ITP001 Axioms: ITP090^5.ax
%------------------------------------------------------------------------------
% File : ITP090^5 : 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 : words^2.ax [Gau20]
% : HL4090^5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 1067 ( 210 unt; 191 typ; 0 def)
% Number of atoms : 20344 ( 736 equ; 0 cnn)
% Maximal formula atoms : 125 ( 19 avg)
% Number of connectives : 28910 ( 69 ~; 32 |; 196 &;27596 @)
% ( 134 <=>; 883 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 8 avg;27596 nst)
% Number of types : 29 ( 28 usr)
% Number of type conns : 172 ( 172 >; 0 *; 0 +; 0 <<)
% Number of symbols : 266 ( 265 usr; 103 con; 0-3 aty)
% Number of variables : 2177 ( 136 ^2036 !; 5 ?;2177 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tp_c_2Ewords_2EBIT__SET,type,
c_2Ewords_2EBIT__SET: $i ).
thf(mem_c_2Ewords_2EBIT__SET,axiom,
mem @ c_2Ewords_2EBIT__SET @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) ).
thf(tp_c_2Ewords_2EINT__MAX,type,
c_2Ewords_2EINT__MAX: del > $i ).
thf(mem_c_2Ewords_2EINT__MAX,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2EINT__MAX @ A_27a ) @ ( arr @ ( ty_2Ebool_2Eitself @ A_27a ) @ ty_2Enum_2Enum ) ) ).
thf(tp_c_2Ewords_2EINT__MIN,type,
c_2Ewords_2EINT__MIN: del > $i ).
thf(mem_c_2Ewords_2EINT__MIN,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2EINT__MIN @ A_27a ) @ ( arr @ ( ty_2Ebool_2Eitself @ A_27a ) @ ty_2Enum_2Enum ) ) ).
thf(tp_c_2Ewords_2EUINT__MAX,type,
c_2Ewords_2EUINT__MAX: del > $i ).
thf(mem_c_2Ewords_2EUINT__MAX,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2EUINT__MAX @ A_27a ) @ ( arr @ ( ty_2Ebool_2Eitself @ A_27a ) @ ty_2Enum_2Enum ) ) ).
thf(stp_c_ty_2Epair_2Eprod_o_o,type,
tp__c_ty_2Epair_2Eprod_o_o: $tType ).
thf(stp_inj_c_ty_2Epair_2Eprod_o_o,type,
inj__c_ty_2Epair_2Eprod_o_o: tp__c_ty_2Epair_2Eprod_o_o > $i ).
thf(stp_surj_c_ty_2Epair_2Eprod_o_o,type,
surj__c_ty_2Epair_2Eprod_o_o: $i > tp__c_ty_2Epair_2Eprod_o_o ).
thf(stp_inj_surj_c_ty_2Epair_2Eprod_o_o,axiom,
! [X: tp__c_ty_2Epair_2Eprod_o_o] :
( ( surj__c_ty_2Epair_2Eprod_o_o @ ( inj__c_ty_2Epair_2Eprod_o_o @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Epair_2Eprod_o_o,axiom,
! [X: tp__c_ty_2Epair_2Eprod_o_o] : ( mem @ ( inj__c_ty_2Epair_2Eprod_o_o @ X ) @ ( ty_2Epair_2Eprod @ bool @ bool ) ) ).
thf(stp_iso_mem_c_ty_2Epair_2Eprod_o_o,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Epair_2Eprod @ bool @ bool ) )
=> ( X
= ( inj__c_ty_2Epair_2Eprod_o_o @ ( surj__c_ty_2Epair_2Eprod_o_o @ X ) ) ) ) ).
thf(tp_c_2Ewords_2Eadd__with__carry,type,
c_2Ewords_2Eadd__with__carry: del > $i ).
thf(mem_c_2Ewords_2Eadd__with__carry,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eadd__with__carry @ A_27a ) @ ( arr @ ( ty_2Epair_2Eprod @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Epair_2Eprod @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool ) ) @ ( ty_2Epair_2Eprod @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Epair_2Eprod @ bool @ bool ) ) ) ) ).
thf(tp_c_2Ewords_2Ebit__count,type,
c_2Ewords_2Ebit__count: del > $i ).
thf(mem_c_2Ewords_2Ebit__count,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Ebit__count @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ty_2Enum_2Enum ) ) ).
thf(tp_c_2Ewords_2Ebit__count__upto,type,
c_2Ewords_2Ebit__count__upto: del > $i ).
thf(mem_c_2Ewords_2Ebit__count__upto,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Ebit__count__upto @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ty_2Enum_2Enum ) ) ) ).
thf(tp_c_2Ewords_2Ebit__field__insert,type,
c_2Ewords_2Ebit__field__insert: del > del > $i ).
thf(mem_c_2Ewords_2Ebit__field__insert,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ewords_2Ebit__field__insert @ A_27a @ A_27b ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ) ) ).
thf(tp_c_2Ewords_2Econcat__word__list,type,
c_2Ewords_2Econcat__word__list: del > del > $i ).
thf(mem_c_2Ewords_2Econcat__word__list,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ewords_2Econcat__word__list @ A_27a @ A_27b ) @ ( arr @ ( ty_2Elist_2Elist @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) ) ) ).
thf(tp_c_2Ewords_2Edimword,type,
c_2Ewords_2Edimword: del > $i ).
thf(mem_c_2Ewords_2Edimword,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Edimword @ A_27a ) @ ( arr @ ( ty_2Ebool_2Eitself @ A_27a ) @ ty_2Enum_2Enum ) ) ).
thf(tp_c_2Ewords_2El2w,type,
c_2Ewords_2El2w: del > $i ).
thf(mem_c_2Ewords_2El2w,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2El2w @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2En2w,type,
c_2Ewords_2En2w: del > $i ).
thf(mem_c_2Ewords_2En2w,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2En2w @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ).
thf(tp_c_2Ewords_2En2w__itself,type,
c_2Ewords_2En2w__itself: del > $i ).
thf(mem_c_2Ewords_2En2w__itself,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2En2w__itself @ A_27a ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Ebool_2Eitself @ A_27a ) ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ).
thf(stp_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,type,
tp__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o: $tType ).
thf(stp_inj_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,type,
inj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o: tp__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o > $i ).
thf(stp_surj_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,type,
surj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o: $i > tp__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o ).
thf(stp_inj_surj_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,axiom,
! [X: tp__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o] :
( ( surj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o @ ( inj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,axiom,
! [X: tp__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o] : ( mem @ ( inj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o @ X ) @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) ) ) ) ).
thf(stp_iso_mem_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) ) ) )
=> ( X
= ( inj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o @ ( surj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o @ X ) ) ) ) ).
thf(stp_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,type,
tp__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o: $tType ).
thf(stp_inj_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,type,
inj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o: tp__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o > $i ).
thf(stp_surj_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,type,
surj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o: $i > tp__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o ).
thf(stp_inj_surj_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,axiom,
! [X: tp__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o] :
( ( surj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o @ ( inj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,axiom,
! [X: tp__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o] : ( mem @ ( inj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o @ X ) @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) ) ) ).
thf(stp_iso_mem_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) ) )
=> ( X
= ( inj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o @ ( surj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o @ X ) ) ) ) ).
thf(tp_c_2Ewords_2Enzcv,type,
c_2Ewords_2Enzcv: del > $i ).
thf(mem_c_2Ewords_2Enzcv,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Enzcv @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) ) ) ) ) ) ).
thf(stp_c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone,type,
tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone: $tType ).
thf(stp_inj_c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone,type,
inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone: tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone > $i ).
thf(stp_surj_c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone,type,
surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone: $i > tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone ).
thf(stp_inj_surj_c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] :
( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( mem @ ( inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ X ) @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) ).
thf(stp_iso_mem_c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) )
=> ( X
= ( inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ X ) ) ) ) ).
thf(tp_c_2Ewords_2Ereduce__and,type,
c_2Ewords_2Ereduce__and: del > $i ).
thf(mem_c_2Ewords_2Ereduce__and,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Ereduce__and @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) ) ).
thf(tp_c_2Ewords_2Ereduce__nand,type,
c_2Ewords_2Ereduce__nand: del > $i ).
thf(mem_c_2Ewords_2Ereduce__nand,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Ereduce__nand @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) ) ).
thf(tp_c_2Ewords_2Ereduce__nor,type,
c_2Ewords_2Ereduce__nor: del > $i ).
thf(mem_c_2Ewords_2Ereduce__nor,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Ereduce__nor @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) ) ).
thf(tp_c_2Ewords_2Ereduce__or,type,
c_2Ewords_2Ereduce__or: del > $i ).
thf(mem_c_2Ewords_2Ereduce__or,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Ereduce__or @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) ) ).
thf(tp_c_2Ewords_2Ereduce__xnor,type,
c_2Ewords_2Ereduce__xnor: del > $i ).
thf(mem_c_2Ewords_2Ereduce__xnor,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Ereduce__xnor @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) ) ).
thf(tp_c_2Ewords_2Ereduce__xor,type,
c_2Ewords_2Ereduce__xor: del > $i ).
thf(mem_c_2Ewords_2Ereduce__xor,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Ereduce__xor @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) ) ).
thf(tp_c_2Ewords_2Es2w,type,
c_2Ewords_2Es2w: del > $i ).
thf(mem_c_2Ewords_2Es2w,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Es2w @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( arr @ ty_2Estring_2Echar @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ) ).
thf(tp_c_2Ewords_2Esaturate__add,type,
c_2Ewords_2Esaturate__add: del > $i ).
thf(mem_c_2Ewords_2Esaturate__add,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Esaturate__add @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Esaturate__mul,type,
c_2Ewords_2Esaturate__mul: del > $i ).
thf(mem_c_2Ewords_2Esaturate__mul,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Esaturate__mul @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Esaturate__n2w,type,
c_2Ewords_2Esaturate__n2w: del > $i ).
thf(mem_c_2Ewords_2Esaturate__n2w,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Esaturate__n2w @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ).
thf(tp_c_2Ewords_2Esaturate__sub,type,
c_2Ewords_2Esaturate__sub: del > $i ).
thf(mem_c_2Ewords_2Esaturate__sub,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Esaturate__sub @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Esaturate__w2w,type,
c_2Ewords_2Esaturate__w2w: del > del > $i ).
thf(mem_c_2Ewords_2Esaturate__w2w,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ewords_2Esaturate__w2w @ A_27a @ A_27b ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) ) ) ).
thf(tp_c_2Ewords_2Esw2sw,type,
c_2Ewords_2Esw2sw: del > del > $i ).
thf(mem_c_2Ewords_2Esw2sw,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ewords_2Esw2sw @ A_27a @ A_27b ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) ) ) ).
thf(tp_c_2Ewords_2Ew2l,type,
c_2Ewords_2Ew2l: del > $i ).
thf(mem_c_2Ewords_2Ew2l,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Ew2l @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) ) ) ) ).
thf(tp_c_2Ewords_2Ew2n,type,
c_2Ewords_2Ew2n: del > $i ).
thf(mem_c_2Ewords_2Ew2n,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Ew2n @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ty_2Enum_2Enum ) ) ).
thf(tp_c_2Ewords_2Ew2s,type,
c_2Ewords_2Ew2s: del > $i ).
thf(mem_c_2Ewords_2Ew2s,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Ew2s @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( arr @ ty_2Enum_2Enum @ ty_2Estring_2Echar ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) ) ) ) ).
thf(tp_c_2Ewords_2Ew2w,type,
c_2Ewords_2Ew2w: del > del > $i ).
thf(mem_c_2Ewords_2Ew2w,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) ) ) ).
thf(tp_c_2Ewords_2Eword__1comp,type,
c_2Ewords_2Eword__1comp: del > $i ).
thf(mem_c_2Ewords_2Eword__1comp,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ).
thf(tp_c_2Ewords_2Eword__2comp,type,
c_2Ewords_2Eword__2comp: del > $i ).
thf(mem_c_2Ewords_2Eword__2comp,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ).
thf(tp_c_2Ewords_2Eword__H,type,
c_2Ewords_2Eword__H: del > $i ).
thf(mem_c_2Ewords_2Eword__H,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__H @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ).
thf(tp_c_2Ewords_2Eword__L,type,
c_2Ewords_2Eword__L: del > $i ).
thf(mem_c_2Ewords_2Eword__L,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__L @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ).
thf(tp_c_2Ewords_2Eword__L2,type,
c_2Ewords_2Eword__L2: del > $i ).
thf(mem_c_2Ewords_2Eword__L2,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__L2 @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ).
thf(tp_c_2Ewords_2Eword__T,type,
c_2Ewords_2Eword__T: del > $i ).
thf(mem_c_2Ewords_2Eword__T,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__T @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ).
thf(tp_c_2Ewords_2Eword__abs,type,
c_2Ewords_2Eword__abs: del > $i ).
thf(mem_c_2Ewords_2Eword__abs,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__abs @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ).
thf(tp_c_2Ewords_2Eword__add,type,
c_2Ewords_2Eword__add: del > $i ).
thf(mem_c_2Ewords_2Eword__add,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__and,type,
c_2Ewords_2Eword__and: del > $i ).
thf(mem_c_2Ewords_2Eword__and,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__and @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__asr,type,
c_2Ewords_2Eword__asr: del > $i ).
thf(mem_c_2Ewords_2Eword__asr,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__asr @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__asr__bv,type,
c_2Ewords_2Eword__asr__bv: del > $i ).
thf(mem_c_2Ewords_2Eword__asr__bv,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__asr__bv @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__bit,type,
c_2Ewords_2Eword__bit: del > $i ).
thf(mem_c_2Ewords_2Eword__bit,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__bit @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool ) ) ) ).
thf(tp_c_2Ewords_2Eword__bits,type,
c_2Ewords_2Eword__bits: del > $i ).
thf(mem_c_2Ewords_2Eword__bits,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__compare,type,
c_2Ewords_2Eword__compare: del > $i ).
thf(mem_c_2Ewords_2Eword__compare,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__compare @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__concat,type,
c_2Ewords_2Eword__concat: del > del > del > $i ).
thf(mem_c_2Ewords_2Eword__concat,axiom,
! [A_27a: del,A_27b: del,A_27c: del] : ( mem @ ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) @ ( ty_2Efcp_2Ecart @ bool @ A_27c ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__div,type,
c_2Ewords_2Eword__div: del > $i ).
thf(mem_c_2Ewords_2Eword__div,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__div @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__extract,type,
c_2Ewords_2Eword__extract: del > del > $i ).
thf(mem_c_2Ewords_2Eword__extract,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__from__bin__list,type,
c_2Ewords_2Eword__from__bin__list: del > $i ).
thf(mem_c_2Ewords_2Eword__from__bin__list,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__from__bin__list @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ).
thf(tp_c_2Ewords_2Eword__from__bin__string,type,
c_2Ewords_2Eword__from__bin__string: del > $i ).
thf(mem_c_2Ewords_2Eword__from__bin__string,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__from__bin__string @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ).
thf(tp_c_2Ewords_2Eword__from__dec__list,type,
c_2Ewords_2Eword__from__dec__list: del > $i ).
thf(mem_c_2Ewords_2Eword__from__dec__list,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__from__dec__list @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ).
thf(tp_c_2Ewords_2Eword__from__dec__string,type,
c_2Ewords_2Eword__from__dec__string: del > $i ).
thf(mem_c_2Ewords_2Eword__from__dec__string,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__from__dec__string @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ).
thf(tp_c_2Ewords_2Eword__from__hex__list,type,
c_2Ewords_2Eword__from__hex__list: del > $i ).
thf(mem_c_2Ewords_2Eword__from__hex__list,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__from__hex__list @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ).
thf(tp_c_2Ewords_2Eword__from__hex__string,type,
c_2Ewords_2Eword__from__hex__string: del > $i ).
thf(mem_c_2Ewords_2Eword__from__hex__string,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__from__hex__string @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ).
thf(tp_c_2Ewords_2Eword__from__oct__list,type,
c_2Ewords_2Eword__from__oct__list: del > $i ).
thf(mem_c_2Ewords_2Eword__from__oct__list,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__from__oct__list @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ).
thf(tp_c_2Ewords_2Eword__from__oct__string,type,
c_2Ewords_2Eword__from__oct__string: del > $i ).
thf(mem_c_2Ewords_2Eword__from__oct__string,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__from__oct__string @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ).
thf(tp_c_2Ewords_2Eword__ge,type,
c_2Ewords_2Eword__ge: del > $i ).
thf(mem_c_2Ewords_2Eword__ge,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__ge @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool ) ) ) ).
thf(tp_c_2Ewords_2Eword__gt,type,
c_2Ewords_2Eword__gt: del > $i ).
thf(mem_c_2Ewords_2Eword__gt,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__gt @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool ) ) ) ).
thf(tp_c_2Ewords_2Eword__hi,type,
c_2Ewords_2Eword__hi: del > $i ).
thf(mem_c_2Ewords_2Eword__hi,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__hi @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool ) ) ) ).
thf(tp_c_2Ewords_2Eword__hs,type,
c_2Ewords_2Eword__hs: del > $i ).
thf(mem_c_2Ewords_2Eword__hs,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__hs @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool ) ) ) ).
thf(tp_c_2Ewords_2Eword__join,type,
c_2Ewords_2Eword__join: del > del > $i ).
thf(mem_c_2Ewords_2Eword__join,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ewords_2Eword__join @ A_27a @ A_27b ) @ ( 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 ) ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__le,type,
c_2Ewords_2Eword__le: del > $i ).
thf(mem_c_2Ewords_2Eword__le,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__le @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool ) ) ) ).
thf(tp_c_2Ewords_2Eword__len,type,
c_2Ewords_2Eword__len: del > $i ).
thf(mem_c_2Ewords_2Eword__len,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__len @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ty_2Enum_2Enum ) ) ).
thf(tp_c_2Ewords_2Eword__lo,type,
c_2Ewords_2Eword__lo: del > $i ).
thf(mem_c_2Ewords_2Eword__lo,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__lo @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool ) ) ) ).
thf(tp_c_2Ewords_2Eword__log2,type,
c_2Ewords_2Eword__log2: del > $i ).
thf(mem_c_2Ewords_2Eword__log2,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__log2 @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ).
thf(tp_c_2Ewords_2Eword__ls,type,
c_2Ewords_2Eword__ls: del > $i ).
thf(mem_c_2Ewords_2Eword__ls,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__ls @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool ) ) ) ).
thf(tp_c_2Ewords_2Eword__lsb,type,
c_2Ewords_2Eword__lsb: del > $i ).
thf(mem_c_2Ewords_2Eword__lsb,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__lsb @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool ) ) ).
thf(tp_c_2Ewords_2Eword__lsl,type,
c_2Ewords_2Eword__lsl: del > $i ).
thf(mem_c_2Ewords_2Eword__lsl,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__lsl__bv,type,
c_2Ewords_2Eword__lsl__bv: del > $i ).
thf(mem_c_2Ewords_2Eword__lsl__bv,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__lsl__bv @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__lsr,type,
c_2Ewords_2Eword__lsr: del > $i ).
thf(mem_c_2Ewords_2Eword__lsr,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__lsr__bv,type,
c_2Ewords_2Eword__lsr__bv: del > $i ).
thf(mem_c_2Ewords_2Eword__lsr__bv,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__lsr__bv @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__lt,type,
c_2Ewords_2Eword__lt: del > $i ).
thf(mem_c_2Ewords_2Eword__lt,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__lt @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool ) ) ) ).
thf(tp_c_2Ewords_2Eword__max,type,
c_2Ewords_2Eword__max: del > $i ).
thf(mem_c_2Ewords_2Eword__max,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__max @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__min,type,
c_2Ewords_2Eword__min: del > $i ).
thf(mem_c_2Ewords_2Eword__min,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__min @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__mod,type,
c_2Ewords_2Eword__mod: del > $i ).
thf(mem_c_2Ewords_2Eword__mod,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__mod @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__modify,type,
c_2Ewords_2Eword__modify: del > $i ).
thf(mem_c_2Ewords_2Eword__modify,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__modify @ A_27a ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ ( arr @ bool @ bool ) ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__msb,type,
c_2Ewords_2Eword__msb: del > $i ).
thf(mem_c_2Ewords_2Eword__msb,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__msb @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool ) ) ).
thf(tp_c_2Ewords_2Eword__mul,type,
c_2Ewords_2Eword__mul: del > $i ).
thf(mem_c_2Ewords_2Eword__mul,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__mul @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__nand,type,
c_2Ewords_2Eword__nand: del > $i ).
thf(mem_c_2Ewords_2Eword__nand,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__nand @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__nor,type,
c_2Ewords_2Eword__nor: del > $i ).
thf(mem_c_2Ewords_2Eword__nor,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__nor @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__or,type,
c_2Ewords_2Eword__or: del > $i ).
thf(mem_c_2Ewords_2Eword__or,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__or @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__quot,type,
c_2Ewords_2Eword__quot: del > $i ).
thf(mem_c_2Ewords_2Eword__quot,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__quot @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__reduce,type,
c_2Ewords_2Eword__reduce: del > $i ).
thf(mem_c_2Ewords_2Eword__reduce,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__reduce @ A_27a ) @ ( arr @ ( arr @ bool @ ( arr @ bool @ bool ) ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__rem,type,
c_2Ewords_2Eword__rem: del > $i ).
thf(mem_c_2Ewords_2Eword__rem,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__rem @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__replicate,type,
c_2Ewords_2Eword__replicate: del > del > $i ).
thf(mem_c_2Ewords_2Eword__replicate,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Ewords_2Eword__replicate @ A_27a @ A_27b ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__reverse,type,
c_2Ewords_2Eword__reverse: del > $i ).
thf(mem_c_2Ewords_2Eword__reverse,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__reverse @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ).
thf(tp_c_2Ewords_2Eword__rol,type,
c_2Ewords_2Eword__rol: del > $i ).
thf(mem_c_2Ewords_2Eword__rol,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__rol @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__rol__bv,type,
c_2Ewords_2Eword__rol__bv: del > $i ).
thf(mem_c_2Ewords_2Eword__rol__bv,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__rol__bv @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__ror,type,
c_2Ewords_2Eword__ror: del > $i ).
thf(mem_c_2Ewords_2Eword__ror,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__ror @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__ror__bv,type,
c_2Ewords_2Eword__ror__bv: del > $i ).
thf(mem_c_2Ewords_2Eword__ror__bv,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__ror__bv @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__rrx,type,
c_2Ewords_2Eword__rrx: del > $i ).
thf(mem_c_2Ewords_2Eword__rrx,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__rrx @ A_27a ) @ ( arr @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__sign__extend,type,
c_2Ewords_2Eword__sign__extend: del > $i ).
thf(mem_c_2Ewords_2Eword__sign__extend,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__sign__extend @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__signed__bits,type,
c_2Ewords_2Eword__signed__bits: del > $i ).
thf(mem_c_2Ewords_2Eword__signed__bits,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__signed__bits @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__slice,type,
c_2Ewords_2Eword__slice: del > $i ).
thf(mem_c_2Ewords_2Eword__slice,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__slice @ A_27a ) @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__smax,type,
c_2Ewords_2Eword__smax: del > $i ).
thf(mem_c_2Ewords_2Eword__smax,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__smax @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__smin,type,
c_2Ewords_2Eword__smin: del > $i ).
thf(mem_c_2Ewords_2Eword__smin,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__smin @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__sub,type,
c_2Ewords_2Eword__sub: del > $i ).
thf(mem_c_2Ewords_2Eword__sub,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__sub @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__to__bin__list,type,
c_2Ewords_2Eword__to__bin__list: del > $i ).
thf(mem_c_2Ewords_2Eword__to__bin__list,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__to__bin__list @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) ) ) ).
thf(tp_c_2Ewords_2Eword__to__bin__string,type,
c_2Ewords_2Eword__to__bin__string: del > $i ).
thf(mem_c_2Ewords_2Eword__to__bin__string,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__to__bin__string @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) ) ).
thf(tp_c_2Ewords_2Eword__to__dec__list,type,
c_2Ewords_2Eword__to__dec__list: del > $i ).
thf(mem_c_2Ewords_2Eword__to__dec__list,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__to__dec__list @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) ) ) ).
thf(tp_c_2Ewords_2Eword__to__dec__string,type,
c_2Ewords_2Eword__to__dec__string: del > $i ).
thf(mem_c_2Ewords_2Eword__to__dec__string,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__to__dec__string @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) ) ).
thf(tp_c_2Ewords_2Eword__to__hex__list,type,
c_2Ewords_2Eword__to__hex__list: del > $i ).
thf(mem_c_2Ewords_2Eword__to__hex__list,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__to__hex__list @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) ) ) ).
thf(tp_c_2Ewords_2Eword__to__hex__string,type,
c_2Ewords_2Eword__to__hex__string: del > $i ).
thf(mem_c_2Ewords_2Eword__to__hex__string,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__to__hex__string @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) ) ).
thf(tp_c_2Ewords_2Eword__to__oct__list,type,
c_2Ewords_2Eword__to__oct__list: del > $i ).
thf(mem_c_2Ewords_2Eword__to__oct__list,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__to__oct__list @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) ) ) ).
thf(tp_c_2Ewords_2Eword__to__oct__string,type,
c_2Ewords_2Eword__to__oct__string: del > $i ).
thf(mem_c_2Ewords_2Eword__to__oct__string,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__to__oct__string @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) ) ).
thf(tp_c_2Ewords_2Eword__xnor,type,
c_2Ewords_2Eword__xnor: del > $i ).
thf(mem_c_2Ewords_2Eword__xnor,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__xnor @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Ewords_2Eword__xor,type,
c_2Ewords_2Eword__xor: del > $i ).
thf(mem_c_2Ewords_2Eword__xor,axiom,
! [A_27a: del] : ( mem @ ( c_2Ewords_2Eword__xor @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(ax_thm_2Ewords_2Edimword__def,axiom,
! [A_27a: del] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(ax_thm_2Ewords_2EINT__MIN__def,axiom,
! [A_27a: del] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( 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 ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2EUINT__MAX__def,axiom,
! [A_27a: del] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2EUINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2EINT__MAX__def,axiom,
! [A_27a: del] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2EINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Ewords_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Ew2n__def,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0w ) )
= ( surj__ty_2Enum_2Enum
@ ( ap @ ( ap @ c_2Esum__num_2ESUM @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V1i: $i] : ( ap @ ( ap @ c_2Ebit_2ESBIT @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0w ) @ V1i ) ) @ V1i ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2En2w__def,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) )
= ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V1i: $i] : ( ap @ ( ap @ c_2Ebit_2EBIT @ V1i ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Ew2w__def,axiom,
! [A_27a: del,A_27b: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ V0w )
= ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0w ) ) ) ) ).
thf(ax_thm_2Ewords_2Esw2sw__def,axiom,
! [A_27a: del,A_27b: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Esw2sw @ A_27a @ A_27b ) @ V0w )
= ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2ESIGN__EXTEND @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0w ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Ew2l__def,axiom,
! [A_27a: del,V0b: tp__ty_2Enum_2Enum,V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Ewords_2Ew2l @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ V1w ) )
= ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumposrep_2En2l @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1w ) ) ) ) ) ).
thf(ax_thm_2Ewords_2El2w__def,axiom,
! [A_27a: del,V0b: tp__ty_2Enum_2Enum,V1l: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2El2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) ) ) ).
thf(ax_thm_2Ewords_2Ew2s__def,axiom,
! [A_27a: del,V0b: tp__ty_2Enum_2Enum,V1f: $i] :
( ( mem @ V1f @ ( arr @ ty_2Enum_2Enum @ ty_2Estring_2Echar ) )
=> ! [V2w: $i] :
( ( mem @ V2w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( surj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Ew2s @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ V1f ) @ V2w ) )
= ( surj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ ( ap @ ( ap @ ( ap @ c_2EASCIInumbers_2En2s @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ V1f ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V2w ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Es2w__def,axiom,
! [A_27a: del,V0b: tp__ty_2Enum_2Enum,V1f: $i] :
( ( mem @ V1f @ ( arr @ ty_2Estring_2Echar @ ty_2Enum_2Enum ) )
=> ! [V2s: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar] :
( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Es2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ V1f ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V2s ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ ( ap @ c_2EASCIInumbers_2Es2n @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ V1f ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V2s ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__from__bin__list__def,axiom,
! [A_27a: del] :
( ( c_2Ewords_2Eword__from__bin__list @ A_27a )
= ( ap @ ( c_2Ewords_2El2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__from__oct__list__def,axiom,
! [A_27a: del] :
( ( c_2Ewords_2Eword__from__oct__list @ A_27a )
= ( ap @ ( c_2Ewords_2El2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__from__dec__list__def,axiom,
! [A_27a: del] :
( ( c_2Ewords_2Eword__from__dec__list @ A_27a )
= ( ap @ ( c_2Ewords_2El2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__from__hex__list__def,axiom,
! [A_27a: del] :
( ( c_2Ewords_2Eword__from__hex__list @ A_27a )
= ( ap @ ( c_2Ewords_2El2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__to__bin__list__def,axiom,
! [A_27a: del] :
( ( c_2Ewords_2Eword__to__bin__list @ A_27a )
= ( ap @ ( c_2Ewords_2Ew2l @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__to__oct__list__def,axiom,
! [A_27a: del] :
( ( c_2Ewords_2Eword__to__oct__list @ A_27a )
= ( ap @ ( c_2Ewords_2Ew2l @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__to__dec__list__def,axiom,
! [A_27a: del] :
( ( c_2Ewords_2Eword__to__dec__list @ A_27a )
= ( ap @ ( c_2Ewords_2Ew2l @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__to__hex__list__def,axiom,
! [A_27a: del] :
( ( c_2Ewords_2Eword__to__hex__list @ A_27a )
= ( ap @ ( c_2Ewords_2Ew2l @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__from__bin__string__def,axiom,
! [A_27a: del] :
( ( c_2Ewords_2Eword__from__bin__string @ A_27a )
= ( ap @ ( ap @ ( c_2Ewords_2Es2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ c_2EASCIInumbers_2EUNHEX ) ) ).
thf(ax_thm_2Ewords_2Eword__from__oct__string__def,axiom,
! [A_27a: del] :
( ( c_2Ewords_2Eword__from__oct__string @ A_27a )
= ( ap @ ( ap @ ( c_2Ewords_2Es2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ c_2EASCIInumbers_2EUNHEX ) ) ).
thf(ax_thm_2Ewords_2Eword__from__dec__string__def,axiom,
! [A_27a: del] :
( ( c_2Ewords_2Eword__from__dec__string @ A_27a )
= ( ap @ ( ap @ ( c_2Ewords_2Es2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ c_2EASCIInumbers_2EUNHEX ) ) ).
thf(ax_thm_2Ewords_2Eword__from__hex__string__def,axiom,
! [A_27a: del] :
( ( c_2Ewords_2Eword__from__hex__string @ A_27a )
= ( ap @ ( ap @ ( c_2Ewords_2Es2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ c_2EASCIInumbers_2EUNHEX ) ) ).
thf(ax_thm_2Ewords_2Eword__to__bin__string__def,axiom,
! [A_27a: del] :
( ( c_2Ewords_2Eword__to__bin__string @ A_27a )
= ( ap @ ( ap @ ( c_2Ewords_2Ew2s @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ c_2EASCIInumbers_2EHEX ) ) ).
thf(ax_thm_2Ewords_2Eword__to__oct__string__def,axiom,
! [A_27a: del] :
( ( c_2Ewords_2Eword__to__oct__string @ A_27a )
= ( ap @ ( ap @ ( c_2Ewords_2Ew2s @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ c_2EASCIInumbers_2EHEX ) ) ).
thf(ax_thm_2Ewords_2Eword__to__dec__string__def,axiom,
! [A_27a: del] :
( ( c_2Ewords_2Eword__to__dec__string @ A_27a )
= ( ap @ ( ap @ ( c_2Ewords_2Ew2s @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ c_2EASCIInumbers_2EHEX ) ) ).
thf(ax_thm_2Ewords_2Eword__to__hex__string__def,axiom,
! [A_27a: del] :
( ( c_2Ewords_2Eword__to__hex__string @ A_27a )
= ( ap @ ( ap @ ( c_2Ewords_2Ew2s @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ c_2EASCIInumbers_2EHEX ) ) ).
thf(ax_thm_2Ewords_2Eword__T__def,axiom,
! [A_27a: del] :
( ( c_2Ewords_2Eword__T @ A_27a )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( c_2Ewords_2EUINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__L__def,axiom,
! [A_27a: del] :
( ( c_2Ewords_2Eword__L @ A_27a )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( c_2Ewords_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__H__def,axiom,
! [A_27a: del] :
( ( c_2Ewords_2Eword__H @ A_27a )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( c_2Ewords_2EINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__1comp__def,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ V0w )
= ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V1i: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0w ) @ V1i ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__and__def,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0v ) @ V1w )
= ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2i: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0v ) @ V2i ) ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V1w ) @ V2i ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__or__def,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ V0v ) @ V1w )
= ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2i: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0v ) @ V2i ) ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V1w ) @ V2i ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__xor__def,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ V0v ) @ V1w )
= ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2i: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0v ) @ V2i ) ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V1w ) @ V2i ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__nand__def,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__nand @ A_27a ) @ V0v ) @ V1w )
= ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2i: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0v ) @ V2i ) ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V1w ) @ V2i ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__nor__def,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__nor @ A_27a ) @ V0v ) @ V1w )
= ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2i: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0v ) @ V2i ) ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V1w ) @ V2i ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__xnor__def,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__xnor @ A_27a ) @ V0v ) @ V1w )
= ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2i: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0v ) @ V2i ) ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V1w ) @ V2i ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__reduce__def,axiom,
! [A_27a: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( ap @ ( c_2Ewords_2Eword__reduce @ A_27a ) @ V0f ) @ V1w ) )
= ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone
@ ( ap @ ( c_2Efcp_2EFCP @ bool @ ty_2Eone_2Eone )
@ ( ap @ ( c_2Ecombin_2EK @ bool @ ty_2Enum_2Enum )
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Elist_2Elist @ bool ) @ bool )
@ ( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V2l: $i] : ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ bool @ bool ) @ V0f ) @ ( ap @ ( c_2Elist_2EHD @ bool ) @ V2l ) ) @ ( ap @ ( c_2Elist_2ETL @ bool ) @ V2l ) ) ) )
@ ( ap
@ ( ap @ ( c_2Elist_2EGENLIST @ bool )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3i: $i] : ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V1w ) @ ( 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 ) ) ) ) ) @ V3i ) ) ) )
@ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__compare__def,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( ap @ ( c_2Ewords_2Eword__compare @ A_27a ) @ V0a ) @ V1b ) )
= ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ V0a ) @ V1b ) ) @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Ereduce__and__def,axiom,
! [A_27a: del] :
( ( c_2Ewords_2Ereduce__and @ A_27a )
= ( ap @ ( c_2Ewords_2Eword__reduce @ A_27a ) @ c_2Ebool_2E_2F_5C ) ) ).
thf(ax_thm_2Ewords_2Ereduce__or__def,axiom,
! [A_27a: del] :
( ( c_2Ewords_2Ereduce__or @ A_27a )
= ( ap @ ( c_2Ewords_2Eword__reduce @ A_27a ) @ c_2Ebool_2E_5C_2F ) ) ).
thf(ax_thm_2Ewords_2Ereduce__xor__def,axiom,
! [A_27a: del] :
( ( c_2Ewords_2Ereduce__xor @ A_27a )
= ( ap @ ( c_2Ewords_2Eword__reduce @ A_27a )
@ ( 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_2Ewords_2Ereduce__nand__def,axiom,
! [A_27a: del] :
( ( c_2Ewords_2Ereduce__nand @ A_27a )
= ( ap @ ( c_2Ewords_2Eword__reduce @ A_27a )
@ ( lam @ bool
@ ^ [V0a: $i] :
( lam @ bool
@ ^ [V1b: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ V0a ) @ V1b ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Ereduce__nor__def,axiom,
! [A_27a: del] :
( ( c_2Ewords_2Ereduce__nor @ A_27a )
= ( ap @ ( c_2Ewords_2Eword__reduce @ A_27a )
@ ( lam @ bool
@ ^ [V0a: $i] :
( lam @ bool
@ ^ [V1b: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ V0a ) @ V1b ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Ereduce__xnor__def,axiom,
! [A_27a: del] :
( ( c_2Ewords_2Ereduce__xnor @ A_27a )
= ( ap @ ( c_2Ewords_2Eword__reduce @ A_27a ) @ ( c_2Emin_2E_3D @ bool ) ) ) ).
thf(ax_thm_2Ewords_2Eword__lsb__def,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Ewords_2Eword__lsb @ A_27a ) @ V0w ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__msb__def,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0w ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0w ) @ ( 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 ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__slice__def,axiom,
! [A_27a: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__slice @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) )
= ( lam @ ( ty_2Efcp_2Ecart @ bool @ A_27a )
@ ^ [V2w: $i] :
( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3i: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V3i ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ V3i ) @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( 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 ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V2w ) @ V3i ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__bits__def,axiom,
! [A_27a: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) )
= ( lam @ ( ty_2Efcp_2Ecart @ bool @ A_27a )
@ ^ [V2w: $i] :
( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3i: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V3i ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( 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 ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V2w ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V3i ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__signed__bits__def,axiom,
! [A_27a: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__signed__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) )
= ( lam @ ( ty_2Efcp_2Ecart @ bool @ A_27a )
@ ^ [V2w: $i] :
( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3i: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( 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 ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V2w ) @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V3i ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__extract__def,axiom,
! [A_27a: del,A_27b: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) )
= ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__bit__def,axiom,
! [A_27a: del,V0b: tp__ty_2Enum_2Enum,V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bit @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ V1w ) )
<=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( 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 ) ) ) ) ) )
& ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V1w ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__reverse__def,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Eword__reverse @ A_27a ) @ V0w )
= ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a )
@ ( 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 ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__modify__def,axiom,
! [A_27a: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ( arr @ bool @ bool ) ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__modify @ A_27a ) @ V0f ) @ V1w )
= ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2i: $i] : ( ap @ ( ap @ V0f @ V2i ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V1w ) @ V2i ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EBIT__SET__ind,axiom,
! [V0P: $i] :
( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) )
=> ( ! [V1i: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
( ( ( ( ( V2n != fo__c_2Enum_2E0 )
& ( p @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
=> ( p @ ( ap @ ( ap @ V0P @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1i ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( ( ( V2n != fo__c_2Enum_2E0 )
& ~ ( p @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
=> ( p @ ( ap @ ( ap @ V0P @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1i ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
=> ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
=> ! [V3v: tp__ty_2Enum_2Enum,V4v1: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V3v ) ) @ ( inj__ty_2Enum_2Enum @ V4v1 ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EBIT__SET__def,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1i: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ c_2Ewords_2EBIT__SET @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( arr @ ty_2Enum_2Enum @ bool ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( c_2Epred__set_2EEMPTY @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( arr @ ty_2Enum_2Enum @ bool ) ) @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( ap @ ( ap @ c_2Ewords_2EBIT__SET @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1i ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ ( ap @ c_2Ewords_2EBIT__SET @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1i ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Ebit__field__insert__def,axiom,
! [A_27a: del,A_27b: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2a: $i] :
( ( mem @ V2a @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Ebit__field__insert @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V2a )
= ( ap @ ( c_2Ewords_2Eword__modify @ A_27a )
@ ( 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_2Efcp_2Efcp__index @ bool @ A_27b ) @ V2a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ V3i ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__sign__extend__def,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__sign__extend @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1w )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2ESIGN__EXTEND @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1w ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__len__def,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Eword__len @ A_27a ) @ V0w ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Ebit__count__upto__def,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Ewords_2Ebit__count__upto @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1w ) )
= ( surj__ty_2Enum_2Enum
@ ( ap @ ( ap @ c_2Esum__num_2ESUM @ ( inj__ty_2Enum_2Enum @ V0n ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2i: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V1w ) @ V2i ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Ebit__count__def,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Ebit__count @ A_27a ) @ V0w ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Ewords_2Ebit__count__upto @ A_27a ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ V0w ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__2comp__def,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0w )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0w ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__add__def,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0v ) @ V1w )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0v ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1w ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__mul__def,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V0v ) @ V1w )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0v ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1w ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__log2__def,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Eword__log2 @ A_27a ) @ V0w )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Ebit_2ELOG2 @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0w ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eadd__with__carry__def,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1y: $i] :
( ( mem @ V1y @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2carry__in: $i] :
( ( mem @ V2carry__in @ bool )
=> ( ( ap @ ( c_2Ewords_2Eadd__with__carry @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Epair_2Eprod @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool ) ) @ V0x ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool ) @ V1y ) @ V2carry__in ) ) )
= ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Epair_2Eprod @ bool @ bool ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3unsigned__sum: $i] :
( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Epair_2Eprod @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Epair_2Eprod @ bool @ bool ) ) )
@ ( lam @ ( ty_2Efcp_2Ecart @ bool @ A_27a )
@ ^ [V4result: $i] :
( ap
@ ( ap @ ( c_2Ebool_2ELET @ bool @ ( ty_2Epair_2Eprod @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Epair_2Eprod @ bool @ bool ) ) )
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ bool @ ( arr @ bool @ ( ty_2Epair_2Eprod @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Epair_2Eprod @ bool @ bool ) ) ) )
@ ( lam @ bool
@ ^ [V5carry__out: $i] :
( lam @ bool
@ ^ [V6overflow: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Epair_2Eprod @ bool @ bool ) ) @ V4result ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ bool @ bool ) @ V5carry__out ) @ V6overflow ) ) ) ) )
@ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V4result ) ) @ V3unsigned__sum ) ) ) )
@ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0x ) ) @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V1y ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0x ) ) @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V4result ) ) ) ) ) ) )
@ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ V3unsigned__sum ) ) ) )
@ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0x ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1y ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ V2carry__in ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__sub__def,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0v ) @ V1w )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0v ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V1w ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__div__def,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__div @ A_27a ) @ V0v ) @ V1w )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0v ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1w ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__mod__def,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__mod @ A_27a ) @ V0v ) @ V1w )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0v ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1w ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__quot__def,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__quot @ A_27a ) @ V0a ) @ V1b )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0a ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V1b ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__div @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V1b ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__div @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0a ) ) @ V1b ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V1b ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__div @ A_27a ) @ V0a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V1b ) ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__div @ A_27a ) @ V0a ) @ V1b ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__rem__def,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__rem @ A_27a ) @ V0a ) @ V1b )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0a ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V1b ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mod @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V1b ) ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mod @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0a ) ) @ V1b ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V1b ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mod @ A_27a ) @ V0a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V1b ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mod @ A_27a ) @ V0a ) @ V1b ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__L2__def,axiom,
! [A_27a: del] :
( ( c_2Ewords_2Eword__L2 @ A_27a )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) ) ).
thf(ax_thm_2Ewords_2Enzcv__def,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( surj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o @ ( ap @ ( ap @ ( c_2Ewords_2Enzcv @ A_27a ) @ V0a ) @ V1b ) )
= ( surj__c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_c_ty_2Epair_2Eprod_o_o
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2q: $i] :
( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) ) ) )
@ ( lam @ ( ty_2Efcp_2Ecart @ bool @ A_27a )
@ ^ [V3r: $i] : ( ap @ ( ap @ ( c_2Epair_2E_2C @ bool @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) ) ) @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V3r ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ V3r ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ bool @ bool ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ V2q ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ V1b ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V1b ) ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V3r ) ) @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0a ) ) ) ) ) ) ) ) )
@ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ V2q ) ) ) )
@ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V1b ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__lt__def,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V0a ) @ V1b ) )
<=> ( p
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) ) ) @ bool )
@ ( ap @ ( c_2Epair_2EUNCURRY @ bool @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) ) @ bool )
@ ( lam @ bool
@ ^ [V2n: $i] :
( ap @ ( c_2Epair_2EUNCURRY @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) @ bool )
@ ( lam @ bool
@ ^ [V3z: $i] :
( ap @ ( c_2Epair_2EUNCURRY @ bool @ bool @ bool )
@ ( lam @ bool
@ ^ [V4c: $i] :
( lam @ bool
@ ^ [V5v: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ V2n ) @ V5v ) ) ) ) ) ) ) ) ) )
@ ( ap @ ( ap @ ( c_2Ewords_2Enzcv @ A_27a ) @ V0a ) @ V1b ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__gt__def,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__gt @ A_27a ) @ V0a ) @ V1b ) )
<=> ( p
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) ) ) @ bool )
@ ( ap @ ( c_2Epair_2EUNCURRY @ bool @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) ) @ bool )
@ ( lam @ bool
@ ^ [V2n: $i] :
( ap @ ( c_2Epair_2EUNCURRY @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) @ bool )
@ ( lam @ bool
@ ^ [V3z: $i] :
( ap @ ( c_2Epair_2EUNCURRY @ bool @ bool @ bool )
@ ( lam @ bool
@ ^ [V4c: $i] :
( lam @ bool
@ ^ [V5v: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ V3z ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ V2n ) @ V5v ) ) ) ) ) ) ) ) ) )
@ ( ap @ ( ap @ ( c_2Ewords_2Enzcv @ A_27a ) @ V0a ) @ V1b ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__le__def,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ V0a ) @ V1b ) )
<=> ( p
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) ) ) @ bool )
@ ( ap @ ( c_2Epair_2EUNCURRY @ bool @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) ) @ bool )
@ ( lam @ bool
@ ^ [V2n: $i] :
( ap @ ( c_2Epair_2EUNCURRY @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) @ bool )
@ ( lam @ bool
@ ^ [V3z: $i] :
( ap @ ( c_2Epair_2EUNCURRY @ bool @ bool @ bool )
@ ( lam @ bool
@ ^ [V4c: $i] :
( lam @ bool
@ ^ [V5v: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ V3z ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ V2n ) @ V5v ) ) ) ) ) ) ) ) ) ) )
@ ( ap @ ( ap @ ( c_2Ewords_2Enzcv @ A_27a ) @ V0a ) @ V1b ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__ge__def,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ge @ A_27a ) @ V0a ) @ V1b ) )
<=> ( p
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) ) ) @ bool )
@ ( ap @ ( c_2Epair_2EUNCURRY @ bool @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) ) @ bool )
@ ( lam @ bool
@ ^ [V2n: $i] :
( ap @ ( c_2Epair_2EUNCURRY @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) @ bool )
@ ( lam @ bool
@ ^ [V3z: $i] :
( ap @ ( c_2Epair_2EUNCURRY @ bool @ bool @ bool )
@ ( lam @ bool
@ ^ [V4c: $i] :
( lam @ bool
@ ^ [V5v: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ V2n ) @ V5v ) ) ) ) ) ) ) ) )
@ ( ap @ ( ap @ ( c_2Ewords_2Enzcv @ A_27a ) @ V0a ) @ V1b ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__ls__def,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V0a ) @ V1b ) )
<=> ( p
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) ) ) @ bool )
@ ( ap @ ( c_2Epair_2EUNCURRY @ bool @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) ) @ bool )
@ ( lam @ bool
@ ^ [V2n: $i] :
( ap @ ( c_2Epair_2EUNCURRY @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) @ bool )
@ ( lam @ bool
@ ^ [V3z: $i] :
( ap @ ( c_2Epair_2EUNCURRY @ bool @ bool @ bool )
@ ( lam @ bool
@ ^ [V4c: $i] :
( lam @ bool
@ ^ [V5v: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ c_2Ebool_2E_7E @ V4c ) ) @ V3z ) ) ) ) ) ) ) ) )
@ ( ap @ ( ap @ ( c_2Ewords_2Enzcv @ A_27a ) @ V0a ) @ V1b ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__hi__def,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__hi @ A_27a ) @ V0a ) @ V1b ) )
<=> ( p
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) ) ) @ bool )
@ ( ap @ ( c_2Epair_2EUNCURRY @ bool @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) ) @ bool )
@ ( lam @ bool
@ ^ [V2n: $i] :
( ap @ ( c_2Epair_2EUNCURRY @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) @ bool )
@ ( lam @ bool
@ ^ [V3z: $i] :
( ap @ ( c_2Epair_2EUNCURRY @ bool @ bool @ bool )
@ ( lam @ bool
@ ^ [V4c: $i] :
( lam @ bool
@ ^ [V5v: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ V4c ) @ ( ap @ c_2Ebool_2E_7E @ V3z ) ) ) ) ) ) ) ) ) )
@ ( ap @ ( ap @ ( c_2Ewords_2Enzcv @ A_27a ) @ V0a ) @ V1b ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__lo__def,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V0a ) @ V1b ) )
<=> ( p
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) ) ) @ bool )
@ ( ap @ ( c_2Epair_2EUNCURRY @ bool @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) ) @ bool )
@ ( lam @ bool
@ ^ [V2n: $i] :
( ap @ ( c_2Epair_2EUNCURRY @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) @ bool )
@ ( lam @ bool
@ ^ [V3z: $i] :
( ap @ ( c_2Epair_2EUNCURRY @ bool @ bool @ bool )
@ ( lam @ bool
@ ^ [V4c: $i] :
( lam @ bool
@ ^ [V5v: $i] : ( ap @ c_2Ebool_2E_7E @ V4c ) ) ) ) ) ) ) ) )
@ ( ap @ ( ap @ ( c_2Ewords_2Enzcv @ A_27a ) @ V0a ) @ V1b ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__hs__def,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__hs @ A_27a ) @ V0a ) @ V1b ) )
<=> ( p
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) ) ) @ bool )
@ ( ap @ ( c_2Epair_2EUNCURRY @ bool @ ( ty_2Epair_2Eprod @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) ) @ bool )
@ ( lam @ bool
@ ^ [V2n: $i] :
( ap @ ( c_2Epair_2EUNCURRY @ bool @ ( ty_2Epair_2Eprod @ bool @ bool ) @ bool )
@ ( lam @ bool
@ ^ [V3z: $i] :
( ap @ ( c_2Epair_2EUNCURRY @ bool @ bool @ bool )
@ ( lam @ bool
@ ^ [V4c: $i] :
( lam @ bool
@ ^ [V5v: $i] : V4c ) ) ) ) ) ) ) )
@ ( ap @ ( ap @ ( c_2Ewords_2Enzcv @ A_27a ) @ V0a ) @ V1b ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__min__def,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__min @ A_27a ) @ V0a ) @ V1b )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V0a ) @ V1b ) ) @ V0a ) @ V1b ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__max__def,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__max @ A_27a ) @ V0a ) @ V1b )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V0a ) @ V1b ) ) @ V1b ) @ V0a ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__smin__def,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__smin @ A_27a ) @ V0a ) @ V1b )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V0a ) @ V1b ) ) @ V0a ) @ V1b ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__smax__def,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__smax @ A_27a ) @ V0a ) @ V1b )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V0a ) @ V1b ) ) @ V1b ) @ V0a ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__abs__def,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Eword__abs @ A_27a ) @ V0w )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V0w ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0w ) ) @ V0w ) ) ) ).
thf(ax_thm_2Ewords_2Eword__lsl__def,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1n ) )
= ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2i: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ V2i ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V2i ) ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0w ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ V2i ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__lsr__def,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1n ) )
= ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2i: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V2i ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0w ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V2i ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__asr__def,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__asr @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1n ) )
= ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2i: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V2i ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0w ) ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0w ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V2i ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__ror__def,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__ror @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1n ) )
= ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2i: $i] : ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0w ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V2i ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__rol__def,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__rol @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1n ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__ror @ A_27a ) @ V0w ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__rrx__def,axiom,
! [A_27a: del,V0c: $i] :
( ( mem @ V0c @ bool )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Eword__rrx @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ bool @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ V0c ) @ V1w ) )
= ( ap @ ( ap @ ( c_2Epair_2E_2C @ bool @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( c_2Ewords_2Eword__lsb @ A_27a ) @ V1w ) )
@ ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2i: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V2i ) @ ( 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 ) ) ) ) ) ) @ V0c ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ V1w ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V2i ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__lsl__bv__def,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1n: $i] :
( ( mem @ V1n @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl__bv @ A_27a ) @ V0w ) @ V1n )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ V0w ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1n ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__lsr__bv__def,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1n: $i] :
( ( mem @ V1n @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr__bv @ A_27a ) @ V0w ) @ V1n )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ V0w ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1n ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__asr__bv__def,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1n: $i] :
( ( mem @ V1n @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__asr__bv @ A_27a ) @ V0w ) @ V1n )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__asr @ A_27a ) @ V0w ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1n ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__ror__bv__def,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1n: $i] :
( ( mem @ V1n @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__ror__bv @ A_27a ) @ V0w ) @ V1n )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__ror @ A_27a ) @ V0w ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1n ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__rol__bv__def,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1n: $i] :
( ( mem @ V1n @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__rol__bv @ A_27a ) @ V0w ) @ V1n )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__rol @ A_27a ) @ V0w ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1n ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__join__def,axiom,
! [A_27a: del,A_27b: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__join @ A_27a @ A_27b ) @ V0v ) @ V1w )
= ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Efcp_2Ecart @ bool @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( ty_2Efcp_2Ecart @ bool @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) )
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Efcp_2Ecart @ bool @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( ty_2Efcp_2Ecart @ bool @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) ) )
@ ( lam @ ( ty_2Efcp_2Ecart @ bool @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) )
@ ^ [V2cv: $i] :
( lam @ ( ty_2Efcp_2Ecart @ bool @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) )
@ ^ [V3cw: $i] : ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) @ V2cv ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) @ V3cw ) ) ) )
@ ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) @ V0v ) ) )
@ ( ap @ ( c_2Ewords_2Ew2w @ A_27b @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) @ V1w ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__concat__def,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c ) @ V0v ) @ V1w )
= ( ap @ ( c_2Ewords_2Ew2w @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ A_27c ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__join @ A_27a @ A_27b ) @ V0v ) @ V1w ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Eword__replicate__def,axiom,
! [A_27a: del,A_27b: del,V0n: tp__ty_2Enum_2Enum,V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__replicate @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1w )
= ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2i: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ V2i ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V1w ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ V2i ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Econcat__word__list__def,axiom,
! [A_27a: del,A_27b: del] :
( ( ( ap @ ( c_2Ewords_2Econcat__word__list @ A_27a @ A_27b ) @ ( c_2Elist_2ENIL @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ! [V0h: $i] :
( ( mem @ V0h @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1t: $i] :
( ( mem @ V1t @ ( ty_2Elist_2Elist @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) )
=> ( ( ap @ ( c_2Ewords_2Econcat__word__list @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ V0h ) @ V1t ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27b ) @ ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ V0h ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27b ) @ ( ap @ ( c_2Ewords_2Econcat__word__list @ A_27a @ A_27b ) @ V1t ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Esaturate__n2w__def,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( ap @ ( c_2Ewords_2Esaturate__n2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( c_2Ewords_2Eword__T @ A_27a ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
thf(ax_thm_2Ewords_2Esaturate__w2w__def,axiom,
! [A_27a: del,A_27b: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Esaturate__w2w @ A_27a @ A_27b ) @ V0w )
= ( ap @ ( c_2Ewords_2Esaturate__n2w @ A_27b ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0w ) ) ) ) ).
thf(ax_thm_2Ewords_2Esaturate__add__def,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Esaturate__add @ A_27a ) @ V0a ) @ V1b )
= ( ap @ ( c_2Ewords_2Esaturate__n2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1b ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Esaturate__sub__def,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Esaturate__sub @ A_27a ) @ V0a ) @ V1b )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1b ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2Esaturate__mul__def,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Esaturate__mul @ A_27a ) @ V0a ) @ V1b )
= ( ap @ ( c_2Ewords_2Esaturate__n2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1b ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EZERO__LT__dimword,axiom,
! [A_27a: del] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).
thf(conj_thm_2Ewords_2EDIMINDEX__GT__0,axiom,
! [A_27a: del] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimword__IS__TWICE__INT__MIN,axiom,
! [A_27a: del] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( c_2Ewords_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimword__sub__int__min,axiom,
! [A_27a: del] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Ewords_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).
thf(conj_thm_2Ewords_2EONE__LT__dimword,axiom,
! [A_27a: del] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).
thf(conj_thm_2Ewords_2EEXISTS__HB,axiom,
! [A_27a: del] :
? [V0m: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ).
thf(conj_thm_2Ewords_2EMOD__DIMINDEX,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( 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 @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
thf(conj_thm_2Ewords_2EBITS__ZEROL__DIMINDEX,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( 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 @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
= V0n ) ) ).
thf(conj_thm_2Ewords_2EMOD__2EXP__DIMINDEX,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2EMOD__2EXP @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
thf(conj_thm_2Ewords_2EINT__MIN__SUM,axiom,
! [A_27a: del,A_27b: del] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2EINT__MIN @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( 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 @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Ewords_2EINT__MIN @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) @ ( ap @ ( c_2Ewords_2EINT__MIN @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EZERO__LT__INT__MIN,axiom,
! [A_27a: del] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( c_2Ewords_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).
thf(conj_thm_2Ewords_2EZERO__LT__INT__MAX,axiom,
! [A_27a: del] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( c_2Ewords_2EINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EZERO__LE__INT__MAX,axiom,
! [A_27a: del] : ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( c_2Ewords_2EINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).
thf(conj_thm_2Ewords_2EZERO__LT__UINT__MAX,axiom,
! [A_27a: del] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( c_2Ewords_2EUINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).
thf(conj_thm_2Ewords_2EINT__MIN__LT__DIMWORD,axiom,
! [A_27a: del] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Ewords_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).
thf(conj_thm_2Ewords_2EINT__MAX__LT__DIMWORD,axiom,
! [A_27a: del] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Ewords_2EINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__lt__dimword,axiom,
! [A_27a: del] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).
thf(conj_thm_2Ewords_2EBOUND__ORDER,axiom,
! [A_27a: del] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Ewords_2EINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Ewords_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Ewords_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Ewords_2EUINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Ewords_2EUINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__dimword__iso,axiom,
! [A_27a: del,A_27b: del] :
( ( ( surj__ty_2Enum_2Enum @ ( 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 @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Edimword @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__dimword__le__iso,axiom,
! [A_27a: del,A_27b: del] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__dimword__lt__iso,axiom,
! [A_27a: del,A_27b: del] :
( ( p @ ( 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 ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__int__min__iso,axiom,
! [A_27a: del,A_27b: del] :
( ( ( surj__ty_2Enum_2Enum @ ( 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 @ ( c_2Ewords_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2EINT__MIN @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__int__min__le__iso,axiom,
! [A_27a: del,A_27b: del] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Ewords_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Ewords_2EINT__MIN @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__int__min__lt__iso,axiom,
! [A_27a: del,A_27b: del] :
( ( p @ ( 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 ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Ewords_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Ewords_2EINT__MIN @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__int__max__iso,axiom,
! [A_27a: del,A_27b: del] :
( ( ( surj__ty_2Enum_2Enum @ ( 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 @ ( c_2Ewords_2EINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2EINT__MAX @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__int__max__le__iso,axiom,
! [A_27a: del,A_27b: del] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Ewords_2EINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Ewords_2EINT__MAX @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__int__max__lt__iso,axiom,
! [A_27a: del,A_27b: del] :
( ( p @ ( 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 ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Ewords_2EINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Ewords_2EINT__MAX @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__uint__max__iso,axiom,
! [A_27a: del,A_27b: del] :
( ( ( surj__ty_2Enum_2Enum @ ( 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 @ ( c_2Ewords_2EUINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2EUINT__MAX @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__uint__max__le__iso,axiom,
! [A_27a: del,A_27b: del] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Ewords_2EUINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Ewords_2EUINT__MAX @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__uint__max__lt__iso,axiom,
! [A_27a: del,A_27b: del] :
( ( p @ ( 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 ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Ewords_2EUINT__MAX @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Ewords_2EUINT__MAX @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Ew2n__n2w,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(conj_thm_2Ewords_2En2w__w2n,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0w ) )
= V0w ) ) ).
thf(conj_thm_2Ewords_2Eword__nchotomy,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ? [V1n: tp__ty_2Enum_2Enum] :
( V0w
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
thf(conj_thm_2Ewords_2En2w__mod,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ).
thf(conj_thm_2Ewords_2En2w__11,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
( ( ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
<=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eranged__word__nchotomy,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ? [V1n: tp__ty_2Enum_2Enum] :
( ( V0w
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__1__cases,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
=> ( ( V0a
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
| ( V0a
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Emod__dimindex,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__INDUCT,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool ) )
=> ( ( ( p @ ( ap @ V0P @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
& ! [V1n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
=> ( ( p @ ( ap @ V0P @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
=> ( p @ ( ap @ V0P @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( p @ ( ap @ V0P @ V2x ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Ew2n__11,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0v ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1w ) ) )
<=> ( V0v = V1w ) ) ) ) ).
thf(conj_thm_2Ewords_2Ew2n__lt,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0w ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__0__n2w,axiom,
! [A_27a: del] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
= fo__c_2Enum_2E0 ) ).
thf(conj_thm_2Ewords_2Eword__1__n2w,axiom,
! [A_27a: del] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Ew2n__eq__0,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0w ) )
= fo__c_2Enum_2E0 )
<=> ( V0w
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
thf(conj_thm_2Ewords_2En2w__dimword,axiom,
! [A_27a: del] :
( ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ).
thf(conj_thm_2Ewords_2Eword__2comp__dimindex__1,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
=> ( ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0w )
= V0w ) ) ) ).
thf(conj_thm_2Ewords_2Eword__add__n2w,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__mul__n2w,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__log2__n2w,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( ap @ ( c_2Ewords_2Eword__log2 @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Ebit_2ELOG2 @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__1comp__n2w,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__2comp__n2w,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__lsb,axiom,
! [A_27a: del] :
( ( c_2Ewords_2Eword__lsb @ A_27a )
= ( ap @ ( c_2Ewords_2Eword__bit @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ).
thf(conj_thm_2Ewords_2Eword__msb,axiom,
! [A_27a: del] :
( ( c_2Ewords_2Eword__msb @ A_27a )
= ( ap @ ( c_2Ewords_2Eword__bit @ A_27a ) @ ( 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 ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__lsb__n2w,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( c_2Ewords_2Eword__lsb @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
<=> ( p @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__msb__n2w,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( 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 @ V0n ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__msb__n2w__numeric,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Ewords_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__and__n2w,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ c_2Ebool_2E_2F_5C ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__or__n2w,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ c_2Ebool_2E_5C_2F ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__xor__n2w,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a )
@ ( ap
@ ( ap
@ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
@ ( lam @ bool
@ ^ [V2x: $i] :
( lam @ bool
@ ^ [V3y: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ V2x ) @ V3y ) ) ) ) )
@ ( inj__ty_2Enum_2Enum @ V0n ) )
@ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__nand__n2w,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__nand @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a )
@ ( ap
@ ( ap
@ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
@ ( lam @ bool
@ ^ [V2x: $i] :
( lam @ bool
@ ^ [V3y: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ V2x ) @ V3y ) ) ) ) )
@ ( inj__ty_2Enum_2Enum @ V0n ) )
@ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__nor__n2w,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__nor @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a )
@ ( ap
@ ( ap
@ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
@ ( lam @ bool
@ ^ [V2x: $i] :
( lam @ bool
@ ^ [V3y: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ V2x ) @ V3y ) ) ) ) )
@ ( inj__ty_2Enum_2Enum @ V0n ) )
@ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__xnor__n2w,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__xnor @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( c_2Emin_2E_3D @ bool ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ).
thf(conj_thm_2Ewords_2El2w__w2l,axiom,
! [A_27a: del,V0b: tp__ty_2Enum_2Enum,V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2El2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Ew2l @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ V1w ) )
= V1w ) ) ) ).
thf(conj_thm_2Ewords_2Ew2l__l2w,axiom,
! [A_27a: del,V0b: tp__ty_2Enum_2Enum,V1l: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
( ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Ewords_2Ew2l @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( ap @ ( ap @ ( c_2Ewords_2El2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) ) )
= ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumposrep_2En2l @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Es2w__w2s,axiom,
! [A_27a: del,V0c2n: $i] :
( ( mem @ V0c2n @ ( arr @ ty_2Estring_2Echar @ ty_2Enum_2Enum ) )
=> ! [V1n2c: $i] :
( ( mem @ V1n2c @ ( arr @ ty_2Enum_2Enum @ ty_2Estring_2Echar ) )
=> ! [V2b: tp__ty_2Enum_2Enum,V3w: $i] :
( ( mem @ V3w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) )
& ! [V4x: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V4x ) ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ V0c2n @ ( ap @ V1n2c @ ( inj__ty_2Enum_2Enum @ V4x ) ) ) )
= V4x ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Es2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) @ V0c2n ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Ew2s @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2b ) ) @ V1n2c ) @ V3w ) )
= V3w ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Ew2s__s2w,axiom,
! [A_27a: del,V0b: tp__ty_2Enum_2Enum,V1c2n: $i] :
( ( mem @ V1c2n @ ( arr @ ty_2Estring_2Echar @ ty_2Enum_2Enum ) )
=> ! [V2n2c: $i] :
( ( mem @ V2n2c @ ( arr @ ty_2Enum_2Enum @ ty_2Estring_2Echar ) )
=> ! [V3s: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar] :
( ( surj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Ew2s @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ V2n2c ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Es2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ V1c2n ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V3s ) ) ) )
= ( surj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ ( ap @ ( ap @ ( ap @ c_2EASCIInumbers_2En2s @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ V2n2c ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ ( ap @ c_2EASCIInumbers_2Es2n @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ V1c2n ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V3s ) ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2ENUMERAL__LESS__THM,axiom,
( ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) )
<=> ( ( V0m
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
& ! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) )
<=> ( ( V2m
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) )
| ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__bin__list,axiom,
! [A_27a: del] :
( ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) ) @ ( c_2Ewords_2Eword__from__bin__list @ A_27a ) ) @ ( c_2Ewords_2Eword__to__bin__list @ A_27a ) )
= ( c_2Ecombin_2EI @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ).
thf(conj_thm_2Ewords_2Eword__oct__list,axiom,
! [A_27a: del] :
( ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) ) @ ( c_2Ewords_2Eword__from__oct__list @ A_27a ) ) @ ( c_2Ewords_2Eword__to__oct__list @ A_27a ) )
= ( c_2Ecombin_2EI @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ).
thf(conj_thm_2Ewords_2Eword__dec__list,axiom,
! [A_27a: del] :
( ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) ) @ ( c_2Ewords_2Eword__from__dec__list @ A_27a ) ) @ ( c_2Ewords_2Eword__to__dec__list @ A_27a ) )
= ( c_2Ecombin_2EI @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ).
thf(conj_thm_2Ewords_2Eword__hex__list,axiom,
! [A_27a: del] :
( ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) ) @ ( c_2Ewords_2Eword__from__hex__list @ A_27a ) ) @ ( c_2Ewords_2Eword__to__hex__list @ A_27a ) )
= ( c_2Ecombin_2EI @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ).
thf(conj_thm_2Ewords_2Eword__bin__string,axiom,
! [A_27a: del] :
( ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) @ ( c_2Ewords_2Eword__from__bin__string @ A_27a ) ) @ ( c_2Ewords_2Eword__to__bin__string @ A_27a ) )
= ( c_2Ecombin_2EI @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ).
thf(conj_thm_2Ewords_2Eword__oct__string,axiom,
! [A_27a: del] :
( ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) @ ( c_2Ewords_2Eword__from__oct__string @ A_27a ) ) @ ( c_2Ewords_2Eword__to__oct__string @ A_27a ) )
= ( c_2Ecombin_2EI @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ).
thf(conj_thm_2Ewords_2Eword__dec__string,axiom,
! [A_27a: del] :
( ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) @ ( c_2Ewords_2Eword__from__dec__string @ A_27a ) ) @ ( c_2Ewords_2Eword__to__dec__string @ A_27a ) )
= ( c_2Ecombin_2EI @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ).
thf(conj_thm_2Ewords_2Eword__hex__string,axiom,
! [A_27a: del] :
( ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) @ ( c_2Ewords_2Eword__from__hex__string @ A_27a ) ) @ ( c_2Ewords_2Eword__to__hex__string @ A_27a ) )
= ( c_2Ecombin_2EI @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ).
thf(conj_thm_2Ewords_2Eword__0,axiom,
! [A_27a: del,V0i: tp__ty_2Enum_2Enum] :
( ( 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_2Efcp_2Efcp__index @ bool @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Enum_2Enum @ V0i ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__eq__0,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( V0w
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> ! [V1i: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
=> ~ ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1i ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__T,axiom,
! [A_27a: del,V0i: tp__ty_2Enum_2Enum] :
( ( 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_2Efcp_2Efcp__index @ bool @ A_27a ) @ ( c_2Ewords_2Eword__T @ A_27a ) ) @ ( inj__ty_2Enum_2Enum @ V0i ) ) ) ) ).
thf(conj_thm_2Ewords_2EFCP__T__F,axiom,
! [A_27a: del,A_27b: del] :
( ( ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a ) @ ( ap @ ( c_2Ecombin_2EK @ bool @ ty_2Enum_2Enum ) @ c_2Ebool_2ET ) )
= ( c_2Ewords_2Eword__T @ A_27a ) )
& ( ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27b ) @ ( ap @ ( c_2Ecombin_2EK @ bool @ ty_2Enum_2Enum ) @ c_2Ebool_2EF ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__L,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( 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_2Efcp_2Efcp__index @ bool @ A_27a ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
<=> ( V0n
= ( surj__ty_2Enum_2Enum @ ( 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 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__H,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( 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_2Efcp_2Efcp__index @ bool @ A_27a ) @ ( c_2Ewords_2Eword__H @ A_27a ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( 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 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__L2,axiom,
! [A_27a: del] :
( ( c_2Ewords_2Eword__L2 @ A_27a )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__NEG__1,axiom,
! [A_27a: del] :
( ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
= ( c_2Ewords_2Eword__T @ A_27a ) ) ).
thf(conj_thm_2Ewords_2EWORD__NEG__1__T,axiom,
! [A_27a: del,V0i: tp__ty_2Enum_2Enum] :
( ( 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_2Efcp_2Efcp__index @ bool @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0i ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__MSB__1COMP,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ V0w ) ) )
<=> ~ ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0w ) ) ) ) ).
thf(conj_thm_2Ewords_2Ew2n__minus1,axiom,
! [A_27a: del] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Ew2n__plus1,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0a ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ V0a ) @ ( c_2Ewords_2Eword__T @ A_27a ) ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__NOT__NOT,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ V0a ) )
= V0a ) ) ).
thf(conj_thm_2Ewords_2EWORD__DE__MORGAN__THM,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0a ) @ V1b ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ V1b ) ) )
& ( ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ V0a ) @ V1b ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ V1b ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__NOT__XOR,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ V1b ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ V0a ) @ V1b ) )
& ( ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ V0a ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ V1b ) )
= ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ V0a ) @ V1b ) ) )
& ( ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ V0a ) ) @ V1b )
= ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ V0a ) @ V1b ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__AND__CLAUSES,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ ( c_2Ewords_2Eword__T @ A_27a ) ) @ V0a )
= V0a )
& ( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0a ) @ ( c_2Ewords_2Eword__T @ A_27a ) )
= V0a )
& ( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V0a )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0a ) @ V0a )
= V0a ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__OR__CLAUSES,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ ( c_2Ewords_2Eword__T @ A_27a ) ) @ V0a )
= ( c_2Ewords_2Eword__T @ A_27a ) )
& ( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ V0a ) @ ( c_2Ewords_2Eword__T @ A_27a ) )
= ( c_2Ewords_2Eword__T @ A_27a ) )
& ( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V0a )
= V0a )
& ( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ V0a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= V0a )
& ( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ V0a ) @ V0a )
= V0a ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__XOR__CLAUSES,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ ( c_2Ewords_2Eword__T @ A_27a ) ) @ V0a )
= ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ V0a ) )
& ( ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ V0a ) @ ( c_2Ewords_2Eword__T @ A_27a ) )
= ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ V0a ) )
& ( ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V0a )
= V0a )
& ( ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ V0a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= V0a )
& ( ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ V0a ) @ V0a )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__AND__ASSOC,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0a ) @ V1b ) ) @ V2c )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V1b ) @ V2c ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__OR__ASSOC,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ V0a ) @ V1b ) ) @ V2c )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ V0a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ V1b ) @ V2c ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__XOR__ASSOC,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ V0a ) @ V1b ) ) @ V2c )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ V0a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ V1b ) @ V2c ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__AND__COMM,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0a ) @ V1b )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V1b ) @ V0a ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__OR__COMM,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ V0a ) @ V1b )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ V1b ) @ V0a ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__XOR__COMM,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ V0a ) @ V1b )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ V1b ) @ V0a ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__AND__IDEM,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0a ) @ V0a )
= V0a ) ) ).
thf(conj_thm_2Ewords_2EWORD__OR__IDEM,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ V0a ) @ V0a )
= V0a ) ) ).
thf(conj_thm_2Ewords_2EWORD__AND__ABSORD,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ V0a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0a ) @ V1b ) )
= V0a ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__OR__ABSORB,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ V0a ) @ V1b ) )
= V0a ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__AND__COMP,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0a ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ V0a ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__OR__COMP,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ V0a ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ V0a ) )
= ( c_2Ewords_2Eword__T @ A_27a ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__XOR__COMP,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ V0a ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ V0a ) )
= ( c_2Ewords_2Eword__T @ A_27a ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__RIGHT__AND__OVER__OR,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ V0a ) @ V1b ) ) @ V2c )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0a ) @ V2c ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V1b ) @ V2c ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__RIGHT__OR__OVER__AND,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0a ) @ V1b ) ) @ V2c )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ V0a ) @ V2c ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ V1b ) @ V2c ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__RIGHT__AND__OVER__XOR,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ V0a ) @ V1b ) ) @ V2c )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0a ) @ V2c ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V1b ) @ V2c ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LEFT__AND__OVER__OR,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ V1b ) @ V2c ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0a ) @ V1b ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0a ) @ V2c ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LEFT__OR__OVER__AND,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ V0a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V1b ) @ V2c ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ V0a ) @ V1b ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ V0a ) @ V2c ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LEFT__AND__OVER__XOR,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ V1b ) @ V2c ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0a ) @ V1b ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0a ) @ V2c ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__XOR,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ V0a ) @ V1b )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0a ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ V1b ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V1b ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ V0a ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__NAND__NOT__AND,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__nand @ A_27a ) @ V0a ) @ V1b )
= ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0a ) @ V1b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__NOR__NOT__OR,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__nor @ A_27a ) @ V0a ) @ V1b )
= ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ V0a ) @ V1b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__XNOR__NOT__XOR,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__xnor @ A_27a ) @ V0a ) @ V1b )
= ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ V0a ) @ V1b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__ADD__OR,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0a ) @ V1b )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0a ) @ V1b )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ V0a ) @ V1b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__ADD__XOR,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0a ) @ V1b )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0a ) @ V1b )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ V0a ) @ V1b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__AND__EXP__SUB1,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__msb__add__word__L,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0a ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) ) )
<=> ~ ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0a ) ) ) ) ).
thf(conj_thm_2Ewords_2Ew2w,axiom,
! [A_27a: del,A_27b: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1i: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27b ) @ ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ V0w ) ) @ ( inj__ty_2Enum_2Enum @ V1i ) ) )
<=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
& ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1i ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Esw2sw,axiom,
! [A_27a: del,A_27b: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1i: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27b ) @ ( ap @ ( c_2Ewords_2Esw2sw @ A_27a @ A_27b ) @ V0w ) ) @ ( inj__ty_2Enum_2Enum @ V1i ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( 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 @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1i ) ) ) @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0w ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Ew2w__id,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27a ) @ V0w )
= V0w ) ) ).
thf(conj_thm_2Ewords_2Esw2sw__id,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Esw2sw @ A_27a @ A_27a ) @ V0w )
= V0w ) ) ).
thf(conj_thm_2Ewords_2Ew2w__w2w,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Ew2w @ A_27b @ A_27c ) @ ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ V0w ) )
= ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27c ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0w ) ) ) ) ).
thf(conj_thm_2Ewords_2Esw2sw__sw2sw,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Esw2sw @ A_27b @ A_27c ) @ ( ap @ ( c_2Ewords_2Esw2sw @ A_27a @ A_27b ) @ V0w ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27c ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( 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 @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27c ) @ ( c_2Ebool_2Ethe__value @ A_27c ) ) ) ) ) @ ( ap @ ( c_2Ewords_2Esw2sw @ A_27b @ A_27c ) @ ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ V0w ) ) ) @ ( ap @ ( c_2Ewords_2Esw2sw @ A_27a @ A_27c ) @ V0w ) ) ) ) ).
thf(conj_thm_2Ewords_2Esw2sw__w2w,axiom,
! [A_27a: del,A_27b: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Esw2sw @ A_27a @ A_27b ) @ V0w )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) ) @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0w ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27b ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27b ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ V0w ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__bit,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bit @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ V0w ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__slice__n2w,axiom,
! [A_27a: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__slice @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2ESLICE @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( 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 @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__bits__n2w,axiom,
! [A_27a: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( 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 @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__bit__n2w,axiom,
! [A_27a: del,V0b: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bit @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
<=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( 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 ) ) ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__signed__bits__n2w,axiom,
! [A_27a: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__signed__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2ESIGN__EXTEND @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( 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 @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__sign__extend__bits,axiom,
! [A_27a: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2w: $i] :
( ( mem @ V2w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__signed__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V2w )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__sign__extend @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V2w ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__index__n2w,axiom,
! [A_27a: del,V0index_20too_20large: $i] :
( ( mem @ V0index_20too_20large @ bool )
=> ! [V1n: tp__ty_2Enum_2Enum,V2i: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( 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_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V2i ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( 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_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2i ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__index,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1i: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1i ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__bits__w2w,axiom,
! [A_27a: del,A_27b: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1h: tp__ty_2Enum_2Enum,V2l: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V1h ) ) @ ( inj__ty_2Enum_2Enum @ V2l ) ) @ ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ V0w ) )
= ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V1h ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2l ) ) @ V0w ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__reverse__n2w,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( ap @ ( c_2Ewords_2Eword__reverse @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Ebit_2EBIT__REVERSE @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__modify__n2w,axiom,
! [A_27a: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ( arr @ bool @ bool ) ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__modify @ A_27a ) @ V0f ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBIT__MODIFY @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ V0f ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Efcp__n2w,axiom,
! [A_27a: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a ) @ V0f )
= ( ap
@ ( ap @ ( c_2Ewords_2Eword__modify @ A_27a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V1i: $i] :
( lam @ bool
@ ^ [V2b: $i] : ( ap @ V0f @ V1i ) ) ) )
@ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Ew2n__w2w,axiom,
! [A_27a: del,A_27b: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Ew2n @ A_27b ) @ ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ V0w ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0w ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0w ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Ew2n__w2w__le,axiom,
! [A_27a: del,A_27b: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Ewords_2Ew2n @ A_27b ) @ ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ V0w ) ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0w ) ) ) ) ).
thf(conj_thm_2Ewords_2Ew2w__lt,axiom,
! [A_27a: del,A_27b: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Ewords_2Ew2n @ A_27b ) @ ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ V0w ) ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Ew2w__n2w,axiom,
! [A_27a: del,A_27b: del,V0n: tp__ty_2Enum_2Enum] :
( ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( 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 @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Ew2w__0,axiom,
! [A_27a: del,A_27b: del] :
( ( ap @ ( c_2Ewords_2Ew2w @ A_27b @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ).
thf(conj_thm_2Ewords_2Ew2n__11__lift,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) )
=> ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27c ) @ ( c_2Ebool_2Ethe__value @ A_27c ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27c ) @ ( c_2Ebool_2Ethe__value @ A_27c ) ) ) ) )
=> ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0a ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Ew2n @ A_27b ) @ V1b ) ) )
<=> ( ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27c ) @ V0a )
= ( ap @ ( c_2Ewords_2Ew2w @ A_27b @ A_27c ) @ V1b ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__extract__n2w,axiom,
! [A_27a: del,A_27b: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( 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 @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( 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 ) ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( 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 @ V1l ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ).
thf(conj_thm_2Ewords_2En2w__BITS,axiom,
! [A_27a: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
=> ( ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__extract__w2w,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1h: tp__ty_2Enum_2Enum,V2l: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27b @ A_27c ) @ ( inj__ty_2Enum_2Enum @ V1h ) ) @ ( inj__ty_2Enum_2Enum @ V2l ) ) @ ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ V0w ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27c ) @ ( inj__ty_2Enum_2Enum @ V1h ) ) @ ( inj__ty_2Enum_2Enum @ V2l ) ) @ V0w ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__w2w__EXTRACT,axiom,
! [A_27a: del,A_27b: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ V0w )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( 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 @ fo__c_2Enum_2E0 ) ) @ V0w ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__EQ,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ! [V2x: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2x ) ) @ ( 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 @ V2x ) ) @ V0v ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bit @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2x ) ) @ V1w ) ) ) )
<=> ( V0v = V1w ) ) ) ) ).
thf(conj_thm_2Ewords_2EBIT__UPDATE,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1x: $i] :
( ( mem @ V1x @ bool )
=> ( ( ap @ ( ap @ ( c_2Efcp_2E_3A_2B @ bool @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1x )
= ( ap @ ( c_2Ewords_2Eword__modify @ A_27a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2i: $i] :
( lam @ bool
@ ^ [V3b: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V2i ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ V1x ) @ V3b ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__MODIFY__BIT,axiom,
! [A_27a: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ ty_2Enum_2Enum @ ( arr @ bool @ bool ) ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2i: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2i ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__modify @ A_27a ) @ V0f ) @ V1w ) ) @ ( inj__ty_2Enum_2Enum @ V2i ) ) )
<=> ( p @ ( ap @ ( ap @ V0f @ ( inj__ty_2Enum_2Enum @ V2i ) ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V1w ) @ ( inj__ty_2Enum_2Enum @ V2i ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__BIT__BITS,axiom,
! [A_27a: del,V0b: tp__ty_2Enum_2Enum,V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bit @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ V1w ) )
<=> ( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ V1w )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__BITS__COMP__THM,axiom,
! [A_27a: del,V0h1: tp__ty_2Enum_2Enum,V1l1: tp__ty_2Enum_2Enum,V2h2: tp__ty_2Enum_2Enum,V3l2: tp__ty_2Enum_2Enum,V4w: $i] :
( ( mem @ V4w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2h2 ) ) @ ( inj__ty_2Enum_2Enum @ V3l2 ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h1 ) ) @ ( inj__ty_2Enum_2Enum @ V1l1 ) ) @ V4w ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V0h1 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2h2 ) ) @ ( inj__ty_2Enum_2Enum @ V1l1 ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3l2 ) ) @ ( inj__ty_2Enum_2Enum @ V1l1 ) ) ) @ V4w ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__BITS__EXTRACT,axiom,
! [A_27a: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2w: $i] :
( ( mem @ V2w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V2w )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V2w ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__BITS__LSR,axiom,
! [A_27a: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2w: $i] :
( ( mem @ V2w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V3n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V2w ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ V2w ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__BITS__ZERO,axiom,
! [A_27a: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2w: $i] :
( ( mem @ V2w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V2w )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__BITS__ZERO2,axiom,
! [A_27a: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__BITS__ZERO3,axiom,
! [A_27a: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2w: $i] :
( ( mem @ V2w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V2w )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__BITS__LT,axiom,
! [A_27a: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2w: $i] :
( ( mem @ V2w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V2w ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__EXTRACT__LT,axiom,
! [A_27a: del,A_27b: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2w: $i] :
( ( mem @ V2w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Ewords_2Ew2n @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V2w ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__EXTRACT__ZERO,axiom,
! [A_27a: del,A_27b: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2w: $i] :
( ( mem @ V2w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V2w )
= ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__EXTRACT__ZERO2,axiom,
! [A_27a: del,A_27b: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27b @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__EXTRACT__ZERO3,axiom,
! [A_27a: del,A_27b: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2w: $i] :
( ( mem @ V2w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V2w )
= ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__SLICE__THM,axiom,
! [A_27a: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2w: $i] :
( ( mem @ V2w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__slice @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V2w )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V2w ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__SLICE__ZERO,axiom,
! [A_27a: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2w: $i] :
( ( mem @ V2w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__slice @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V2w )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__SLICE__ZERO2,axiom,
! [A_27a: del,V0l: tp__ty_2Enum_2Enum,V1h: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__slice @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1h ) ) @ ( inj__ty_2Enum_2Enum @ V0l ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__SLICE__BITS__THM,axiom,
! [A_27a: del,V0h: tp__ty_2Enum_2Enum,V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__slice @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V1w )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V1w ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__BITS__SLICE__THM,axiom,
! [A_27a: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2w: $i] :
( ( mem @ V2w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__slice @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V2w ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V2w ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__SLICE__COMP__THM,axiom,
! [A_27a: del,V0h: tp__ty_2Enum_2Enum,V1m_27: tp__ty_2Enum_2Enum,V2m: tp__ty_2Enum_2Enum,V3l: tp__ty_2Enum_2Enum,V4w: $i] :
( ( mem @ V4w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3l ) ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) )
& ( V1m_27
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__slice @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1m_27 ) ) @ V4w ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__slice @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3l ) ) @ V4w ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__slice @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V3l ) ) @ V4w ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__EXTRACT__COMP__THM,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27c ) )
=> ! [V1h: tp__ty_2Enum_2Enum,V2l: tp__ty_2Enum_2Enum,V3m: tp__ty_2Enum_2Enum,V4n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27b @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1h ) ) @ ( inj__ty_2Enum_2Enum @ V2l ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27c @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V3m ) ) @ ( inj__ty_2Enum_2Enum @ V4n ) ) @ V0w ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27c @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V3m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1h ) ) @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27c ) @ ( c_2Ebool_2Ethe__value @ A_27c ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2l ) ) @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) @ V0w ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__EXTRACT__BITS__COMP,axiom,
! [A_27a: del,A_27b: del,V0n: $i] :
( ( mem @ V0n @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1l: tp__ty_2Enum_2Enum,V2k: tp__ty_2Enum_2Enum,V3j: tp__ty_2Enum_2Enum,V4h: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V3j ) ) @ ( inj__ty_2Enum_2Enum @ V2k ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V4h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V0n ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V4h ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3j ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2k ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) @ V0n ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__ALL__BITS,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1h: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( 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 @ V1h ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0w )
= V0w ) ) ) ).
thf(conj_thm_2Ewords_2EEXTRACT__ALL__BITS,axiom,
! [A_27a: del,A_27b: del,V0h: tp__ty_2Enum_2Enum,V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( 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 @ V0h ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V1w )
= ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ V1w ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__BITS__MIN__HIGH,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1h: tp__ty_2Enum_2Enum,V2l: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( 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 @ V1h ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1h ) ) @ ( inj__ty_2Enum_2Enum @ V2l ) ) @ V0w )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( 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 @ V2l ) ) @ V0w ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__EXTRACT__MIN__HIGH,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2w: $i] :
( ( mem @ V2w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V2w )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( 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 @ V1l ) ) @ V2w ) ) ) )
& ! [V3h: tp__ty_2Enum_2Enum,V4l: tp__ty_2Enum_2Enum,V5w: $i] :
( ( mem @ V5w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( inj__ty_2Enum_2Enum @ V4l ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( inj__ty_2Enum_2Enum @ V4l ) ) ) @ ( inj__ty_2Enum_2Enum @ V3h ) ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V3h ) ) @ ( inj__ty_2Enum_2Enum @ V4l ) ) @ V5w )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( inj__ty_2Enum_2Enum @ V4l ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V4l ) ) @ V5w ) ) ) ) ) ).
thf(conj_thm_2Ewords_2ECONCAT__EXTRACT,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0h: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2l: tp__ty_2Enum_2Enum,V3w: $i] :
( ( mem @ V3w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
= ( 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 @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2l ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ A_27c ) @ ( c_2Ebool_2Ethe__value @ A_27c ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2l ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ A_27d ) @ ( c_2Ebool_2Ethe__value @ A_27d ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ ( ty_2Esum_2Esum @ A_27b @ A_27c ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Esum_2Esum @ A_27b @ A_27c ) ) ) )
!= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__concat @ A_27b @ A_27c @ A_27d ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V3w ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27c ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2l ) ) @ V3w ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27d ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V2l ) ) @ V3w ) ) ) ) ).
thf(conj_thm_2Ewords_2EEXTRACT__CONCAT,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) )
=> ( ( ( 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 ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( 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 @ ( c_2Efcp_2Edimindex @ A_27c ) @ ( c_2Ebool_2Ethe__value @ A_27c ) ) ) ) )
=> ( ( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27c @ A_27b ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c ) @ V0v ) @ V1w ) )
= V1w )
& ( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27c @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( 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 @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c ) @ V0v ) @ V1w ) )
= V0v ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EEXTRACT__JOIN,axiom,
! [A_27a: del,A_27b: del,V0h: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2m_27: tp__ty_2Enum_2Enum,V3l: tp__ty_2Enum_2Enum,V4s: tp__ty_2Enum_2Enum,V5w: $i] :
( ( mem @ V5w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3l ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2m_27 ) ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) )
& ( V2m_27
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
& ( V4s
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2m_27 ) ) @ ( inj__ty_2Enum_2Enum @ V3l ) ) ) ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27b ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V2m_27 ) ) @ V5w ) ) @ ( inj__ty_2Enum_2Enum @ V4s ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V3l ) ) @ V5w ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( inj__ty_2Enum_2Enum @ V3l ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( 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 @ V3l ) ) @ V5w ) ) ) ) ).
thf(conj_thm_2Ewords_2EEXTRACT__JOIN__ADD,axiom,
! [A_27a: del,A_27b: del,V0h: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2m_27: tp__ty_2Enum_2Enum,V3l: tp__ty_2Enum_2Enum,V4s: tp__ty_2Enum_2Enum,V5w: $i] :
( ( mem @ V5w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3l ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2m_27 ) ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) )
& ( V2m_27
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
& ( V4s
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2m_27 ) ) @ ( inj__ty_2Enum_2Enum @ V3l ) ) ) ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27b ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V2m_27 ) ) @ V5w ) ) @ ( inj__ty_2Enum_2Enum @ V4s ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V3l ) ) @ V5w ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( inj__ty_2Enum_2Enum @ V3l ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( 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 @ V3l ) ) @ V5w ) ) ) ) ).
thf(conj_thm_2Ewords_2EEXTEND__EXTRACT,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2w: $i] :
( ( mem @ V2w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ A_27c ) @ ( c_2Ebool_2Ethe__value @ A_27c ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V2w )
= ( ap @ ( c_2Ewords_2Ew2w @ A_27c @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27c ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V2w ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__SLICE__OVER__BITWISE,axiom,
! [A_27a: del] :
( ! [V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2v: $i] :
( ( mem @ V2v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V3w: $i] :
( ( mem @ V3w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__slice @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V2v ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__slice @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V3w ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__slice @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V2v ) @ V3w ) ) ) ) )
& ! [V4h: tp__ty_2Enum_2Enum,V5l: tp__ty_2Enum_2Enum,V6v: $i] :
( ( mem @ V6v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V7w: $i] :
( ( mem @ V7w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__slice @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V4h ) ) @ ( inj__ty_2Enum_2Enum @ V5l ) ) @ V6v ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__slice @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V4h ) ) @ ( inj__ty_2Enum_2Enum @ V5l ) ) @ V7w ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__slice @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V4h ) ) @ ( inj__ty_2Enum_2Enum @ V5l ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ V6v ) @ V7w ) ) ) ) )
& ! [V8h: tp__ty_2Enum_2Enum,V9l: tp__ty_2Enum_2Enum,V10v: $i] :
( ( mem @ V10v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V11w: $i] :
( ( mem @ V11w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__slice @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V8h ) ) @ ( inj__ty_2Enum_2Enum @ V9l ) ) @ V10v ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__slice @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V8h ) ) @ ( inj__ty_2Enum_2Enum @ V9l ) ) @ V11w ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__slice @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V8h ) ) @ ( inj__ty_2Enum_2Enum @ V9l ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ V10v ) @ V11w ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__BITS__OVER__BITWISE,axiom,
! [A_27a: del] :
( ! [V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2v: $i] :
( ( mem @ V2v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V3w: $i] :
( ( mem @ V3w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V2v ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V3w ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V2v ) @ V3w ) ) ) ) )
& ! [V4h: tp__ty_2Enum_2Enum,V5l: tp__ty_2Enum_2Enum,V6v: $i] :
( ( mem @ V6v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V7w: $i] :
( ( mem @ V7w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V4h ) ) @ ( inj__ty_2Enum_2Enum @ V5l ) ) @ V6v ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V4h ) ) @ ( inj__ty_2Enum_2Enum @ V5l ) ) @ V7w ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V4h ) ) @ ( inj__ty_2Enum_2Enum @ V5l ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ V6v ) @ V7w ) ) ) ) )
& ! [V8h: tp__ty_2Enum_2Enum,V9l: tp__ty_2Enum_2Enum,V10v: $i] :
( ( mem @ V10v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V11w: $i] :
( ( mem @ V11w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V8h ) ) @ ( inj__ty_2Enum_2Enum @ V9l ) ) @ V10v ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V8h ) ) @ ( inj__ty_2Enum_2Enum @ V9l ) ) @ V11w ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V8h ) ) @ ( inj__ty_2Enum_2Enum @ V9l ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ V10v ) @ V11w ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__w2w__OVER__BITWISE,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27b ) @ ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ V0v ) ) @ ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ V1w ) )
= ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0v ) @ V1w ) ) ) ) )
& ! [V2v: $i] :
( ( mem @ V2v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V3w: $i] :
( ( mem @ V3w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27b ) @ ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ V2v ) ) @ ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ V3w ) )
= ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ V2v ) @ V3w ) ) ) ) )
& ! [V4v: $i] :
( ( mem @ V4v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V5w: $i] :
( ( mem @ V5w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27b ) @ ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ V4v ) ) @ ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ V5w ) )
= ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ V4v ) @ V5w ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__EXTRACT__OVER__BITWISE,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del] :
( ! [V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2v: $i] :
( ( mem @ V2v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V3w: $i] :
( ( mem @ V3w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V2v ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V3w ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V2v ) @ V3w ) ) ) ) )
& ! [V4h: tp__ty_2Enum_2Enum,V5l: tp__ty_2Enum_2Enum,V6v: $i] :
( ( mem @ V6v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V7w: $i] :
( ( mem @ V7w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27c ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27c ) @ ( inj__ty_2Enum_2Enum @ V4h ) ) @ ( inj__ty_2Enum_2Enum @ V5l ) ) @ V6v ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27c ) @ ( inj__ty_2Enum_2Enum @ V4h ) ) @ ( inj__ty_2Enum_2Enum @ V5l ) ) @ V7w ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27c ) @ ( inj__ty_2Enum_2Enum @ V4h ) ) @ ( inj__ty_2Enum_2Enum @ V5l ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ V6v ) @ V7w ) ) ) ) )
& ! [V8h: tp__ty_2Enum_2Enum,V9l: tp__ty_2Enum_2Enum,V10v: $i] :
( ( mem @ V10v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V11w: $i] :
( ( mem @ V11w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27d ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27d ) @ ( inj__ty_2Enum_2Enum @ V8h ) ) @ ( inj__ty_2Enum_2Enum @ V9l ) ) @ V10v ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27d ) @ ( inj__ty_2Enum_2Enum @ V8h ) ) @ ( inj__ty_2Enum_2Enum @ V9l ) ) @ V11w ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27d ) @ ( inj__ty_2Enum_2Enum @ V8h ) ) @ ( inj__ty_2Enum_2Enum @ V9l ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ V10v ) @ V11w ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__w2w__OVER__ADD,axiom,
! [A_27a: del,A_27b: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0a ) @ V1b ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27b ) @ ( 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 @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27b ) @ ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ V0a ) ) @ ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ V1b ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__w2w__OVER__MUL,axiom,
! [A_27a: del,A_27b: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V0a ) @ V1b ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27b ) @ ( 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 @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27b ) @ ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ V0a ) ) @ ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ V1b ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__EXTRACT__OVER__ADD,axiom,
! [A_27a: del,A_27b: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2h: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2h ) ) )
& ( 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 @ V2h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0a ) @ V1b ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V2h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0a ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V2h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V1b ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__EXTRACT__OVER__MUL,axiom,
! [A_27a: del,A_27b: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2h: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V2h ) ) )
& ( 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 @ V2h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V0a ) @ V1b ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V2h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0a ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V2h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V1b ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__EXTRACT__OVER__ADD2,axiom,
! [A_27a: del,A_27b: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2h: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2h ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27b @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V2h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V2h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0a ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V2h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V1b ) ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V2h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0a ) @ V1b ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__EXTRACT__OVER__MUL2,axiom,
! [A_27a: del,A_27b: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2h: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2h ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27b @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V2h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V2h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0a ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V2h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V1b ) ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V2h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V0a ) @ V1b ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__EXTRACT__ID,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1h: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0w ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1h ) ) ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0w )
= V0w ) ) ) ).
thf(conj_thm_2Ewords_2EBIT__SET,axiom,
! [V0i: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0i ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0i ) ) @ ( ap @ ( ap @ c_2Ewords_2EBIT__SET @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LITERAL__AND,axiom,
! [A_27a: del] :
( ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( ap @ c_2Ebit_2ELOG2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Ebit_2ELOG2 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) @ c_2Ebool_2E_2F_5C ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
& ! [V2n: tp__ty_2Enum_2Enum,V3m: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V3m ) ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a )
@ ( ap
@ ( ap
@ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Ebit_2ELOG2 @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
@ ( lam @ bool
@ ^ [V4a: $i] :
( lam @ bool
@ ^ [V5b: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ V4a ) @ ( ap @ c_2Ebool_2E_7E @ V5b ) ) ) ) )
@ ( inj__ty_2Enum_2Enum @ V2n ) )
@ ( inj__ty_2Enum_2Enum @ V3m ) ) ) )
& ! [V6n: tp__ty_2Enum_2Enum,V7m: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V7m ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V6n ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a )
@ ( ap
@ ( ap
@ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Ebit_2ELOG2 @ ( inj__ty_2Enum_2Enum @ V6n ) ) ) )
@ ( lam @ bool
@ ^ [V8a: $i] :
( lam @ bool
@ ^ [V9b: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ V8a ) @ ( ap @ c_2Ebool_2E_7E @ V9b ) ) ) ) )
@ ( inj__ty_2Enum_2Enum @ V6n ) )
@ ( inj__ty_2Enum_2Enum @ V7m ) ) ) )
& ! [V10n: tp__ty_2Enum_2Enum,V11m: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V10n ) ) ) ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V11m ) ) ) )
= ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2EMAX @ ( ap @ c_2Ebit_2ELOG2 @ ( inj__ty_2Enum_2Enum @ V10n ) ) ) @ ( ap @ c_2Ebit_2ELOG2 @ ( inj__ty_2Enum_2Enum @ V11m ) ) ) ) ) @ c_2Ebool_2E_5C_2F ) @ ( inj__ty_2Enum_2Enum @ V10n ) ) @ ( inj__ty_2Enum_2Enum @ V11m ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LITERAL__OR,axiom,
! [A_27a: del] :
( ! [V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2EMAX @ ( ap @ c_2Ebit_2ELOG2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Ebit_2ELOG2 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) @ c_2Ebool_2E_5C_2F ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
& ! [V2n: tp__ty_2Enum_2Enum,V3m: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V3m ) ) ) )
= ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a )
@ ( ap @ ( c_2Ewords_2En2w @ A_27a )
@ ( ap
@ ( ap
@ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Ebit_2ELOG2 @ ( inj__ty_2Enum_2Enum @ V3m ) ) ) )
@ ( lam @ bool
@ ^ [V4a: $i] :
( lam @ bool
@ ^ [V5b: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ V4a ) @ ( ap @ c_2Ebool_2E_7E @ V5b ) ) ) ) )
@ ( inj__ty_2Enum_2Enum @ V3m ) )
@ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) )
& ! [V6n: tp__ty_2Enum_2Enum,V7m: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V7m ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V6n ) ) )
= ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a )
@ ( ap @ ( c_2Ewords_2En2w @ A_27a )
@ ( ap
@ ( ap
@ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Ebit_2ELOG2 @ ( inj__ty_2Enum_2Enum @ V7m ) ) ) )
@ ( lam @ bool
@ ^ [V8a: $i] :
( lam @ bool
@ ^ [V9b: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ V8a ) @ ( ap @ c_2Ebool_2E_7E @ V9b ) ) ) ) )
@ ( inj__ty_2Enum_2Enum @ V7m ) )
@ ( inj__ty_2Enum_2Enum @ V6n ) ) ) ) )
& ! [V10n: tp__ty_2Enum_2Enum,V11m: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V10n ) ) ) ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V11m ) ) ) )
= ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( ap @ c_2Ebit_2ELOG2 @ ( inj__ty_2Enum_2Enum @ V10n ) ) ) @ ( ap @ c_2Ebit_2ELOG2 @ ( inj__ty_2Enum_2Enum @ V11m ) ) ) ) ) @ c_2Ebool_2E_2F_5C ) @ ( inj__ty_2Enum_2Enum @ V10n ) ) @ ( inj__ty_2Enum_2Enum @ V11m ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LITERAL__XOR,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a )
@ ( ap
@ ( ap
@ ( ap @ ( ap @ c_2Ebit_2EBITWISE @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2EMAX @ ( ap @ c_2Ebit_2ELOG2 @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ c_2Ebit_2ELOG2 @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) )
@ ( lam @ bool
@ ^ [V2x: $i] :
( lam @ bool
@ ^ [V3y: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ V2x ) @ V3y ) ) ) ) )
@ ( inj__ty_2Enum_2Enum @ V0n ) )
@ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__replicate__concat__word__list,axiom,
! [A_27a: del,A_27b: del,V0n: tp__ty_2Enum_2Enum,V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__replicate @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1w )
= ( ap @ ( c_2Ewords_2Econcat__word__list @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Elist_2EGENLIST @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( c_2Ecombin_2EK @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ty_2Enum_2Enum ) @ V1w ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Ebit__field__insert,axiom,
! [A_27a: del,A_27b: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2a: $i] :
( ( mem @ V2a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V3b: $i] :
( ( mem @ V3b @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Ebit__field__insert @ A_27b @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V2a ) @ V3b )
= ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) )
@ ( lam @ ( ty_2Efcp_2Ecart @ bool @ A_27b )
@ ^ [V4mask: $i] : ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27b ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27b ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27b ) @ ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ V2a ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) @ V4mask ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27b ) @ V3b ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27b ) @ V4mask ) ) ) ) )
@ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__slice @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27b ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__join__index,axiom,
! [A_27a: del,A_27b: del,V0i: tp__ty_2Enum_2Enum,V1a: $i] :
( ( mem @ V1a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2b: $i] :
( ( mem @ V2b @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) )
=> ( ( ( 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 ) ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0i ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) ) ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__join @ A_27a @ A_27b ) @ V1a ) @ V2b ) ) @ ( inj__ty_2Enum_2Enum @ V0i ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0i ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27b ) @ V2b ) @ ( inj__ty_2Enum_2Enum @ V0i ) ) ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V1a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0i ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) ) ) ) ) ) ) ).
thf(stp_c_ty_2Elist_2Elist_c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone,type,
tp__c_ty_2Elist_2Elist_c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone: $tType ).
thf(stp_inj_c_ty_2Elist_2Elist_c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone,type,
inj__c_ty_2Elist_2Elist_c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone: tp__c_ty_2Elist_2Elist_c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone > $i ).
thf(stp_surj_c_ty_2Elist_2Elist_c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone,type,
surj__c_ty_2Elist_2Elist_c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone: $i > tp__c_ty_2Elist_2Elist_c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone ).
thf(stp_inj_surj_c_ty_2Elist_2Elist_c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Elist_2Elist_c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] :
( ( surj__c_ty_2Elist_2Elist_c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( inj__c_ty_2Elist_2Elist_c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Elist_2Elist_c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Elist_2Elist_c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( mem @ ( inj__c_ty_2Elist_2Elist_c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ X ) @ ( ty_2Elist_2Elist @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) ) ).
thf(stp_iso_mem_c_ty_2Elist_2Elist_c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Elist_2Elist @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) )
=> ( X
= ( inj__c_ty_2Elist_2Elist_c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( surj__c_ty_2Elist_2Elist_c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ X ) ) ) ) ).
thf(conj_thm_2Ewords_2Efoldl__reduce__and,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2Ereduce__and @ A_27a ) @ V0w ) )
= ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Elist_2Elist @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) )
@ ( lam @ ( ty_2Elist_2Elist @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) )
@ ^ [V1l: $i] : ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) @ ( c_2Ewords_2Eword__and @ ty_2Eone_2Eone ) ) @ ( ap @ ( c_2Elist_2EHD @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) @ V1l ) ) @ ( ap @ ( c_2Elist_2ETL @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) @ V1l ) ) ) )
@ ( ap
@ ( ap @ ( c_2Elist_2EGENLIST @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2i: $i] :
( ap
@ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3n: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ ty_2Eone_2Eone ) @ V3n ) @ V3n ) @ 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 ) ) ) ) ) @ V2i ) ) ) )
@ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Efoldl__reduce__or,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2Ereduce__or @ A_27a ) @ V0w ) )
= ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Elist_2Elist @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) )
@ ( lam @ ( ty_2Elist_2Elist @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) )
@ ^ [V1l: $i] : ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) @ ( c_2Ewords_2Eword__or @ ty_2Eone_2Eone ) ) @ ( ap @ ( c_2Elist_2EHD @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) @ V1l ) ) @ ( ap @ ( c_2Elist_2ETL @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) @ V1l ) ) ) )
@ ( ap
@ ( ap @ ( c_2Elist_2EGENLIST @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2i: $i] :
( ap
@ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3n: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ ty_2Eone_2Eone ) @ V3n ) @ V3n ) @ 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 ) ) ) ) ) @ V2i ) ) ) )
@ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Efoldl__reduce__xor,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2Ereduce__xor @ A_27a ) @ V0w ) )
= ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Elist_2Elist @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) )
@ ( lam @ ( ty_2Elist_2Elist @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) )
@ ^ [V1l: $i] : ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) @ ( c_2Ewords_2Eword__xor @ ty_2Eone_2Eone ) ) @ ( ap @ ( c_2Elist_2EHD @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) @ V1l ) ) @ ( ap @ ( c_2Elist_2ETL @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) @ V1l ) ) ) )
@ ( ap
@ ( ap @ ( c_2Elist_2EGENLIST @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2i: $i] :
( ap
@ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3n: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ ty_2Eone_2Eone ) @ V3n ) @ V3n ) @ 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 ) ) ) ) ) @ V2i ) ) ) )
@ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Efoldl__reduce__nand,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2Ereduce__nand @ A_27a ) @ V0w ) )
= ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Elist_2Elist @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) )
@ ( lam @ ( ty_2Elist_2Elist @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) )
@ ^ [V1l: $i] : ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) @ ( c_2Ewords_2Eword__nand @ ty_2Eone_2Eone ) ) @ ( ap @ ( c_2Elist_2EHD @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) @ V1l ) ) @ ( ap @ ( c_2Elist_2ETL @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) @ V1l ) ) ) )
@ ( ap
@ ( ap @ ( c_2Elist_2EGENLIST @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2i: $i] :
( ap
@ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3n: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ ty_2Eone_2Eone ) @ V3n ) @ V3n ) @ 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 ) ) ) ) ) @ V2i ) ) ) )
@ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Efoldl__reduce__nor,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2Ereduce__nor @ A_27a ) @ V0w ) )
= ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Elist_2Elist @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) )
@ ( lam @ ( ty_2Elist_2Elist @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) )
@ ^ [V1l: $i] : ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) @ ( c_2Ewords_2Eword__nor @ ty_2Eone_2Eone ) ) @ ( ap @ ( c_2Elist_2EHD @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) @ V1l ) ) @ ( ap @ ( c_2Elist_2ETL @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) @ V1l ) ) ) )
@ ( ap
@ ( ap @ ( c_2Elist_2EGENLIST @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2i: $i] :
( ap
@ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3n: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ ty_2Eone_2Eone ) @ V3n ) @ V3n ) @ 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 ) ) ) ) ) @ V2i ) ) ) )
@ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Efoldl__reduce__xnor,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2Ereduce__xnor @ A_27a ) @ V0w ) )
= ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Elist_2Elist @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) )
@ ( lam @ ( ty_2Elist_2Elist @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) )
@ ^ [V1l: $i] : ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) @ ( c_2Ewords_2Eword__xnor @ ty_2Eone_2Eone ) ) @ ( ap @ ( c_2Elist_2EHD @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) @ V1l ) ) @ ( ap @ ( c_2Elist_2ETL @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) @ V1l ) ) ) )
@ ( ap
@ ( ap @ ( c_2Elist_2EGENLIST @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2i: $i] :
( ap
@ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3n: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ ty_2Eone_2Eone ) @ V3n ) @ V3n ) @ 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 ) ) ) ) ) @ V2i ) ) ) )
@ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2ELOG2__w2n__lt,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( V0w
!= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Ebit_2ELOG2 @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0w ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2ELOG2__w2n,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( V0w
!= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Ebit_2ELOG2 @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0w ) ) )
= ( surj__ty_2Enum_2Enum
@ ( 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 ) ) ) ) )
@ ( ap @ c_2Ewhile_2ELEAST
@ ( 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 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2ELEAST__BIT__LT,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( V0w
!= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
=> ( p
@ ( ap
@ ( ap @ c_2Eprim__rec_2E_3C
@ ( ap @ c_2Ewhile_2ELEAST
@ ( lam @ ty_2Enum_2Enum
@ ^ [V1i: $i] : ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0w ) @ V1i ) ) ) )
@ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__reduce__n2w,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1f: $i] :
( ( mem @ V1f @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
=> ( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( ap @ ( c_2Ewords_2Eword__reduce @ A_27a ) @ V1f ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
= ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone
@ ( ap @ ( c_2Efcp_2EFCP @ bool @ ty_2Eone_2Eone )
@ ( ap @ ( c_2Ecombin_2EK @ bool @ ty_2Enum_2Enum )
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Elist_2Elist @ bool ) @ bool )
@ ( lam @ ( ty_2Elist_2Elist @ bool )
@ ^ [V2l: $i] : ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ bool @ bool ) @ V1f ) @ ( ap @ ( c_2Elist_2EHD @ bool ) @ V2l ) ) @ ( ap @ ( c_2Elist_2ETL @ bool ) @ V2l ) ) ) )
@ ( ap @ ( ap @ ( ap @ c_2Enumposrep_2EBOOLIFY @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( c_2Elist_2ENIL @ bool ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2ENOT__UINTMAXw,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( V0w
!= ( c_2Ewords_2Eword__T @ A_27a ) )
=> ? [V1i: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
& ~ ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1i ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2ENOT__0w,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( V0w
!= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
=> ? [V1i: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1i ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
& ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1i ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Ereduce__and,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2Ereduce__and @ A_27a ) @ V0w ) )
= ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ V0w ) @ ( c_2Ewords_2Eword__T @ A_27a ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Ereduce__or,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( c_2Ewords_2Ereduce__or @ A_27a ) @ V0w ) )
= ( surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ ty_2Eone_2Eone ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ V0w ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ ty_2Eone_2Eone ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__ADD__0,axiom,
! [A_27a: del] :
( ! [V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0w ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= V0w ) )
& ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V1w )
= V1w ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__ADD__ASSOC,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0v ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V1w ) @ V2x ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0v ) @ V1w ) ) @ V2x ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__MULT__ASSOC,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V0v ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V1w ) @ V2x ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V0v ) @ V1w ) ) @ V2x ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__ADD__COMM,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0v ) @ V1w )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V1w ) @ V0v ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__MULT__COMM,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V0v ) @ V1w )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V1w ) @ V0v ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__MULT__CLAUSES,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V0v )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ( ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V0v ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ( ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ V0v )
= V0v )
& ( ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V0v ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
= V0v )
& ( ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0v ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ V1w )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V0v ) @ V1w ) ) @ V1w ) )
& ( ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V0v ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V1w ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0v ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V0v ) @ V1w ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LEFT__ADD__DISTRIB,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V0v ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V1w ) @ V2x ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V0v ) @ V1w ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V0v ) @ V2x ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__RIGHT__ADD__DISTRIB,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0v ) @ V1w ) ) @ V2x )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V0v ) @ V2x ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V1w ) @ V2x ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__ADD__SUB__ASSOC,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0v ) @ V1w ) ) @ V2x )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0v ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V1w ) @ V2x ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__ADD__SUB__SYM,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0v ) @ V1w ) ) @ V2x )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0v ) @ V2x ) ) @ V1w ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__ADD__LINV,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0w ) ) @ V0w )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__ADD__RINV,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0w ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0w ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__SUB__REFL,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0w ) @ V0w )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__SUB__ADD2,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0v ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V1w ) @ V0v ) )
= V1w ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__ADD__SUB,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0v ) @ V1w ) ) @ V1w )
= V0v ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__SUB__ADD,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0v ) @ V1w ) ) @ V1w )
= V0v ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__ADD__EQ__SUB,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0v ) @ V1w )
= V2x )
<=> ( V0v
= ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V2x ) @ V1w ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__ADD__INV__0__EQ,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0v ) @ V1w )
= V0v )
<=> ( V1w
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__EQ__ADD__LCANCEL,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0v ) @ V1w )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0v ) @ V2x ) )
<=> ( V1w = V2x ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__EQ__ADD__RCANCEL,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0v ) @ V1w )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V2x ) @ V1w ) )
<=> ( V0v = V2x ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__NEG,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0w )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ V0w ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__NOT,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ V0w )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0w ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__NEG__0,axiom,
! [A_27a: del] :
( ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__NEG__ADD,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0v ) @ V1w ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0v ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V1w ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__NEG__NEG,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0w ) )
= V0w ) ) ).
thf(conj_thm_2Ewords_2EWORD__SUB__LNEG,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0v ) ) @ V1w )
= ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0v ) @ V1w ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__SUB__RNEG,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0v ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V1w ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0v ) @ V1w ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__SUB__SUB,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0v ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V1w ) @ V2x ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0v ) @ V2x ) ) @ V1w ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__SUB__SUB2,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0v ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0v ) @ V1w ) )
= V1w ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__EQ__SUB__LADD,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( V0v
= ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V1w ) @ V2x ) )
<=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0v ) @ V2x )
= V1w ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__EQ__SUB__RADD,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0v ) @ V1w )
= V2x )
<=> ( V0v
= ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V2x ) @ V1w ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__EQ__SUB__ZERO,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1v: $i] :
( ( mem @ V1v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V1v ) @ V0w )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> ( V1v = V0w ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LCANCEL__SUB,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0v ) @ V1w )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V2x ) @ V1w ) )
<=> ( V0v = V2x ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__RCANCEL__SUB,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0v ) @ V1w )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0v ) @ V2x ) )
<=> ( V1w = V2x ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__SUB__PLUS,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0v ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V1w ) @ V2x ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0v ) @ V1w ) ) @ V2x ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__SUB__LZERO,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V0w )
= ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0w ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__SUB__RZERO,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0w ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= V0w ) ) ).
thf(conj_thm_2Ewords_2EWORD__ADD__LID__UNIQ,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0v ) @ V1w )
= V1w )
<=> ( V0v
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__ADD__RID__UNIQ,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0v ) @ V1w )
= V0v )
<=> ( V1w
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__SUM__ZERO,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0a ) @ V1b )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> ( V0a
= ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V1b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__ADD__SUB2,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V1w ) @ V0v ) ) @ V1w )
= V0v ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__ADD__SUB3,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1x: $i] :
( ( mem @ V1x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0v ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0v ) @ V1x ) )
= ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V1x ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__SUB__SUB3,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1v: $i] :
( ( mem @ V1v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V1v ) @ V0w ) ) @ V1v )
= ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0w ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__EQ__NEG,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0v )
= ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V1w ) )
<=> ( V0v = V1w ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__NEG__EQ,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1v: $i] :
( ( mem @ V1v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V1v )
= V0w )
<=> ( V1v
= ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0w ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__NEG__EQ__0,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0v )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> ( V0v
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__SUB,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V1w ) ) @ V0v )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0v ) @ V1w ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__SUB__NEG,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0v ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V1w ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V1w ) @ V0v ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__NEG__SUB,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1v: $i] :
( ( mem @ V1v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V1v ) @ V0w ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0w ) @ V1v ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__SUB__TRIANGLE,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0v ) @ V1w ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V1w ) @ V2x ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0v ) @ V2x ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__NOT__0,axiom,
! [A_27a: del] :
( ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( c_2Ewords_2Eword__T @ A_27a ) ) ).
thf(conj_thm_2Ewords_2EWORD__NOT__T,axiom,
! [A_27a: del] :
( ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ ( c_2Ewords_2Eword__T @ A_27a ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__NEG__T,axiom,
! [A_27a: del] :
( ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( c_2Ewords_2Eword__T @ A_27a ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__MULT__SUC,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V0v ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V0v ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ V0v ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__NEG__LMUL,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V0v ) @ V1w ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0v ) ) @ V1w ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__NEG__RMUL,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V0v ) @ V1w ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V0v ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V1w ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__NEG__MUL,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0w )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ V0w ) ) ) ).
thf(conj_thm_2Ewords_2Esw2sw__w2w__add,axiom,
! [A_27a: del,A_27b: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Esw2sw @ A_27a @ A_27b ) @ V0w )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) ) @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0w ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27b ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27b ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ V0w ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__ADD__BIT0,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0a ) @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> ~ ( ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__ADD__BIT,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1a: $i] :
( ( mem @ V1a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2b: $i] :
( ( mem @ V2b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( 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_2Efcp_2Efcp__index @ bool @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V1a ) @ V2b ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V1a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V2b ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( 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 @ fo__c_2Enum_2E0 ) ) @ V1a ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( 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 @ fo__c_2Enum_2E0 ) ) @ V2b ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V1a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V2b ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V1a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V2b ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LEFT__SUB__DISTRIB,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V0v ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V1w ) @ V2x ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V0v ) @ V1w ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V0v ) @ V2x ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__RIGHT__SUB__DISTRIB,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2x: $i] :
( ( mem @ V2x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V1w ) @ V2x ) ) @ V0v )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V1w ) @ V0v ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V2x ) @ V0v ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LITERAL__MULT,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
= ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) )
& ! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27b ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27b ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27b ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LITERAL__ADD,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
= ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) )
& ! [V2m: tp__ty_2Enum_2Enum,V3n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27b ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27b ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27b ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__SUB__INTRO,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0x: $i] :
( ( mem @ V0x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1y: $i] :
( ( mem @ V1y @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V1y ) ) @ V0x )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0x ) @ V1y ) ) ) )
& ! [V2x: $i] :
( ( mem @ V2x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V3y: $i] :
( ( mem @ V3y @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V2x ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V3y ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V2x ) @ V3y ) ) ) )
& ! [V4x: $i] :
( ( mem @ V4x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V5y: $i] :
( ( mem @ V5y @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V6z: $i] :
( ( mem @ V6z @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V4x ) ) @ V5y ) ) @ V6z )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V6z ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V4x ) @ V5y ) ) ) ) ) )
& ! [V7x: $i] :
( ( mem @ V7x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V8y: $i] :
( ( mem @ V8y @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V9z: $i] :
( ( mem @ V9z @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V9z ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V7x ) ) @ V8y ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V9z ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V7x ) @ V8y ) ) ) ) ) )
& ! [V10x: $i] :
( ( mem @ V10x @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27b ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27b ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ V10x )
= ( ap @ ( c_2Ewords_2Eword__2comp @ A_27b ) @ V10x ) ) )
& ! [V11x: $i] :
( ( mem @ V11x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V12y: $i] :
( ( mem @ V12y @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V13z: $i] :
( ( mem @ V13z @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V13z ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V11x ) ) @ V12y ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V13z ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V11x ) @ V12y ) ) ) ) ) )
& ! [V14x: $i] :
( ( mem @ V14x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V15y: $i] :
( ( mem @ V15y @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V16z: $i] :
( ( mem @ V16z @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V14x ) ) @ V15y ) ) @ V16z )
= ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V14x ) @ V15y ) ) @ V16z ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2En2w__SUC,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2En2w__sub,axiom,
! [A_27a: del,V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) )
=> ( ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2En2w__sub__eq__0,axiom,
! [A_27a: del,V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
=> ( ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__H__WORD__L,axiom,
! [A_27a: del] :
( ( c_2Ewords_2Eword__H @ A_27a )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__L__MULT,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( c_2Ewords_2Eword__L @ A_27a ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ c_2Earithmetic_2EEVEN @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) ) ).
thf(conj_thm_2Ewords_2EASR__ADD,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__asr @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__asr @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__asr @ A_27a ) @ V0w ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ).
thf(conj_thm_2Ewords_2ELSR__ADD,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ V0w ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EROR__ADD,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__ror @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ror @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__ror @ A_27a ) @ V0w ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ).
thf(conj_thm_2Ewords_2ELSL__ADD,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ V0w ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EASR__LIMIT,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__asr @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1n ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0w ) ) @ ( c_2Ewords_2Eword__T @ A_27a ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EASR__UINT__MAX,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__asr @ A_27a ) @ ( c_2Ewords_2Eword__T @ A_27a ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) )
= ( c_2Ewords_2Eword__T @ A_27a ) ) ).
thf(conj_thm_2Ewords_2ELSR__LIMIT,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1n ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
thf(conj_thm_2Ewords_2ELSL__LIMIT,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1n ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EROR__CYCLE,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__ror @ A_27a ) @ V0w ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
= V0w ) ) ).
thf(conj_thm_2Ewords_2EROR__MOD,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__ror @ A_27a ) @ V0w ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__ror @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
thf(conj_thm_2Ewords_2EROL__MOD,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__rol @ A_27a ) @ V0w ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__rol @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
thf(conj_thm_2Ewords_2ELSL__ONE,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ V0w ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0w ) @ V0w ) ) ) ).
thf(conj_thm_2Ewords_2EROR__UINT__MAX,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__ror @ A_27a ) @ ( c_2Ewords_2Eword__T @ A_27a ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) )
= ( c_2Ewords_2Eword__T @ A_27a ) ) ).
thf(conj_thm_2Ewords_2EROR__ROL,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( ( ap @ ( ap @ ( c_2Ewords_2Eword__rol @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ror @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) )
= V0w )
& ( ( ap @ ( ap @ ( c_2Ewords_2Eword__ror @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__rol @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) )
= V0w ) ) ) ).
thf(conj_thm_2Ewords_2EMOD__COMPLEMENT,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1q: tp__ty_2Enum_2Enum,V2a: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1q ) ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1q ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1q ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( inj__ty_2Enum_2Enum @ V2a ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V2a ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EROL__ADD,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1m: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__rol @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__rol @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__rol @ A_27a ) @ V0w ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EZERO__SHIFT,axiom,
! [A_27a: del] :
( ! [V0n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ! [V1n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__asr @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ! [V2n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ! [V3n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__rol @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ! [V4n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__ror @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( inj__ty_2Enum_2Enum @ V4n ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ).
thf(conj_thm_2Ewords_2ESHIFT__ZERO,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,A_27e: del] :
( ! [V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ V0a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) )
= V0a ) )
& ! [V1a: $i] :
( ( mem @ V1a @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__asr @ A_27b ) @ V1a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) )
= V1a ) )
& ! [V2a: $i] :
( ( mem @ V2a @ ( ty_2Efcp_2Ecart @ bool @ A_27c ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27c ) @ V2a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) )
= V2a ) )
& ! [V3a: $i] :
( ( mem @ V3a @ ( ty_2Efcp_2Ecart @ bool @ A_27d ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__rol @ A_27d ) @ V3a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) )
= V3a ) )
& ! [V4a: $i] :
( ( mem @ V4a @ ( ty_2Efcp_2Ecart @ bool @ A_27e ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__ror @ A_27e ) @ V4a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) )
= V4a ) ) ) ).
thf(conj_thm_2Ewords_2Eword__lsl__n2w,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( 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 @ V0n ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__1__lsl,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__lsr__n2w,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1n ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( 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 ) ) @ V0w ) ) ) ).
thf(conj_thm_2Ewords_2ELSL__UINT__MAX,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ ( c_2Ewords_2Eword__T @ A_27a ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__asr__n2w,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__asr @ A_27a ) @ V1w ) @ ( inj__ty_2Enum_2Enum @ V0n ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V1w ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ V1w ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ V1w ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__ror__n2w,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1a: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__ror @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) )
= ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2x: $i] : ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( 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 ) ) ) ) ) @ V2x ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ V2x ) @ ( 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__ty_2Enum_2Enum @ V1a ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ V2x ) ) ) ) ) ) )
@ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__rrx__n2w,axiom,
! [A_27a: del,V0c: $i] :
( ( mem @ V0c @ bool )
=> ! [V1a: tp__ty_2Enum_2Enum] :
( ( ap @ ( c_2Ewords_2Eword__rrx @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ bool @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ V0c ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) ) )
= ( ap @ ( ap @ ( c_2Epair_2E_2C @ bool @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V1a ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EBITS @ ( 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 ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1a ) ) ) @ ( ap @ ( ap @ c_2Ebit_2ESBIT @ V0c ) @ ( 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 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__ror,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__ror @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1n ) )
= ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2x: $i] : ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( 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 ) ) ) ) ) @ V2x ) @ V0w ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ V2x ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0w ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ V2x ) ) ) ) )
@ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__asr,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__asr @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1n ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0w ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__slice @ A_27a ) @ ( 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 ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( c_2Ewords_2Eword__T @ A_27a ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Ew2n__lsr,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1m: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0w ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__MUL__LSL,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ V0a ) @ ( inj__ty_2Enum_2Enum @ V1n ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ V0a ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__ADD__LSL,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1a: $i] :
( ( mem @ V1a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2b: $i] :
( ( mem @ V2b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V1a ) @ V2b ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ V1a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ V2b ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__DIV__LSR,axiom,
! [A_27a: del,V0m: $i] :
( ( mem @ V0m @ ( 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 ) ) ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ V0m ) @ ( inj__ty_2Enum_2Enum @ V1n ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__div @ A_27a ) @ V0m ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__MOD__1,axiom,
! [A_27a: del,V0m: $i] :
( ( mem @ V0m @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__mod @ A_27a ) @ V0m ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__MOD__POW2,axiom,
! [A_27a: del,V0m: $i] :
( ( mem @ V0m @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1v: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1v ) ) @ ( 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 ) ) ) ) ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__mod @ A_27a ) @ V0m ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1v ) ) ) ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1v ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0m ) ) ) ) ).
thf(conj_thm_2Ewords_2ESHIFT__1__SUB__1,axiom,
! [A_27a: del,V0i: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
( ( 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_2Efcp_2Efcp__index @ bool @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0i ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0i ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).
thf(conj_thm_2Ewords_2ELSR__BITWISE,axiom,
! [A_27a: del] :
( ! [V0n: tp__ty_2Enum_2Enum,V1v: $i] :
( ( mem @ V1v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2w: $i] :
( ( mem @ V2w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ V2w ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ V1v ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V2w ) @ V1v ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
& ! [V3n: tp__ty_2Enum_2Enum,V4v: $i] :
( ( mem @ V4v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V5w: $i] :
( ( mem @ V5w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ V5w ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ V4v ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ V5w ) @ V4v ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) )
& ! [V6n: tp__ty_2Enum_2Enum,V7v: $i] :
( ( mem @ V7v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V8w: $i] :
( ( mem @ V8w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ V8w ) @ ( inj__ty_2Enum_2Enum @ V6n ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ V7v ) @ ( inj__ty_2Enum_2Enum @ V6n ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ V8w ) @ V7v ) ) @ ( inj__ty_2Enum_2Enum @ V6n ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2ELSL__BITWISE,axiom,
! [A_27a: del] :
( ! [V0n: tp__ty_2Enum_2Enum,V1v: $i] :
( ( mem @ V1v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2w: $i] :
( ( mem @ V2w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ V2w ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ V1v ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V2w ) @ V1v ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
& ! [V3n: tp__ty_2Enum_2Enum,V4v: $i] :
( ( mem @ V4v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V5w: $i] :
( ( mem @ V5w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ V5w ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ V4v ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ V5w ) @ V4v ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) )
& ! [V6n: tp__ty_2Enum_2Enum,V7v: $i] :
( ( mem @ V7v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V8w: $i] :
( ( mem @ V8w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ V8w ) @ ( inj__ty_2Enum_2Enum @ V6n ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ V7v ) @ ( inj__ty_2Enum_2Enum @ V6n ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ V8w ) @ V7v ) ) @ ( inj__ty_2Enum_2Enum @ V6n ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EROR__BITWISE,axiom,
! [A_27a: del] :
( ! [V0n: tp__ty_2Enum_2Enum,V1v: $i] :
( ( mem @ V1v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2w: $i] :
( ( mem @ V2w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ror @ A_27a ) @ V2w ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ror @ A_27a ) @ V1v ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__ror @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V2w ) @ V1v ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
& ! [V3n: tp__ty_2Enum_2Enum,V4v: $i] :
( ( mem @ V4v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V5w: $i] :
( ( mem @ V5w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ror @ A_27a ) @ V5w ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ror @ A_27a ) @ V4v ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__ror @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ V5w ) @ V4v ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) )
& ! [V6n: tp__ty_2Enum_2Enum,V7v: $i] :
( ( mem @ V7v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V8w: $i] :
( ( mem @ V8w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ror @ A_27a ) @ V8w ) @ ( inj__ty_2Enum_2Enum @ V6n ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ror @ A_27a ) @ V7v ) @ ( inj__ty_2Enum_2Enum @ V6n ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__ror @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ V8w ) @ V7v ) ) @ ( inj__ty_2Enum_2Enum @ V6n ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EROL__BITWISE,axiom,
! [A_27a: del,A_27b: del,A_27c: del] :
( ! [V0n: tp__ty_2Enum_2Enum,V1v: $i] :
( ( mem @ V1v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2w: $i] :
( ( mem @ V2w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__rol @ A_27a ) @ V2w ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__rol @ A_27a ) @ V1v ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__rol @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V2w ) @ V1v ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
& ! [V3n: tp__ty_2Enum_2Enum,V4v: $i] :
( ( mem @ V4v @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) )
=> ! [V5w: $i] :
( ( mem @ V5w @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27b ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__rol @ A_27b ) @ V5w ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__rol @ A_27b ) @ V4v ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__rol @ A_27b ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27b ) @ V5w ) @ V4v ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) )
& ! [V6n: tp__ty_2Enum_2Enum,V7v: $i] :
( ( mem @ V7v @ ( ty_2Efcp_2Ecart @ bool @ A_27c ) )
=> ! [V8w: $i] :
( ( mem @ V8w @ ( ty_2Efcp_2Ecart @ bool @ A_27c ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27c ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__rol @ A_27c ) @ V8w ) @ ( inj__ty_2Enum_2Enum @ V6n ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__rol @ A_27c ) @ V7v ) @ ( inj__ty_2Enum_2Enum @ V6n ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__rol @ A_27c ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27c ) @ V8w ) @ V7v ) ) @ ( inj__ty_2Enum_2Enum @ V6n ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__2COMP__LSL,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1a: $i] :
( ( mem @ V1a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V1a ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) )
= ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ V1a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Ew2w__LSL,axiom,
! [A_27a: del,A_27b: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27b ) @ ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( 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 ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0w ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
thf(conj_thm_2Ewords_2En2w__DIV,axiom,
! [A_27a: del,V0a: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
=> ( ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__BITS__LSL,axiom,
! [A_27a: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum,V3w: $i] :
( ( mem @ V3w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ V3w ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ V3w ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__EXTRACT__LSL,axiom,
! [A_27a: del,A_27b: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum,V3w: $i] :
( ( mem @ V3w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( 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 @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ V3w ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ V3w ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__EXTRACT__LSL2,axiom,
! [A_27a: del,A_27b: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum,V3w: $i] :
( ( mem @ V3w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V3w ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V3w ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EEXTRACT__JOIN__LSL,axiom,
! [A_27a: del,A_27b: del,V0h: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2m_27: tp__ty_2Enum_2Enum,V3l: tp__ty_2Enum_2Enum,V4s: tp__ty_2Enum_2Enum,V5n: tp__ty_2Enum_2Enum,V6w: $i] :
( ( mem @ V6w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3l ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2m_27 ) ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) )
& ( V2m_27
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
& ( V4s
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2m_27 ) ) @ ( inj__ty_2Enum_2Enum @ V3l ) ) ) @ ( inj__ty_2Enum_2Enum @ V5n ) ) ) ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27b ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V2m_27 ) ) @ V6w ) ) @ ( inj__ty_2Enum_2Enum @ V4s ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V3l ) ) @ V6w ) ) @ ( inj__ty_2Enum_2Enum @ V5n ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( inj__ty_2Enum_2Enum @ V3l ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( 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 @ V3l ) ) @ V6w ) ) @ ( inj__ty_2Enum_2Enum @ V5n ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EEXTRACT__JOIN__ADD__LSL,axiom,
! [A_27a: del,A_27b: del,V0h: tp__ty_2Enum_2Enum,V1m: tp__ty_2Enum_2Enum,V2m_27: tp__ty_2Enum_2Enum,V3l: tp__ty_2Enum_2Enum,V4s: tp__ty_2Enum_2Enum,V5n: tp__ty_2Enum_2Enum,V6w: $i] :
( ( mem @ V6w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3l ) ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2m_27 ) ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) )
& ( V2m_27
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
& ( V4s
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2m_27 ) ) @ ( inj__ty_2Enum_2Enum @ V3l ) ) ) @ ( inj__ty_2Enum_2Enum @ V5n ) ) ) ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27b ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V2m_27 ) ) @ V6w ) ) @ ( inj__ty_2Enum_2Enum @ V4s ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ ( inj__ty_2Enum_2Enum @ V3l ) ) @ V6w ) ) @ ( inj__ty_2Enum_2Enum @ V5n ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMIN @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( inj__ty_2Enum_2Enum @ V3l ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( 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 @ V3l ) ) @ V6w ) ) @ ( inj__ty_2Enum_2Enum @ V5n ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__extract__mask,axiom,
! [A_27a: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2a: $i] :
( ( mem @ V2a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V2a )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ V2a ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__bits__mask,axiom,
! [A_27a: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2a: $i] :
( ( mem @ V2a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bits @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V2a )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ V2a ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__extract__w2w__mask,axiom,
! [A_27a: del,A_27b: del,V0h: tp__ty_2Enum_2Enum,V1l: tp__ty_2Enum_2Enum,V2a: $i] :
( ( mem @ V2a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ V2a )
= ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1l ) ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ V2a ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( inj__ty_2Enum_2Enum @ V1l ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__shift__bv,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_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1n ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl__bv @ A_27a ) @ V0w ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) )
& ! [V2w: $i] :
( ( mem @ V2w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V3n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__asr @ A_27a ) @ V2w ) @ ( inj__ty_2Enum_2Enum @ V3n ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__asr__bv @ A_27a ) @ V2w ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) )
& ! [V4w: $i] :
( ( mem @ V4w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V5n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V5n ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ V4w ) @ ( inj__ty_2Enum_2Enum @ V5n ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr__bv @ A_27a ) @ V4w ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V5n ) ) ) ) ) )
& ! [V6w: $i] :
( ( mem @ V6w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V7n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__ror @ A_27a ) @ V6w ) @ ( inj__ty_2Enum_2Enum @ V7n ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__ror__bv @ A_27a ) @ V6w ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V7n ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) )
& ! [V8w: $i] :
( ( mem @ V8w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V9n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__rol @ A_27a ) @ V8w ) @ ( inj__ty_2Enum_2Enum @ V9n ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__rol__bv @ A_27a ) @ V8w ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V9n ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Elsl__lsr,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 @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0w ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) )
= V0w ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__NEG__L,axiom,
! [A_27a: del] :
( ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( c_2Ewords_2Eword__L @ A_27a ) )
= ( c_2Ewords_2Eword__L @ A_27a ) ) ).
thf(conj_thm_2Ewords_2Eword__L__MULT__NEG,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ ( c_2Ewords_2Eword__L @ A_27a ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ c_2Earithmetic_2EEVEN @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) ) ).
thf(conj_thm_2Ewords_2Eword__L2__MULT,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del] :
( ( ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ ( c_2Ewords_2Eword__L2 @ A_27a ) ) @ ( c_2Ewords_2Eword__L2 @ A_27a ) )
= ( c_2Ewords_2Eword__L2 @ A_27a ) )
& ( ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27b ) @ ( c_2Ewords_2Eword__L @ A_27b ) ) @ ( c_2Ewords_2Eword__L2 @ A_27b ) )
= ( c_2Ewords_2Eword__L2 @ A_27b ) )
& ! [V0n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27c ) @ ( ap @ ( c_2Ewords_2En2w @ A_27c ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( c_2Ewords_2Eword__L2 @ A_27c ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27c ) ) @ ( ap @ c_2Earithmetic_2EEVEN @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27c ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( c_2Ewords_2Eword__L2 @ A_27c ) ) )
& ! [V1n: tp__ty_2Enum_2Enum] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27d ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27d ) @ ( ap @ ( c_2Ewords_2En2w @ A_27d ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) @ ( c_2Ewords_2Eword__L2 @ A_27d ) )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27d ) ) @ ( ap @ c_2Earithmetic_2EEVEN @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27d ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( c_2Ewords_2Eword__L2 @ A_27d ) ) ) ) ).
thf(conj_thm_2Ewords_2ETWO__COMP__NEG,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0a ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( 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 @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ V0a ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) ) ) @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0a ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0a ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2ETWO__COMP__POS__NEG,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( V0a
!= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ( V0a
!= ( c_2Ewords_2Eword__L @ A_27a ) ) )
=> ( ~ ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0a ) )
<=> ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0a ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__0__POS,axiom,
! [A_27a: del] :
~ ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ).
thf(conj_thm_2Ewords_2ETWO__COMP__POS,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ~ ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0a ) )
=> ( ( V0a
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
| ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0a ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__H__POS,axiom,
! [A_27a: del] :
~ ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ ( c_2Ewords_2Eword__H @ A_27a ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__L__NEG,axiom,
! [A_27a: del] : ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__GREATER,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__gt @ A_27a ) @ V0a ) @ V1b ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V1b ) @ V0a ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__GREATER__EQ,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ge @ A_27a ) @ V0a ) @ V1b ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ V1b ) @ V0a ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__NOT__LESS,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ~ ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V0a ) @ V1b ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ V1b ) @ V0a ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LT,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V0a ) @ V1b ) )
<=> ( ( ( ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0a ) )
<=> ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V1b ) ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1b ) ) ) )
| ( ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0a ) )
& ~ ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V1b ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__GT,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__gt @ A_27a ) @ V0a ) @ V1b ) )
<=> ( ( ( ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V1b ) )
<=> ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0a ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1b ) ) ) )
| ( ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V1b ) )
& ~ ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0a ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LE,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ V0a ) @ V1b ) )
<=> ( ( ( ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0a ) )
<=> ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V1b ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1b ) ) ) )
| ( ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0a ) )
& ~ ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V1b ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__GE,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ge @ A_27a ) @ V0a ) @ V1b ) )
<=> ( ( ( ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V1b ) )
<=> ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0a ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E_3D @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1b ) ) ) )
| ( ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V1b ) )
& ~ ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0a ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LO,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V0a ) @ V1b ) )
<=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1b ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LS,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V0a ) @ V1b ) )
<=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1b ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__HI,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__hi @ A_27a ) @ V0a ) @ V1b ) )
<=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1b ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__HS,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__hs @ A_27a ) @ V0a ) @ V1b ) )
<=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E_3D @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1b ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__NOT__LESS__EQUAL,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ~ ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ V0a ) @ V1b ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V1b ) @ V0a ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LESS__OR__EQ,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ V0a ) @ V1b ) )
<=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V0a ) @ V1b ) )
| ( V0a = V1b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__GREATER__OR__EQ,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ge @ A_27a ) @ V0a ) @ V1b ) )
<=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__gt @ A_27a ) @ V0a ) @ V1b ) )
| ( V0a = V1b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LESS__TRANS,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V0a ) @ V1b ) )
& ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V1b ) @ V2c ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V0a ) @ V2c ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LESS__EQ__TRANS,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ V0a ) @ V1b ) )
& ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ V1b ) @ V2c ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ V0a ) @ V2c ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LESS__EQ__LESS__TRANS,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ V0a ) @ V1b ) )
& ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V1b ) @ V2c ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V0a ) @ V2c ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LESS__LESS__EQ__TRANS,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V0a ) @ V1b ) )
& ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ V1b ) @ V2c ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V0a ) @ V2c ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LESS__EQ__CASES,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ V0a ) @ V1b ) )
| ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ V1b ) @ V0a ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LESS__CASES,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V0a ) @ V1b ) )
| ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ V1b ) @ V0a ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LESS__CASES__IMP,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V0a ) @ V1b ) )
& ( V0a != V1b ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V1b ) @ V0a ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LESS__ANTISYM,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ~ ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V0a ) @ V1b ) )
& ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V1b ) @ V0a ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LESS__EQ__ANTISYM,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ~ ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V0a ) @ V1b ) )
& ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ V1b ) @ V0a ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LESS__EQ__REFL,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ V0a ) @ V0a ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LESS__EQUAL__ANTISYM,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ V0a ) @ V1b ) )
& ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ V1b ) @ V0a ) ) )
=> ( V0a = V1b ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LESS__IMP__LESS__OR__EQ,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V0a ) @ V1b ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ V0a ) @ V1b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LESS__REFL,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ~ ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V0a ) @ V0a ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LESS__LESS__CASES,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( V0a = V1b )
| ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V0a ) @ V1b ) )
| ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V1b ) @ V0a ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__NOT__GREATER,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ~ ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__gt @ A_27a ) @ V0a ) @ V1b ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ V0a ) @ V1b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LESS__NOT__EQ,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V0a ) @ V1b ) )
=> ( V0a != V1b ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__NOT__LESS__EQ,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( V0a = V1b )
=> ~ ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V0a ) @ V1b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__HIGHER,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__hi @ A_27a ) @ V0a ) @ V1b ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V1b ) @ V0a ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__HIGHER__EQ,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__hs @ A_27a ) @ V0a ) @ V1b ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V1b ) @ V0a ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__NOT__LOWER,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ~ ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V0a ) @ V1b ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V1b ) @ V0a ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__NOT__LOWER__EQUAL,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ~ ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V0a ) @ V1b ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V1b ) @ V0a ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LOWER__OR__EQ,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V0a ) @ V1b ) )
<=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V0a ) @ V1b ) )
| ( V0a = V1b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__HIGHER__OR__EQ,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__hs @ A_27a ) @ V0a ) @ V1b ) )
<=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__hi @ A_27a ) @ V0a ) @ V1b ) )
| ( V0a = V1b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LOWER__TRANS,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V0a ) @ V1b ) )
& ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V1b ) @ V2c ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V0a ) @ V2c ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LOWER__EQ__TRANS,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V0a ) @ V1b ) )
& ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V1b ) @ V2c ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V0a ) @ V2c ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LOWER__EQ__LOWER__TRANS,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V0a ) @ V1b ) )
& ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V1b ) @ V2c ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V0a ) @ V2c ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LOWER__LOWER__EQ__TRANS,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V0a ) @ V1b ) )
& ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V1b ) @ V2c ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V0a ) @ V2c ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LOWER__EQ__CASES,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V0a ) @ V1b ) )
| ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V1b ) @ V0a ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LOWER__CASES,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V0a ) @ V1b ) )
| ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V1b ) @ V0a ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LOWER__CASES__IMP,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V0a ) @ V1b ) )
& ( V0a != V1b ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V1b ) @ V0a ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LOWER__ANTISYM,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ~ ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V0a ) @ V1b ) )
& ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V1b ) @ V0a ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LOWER__EQ__ANTISYM,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ~ ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V0a ) @ V1b ) )
& ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V1b ) @ V0a ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LOWER__EQ__REFL,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V0a ) @ V0a ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LOWER__EQUAL__ANTISYM,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V0a ) @ V1b ) )
& ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V1b ) @ V0a ) ) )
=> ( V0a = V1b ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LOWER__IMP__LOWER__OR__EQ,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V0a ) @ V1b ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V0a ) @ V1b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LOWER__REFL,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ~ ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V0a ) @ V0a ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LOWER__LOWER__CASES,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( V0a = V1b )
| ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V0a ) @ V1b ) )
| ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V1b ) @ V0a ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__NOT__HIGHER,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ~ ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__hi @ A_27a ) @ V0a ) @ V1b ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V0a ) @ V1b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LOWER__NOT__EQ,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V0a ) @ V1b ) )
=> ( V0a != V1b ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__NOT__LOWER__EQ,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( V0a = V1b )
=> ~ ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V0a ) @ V1b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__L__PLUS__H,axiom,
! [A_27a: del] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) @ ( c_2Ewords_2Eword__H @ A_27a ) )
= ( c_2Ewords_2Eword__T @ A_27a ) ) ).
thf(conj_thm_2Ewords_2EWORD__L__LESS__EQ,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) @ V0a ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LESS__EQ__H,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ V0a ) @ ( c_2Ewords_2Eword__H @ A_27a ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__L__LESS__H,axiom,
! [A_27a: del] : ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) @ ( c_2Ewords_2Eword__H @ A_27a ) ) ) ).
thf(conj_thm_2Ewords_2ENOT__INT__MIN__ZERO,axiom,
! [A_27a: del] :
( ( c_2Ewords_2Eword__L @ A_27a )
!= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ).
thf(conj_thm_2Ewords_2EZERO__LO__INT__MIN,axiom,
! [A_27a: del] : ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__0__LS,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V0w ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LS__T,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V0w ) @ ( c_2Ewords_2Eword__T @ A_27a ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__ADD__LEFT__LO,axiom,
! [A_27a: del,V0b: $i] :
( ( mem @ V0b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1c: $i] :
( ( mem @ V1c @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2a: $i] :
( ( mem @ V2a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V2a ) @ V0b ) ) @ V1c ) )
<=> ( p
@ ( ap
@ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V0b ) @ V1c ) )
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool )
@ ( lam @ ( ty_2Efcp_2Ecart @ bool @ A_27a )
@ ^ [V3x: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V2a ) @ V3x ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ V0b ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V1c ) ) @ V3x ) ) @ V2a ) ) ) ) )
@ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1c ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0b ) ) ) ) )
@ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0b ) ) @ V2a ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V2a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0b ) ) @ V1c ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__ADD__LEFT__LS,axiom,
! [A_27a: del,V0b: $i] :
( ( mem @ V0b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1c: $i] :
( ( mem @ V1c @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2a: $i] :
( ( mem @ V2a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V2a ) @ V0b ) ) @ V1c ) )
<=> ( p
@ ( ap
@ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V0b ) @ V1c ) )
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool )
@ ( lam @ ( ty_2Efcp_2Ecart @ bool @ A_27a )
@ ^ [V3x: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V2a ) @ V3x ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ V0b ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V1c ) ) @ V3x ) ) @ V2a ) ) ) ) )
@ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1c ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0b ) ) ) ) )
@ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0b ) ) @ V2a ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V2a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0b ) ) @ V1c ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__ADD__RIGHT__LS,axiom,
! [A_27a: del,V0c: $i] :
( ( mem @ V0c @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1a: $i] :
( ( mem @ V1a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2b: $i] :
( ( mem @ V2b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V1a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V2b ) @ V0c ) ) )
<=> ( p
@ ( ap
@ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V0c ) @ V1a ) )
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool )
@ ( lam @ ( ty_2Efcp_2Ecart @ bool @ A_27a )
@ ^ [V3x: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V3x ) @ V2b ) ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ V0c ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V2b ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V1a ) ) @ V3x ) ) ) ) ) )
@ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1a ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0c ) ) ) ) )
@ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V2b ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0c ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0c ) ) @ V1a ) ) @ V2b ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__ADD__RIGHT__LO,axiom,
! [A_27a: del,V0c: $i] :
( ( mem @ V0c @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1a: $i] :
( ( mem @ V1a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2b: $i] :
( ( mem @ V2b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V1a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V2b ) @ V0c ) ) )
<=> ( p
@ ( ap
@ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V0c ) @ V1a ) )
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool )
@ ( lam @ ( ty_2Efcp_2Ecart @ bool @ A_27a )
@ ^ [V3x: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V3x ) @ V2b ) ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ V0c ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V2b ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V1a ) ) @ V3x ) ) ) ) ) )
@ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1a ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0c ) ) ) ) )
@ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V2b ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0c ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0c ) ) @ V1a ) ) @ V2b ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__MSB__INT__MIN__LS,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0a ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) @ V0a ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LT__LO,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V0a ) @ V1b ) )
<=> ( ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) @ V0a ) )
& ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V1b ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) )
| ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V0a ) @ V1b ) ) ) )
| ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V0a ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) )
& ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V1b ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) )
& ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V0a ) @ V1b ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LE__LS,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ V0a ) @ V1b ) )
<=> ( ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) @ V0a ) )
& ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V1b ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) )
| ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V0a ) @ V1b ) ) ) )
| ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V0a ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) )
& ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V1b ) @ ( c_2Ewords_2Eword__L @ A_27a ) ) )
& ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V0a ) @ V1b ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LESS__NEG__LEFT,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0a ) ) @ V1b ) )
<=> ( ( V1b
!= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ( ( V0a
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
| ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V1b ) ) @ V0a ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LESS__NEG__RIGHT,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V0a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V1b ) ) )
<=> ( ( V1b
!= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ( ( V0a
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
| ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V1b ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0a ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LS__word__0,axiom,
! [A_27a: del,V0n: $i] :
( ( mem @ V0n @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V0n ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
<=> ( V0n
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LO__word__0,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0n: $i] :
( ( mem @ V0n @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V0n ) )
<=> ( V0n
!= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) )
& ! [V1n: $i] :
( ( mem @ V1n @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) )
=> ~ ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27b ) @ V1n ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__ADD__LEFT__LO2,axiom,
! [A_27a: del,V0c: $i] :
( ( mem @ V0c @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1a: $i] :
( ( mem @ V1a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0c ) @ V1a ) ) @ V1a ) )
<=> ( ( V1a
!= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ( ( ( V0c
!= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0c ) ) @ V1a ) ) )
| ( V1a
= ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0c ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__ADD__LEFT__LS2,axiom,
! [A_27a: del,V0c: $i] :
( ( mem @ V0c @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1a: $i] :
( ( mem @ V1a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0c ) @ V1a ) ) @ V1a ) )
<=> ( ( V0c
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
| ( ( V1a
!= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0c ) ) @ V1a ) )
| ( V1a
= ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0c ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__ADD__RIGHT__LO2,axiom,
! [A_27a: del,V0c: $i] :
( ( mem @ V0c @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1a: $i] :
( ( mem @ V1a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V1a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0c ) @ V1a ) ) )
<=> ( ( V0c
!= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ( ( V1a
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
| ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V1a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0c ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__ADD__RIGHT__LS2,axiom,
! [A_27a: del,V0c: $i] :
( ( mem @ V0c @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1a: $i] :
( ( mem @ V1a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V1a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0c ) @ V1a ) ) )
<=> ( ( V1a
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
| ( V0c
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
| ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V1a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0c ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__msb__neg,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0w ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V0w ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__abs,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Eword__abs @ A_27a ) @ V0w )
= ( ap @ ( c_2Efcp_2EFCP @ bool @ A_27a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V1i: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0w ) ) ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0w ) @ V1i ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0w ) ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0w ) ) @ V1i ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__abs__word__abs,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Eword__abs @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__abs @ A_27a ) @ V0w ) )
= ( ap @ ( c_2Ewords_2Eword__abs @ A_27a ) @ V0w ) ) ) ).
thf(conj_thm_2Ewords_2Eword__abs__neg,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Eword__abs @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V0w ) )
= ( ap @ ( c_2Ewords_2Eword__abs @ A_27a ) @ V0w ) ) ) ).
thf(conj_thm_2Ewords_2Eword__abs__diff,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Eword__abs @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0a ) @ V1b ) )
= ( ap @ ( c_2Ewords_2Eword__abs @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V1b ) @ V0a ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EFST__ADD__WITH__CARRY,axiom,
! [A_27a: del,A_27b: del,A_27c: del] :
( ! [V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Epair_2EFST @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Epair_2Eprod @ bool @ bool ) ) @ ( ap @ ( c_2Ewords_2Eadd__with__carry @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Epair_2Eprod @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool ) ) @ V0a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool ) @ V1b ) @ c_2Ebool_2EF ) ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0a ) @ V1b ) ) ) )
& ! [V2a: $i] :
( ( mem @ V2a @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) )
=> ! [V3b: $i] :
( ( mem @ V3b @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) )
=> ( ( ap @ ( c_2Epair_2EFST @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) @ ( ty_2Epair_2Eprod @ bool @ bool ) ) @ ( ap @ ( c_2Ewords_2Eadd__with__carry @ A_27b ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) @ ( ty_2Epair_2Eprod @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) @ bool ) ) @ V2a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) @ bool ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27b ) @ V3b ) ) @ c_2Ebool_2ET ) ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27b ) @ V2a ) @ V3b ) ) ) )
& ! [V4a: $i] :
( ( mem @ V4a @ ( ty_2Efcp_2Ecart @ bool @ A_27c ) )
=> ! [V5b: $i] :
( ( mem @ V5b @ ( ty_2Efcp_2Ecart @ bool @ A_27c ) )
=> ( ( ap @ ( c_2Epair_2EFST @ ( ty_2Efcp_2Ecart @ bool @ A_27c ) @ ( ty_2Epair_2Eprod @ bool @ bool ) ) @ ( ap @ ( c_2Ewords_2Eadd__with__carry @ A_27c ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Efcp_2Ecart @ bool @ A_27c ) @ ( ty_2Epair_2Eprod @ ( ty_2Efcp_2Ecart @ bool @ A_27c ) @ bool ) ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27c ) @ V4a ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Efcp_2Ecart @ bool @ A_27c ) @ bool ) @ V5b ) @ c_2Ebool_2ET ) ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27c ) @ V5b ) @ V4a ) ) ) )
& ! [V6n: tp__ty_2Enum_2Enum,V7a: $i] :
( ( mem @ V7a @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) )
=> ( ( ap @ ( c_2Epair_2EFST @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) @ ( ty_2Epair_2Eprod @ bool @ bool ) ) @ ( ap @ ( c_2Ewords_2Eadd__with__carry @ A_27b ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) @ ( ty_2Epair_2Eprod @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) @ bool ) ) @ V7a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) @ bool ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V6n ) ) ) @ c_2Ebool_2ET ) ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27b ) @ V7a ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27b ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V6n ) ) ) ) ) )
& ! [V8n: tp__ty_2Enum_2Enum,V9b: $i] :
( ( mem @ V9b @ ( ty_2Efcp_2Ecart @ bool @ A_27c ) )
=> ( ( ap @ ( c_2Epair_2EFST @ ( ty_2Efcp_2Ecart @ bool @ A_27c ) @ ( ty_2Epair_2Eprod @ bool @ bool ) ) @ ( ap @ ( c_2Ewords_2Eadd__with__carry @ A_27c ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Efcp_2Ecart @ bool @ A_27c ) @ ( ty_2Epair_2Eprod @ ( ty_2Efcp_2Ecart @ bool @ A_27c ) @ bool ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27c ) @ ( inj__ty_2Enum_2Enum @ V8n ) ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Efcp_2Ecart @ bool @ A_27c ) @ bool ) @ V9b ) @ c_2Ebool_2ET ) ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27c ) @ V9b ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27c ) @ ( ap @ ( c_2Ewords_2En2w @ A_27c ) @ ( inj__ty_2Enum_2Enum @ V8n ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EADD__WITH__CARRY__SUB,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1y: $i] :
( ( mem @ V1y @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Eadd__with__carry @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Epair_2Eprod @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool ) ) @ V0x ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ V1y ) ) @ c_2Ebool_2ET ) ) )
= ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Epair_2Eprod @ bool @ bool ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0x ) @ V1y ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ bool @ bool ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V1y ) @ V0x ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0x ) ) @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V1y ) ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0x ) @ V1y ) ) ) @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0x ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__eq__n2w,axiom,
! [A_27a: del] :
( ! [V0m: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
( ( ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ c_2Ebit_2EMOD__2EXP__EQ @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
& ! [V2n: tp__ty_2Enum_2Enum] :
( ( ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2n ) )
= ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Ebit_2EMOD__2EXP__MAX @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
& ! [V3n: tp__ty_2Enum_2Enum] :
( ( ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Ebit_2EMOD__2EXP__MAX @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__lt__n2w,axiom,
! [A_27a: del,V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) )
<=> ( p
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ bool @ bool )
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ bool @ ( arr @ bool @ bool ) )
@ ( lam @ bool
@ ^ [V2sa: $i] :
( lam @ bool
@ ^ [V3sb: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ V2sa ) @ V3sb ) ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ V2sa ) @ ( ap @ c_2Ebool_2E_7E @ V3sb ) ) ) ) ) )
@ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( 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 @ V0a ) ) ) )
@ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( 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 @ V1b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__gt__n2w,axiom,
! [A_27a: del,V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__gt @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) )
<=> ( p
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ bool @ bool )
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ bool @ ( arr @ bool @ bool ) )
@ ( lam @ bool
@ ^ [V2sa: $i] :
( lam @ bool
@ ^ [V3sb: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ V2sa ) @ V3sb ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3E @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ V2sa ) ) @ V3sb ) ) ) ) )
@ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( 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 @ V0a ) ) ) )
@ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( 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 @ V1b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__le__n2w,axiom,
! [A_27a: del,V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) )
<=> ( p
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ bool @ bool )
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ bool @ ( arr @ bool @ bool ) )
@ ( lam @ bool
@ ^ [V2sa: $i] :
( lam @ bool
@ ^ [V3sb: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ V2sa ) @ V3sb ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ V2sa ) @ ( ap @ c_2Ebool_2E_7E @ V3sb ) ) ) ) ) )
@ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( 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 @ V0a ) ) ) )
@ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( 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 @ V1b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__ge__n2w,axiom,
! [A_27a: del,V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ge @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) )
<=> ( p
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ bool @ bool )
@ ( ap
@ ( ap @ ( c_2Ebool_2ELET @ bool @ ( arr @ bool @ bool ) )
@ ( lam @ bool
@ ^ [V2sa: $i] :
( lam @ bool
@ ^ [V3sb: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ V2sa ) @ V3sb ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3E_3D @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ V2sa ) ) @ V3sb ) ) ) ) )
@ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( 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 @ V0a ) ) ) )
@ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( 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 @ V1b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__ls__n2w,axiom,
! [A_27a: del,V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__hi__n2w,axiom,
! [A_27a: del,V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__hi @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__lo__n2w,axiom,
! [A_27a: del,V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__hs__n2w,axiom,
! [A_27a: del,V0a: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__hs @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3E_3D @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Ew2n__add,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ~ ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V0a ) )
& ~ ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ V1b ) ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0a ) @ V1b ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0a ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1b ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Esaturate__w2w__n2w,axiom,
! [A_27a: del,A_27b: del,V0n: tp__ty_2Enum_2Enum] :
( ( ap @ ( c_2Ewords_2Esaturate__w2w @ A_27a @ A_27b ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
= ( ap
@ ( ap @ ( c_2Ebool_2ELET @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V1m: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Ewords_2Edimword @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ V1m ) ) ) @ ( c_2Ewords_2Eword__T @ A_27b ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ V1m ) ) ) )
@ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Esaturate__w2w,axiom,
! [A_27a: del,A_27b: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( c_2Ewords_2Esaturate__w2w @ A_27a @ A_27b ) @ V0w )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ ( ap @ ( c_2Ewords_2Ew2w @ A_27b @ A_27a ) @ ( c_2Ewords_2Eword__T @ A_27b ) ) ) @ V0w ) ) ) @ ( c_2Ewords_2Eword__T @ A_27b ) ) @ ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ V0w ) ) ) ) ).
thf(conj_thm_2Ewords_2Esaturate__sub,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Esaturate__sub @ A_27a ) @ V0a ) @ V1b )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V0a ) @ V1b ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0a ) @ V1b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Esaturate__add,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Esaturate__add @ A_27a ) @ V0a ) @ V1b )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ ( c_2Ewords_2Eword__T @ A_27a ) ) @ V0a ) ) @ V1b ) ) @ ( c_2Ewords_2Eword__T @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0a ) @ V1b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2ENOT__FINITE__IMP__dimword__2,axiom,
! [A_27a: del] :
( ~ ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Esaturate__mul,axiom,
! [A_27a: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Esaturate__mul @ A_27a ) @ V0a ) @ V1b )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ ( ty_2Esum_2Esum @ A_27a @ A_27a ) ) @ ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ ( ty_2Esum_2Esum @ A_27a @ A_27a ) ) @ ( c_2Ewords_2Eword__T @ A_27a ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ ( ty_2Esum_2Esum @ A_27a @ A_27a ) ) @ ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ ( ty_2Esum_2Esum @ A_27a @ A_27a ) ) @ V0a ) ) @ ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ ( ty_2Esum_2Esum @ A_27a @ A_27a ) ) @ V1b ) ) ) ) ) @ ( c_2Ewords_2Eword__T @ A_27a ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ V0a ) @ V1b ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__DIVISION,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( V0w
!= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
=> ! [V1v: $i] :
( ( mem @ V1v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( V1v
= ( ap @ ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mul @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__div @ A_27a ) @ V1v ) @ V0w ) ) @ V0w ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mod @ A_27a ) @ V1v ) @ V0w ) ) )
& ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__mod @ A_27a ) @ V1v ) @ V0w ) ) @ V0w ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__reverse__0,axiom,
! [A_27a: del] :
( ( ap @ ( c_2Ewords_2Eword__reverse @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ).
thf(conj_thm_2Ewords_2Eword__reverse__word__T,axiom,
! [A_27a: del] :
( ( ap @ ( c_2Ewords_2Eword__reverse @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
= ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Esw2sw__0,axiom,
! [A_27a: del,A_27b: del] :
( ( ap @ ( c_2Ewords_2Esw2sw @ A_27a @ A_27b ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ).
thf(conj_thm_2Ewords_2Esw2sw__word__T,axiom,
! [A_27a: del,A_27b: del] :
( ( ap @ ( c_2Ewords_2Esw2sw @ A_27b @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27b ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
= ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__div__1,axiom,
! [A_27a: del,V0v: $i] :
( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__div @ A_27a ) @ V0v ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
= V0v ) ) ).
thf(conj_thm_2Ewords_2Eword__bit__0,axiom,
! [A_27a: del,V0h: tp__ty_2Enum_2Enum] :
~ ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bit @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0h ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__lsb__word__T,axiom,
! [A_27a: del] : ( p @ ( ap @ ( c_2Ewords_2Eword__lsb @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__msb__word__T,axiom,
! [A_27a: del] : ( p @ ( ap @ ( c_2Ewords_2Eword__msb @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__bit__0__word__T,axiom,
! [A_27a: del] : ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__bit @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__log2__1,axiom,
! [A_27a: del] :
( ( ap @ ( c_2Ewords_2Eword__log2 @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ).
thf(conj_thm_2Ewords_2Eword__join__0,axiom,
! [A_27a: del,A_27b: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__join @ A_27b @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V0a )
= ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ ( ty_2Esum_2Esum @ A_27b @ A_27a ) ) @ V0a ) ) ) ).
thf(conj_thm_2Ewords_2Eword__concat__0__0,axiom,
! [A_27a: del,A_27b: del,A_27c: del] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27c ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ).
thf(conj_thm_2Ewords_2Ew2w__eq__n2w,axiom,
! [A_27a: del,A_27b: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1y: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1y ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) )
=> ( ( ( ap @ ( c_2Ewords_2Ew2w @ A_27a @ A_27b ) @ V0x )
= ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) )
<=> ( V0x
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__extract__eq__n2w,axiom,
! [A_27a: del,A_27b: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1h: tp__ty_2Enum_2Enum,V2y: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( 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 @ V1h ) ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2y ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) )
=> ( ( ( ap @ ( ap @ ( ap @ ( c_2Ewords_2Eword__extract @ A_27a @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V1h ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0x )
= ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) )
<=> ( V0x
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V2y ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__concat__0,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0x: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27c ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__concat__0__eq,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) )
=> ! [V1y: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27a ) @ ( c_2Epred__set_2EUNIV @ A_27a ) ) )
& ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27c ) @ ( c_2Ebool_2Ethe__value @ A_27c ) ) ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1y ) ) @ ( ap @ ( c_2Ewords_2Edimword @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) ) )
=> ( ( ( ap @ ( ap @ ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V0x )
= ( ap @ ( c_2Ewords_2En2w @ A_27c ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) )
<=> ( V0x
= ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V1y ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__concat__assoc,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,A_27e: del,A_27f: del,V0a: $i] :
( ( mem @ V0a @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) )
=> ! [V2c: $i] :
( ( mem @ V2c @ ( ty_2Efcp_2Ecart @ bool @ A_27c ) )
=> ( ( ( 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 ) ) )
& ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ A_27c ) @ ( c_2Epred__set_2EUNIV @ A_27c ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ A_27d ) @ ( c_2Ebool_2Ethe__value @ A_27d ) ) )
= ( surj__ty_2Enum_2Enum @ ( 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 ) ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ A_27e ) @ ( c_2Ebool_2Ethe__value @ A_27e ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Efcp_2Edimindex @ A_27b ) @ ( c_2Ebool_2Ethe__value @ A_27b ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27c ) @ ( c_2Ebool_2Ethe__value @ A_27c ) ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ A_27f ) @ ( c_2Ebool_2Ethe__value @ A_27f ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( c_2Efcp_2Edimindex @ A_27d ) @ ( c_2Ebool_2Ethe__value @ A_27d ) ) ) @ ( ap @ ( c_2Efcp_2Edimindex @ A_27c ) @ ( c_2Ebool_2Ethe__value @ A_27c ) ) ) ) ) )
=> ( ( ap @ ( ap @ ( c_2Ewords_2Eword__concat @ A_27d @ A_27c @ A_27f ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27d ) @ V0a ) @ V1b ) ) @ V2c )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__concat @ A_27a @ A_27e @ A_27f ) @ V0a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__concat @ A_27b @ A_27c @ A_27e ) @ V1b ) @ V2c ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__join__word__T,axiom,
! [A_27a: del,A_27b: del] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__join @ A_27a @ A_27b ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27b ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
= ( ap @ ( c_2Ewords_2Eword__2comp @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( ap @ ( c_2Ewords_2En2w @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__concat__word__T,axiom,
! [A_27a: del,A_27b: del,A_27c: del] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__concat @ A_27a @ A_27b @ A_27c ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27b ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
= ( ap @ ( c_2Ewords_2Ew2w @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) @ A_27c ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( ap @ ( c_2Ewords_2En2w @ ( ty_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Elsr__1__word__T,axiom,
! [A_27a: del] :
( ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) )
= ( c_2Ewords_2Eword__H @ A_27a ) ) ).
thf(conj_thm_2Ewords_2Eword__rrx__0,axiom,
! [A_27a: del,A_27b: del] :
( ( ( ap @ ( c_2Ewords_2Eword__rrx @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ bool @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ c_2Ebool_2EF ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
= ( ap @ ( ap @ ( c_2Epair_2E_2C @ bool @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ c_2Ebool_2EF ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
& ( ( ap @ ( c_2Ewords_2Eword__rrx @ A_27b ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ bool @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) ) @ c_2Ebool_2ET ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
= ( ap @ ( ap @ ( c_2Epair_2E_2C @ bool @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) ) @ c_2Ebool_2EF ) @ ( c_2Ewords_2Eword__L @ A_27b ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__rrx__word__T,axiom,
! [A_27a: del,A_27b: del] :
( ( ( ap @ ( c_2Ewords_2Eword__rrx @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ bool @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ c_2Ebool_2EF ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
= ( ap @ ( ap @ ( c_2Epair_2E_2C @ bool @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ c_2Ebool_2ET ) @ ( c_2Ewords_2Eword__H @ A_27a ) ) )
& ( ( ap @ ( c_2Ewords_2Eword__rrx @ A_27b ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ bool @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) ) @ c_2Ebool_2ET ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27b ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
= ( ap @ ( ap @ ( c_2Epair_2E_2C @ bool @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) ) @ c_2Ebool_2ET ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27b ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__T__not__zero,axiom,
! [A_27a: del] :
( ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
!= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LS__word__T,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0n: $i] :
( ( mem @ V0n @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ V0n ) )
<=> ( V0n
= ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
& ! [V1n: $i] :
( ( mem @ V1n @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27b ) @ V1n ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27b ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LO__word__T,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0n: $i] :
( ( mem @ V0n @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ~ ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ V0n ) ) )
& ! [V1n: $i] :
( ( mem @ V1n @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27b ) @ V1n ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27b ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
<=> ( V1n
!= ( ap @ ( c_2Ewords_2Eword__2comp @ A_27b ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LESS__0__word__T,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del] :
( ~ ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ~ ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27b ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27b ) @ ( ap @ ( c_2Ewords_2En2w @ A_27b ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27c ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27c ) @ ( ap @ ( c_2Ewords_2En2w @ A_27c ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27c ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
& ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27d ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27d ) @ ( ap @ ( c_2Ewords_2En2w @ A_27d ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27d ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__reverse__thm,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1v: $i] :
( ( mem @ V1v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2n: tp__ty_2Enum_2Enum] :
( ( ( ap @ ( c_2Ewords_2Eword__reverse @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__reverse @ A_27a ) @ V0w ) )
= V0w )
& ( ( ap @ ( c_2Ewords_2Eword__reverse @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__reverse @ A_27a ) @ V0w ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
& ( ( ap @ ( c_2Ewords_2Eword__reverse @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__lsl @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__reverse @ A_27a ) @ V0w ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) )
& ( ( ap @ ( c_2Ewords_2Eword__reverse @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ V0w ) @ V1v ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__or @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__reverse @ A_27a ) @ V0w ) ) @ ( ap @ ( c_2Ewords_2Eword__reverse @ A_27a ) @ V1v ) ) )
& ( ( ap @ ( c_2Ewords_2Eword__reverse @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ V0w ) @ V1v ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__and @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__reverse @ A_27a ) @ V0w ) ) @ ( ap @ ( c_2Ewords_2Eword__reverse @ A_27a ) @ V1v ) ) )
& ( ( ap @ ( c_2Ewords_2Eword__reverse @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ V0w ) @ V1v ) )
= ( ap @ ( ap @ ( c_2Ewords_2Eword__xor @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__reverse @ A_27a ) @ V0w ) ) @ ( ap @ ( c_2Ewords_2Eword__reverse @ A_27a ) @ V1v ) ) )
& ( ( ap @ ( c_2Ewords_2Eword__reverse @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ V0w ) )
= ( ap @ ( c_2Ewords_2Eword__1comp @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__reverse @ A_27a ) @ V0w ) ) )
& ( ( ap @ ( c_2Ewords_2Eword__reverse @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ( ( ap @ ( c_2Ewords_2Eword__reverse @ A_27a ) @ ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
= ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
& ( ( ( ap @ ( c_2Ewords_2Eword__reverse @ A_27a ) @ V0w )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
<=> ( V0w
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
& ( ( ( ap @ ( c_2Ewords_2Eword__reverse @ A_27a ) @ V0w )
= ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
<=> ( V0w
= ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Ebit__count__upto__0,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Ewords_2Ebit__count__upto @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V0w ) )
= fo__c_2Enum_2E0 ) ) ).
thf(conj_thm_2Ewords_2Ebit__count__upto__SUC,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1n: tp__ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Ewords_2Ebit__count__upto @ A_27a ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ V0w ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V0w ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Ebit__count__upto @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ V0w ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Ebit__count__upto__is__zero,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum,V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Ewords_2Ebit__count__upto @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ V1w ) )
= fo__c_2Enum_2E0 )
<=> ! [V2i: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2i ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
=> ~ ( p @ ( ap @ ( ap @ ( c_2Efcp_2Efcp__index @ bool @ A_27a ) @ V1w ) @ ( inj__ty_2Enum_2Enum @ V2i ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Ebit__count__is__zero,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Ebit__count @ A_27a ) @ V0w ) )
= fo__c_2Enum_2E0 )
<=> ( V0w
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__FINITE,axiom,
! [A_27a: del,V0s: $i] :
( ( mem @ V0s @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool ) )
=> ( p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ V0s ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__SET__INDUCT,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool ) @ bool ) )
=> ( ( ( p @ ( ap @ V0P @ ( c_2Epred__set_2EEMPTY @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) )
& ! [V1s: $i] :
( ( mem @ V1s @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool ) )
=> ( ( p @ ( ap @ V0P @ V1s ) )
=> ! [V2e: $i] :
( ( mem @ V2e @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ V2e ) @ V1s ) )
=> ( p @ ( ap @ V0P @ ( ap @ ( ap @ ( c_2Epred__set_2EINSERT @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ V2e ) @ V1s ) ) ) ) ) ) ) )
=> ! [V3s: $i] :
( ( mem @ V3s @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool ) )
=> ( p @ ( ap @ V0P @ V3s ) ) ) ) ) ).
thf(conj_thm_2Ewords_2ESUC__WORD__PRED,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( V0x
!= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0x ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0x ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__PRED__THM,axiom,
! [A_27a: del,V0m: $i] :
( ( mem @ V0m @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( V0m
!= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0m ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0m ) ) ) ) ) ).
thf(conj_thm_2Ewords_2ELSR__LESS,axiom,
! [A_27a: del,V0m: tp__ty_2Enum_2Enum,V1y: $i] :
( ( mem @ V1y @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( V1y
!= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) )
=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lsr @ A_27a ) @ V1y ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1y ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Eword__sub__w2n,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1y: $i] :
( ( mem @ V1y @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V1y ) @ V0x ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0x ) @ V1y ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2D @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0x ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1y ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LE__EQ__LS,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1y: $i] :
( ( mem @ V1y @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V0x ) )
& ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V1y ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ V0x ) @ V1y ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__ls @ A_27a ) @ V0x ) @ V1y ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LT__EQ__LO,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1y: $i] :
( ( mem @ V1y @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V0x ) )
& ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V1y ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V0x ) @ V1y ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lo @ A_27a ) @ V0x ) @ V1y ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__ZERO__LE,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V0w ) )
<=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0w ) ) @ ( ap @ ( c_2Ewords_2EINT__MIN @ A_27a ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__LT__SUB__UPPER,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1y: $i] :
( ( mem @ V1y @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V1y ) )
& ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V1y ) @ V0x ) ) )
=> ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0x ) @ V1y ) ) @ V0x ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__SUB__LT,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1y: $i] :
( ( mem @ V1y @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V1y ) )
& ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ V1y ) @ V0x ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0x ) @ V1y ) ) )
& ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__lt @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0x ) @ V1y ) ) @ V0x ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EWORD__SUB__LE,axiom,
! [A_27a: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1y: $i] :
( ( mem @ V1y @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V1y ) )
& ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ V1y ) @ V0x ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0x ) @ V1y ) ) )
& ( p @ ( ap @ ( ap @ ( c_2Ewords_2Eword__le @ A_27a ) @ ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0x ) @ V1y ) ) @ V0x ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__1,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ ty_2Eone_2Eone ) @ ( c_2Ebool_2Ethe__value @ ty_2Eone_2Eone ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Efinite__1,axiom,
p @ ( ap @ ( c_2Epred__set_2EFINITE @ ty_2Eone_2Eone ) @ ( c_2Epred__set_2EUNIV @ ty_2Eone_2Eone ) ) ).
thf(conj_thm_2Ewords_2EINT__MIN__1,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2EINT__MIN @ ty_2Eone_2Eone ) @ ( c_2Ebool_2Ethe__value @ ty_2Eone_2Eone ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimword__1,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Edimword @ ty_2Eone_2Eone ) @ ( c_2Ebool_2Ethe__value @ ty_2Eone_2Eone ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(stp_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
tp__c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: $tType ).
thf(stp_inj_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
inj__c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: tp__c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone > $i ).
thf(stp_surj_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
surj__c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: $i > tp__c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone ).
thf(stp_inj_surj_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] :
( ( surj__c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( inj__c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ( mem @ ( inj__c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ).
thf(stp_iso_mem_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) )
=> ( X
= ( inj__c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( surj__c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__2,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Efinite__2,axiom,
p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) @ ( c_2Epred__set_2EUNIV @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ).
thf(conj_thm_2Ewords_2EINT__MIN__2,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2EINT__MIN @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimword__2,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Edimword @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(stp_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
tp__c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: $tType ).
thf(stp_inj_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
inj__c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: tp__c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone > $i ).
thf(stp_surj_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
surj__c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: $i > tp__c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone ).
thf(stp_inj_surj_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone] :
( ( surj__c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ ( inj__c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone] : ( mem @ ( inj__c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ).
thf(stp_iso_mem_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) )
=> ( X
= ( inj__c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ ( surj__c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__3,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Efinite__3,axiom,
p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) @ ( c_2Epred__set_2EUNIV @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ).
thf(conj_thm_2Ewords_2EINT__MIN__3,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2EINT__MIN @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimword__3,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Edimword @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(stp_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: $tType ).
thf(stp_inj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone > $i ).
thf(stp_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: $i > tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone ).
thf(stp_inj_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] :
( ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ( mem @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ).
thf(stp_iso_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) )
=> ( X
= ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__4,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Efinite__4,axiom,
p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) @ ( c_2Epred__set_2EUNIV @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ).
thf(conj_thm_2Ewords_2EINT__MIN__4,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2EINT__MIN @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimword__4,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Edimword @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
thf(stp_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: $tType ).
thf(stp_inj_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone > $i ).
thf(stp_surj_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
surj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: $i > tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone ).
thf(stp_inj_surj_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] :
( ( surj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ( mem @ ( inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ).
thf(stp_iso_mem_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) )
=> ( X
= ( inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( surj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__5,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Efinite__5,axiom,
p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) @ ( c_2Epred__set_2EUNIV @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ).
thf(conj_thm_2Ewords_2EINT__MIN__5,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2EINT__MIN @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimword__5,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Edimword @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ).
thf(stp_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: $tType ).
thf(stp_inj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone > $i ).
thf(stp_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: $i > tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone ).
thf(stp_inj_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone] :
( ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone] : ( mem @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ).
thf(stp_iso_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) )
=> ( X
= ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__6,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Efinite__6,axiom,
p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) @ ( c_2Epred__set_2EUNIV @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ).
thf(conj_thm_2Ewords_2EINT__MIN__6,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2EINT__MIN @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimword__6,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Edimword @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ).
thf(stp_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: $tType ).
thf(stp_inj_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone > $i ).
thf(stp_surj_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
surj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: $i > tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone ).
thf(stp_inj_surj_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone] :
( ( surj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ ( inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone] : ( mem @ ( inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ).
thf(stp_iso_mem_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) )
=> ( X
= ( inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ ( surj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__7,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Efinite__7,axiom,
p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) @ ( c_2Epred__set_2EUNIV @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ).
thf(conj_thm_2Ewords_2EINT__MIN__7,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2EINT__MIN @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimword__7,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Edimword @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ).
thf(stp_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: $tType ).
thf(stp_inj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone > $i ).
thf(stp_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: $i > tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone ).
thf(stp_inj_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] :
( ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ( mem @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ).
thf(stp_iso_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) )
=> ( X
= ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__8,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Efinite__8,axiom,
p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EINT__MIN__8,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2EINT__MIN @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimword__8,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Edimword @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(stp_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: $tType ).
thf(stp_inj_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone > $i ).
thf(stp_surj_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
surj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: $i > tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone ).
thf(stp_inj_surj_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] :
( ( surj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ( mem @ ( inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ).
thf(stp_iso_mem_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) )
=> ( X
= ( inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( surj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__9,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Efinite__9,axiom,
p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EINT__MIN__9,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2EINT__MIN @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimword__9,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Edimword @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(stp_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: $tType ).
thf(stp_inj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone > $i ).
thf(stp_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: $i > tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone ).
thf(stp_inj_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] :
( ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ( mem @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ).
thf(stp_iso_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) )
=> ( X
= ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__10,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Efinite__10,axiom,
p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EINT__MIN__10,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2EINT__MIN @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimword__10,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Edimword @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(stp_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: $tType ).
thf(stp_inj_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone > $i ).
thf(stp_surj_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
surj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: $i > tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone ).
thf(stp_inj_surj_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] :
( ( surj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ( mem @ ( inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ).
thf(stp_iso_mem_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) )
=> ( X
= ( inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( surj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__11,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Efinite__11,axiom,
p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EINT__MIN__11,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2EINT__MIN @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimword__11,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Edimword @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(stp_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: $tType ).
thf(stp_inj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone > $i ).
thf(stp_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: $i > tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone ).
thf(stp_inj_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone] :
( ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone] : ( mem @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ).
thf(stp_iso_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) )
=> ( X
= ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__12,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Efinite__12,axiom,
p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EINT__MIN__12,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2EINT__MIN @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimword__12,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Edimword @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(stp_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: $tType ).
thf(stp_inj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone > $i ).
thf(stp_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: $i > tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone ).
thf(stp_inj_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] :
( ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ( mem @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ).
thf(stp_iso_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) )
=> ( X
= ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__16,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Efinite__16,axiom,
p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EINT__MIN__16,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2EINT__MIN @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimword__16,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Edimword @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(stp_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: $tType ).
thf(stp_inj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone > $i ).
thf(stp_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: $i > tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone ).
thf(stp_inj_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] :
( ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ( mem @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ).
thf(stp_iso_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) )
=> ( X
= ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__20,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( 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(conj_thm_2Ewords_2Efinite__20,axiom,
p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EINT__MIN__20,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2EINT__MIN @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimword__20,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Edimword @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(stp_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: $tType ).
thf(stp_inj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone > $i ).
thf(stp_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: $i > tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone ).
thf(stp_inj_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone] :
( ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone] : ( mem @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ).
thf(stp_iso_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) )
=> ( X
= ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__24,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Efinite__24,axiom,
p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EINT__MIN__24,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2EINT__MIN @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimword__24,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Edimword @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(stp_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: $tType ).
thf(stp_inj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone > $i ).
thf(stp_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: $i > tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone ).
thf(stp_inj_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone] :
( ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone] : ( mem @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ).
thf(stp_iso_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) )
=> ( X
= ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) ) ) ) ).
thf(stp_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: $tType ).
thf(stp_inj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone > $i ).
thf(stp_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: $i > tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone ).
thf(stp_inj_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone] :
( ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone] : ( mem @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ).
thf(stp_iso_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) )
=> ( X
= ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__28,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Efinite__28,axiom,
p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EINT__MIN__28,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2EINT__MIN @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimword__28,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Edimword @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(stp_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: $tType ).
thf(stp_inj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone > $i ).
thf(stp_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: $i > tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone ).
thf(stp_inj_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone] :
( ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone] : ( mem @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ).
thf(stp_iso_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) )
=> ( X
= ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) ) ) ) ).
thf(stp_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: $tType ).
thf(stp_inj_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone > $i ).
thf(stp_surj_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
surj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: $i > tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone ).
thf(stp_inj_surj_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone] :
( ( surj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ ( inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone] : ( mem @ ( inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ).
thf(stp_iso_mem_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) )
=> ( X
= ( inj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ ( surj__c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__30,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Efinite__30,axiom,
p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EINT__MIN__30,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2EINT__MIN @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimword__30,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Edimword @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(stp_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: $tType ).
thf(stp_inj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone > $i ).
thf(stp_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: $i > tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone ).
thf(stp_inj_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] :
( ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ( mem @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) ).
thf(stp_iso_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) )
=> ( X
= ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__32,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Efinite__32,axiom,
p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EINT__MIN__32,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2EINT__MIN @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimword__32,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Edimword @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(stp_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: $tType ).
thf(stp_inj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone > $i ).
thf(stp_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: $i > tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone ).
thf(stp_inj_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone] :
( ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone] : ( mem @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) ).
thf(stp_iso_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) )
=> ( X
= ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__48,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( 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(conj_thm_2Ewords_2Efinite__48,axiom,
p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EINT__MIN__48,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2EINT__MIN @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimword__48,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Edimword @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(stp_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: $tType ).
thf(stp_inj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone > $i ).
thf(stp_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: $i > tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone ).
thf(stp_inj_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] :
( ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ( mem @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) ) ).
thf(stp_iso_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) )
=> ( X
= ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__64,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Efinite__64,axiom,
p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EINT__MIN__64,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2EINT__MIN @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimword__64,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Edimword @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(stp_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: $tType ).
thf(stp_inj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone > $i ).
thf(stp_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,type,
surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone: $i > tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone ).
thf(stp_inj_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone] :
( ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone] : ( mem @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) ) ).
thf(stp_iso_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) )
=> ( X
= ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit1_ty_2Eone_2Eone @ X ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__96,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( 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(conj_thm_2Ewords_2Efinite__96,axiom,
p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EINT__MIN__96,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2EINT__MIN @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimword__96,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Edimword @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit1 @ ty_2Eone_2Eone ) ) ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(stp_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: $tType ).
thf(stp_inj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone > $i ).
thf(stp_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,
surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone: $i > tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone ).
thf(stp_inj_surj_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] :
( ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: tp__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ( mem @ ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) ) ) ).
thf(stp_iso_mem_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) ) )
=> ( X
= ( inj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ ( surj__c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimindex__128,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Efcp_2Edimindex @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Efinite__128,axiom,
p @ ( ap @ ( c_2Epred__set_2EFINITE @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) ) ) @ ( c_2Epred__set_2EUNIV @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2EINT__MIN__128,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2EINT__MIN @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2Edimword__128,axiom,
( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Ewords_2Edimword @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) ) ) @ ( c_2Ebool_2Ethe__value @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ( ty_2Efcp_2Ebit0 @ ty_2Eone_2Eone ) ) ) ) ) ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Ewords_2En2w__itself__primitive__def,axiom,
! [A_27a: del] :
( ( c_2Ewords_2En2w__itself @ A_27a )
= ( ap
@ ( ap @ ( c_2Erelation_2EWFREC @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Ebool_2Eitself @ A_27a ) ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
@ ( ap @ ( c_2Emin_2E_40 @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Ebool_2Eitself @ A_27a ) ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Ebool_2Eitself @ A_27a ) ) @ bool ) ) )
@ ( lam @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Ebool_2Eitself @ A_27a ) ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Ebool_2Eitself @ A_27a ) ) @ bool ) )
@ ^ [V0R: $i] : ( ap @ ( c_2Erelation_2EWF @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Ebool_2Eitself @ A_27a ) ) ) @ V0R ) ) ) )
@ ( lam @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Ebool_2Eitself @ A_27a ) ) @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
@ ^ [V1n2w__itself: $i] :
( lam @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Ebool_2Eitself @ A_27a ) )
@ ^ [V2a: $i] :
( ap @ ( ap @ ( c_2Epair_2Epair__CASE @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ty_2Enum_2Enum @ ( ty_2Ebool_2Eitself @ A_27a ) ) @ V2a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3v: $i] :
( lam @ ( ty_2Ebool_2Eitself @ A_27a )
@ ^ [V4v1: $i] : ( ap @ ( c_2Ecombin_2EI @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ V3v ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2En2w__itself__ind,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Ebool_2Eitself @ A_27a ) ) @ bool ) )
=> ( ! [V1n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0P @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Ebool_2Eitself @ A_27a ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) ) )
=> ! [V2v: tp__ty_2Enum_2Enum,V3v1: $i] :
( ( mem @ V3v1 @ ( ty_2Ebool_2Eitself @ A_27a ) )
=> ( p @ ( ap @ V0P @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Ebool_2Eitself @ A_27a ) ) @ ( inj__ty_2Enum_2Enum @ V2v ) ) @ V3v1 ) ) ) ) ) ) ).
thf(conj_thm_2Ewords_2En2w__itself__def,axiom,
! [A_27a: del,V0n: tp__ty_2Enum_2Enum] :
( ( ap @ ( c_2Ewords_2En2w__itself @ A_27a ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Ebool_2Eitself @ A_27a ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( c_2Ebool_2Ethe__value @ A_27a ) ) )
= ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ).
%------------------------------------------------------------------------------