ITP001 Axioms: ITP087^5.ax
%------------------------------------------------------------------------------
% File : ITP087^5 : 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 : quote^2.ax [Gau20]
% : HL4087^5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 83 ( 11 unt; 28 typ; 0 def)
% Number of atoms : 956 ( 87 equ; 0 cnn)
% Maximal formula atoms : 145 ( 11 avg)
% Number of connectives : 1872 ( 4 ~; 6 |; 60 &;1682 @)
% ( 8 <=>; 112 =>; 0 <=; 0 <~>)
% Maximal formula depth : 56 ( 11 avg;1682 nst)
% Number of types : 4 ( 3 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 67 ( 66 usr; 49 con; 0-2 aty)
% Number of variables : 231 ( 22 ^ 195 !; 14 ?; 231 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tp_ty_2Equote_2Eindex,type,
ty_2Equote_2Eindex: del ).
thf(tp_ty_2Equote_2Evarmap,type,
ty_2Equote_2Evarmap: del > del ).
thf(tp_c_2Equote_2EEmpty__vm,type,
c_2Equote_2EEmpty__vm: del > $i ).
thf(mem_c_2Equote_2EEmpty__vm,axiom,
! [A_27a: del] : ( mem @ ( c_2Equote_2EEmpty__vm @ A_27a ) @ ( ty_2Equote_2Evarmap @ A_27a ) ) ).
thf(stp_ty_2Equote_2Eindex,type,
tp__ty_2Equote_2Eindex: $tType ).
thf(stp_inj_ty_2Equote_2Eindex,type,
inj__ty_2Equote_2Eindex: tp__ty_2Equote_2Eindex > $i ).
thf(stp_surj_ty_2Equote_2Eindex,type,
surj__ty_2Equote_2Eindex: $i > tp__ty_2Equote_2Eindex ).
thf(stp_inj_surj_ty_2Equote_2Eindex,axiom,
! [X: tp__ty_2Equote_2Eindex] :
( ( surj__ty_2Equote_2Eindex @ ( inj__ty_2Equote_2Eindex @ X ) )
= X ) ).
thf(stp_inj_mem_ty_2Equote_2Eindex,axiom,
! [X: tp__ty_2Equote_2Eindex] : ( mem @ ( inj__ty_2Equote_2Eindex @ X ) @ ty_2Equote_2Eindex ) ).
thf(stp_iso_mem_ty_2Equote_2Eindex,axiom,
! [X: $i] :
( ( mem @ X @ ty_2Equote_2Eindex )
=> ( X
= ( inj__ty_2Equote_2Eindex @ ( surj__ty_2Equote_2Eindex @ X ) ) ) ) ).
thf(tp_c_2Equote_2EEnd__idx,type,
c_2Equote_2EEnd__idx: $i ).
thf(mem_c_2Equote_2EEnd__idx,axiom,
mem @ c_2Equote_2EEnd__idx @ ty_2Equote_2Eindex ).
thf(stp_fo_c_2Equote_2EEnd__idx,type,
fo__c_2Equote_2EEnd__idx: tp__ty_2Equote_2Eindex ).
thf(stp_eq_fo_c_2Equote_2EEnd__idx,axiom,
( ( inj__ty_2Equote_2Eindex @ fo__c_2Equote_2EEnd__idx )
= c_2Equote_2EEnd__idx ) ).
thf(tp_c_2Equote_2ELeft__idx,type,
c_2Equote_2ELeft__idx: $i ).
thf(mem_c_2Equote_2ELeft__idx,axiom,
mem @ c_2Equote_2ELeft__idx @ ( arr @ ty_2Equote_2Eindex @ ty_2Equote_2Eindex ) ).
thf(stp_fo_c_2Equote_2ELeft__idx,type,
fo__c_2Equote_2ELeft__idx: tp__ty_2Equote_2Eindex > tp__ty_2Equote_2Eindex ).
thf(stp_eq_fo_c_2Equote_2ELeft__idx,axiom,
! [X0: tp__ty_2Equote_2Eindex] :
( ( inj__ty_2Equote_2Eindex @ ( fo__c_2Equote_2ELeft__idx @ X0 ) )
= ( ap @ c_2Equote_2ELeft__idx @ ( inj__ty_2Equote_2Eindex @ X0 ) ) ) ).
thf(tp_c_2Equote_2ENode__vm,type,
c_2Equote_2ENode__vm: del > $i ).
thf(mem_c_2Equote_2ENode__vm,axiom,
! [A_27a: del] : ( mem @ ( c_2Equote_2ENode__vm @ A_27a ) @ ( arr @ A_27a @ ( arr @ ( ty_2Equote_2Evarmap @ A_27a ) @ ( arr @ ( ty_2Equote_2Evarmap @ A_27a ) @ ( ty_2Equote_2Evarmap @ A_27a ) ) ) ) ) ).
thf(tp_c_2Equote_2ERight__idx,type,
c_2Equote_2ERight__idx: $i ).
thf(mem_c_2Equote_2ERight__idx,axiom,
mem @ c_2Equote_2ERight__idx @ ( arr @ ty_2Equote_2Eindex @ ty_2Equote_2Eindex ) ).
thf(stp_fo_c_2Equote_2ERight__idx,type,
fo__c_2Equote_2ERight__idx: tp__ty_2Equote_2Eindex > tp__ty_2Equote_2Eindex ).
thf(stp_eq_fo_c_2Equote_2ERight__idx,axiom,
! [X0: tp__ty_2Equote_2Eindex] :
( ( inj__ty_2Equote_2Eindex @ ( fo__c_2Equote_2ERight__idx @ X0 ) )
= ( ap @ c_2Equote_2ERight__idx @ ( inj__ty_2Equote_2Eindex @ X0 ) ) ) ).
thf(tp_c_2Equote_2Eindex__CASE,type,
c_2Equote_2Eindex__CASE: del > $i ).
thf(mem_c_2Equote_2Eindex__CASE,axiom,
! [A_27a: del] : ( mem @ ( c_2Equote_2Eindex__CASE @ A_27a ) @ ( arr @ ty_2Equote_2Eindex @ ( arr @ ( arr @ ty_2Equote_2Eindex @ A_27a ) @ ( arr @ ( arr @ ty_2Equote_2Eindex @ A_27a ) @ ( arr @ A_27a @ A_27a ) ) ) ) ) ).
thf(tp_c_2Equote_2Eindex__compare,type,
c_2Equote_2Eindex__compare: $i ).
thf(mem_c_2Equote_2Eindex__compare,axiom,
mem @ c_2Equote_2Eindex__compare @ ( arr @ ty_2Equote_2Eindex @ ( arr @ ty_2Equote_2Eindex @ ty_2EternaryComparisons_2Eordering ) ) ).
thf(stp_fo_c_2Equote_2Eindex__compare,type,
fo__c_2Equote_2Eindex__compare: tp__ty_2Equote_2Eindex > tp__ty_2Equote_2Eindex > tp__ty_2EternaryComparisons_2Eordering ).
thf(stp_eq_fo_c_2Equote_2Eindex__compare,axiom,
! [X0: tp__ty_2Equote_2Eindex,X1: tp__ty_2Equote_2Eindex] :
( ( inj__ty_2EternaryComparisons_2Eordering @ ( fo__c_2Equote_2Eindex__compare @ X0 @ X1 ) )
= ( ap @ ( ap @ c_2Equote_2Eindex__compare @ ( inj__ty_2Equote_2Eindex @ X0 ) ) @ ( inj__ty_2Equote_2Eindex @ X1 ) ) ) ).
thf(tp_c_2Equote_2Eindex__lt,type,
c_2Equote_2Eindex__lt: $i ).
thf(mem_c_2Equote_2Eindex__lt,axiom,
mem @ c_2Equote_2Eindex__lt @ ( arr @ ty_2Equote_2Eindex @ ( arr @ ty_2Equote_2Eindex @ bool ) ) ).
thf(tp_c_2Equote_2Eindex__size,type,
c_2Equote_2Eindex__size: $i ).
thf(mem_c_2Equote_2Eindex__size,axiom,
mem @ c_2Equote_2Eindex__size @ ( arr @ ty_2Equote_2Eindex @ ty_2Enum_2Enum ) ).
thf(stp_fo_c_2Equote_2Eindex__size,type,
fo__c_2Equote_2Eindex__size: tp__ty_2Equote_2Eindex > tp__ty_2Enum_2Enum ).
thf(stp_eq_fo_c_2Equote_2Eindex__size,axiom,
! [X0: tp__ty_2Equote_2Eindex] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2Equote_2Eindex__size @ X0 ) )
= ( ap @ c_2Equote_2Eindex__size @ ( inj__ty_2Equote_2Eindex @ X0 ) ) ) ).
thf(tp_c_2Equote_2Evarmap__CASE,type,
c_2Equote_2Evarmap__CASE: del > del > $i ).
thf(mem_c_2Equote_2Evarmap__CASE,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Equote_2Evarmap__CASE @ A_27a @ A_27b ) @ ( arr @ ( ty_2Equote_2Evarmap @ A_27a ) @ ( arr @ A_27b @ ( arr @ ( arr @ A_27a @ ( arr @ ( ty_2Equote_2Evarmap @ A_27a ) @ ( arr @ ( ty_2Equote_2Evarmap @ A_27a ) @ A_27b ) ) ) @ A_27b ) ) ) ) ).
thf(tp_c_2Equote_2Evarmap__find,type,
c_2Equote_2Evarmap__find: del > $i ).
thf(mem_c_2Equote_2Evarmap__find,axiom,
! [A_27a: del] : ( mem @ ( c_2Equote_2Evarmap__find @ A_27a ) @ ( arr @ ty_2Equote_2Eindex @ ( arr @ ( ty_2Equote_2Evarmap @ A_27a ) @ A_27a ) ) ) ).
thf(tp_c_2Equote_2Evarmap__size,type,
c_2Equote_2Evarmap__size: del > $i ).
thf(mem_c_2Equote_2Evarmap__size,axiom,
! [A_27a: del] : ( mem @ ( c_2Equote_2Evarmap__size @ A_27a ) @ ( arr @ ( arr @ A_27a @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Equote_2Evarmap @ A_27a ) @ ty_2Enum_2Enum ) ) ) ).
thf(stp_c_ty_2Eind__type_2Erecspace_o,type,
tp__c_ty_2Eind__type_2Erecspace_o: $tType ).
thf(stp_inj_c_ty_2Eind__type_2Erecspace_o,type,
inj__c_ty_2Eind__type_2Erecspace_o: tp__c_ty_2Eind__type_2Erecspace_o > $i ).
thf(stp_surj_c_ty_2Eind__type_2Erecspace_o,type,
surj__c_ty_2Eind__type_2Erecspace_o: $i > tp__c_ty_2Eind__type_2Erecspace_o ).
thf(stp_inj_surj_c_ty_2Eind__type_2Erecspace_o,axiom,
! [X: tp__c_ty_2Eind__type_2Erecspace_o] :
( ( surj__c_ty_2Eind__type_2Erecspace_o @ ( inj__c_ty_2Eind__type_2Erecspace_o @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Eind__type_2Erecspace_o,axiom,
! [X: tp__c_ty_2Eind__type_2Erecspace_o] : ( mem @ ( inj__c_ty_2Eind__type_2Erecspace_o @ X ) @ ( ty_2Eind__type_2Erecspace @ bool ) ) ).
thf(stp_iso_mem_c_ty_2Eind__type_2Erecspace_o,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Eind__type_2Erecspace @ bool ) )
=> ( X
= ( inj__c_ty_2Eind__type_2Erecspace_o @ ( surj__c_ty_2Eind__type_2Erecspace_o @ X ) ) ) ) ).
thf(ax_thm_2Equote_2Eindex__TY__DEF,axiom,
? [V0rep: $i] :
( ( mem @ V0rep @ ( arr @ ty_2Equote_2Eindex @ ( ty_2Eind__type_2Erecspace @ bool ) ) )
& ( p
@ ( ap
@ ( ap @ ( c_2Ebool_2ETYPE__DEFINITION @ ( ty_2Eind__type_2Erecspace @ bool ) @ ty_2Equote_2Eindex )
@ ( lam @ ( ty_2Eind__type_2Erecspace @ bool )
@ ^ [V1a0: $i] :
( ap @ ( c_2Ebool_2E_21 @ ( arr @ ( ty_2Eind__type_2Erecspace @ bool ) @ bool ) )
@ ( lam @ ( arr @ ( ty_2Eind__type_2Erecspace @ bool ) @ bool )
@ ^ [V2_27index_27: $i] :
( ap
@ ( ap @ c_2Emin_2E_3D_3D_3E
@ ( ap @ ( c_2Ebool_2E_21 @ ( ty_2Eind__type_2Erecspace @ bool ) )
@ ( lam @ ( ty_2Eind__type_2Erecspace @ bool )
@ ^ [V3a0: $i] :
( ap
@ ( ap @ c_2Emin_2E_3D_3D_3E
@ ( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap @ ( c_2Ebool_2E_3F @ ( ty_2Eind__type_2Erecspace @ bool ) )
@ ( lam @ ( ty_2Eind__type_2Erecspace @ bool )
@ ^ [V4a: $i] :
( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eind__type_2Erecspace @ bool ) ) @ V3a0 )
@ ( ap
@ ( lam @ ( ty_2Eind__type_2Erecspace @ bool )
@ ^ [V5a: $i] :
( ap @ ( ap @ ( ap @ ( c_2Eind__type_2ECONSTR @ bool ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( c_2Ebool_2EARB @ bool ) )
@ ( ap @ ( ap @ ( c_2Eind__type_2EFCONS @ ( ty_2Eind__type_2Erecspace @ bool ) ) @ V5a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6n: $i] : ( c_2Eind__type_2EBOTTOM @ bool ) ) ) ) )
@ V4a ) ) )
@ ( ap @ V2_27index_27 @ V4a ) ) ) ) )
@ ( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap @ ( c_2Ebool_2E_3F @ ( ty_2Eind__type_2Erecspace @ bool ) )
@ ( lam @ ( ty_2Eind__type_2Erecspace @ bool )
@ ^ [V7a: $i] :
( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eind__type_2Erecspace @ bool ) ) @ V3a0 )
@ ( ap
@ ( lam @ ( ty_2Eind__type_2Erecspace @ bool )
@ ^ [V8a: $i] :
( ap @ ( ap @ ( ap @ ( c_2Eind__type_2ECONSTR @ bool ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( c_2Ebool_2EARB @ bool ) )
@ ( ap @ ( ap @ ( c_2Eind__type_2EFCONS @ ( ty_2Eind__type_2Erecspace @ bool ) ) @ V8a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V9n: $i] : ( c_2Eind__type_2EBOTTOM @ bool ) ) ) ) )
@ V7a ) ) )
@ ( ap @ V2_27index_27 @ V7a ) ) ) ) )
@ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eind__type_2Erecspace @ bool ) ) @ V3a0 )
@ ( ap @ ( ap @ ( ap @ ( c_2Eind__type_2ECONSTR @ bool ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ ( c_2Ebool_2EARB @ bool ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V10n: $i] : ( c_2Eind__type_2EBOTTOM @ bool ) ) ) ) ) ) )
@ ( ap @ V2_27index_27 @ V3a0 ) ) ) ) )
@ ( ap @ V2_27index_27 @ V1a0 ) ) ) ) ) )
@ V0rep ) ) ) ).
thf(ax_thm_2Equote_2Eindex__case__def,axiom,
! [A_27a: del] :
( ! [V0a: tp__ty_2Equote_2Eindex,V1f: $i] :
( ( mem @ V1f @ ( arr @ ty_2Equote_2Eindex @ A_27a ) )
=> ! [V2f1: $i] :
( ( mem @ V2f1 @ ( arr @ ty_2Equote_2Eindex @ A_27a ) )
=> ! [V3v: $i] :
( ( mem @ V3v @ A_27a )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equote_2Eindex__CASE @ A_27a ) @ ( ap @ c_2Equote_2ELeft__idx @ ( inj__ty_2Equote_2Eindex @ V0a ) ) ) @ V1f ) @ V2f1 ) @ V3v )
= ( ap @ V1f @ ( inj__ty_2Equote_2Eindex @ V0a ) ) ) ) ) )
& ! [V4a: tp__ty_2Equote_2Eindex,V5f: $i] :
( ( mem @ V5f @ ( arr @ ty_2Equote_2Eindex @ A_27a ) )
=> ! [V6f1: $i] :
( ( mem @ V6f1 @ ( arr @ ty_2Equote_2Eindex @ A_27a ) )
=> ! [V7v: $i] :
( ( mem @ V7v @ A_27a )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equote_2Eindex__CASE @ A_27a ) @ ( ap @ c_2Equote_2ERight__idx @ ( inj__ty_2Equote_2Eindex @ V4a ) ) ) @ V5f ) @ V6f1 ) @ V7v )
= ( ap @ V6f1 @ ( inj__ty_2Equote_2Eindex @ V4a ) ) ) ) ) )
& ! [V8f: $i] :
( ( mem @ V8f @ ( arr @ ty_2Equote_2Eindex @ A_27a ) )
=> ! [V9f1: $i] :
( ( mem @ V9f1 @ ( arr @ ty_2Equote_2Eindex @ A_27a ) )
=> ! [V10v: $i] :
( ( mem @ V10v @ A_27a )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equote_2Eindex__CASE @ A_27a ) @ ( inj__ty_2Equote_2Eindex @ fo__c_2Equote_2EEnd__idx ) ) @ V8f ) @ V9f1 ) @ V10v )
= V10v ) ) ) ) ) ).
thf(ax_thm_2Equote_2Eindex__size__def,axiom,
( ! [V0a: tp__ty_2Equote_2Eindex] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Equote_2Eindex__size @ ( ap @ c_2Equote_2ELeft__idx @ ( inj__ty_2Equote_2Eindex @ V0a ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2Equote_2Eindex__size @ ( inj__ty_2Equote_2Eindex @ V0a ) ) ) ) )
& ! [V1a: tp__ty_2Equote_2Eindex] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Equote_2Eindex__size @ ( ap @ c_2Equote_2ERight__idx @ ( inj__ty_2Equote_2Eindex @ V1a ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2Equote_2Eindex__size @ ( inj__ty_2Equote_2Eindex @ V1a ) ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Equote_2Eindex__size @ ( inj__ty_2Equote_2Eindex @ fo__c_2Equote_2EEnd__idx ) ) )
= fo__c_2Enum_2E0 ) ) ).
thf(conj_thm_2Equote_2Edatatype__index,axiom,
! [V0index: $i] :
( ( mem @ V0index @ ( arr @ ( arr @ ty_2Equote_2Eindex @ ty_2Equote_2Eindex ) @ ( arr @ ( arr @ ty_2Equote_2Eindex @ ty_2Equote_2Eindex ) @ ( arr @ ty_2Equote_2Eindex @ bool ) ) ) )
=> ( p @ ( ap @ ( c_2Ebool_2EDATATYPE @ bool ) @ ( ap @ ( ap @ ( ap @ V0index @ c_2Equote_2ELeft__idx ) @ c_2Equote_2ERight__idx ) @ ( inj__ty_2Equote_2Eindex @ fo__c_2Equote_2EEnd__idx ) ) ) ) ) ).
thf(conj_thm_2Equote_2Eindex__11,axiom,
( ! [V0a: tp__ty_2Equote_2Eindex,V1a_27: tp__ty_2Equote_2Eindex] :
( ( ( surj__ty_2Equote_2Eindex @ ( ap @ c_2Equote_2ELeft__idx @ ( inj__ty_2Equote_2Eindex @ V0a ) ) )
= ( surj__ty_2Equote_2Eindex @ ( ap @ c_2Equote_2ELeft__idx @ ( inj__ty_2Equote_2Eindex @ V1a_27 ) ) ) )
<=> ( V0a = V1a_27 ) )
& ! [V2a: tp__ty_2Equote_2Eindex,V3a_27: tp__ty_2Equote_2Eindex] :
( ( ( surj__ty_2Equote_2Eindex @ ( ap @ c_2Equote_2ERight__idx @ ( inj__ty_2Equote_2Eindex @ V2a ) ) )
= ( surj__ty_2Equote_2Eindex @ ( ap @ c_2Equote_2ERight__idx @ ( inj__ty_2Equote_2Eindex @ V3a_27 ) ) ) )
<=> ( V2a = V3a_27 ) ) ) ).
thf(conj_thm_2Equote_2Eindex__distinct,axiom,
( ! [V0a_27: tp__ty_2Equote_2Eindex,V1a: tp__ty_2Equote_2Eindex] :
( ( surj__ty_2Equote_2Eindex @ ( ap @ c_2Equote_2ELeft__idx @ ( inj__ty_2Equote_2Eindex @ V1a ) ) )
!= ( surj__ty_2Equote_2Eindex @ ( ap @ c_2Equote_2ERight__idx @ ( inj__ty_2Equote_2Eindex @ V0a_27 ) ) ) )
& ! [V2a: tp__ty_2Equote_2Eindex] :
( ( surj__ty_2Equote_2Eindex @ ( ap @ c_2Equote_2ELeft__idx @ ( inj__ty_2Equote_2Eindex @ V2a ) ) )
!= fo__c_2Equote_2EEnd__idx )
& ! [V3a: tp__ty_2Equote_2Eindex] :
( ( surj__ty_2Equote_2Eindex @ ( ap @ c_2Equote_2ERight__idx @ ( inj__ty_2Equote_2Eindex @ V3a ) ) )
!= fo__c_2Equote_2EEnd__idx ) ) ).
thf(conj_thm_2Equote_2Eindex__nchotomy,axiom,
! [V0ii: tp__ty_2Equote_2Eindex] :
( ? [V1i: tp__ty_2Equote_2Eindex] :
( V0ii
= ( surj__ty_2Equote_2Eindex @ ( ap @ c_2Equote_2ELeft__idx @ ( inj__ty_2Equote_2Eindex @ V1i ) ) ) )
| ? [V2i: tp__ty_2Equote_2Eindex] :
( V0ii
= ( surj__ty_2Equote_2Eindex @ ( ap @ c_2Equote_2ERight__idx @ ( inj__ty_2Equote_2Eindex @ V2i ) ) ) )
| ( V0ii = fo__c_2Equote_2EEnd__idx ) ) ).
thf(conj_thm_2Equote_2Eindex__Axiom,axiom,
! [A_27a: del,V0f0: $i] :
( ( mem @ V0f0 @ ( arr @ ty_2Equote_2Eindex @ ( arr @ A_27a @ A_27a ) ) )
=> ! [V1f1: $i] :
( ( mem @ V1f1 @ ( arr @ ty_2Equote_2Eindex @ ( arr @ A_27a @ A_27a ) ) )
=> ! [V2f2: $i] :
( ( mem @ V2f2 @ A_27a )
=> ? [V3fn: $i] :
( ( mem @ V3fn @ ( arr @ ty_2Equote_2Eindex @ A_27a ) )
& ! [V4a: tp__ty_2Equote_2Eindex] :
( ( ap @ V3fn @ ( ap @ c_2Equote_2ELeft__idx @ ( inj__ty_2Equote_2Eindex @ V4a ) ) )
= ( ap @ ( ap @ V0f0 @ ( inj__ty_2Equote_2Eindex @ V4a ) ) @ ( ap @ V3fn @ ( inj__ty_2Equote_2Eindex @ V4a ) ) ) )
& ! [V5a: tp__ty_2Equote_2Eindex] :
( ( ap @ V3fn @ ( ap @ c_2Equote_2ERight__idx @ ( inj__ty_2Equote_2Eindex @ V5a ) ) )
= ( ap @ ( ap @ V1f1 @ ( inj__ty_2Equote_2Eindex @ V5a ) ) @ ( ap @ V3fn @ ( inj__ty_2Equote_2Eindex @ V5a ) ) ) )
& ( ( ap @ V3fn @ ( inj__ty_2Equote_2Eindex @ fo__c_2Equote_2EEnd__idx ) )
= V2f2 ) ) ) ) ) ).
thf(conj_thm_2Equote_2Eindex__induction,axiom,
! [V0P: $i] :
( ( mem @ V0P @ ( arr @ ty_2Equote_2Eindex @ bool ) )
=> ( ( ! [V1i: tp__ty_2Equote_2Eindex] :
( ( p @ ( ap @ V0P @ ( inj__ty_2Equote_2Eindex @ V1i ) ) )
=> ( p @ ( ap @ V0P @ ( ap @ c_2Equote_2ELeft__idx @ ( inj__ty_2Equote_2Eindex @ V1i ) ) ) ) )
& ! [V2i: tp__ty_2Equote_2Eindex] :
( ( p @ ( ap @ V0P @ ( inj__ty_2Equote_2Eindex @ V2i ) ) )
=> ( p @ ( ap @ V0P @ ( ap @ c_2Equote_2ERight__idx @ ( inj__ty_2Equote_2Eindex @ V2i ) ) ) ) )
& ( p @ ( ap @ V0P @ ( inj__ty_2Equote_2Eindex @ fo__c_2Equote_2EEnd__idx ) ) ) )
=> ! [V3i: tp__ty_2Equote_2Eindex] : ( p @ ( ap @ V0P @ ( inj__ty_2Equote_2Eindex @ V3i ) ) ) ) ) ).
thf(conj_thm_2Equote_2Eindex__case__cong,axiom,
! [A_27a: del,V0f_27: $i] :
( ( mem @ V0f_27 @ ( arr @ ty_2Equote_2Eindex @ A_27a ) )
=> ! [V1f1_27: $i] :
( ( mem @ V1f1_27 @ ( arr @ ty_2Equote_2Eindex @ A_27a ) )
=> ! [V2v_27: $i] :
( ( mem @ V2v_27 @ A_27a )
=> ! [V3M: tp__ty_2Equote_2Eindex,V4M_27: tp__ty_2Equote_2Eindex,V5f: $i] :
( ( mem @ V5f @ ( arr @ ty_2Equote_2Eindex @ A_27a ) )
=> ! [V6f1: $i] :
( ( mem @ V6f1 @ ( arr @ ty_2Equote_2Eindex @ A_27a ) )
=> ! [V7v: $i] :
( ( mem @ V7v @ A_27a )
=> ( ( ( V3M = V4M_27 )
& ! [V8a: tp__ty_2Equote_2Eindex] :
( ( V4M_27
= ( surj__ty_2Equote_2Eindex @ ( ap @ c_2Equote_2ELeft__idx @ ( inj__ty_2Equote_2Eindex @ V8a ) ) ) )
=> ( ( ap @ V5f @ ( inj__ty_2Equote_2Eindex @ V8a ) )
= ( ap @ V0f_27 @ ( inj__ty_2Equote_2Eindex @ V8a ) ) ) )
& ! [V9a: tp__ty_2Equote_2Eindex] :
( ( V4M_27
= ( surj__ty_2Equote_2Eindex @ ( ap @ c_2Equote_2ERight__idx @ ( inj__ty_2Equote_2Eindex @ V9a ) ) ) )
=> ( ( ap @ V6f1 @ ( inj__ty_2Equote_2Eindex @ V9a ) )
= ( ap @ V1f1_27 @ ( inj__ty_2Equote_2Eindex @ V9a ) ) ) )
& ( ( V4M_27 = fo__c_2Equote_2EEnd__idx )
=> ( V7v = V2v_27 ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equote_2Eindex__CASE @ A_27a ) @ ( inj__ty_2Equote_2Eindex @ V3M ) ) @ V5f ) @ V6f1 ) @ V7v )
= ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equote_2Eindex__CASE @ A_27a ) @ ( inj__ty_2Equote_2Eindex @ V4M_27 ) ) @ V0f_27 ) @ V1f1_27 ) @ V2v_27 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equote_2Eindex__case__eq,axiom,
! [A_27a: del,V0x: tp__ty_2Equote_2Eindex,V1f: $i] :
( ( mem @ V1f @ ( arr @ ty_2Equote_2Eindex @ A_27a ) )
=> ! [V2f1: $i] :
( ( mem @ V2f1 @ ( arr @ ty_2Equote_2Eindex @ A_27a ) )
=> ! [V3v: $i] :
( ( mem @ V3v @ A_27a )
=> ! [V4v_27: $i] :
( ( mem @ V4v_27 @ A_27a )
=> ( ( ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equote_2Eindex__CASE @ A_27a ) @ ( inj__ty_2Equote_2Eindex @ V0x ) ) @ V1f ) @ V2f1 ) @ V3v )
= V4v_27 )
<=> ( ? [V5i: tp__ty_2Equote_2Eindex] :
( ( V0x
= ( surj__ty_2Equote_2Eindex @ ( ap @ c_2Equote_2ELeft__idx @ ( inj__ty_2Equote_2Eindex @ V5i ) ) ) )
& ( ( ap @ V1f @ ( inj__ty_2Equote_2Eindex @ V5i ) )
= V4v_27 ) )
| ? [V6i: tp__ty_2Equote_2Eindex] :
( ( V0x
= ( surj__ty_2Equote_2Eindex @ ( ap @ c_2Equote_2ERight__idx @ ( inj__ty_2Equote_2Eindex @ V6i ) ) ) )
& ( ( ap @ V2f1 @ ( inj__ty_2Equote_2Eindex @ V6i ) )
= V4v_27 ) )
| ( ( V0x = fo__c_2Equote_2EEnd__idx )
& ( V3v = V4v_27 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equote_2Eindex__compare__ind,axiom,
! [V0P: $i] :
( ( mem @ V0P @ ( arr @ ty_2Equote_2Eindex @ ( arr @ ty_2Equote_2Eindex @ bool ) ) )
=> ( ( ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Equote_2Eindex @ fo__c_2Equote_2EEnd__idx ) ) @ ( inj__ty_2Equote_2Eindex @ fo__c_2Equote_2EEnd__idx ) ) )
& ! [V1v10: tp__ty_2Equote_2Eindex] : ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Equote_2Eindex @ fo__c_2Equote_2EEnd__idx ) ) @ ( ap @ c_2Equote_2ELeft__idx @ ( inj__ty_2Equote_2Eindex @ V1v10 ) ) ) )
& ! [V2v11: tp__ty_2Equote_2Eindex] : ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Equote_2Eindex @ fo__c_2Equote_2EEnd__idx ) ) @ ( ap @ c_2Equote_2ERight__idx @ ( inj__ty_2Equote_2Eindex @ V2v11 ) ) ) )
& ! [V3v2: tp__ty_2Equote_2Eindex] : ( p @ ( ap @ ( ap @ V0P @ ( ap @ c_2Equote_2ELeft__idx @ ( inj__ty_2Equote_2Eindex @ V3v2 ) ) ) @ ( inj__ty_2Equote_2Eindex @ fo__c_2Equote_2EEnd__idx ) ) )
& ! [V4v3: tp__ty_2Equote_2Eindex] : ( p @ ( ap @ ( ap @ V0P @ ( ap @ c_2Equote_2ERight__idx @ ( inj__ty_2Equote_2Eindex @ V4v3 ) ) ) @ ( inj__ty_2Equote_2Eindex @ fo__c_2Equote_2EEnd__idx ) ) )
& ! [V5n_27: tp__ty_2Equote_2Eindex,V6m_27: tp__ty_2Equote_2Eindex] :
( ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Equote_2Eindex @ V5n_27 ) ) @ ( inj__ty_2Equote_2Eindex @ V6m_27 ) ) )
=> ( p @ ( ap @ ( ap @ V0P @ ( ap @ c_2Equote_2ELeft__idx @ ( inj__ty_2Equote_2Eindex @ V5n_27 ) ) ) @ ( ap @ c_2Equote_2ELeft__idx @ ( inj__ty_2Equote_2Eindex @ V6m_27 ) ) ) ) )
& ! [V7n_27: tp__ty_2Equote_2Eindex,V8m_27: tp__ty_2Equote_2Eindex] : ( p @ ( ap @ ( ap @ V0P @ ( ap @ c_2Equote_2ELeft__idx @ ( inj__ty_2Equote_2Eindex @ V7n_27 ) ) ) @ ( ap @ c_2Equote_2ERight__idx @ ( inj__ty_2Equote_2Eindex @ V8m_27 ) ) ) )
& ! [V9n_27: tp__ty_2Equote_2Eindex,V10m_27: tp__ty_2Equote_2Eindex] :
( ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Equote_2Eindex @ V9n_27 ) ) @ ( inj__ty_2Equote_2Eindex @ V10m_27 ) ) )
=> ( p @ ( ap @ ( ap @ V0P @ ( ap @ c_2Equote_2ERight__idx @ ( inj__ty_2Equote_2Eindex @ V9n_27 ) ) ) @ ( ap @ c_2Equote_2ERight__idx @ ( inj__ty_2Equote_2Eindex @ V10m_27 ) ) ) ) )
& ! [V11n_27: tp__ty_2Equote_2Eindex,V12m_27: tp__ty_2Equote_2Eindex] : ( p @ ( ap @ ( ap @ V0P @ ( ap @ c_2Equote_2ERight__idx @ ( inj__ty_2Equote_2Eindex @ V11n_27 ) ) ) @ ( ap @ c_2Equote_2ELeft__idx @ ( inj__ty_2Equote_2Eindex @ V12m_27 ) ) ) ) )
=> ! [V13v: tp__ty_2Equote_2Eindex,V14v1: tp__ty_2Equote_2Eindex] : ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Equote_2Eindex @ V13v ) ) @ ( inj__ty_2Equote_2Eindex @ V14v1 ) ) ) ) ) ).
thf(conj_thm_2Equote_2Eindex__compare__def,axiom,
( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ c_2Equote_2Eindex__compare @ ( inj__ty_2Equote_2Eindex @ fo__c_2Equote_2EEnd__idx ) ) @ ( inj__ty_2Equote_2Eindex @ fo__c_2Equote_2EEnd__idx ) ) )
= fo__c_2EternaryComparisons_2EEQUAL )
& ! [V0v10: tp__ty_2Equote_2Eindex] :
( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ c_2Equote_2Eindex__compare @ ( inj__ty_2Equote_2Eindex @ fo__c_2Equote_2EEnd__idx ) ) @ ( ap @ c_2Equote_2ELeft__idx @ ( inj__ty_2Equote_2Eindex @ V0v10 ) ) ) )
= fo__c_2EternaryComparisons_2ELESS )
& ! [V1v11: tp__ty_2Equote_2Eindex] :
( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ c_2Equote_2Eindex__compare @ ( inj__ty_2Equote_2Eindex @ fo__c_2Equote_2EEnd__idx ) ) @ ( ap @ c_2Equote_2ERight__idx @ ( inj__ty_2Equote_2Eindex @ V1v11 ) ) ) )
= fo__c_2EternaryComparisons_2ELESS )
& ! [V2v2: tp__ty_2Equote_2Eindex] :
( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ c_2Equote_2Eindex__compare @ ( ap @ c_2Equote_2ELeft__idx @ ( inj__ty_2Equote_2Eindex @ V2v2 ) ) ) @ ( inj__ty_2Equote_2Eindex @ fo__c_2Equote_2EEnd__idx ) ) )
= fo__c_2EternaryComparisons_2EGREATER )
& ! [V3v3: tp__ty_2Equote_2Eindex] :
( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ c_2Equote_2Eindex__compare @ ( ap @ c_2Equote_2ERight__idx @ ( inj__ty_2Equote_2Eindex @ V3v3 ) ) ) @ ( inj__ty_2Equote_2Eindex @ fo__c_2Equote_2EEnd__idx ) ) )
= fo__c_2EternaryComparisons_2EGREATER )
& ! [V4n_27: tp__ty_2Equote_2Eindex,V5m_27: tp__ty_2Equote_2Eindex] :
( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ c_2Equote_2Eindex__compare @ ( ap @ c_2Equote_2ELeft__idx @ ( inj__ty_2Equote_2Eindex @ V4n_27 ) ) ) @ ( ap @ c_2Equote_2ELeft__idx @ ( inj__ty_2Equote_2Eindex @ V5m_27 ) ) ) )
= ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ c_2Equote_2Eindex__compare @ ( inj__ty_2Equote_2Eindex @ V4n_27 ) ) @ ( inj__ty_2Equote_2Eindex @ V5m_27 ) ) ) )
& ! [V6n_27: tp__ty_2Equote_2Eindex,V7m_27: tp__ty_2Equote_2Eindex] :
( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ c_2Equote_2Eindex__compare @ ( ap @ c_2Equote_2ELeft__idx @ ( inj__ty_2Equote_2Eindex @ V6n_27 ) ) ) @ ( ap @ c_2Equote_2ERight__idx @ ( inj__ty_2Equote_2Eindex @ V7m_27 ) ) ) )
= fo__c_2EternaryComparisons_2ELESS )
& ! [V8n_27: tp__ty_2Equote_2Eindex,V9m_27: tp__ty_2Equote_2Eindex] :
( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ c_2Equote_2Eindex__compare @ ( ap @ c_2Equote_2ERight__idx @ ( inj__ty_2Equote_2Eindex @ V8n_27 ) ) ) @ ( ap @ c_2Equote_2ERight__idx @ ( inj__ty_2Equote_2Eindex @ V9m_27 ) ) ) )
= ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ c_2Equote_2Eindex__compare @ ( inj__ty_2Equote_2Eindex @ V8n_27 ) ) @ ( inj__ty_2Equote_2Eindex @ V9m_27 ) ) ) )
& ! [V10n_27: tp__ty_2Equote_2Eindex,V11m_27: tp__ty_2Equote_2Eindex] :
( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ c_2Equote_2Eindex__compare @ ( ap @ c_2Equote_2ERight__idx @ ( inj__ty_2Equote_2Eindex @ V10n_27 ) ) ) @ ( ap @ c_2Equote_2ELeft__idx @ ( inj__ty_2Equote_2Eindex @ V11m_27 ) ) ) )
= fo__c_2EternaryComparisons_2EGREATER ) ) ).
thf(conj_thm_2Equote_2Ecompare__index__equal,axiom,
! [V0i1: tp__ty_2Equote_2Eindex,V1i2: tp__ty_2Equote_2Eindex] :
( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ c_2Equote_2Eindex__compare @ ( inj__ty_2Equote_2Eindex @ V0i1 ) ) @ ( inj__ty_2Equote_2Eindex @ V1i2 ) ) )
= fo__c_2EternaryComparisons_2EEQUAL )
<=> ( V0i1 = V1i2 ) ) ).
thf(stp_c_ty_2Elist_2Elist_ty_2Equote_2Eindex,type,
tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex: $tType ).
thf(stp_inj_c_ty_2Elist_2Elist_ty_2Equote_2Eindex,type,
inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex > $i ).
thf(stp_surj_c_ty_2Elist_2Elist_ty_2Equote_2Eindex,type,
surj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex: $i > tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex ).
thf(stp_inj_surj_c_ty_2Elist_2Elist_ty_2Equote_2Eindex,axiom,
! [X: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex] :
( ( surj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ X ) )
= X ) ).
thf(stp_inj_mem_c_ty_2Elist_2Elist_ty_2Equote_2Eindex,axiom,
! [X: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex] : ( mem @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ X ) @ ( ty_2Elist_2Elist @ ty_2Equote_2Eindex ) ) ).
thf(stp_iso_mem_c_ty_2Elist_2Elist_ty_2Equote_2Eindex,axiom,
! [X: $i] :
( ( mem @ X @ ( ty_2Elist_2Elist @ ty_2Equote_2Eindex ) )
=> ( X
= ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ ( surj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ X ) ) ) ) ).
thf(conj_thm_2Equote_2Ecompare__list__index,axiom,
! [V0l1: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex,V1l2: tp__c_ty_2Elist_2Elist_ty_2Equote_2Eindex] :
( ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ ( ap @ ( c_2EternaryComparisons_2Elist__compare @ ty_2Equote_2Eindex @ ty_2Equote_2Eindex ) @ c_2Equote_2Eindex__compare ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V0l1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Equote_2Eindex @ V1l2 ) ) )
= fo__c_2EternaryComparisons_2EEQUAL )
<=> ( V0l1 = V1l2 ) ) ).
thf(ax_thm_2Equote_2Eindex__lt__def,axiom,
! [V0i1: tp__ty_2Equote_2Eindex,V1i2: tp__ty_2Equote_2Eindex] :
( ( p @ ( ap @ ( ap @ c_2Equote_2Eindex__lt @ ( inj__ty_2Equote_2Eindex @ V0i1 ) ) @ ( inj__ty_2Equote_2Eindex @ V1i2 ) ) )
<=> ( ( surj__ty_2EternaryComparisons_2Eordering @ ( ap @ ( ap @ c_2Equote_2Eindex__compare @ ( inj__ty_2Equote_2Eindex @ V0i1 ) ) @ ( inj__ty_2Equote_2Eindex @ V1i2 ) ) )
= fo__c_2EternaryComparisons_2ELESS ) ) ).
thf(ax_thm_2Equote_2Evarmap__TY__DEF,axiom,
! [A_27a: del] :
? [V0rep: $i] :
( ( mem @ V0rep @ ( arr @ ( ty_2Equote_2Evarmap @ A_27a ) @ ( ty_2Eind__type_2Erecspace @ A_27a ) ) )
& ( p
@ ( ap
@ ( ap @ ( c_2Ebool_2ETYPE__DEFINITION @ ( ty_2Eind__type_2Erecspace @ A_27a ) @ ( ty_2Equote_2Evarmap @ A_27a ) )
@ ( lam @ ( ty_2Eind__type_2Erecspace @ A_27a )
@ ^ [V1a0_27: $i] :
( ap @ ( c_2Ebool_2E_21 @ ( arr @ ( ty_2Eind__type_2Erecspace @ A_27a ) @ bool ) )
@ ( lam @ ( arr @ ( ty_2Eind__type_2Erecspace @ A_27a ) @ bool )
@ ^ [V2_27varmap_27: $i] :
( ap
@ ( ap @ c_2Emin_2E_3D_3D_3E
@ ( ap @ ( c_2Ebool_2E_21 @ ( ty_2Eind__type_2Erecspace @ A_27a ) )
@ ( lam @ ( ty_2Eind__type_2Erecspace @ A_27a )
@ ^ [V3a0_27: $i] :
( ap
@ ( ap @ c_2Emin_2E_3D_3D_3E
@ ( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eind__type_2Erecspace @ A_27a ) ) @ V3a0_27 )
@ ( ap @ ( ap @ ( ap @ ( c_2Eind__type_2ECONSTR @ A_27a ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( c_2Ebool_2EARB @ A_27a ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4n: $i] : ( c_2Eind__type_2EBOTTOM @ A_27a ) ) ) ) )
@ ( ap @ ( c_2Ebool_2E_3F @ A_27a )
@ ( lam @ A_27a
@ ^ [V5a0: $i] :
( ap @ ( c_2Ebool_2E_3F @ ( ty_2Eind__type_2Erecspace @ A_27a ) )
@ ( lam @ ( ty_2Eind__type_2Erecspace @ A_27a )
@ ^ [V6a1: $i] :
( ap @ ( c_2Ebool_2E_3F @ ( ty_2Eind__type_2Erecspace @ A_27a ) )
@ ( lam @ ( ty_2Eind__type_2Erecspace @ A_27a )
@ ^ [V7a2: $i] :
( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eind__type_2Erecspace @ A_27a ) ) @ V3a0_27 )
@ ( ap
@ ( ap
@ ( ap
@ ( lam @ A_27a
@ ^ [V8a0: $i] :
( lam @ ( ty_2Eind__type_2Erecspace @ A_27a )
@ ^ [V9a1: $i] :
( lam @ ( ty_2Eind__type_2Erecspace @ A_27a )
@ ^ [V10a2: $i] :
( ap @ ( ap @ ( ap @ ( c_2Eind__type_2ECONSTR @ A_27a ) @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ V8a0 )
@ ( ap @ ( ap @ ( c_2Eind__type_2EFCONS @ ( ty_2Eind__type_2Erecspace @ A_27a ) ) @ V9a1 )
@ ( ap @ ( ap @ ( c_2Eind__type_2EFCONS @ ( ty_2Eind__type_2Erecspace @ A_27a ) ) @ V10a2 )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V11n: $i] : ( c_2Eind__type_2EBOTTOM @ A_27a ) ) ) ) ) ) ) )
@ V5a0 )
@ V6a1 )
@ V7a2 ) ) )
@ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V2_27varmap_27 @ V6a1 ) ) @ ( ap @ V2_27varmap_27 @ V7a2 ) ) ) ) ) ) ) ) ) ) )
@ ( ap @ V2_27varmap_27 @ V3a0_27 ) ) ) ) )
@ ( ap @ V2_27varmap_27 @ V1a0_27 ) ) ) ) ) )
@ V0rep ) ) ) ).
thf(ax_thm_2Equote_2Evarmap__case__def,axiom,
! [A_27a: del,A_27b: del] :
( ! [V0v: $i] :
( ( mem @ V0v @ A_27b )
=> ! [V1f: $i] :
( ( mem @ V1f @ ( arr @ A_27a @ ( arr @ ( ty_2Equote_2Evarmap @ A_27a ) @ ( arr @ ( ty_2Equote_2Evarmap @ A_27a ) @ A_27b ) ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Equote_2Evarmap__CASE @ A_27a @ A_27b ) @ ( c_2Equote_2EEmpty__vm @ A_27a ) ) @ V0v ) @ V1f )
= V0v ) ) )
& ! [V2a0: $i] :
( ( mem @ V2a0 @ A_27a )
=> ! [V3a1: $i] :
( ( mem @ V3a1 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V4a2: $i] :
( ( mem @ V4a2 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V5v: $i] :
( ( mem @ V5v @ A_27b )
=> ! [V6f: $i] :
( ( mem @ V6f @ ( arr @ A_27a @ ( arr @ ( ty_2Equote_2Evarmap @ A_27a ) @ ( arr @ ( ty_2Equote_2Evarmap @ A_27a ) @ A_27b ) ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Equote_2Evarmap__CASE @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Equote_2ENode__vm @ A_27a ) @ V2a0 ) @ V3a1 ) @ V4a2 ) ) @ V5v ) @ V6f )
= ( ap @ ( ap @ ( ap @ V6f @ V2a0 ) @ V3a1 ) @ V4a2 ) ) ) ) ) ) ) ) ).
thf(ax_thm_2Equote_2Evarmap__size__def,axiom,
! [A_27a: del] :
( ! [V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Equote_2Evarmap__size @ A_27a ) @ V0f ) @ ( c_2Equote_2EEmpty__vm @ A_27a ) ) )
= fo__c_2Enum_2E0 ) )
& ! [V1f: $i] :
( ( mem @ V1f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
=> ! [V2a0: $i] :
( ( mem @ V2a0 @ A_27a )
=> ! [V3a1: $i] :
( ( mem @ V3a1 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V4a2: $i] :
( ( mem @ V4a2 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Equote_2Evarmap__size @ A_27a ) @ V1f ) @ ( ap @ ( ap @ ( ap @ ( c_2Equote_2ENode__vm @ A_27a ) @ V2a0 ) @ V3a1 ) @ V4a2 ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ V1f @ V2a0 ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ ( c_2Equote_2Evarmap__size @ A_27a ) @ V1f ) @ V3a1 ) ) @ ( ap @ ( ap @ ( c_2Equote_2Evarmap__size @ A_27a ) @ V1f ) @ V4a2 ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equote_2Edatatype__varmap,axiom,
! [A_27a: del,V0varmap: $i] :
( ( mem @ V0varmap @ ( arr @ ( ty_2Equote_2Evarmap @ A_27a ) @ ( arr @ ( arr @ A_27a @ ( arr @ ( ty_2Equote_2Evarmap @ A_27a ) @ ( arr @ ( ty_2Equote_2Evarmap @ A_27a ) @ ( ty_2Equote_2Evarmap @ A_27a ) ) ) ) @ bool ) ) )
=> ( p @ ( ap @ ( c_2Ebool_2EDATATYPE @ bool ) @ ( ap @ ( ap @ V0varmap @ ( c_2Equote_2EEmpty__vm @ A_27a ) ) @ ( c_2Equote_2ENode__vm @ A_27a ) ) ) ) ) ).
thf(conj_thm_2Equote_2Evarmap__11,axiom,
! [A_27a: del,V0a0: $i] :
( ( mem @ V0a0 @ A_27a )
=> ! [V1a1: $i] :
( ( mem @ V1a1 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V2a2: $i] :
( ( mem @ V2a2 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V3a0_27: $i] :
( ( mem @ V3a0_27 @ A_27a )
=> ! [V4a1_27: $i] :
( ( mem @ V4a1_27 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V5a2_27: $i] :
( ( mem @ V5a2_27 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ( ( ( ap @ ( ap @ ( ap @ ( c_2Equote_2ENode__vm @ A_27a ) @ V0a0 ) @ V1a1 ) @ V2a2 )
= ( ap @ ( ap @ ( ap @ ( c_2Equote_2ENode__vm @ A_27a ) @ V3a0_27 ) @ V4a1_27 ) @ V5a2_27 ) )
<=> ( ( V0a0 = V3a0_27 )
& ( V1a1 = V4a1_27 )
& ( V2a2 = V5a2_27 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equote_2Evarmap__distinct,axiom,
! [A_27a: del,V0a2: $i] :
( ( mem @ V0a2 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V1a1: $i] :
( ( mem @ V1a1 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V2a0: $i] :
( ( mem @ V2a0 @ A_27a )
=> ( ( c_2Equote_2EEmpty__vm @ A_27a )
!= ( ap @ ( ap @ ( ap @ ( c_2Equote_2ENode__vm @ A_27a ) @ V2a0 ) @ V1a1 ) @ V0a2 ) ) ) ) ) ).
thf(conj_thm_2Equote_2Evarmap__nchotomy,axiom,
! [A_27a: del,V0vv: $i] :
( ( mem @ V0vv @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ( ( V0vv
= ( c_2Equote_2EEmpty__vm @ A_27a ) )
| ? [V1a: $i] :
( ( mem @ V1a @ A_27a )
& ? [V2v: $i] :
( ( mem @ V2v @ ( ty_2Equote_2Evarmap @ A_27a ) )
& ? [V3v0: $i] :
( ( mem @ V3v0 @ ( ty_2Equote_2Evarmap @ A_27a ) )
& ( V0vv
= ( ap @ ( ap @ ( ap @ ( c_2Equote_2ENode__vm @ A_27a ) @ V1a ) @ V2v ) @ V3v0 ) ) ) ) ) ) ) ).
thf(conj_thm_2Equote_2Evarmap__Axiom,axiom,
! [A_27a: del,A_27b: del,V0f0: $i] :
( ( mem @ V0f0 @ A_27b )
=> ! [V1f1: $i] :
( ( mem @ V1f1 @ ( arr @ A_27a @ ( arr @ ( ty_2Equote_2Evarmap @ A_27a ) @ ( arr @ ( ty_2Equote_2Evarmap @ A_27a ) @ ( arr @ A_27b @ ( arr @ A_27b @ A_27b ) ) ) ) ) )
=> ? [V2fn: $i] :
( ( mem @ V2fn @ ( arr @ ( ty_2Equote_2Evarmap @ A_27a ) @ A_27b ) )
& ( ( ap @ V2fn @ ( c_2Equote_2EEmpty__vm @ A_27a ) )
= V0f0 )
& ! [V3a0: $i] :
( ( mem @ V3a0 @ A_27a )
=> ! [V4a1: $i] :
( ( mem @ V4a1 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V5a2: $i] :
( ( mem @ V5a2 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ( ( ap @ V2fn @ ( ap @ ( ap @ ( ap @ ( c_2Equote_2ENode__vm @ A_27a ) @ V3a0 ) @ V4a1 ) @ V5a2 ) )
= ( ap @ ( ap @ ( ap @ ( ap @ ( ap @ V1f1 @ V3a0 ) @ V4a1 ) @ V5a2 ) @ ( ap @ V2fn @ V4a1 ) ) @ ( ap @ V2fn @ V5a2 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equote_2Evarmap__induction,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ ( ty_2Equote_2Evarmap @ A_27a ) @ bool ) )
=> ( ( ( p @ ( ap @ V0P @ ( c_2Equote_2EEmpty__vm @ A_27a ) ) )
& ! [V1v: $i] :
( ( mem @ V1v @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V2v0: $i] :
( ( mem @ V2v0 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ( ( ( p @ ( ap @ V0P @ V1v ) )
& ( p @ ( ap @ V0P @ V2v0 ) ) )
=> ! [V3a: $i] :
( ( mem @ V3a @ A_27a )
=> ( p @ ( ap @ V0P @ ( ap @ ( ap @ ( ap @ ( c_2Equote_2ENode__vm @ A_27a ) @ V3a ) @ V1v ) @ V2v0 ) ) ) ) ) ) ) )
=> ! [V4v: $i] :
( ( mem @ V4v @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ( p @ ( ap @ V0P @ V4v ) ) ) ) ) ).
thf(conj_thm_2Equote_2Evarmap__case__cong,axiom,
! [A_27a: del,A_27b: del,V0v_27: $i] :
( ( mem @ V0v_27 @ A_27b )
=> ! [V1f_27: $i] :
( ( mem @ V1f_27 @ ( arr @ A_27a @ ( arr @ ( ty_2Equote_2Evarmap @ A_27a ) @ ( arr @ ( ty_2Equote_2Evarmap @ A_27a ) @ A_27b ) ) ) )
=> ! [V2M: $i] :
( ( mem @ V2M @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V3M_27: $i] :
( ( mem @ V3M_27 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V4v: $i] :
( ( mem @ V4v @ A_27b )
=> ! [V5f: $i] :
( ( mem @ V5f @ ( arr @ A_27a @ ( arr @ ( ty_2Equote_2Evarmap @ A_27a ) @ ( arr @ ( ty_2Equote_2Evarmap @ A_27a ) @ A_27b ) ) ) )
=> ( ( ( V2M = V3M_27 )
& ( ( V3M_27
= ( c_2Equote_2EEmpty__vm @ A_27a ) )
=> ( V4v = V0v_27 ) )
& ! [V6a0: $i] :
( ( mem @ V6a0 @ A_27a )
=> ! [V7a1: $i] :
( ( mem @ V7a1 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V8a2: $i] :
( ( mem @ V8a2 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ( ( V3M_27
= ( ap @ ( ap @ ( ap @ ( c_2Equote_2ENode__vm @ A_27a ) @ V6a0 ) @ V7a1 ) @ V8a2 ) )
=> ( ( ap @ ( ap @ ( ap @ V5f @ V6a0 ) @ V7a1 ) @ V8a2 )
= ( ap @ ( ap @ ( ap @ V1f_27 @ V6a0 ) @ V7a1 ) @ V8a2 ) ) ) ) ) ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Equote_2Evarmap__CASE @ A_27a @ A_27b ) @ V2M ) @ V4v ) @ V5f )
= ( ap @ ( ap @ ( ap @ ( c_2Equote_2Evarmap__CASE @ A_27a @ A_27b ) @ V3M_27 ) @ V0v_27 ) @ V1f_27 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equote_2Evarmap__case__eq,axiom,
! [A_27a: del,A_27b: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V1v: $i] :
( ( mem @ V1v @ A_27b )
=> ! [V2f: $i] :
( ( mem @ V2f @ ( arr @ A_27a @ ( arr @ ( ty_2Equote_2Evarmap @ A_27a ) @ ( arr @ ( ty_2Equote_2Evarmap @ A_27a ) @ A_27b ) ) ) )
=> ! [V3v_27: $i] :
( ( mem @ V3v_27 @ A_27b )
=> ( ( ( ap @ ( ap @ ( ap @ ( c_2Equote_2Evarmap__CASE @ A_27a @ A_27b ) @ V0x ) @ V1v ) @ V2f )
= V3v_27 )
<=> ( ( ( V0x
= ( c_2Equote_2EEmpty__vm @ A_27a ) )
& ( V1v = V3v_27 ) )
| ? [V4a: $i] :
( ( mem @ V4a @ A_27a )
& ? [V5v_27_27: $i] :
( ( mem @ V5v_27_27 @ ( ty_2Equote_2Evarmap @ A_27a ) )
& ? [V6v0: $i] :
( ( mem @ V6v0 @ ( ty_2Equote_2Evarmap @ A_27a ) )
& ( V0x
= ( ap @ ( ap @ ( ap @ ( c_2Equote_2ENode__vm @ A_27a ) @ V4a ) @ V5v_27_27 ) @ V6v0 ) )
& ( ( ap @ ( ap @ ( ap @ V2f @ V4a ) @ V5v_27_27 ) @ V6v0 )
= V3v_27 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equote_2Evarmap__find__ind,axiom,
! [A_27a: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ ty_2Equote_2Eindex @ ( arr @ ( ty_2Equote_2Evarmap @ A_27a ) @ bool ) ) )
=> ( ( ! [V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ! [V2v1: $i] :
( ( mem @ V2v1 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V3v2: $i] :
( ( mem @ V3v2 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Equote_2Eindex @ fo__c_2Equote_2EEnd__idx ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Equote_2ENode__vm @ A_27a ) @ V1x ) @ V2v1 ) @ V3v2 ) ) ) ) ) )
& ! [V4i1: tp__ty_2Equote_2Eindex,V5x: $i] :
( ( mem @ V5x @ A_27a )
=> ! [V6v1: $i] :
( ( mem @ V6v1 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V7v2: $i] :
( ( mem @ V7v2 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Equote_2Eindex @ V4i1 ) ) @ V7v2 ) )
=> ( p @ ( ap @ ( ap @ V0P @ ( ap @ c_2Equote_2ERight__idx @ ( inj__ty_2Equote_2Eindex @ V4i1 ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Equote_2ENode__vm @ A_27a ) @ V5x ) @ V6v1 ) @ V7v2 ) ) ) ) ) ) )
& ! [V8i1: tp__ty_2Equote_2Eindex,V9x: $i] :
( ( mem @ V9x @ A_27a )
=> ! [V10v1: $i] :
( ( mem @ V10v1 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V11v2: $i] :
( ( mem @ V11v2 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Equote_2Eindex @ V8i1 ) ) @ V10v1 ) )
=> ( p @ ( ap @ ( ap @ V0P @ ( ap @ c_2Equote_2ELeft__idx @ ( inj__ty_2Equote_2Eindex @ V8i1 ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Equote_2ENode__vm @ A_27a ) @ V9x ) @ V10v1 ) @ V11v2 ) ) ) ) ) ) )
& ! [V12i: tp__ty_2Equote_2Eindex] : ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Equote_2Eindex @ V12i ) ) @ ( c_2Equote_2EEmpty__vm @ A_27a ) ) ) )
=> ! [V13v: tp__ty_2Equote_2Eindex,V14v1: $i] :
( ( mem @ V14v1 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Equote_2Eindex @ V13v ) ) @ V14v1 ) ) ) ) ) ).
thf(conj_thm_2Equote_2Evarmap__find__def,axiom,
! [A_27a: del] :
( ! [V0x: $i] :
( ( mem @ V0x @ A_27a )
=> ! [V1v2: $i] :
( ( mem @ V1v2 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V2v1: $i] :
( ( mem @ V2v1 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Equote_2Evarmap__find @ A_27a ) @ ( inj__ty_2Equote_2Eindex @ fo__c_2Equote_2EEnd__idx ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Equote_2ENode__vm @ A_27a ) @ V0x ) @ V2v1 ) @ V1v2 ) )
= V0x ) ) ) )
& ! [V3x: $i] :
( ( mem @ V3x @ A_27a )
=> ! [V4v2: $i] :
( ( mem @ V4v2 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V5v1: $i] :
( ( mem @ V5v1 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V6i1: tp__ty_2Equote_2Eindex] :
( ( ap @ ( ap @ ( c_2Equote_2Evarmap__find @ A_27a ) @ ( ap @ c_2Equote_2ERight__idx @ ( inj__ty_2Equote_2Eindex @ V6i1 ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Equote_2ENode__vm @ A_27a ) @ V3x ) @ V5v1 ) @ V4v2 ) )
= ( ap @ ( ap @ ( c_2Equote_2Evarmap__find @ A_27a ) @ ( inj__ty_2Equote_2Eindex @ V6i1 ) ) @ V4v2 ) ) ) ) )
& ! [V7x: $i] :
( ( mem @ V7x @ A_27a )
=> ! [V8v2: $i] :
( ( mem @ V8v2 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V9v1: $i] :
( ( mem @ V9v1 @ ( ty_2Equote_2Evarmap @ A_27a ) )
=> ! [V10i1: tp__ty_2Equote_2Eindex] :
( ( ap @ ( ap @ ( c_2Equote_2Evarmap__find @ A_27a ) @ ( ap @ c_2Equote_2ELeft__idx @ ( inj__ty_2Equote_2Eindex @ V10i1 ) ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Equote_2ENode__vm @ A_27a ) @ V7x ) @ V9v1 ) @ V8v2 ) )
= ( ap @ ( ap @ ( c_2Equote_2Evarmap__find @ A_27a ) @ ( inj__ty_2Equote_2Eindex @ V10i1 ) ) @ V9v1 ) ) ) ) )
& ! [V11i: tp__ty_2Equote_2Eindex] :
( ( ap @ ( ap @ ( c_2Equote_2Evarmap__find @ A_27a ) @ ( inj__ty_2Equote_2Eindex @ V11i ) ) @ ( c_2Equote_2EEmpty__vm @ A_27a ) )
= ( ap @ ( c_2Emin_2E_40 @ A_27a )
@ ( lam @ A_27a
@ ^ [V12x: $i] : c_2Ebool_2ET ) ) ) ) ).
%------------------------------------------------------------------------------