ITP001 Axioms: ITP094^5.ax
%------------------------------------------------------------------------------
% File : ITP094^5 : 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 : bitstring^2.ax [Gau20]
% : HL4094^5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 184 ( 63 unt; 34 typ; 0 def)
% Number of atoms : 4059 ( 147 equ; 0 cnn)
% Maximal formula atoms : 326 ( 22 avg)
% Number of connectives : 5492 ( 2 ~; 0 |; 68 &;5307 @)
% ( 35 <=>; 80 =>; 0 <=; 0 <~>)
% Maximal formula depth : 58 ( 7 avg;5307 nst)
% Number of types : 2 ( 1 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 160 ( 159 usr; 153 con; 0-2 aty)
% Number of variables : 454 ( 24 ^ 428 !; 2 ?; 454 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tp_c_2Ebitstring_2Eadd,type,
c_2Ebitstring_2Eadd: $i ).
thf(mem_c_2Ebitstring_2Eadd,axiom,
mem @ c_2Ebitstring_2Eadd @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Elist_2Elist @ bool ) ) ) ).
thf(tp_c_2Ebitstring_2Eband,type,
c_2Ebitstring_2Eband: $i ).
thf(mem_c_2Ebitstring_2Eband,axiom,
mem @ c_2Ebitstring_2Eband @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Elist_2Elist @ bool ) ) ) ).
thf(tp_c_2Ebitstring_2Ebitify,type,
c_2Ebitstring_2Ebitify: $i ).
thf(mem_c_2Ebitstring_2Ebitify,axiom,
mem @ c_2Ebitstring_2Ebitify @ ( arr @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) ) ) ).
thf(tp_c_2Ebitstring_2Ebitwise,type,
c_2Ebitstring_2Ebitwise: $i ).
thf(mem_c_2Ebitstring_2Ebitwise,axiom,
mem @ c_2Ebitstring_2Ebitwise @ ( arr @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Elist_2Elist @ bool ) ) ) ) ).
thf(tp_c_2Ebitstring_2Ebnand,type,
c_2Ebitstring_2Ebnand: $i ).
thf(mem_c_2Ebitstring_2Ebnand,axiom,
mem @ c_2Ebitstring_2Ebnand @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Elist_2Elist @ bool ) ) ) ).
thf(tp_c_2Ebitstring_2Ebnor,type,
c_2Ebitstring_2Ebnor: $i ).
thf(mem_c_2Ebitstring_2Ebnor,axiom,
mem @ c_2Ebitstring_2Ebnor @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Elist_2Elist @ bool ) ) ) ).
thf(tp_c_2Ebitstring_2Ebnot,type,
c_2Ebitstring_2Ebnot: $i ).
thf(mem_c_2Ebitstring_2Ebnot,axiom,
mem @ c_2Ebitstring_2Ebnot @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Elist_2Elist @ bool ) ) ).
thf(tp_c_2Ebitstring_2Eboolify,type,
c_2Ebitstring_2Eboolify: $i ).
thf(mem_c_2Ebitstring_2Eboolify,axiom,
mem @ c_2Ebitstring_2Eboolify @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( arr @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) @ ( ty_2Elist_2Elist @ bool ) ) ) ).
thf(tp_c_2Ebitstring_2Ebor,type,
c_2Ebitstring_2Ebor: $i ).
thf(mem_c_2Ebitstring_2Ebor,axiom,
mem @ c_2Ebitstring_2Ebor @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Elist_2Elist @ bool ) ) ) ).
thf(tp_c_2Ebitstring_2Ebxnor,type,
c_2Ebitstring_2Ebxnor: $i ).
thf(mem_c_2Ebitstring_2Ebxnor,axiom,
mem @ c_2Ebitstring_2Ebxnor @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Elist_2Elist @ bool ) ) ) ).
thf(tp_c_2Ebitstring_2Ebxor,type,
c_2Ebitstring_2Ebxor: $i ).
thf(mem_c_2Ebitstring_2Ebxor,axiom,
mem @ c_2Ebitstring_2Ebxor @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Elist_2Elist @ bool ) ) ) ).
thf(tp_c_2Ebitstring_2Eextend,type,
c_2Ebitstring_2Eextend: $i ).
thf(mem_c_2Ebitstring_2Eextend,axiom,
mem @ c_2Ebitstring_2Eextend @ ( arr @ bool @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Elist_2Elist @ bool ) ) ) ) ).
thf(tp_c_2Ebitstring_2Efield,type,
c_2Ebitstring_2Efield: $i ).
thf(mem_c_2Ebitstring_2Efield,axiom,
mem @ c_2Ebitstring_2Efield @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Elist_2Elist @ bool ) ) ) ) ).
thf(tp_c_2Ebitstring_2Efield__insert,type,
c_2Ebitstring_2Efield__insert: $i ).
thf(mem_c_2Ebitstring_2Efield__insert,axiom,
mem @ c_2Ebitstring_2Efield__insert @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Elist_2Elist @ bool ) ) ) ) ) ).
thf(tp_c_2Ebitstring_2Efixwidth,type,
c_2Ebitstring_2Efixwidth: $i ).
thf(mem_c_2Ebitstring_2Efixwidth,axiom,
mem @ c_2Ebitstring_2Efixwidth @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Elist_2Elist @ bool ) ) ) ).
thf(tp_c_2Ebitstring_2Emodify,type,
c_2Ebitstring_2Emodify: $i ).
thf(mem_c_2Ebitstring_2Emodify,axiom,
mem @ c_2Ebitstring_2Emodify @ ( arr @ ( arr @ ty_2Enum_2Enum @ ( arr @ bool @ bool ) ) @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Elist_2Elist @ bool ) ) ) ).
thf(tp_c_2Ebitstring_2En2v,type,
c_2Ebitstring_2En2v: $i ).
thf(mem_c_2Ebitstring_2En2v,axiom,
mem @ c_2Ebitstring_2En2v @ ( arr @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ).
thf(tp_c_2Ebitstring_2Ereplicate,type,
c_2Ebitstring_2Ereplicate: $i ).
thf(mem_c_2Ebitstring_2Ereplicate,axiom,
mem @ c_2Ebitstring_2Ereplicate @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( arr @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ).
thf(tp_c_2Ebitstring_2Erev__count__list,type,
c_2Ebitstring_2Erev__count__list: $i ).
thf(mem_c_2Ebitstring_2Erev__count__list,axiom,
mem @ c_2Ebitstring_2Erev__count__list @ ( arr @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) ) ).
thf(tp_c_2Ebitstring_2Erotate,type,
c_2Ebitstring_2Erotate: $i ).
thf(mem_c_2Ebitstring_2Erotate,axiom,
mem @ c_2Ebitstring_2Erotate @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( arr @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ).
thf(tp_c_2Ebitstring_2Es2v,type,
c_2Ebitstring_2Es2v: $i ).
thf(mem_c_2Ebitstring_2Es2v,axiom,
mem @ c_2Ebitstring_2Es2v @ ( arr @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ( ty_2Elist_2Elist @ bool ) ) ).
thf(tp_c_2Ebitstring_2Eshiftl,type,
c_2Ebitstring_2Eshiftl: $i ).
thf(mem_c_2Ebitstring_2Eshiftl,axiom,
mem @ c_2Ebitstring_2Eshiftl @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( arr @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ).
thf(tp_c_2Ebitstring_2Eshiftr,type,
c_2Ebitstring_2Eshiftr: $i ).
thf(mem_c_2Ebitstring_2Eshiftr,axiom,
mem @ c_2Ebitstring_2Eshiftr @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( arr @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) ) ) ).
thf(tp_c_2Ebitstring_2Esign__extend,type,
c_2Ebitstring_2Esign__extend: del > $i ).
thf(mem_c_2Ebitstring_2Esign__extend,axiom,
! [A_27a: del] : ( mem @ ( c_2Ebitstring_2Esign__extend @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) ) ) ).
thf(tp_c_2Ebitstring_2Etestbit,type,
c_2Ebitstring_2Etestbit: $i ).
thf(mem_c_2Ebitstring_2Etestbit,axiom,
mem @ c_2Ebitstring_2Etestbit @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ bool ) ) ).
thf(tp_c_2Ebitstring_2Ev2n,type,
c_2Ebitstring_2Ev2n: $i ).
thf(mem_c_2Ebitstring_2Ev2n,axiom,
mem @ c_2Ebitstring_2Ev2n @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ty_2Enum_2Enum ) ).
thf(stp_fo_c_2Ebitstring_2Ev2n,type,
fo__c_2Ebitstring_2Ev2n: tp__c_ty_2Elist_2Elist_o > tp__ty_2Enum_2Enum ).
thf(stp_eq_fo_c_2Ebitstring_2Ev2n,axiom,
! [X0: tp__c_ty_2Elist_2Elist_o] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2Ebitstring_2Ev2n @ X0 ) )
= ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ X0 ) ) ) ).
thf(tp_c_2Ebitstring_2Ev2s,type,
c_2Ebitstring_2Ev2s: $i ).
thf(mem_c_2Ebitstring_2Ev2s,axiom,
mem @ c_2Ebitstring_2Ev2s @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) ).
thf(tp_c_2Ebitstring_2Ev2w,type,
c_2Ebitstring_2Ev2w: del > $i ).
thf(mem_c_2Ebitstring_2Ev2w,axiom,
! [A_27a: del] : ( mem @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ).
thf(tp_c_2Ebitstring_2Ew2v,type,
c_2Ebitstring_2Ew2v: del > $i ).
thf(mem_c_2Ebitstring_2Ew2v,axiom,
! [A_27a: del] : ( mem @ ( c_2Ebitstring_2Ew2v @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Elist_2Elist @ bool ) ) ) ).
thf(tp_c_2Ebitstring_2Ezero__extend,type,
c_2Ebitstring_2Ezero__extend: $i ).
thf(mem_c_2Ebitstring_2Ezero__extend,axiom,
mem @ c_2Ebitstring_2Ezero__extend @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Elist_2Elist @ bool ) ) ) ).
thf(ax_thm_2Ebitstring_2Eextend__def,axiom,
( ! [V0v0: $i] :
( ( mem @ V0v0 @ bool )
=> ! [V1l: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ c_2Ebitstring_2Eextend @ V0v0 ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1l ) ) )
= V1l ) )
& ! [V2c: $i] :
( ( mem @ V2c @ bool )
=> ! [V3n: tp__ty_2Enum_2Enum,V4l: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ c_2Ebitstring_2Eextend @ V2c ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V4l ) ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ c_2Ebitstring_2Eextend @ V2c ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ bool ) @ V2c ) @ ( inj__c_ty_2Elist_2Elist_o @ V4l ) ) ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eextend__def__compute,axiom,
( ! [V0v0: $i] :
( ( mem @ V0v0 @ bool )
=> ! [V1l: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ c_2Ebitstring_2Eextend @ V0v0 ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1l ) ) )
= V1l ) )
& ! [V2c: $i] :
( ( mem @ V2c @ bool )
=> ! [V3n: tp__ty_2Enum_2Enum,V4l: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ c_2Ebitstring_2Eextend @ V2c ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V4l ) ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ c_2Ebitstring_2Eextend @ V2c ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ bool ) @ V2c ) @ ( inj__c_ty_2Elist_2Elist_o @ V4l ) ) ) ) ) )
& ! [V5c: $i] :
( ( mem @ V5c @ bool )
=> ! [V6n: tp__ty_2Enum_2Enum,V7l: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ c_2Ebitstring_2Eextend @ V5c ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V6n ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V7l ) ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ c_2Ebitstring_2Eextend @ V5c ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V6n ) ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ bool ) @ V5c ) @ ( inj__c_ty_2Elist_2Elist_o @ V7l ) ) ) ) ) ) ) ).
thf(ax_thm_2Ebitstring_2Eboolify__def,axiom,
( ! [V0a: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2Ebitstring_2Eboolify @ ( inj__c_ty_2Elist_2Elist_o @ V0a ) ) @ ( c_2Elist_2ENIL @ ty_2Enum_2Enum ) ) )
= V0a )
& ! [V1a: tp__c_ty_2Elist_2Elist_o,V2n: tp__ty_2Enum_2Enum,V3l: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2Ebitstring_2Eboolify @ ( inj__c_ty_2Elist_2Elist_o @ V1a ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V3l ) ) ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2Ebitstring_2Eboolify @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ bool ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1a ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V3l ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Ebitify__ind,axiom,
! [V0P: $i] :
( ( mem @ V0P @ ( arr @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ bool ) ) )
=> ( ( ! [V1a: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ V0P @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1a ) ) @ ( c_2Elist_2ENIL @ bool ) ) )
& ! [V2a: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum,V3l: tp__c_ty_2Elist_2Elist_o] :
( ( p @ ( ap @ ( ap @ V0P @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V2a ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V3l ) ) )
=> ( p @ ( ap @ ( ap @ V0P @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V2a ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ bool ) @ c_2Ebool_2EF ) @ ( inj__c_ty_2Elist_2Elist_o @ V3l ) ) ) ) )
& ! [V4a: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum,V5l: tp__c_ty_2Elist_2Elist_o] :
( ( p @ ( ap @ ( ap @ V0P @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V4a ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V5l ) ) )
=> ( p @ ( ap @ ( ap @ V0P @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V4a ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ bool ) @ c_2Ebool_2ET ) @ ( inj__c_ty_2Elist_2Elist_o @ V5l ) ) ) ) ) )
=> ! [V6v: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum,V7v1: tp__c_ty_2Elist_2Elist_o] : ( p @ ( ap @ ( ap @ V0P @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V6v ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V7v1 ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Ebitify__def,axiom,
( ! [V0a: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
( ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebitstring_2Ebitify @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V0a ) ) @ ( c_2Elist_2ENIL @ bool ) ) )
= V0a )
& ! [V1l: tp__c_ty_2Elist_2Elist_o,V2a: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
( ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebitstring_2Ebitify @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V2a ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ bool ) @ c_2Ebool_2EF ) @ ( inj__c_ty_2Elist_2Elist_o @ V1l ) ) ) )
= ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebitstring_2Ebitify @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V2a ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1l ) ) ) )
& ! [V3l: tp__c_ty_2Elist_2Elist_o,V4a: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
( ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebitstring_2Ebitify @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V4a ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ bool ) @ c_2Ebool_2ET ) @ ( inj__c_ty_2Elist_2Elist_o @ V3l ) ) ) )
= ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebitstring_2Ebitify @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V4a ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V3l ) ) ) ) ) ).
thf(ax_thm_2Ebitstring_2En2v__def,axiom,
! [V0n: tp__ty_2Enum_2Enum] :
( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ c_2Ebitstring_2En2v @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2Ebitstring_2Eboolify @ ( c_2Elist_2ENIL @ bool ) ) @ ( ap @ c_2Enumposrep_2Enum__to__bin__list @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
thf(ax_thm_2Ebitstring_2Ev2n__def,axiom,
! [V0l: tp__c_ty_2Elist_2Elist_o] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V0l ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumposrep_2Enum__from__bin__list @ ( ap @ ( ap @ c_2Ebitstring_2Ebitify @ ( c_2Elist_2ENIL @ ty_2Enum_2Enum ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0l ) ) ) ) ) ).
thf(ax_thm_2Ebitstring_2Es2v__def,axiom,
( c_2Ebitstring_2Es2v
= ( ap @ ( c_2Elist_2EMAP @ ty_2Estring_2Echar @ bool )
@ ( lam @ ty_2Estring_2Echar
@ ^ [V0c: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Estring_2Echar ) @ V0c ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Estring_2Echar ) @ V0c ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Ebitstring_2Ev2s__def,axiom,
( c_2Ebitstring_2Ev2s
= ( ap @ ( c_2Elist_2EMAP @ bool @ ty_2Estring_2Echar )
@ ( lam @ bool
@ ^ [V0b: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Estring_2Echar ) @ V0b ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Ebitstring_2Ezero__extend__def,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1v: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2Ebitstring_2Ezero__extend @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EPAD__LEFT @ bool ) @ c_2Ebool_2EF ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) ) ).
thf(ax_thm_2Ebitstring_2Esign__extend__def,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1v: $i] :
( ( mem @ V1v @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ebitstring_2Esign__extend @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1v )
= ( ap @ ( ap @ ( ap @ ( c_2Elist_2EPAD__LEFT @ A_27a ) @ ( ap @ ( c_2Elist_2EHD @ A_27a ) @ V1v ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1v ) ) ) ).
thf(ax_thm_2Ebitstring_2Efixwidth__def,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1v: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) )
= ( surj__c_ty_2Elist_2Elist_o
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2l: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Elist_2Elist @ bool ) ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ V2l ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ c_2Ebitstring_2Ezero__extend @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2EDROP @ bool ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ V2l ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) ) )
@ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) ) ) ).
thf(ax_thm_2Ebitstring_2Eshiftl__def,axiom,
! [V0v: tp__c_ty_2Elist_2Elist_o,V1m: tp__ty_2Enum_2Enum] :
( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2Ebitstring_2Eshiftl @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EPAD__RIGHT @ bool ) @ c_2Ebool_2EF ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) ) ).
thf(ax_thm_2Ebitstring_2Eshiftr__def,axiom,
! [V0v: tp__c_ty_2Elist_2Elist_o,V1m: tp__ty_2Enum_2Enum] :
( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2Ebitstring_2Eshiftr @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ bool ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) ) ).
thf(ax_thm_2Ebitstring_2Efield__def,axiom,
! [V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2v: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ c_2Ebitstring_2Efield @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V2v ) ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) @ ( ap @ ( ap @ c_2Ebitstring_2Eshiftr @ ( inj__c_ty_2Elist_2Elist_o @ V2v ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) ) ) ).
thf(ax_thm_2Ebitstring_2Erotate__def,axiom,
! [V0v: tp__c_ty_2Elist_2Elist_o,V1m: tp__ty_2Enum_2Enum] :
( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2Ebitstring_2Erotate @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
= ( surj__c_ty_2Elist_2Elist_o
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2l: $i] :
( ap
@ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3x: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Elist_2Elist @ bool ) ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V2l ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V3x ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ bool ) @ ( ap @ ( ap @ ( ap @ c_2Ebitstring_2Efield @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ V3x ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) @ ( ap @ ( ap @ ( ap @ c_2Ebitstring_2Efield @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ V2l ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V3x ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) ) ) )
@ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ V2l ) ) ) )
@ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) ) ) ).
thf(ax_thm_2Ebitstring_2Etestbit__def,axiom,
! [V0b: tp__ty_2Enum_2Enum,V1v: tp__c_ty_2Elist_2Elist_o] :
( ( p @ ( ap @ ( ap @ c_2Ebitstring_2Etestbit @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) )
<=> ( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ c_2Ebitstring_2Efield @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ bool ) @ c_2Ebool_2ET ) @ ( c_2Elist_2ENIL @ bool ) ) ) ) ) ).
thf(ax_thm_2Ebitstring_2Ew2v__def,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( c_2Ebitstring_2Ew2v @ A_27a ) @ V0w ) )
= ( surj__c_ty_2Elist_2Elist_o
@ ( ap
@ ( ap @ ( c_2Elist_2EGENLIST @ bool )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V1i: $i] : ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0w ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( 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 ) ) ) ) ) @ V1i ) ) ) )
@ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ).
thf(ax_thm_2Ebitstring_2Ev2w__def,axiom,
! [A_27a: del,V0v: tp__c_ty_2Elist_2Elist_o] :
( ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) )
= ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V1i: $i] : ( ap @ ( ap @ c_2Ebitstring_2Etestbit @ V1i ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) ) ) ).
thf(ax_thm_2Ebitstring_2Erev__count__list__def,axiom,
! [V0n: tp__ty_2Enum_2Enum] :
( ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ c_2Ebitstring_2Erev__count__list @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
= ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum
@ ( ap
@ ( ap @ ( c_2Elist_2EGENLIST @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V1i: $i] : ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V1i ) ) )
@ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
thf(stp_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_o,type,
tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_o: $tType ).
thf(stp_inj_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_o,type,
inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_o: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_o > $i ).
thf(stp_surj_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_o,type,
surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_o: $i > tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_o ).
thf(stp_inj_surj_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_o,axiom,
! [X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_o] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_o @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_o @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_o,axiom,
! [X: tp__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_o] : ( mem @ ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_o @ X ) @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ bool ) ) ).
thf(stp_iso_mem_c_ty_2Epair_2Eprod_ty_2Enum_2Enum_o,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ bool ) )
=> ( X
= ( inj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_o @ ( surj__c_ty_2Epair_2Eprod_ty_2Enum_2Enum_o @ X ) ) ) ) ).
thf(ax_thm_2Ebitstring_2Emodify__def,axiom,
! [V0f: $i] :
( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ( arr @ bool @ bool ) ) )
=> ! [V1v: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2Ebitstring_2Emodify @ V0f ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ bool ) @ bool ) @ ( ap @ ( c_2Epair_2EUNCURRY @ ty_2Enum_2Enum @ bool @ bool ) @ V0f ) ) @ ( ap @ ( c_2Elist_2EZIP @ ty_2Enum_2Enum @ bool ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) @ ( ty_2Elist_2Elist @ bool ) ) @ ( ap @ c_2Ebitstring_2Erev__count__list @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) ) ) ) ) ).
thf(ax_thm_2Ebitstring_2Efield__insert__def,axiom,
! [V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2s: tp__c_ty_2Elist_2Elist_o] :
( ( ap @ ( ap @ ( ap @ c_2Ebitstring_2Efield__insert @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V2s ) )
= ( ap @ c_2Ebitstring_2Emodify
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3i: $i] : ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V3i ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ V3i ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) ) @ ( ap @ ( ap @ c_2Ebitstring_2Etestbit @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ V3i ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V2s ) ) ) ) ) ) ).
thf(ax_thm_2Ebitstring_2Eadd__def,axiom,
! [V0a: tp__c_ty_2Elist_2Elist_o,V1b: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2Ebitstring_2Eadd @ ( inj__c_ty_2Elist_2Elist_o @ V0a ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1b ) ) )
= ( surj__c_ty_2Elist_2Elist_o
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2m: $i] : ( ap @ ( ap @ c_2Ebitstring_2Ezero__extend @ V2m ) @ ( ap @ c_2Ebitstring_2En2v @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V0a ) ) ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V1b ) ) ) ) ) ) )
@ ( ap @ ( ap @ c_2Earithmetic_2EMAX @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V0a ) ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V1b ) ) ) ) ) ) ).
thf(ax_thm_2Ebitstring_2Ebitwise__def,axiom,
! [V0f: $i] :
( ( mem @ V0f @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
=> ! [V1v1: tp__c_ty_2Elist_2Elist_o,V2v2: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ c_2Ebitstring_2Ebitwise @ V0f ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v1 ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V2v2 ) ) )
= ( surj__c_ty_2Elist_2Elist_o
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3m: $i] : ( ap @ ( ap @ ( c_2Elist_2EMAP @ ( ty_2Epair_2Eprod @ bool @ bool ) @ bool ) @ ( ap @ ( c_2Epair_2EUNCURRY @ bool @ bool @ bool ) @ V0f ) ) @ ( ap @ ( c_2Elist_2EZIP @ bool @ bool ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Elist_2Elist @ bool ) ) @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ V3m ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v1 ) ) ) @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ V3m ) @ ( inj__c_ty_2Elist_2Elist_o @ V2v2 ) ) ) ) ) ) )
@ ( ap @ ( ap @ c_2Earithmetic_2EMAX @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v1 ) ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V2v2 ) ) ) ) ) ) ) ).
thf(ax_thm_2Ebitstring_2Ebnot__def,axiom,
( c_2Ebitstring_2Ebnot
= ( ap @ ( c_2Elist_2EMAP @ bool @ bool ) @ c_2Ebool_2E_7E ) ) ).
thf(ax_thm_2Ebitstring_2Ebor__def,axiom,
( c_2Ebitstring_2Ebor
= ( ap @ c_2Ebitstring_2Ebitwise @ c_2Ebool_2E_5C_2F ) ) ).
thf(ax_thm_2Ebitstring_2Eband__def,axiom,
( c_2Ebitstring_2Eband
= ( ap @ c_2Ebitstring_2Ebitwise @ c_2Ebool_2E_2F_5C ) ) ).
thf(ax_thm_2Ebitstring_2Ebxor__def,axiom,
( c_2Ebitstring_2Ebxor
= ( ap @ c_2Ebitstring_2Ebitwise
@ ( lam @ bool
@ ^ [V0x: $i] :
( lam @ bool
@ ^ [V1y: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ V0x ) @ V1y ) ) ) ) ) ) ).
thf(ax_thm_2Ebitstring_2Ebnor__def,axiom,
( c_2Ebitstring_2Ebnor
= ( ap @ c_2Ebitstring_2Ebitwise
@ ( lam @ bool
@ ^ [V0x: $i] :
( lam @ bool
@ ^ [V1y: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ V0x ) @ V1y ) ) ) ) ) ) ).
thf(ax_thm_2Ebitstring_2Ebxnor__def,axiom,
( c_2Ebitstring_2Ebxnor
= ( ap @ c_2Ebitstring_2Ebitwise @ ( c_2Emin_2E_3D @ bool ) ) ) ).
thf(ax_thm_2Ebitstring_2Ebnand__def,axiom,
( c_2Ebitstring_2Ebnand
= ( ap @ c_2Ebitstring_2Ebitwise
@ ( lam @ bool
@ ^ [V0x: $i] :
( lam @ bool
@ ^ [V1y: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ V0x ) @ V1y ) ) ) ) ) ) ).
thf(ax_thm_2Ebitstring_2Ereplicate__def,axiom,
! [V0v: tp__c_ty_2Elist_2Elist_o,V1n: tp__ty_2Enum_2Enum] :
( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2Ebitstring_2Ereplicate @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( c_2Elist_2EFLAT @ bool ) @ ( ap @ ( ap @ ( c_2Elist_2EGENLIST @ ( ty_2Elist_2Elist @ bool ) ) @ ( ap @ ( c_2Ecombin_2EK @ ( ty_2Elist_2Elist @ bool ) @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eextend__cons,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1c: $i] :
( ( mem @ V1c @ bool )
=> ! [V2l: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ c_2Ebitstring_2Eextend @ V1c ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V2l ) ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ bool ) @ V1c ) @ ( ap @ ( ap @ ( ap @ c_2Ebitstring_2Eextend @ V1c ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V2l ) ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Epad__left__extend,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1l: tp__c_ty_2Elist_2Elist_o,V2c: $i] :
( ( mem @ V2c @ bool )
=> ( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EPAD__LEFT @ bool ) @ V2c ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1l ) ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ c_2Ebitstring_2Eextend @ V2c ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V1l ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1l ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eextend,axiom,
( ! [V0n: tp__ty_2Enum_2Enum,V1v: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2Ebitstring_2Ezero__extend @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ c_2Ebitstring_2Eextend @ c_2Ebool_2EF ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) )
& ! [V2n: tp__ty_2Enum_2Enum,V3v: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( c_2Ebitstring_2Esign__extend @ bool ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V3v ) ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ c_2Ebitstring_2Eextend @ ( ap @ ( c_2Elist_2EHD @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V3v ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V3v ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V3v ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Efixwidth,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1v: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) )
= ( surj__c_ty_2Elist_2Elist_o
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ bool ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2l: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Elist_2Elist @ bool ) ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ V2l ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ ( ap @ c_2Ebitstring_2Eextend @ c_2Ebool_2EF ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V2l ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2EDROP @ bool ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ V2l ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) ) )
@ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Efixwidth__id,axiom,
! [V0w: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V0w ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0w ) ) )
= V0w ) ).
thf(conj_thm_2Ebitstring_2Efixwidth__id__imp,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1w: tp__c_ty_2Elist_2Elist_o] :
( ( V0n
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V1w ) ) ) )
=> ( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1w ) ) )
= V1w ) ) ).
thf(conj_thm_2Ebitstring_2Eboolify__reverse__map,axiom,
! [V0v: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum,V1a: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2Ebitstring_2Eboolify @ ( inj__c_ty_2Elist_2Elist_o @ V1a ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V0v ) ) )
= ( surj__c_ty_2Elist_2Elist_o
@ ( ap
@ ( ap @ ( c_2Elist_2EAPPEND @ bool )
@ ( ap @ ( c_2Elist_2EREVERSE @ bool )
@ ( ap
@ ( ap @ ( c_2Elist_2EMAP @ ty_2Enum_2Enum @ bool )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2n: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V2n ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) )
@ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V0v ) ) ) )
@ ( inj__c_ty_2Elist_2Elist_o @ V1a ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Ebitify__reverse__map,axiom,
! [V0v: tp__c_ty_2Elist_2Elist_o,V1a: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
( ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebitstring_2Ebitify @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1a ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) )
= ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum
@ ( ap
@ ( ap @ ( c_2Elist_2EAPPEND @ ty_2Enum_2Enum )
@ ( ap @ ( c_2Elist_2EREVERSE @ ty_2Enum_2Enum )
@ ( ap
@ ( ap @ ( c_2Elist_2EMAP @ bool @ ty_2Enum_2Enum )
@ ( lam @ bool
@ ^ [V2b: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ V2b ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
@ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) )
@ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1a ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eevery__bit__bitify,axiom,
! [V0v: tp__c_ty_2Elist_2Elist_o] : ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2E_3E @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Ebitstring_2Ebitify @ ( c_2Elist_2ENIL @ ty_2Enum_2Enum ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Elength__pad__left,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ! [V1n: tp__ty_2Enum_2Enum,V2a: $i] :
( ( mem @ V2a @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EPAD__LEFT @ A_27a ) @ V0x ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V2a ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2a ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2a ) ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Elength__pad__right,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ! [V1n: tp__ty_2Enum_2Enum,V2a: $i] :
( ( mem @ V2a @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EPAD__RIGHT @ A_27a ) @ V0x ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V2a ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2a ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2a ) ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Elength__zero__extend,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1v: tp__c_ty_2Elist_2Elist_o] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( ap @ ( ap @ c_2Ebitstring_2Ezero__extend @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) )
= V0n ) ) ).
thf(conj_thm_2Ebitstring_2Elength__sign__extend,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1v: $i] :
( ( mem @ V1v @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V1v ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ ( ap @ ( ap @ ( c_2Ebitstring_2Esign__extend @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1v ) ) )
= V0n ) ) ) ).
thf(conj_thm_2Ebitstring_2Elength__fixwidth,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1v: tp__c_ty_2Elist_2Elist_o] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) )
= V0n ) ).
thf(conj_thm_2Ebitstring_2Elength__field,axiom,
! [V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2v: tp__c_ty_2Elist_2Elist_o] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( ap @ ( ap @ ( ap @ c_2Ebitstring_2Efield @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V2v ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Elength__bitify,axiom,
! [V0v: tp__c_ty_2Elist_2Elist_o,V1l: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Ebitstring_2Ebitify @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Elist_2ELENGTH @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Elength__bitify__null,axiom,
! [A_27a: del,V0v: tp__c_ty_2Elist_2Elist_o,V1l: $i] :
( ( mem @ V1l @ A_27a )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Ebitstring_2Ebitify @ ( c_2Elist_2ENIL @ ty_2Enum_2Enum ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Elength__shiftr,axiom,
! [V0v: tp__c_ty_2Elist_2Elist_o,V1n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( ap @ ( ap @ c_2Ebitstring_2Eshiftr @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Elength__rev__count__list,axiom,
! [V0n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ ty_2Enum_2Enum ) @ ( ap @ c_2Ebitstring_2Erev__count__list @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
= V0n ) ).
thf(conj_thm_2Ebitstring_2Elength__w2v,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( ap @ ( c_2Ebitstring_2Ew2v @ A_27a ) @ V0w ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Elength__rotate,axiom,
! [V0v: tp__c_ty_2Elist_2Elist_o,V1n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( ap @ ( ap @ c_2Ebitstring_2Erotate @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eel__rev__count__list,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1i: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Elist_2EEL @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( ap @ c_2Ebitstring_2Erev__count__list @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1i ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eel__zero__extend,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1i: tp__ty_2Enum_2Enum,V2v: tp__c_ty_2Elist_2Elist_o] :
( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEL @ bool ) @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( ap @ ( ap @ c_2Ebitstring_2Ezero__extend @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V2v ) ) ) )
<=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V2v ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1i ) ) )
& ( p @ ( ap @ ( ap @ ( c_2Elist_2EEL @ bool ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V2v ) ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V2v ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eel__sign__extend,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1i: tp__ty_2Enum_2Enum,V2v: $i] :
( ( mem @ V2v @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( ap @ ( ap @ ( c_2Ebitstring_2Esign__extend @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V2v ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2v ) ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V2v ) ) @ ( ap @ ( ap @ ( c_2Elist_2EEL @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V2v ) ) ) ) @ V2v ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eel__fixwidth,axiom,
! [V0i: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum,V2w: tp__c_ty_2Elist_2Elist_o] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0i ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEL @ bool ) @ ( inj__ty_2Enum_2Enum @ V0i ) ) @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V2w ) ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V2w ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V2w ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0i ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2EEL @ bool ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0i ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V2w ) ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V2w ) ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2EEL @ bool ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0i ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V2w ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V2w ) ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eel__field,axiom,
! [V0v: tp__c_ty_2Elist_2Elist_o,V1h: tp__ty_2Enum_2Enum,V2l: tp__ty_2Enum_2Enum,V3i: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3i ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1h ) ) ) @ ( inj__ty_2Enum_2Enum @ V2l ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEL @ bool ) @ ( inj__ty_2Enum_2Enum @ V3i ) ) @ ( ap @ ( ap @ ( ap @ c_2Ebitstring_2Efield @ ( inj__ty_2Enum_2Enum @ V1h ) ) @ ( inj__ty_2Enum_2Enum @ V2l ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) )
<=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1h ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3i ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) ) )
& ( p @ ( ap @ ( ap @ ( c_2Elist_2EEL @ bool ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3i ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1h ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eel__w2v,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEL @ bool ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Ebitstring_2Ew2v @ A_27a ) @ V0w ) ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0w ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( 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 ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eel__shiftr,axiom,
! [V0i: tp__ty_2Enum_2Enum,V1v: tp__c_ty_2Elist_2Elist_o,V2n: tp__ty_2Enum_2Enum,V3d: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V3d ) ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0i ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V3d ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V3d ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEL @ bool ) @ ( inj__ty_2Enum_2Enum @ V0i ) ) @ ( ap @ ( ap @ c_2Ebitstring_2Eshiftr @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( inj__ty_2Enum_2Enum @ V3d ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
<=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3d ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0i ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) ) )
& ( p @ ( ap @ ( ap @ ( c_2Elist_2EEL @ bool ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0i ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V3d ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eshiftr__0,axiom,
! [V0v: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2Ebitstring_2Eshiftr @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= V0v ) ).
thf(conj_thm_2Ebitstring_2Efield__fixwidth,axiom,
! [V0h: tp__ty_2Enum_2Enum,V1v: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ c_2Ebitstring_2Efield @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Etestbit,axiom,
! [V0b: tp__ty_2Enum_2Enum,V1v: tp__c_ty_2Elist_2Elist_o] :
( ( p @ ( ap @ ( ap @ c_2Ebitstring_2Etestbit @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) )
<=> ( p
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ bool )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2n: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ V2n ) ) @ ( ap @ ( ap @ ( c_2Elist_2EEL @ bool ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ V2n ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) ) )
@ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Etestbit__geq__len,axiom,
! [V0v: tp__c_ty_2Elist_2Elist_o,V1i: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) @ ( inj__ty_2Enum_2Enum @ V1i ) ) )
=> ~ ( p @ ( ap @ ( ap @ c_2Ebitstring_2Etestbit @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Etestbit__el,axiom,
! [V0v: tp__c_ty_2Elist_2Elist_o,V1i: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2Ebitstring_2Etestbit @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EEL @ bool ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1i ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Ebit__v2w,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1v: tp__c_ty_2Elist_2Elist_o] :
( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bit @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) )
<=> ( ( 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_2Ebitstring_2Etestbit @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eword__index__v2w,axiom,
! [A_27a: del,V0index_20too_20large: $i] :
( ( mem @ V0index_20too_20large @ bool )
=> ! [V1v: tp__c_ty_2Elist_2Elist_o,V2i: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) @ ( inj__ty_2Enum_2Enum @ V2i ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2i ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( ap @ ( ap @ c_2Ebitstring_2Etestbit @ ( inj__ty_2Enum_2Enum @ V2i ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EFAIL @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) @ bool ) @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) ) @ V0index_20too_20large ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) @ ( inj__ty_2Enum_2Enum @ V2i ) ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Etestbit__w2v,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Ebitstring_2Etestbit @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Ebitstring_2Ew2v @ A_27a ) @ V1w ) ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bit @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1w ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Ew2v__v2w,axiom,
! [A_27a: del,V0v: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( c_2Ebitstring_2Ew2v @ A_27a ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Ev2w__w2v,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( ap @ ( c_2Ebitstring_2Ew2v @ A_27a ) @ V0w ) )
= V0w ) ) ).
thf(conj_thm_2Ebitstring_2Ev2w__fixwidth,axiom,
! [A_27a: del,V0v: tp__c_ty_2Elist_2Elist_o] :
( ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) )
= ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) ).
thf(conj_thm_2Ebitstring_2Efixwidth__fixwidth,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1v: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Ebitstring__nchotomy,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ? [V1v: tp__c_ty_2Elist_2Elist_o] :
( V0w
= ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eranged__bitstring__nchotomy,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ? [V1v: tp__c_ty_2Elist_2Elist_o] :
( ( V0w
= ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) )
& ( p @ ( ap @ c_2Emarker_2EAbbrev @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Efixwidth__eq,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1v: tp__c_ty_2Elist_2Elist_o,V2w: tp__c_ty_2Elist_2Elist_o] :
( ( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V2w ) ) ) )
<=> ! [V3i: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3i ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
=> ( ( p @ ( ap @ ( ap @ c_2Ebitstring_2Etestbit @ ( inj__ty_2Enum_2Enum @ V3i ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Ebitstring_2Etestbit @ ( inj__ty_2Enum_2Enum @ V3i ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V2w ) ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Ev2w__11,axiom,
! [A_27a: del,V0v: tp__c_ty_2Elist_2Elist_o,V1w: tp__c_ty_2Elist_2Elist_o] :
( ( ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) )
= ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V1w ) ) )
<=> ( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1w ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Efield__concat__right,axiom,
! [V0h: tp__ty_2Enum_2Enum,V1a: tp__c_ty_2Elist_2Elist_o,V2b: tp__c_ty_2Elist_2Elist_o] :
( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V2b ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) )
=> ( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ c_2Ebitstring_2Efield @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V1a ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V2b ) ) ) )
= V2b ) ) ).
thf(conj_thm_2Ebitstring_2Efield__concat__left,axiom,
! [V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2a: tp__c_ty_2Elist_2Elist_o,V3b: tp__c_ty_2Elist_2Elist_o] :
( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V3b ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) )
=> ( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ c_2Ebitstring_2Efield @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V2a ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V3b ) ) ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ c_2Ebitstring_2Efield @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V3b ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V3b ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V2a ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Efield__id__imp,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1v: tp__c_ty_2Elist_2Elist_o] :
( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) )
=> ( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ c_2Ebitstring_2Efield @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) )
= V1v ) ) ).
thf(conj_thm_2Ebitstring_2Eshiftl__replicate__F,axiom,
! [V0v: tp__c_ty_2Elist_2Elist_o,V1n: tp__ty_2Enum_2Enum] :
( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ c_2Ebitstring_2Eshiftl @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
= ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) @ ( ap @ ( ap @ c_2Ebitstring_2Ereplicate @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ bool ) @ c_2Ebool_2EF ) @ ( c_2Elist_2ENIL @ bool ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eword__lsb__v2w,axiom,
! [A_27a: del,V0v: tp__c_ty_2Elist_2Elist_o] :
( ( p @ ( ap @ ( c_2Ewords_2Eword__lsb @ A_27a ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) )
<=> ( ( V0v
!= ( surj__c_ty_2Elist_2Elist_o @ ( c_2Elist_2ENIL @ bool ) ) )
& ( p @ ( ap @ ( c_2Elist_2ELAST @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eword__msb__v2w,axiom,
! [A_27a: del,V0v: tp__c_ty_2Elist_2Elist_o] :
( ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Ebitstring_2Etestbit @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( 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 ) ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Ew2w__v2w,axiom,
! [A_27a: del,A_27b: del,V0v: tp__c_ty_2Elist_2Elist_o] :
( ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) )
= ( ap @ ( c_2Ebitstring_2Ev2w @ A_27b ) @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( 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_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Esw2sw__v2w,axiom,
! [A_27a: del,A_27b: del,V0v: tp__c_ty_2Elist_2Elist_o] :
( ( ap @ ( c_2Ewords_2Esw2sw @ A_27a @ A_27b ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( 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_2Ebitstring_2Ev2w @ A_27b ) @ ( ap @ ( ap @ ( c_2Ebitstring_2Esign__extend @ bool ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27b ) @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2En2w__v2n,axiom,
! [A_27a: del,V0v: tp__c_ty_2Elist_2Elist_o] :
( ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) )
= ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) ).
thf(conj_thm_2Ebitstring_2Ev2n__n2v,axiom,
! [V0n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Ebitstring_2Ev2n @ ( ap @ c_2Ebitstring_2En2v @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
= V0n ) ).
thf(conj_thm_2Ebitstring_2Ev2w__n2v,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( ap @ c_2Ebitstring_2En2v @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ).
thf(conj_thm_2Ebitstring_2Ew2n__v2w,axiom,
! [A_27a: del,V0v: tp__c_ty_2Elist_2Elist_o] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2EMOD__2EXP @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Ev2n__lt,axiom,
! [V0v: tp__c_ty_2Elist_2Elist_o] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eword__and__v2w,axiom,
! [A_27a: del,V0v: tp__c_ty_2Elist_2Elist_o,V1w: tp__c_ty_2Elist_2Elist_o] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V1w ) ) )
= ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( ap @ ( ap @ c_2Ebitstring_2Eband @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1w ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eword__or__v2w,axiom,
! [A_27a: del,V0v: tp__c_ty_2Elist_2Elist_o,V1w: tp__c_ty_2Elist_2Elist_o] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V1w ) ) )
= ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( ap @ ( ap @ c_2Ebitstring_2Ebor @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1w ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eword__xor__v2w,axiom,
! [A_27a: del,V0v: tp__c_ty_2Elist_2Elist_o,V1w: tp__c_ty_2Elist_2Elist_o] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V1w ) ) )
= ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( ap @ ( ap @ c_2Ebitstring_2Ebxor @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1w ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eword__nand__v2w,axiom,
! [A_27a: del,V0v: tp__c_ty_2Elist_2Elist_o,V1w: tp__c_ty_2Elist_2Elist_o] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__nand @ A_27a ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V1w ) ) )
= ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( ap @ ( ap @ c_2Ebitstring_2Ebnand @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1w ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eword__nor__v2w,axiom,
! [A_27a: del,V0v: tp__c_ty_2Elist_2Elist_o,V1w: tp__c_ty_2Elist_2Elist_o] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__nor @ A_27a ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V1w ) ) )
= ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( ap @ ( ap @ c_2Ebitstring_2Ebnor @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1w ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eword__xnor__v2w,axiom,
! [A_27a: del,V0v: tp__c_ty_2Elist_2Elist_o,V1w: tp__c_ty_2Elist_2Elist_o] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__xnor @ A_27a ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V1w ) ) )
= ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( ap @ ( ap @ c_2Ebitstring_2Ebxnor @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1w ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eword__1comp__v2w,axiom,
! [A_27a: del,V0v: tp__c_ty_2Elist_2Elist_o] :
( ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) )
= ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( ap @ c_2Ebitstring_2Ebnot @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eword__lsl__v2w,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1v: tp__c_ty_2Elist_2Elist_o] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) )
= ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( ap @ ( ap @ c_2Ebitstring_2Eshiftl @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eword__lsr__v2w,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1v: tp__c_ty_2Elist_2Elist_o] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) )
= ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( ap @ ( ap @ c_2Ebitstring_2Eshiftr @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eword__modify__v2w,axiom,
! [A_27a: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ( arr @ bool @ bool ) ) )
=> ! [V1v: tp__c_ty_2Elist_2Elist_o] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__modify @ A_27a ) @ V0f ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) )
= ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( ap @ ( ap @ c_2Ebitstring_2Emodify @ V0f ) @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eword__bits__v2w,axiom,
! [A_27a: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2v: tp__c_ty_2Elist_2Elist_o] :
( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V2v ) ) )
= ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( ap @ ( ap @ ( ap @ c_2Ebitstring_2Efield @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V2v ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eword__extract__v2w,axiom,
! [A_27a: del,A_27b: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2v: tp__c_ty_2Elist_2Elist_o] :
( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V2v ) ) )
= ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V2v ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eword__slice__v2w,axiom,
! [A_27a: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2v: tp__c_ty_2Elist_2Elist_o] :
( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__slice @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V2v ) ) )
= ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( ap @ ( ap @ c_2Ebitstring_2Eshiftl @ ( ap @ ( ap @ ( ap @ c_2Ebitstring_2Efield @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V2v ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eword__asr__v2w,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1v: tp__c_ty_2Elist_2Elist_o] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__asr @ A_27a ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) )
= ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
@ ( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V2l: $i] : ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( ap @ ( ap @ ( c_2Ebitstring_2Esign__extend @ bool ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Elist_2Elist @ bool ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ bool ) @ ( ap @ ( c_2Elist_2EHD @ bool ) @ V2l ) ) @ ( c_2Elist_2ENIL @ bool ) ) ) @ ( ap @ ( ap @ c_2Ebitstring_2Eshiftr @ V2l ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) )
@ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eword__ror__v2w,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1v: tp__c_ty_2Elist_2Elist_o] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__ror @ A_27a ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) )
= ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( ap @ ( ap @ c_2Ebitstring_2Erotate @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eword__reverse__v2w,axiom,
! [A_27a: del,V0v: tp__c_ty_2Elist_2Elist_o] :
( ( ap @ ( c_2Ewords_2Eword__reverse @ A_27a ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) )
= ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( ap @ ( c_2Elist_2EREVERSE @ bool ) @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eword__join__v2w,axiom,
! [A_27a: del,A_27b: del,V0v1: tp__c_ty_2Elist_2Elist_o,V1v2: tp__c_ty_2Elist_2Elist_o] :
( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) )
& ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ ( c_2Epred__set_2EUNIV @ A_27b ) ) ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__join @ A_27a @ A_27b ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v1 ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27b ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v2 ) ) )
= ( ap @ ( c_2Ebitstring_2Ev2w @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v1 ) ) @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v2 ) ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eword__concat__v2w,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0v1: tp__c_ty_2Elist_2Elist_o,V1v2: tp__c_ty_2Elist_2Elist_o] :
( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) )
& ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ ( c_2Epred__set_2EUNIV @ A_27b ) ) ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v1 ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27b ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v2 ) ) )
= ( ap @ ( c_2Ebitstring_2Ev2w @ A_27c ) @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( ap @ ( c_2Efcp_2Edimindex @ A_27c ) @ ( c_2Ebool_2Ethe__value @ A_27c ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( 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 @ ( ap @ ( c_2Elist_2EAPPEND @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v1 ) ) @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v2 ) ) ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eword__join__v2w__rwt,axiom,
! [A_27a: del,A_27b: del,V0bad_20domain: $i] :
( ( mem @ V0bad_20domain @ bool )
=> ! [V1v1: tp__c_ty_2Elist_2Elist_o,V2v2: tp__c_ty_2Elist_2Elist_o] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__join @ A_27a @ A_27b ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v1 ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27b ) @ ( inj__c_ty_2Elist_2Elist_o @ V2v2 ) ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) ) @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ ( c_2Epred__set_2EUNIV @ A_27b ) ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v1 ) ) @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V2v2 ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EFAIL @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) @ ( ty_2Efcp_2Ecart @ bool @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) ) ) @ bool ) @ ( c_2Ewords_2Eword__join @ A_27a @ A_27b ) ) @ V0bad_20domain ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v1 ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27b ) @ ( inj__c_ty_2Elist_2Elist_o @ V2v2 ) ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eword__concat__v2w__rwt,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0bad_20domain: $i] :
( ( mem @ V0bad_20domain @ bool )
=> ! [V1v1: tp__c_ty_2Elist_2Elist_o,V2v2: tp__c_ty_2Elist_2Elist_o] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v1 ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27b ) @ ( inj__c_ty_2Elist_2Elist_o @ V2v2 ) ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27c ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) ) @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27b ) @ ( c_2Epred__set_2EUNIV @ A_27b ) ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27c ) @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( ap @ ( c_2Efcp_2Edimindex @ A_27c ) @ ( c_2Ebool_2Ethe__value @ A_27c ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( 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 @ ( ap @ ( c_2Elist_2EAPPEND @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v1 ) ) @ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V2v2 ) ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Ecombin_2EFAIL @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) @ ( ty_2Efcp_2Ecart @ bool @ A_27c ) ) ) @ bool ) @ ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c ) ) @ V0bad_20domain ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v1 ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27b ) @ ( inj__c_ty_2Elist_2Elist_o @ V2v2 ) ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eword__reduce__v2w,axiom,
! [A_27a: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
=> ! [V1v: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( ap @ ( c_2Ewords_2Eword__reduce @ A_27a ) @ V0f ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) )
= ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) )
@ ( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V2l: $i] : ( ap @ ( c_2Ebitstring_2Ev2w @ ty_2Eone_2Eone ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ bool ) @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ bool @ bool ) @ V0f ) @ ( ap @ ( c_2Elist_2EHD @ bool ) @ V2l ) ) @ ( ap @ ( c_2Elist_2ETL @ bool ) @ V2l ) ) ) @ ( c_2Elist_2ENIL @ bool ) ) ) ) )
@ ( ap @ ( ap @ c_2Ebitstring_2Efixwidth @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Ereduce__and__v2w,axiom,
! [A_27a: del,V0v: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2Ereduce__and @ A_27a ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) )
= ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( ap @ ( c_2Ewords_2Eword__reduce @ A_27a ) @ c_2Ebool_2E_2F_5C ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Ereduce__or__v2w,axiom,
! [A_27a: del,V0v: tp__c_ty_2Elist_2Elist_o] :
( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2Ereduce__or @ A_27a ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) )
= ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( ap @ ( c_2Ewords_2Eword__reduce @ A_27a ) @ c_2Ebool_2E_5C_2F ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eextract__v2w,axiom,
! [A_27a: del,A_27b: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2v: tp__c_ty_2Elist_2Elist_o] :
( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Elist_2ELENGTH @ bool ) @ ( inj__c_ty_2Elist_2Elist_o @ V2v ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) )
& ( 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 @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V2v ) ) )
= ( ap @ ( c_2Ebitstring_2Ev2w @ A_27b ) @ ( ap @ ( ap @ ( ap @ c_2Ebitstring_2Efield @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V2v ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eword__bit__last__shiftr,axiom,
! [A_27a: del,V0i: tp__ty_2Enum_2Enum,V1v: tp__c_ty_2Elist_2Elist_o] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0i ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bit @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0i ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) )
<=> ( p
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Elist_2Elist @ bool ) @ bool )
@ ( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V2l: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( c_2Elist_2ENULL @ bool ) @ V2l ) ) ) @ ( ap @ ( c_2Elist_2ELAST @ bool ) @ V2l ) ) ) )
@ ( ap @ ( ap @ c_2Ebitstring_2Eshiftr @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) @ ( inj__ty_2Enum_2Enum @ V0i ) ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eops__to__v2w,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,A_27e: del,A_27f: del,A_27g: del,A_27h: del,A_27i: del,A_27j: del,A_27k: del,A_27l: del,A_27m: del,A_27n: del,A_27o: del,A_27p: del,A_27q: del,A_27r: del,A_27s: del,A_27t: del] :
( ! [V0v: tp__c_ty_2Elist_2Elist_o,V1n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27c ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27c ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27c ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27c ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27c ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27c ) @ ( ap @ c_2Ebitstring_2En2v @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) )
& ! [V2v: tp__c_ty_2Elist_2Elist_o,V3n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27d ) @ ( ap @ ( c_2Ewords_2En2w @ A_27d ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27d ) @ ( inj__c_ty_2Elist_2Elist_o @ V2v ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27d ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27d ) @ ( ap @ c_2Ebitstring_2En2v @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27d ) @ ( inj__c_ty_2Elist_2Elist_o @ V2v ) ) ) )
& ! [V4v: tp__c_ty_2Elist_2Elist_o,V5n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27e ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27e ) @ ( inj__c_ty_2Elist_2Elist_o @ V4v ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27e ) @ ( inj__ty_2Enum_2Enum @ V5n ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27e ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27e ) @ ( inj__c_ty_2Elist_2Elist_o @ V4v ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27e ) @ ( ap @ c_2Ebitstring_2En2v @ ( inj__ty_2Enum_2Enum @ V5n ) ) ) ) )
& ! [V6v: tp__c_ty_2Elist_2Elist_o,V7n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27f ) @ ( ap @ ( c_2Ewords_2En2w @ A_27f ) @ ( inj__ty_2Enum_2Enum @ V7n ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27f ) @ ( inj__c_ty_2Elist_2Elist_o @ V6v ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27f ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27f ) @ ( ap @ c_2Ebitstring_2En2v @ ( inj__ty_2Enum_2Enum @ V7n ) ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27f ) @ ( inj__c_ty_2Elist_2Elist_o @ V6v ) ) ) )
& ! [V8v: tp__c_ty_2Elist_2Elist_o,V9n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27g ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27g ) @ ( inj__c_ty_2Elist_2Elist_o @ V8v ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27g ) @ ( inj__ty_2Enum_2Enum @ V9n ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27g ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27g ) @ ( inj__c_ty_2Elist_2Elist_o @ V8v ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27g ) @ ( ap @ c_2Ebitstring_2En2v @ ( inj__ty_2Enum_2Enum @ V9n ) ) ) ) )
& ! [V10v: tp__c_ty_2Elist_2Elist_o,V11n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27h ) @ ( ap @ ( c_2Ewords_2En2w @ A_27h ) @ ( inj__ty_2Enum_2Enum @ V11n ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27h ) @ ( inj__c_ty_2Elist_2Elist_o @ V10v ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27h ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27h ) @ ( ap @ c_2Ebitstring_2En2v @ ( inj__ty_2Enum_2Enum @ V11n ) ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27h ) @ ( inj__c_ty_2Elist_2Elist_o @ V10v ) ) ) )
& ! [V12v: tp__c_ty_2Elist_2Elist_o,V13n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__nor @ A_27i ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27i ) @ ( inj__c_ty_2Elist_2Elist_o @ V12v ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27i ) @ ( inj__ty_2Enum_2Enum @ V13n ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__nor @ A_27i ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27i ) @ ( inj__c_ty_2Elist_2Elist_o @ V12v ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27i ) @ ( ap @ c_2Ebitstring_2En2v @ ( inj__ty_2Enum_2Enum @ V13n ) ) ) ) )
& ! [V14v: tp__c_ty_2Elist_2Elist_o,V15n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__nor @ A_27j ) @ ( ap @ ( c_2Ewords_2En2w @ A_27j ) @ ( inj__ty_2Enum_2Enum @ V15n ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27j ) @ ( inj__c_ty_2Elist_2Elist_o @ V14v ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__nor @ A_27j ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27j ) @ ( ap @ c_2Ebitstring_2En2v @ ( inj__ty_2Enum_2Enum @ V15n ) ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27j ) @ ( inj__c_ty_2Elist_2Elist_o @ V14v ) ) ) )
& ! [V16v: tp__c_ty_2Elist_2Elist_o,V17n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__nand @ A_27k ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27k ) @ ( inj__c_ty_2Elist_2Elist_o @ V16v ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27k ) @ ( inj__ty_2Enum_2Enum @ V17n ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__nand @ A_27k ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27k ) @ ( inj__c_ty_2Elist_2Elist_o @ V16v ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27k ) @ ( ap @ c_2Ebitstring_2En2v @ ( inj__ty_2Enum_2Enum @ V17n ) ) ) ) )
& ! [V18v: tp__c_ty_2Elist_2Elist_o,V19n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__nand @ A_27l ) @ ( ap @ ( c_2Ewords_2En2w @ A_27l ) @ ( inj__ty_2Enum_2Enum @ V19n ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27l ) @ ( inj__c_ty_2Elist_2Elist_o @ V18v ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__nand @ A_27l ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27l ) @ ( ap @ c_2Ebitstring_2En2v @ ( inj__ty_2Enum_2Enum @ V19n ) ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27l ) @ ( inj__c_ty_2Elist_2Elist_o @ V18v ) ) ) )
& ! [V20v: tp__c_ty_2Elist_2Elist_o,V21n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__xnor @ A_27m ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27m ) @ ( inj__c_ty_2Elist_2Elist_o @ V20v ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27m ) @ ( inj__ty_2Enum_2Enum @ V21n ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__xnor @ A_27m ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27m ) @ ( inj__c_ty_2Elist_2Elist_o @ V20v ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27m ) @ ( ap @ c_2Ebitstring_2En2v @ ( inj__ty_2Enum_2Enum @ V21n ) ) ) ) )
& ! [V22v: tp__c_ty_2Elist_2Elist_o,V23n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__xnor @ A_27n ) @ ( ap @ ( c_2Ewords_2En2w @ A_27n ) @ ( inj__ty_2Enum_2Enum @ V23n ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27n ) @ ( inj__c_ty_2Elist_2Elist_o @ V22v ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__xnor @ A_27n ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27n ) @ ( ap @ c_2Ebitstring_2En2v @ ( inj__ty_2Enum_2Enum @ V23n ) ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27n ) @ ( inj__c_ty_2Elist_2Elist_o @ V22v ) ) ) )
& ! [V24v: tp__c_ty_2Elist_2Elist_o,V25n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27o ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V24v ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V25n ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27o ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V24v ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27b ) @ ( ap @ c_2Ebitstring_2En2v @ ( inj__ty_2Enum_2Enum @ V25n ) ) ) ) )
& ! [V26v: tp__c_ty_2Elist_2Elist_o,V27n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27p ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V27n ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27b ) @ ( inj__c_ty_2Elist_2Elist_o @ V26v ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27p ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( ap @ c_2Ebitstring_2En2v @ ( inj__ty_2Enum_2Enum @ V27n ) ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27b ) @ ( inj__c_ty_2Elist_2Elist_o @ V26v ) ) ) )
& ! [V28v: tp__c_ty_2Elist_2Elist_o,V29n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__join @ A_27q @ A_27r ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27q ) @ ( inj__c_ty_2Elist_2Elist_o @ V28v ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27r ) @ ( inj__ty_2Enum_2Enum @ V29n ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__join @ A_27q @ A_27r ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27q ) @ ( inj__c_ty_2Elist_2Elist_o @ V28v ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27r ) @ ( ap @ c_2Ebitstring_2En2v @ ( inj__ty_2Enum_2Enum @ V29n ) ) ) ) )
& ! [V30v: tp__c_ty_2Elist_2Elist_o,V31n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__join @ A_27s @ A_27t ) @ ( ap @ ( c_2Ewords_2En2w @ A_27s ) @ ( inj__ty_2Enum_2Enum @ V31n ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27t ) @ ( inj__c_ty_2Elist_2Elist_o @ V30v ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__join @ A_27s @ A_27t ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27s ) @ ( ap @ c_2Ebitstring_2En2v @ ( inj__ty_2Enum_2Enum @ V31n ) ) ) ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27t ) @ ( inj__c_ty_2Elist_2Elist_o @ V30v ) ) ) ) ) ).
thf(conj_thm_2Ebitstring_2Eops__to__n2w,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,A_27e: del,A_27f: del,A_27g: del,A_27h: del,A_27i: del,A_27j: del,A_27k: del,A_27l: del,A_27m: del,A_27n: del,A_27o: del] :
( ! [V0v: tp__c_ty_2Elist_2Elist_o] :
( ( ap @ ( c_2Ewords_2Eword__2comp @ A_27b ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27b ) @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) )
= ( ap @ ( c_2Ewords_2Eword__2comp @ A_27b ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V0v ) ) ) ) )
& ! [V1v: tp__c_ty_2Elist_2Elist_o] :
( ( ap @ ( c_2Ewords_2Eword__log2 @ A_27c ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27c ) @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) )
= ( ap @ ( c_2Ewords_2Eword__log2 @ A_27c ) @ ( ap @ ( c_2Ewords_2En2w @ A_27c ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V1v ) ) ) ) )
& ! [V2v: tp__c_ty_2Elist_2Elist_o,V3n: tp__ty_2Enum_2Enum] :
( ( ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V2v ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
<=> ( ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V2v ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) )
& ! [V4v: tp__c_ty_2Elist_2Elist_o,V5n: tp__ty_2Enum_2Enum] :
( ( ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V5n ) )
= ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V4v ) ) )
<=> ( ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V5n ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V4v ) ) ) ) )
& ! [V6v: tp__c_ty_2Elist_2Elist_o,V7w: $i] :
( ( mem @ V7w @ ( ty_2Efcp_2Ecart @ bool @ A_27d ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27d ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27d ) @ ( inj__c_ty_2Elist_2Elist_o @ V6v ) ) ) @ V7w )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27d ) @ ( ap @ ( c_2Ewords_2En2w @ A_27d ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V6v ) ) ) ) @ V7w ) ) )
& ! [V8v: tp__c_ty_2Elist_2Elist_o,V9w: $i] :
( ( mem @ V9w @ ( ty_2Efcp_2Ecart @ bool @ A_27e ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27e ) @ V9w ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27e ) @ ( inj__c_ty_2Elist_2Elist_o @ V8v ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27e ) @ V9w ) @ ( ap @ ( c_2Ewords_2En2w @ A_27e ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V8v ) ) ) ) ) )
& ! [V10v: tp__c_ty_2Elist_2Elist_o,V11w: $i] :
( ( mem @ V11w @ ( ty_2Efcp_2Ecart @ bool @ A_27f ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27f ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27f ) @ ( inj__c_ty_2Elist_2Elist_o @ V10v ) ) ) @ V11w )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27f ) @ ( ap @ ( c_2Ewords_2En2w @ A_27f ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V10v ) ) ) ) @ V11w ) ) )
& ! [V12v: tp__c_ty_2Elist_2Elist_o,V13w: $i] :
( ( mem @ V13w @ ( ty_2Efcp_2Ecart @ bool @ A_27g ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27g ) @ V13w ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27g ) @ ( inj__c_ty_2Elist_2Elist_o @ V12v ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27g ) @ V13w ) @ ( ap @ ( c_2Ewords_2En2w @ A_27g ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V12v ) ) ) ) ) )
& ! [V14v: tp__c_ty_2Elist_2Elist_o,V15w: $i] :
( ( mem @ V15w @ ( ty_2Efcp_2Ecart @ bool @ A_27h ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27h ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27h ) @ ( inj__c_ty_2Elist_2Elist_o @ V14v ) ) ) @ V15w )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27h ) @ ( ap @ ( c_2Ewords_2En2w @ A_27h ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V14v ) ) ) ) @ V15w ) ) )
& ! [V16v: tp__c_ty_2Elist_2Elist_o,V17w: $i] :
( ( mem @ V17w @ ( ty_2Efcp_2Ecart @ bool @ A_27i ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27i ) @ V17w ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27i ) @ ( inj__c_ty_2Elist_2Elist_o @ V16v ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27i ) @ V17w ) @ ( ap @ ( c_2Ewords_2En2w @ A_27i ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V16v ) ) ) ) ) )
& ! [V18v: tp__c_ty_2Elist_2Elist_o,V19w: $i] :
( ( mem @ V19w @ ( ty_2Efcp_2Ecart @ bool @ A_27j ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__quot @ A_27j ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27j ) @ ( inj__c_ty_2Elist_2Elist_o @ V18v ) ) ) @ V19w )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__quot @ A_27j ) @ ( ap @ ( c_2Ewords_2En2w @ A_27j ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V18v ) ) ) ) @ V19w ) ) )
& ! [V20v: tp__c_ty_2Elist_2Elist_o,V21w: $i] :
( ( mem @ V21w @ ( ty_2Efcp_2Ecart @ bool @ A_27k ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__quot @ A_27k ) @ V21w ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27k ) @ ( inj__c_ty_2Elist_2Elist_o @ V20v ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__quot @ A_27k ) @ V21w ) @ ( ap @ ( c_2Ewords_2En2w @ A_27k ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V20v ) ) ) ) ) )
& ! [V22v: tp__c_ty_2Elist_2Elist_o,V23w: $i] :
( ( mem @ V23w @ ( ty_2Efcp_2Ecart @ bool @ A_27l ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__div @ A_27l ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27l ) @ ( inj__c_ty_2Elist_2Elist_o @ V22v ) ) ) @ V23w )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__div @ A_27l ) @ ( ap @ ( c_2Ewords_2En2w @ A_27l ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V22v ) ) ) ) @ V23w ) ) )
& ! [V24v: tp__c_ty_2Elist_2Elist_o,V25w: $i] :
( ( mem @ V25w @ ( ty_2Efcp_2Ecart @ bool @ A_27m ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__div @ A_27m ) @ V25w ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27m ) @ ( inj__c_ty_2Elist_2Elist_o @ V24v ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__div @ A_27m ) @ V25w ) @ ( ap @ ( c_2Ewords_2En2w @ A_27m ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V24v ) ) ) ) ) )
& ! [V26v: tp__c_ty_2Elist_2Elist_o,V27w: $i] :
( ( mem @ V27w @ ( ty_2Efcp_2Ecart @ bool @ A_27n ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__mod @ A_27n ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27n ) @ ( inj__c_ty_2Elist_2Elist_o @ V26v ) ) ) @ V27w )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__mod @ A_27n ) @ ( ap @ ( c_2Ewords_2En2w @ A_27n ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V26v ) ) ) ) @ V27w ) ) )
& ! [V28v: tp__c_ty_2Elist_2Elist_o,V29w: $i] :
( ( mem @ V29w @ ( ty_2Efcp_2Ecart @ bool @ A_27o ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__mod @ A_27o ) @ V29w ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27o ) @ ( inj__c_ty_2Elist_2Elist_o @ V28v ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__mod @ A_27o ) @ V29w ) @ ( ap @ ( c_2Ewords_2En2w @ A_27o ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V28v ) ) ) ) ) )
& ! [V30v: tp__c_ty_2Elist_2Elist_o,V31w: $i] :
( ( mem @ V31w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V30v ) ) ) @ V31w ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V30v ) ) ) ) @ V31w ) ) ) )
& ! [V32v: tp__c_ty_2Elist_2Elist_o,V33w: $i] :
( ( mem @ V33w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V33w ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V32v ) ) ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V33w ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V32v ) ) ) ) ) ) )
& ! [V34v: tp__c_ty_2Elist_2Elist_o,V35w: $i] :
( ( mem @ V35w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__gt @ A_27a ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V34v ) ) ) @ V35w ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__gt @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V34v ) ) ) ) @ V35w ) ) ) )
& ! [V36v: tp__c_ty_2Elist_2Elist_o,V37w: $i] :
( ( mem @ V37w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__gt @ A_27a ) @ V37w ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V36v ) ) ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__gt @ A_27a ) @ V37w ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V36v ) ) ) ) ) ) )
& ! [V38v: tp__c_ty_2Elist_2Elist_o,V39w: $i] :
( ( mem @ V39w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V38v ) ) ) @ V39w ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V38v ) ) ) ) @ V39w ) ) ) )
& ! [V40v: tp__c_ty_2Elist_2Elist_o,V41w: $i] :
( ( mem @ V41w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ V41w ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V40v ) ) ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ V41w ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V40v ) ) ) ) ) ) )
& ! [V42v: tp__c_ty_2Elist_2Elist_o,V43w: $i] :
( ( mem @ V43w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ge @ A_27a ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V42v ) ) ) @ V43w ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ge @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V42v ) ) ) ) @ V43w ) ) ) )
& ! [V44v: tp__c_ty_2Elist_2Elist_o,V45w: $i] :
( ( mem @ V45w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ge @ A_27a ) @ V45w ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V44v ) ) ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ge @ A_27a ) @ V45w ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V44v ) ) ) ) ) ) )
& ! [V46v: tp__c_ty_2Elist_2Elist_o,V47w: $i] :
( ( mem @ V47w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V46v ) ) ) @ V47w ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V46v ) ) ) ) @ V47w ) ) ) )
& ! [V48v: tp__c_ty_2Elist_2Elist_o,V49w: $i] :
( ( mem @ V49w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V49w ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V48v ) ) ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V49w ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V48v ) ) ) ) ) ) )
& ! [V50v: tp__c_ty_2Elist_2Elist_o,V51w: $i] :
( ( mem @ V51w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__hi @ A_27a ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V50v ) ) ) @ V51w ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__hi @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V50v ) ) ) ) @ V51w ) ) ) )
& ! [V52v: tp__c_ty_2Elist_2Elist_o,V53w: $i] :
( ( mem @ V53w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__hi @ A_27a ) @ V53w ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V52v ) ) ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__hi @ A_27a ) @ V53w ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V52v ) ) ) ) ) ) )
& ! [V54v: tp__c_ty_2Elist_2Elist_o,V55w: $i] :
( ( mem @ V55w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V54v ) ) ) @ V55w ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V54v ) ) ) ) @ V55w ) ) ) )
& ! [V56v: tp__c_ty_2Elist_2Elist_o,V57w: $i] :
( ( mem @ V57w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V57w ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V56v ) ) ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V57w ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V56v ) ) ) ) ) ) )
& ! [V58v: tp__c_ty_2Elist_2Elist_o,V59w: $i] :
( ( mem @ V59w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__hs @ A_27a ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V58v ) ) ) @ V59w ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__hs @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V58v ) ) ) ) @ V59w ) ) ) )
& ! [V60v: tp__c_ty_2Elist_2Elist_o,V61w: $i] :
( ( mem @ V61w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__hs @ A_27a ) @ V61w ) @ ( ap @ ( c_2Ebitstring_2Ev2w @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_o @ V60v ) ) ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__hs @ A_27a ) @ V61w ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Ebitstring_2Ev2n @ ( inj__c_ty_2Elist_2Elist_o @ V60v ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------