w__pos,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ).
thf(conj_thm_2Einteger__word_2Eword__quot,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( V1b
!= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__quot @ A_27a ) @ V0a ) @ V1b )
= ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( ap @ ( ap @ c_2Einteger_2Eint__quot @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V1b ) ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Eword__rem,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( V1b
!= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__rem @ A_27a ) @ V0a ) @ V1b )
= ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( ap @ ( ap @ c_2Einteger_2Eint__rem @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V1b ) ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Esaturate__i2w__0,axiom,
! [A_27a: del] :
( ( ap @ ( c_2Einteger__word_2Esaturate__i2w @ A_27a ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ).
thf(conj_thm_2Einteger__word_2Esaturate__i2sw__0,axiom,
! [A_27a: del] :
( ( ap @ ( c_2Einteger__word_2Esaturate__i2sw @ A_27a ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ).
thf(conj_thm_2Einteger__word_2Esaturate__w2sw,axiom,
! [A_27a: del,A_27b: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Einteger__word_2Esaturate__w2sw @ A_27a @ A_27b ) @ V0w )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ ( ap @ ( c_2Ewords_2Ew2w @ A_27b @ A_27a ) @ ( c_2Ewords_2Eword__H @ A_27b ) ) ) @ V0w ) ) ) @ ( c_2Ewords_2Eword__H @ A_27b ) ) @ ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ V0w ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Esaturate__i2sw,axiom,
! [A_27a: del,V0i: tp__ty_2Einteger_2Eint] :
( ( ap @ ( c_2Einteger__word_2Esaturate__i2w @ A_27a ) @ ( inj__ty_2Einteger_2Eint @ V0i ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__lt @ ( inj__ty_2Einteger_2Eint @ V0i ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Ewords_2Esaturate__n2w @ A_27a ) @ ( ap @ c_2Einteger_2ENum @ ( inj__ty_2Einteger_2Eint @ V0i ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Esaturate__sw2w,axiom,
! [A_27a: del,A_27b: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Einteger__word_2Esaturate__sw2w @ A_27a @ A_27b ) @ V0w )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V0w ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Ewords_2Esaturate__w2w @ A_27a @ A_27b ) @ V0w ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Esaturate__sw2sw,axiom,
! [A_27a: del,A_27b: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Einteger__word_2Esaturate__sw2sw @ A_27a @ A_27b ) @ V0w )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) @ ( ap @ ( c_2Ewords_2Esw2sw @ A_27a @ A_27b ) @ V0w ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ ( ap @ ( c_2Ewords_2Esw2sw @ A_27b @ A_27a ) @ ( c_2Ewords_2Eword__H @ A_27b ) ) ) @ V0w ) ) @ ( c_2Ewords_2Eword__H @ A_27b ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ V0w ) @ ( ap @ ( c_2Ewords_2Esw2sw @ A_27b @ A_27a ) @ ( c_2Ewords_2Eword__L @ A_27b ) ) ) ) @ ( c_2Ewords_2Eword__L @ A_27b ) ) @ ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ V0w ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Esigned__saturate__sub,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Einteger__word_2Esigned__saturate__sub @ A_27a ) @ V0a ) @ V1b )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ V1b ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V0a ) ) @ ( c_2Ewords_2Eword__H @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0a ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0a ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ V1b ) ) ) @ ( ap @ ( ap @ ( c_2Einteger__word_2Esigned__saturate__add @ A_27a ) @ V0a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V1b ) ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Esigned__saturate__add,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Einteger__word_2Esigned__saturate__add @ A_27a ) @ V0a ) @ V1b )
= ( ap
@ ( ap @ ( c_2Ebool_2ELET @ bool @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ bool @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) )
@ ( lam @ ( ty_2Efcp_2Ecart @ bool @ A_27a )
@ ^ [V2sum: $i] :
( lam @ bool
@ ^ [V3msba: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ V3msba ) @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V1b ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ V3msba ) @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V2sum ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ V3msba ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) @ ( c_2Ewords_2Eword__H @ A_27a ) ) ) @ V2sum ) ) ) )
@ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0a ) @ V1b ) ) )
@ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0a ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Edifferent__sign__then__no__overflow,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1y: $i] :
( ( mem @ V1y @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ~ ( ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0x ) )
<=> ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V1y ) ) )
=> ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0x ) @ V1y ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0x ) ) @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V1y ) ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Ew2i__i2w__pos,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Ewords_2EINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
=> ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Ew2i__i2w__neg,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Ewords_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
=> ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__neg @ ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Eoverflow,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1y: $i] :
( ( mem @ V1y @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0x ) @ V1y ) ) )
!= ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0x ) ) @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V1y ) ) ) )
<=> ( ( ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0x ) )
<=> ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V1y ) ) )
& ~ ( ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0x ) )
<=> ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0x ) @ V1y ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Esub__overflow,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1y: $i] :
( ( mem @ V1y @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0x ) @ V1y ) ) )
!= ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0x ) ) @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V1y ) ) ) )
<=> ( ~ ( ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0x ) )
<=> ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V1y ) ) )
& ~ ( ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0x ) )
<=> ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0x ) @ V1y ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Eoverflow__add,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1y: $i] :
( ( mem @ V1y @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0x ) @ V1y ) ) )
!= ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__add @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0x ) ) @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V1y ) ) ) )
<=> ( p @ ( ap @ ( c_2Epair_2ESND @ bool @ bool ) @ ( ap @ ( c_2Epair_2ESND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Epair_2Eprod @ bool @ bool ) ) @ ( ap @ ( c_2Ewords_2Eadd__with__carry @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Epair_2Eprod @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool ) ) @ V0x ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool ) @ V1y ) @ c_2Ebool_2EF ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Eoverflow__sub,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1y: $i] :
( ( mem @ V1y @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0x ) @ V1y ) ) )
!= ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0x ) ) @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V1y ) ) ) )
<=> ( p @ ( ap @ ( c_2Epair_2ESND @ bool @ bool ) @ ( ap @ ( c_2Epair_2ESND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Epair_2Eprod @ bool @ bool ) ) @ ( ap @ ( c_2Ewords_2Eadd__with__carry @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Epair_2Eprod @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool ) ) @ V0x ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ V1y ) ) @ c_2Ebool_2ET ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Ei2w__w2n__w2w,axiom,
! [A_27a: del,A_27b: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Einteger__word_2Ei2w @ A_27b ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0w ) ) )
= ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ V0w ) ) ) ).
thf(conj_thm_2Einteger__word_2Ei2w__w2n,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0w ) ) )
= V0w ) ) ).
thf(conj_thm_2Einteger__word_2Ew2n__i2w,axiom,
! [A_27a: del,V0n: tp__ty_2Einteger_2Eint] :
( ( surj__ty_2Einteger_2Eint @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ ( ap @ ( c_2Einteger__word_2Ei2w @ A_27a ) @ ( inj__ty_2Einteger_2Eint @ V0n ) ) ) ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ c_2Einteger_2Eint__mod @ ( inj__ty_2Einteger_2Eint @ V0n ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ).
thf(conj_thm_2Einteger__word_2Ew2i__eq__w2n,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( surj__ty_2Einteger_2Eint @ ( ap @ ( c_2Einteger__word_2Ew2i @ A_27a ) @ V0w ) )
= ( surj__ty_2Einteger_2Eint @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Einteger_2Eint ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0w ) ) @ ( ap @ ( c_2Ewords_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0w ) ) ) @ ( ap @ ( ap @ c_2Einteger_2Eint__sub @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0w ) ) ) @ ( ap @ c_2Einteger_2Eint__of__num @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------