ITP001 Axioms: ITP095_5.ax
%------------------------------------------------------------------------------
% File : ITP095_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 : blast_2.ax [Gau20]
% : HL4095_5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 74 ( 8 unt; 28 typ; 0 def)
% Number of atoms : 1535 ( 32 equ)
% Maximal formula atoms : 12 ( 20 avg)
% Number of connectives : 115 ( 3 ~; 2 |; 7 &)
% ( 19 <=>; 84 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 1377 (1377 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 85 ( 24 >; 61 *; 0 +; 0 <<)
% Number of predicates : 55 ( 54 usr; 25 prp; 0-3 aty)
% Number of functors : 28 ( 28 usr; 4 con; 0-5 aty)
% Number of variables : 184 ( 184 !; 0 ?; 184 :)
% SPC : TF0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tp_c_2Eblast_2EBCARRY,type,
c_2Eblast_2EBCARRY: $i ).
tff(mem_c_2Eblast_2EBCARRY,axiom,
mem(c_2Eblast_2EBCARRY,arr(ty_2Enum_2Enum,arr(arr(ty_2Enum_2Enum,bool),arr(arr(ty_2Enum_2Enum,bool),arr(bool,bool))))) ).
tff(tp_c_2Eblast_2EBSUM,type,
c_2Eblast_2EBSUM: $i ).
tff(mem_c_2Eblast_2EBSUM,axiom,
mem(c_2Eblast_2EBSUM,arr(ty_2Enum_2Enum,arr(arr(ty_2Enum_2Enum,bool),arr(arr(ty_2Enum_2Enum,bool),arr(bool,bool))))) ).
tff(tp_c_2Eblast_2Ebcarry,type,
c_2Eblast_2Ebcarry: $i ).
tff(mem_c_2Eblast_2Ebcarry,axiom,
mem(c_2Eblast_2Ebcarry,arr(bool,arr(bool,arr(bool,bool)))) ).
tff(stp_fo_c_2Eblast_2Ebcarry,type,
fo__c_2Eblast_2Ebcarry: ( tp__o * tp__o * tp__o ) > tp__o ).
tff(stp_eq_fo_c_2Eblast_2Ebcarry,axiom,
! [X0: tp__o,X1: tp__o,X2: tp__o] : ( inj__o(fo__c_2Eblast_2Ebcarry(X0,X1,X2)) = ap(ap(ap(c_2Eblast_2Ebcarry,inj__o(X0)),inj__o(X1)),inj__o(X2)) ) ).
tff(tp_c_2Eblast_2Ebsum,type,
c_2Eblast_2Ebsum: $i ).
tff(mem_c_2Eblast_2Ebsum,axiom,
mem(c_2Eblast_2Ebsum,arr(bool,arr(bool,arr(bool,bool)))) ).
tff(stp_fo_c_2Eblast_2Ebsum,type,
fo__c_2Eblast_2Ebsum: ( tp__o * tp__o * tp__o ) > tp__o ).
tff(stp_eq_fo_c_2Eblast_2Ebsum,axiom,
! [X0: tp__o,X1: tp__o,X2: tp__o] : ( inj__o(fo__c_2Eblast_2Ebsum(X0,X1,X2)) = ap(ap(ap(c_2Eblast_2Ebsum,inj__o(X0)),inj__o(X1)),inj__o(X2)) ) ).
tff(ax_thm_2Eblast_2Ebcarry__def,axiom,
! [V0x: tp__o,V1y: tp__o,V2c: tp__o] :
( p(ap(ap(ap(c_2Eblast_2Ebcarry,inj__o(V0x)),inj__o(V1y)),inj__o(V2c)))
<=> ( ( p(inj__o(V0x))
& p(inj__o(V1y)) )
| ( ( p(inj__o(V0x))
| p(inj__o(V1y)) )
& p(inj__o(V2c)) ) ) ) ).
tff(ax_thm_2Eblast_2EBCARRY__def,axiom,
( ! [V0x: $i] :
( mem(V0x,arr(ty_2Enum_2Enum,bool))
=> ! [V1y: $i] :
( mem(V1y,arr(ty_2Enum_2Enum,bool))
=> ! [V2c: tp__o] :
( p(ap(ap(ap(ap(c_2Eblast_2EBCARRY,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),V0x),V1y),inj__o(V2c)))
<=> p(inj__o(V2c)) ) ) )
& ! [V3i: tp__ty_2Enum_2Enum,V4x: $i] :
( mem(V4x,arr(ty_2Enum_2Enum,bool))
=> ! [V5y: $i] :
( mem(V5y,arr(ty_2Enum_2Enum,bool))
=> ! [V6c: tp__o] :
( p(ap(ap(ap(ap(c_2Eblast_2EBCARRY,ap(c_2Enum_2ESUC,inj__ty_2Enum_2Enum(V3i))),V4x),V5y),inj__o(V6c)))
<=> p(ap(ap(ap(c_2Eblast_2Ebcarry,ap(V4x,inj__ty_2Enum_2Enum(V3i))),ap(V5y,inj__ty_2Enum_2Enum(V3i))),ap(ap(ap(ap(c_2Eblast_2EBCARRY,inj__ty_2Enum_2Enum(V3i)),V4x),V5y),inj__o(V6c)))) ) ) ) ) ).
tff(conj_thm_2Eblast_2EBCARRY__def__compute,axiom,
( ! [V0x: $i] :
( mem(V0x,arr(ty_2Enum_2Enum,bool))
=> ! [V1y: $i] :
( mem(V1y,arr(ty_2Enum_2Enum,bool))
=> ! [V2c: tp__o] :
( p(ap(ap(ap(ap(c_2Eblast_2EBCARRY,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),V0x),V1y),inj__o(V2c)))
<=> p(inj__o(V2c)) ) ) )
& ! [V3i: tp__ty_2Enum_2Enum,V4x: $i] :
( mem(V4x,arr(ty_2Enum_2Enum,bool))
=> ! [V5y: $i] :
( mem(V5y,arr(ty_2Enum_2Enum,bool))
=> ! [V6c: tp__o] :
( p(ap(ap(ap(ap(c_2Eblast_2EBCARRY,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V3i)))),V4x),V5y),inj__o(V6c)))
<=> p(ap(ap(ap(c_2Eblast_2Ebcarry,ap(V4x,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V3i)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))),ap(V5y,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V3i)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))))),ap(ap(ap(ap(c_2Eblast_2EBCARRY,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V3i)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),V4x),V5y),inj__o(V6c)))) ) ) )
& ! [V7i: tp__ty_2Enum_2Enum,V8x: $i] :
( mem(V8x,arr(ty_2Enum_2Enum,bool))
=> ! [V9y: $i] :
( mem(V9y,arr(ty_2Enum_2Enum,bool))
=> ! [V10c: tp__o] :
( p(ap(ap(ap(ap(c_2Eblast_2EBCARRY,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,inj__ty_2Enum_2Enum(V7i)))),V8x),V9y),inj__o(V10c)))
<=> p(ap(ap(ap(c_2Eblast_2Ebcarry,ap(V8x,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V7i))))),ap(V9y,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V7i))))),ap(ap(ap(ap(c_2Eblast_2EBCARRY,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(V7i)))),V8x),V9y),inj__o(V10c)))) ) ) ) ) ).
tff(ax_thm_2Eblast_2Ebsum__def,axiom,
! [V0x: tp__o,V1y: tp__o,V2c: tp__o] :
( p(ap(ap(ap(c_2Eblast_2Ebsum,inj__o(V0x)),inj__o(V1y)),inj__o(V2c)))
<=> ( ( p(inj__o(V0x))
<=> ~ p(inj__o(V1y)) )
<=> ~ p(inj__o(V2c)) ) ) ).
tff(ax_thm_2Eblast_2EBSUM__def,axiom,
! [V0i: tp__ty_2Enum_2Enum,V1x: $i] :
( mem(V1x,arr(ty_2Enum_2Enum,bool))
=> ! [V2y: $i] :
( mem(V2y,arr(ty_2Enum_2Enum,bool))
=> ! [V3c: tp__o] :
( p(ap(ap(ap(ap(c_2Eblast_2EBSUM,inj__ty_2Enum_2Enum(V0i)),V1x),V2y),inj__o(V3c)))
<=> p(ap(ap(ap(c_2Eblast_2Ebsum,ap(V1x,inj__ty_2Enum_2Enum(V0i))),ap(V2y,inj__ty_2Enum_2Enum(V0i))),ap(ap(ap(ap(c_2Eblast_2EBCARRY,inj__ty_2Enum_2Enum(V0i)),V1x),V2y),inj__o(V3c)))) ) ) ) ).
tff(lamtp_f2309,type,
f2309: tp__ty_2Enum_2Enum > $i ).
tff(lameq_f2309,axiom,
! [V1x: tp__ty_2Enum_2Enum,V4i: tp__ty_2Enum_2Enum] : ( ap(f2309(V1x),inj__ty_2Enum_2Enum(V4i)) = ap(ap(c_2Ebit_2EBIT,inj__ty_2Enum_2Enum(V4i)),inj__ty_2Enum_2Enum(V1x)) ) ).
tff(lamtp_f2310,type,
f2310: tp__ty_2Enum_2Enum > $i ).
tff(lameq_f2310,axiom,
! [V2y: tp__ty_2Enum_2Enum,V5i: tp__ty_2Enum_2Enum] : ( ap(f2310(V2y),inj__ty_2Enum_2Enum(V5i)) = ap(ap(c_2Ebit_2EBIT,inj__ty_2Enum_2Enum(V5i)),inj__ty_2Enum_2Enum(V2y)) ) ).
tff(conj_thm_2Eblast_2EBCARRY__LEM,axiom,
! [V0i: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum,V2y: tp__ty_2Enum_2Enum,V3c: tp__o] :
( p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)),inj__ty_2Enum_2Enum(V0i)))
=> ( p(ap(ap(ap(ap(c_2Eblast_2EBCARRY,inj__ty_2Enum_2Enum(V0i)),f2309(V1x)),f2310(V2y)),inj__o(V3c)))
<=> p(ap(ap(c_2Ebit_2EBIT,inj__ty_2Enum_2Enum(V0i)),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(c_2Ebit_2EBITS,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V0i)),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(V1x))),ap(ap(ap(c_2Ebit_2EBITS,ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V0i)),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(V2y)))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),inj__o(V3c)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))) ) ) ).
tff(conj_thm_2Eblast_2EBCARRY__EQ,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1c: tp__o,V2x1: $i] :
( mem(V2x1,arr(ty_2Enum_2Enum,bool))
=> ! [V3x2: $i] :
( mem(V3x2,arr(ty_2Enum_2Enum,bool))
=> ! [V4y1: $i] :
( mem(V4y1,arr(ty_2Enum_2Enum,bool))
=> ! [V5y2: $i] :
( mem(V5y2,arr(ty_2Enum_2Enum,bool))
=> ( ! [V6i: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Eprim__rec_2E_3C,inj__ty_2Enum_2Enum(V6i)),inj__ty_2Enum_2Enum(V0n)))
=> ( ( p(ap(V2x1,inj__ty_2Enum_2Enum(V6i)))
<=> p(ap(V3x2,inj__ty_2Enum_2Enum(V6i))) )
& ( p(ap(V4y1,inj__ty_2Enum_2Enum(V6i)))
<=> p(ap(V5y2,inj__ty_2Enum_2Enum(V6i))) ) ) )
=> ( p(ap(ap(ap(ap(c_2Eblast_2EBCARRY,inj__ty_2Enum_2Enum(V0n)),V2x1),V4y1),inj__o(V1c)))
<=> p(ap(ap(ap(ap(c_2Eblast_2EBCARRY,inj__ty_2Enum_2Enum(V0n)),V3x2),V5y2),inj__o(V1c))) ) ) ) ) ) ) ).
tff(conj_thm_2Eblast_2EBSUM__EQ,axiom,
! [V0n: tp__ty_2Enum_2Enum,V1c: tp__o,V2x1: $i] :
( mem(V2x1,arr(ty_2Enum_2Enum,bool))
=> ! [V3x2: $i] :
( mem(V3x2,arr(ty_2Enum_2Enum,bool))
=> ! [V4y1: $i] :
( mem(V4y1,arr(ty_2Enum_2Enum,bool))
=> ! [V5y2: $i] :
( mem(V5y2,arr(ty_2Enum_2Enum,bool))
=> ( ! [V6i: tp__ty_2Enum_2Enum] :
( p(ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V6i)),inj__ty_2Enum_2Enum(V0n)))
=> ( ( p(ap(V2x1,inj__ty_2Enum_2Enum(V6i)))
<=> p(ap(V3x2,inj__ty_2Enum_2Enum(V6i))) )
& ( p(ap(V4y1,inj__ty_2Enum_2Enum(V6i)))
<=> p(ap(V5y2,inj__ty_2Enum_2Enum(V6i))) ) ) )
=> ( p(ap(ap(ap(ap(c_2Eblast_2EBSUM,inj__ty_2Enum_2Enum(V0n)),V2x1),V4y1),inj__o(V1c)))
<=> p(ap(ap(ap(ap(c_2Eblast_2EBSUM,inj__ty_2Enum_2Enum(V0n)),V3x2),V5y2),inj__o(V1c))) ) ) ) ) ) ) ).
tff(conj_thm_2Eblast_2EBSUM__LEM,axiom,
! [V0i: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum,V2y: tp__ty_2Enum_2Enum,V3c: tp__o] :
( p(ap(ap(ap(ap(c_2Eblast_2EBSUM,inj__ty_2Enum_2Enum(V0i)),f2309(V1x)),f2310(V2y)),inj__o(V3c)))
<=> p(ap(ap(c_2Ebit_2EBIT,inj__ty_2Enum_2Enum(V0i)),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V1x)),inj__ty_2Enum_2Enum(V2y))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),inj__o(V3c)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO)))),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))) ) ).
tff(lamtp_f2311,type,
f2311: ( del * $i * $i ) > $i ).
tff(lameq_f2311,axiom,
! [A_27a: del,V1y: $i] :
( mem(V1y,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V0x: $i] :
( mem(V0x,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2i: tp__ty_2Enum_2Enum] : ( ap(f2311(A_27a,V1y,V0x),inj__ty_2Enum_2Enum(V2i)) = ap(ap(ap(ap(c_2Eblast_2EBSUM,inj__ty_2Enum_2Enum(V2i)),ap(c_2Efcp_2Efcp__index(bool,A_27a),V0x)),ap(c_2Efcp_2Efcp__index(bool,A_27a),V1y)),inj__o(fo__c_2Ebool_2EF)) ) ) ) ).
tff(conj_thm_2Eblast_2EBITWISE__ADD,axiom,
! [A_27a: del,V0x: $i] :
( mem(V0x,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1y: $i] :
( mem(V1y,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(ap(c_2Ewords_2Eword__add(A_27a),V0x),V1y) = ap(c_2Efcp_2EFCP(bool,A_27a),f2311(A_27a,V1y,V0x)) ) ) ) ).
tff(lamtp_f2312,type,
f2312: ( del * $i * $i ) > $i ).
tff(lameq_f2312,axiom,
! [A_27a: del,V1y: $i] :
( mem(V1y,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V0x: $i] :
( mem(V0x,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2i: tp__ty_2Enum_2Enum] : ( ap(f2312(A_27a,V1y,V0x),inj__ty_2Enum_2Enum(V2i)) = ap(ap(ap(ap(c_2Eblast_2EBSUM,inj__ty_2Enum_2Enum(V2i)),ap(c_2Efcp_2Efcp__index(bool,A_27a),V0x)),ap(ap(c_2Ecombin_2Eo(ty_2Enum_2Enum,bool,bool),c_2Ebool_2E_7E),ap(c_2Efcp_2Efcp__index(bool,A_27a),V1y))),inj__o(fo__c_2Ebool_2ET)) ) ) ) ).
tff(conj_thm_2Eblast_2EBITWISE__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(ap(c_2Ewords_2Eword__sub(A_27a),V0x),V1y) = ap(c_2Efcp_2EFCP(bool,A_27a),f2312(A_27a,V1y,V0x)) ) ) ) ).
tff(conj_thm_2Eblast_2EBITWISE__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__lo(A_27a),V0x),V1y))
<=> ~ p(ap(ap(ap(ap(c_2Eblast_2EBCARRY,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Efcp_2Efcp__index(bool,A_27a),V0x)),ap(ap(c_2Ecombin_2Eo(ty_2Enum_2Enum,bool,bool),c_2Ebool_2E_7E),ap(c_2Efcp_2Efcp__index(bool,A_27a),V1y))),inj__o(fo__c_2Ebool_2ET))) ) ) ) ).
tff(lamtp_f2313,type,
f2313: ( del * $i * tp__ty_2Enum_2Enum * $i ) > $i ).
tff(lameq_f2313,axiom,
! [A_27a: del,V1m: $i] :
( mem(V1m,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V3j: tp__ty_2Enum_2Enum,V0w: $i] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V4i: tp__ty_2Enum_2Enum] : ( ap(f2313(A_27a,V1m,V3j,V0w),inj__ty_2Enum_2Enum(V4i)) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0w),inj__ty_2Enum_2Enum(V3j))),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V3j)),inj__ty_2Enum_2Enum(V4i))),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V1m),ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V4i)),inj__ty_2Enum_2Enum(V3j))))) ) ) ) ).
tff(lamtp_f2314,type,
f2314: ( del * $i * $i * $i ) > $i ).
tff(lameq_f2314,axiom,
! [A_27a: del,V1m: $i] :
( mem(V1m,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V0w: $i] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2a: $i] :
( mem(V2a,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V3j: tp__ty_2Enum_2Enum] : ( ap(f2314(A_27a,V1m,V0w,V2a),inj__ty_2Enum_2Enum(V3j)) = ap(ap(c_2Ewords_2Eword__add(A_27a),V2a),ap(c_2Efcp_2EFCP(bool,A_27a),f2313(A_27a,V1m,V3j,V0w))) ) ) ) ) ).
tff(lamtp_f2315,type,
f2315: ( del * $i * $i ) > $i ).
tff(lameq_f2315,axiom,
! [A_27a: del,V1m: $i] :
( mem(V1m,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V0w: $i] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2a: $i] : ( ap(f2315(A_27a,V1m,V0w),V2a) = f2314(A_27a,V1m,V0w,V2a) ) ) ) ).
tff(conj_thm_2Eblast_2EBITWISE__MUL,axiom,
! [A_27a: del,V0w: $i] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1m: $i] :
( mem(V1m,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(ap(c_2Ewords_2Eword__mul(A_27a),V0w),V1m) = ap(ap(ap(c_2Elist_2EFOLDL(ty_2Enum_2Enum,ty_2Efcp_2Ecart(bool,A_27a)),f2315(A_27a,V1m,V0w)),ap(c_2Ewords_2En2w(A_27a),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))),ap(c_2Erich__list_2ECOUNT__LIST,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ) ) ).
tff(lamtp_f2316,type,
f2316: ( del * $i * $i * tp__ty_2Enum_2Enum * tp__o ) > $i ).
tff(lameq_f2316,axiom,
! [A_27a: del,V1m: $i] :
( mem(V1m,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V0w: $i] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2k: tp__ty_2Enum_2Enum,V3a: tp__o,V4j: tp__ty_2Enum_2Enum] : ( ap(f2316(A_27a,V1m,V0w,V2k,V3a),inj__ty_2Enum_2Enum(V4j)) = ap(ap(c_2Ebool_2E_5C_2F,inj__o(V3a)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Efcp_2Ecart(bool,A_27a)),ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),ap(c_2Ebit_2ELOG2,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)),V1m)),ap(c_2Ewords_2En2w(A_27a),inj__ty_2Enum_2Enum(V4j)))),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Earithmetic_2E_3C_3D,inj__ty_2Enum_2Enum(V4j)),inj__ty_2Enum_2Enum(V2k))),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0w),ap(ap(c_2Earithmetic_2E_2D,inj__ty_2Enum_2Enum(V2k)),inj__ty_2Enum_2Enum(V4j)))))) ) ) ) ).
tff(lamtp_f2317,type,
f2317: ( del * $i * $i * tp__ty_2Enum_2Enum ) > $i ).
tff(lameq_f2317,axiom,
! [A_27a: del,V1m: $i] :
( mem(V1m,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V0w: $i] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2k: tp__ty_2Enum_2Enum,V3a: tp__o] : ( ap(f2317(A_27a,V1m,V0w,V2k),inj__o(V3a)) = f2316(A_27a,V1m,V0w,V2k,V3a) ) ) ) ).
tff(lamtp_f2318,type,
f2318: ( del * $i * $i ) > $i ).
tff(lameq_f2318,axiom,
! [A_27a: del,V0w: $i] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1m: $i] :
( mem(V1m,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2k: tp__ty_2Enum_2Enum] : ( ap(f2318(A_27a,V0w,V1m),inj__ty_2Enum_2Enum(V2k)) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(ap(c_2Elist_2EFOLDL(ty_2Enum_2Enum,bool),f2317(A_27a,V1m,V0w,V2k)),inj__o(fo__c_2Ebool_2EF)),ap(c_2Erich__list_2ECOUNT__LIST,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))),ap(ap(c_2Emin_2E_3D(ty_2Efcp_2Ecart(bool,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))))),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Ebit_2ELOG2,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))))),V1m)),ap(c_2Ewords_2En2w(A_27a),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) ) ) ) ).
tff(conj_thm_2Eblast_2Eword__lsl__bv__expand,axiom,
! [A_27a: del,V0w: $i] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1m: $i] :
( mem(V1m,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(ap(c_2Ewords_2Eword__lsl__bv(A_27a),V0w),V1m) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Efcp_2EFCP(bool,A_27a),ap(c_2Ecombin_2EK(bool,ty_2Enum_2Enum),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_7E,ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V1m),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0w),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))))),ap(c_2Efcp_2EFCP(bool,A_27a),f2318(A_27a,V0w,V1m))) ) ) ) ).
tff(lamtp_f2319,type,
f2319: ( del * $i * $i * tp__ty_2Enum_2Enum * tp__o ) > $i ).
tff(lameq_f2319,axiom,
! [A_27a: del,V1m: $i] :
( mem(V1m,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V0w: $i] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2k: tp__ty_2Enum_2Enum,V3a: tp__o,V4j: tp__ty_2Enum_2Enum] : ( ap(f2319(A_27a,V1m,V0w,V2k,V3a),inj__ty_2Enum_2Enum(V4j)) = ap(ap(c_2Ebool_2E_5C_2F,inj__o(V3a)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Efcp_2Ecart(bool,A_27a)),ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),ap(c_2Ebit_2ELOG2,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)),V1m)),ap(c_2Ewords_2En2w(A_27a),inj__ty_2Enum_2Enum(V4j)))),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V2k)),inj__ty_2Enum_2Enum(V4j))),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,inj__ty_2Enum_2Enum(V2k)),inj__ty_2Enum_2Enum(V4j)))))) ) ) ) ).
tff(lamtp_f2320,type,
f2320: ( del * $i * $i * tp__ty_2Enum_2Enum ) > $i ).
tff(lameq_f2320,axiom,
! [A_27a: del,V1m: $i] :
( mem(V1m,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V0w: $i] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2k: tp__ty_2Enum_2Enum,V3a: tp__o] : ( ap(f2320(A_27a,V1m,V0w,V2k),inj__o(V3a)) = f2319(A_27a,V1m,V0w,V2k,V3a) ) ) ) ).
tff(lamtp_f2321,type,
f2321: ( del * $i * $i ) > $i ).
tff(lameq_f2321,axiom,
! [A_27a: del,V0w: $i] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1m: $i] :
( mem(V1m,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2k: tp__ty_2Enum_2Enum] : ( ap(f2321(A_27a,V0w,V1m),inj__ty_2Enum_2Enum(V2k)) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(ap(c_2Elist_2EFOLDL(ty_2Enum_2Enum,bool),f2320(A_27a,V1m,V0w,V2k)),inj__o(fo__c_2Ebool_2EF)),ap(c_2Erich__list_2ECOUNT__LIST,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))),ap(ap(c_2Emin_2E_3D(ty_2Efcp_2Ecart(bool,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))))),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Ebit_2ELOG2,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))))),V1m)),ap(c_2Ewords_2En2w(A_27a),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))) ) ) ) ).
tff(conj_thm_2Eblast_2Eword__lsr__bv__expand,axiom,
! [A_27a: del,V0w: $i] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1m: $i] :
( mem(V1m,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(ap(c_2Ewords_2Eword__lsr__bv(A_27a),V0w),V1m) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Efcp_2EFCP(bool,A_27a),ap(c_2Ecombin_2EK(bool,ty_2Enum_2Enum),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_7E,ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V1m),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0w),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0)))))),ap(c_2Efcp_2EFCP(bool,A_27a),f2321(A_27a,V0w,V1m))) ) ) ) ).
tff(lamtp_f2322,type,
f2322: ( del * $i * $i * tp__ty_2Enum_2Enum * tp__o ) > $i ).
tff(lameq_f2322,axiom,
! [A_27a: del,V1m: $i] :
( mem(V1m,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V0w: $i] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2k: tp__ty_2Enum_2Enum,V3a: tp__o,V4j: tp__ty_2Enum_2Enum] : ( ap(f2322(A_27a,V1m,V0w,V2k,V3a),inj__ty_2Enum_2Enum(V4j)) = ap(ap(c_2Ebool_2E_5C_2F,inj__o(V3a)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Efcp_2Ecart(bool,A_27a)),ap(ap(ap(c_2Ewords_2Eword__bits(A_27a),ap(c_2Ebit_2ELOG2,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)),V1m)),ap(c_2Ewords_2En2w(A_27a),inj__ty_2Enum_2Enum(V4j)))),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),ap(ap(c_2Ewords_2Eword__asr(A_27a),V0w),inj__ty_2Enum_2Enum(V4j))),inj__ty_2Enum_2Enum(V2k)))) ) ) ) ).
tff(lamtp_f2323,type,
f2323: ( del * $i * $i * tp__ty_2Enum_2Enum ) > $i ).
tff(lameq_f2323,axiom,
! [A_27a: del,V1m: $i] :
( mem(V1m,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V0w: $i] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2k: tp__ty_2Enum_2Enum,V3a: tp__o] : ( ap(f2323(A_27a,V1m,V0w,V2k),inj__o(V3a)) = f2322(A_27a,V1m,V0w,V2k,V3a) ) ) ) ).
tff(lamtp_f2324,type,
f2324: ( del * $i * $i ) > $i ).
tff(lameq_f2324,axiom,
! [A_27a: del,V1m: $i] :
( mem(V1m,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V0w: $i] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2k: tp__ty_2Enum_2Enum] : ( ap(f2324(A_27a,V1m,V0w),inj__ty_2Enum_2Enum(V2k)) = ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Ebool_2E_2F_5C,ap(ap(ap(c_2Elist_2EFOLDL(ty_2Enum_2Enum,bool),f2323(A_27a,V1m,V0w,V2k)),inj__o(fo__c_2Ebool_2EF)),ap(c_2Erich__list_2ECOUNT__LIST,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))),ap(ap(c_2Emin_2E_3D(ty_2Efcp_2Ecart(bool,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))))),ap(ap(c_2Earithmetic_2E_2B,ap(c_2Ebit_2ELOG2,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))))),V1m)),ap(c_2Ewords_2En2w(A_27a),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ewords_2Eword__lo(A_27a),ap(c_2Ewords_2En2w(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)))))),V1m)),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))))))) ) ) ) ).
tff(conj_thm_2Eblast_2Eword__asr__bv__expand,axiom,
! [A_27a: del,V0w: $i] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1m: $i] :
( mem(V1m,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(ap(c_2Ewords_2Eword__asr__bv(A_27a),V0w),V1m) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool,A_27a)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2EZERO))))),ap(c_2Efcp_2EFCP(bool,A_27a),ap(c_2Ecombin_2EK(bool,ty_2Enum_2Enum),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0w),inj__ty_2Enum_2Enum(fo__c_2Enum_2E0))))),ap(c_2Efcp_2EFCP(bool,A_27a),f2324(A_27a,V1m,V0w))) ) ) ) ).
tff(lamtp_f2325,type,
f2325: ( del * $i * tp__ty_2Enum_2Enum * $i * tp__o ) > $i ).
tff(lameq_f2325,axiom,
! [A_27a: del,V1m: $i] :
( mem(V1m,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2k: tp__ty_2Enum_2Enum,V0w: $i] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V3a: tp__o,V4j: tp__ty_2Enum_2Enum] : ( ap(f2325(A_27a,V1m,V2k,V0w,V3a),inj__ty_2Enum_2Enum(V4j)) = ap(ap(c_2Ebool_2E_5C_2F,inj__o(V3a)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Efcp_2Ecart(bool,A_27a)),ap(ap(c_2Ewords_2Eword__mod(A_27a),V1m),ap(c_2Ewords_2En2w(A_27a),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))),ap(c_2Ewords_2En2w(A_27a),inj__ty_2Enum_2Enum(V4j)))),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0w),ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V4j)),inj__ty_2Enum_2Enum(V2k))),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))))) ) ) ) ).
tff(lamtp_f2326,type,
f2326: ( del * $i * tp__ty_2Enum_2Enum * $i ) > $i ).
tff(lameq_f2326,axiom,
! [A_27a: del,V1m: $i] :
( mem(V1m,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2k: tp__ty_2Enum_2Enum,V0w: $i] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V3a: tp__o] : ( ap(f2326(A_27a,V1m,V2k,V0w),inj__o(V3a)) = f2325(A_27a,V1m,V2k,V0w,V3a) ) ) ) ).
tff(lamtp_f2327,type,
f2327: ( del * $i * $i ) > $i ).
tff(lameq_f2327,axiom,
! [A_27a: del,V0w: $i] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1m: $i] :
( mem(V1m,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2k: tp__ty_2Enum_2Enum] : ( ap(f2327(A_27a,V0w,V1m),inj__ty_2Enum_2Enum(V2k)) = ap(ap(ap(c_2Elist_2EFOLDL(ty_2Enum_2Enum,bool),f2326(A_27a,V1m,V2k,V0w)),inj__o(fo__c_2Ebool_2EF)),ap(c_2Erich__list_2ECOUNT__LIST,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ) ) ).
tff(conj_thm_2Eblast_2Eword__ror__bv__expand,axiom,
! [A_27a: del,V0w: $i] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1m: $i] :
( mem(V1m,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(ap(c_2Ewords_2Eword__ror__bv(A_27a),V0w),V1m) = ap(c_2Efcp_2EFCP(bool,A_27a),f2327(A_27a,V0w,V1m)) ) ) ) ).
tff(lamtp_f2328,type,
f2328: ( del * $i * tp__ty_2Enum_2Enum * $i * tp__o ) > $i ).
tff(lameq_f2328,axiom,
! [A_27a: del,V1m: $i] :
( mem(V1m,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2k: tp__ty_2Enum_2Enum,V0w: $i] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V3a: tp__o,V4j: tp__ty_2Enum_2Enum] : ( ap(f2328(A_27a,V1m,V2k,V0w,V3a),inj__ty_2Enum_2Enum(V4j)) = ap(ap(c_2Ebool_2E_5C_2F,inj__o(V3a)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Efcp_2Ecart(bool,A_27a)),ap(ap(c_2Ewords_2Eword__mod(A_27a),V1m),ap(c_2Ewords_2En2w(A_27a),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))),ap(c_2Ewords_2En2w(A_27a),inj__ty_2Enum_2Enum(V4j)))),ap(ap(c_2Efcp_2Efcp__index(bool,A_27a),V0w),ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,inj__ty_2Enum_2Enum(V2k)),ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))),inj__ty_2Enum_2Enum(V4j))),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a))))),ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))))) ) ) ) ).
tff(lamtp_f2329,type,
f2329: ( del * $i * tp__ty_2Enum_2Enum * $i ) > $i ).
tff(lameq_f2329,axiom,
! [A_27a: del,V1m: $i] :
( mem(V1m,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2k: tp__ty_2Enum_2Enum,V0w: $i] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V3a: tp__o] : ( ap(f2329(A_27a,V1m,V2k,V0w),inj__o(V3a)) = f2328(A_27a,V1m,V2k,V0w,V3a) ) ) ) ).
tff(lamtp_f2330,type,
f2330: ( del * $i * $i ) > $i ).
tff(lameq_f2330,axiom,
! [A_27a: del,V0w: $i] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1m: $i] :
( mem(V1m,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V2k: tp__ty_2Enum_2Enum] : ( ap(f2330(A_27a,V0w,V1m),inj__ty_2Enum_2Enum(V2k)) = ap(ap(ap(c_2Elist_2EFOLDL(ty_2Enum_2Enum,bool),f2329(A_27a,V1m,V2k,V0w)),inj__o(fo__c_2Ebool_2EF)),ap(c_2Erich__list_2ECOUNT__LIST,ap(c_2Efcp_2Edimindex(A_27a),c_2Ebool_2Ethe__value(A_27a)))) ) ) ) ).
tff(conj_thm_2Eblast_2Eword__rol__bv__expand,axiom,
! [A_27a: del,V0w: $i] :
( mem(V0w,ty_2Efcp_2Ecart(bool,A_27a))
=> ! [V1m: $i] :
( mem(V1m,ty_2Efcp_2Ecart(bool,A_27a))
=> ( ap(ap(c_2Ewords_2Eword__rol__bv(A_27a),V0w),V1m) = ap(c_2Efcp_2EFCP(bool,A_27a),f2330(A_27a,V0w,V1m)) ) ) ) ).
%------------------------------------------------------------------------------