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 : 59 ( 12 unt; 0 def)
% Number of atoms : 357 ( 92 equ)
% Maximal formula atoms : 27 ( 6 avg)
% Number of connectives : 302 ( 4 ~; 6 |; 64 &)
% ( 8 <=>; 220 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 8 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% Number of functors : 62 ( 62 usr; 26 con; 0-5 aty)
% Number of variables : 241 ( 227 !; 14 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(ne_ty_2Equote_2Eindex,axiom,
ne(ty_2Equote_2Eindex) ).
fof(ne_ty_2Equote_2Evarmap,axiom,
! [A0] :
( ne(A0)
=> ne(ty_2Equote_2Evarmap(A0)) ) ).
fof(mem_c_2Equote_2EEmpty__vm,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Equote_2EEmpty__vm(A_27a),ty_2Equote_2Evarmap(A_27a)) ) ).
fof(mem_c_2Equote_2EEnd__idx,axiom,
mem(c_2Equote_2EEnd__idx,ty_2Equote_2Eindex) ).
fof(mem_c_2Equote_2ELeft__idx,axiom,
mem(c_2Equote_2ELeft__idx,arr(ty_2Equote_2Eindex,ty_2Equote_2Eindex)) ).
fof(mem_c_2Equote_2ENode__vm,axiom,
! [A_27a] :
( ne(A_27a)
=> 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))))) ) ).
fof(mem_c_2Equote_2ERight__idx,axiom,
mem(c_2Equote_2ERight__idx,arr(ty_2Equote_2Eindex,ty_2Equote_2Eindex)) ).
fof(mem_c_2Equote_2Eindex__CASE,axiom,
! [A_27a] :
( ne(A_27a)
=> 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))))) ) ).
fof(mem_c_2Equote_2Eindex__compare,axiom,
mem(c_2Equote_2Eindex__compare,arr(ty_2Equote_2Eindex,arr(ty_2Equote_2Eindex,ty_2EternaryComparisons_2Eordering))) ).
fof(mem_c_2Equote_2Eindex__lt,axiom,
mem(c_2Equote_2Eindex__lt,arr(ty_2Equote_2Eindex,arr(ty_2Equote_2Eindex,bool))) ).
fof(mem_c_2Equote_2Eindex__size,axiom,
mem(c_2Equote_2Eindex__size,arr(ty_2Equote_2Eindex,ty_2Enum_2Enum)) ).
fof(mem_c_2Equote_2Evarmap__CASE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> 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)))) ) ) ).
fof(mem_c_2Equote_2Evarmap__find,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Equote_2Evarmap__find(A_27a),arr(ty_2Equote_2Eindex,arr(ty_2Equote_2Evarmap(A_27a),A_27a))) ) ).
fof(mem_c_2Equote_2Evarmap__size,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Equote_2Evarmap__size(A_27a),arr(arr(A_27a,ty_2Enum_2Enum),arr(ty_2Equote_2Evarmap(A_27a),ty_2Enum_2Enum))) ) ).
fof(lameq_f2118,axiom,
! [V5a] : ap(f2118,V5a) = ap(ap(ap(c_2Eind__type_2ECONSTR(bool),c_2Enum_2E0),c_2Ebool_2EARB(bool)),ap(ap(c_2Eind__type_2EFCONS(ty_2Eind__type_2Erecspace(bool)),V5a),k(ty_2Enum_2Enum,c_2Eind__type_2EBOTTOM(bool)))) ).
fof(lameq_f2119,axiom,
! [V3a0] :
( mem(V3a0,ty_2Eind__type_2Erecspace(bool))
=> ! [V2_27index_27] :
( mem(V2_27index_27,arr(ty_2Eind__type_2Erecspace(bool),bool))
=> ! [V4a] : ap(f2119(V3a0,V2_27index_27),V4a) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Eind__type_2Erecspace(bool)),V3a0),ap(f2118,V4a))),ap(V2_27index_27,V4a)) ) ) ).
fof(lameq_f2120,axiom,
! [V8a] : ap(f2120,V8a) = ap(ap(ap(c_2Eind__type_2ECONSTR(bool),ap(c_2Enum_2ESUC,c_2Enum_2E0)),c_2Ebool_2EARB(bool)),ap(ap(c_2Eind__type_2EFCONS(ty_2Eind__type_2Erecspace(bool)),V8a),k(ty_2Enum_2Enum,c_2Eind__type_2EBOTTOM(bool)))) ).
fof(lameq_f2121,axiom,
! [V3a0] :
( mem(V3a0,ty_2Eind__type_2Erecspace(bool))
=> ! [V2_27index_27] :
( mem(V2_27index_27,arr(ty_2Eind__type_2Erecspace(bool),bool))
=> ! [V7a] : ap(f2121(V3a0,V2_27index_27),V7a) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Eind__type_2Erecspace(bool)),V3a0),ap(f2120,V7a))),ap(V2_27index_27,V7a)) ) ) ).
fof(lameq_f2122,axiom,
! [V2_27index_27] :
( mem(V2_27index_27,arr(ty_2Eind__type_2Erecspace(bool),bool))
=> ! [V3a0] : ap(f2122(V2_27index_27),V3a0) = 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)),f2119(V3a0,V2_27index_27))),ap(ap(c_2Ebool_2E_5C_2F,ap(c_2Ebool_2E_3F(ty_2Eind__type_2Erecspace(bool)),f2121(V3a0,V2_27index_27))),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,c_2Enum_2E0))),c_2Ebool_2EARB(bool)),k(ty_2Enum_2Enum,c_2Eind__type_2EBOTTOM(bool))))))),ap(V2_27index_27,V3a0)) ) ).
fof(lameq_f2123,axiom,
! [V1a0] :
( mem(V1a0,ty_2Eind__type_2Erecspace(bool))
=> ! [V2_27index_27] : ap(f2123(V1a0),V2_27index_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_21(ty_2Eind__type_2Erecspace(bool)),f2122(V2_27index_27))),ap(V2_27index_27,V1a0)) ) ).
fof(lameq_f2124,axiom,
! [V1a0] : ap(f2124,V1a0) = ap(c_2Ebool_2E_21(arr(ty_2Eind__type_2Erecspace(bool),bool)),f2123(V1a0)) ).
fof(ax_thm_2Equote_2Eindex__TY__DEF,axiom,
? [V0rep] :
( 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),f2124),V0rep)) ) ).
fof(ax_thm_2Equote_2Eindex__case__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0a] :
( mem(V0a,ty_2Equote_2Eindex)
=> ! [V1f] :
( mem(V1f,arr(ty_2Equote_2Eindex,A_27a))
=> ! [V2f1] :
( mem(V2f1,arr(ty_2Equote_2Eindex,A_27a))
=> ! [V3v] :
( mem(V3v,A_27a)
=> ap(ap(ap(ap(c_2Equote_2Eindex__CASE(A_27a),ap(c_2Equote_2ELeft__idx,V0a)),V1f),V2f1),V3v) = ap(V1f,V0a) ) ) ) )
& ! [V4a] :
( mem(V4a,ty_2Equote_2Eindex)
=> ! [V5f] :
( mem(V5f,arr(ty_2Equote_2Eindex,A_27a))
=> ! [V6f1] :
( mem(V6f1,arr(ty_2Equote_2Eindex,A_27a))
=> ! [V7v] :
( mem(V7v,A_27a)
=> ap(ap(ap(ap(c_2Equote_2Eindex__CASE(A_27a),ap(c_2Equote_2ERight__idx,V4a)),V5f),V6f1),V7v) = ap(V6f1,V4a) ) ) ) )
& ! [V8f] :
( mem(V8f,arr(ty_2Equote_2Eindex,A_27a))
=> ! [V9f1] :
( mem(V9f1,arr(ty_2Equote_2Eindex,A_27a))
=> ! [V10v] :
( mem(V10v,A_27a)
=> ap(ap(ap(ap(c_2Equote_2Eindex__CASE(A_27a),c_2Equote_2EEnd__idx),V8f),V9f1),V10v) = V10v ) ) ) ) ) ).
fof(ax_thm_2Equote_2Eindex__size__def,axiom,
( ! [V0a] :
( mem(V0a,ty_2Equote_2Eindex)
=> ap(c_2Equote_2Eindex__size,ap(c_2Equote_2ELeft__idx,V0a)) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Equote_2Eindex__size,V0a)) )
& ! [V1a] :
( mem(V1a,ty_2Equote_2Eindex)
=> ap(c_2Equote_2Eindex__size,ap(c_2Equote_2ERight__idx,V1a)) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Equote_2Eindex__size,V1a)) )
& ap(c_2Equote_2Eindex__size,c_2Equote_2EEnd__idx) = c_2Enum_2E0 ) ).
fof(conj_thm_2Equote_2Edatatype__index,axiom,
! [V0index] :
( 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),c_2Equote_2EEnd__idx))) ) ).
fof(conj_thm_2Equote_2Eindex__11,axiom,
( ! [V0a] :
( mem(V0a,ty_2Equote_2Eindex)
=> ! [V1a_27] :
( mem(V1a_27,ty_2Equote_2Eindex)
=> ( ap(c_2Equote_2ELeft__idx,V0a) = ap(c_2Equote_2ELeft__idx,V1a_27)
<=> V0a = V1a_27 ) ) )
& ! [V2a] :
( mem(V2a,ty_2Equote_2Eindex)
=> ! [V3a_27] :
( mem(V3a_27,ty_2Equote_2Eindex)
=> ( ap(c_2Equote_2ERight__idx,V2a) = ap(c_2Equote_2ERight__idx,V3a_27)
<=> V2a = V3a_27 ) ) ) ) ).
fof(conj_thm_2Equote_2Eindex__distinct,axiom,
( ! [V0a_27] :
( mem(V0a_27,ty_2Equote_2Eindex)
=> ! [V1a] :
( mem(V1a,ty_2Equote_2Eindex)
=> ap(c_2Equote_2ELeft__idx,V1a) != ap(c_2Equote_2ERight__idx,V0a_27) ) )
& ! [V2a] :
( mem(V2a,ty_2Equote_2Eindex)
=> ap(c_2Equote_2ELeft__idx,V2a) != c_2Equote_2EEnd__idx )
& ! [V3a] :
( mem(V3a,ty_2Equote_2Eindex)
=> ap(c_2Equote_2ERight__idx,V3a) != c_2Equote_2EEnd__idx ) ) ).
fof(conj_thm_2Equote_2Eindex__nchotomy,axiom,
! [V0ii] :
( mem(V0ii,ty_2Equote_2Eindex)
=> ( ? [V1i] :
( mem(V1i,ty_2Equote_2Eindex)
& V0ii = ap(c_2Equote_2ELeft__idx,V1i) )
| ? [V2i] :
( mem(V2i,ty_2Equote_2Eindex)
& V0ii = ap(c_2Equote_2ERight__idx,V2i) )
| V0ii = c_2Equote_2EEnd__idx ) ) ).
fof(conj_thm_2Equote_2Eindex__Axiom,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f0] :
( mem(V0f0,arr(ty_2Equote_2Eindex,arr(A_27a,A_27a)))
=> ! [V1f1] :
( mem(V1f1,arr(ty_2Equote_2Eindex,arr(A_27a,A_27a)))
=> ! [V2f2] :
( mem(V2f2,A_27a)
=> ? [V3fn] :
( mem(V3fn,arr(ty_2Equote_2Eindex,A_27a))
& ! [V4a] :
( mem(V4a,ty_2Equote_2Eindex)
=> ap(V3fn,ap(c_2Equote_2ELeft__idx,V4a)) = ap(ap(V0f0,V4a),ap(V3fn,V4a)) )
& ! [V5a] :
( mem(V5a,ty_2Equote_2Eindex)
=> ap(V3fn,ap(c_2Equote_2ERight__idx,V5a)) = ap(ap(V1f1,V5a),ap(V3fn,V5a)) )
& ap(V3fn,c_2Equote_2EEnd__idx) = V2f2 ) ) ) ) ) ).
fof(conj_thm_2Equote_2Eindex__induction,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Equote_2Eindex,bool))
=> ( ( ! [V1i] :
( mem(V1i,ty_2Equote_2Eindex)
=> ( p(ap(V0P,V1i))
=> p(ap(V0P,ap(c_2Equote_2ELeft__idx,V1i))) ) )
& ! [V2i] :
( mem(V2i,ty_2Equote_2Eindex)
=> ( p(ap(V0P,V2i))
=> p(ap(V0P,ap(c_2Equote_2ERight__idx,V2i))) ) )
& p(ap(V0P,c_2Equote_2EEnd__idx)) )
=> ! [V3i] :
( mem(V3i,ty_2Equote_2Eindex)
=> p(ap(V0P,V3i)) ) ) ) ).
fof(conj_thm_2Equote_2Eindex__case__cong,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0f_27] :
( mem(V0f_27,arr(ty_2Equote_2Eindex,A_27a))
=> ! [V1f1_27] :
( mem(V1f1_27,arr(ty_2Equote_2Eindex,A_27a))
=> ! [V2v_27] :
( mem(V2v_27,A_27a)
=> ! [V3M] :
( mem(V3M,ty_2Equote_2Eindex)
=> ! [V4M_27] :
( mem(V4M_27,ty_2Equote_2Eindex)
=> ! [V5f] :
( mem(V5f,arr(ty_2Equote_2Eindex,A_27a))
=> ! [V6f1] :
( mem(V6f1,arr(ty_2Equote_2Eindex,A_27a))
=> ! [V7v] :
( mem(V7v,A_27a)
=> ( ( V3M = V4M_27
& ! [V8a] :
( mem(V8a,ty_2Equote_2Eindex)
=> ( V4M_27 = ap(c_2Equote_2ELeft__idx,V8a)
=> ap(V5f,V8a) = ap(V0f_27,V8a) ) )
& ! [V9a] :
( mem(V9a,ty_2Equote_2Eindex)
=> ( V4M_27 = ap(c_2Equote_2ERight__idx,V9a)
=> ap(V6f1,V9a) = ap(V1f1_27,V9a) ) )
& ( V4M_27 = c_2Equote_2EEnd__idx
=> V7v = V2v_27 ) )
=> ap(ap(ap(ap(c_2Equote_2Eindex__CASE(A_27a),V3M),V5f),V6f1),V7v) = ap(ap(ap(ap(c_2Equote_2Eindex__CASE(A_27a),V4M_27),V0f_27),V1f1_27),V2v_27) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equote_2Eindex__case__eq,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,ty_2Equote_2Eindex)
=> ! [V1f] :
( mem(V1f,arr(ty_2Equote_2Eindex,A_27a))
=> ! [V2f1] :
( mem(V2f1,arr(ty_2Equote_2Eindex,A_27a))
=> ! [V3v] :
( mem(V3v,A_27a)
=> ! [V4v_27] :
( mem(V4v_27,A_27a)
=> ( ap(ap(ap(ap(c_2Equote_2Eindex__CASE(A_27a),V0x),V1f),V2f1),V3v) = V4v_27
<=> ( ? [V5i] :
( mem(V5i,ty_2Equote_2Eindex)
& V0x = ap(c_2Equote_2ELeft__idx,V5i)
& ap(V1f,V5i) = V4v_27 )
| ? [V6i] :
( mem(V6i,ty_2Equote_2Eindex)
& V0x = ap(c_2Equote_2ERight__idx,V6i)
& ap(V2f1,V6i) = V4v_27 )
| ( V0x = c_2Equote_2EEnd__idx
& V3v = V4v_27 ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equote_2Eindex__compare__ind,axiom,
! [V0P] :
( mem(V0P,arr(ty_2Equote_2Eindex,arr(ty_2Equote_2Eindex,bool)))
=> ( ( p(ap(ap(V0P,c_2Equote_2EEnd__idx),c_2Equote_2EEnd__idx))
& ! [V1v10] :
( mem(V1v10,ty_2Equote_2Eindex)
=> p(ap(ap(V0P,c_2Equote_2EEnd__idx),ap(c_2Equote_2ELeft__idx,V1v10))) )
& ! [V2v11] :
( mem(V2v11,ty_2Equote_2Eindex)
=> p(ap(ap(V0P,c_2Equote_2EEnd__idx),ap(c_2Equote_2ERight__idx,V2v11))) )
& ! [V3v2] :
( mem(V3v2,ty_2Equote_2Eindex)
=> p(ap(ap(V0P,ap(c_2Equote_2ELeft__idx,V3v2)),c_2Equote_2EEnd__idx)) )
& ! [V4v3] :
( mem(V4v3,ty_2Equote_2Eindex)
=> p(ap(ap(V0P,ap(c_2Equote_2ERight__idx,V4v3)),c_2Equote_2EEnd__idx)) )
& ! [V5n_27] :
( mem(V5n_27,ty_2Equote_2Eindex)
=> ! [V6m_27] :
( mem(V6m_27,ty_2Equote_2Eindex)
=> ( p(ap(ap(V0P,V5n_27),V6m_27))
=> p(ap(ap(V0P,ap(c_2Equote_2ELeft__idx,V5n_27)),ap(c_2Equote_2ELeft__idx,V6m_27))) ) ) )
& ! [V7n_27] :
( mem(V7n_27,ty_2Equote_2Eindex)
=> ! [V8m_27] :
( mem(V8m_27,ty_2Equote_2Eindex)
=> p(ap(ap(V0P,ap(c_2Equote_2ELeft__idx,V7n_27)),ap(c_2Equote_2ERight__idx,V8m_27))) ) )
& ! [V9n_27] :
( mem(V9n_27,ty_2Equote_2Eindex)
=> ! [V10m_27] :
( mem(V10m_27,ty_2Equote_2Eindex)
=> ( p(ap(ap(V0P,V9n_27),V10m_27))
=> p(ap(ap(V0P,ap(c_2Equote_2ERight__idx,V9n_27)),ap(c_2Equote_2ERight__idx,V10m_27))) ) ) )
& ! [V11n_27] :
( mem(V11n_27,ty_2Equote_2Eindex)
=> ! [V12m_27] :
( mem(V12m_27,ty_2Equote_2Eindex)
=> p(ap(ap(V0P,ap(c_2Equote_2ERight__idx,V11n_27)),ap(c_2Equote_2ELeft__idx,V12m_27))) ) ) )
=> ! [V13v] :
( mem(V13v,ty_2Equote_2Eindex)
=> ! [V14v1] :
( mem(V14v1,ty_2Equote_2Eindex)
=> p(ap(ap(V0P,V13v),V14v1)) ) ) ) ) ).
fof(conj_thm_2Equote_2Eindex__compare__def,axiom,
( ap(ap(c_2Equote_2Eindex__compare,c_2Equote_2EEnd__idx),c_2Equote_2EEnd__idx) = c_2EternaryComparisons_2EEQUAL
& ! [V0v10] :
( mem(V0v10,ty_2Equote_2Eindex)
=> ap(ap(c_2Equote_2Eindex__compare,c_2Equote_2EEnd__idx),ap(c_2Equote_2ELeft__idx,V0v10)) = c_2EternaryComparisons_2ELESS )
& ! [V1v11] :
( mem(V1v11,ty_2Equote_2Eindex)
=> ap(ap(c_2Equote_2Eindex__compare,c_2Equote_2EEnd__idx),ap(c_2Equote_2ERight__idx,V1v11)) = c_2EternaryComparisons_2ELESS )
& ! [V2v2] :
( mem(V2v2,ty_2Equote_2Eindex)
=> ap(ap(c_2Equote_2Eindex__compare,ap(c_2Equote_2ELeft__idx,V2v2)),c_2Equote_2EEnd__idx) = c_2EternaryComparisons_2EGREATER )
& ! [V3v3] :
( mem(V3v3,ty_2Equote_2Eindex)
=> ap(ap(c_2Equote_2Eindex__compare,ap(c_2Equote_2ERight__idx,V3v3)),c_2Equote_2EEnd__idx) = c_2EternaryComparisons_2EGREATER )
& ! [V4n_27] :
( mem(V4n_27,ty_2Equote_2Eindex)
=> ! [V5m_27] :
( mem(V5m_27,ty_2Equote_2Eindex)
=> ap(ap(c_2Equote_2Eindex__compare,ap(c_2Equote_2ELeft__idx,V4n_27)),ap(c_2Equote_2ELeft__idx,V5m_27)) = ap(ap(c_2Equote_2Eindex__compare,V4n_27),V5m_27) ) )
& ! [V6n_27] :
( mem(V6n_27,ty_2Equote_2Eindex)
=> ! [V7m_27] :
( mem(V7m_27,ty_2Equote_2Eindex)
=> ap(ap(c_2Equote_2Eindex__compare,ap(c_2Equote_2ELeft__idx,V6n_27)),ap(c_2Equote_2ERight__idx,V7m_27)) = c_2EternaryComparisons_2ELESS ) )
& ! [V8n_27] :
( mem(V8n_27,ty_2Equote_2Eindex)
=> ! [V9m_27] :
( mem(V9m_27,ty_2Equote_2Eindex)
=> ap(ap(c_2Equote_2Eindex__compare,ap(c_2Equote_2ERight__idx,V8n_27)),ap(c_2Equote_2ERight__idx,V9m_27)) = ap(ap(c_2Equote_2Eindex__compare,V8n_27),V9m_27) ) )
& ! [V10n_27] :
( mem(V10n_27,ty_2Equote_2Eindex)
=> ! [V11m_27] :
( mem(V11m_27,ty_2Equote_2Eindex)
=> ap(ap(c_2Equote_2Eindex__compare,ap(c_2Equote_2ERight__idx,V10n_27)),ap(c_2Equote_2ELeft__idx,V11m_27)) = c_2EternaryComparisons_2EGREATER ) ) ) ).
fof(conj_thm_2Equote_2Ecompare__index__equal,axiom,
! [V0i1] :
( mem(V0i1,ty_2Equote_2Eindex)
=> ! [V1i2] :
( mem(V1i2,ty_2Equote_2Eindex)
=> ( ap(ap(c_2Equote_2Eindex__compare,V0i1),V1i2) = c_2EternaryComparisons_2EEQUAL
<=> V0i1 = V1i2 ) ) ) ).
fof(conj_thm_2Equote_2Ecompare__list__index,axiom,
! [V0l1] :
( mem(V0l1,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ! [V1l2] :
( mem(V1l2,ty_2Elist_2Elist(ty_2Equote_2Eindex))
=> ( ap(ap(ap(c_2EternaryComparisons_2Elist__compare(ty_2Equote_2Eindex,ty_2Equote_2Eindex),c_2Equote_2Eindex__compare),V0l1),V1l2) = c_2EternaryComparisons_2EEQUAL
<=> V0l1 = V1l2 ) ) ) ).
fof(ax_thm_2Equote_2Eindex__lt__def,axiom,
! [V0i1] :
( mem(V0i1,ty_2Equote_2Eindex)
=> ! [V1i2] :
( mem(V1i2,ty_2Equote_2Eindex)
=> ( p(ap(ap(c_2Equote_2Eindex__lt,V0i1),V1i2))
<=> ap(ap(c_2Equote_2Eindex__compare,V0i1),V1i2) = c_2EternaryComparisons_2ELESS ) ) ) ).
fof(lameq_f2125,axiom,
! [A_27a,V9a1] :
( mem(V9a1,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V8a0] :
( mem(V8a0,A_27a)
=> ! [V10a2] : ap(f2125(A_27a,V9a1,V8a0),V10a2) = ap(ap(ap(c_2Eind__type_2ECONSTR(A_27a),ap(c_2Enum_2ESUC,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),k(ty_2Enum_2Enum,c_2Eind__type_2EBOTTOM(A_27a))))) ) ) ).
fof(lameq_f2126,axiom,
! [A_27a,V8a0] :
( mem(V8a0,A_27a)
=> ! [V9a1] : ap(f2126(A_27a,V8a0),V9a1) = f2125(A_27a,V9a1,V8a0) ) ).
fof(lameq_f2127,axiom,
! [A_27a,V8a0] : ap(f2127(A_27a),V8a0) = f2126(A_27a,V8a0) ).
fof(lameq_f2128,axiom,
! [A_27a,V5a0] :
( mem(V5a0,A_27a)
=> ! [V3a0_27] :
( mem(V3a0_27,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V6a1] :
( mem(V6a1,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V2_27varmap_27] :
( mem(V2_27varmap_27,arr(ty_2Eind__type_2Erecspace(A_27a),bool))
=> ! [V7a2] : ap(f2128(A_27a,V5a0,V3a0_27,V6a1,V2_27varmap_27),V7a2) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(ty_2Eind__type_2Erecspace(A_27a)),V3a0_27),ap(ap(ap(f2127(A_27a),V5a0),V6a1),V7a2))),ap(ap(c_2Ebool_2E_2F_5C,ap(V2_27varmap_27,V6a1)),ap(V2_27varmap_27,V7a2))) ) ) ) ) ).
fof(lameq_f2129,axiom,
! [A_27a,V2_27varmap_27] :
( mem(V2_27varmap_27,arr(ty_2Eind__type_2Erecspace(A_27a),bool))
=> ! [V3a0_27] :
( mem(V3a0_27,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V5a0] :
( mem(V5a0,A_27a)
=> ! [V6a1] : ap(f2129(A_27a,V2_27varmap_27,V3a0_27,V5a0),V6a1) = ap(c_2Ebool_2E_3F(ty_2Eind__type_2Erecspace(A_27a)),f2128(A_27a,V5a0,V3a0_27,V6a1,V2_27varmap_27)) ) ) ) ).
fof(lameq_f2130,axiom,
! [A_27a,V3a0_27] :
( mem(V3a0_27,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V2_27varmap_27] :
( mem(V2_27varmap_27,arr(ty_2Eind__type_2Erecspace(A_27a),bool))
=> ! [V5a0] : ap(f2130(A_27a,V3a0_27,V2_27varmap_27),V5a0) = ap(c_2Ebool_2E_3F(ty_2Eind__type_2Erecspace(A_27a)),f2129(A_27a,V2_27varmap_27,V3a0_27,V5a0)) ) ) ).
fof(lameq_f2131,axiom,
! [A_27a,V2_27varmap_27] :
( mem(V2_27varmap_27,arr(ty_2Eind__type_2Erecspace(A_27a),bool))
=> ! [V3a0_27] : ap(f2131(A_27a,V2_27varmap_27),V3a0_27) = 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),c_2Enum_2E0),c_2Ebool_2EARB(A_27a)),k(ty_2Enum_2Enum,c_2Eind__type_2EBOTTOM(A_27a))))),ap(c_2Ebool_2E_3F(A_27a),f2130(A_27a,V3a0_27,V2_27varmap_27)))),ap(V2_27varmap_27,V3a0_27)) ) ).
fof(lameq_f2132,axiom,
! [A_27a,V1a0_27] :
( mem(V1a0_27,ty_2Eind__type_2Erecspace(A_27a))
=> ! [V2_27varmap_27] : ap(f2132(A_27a,V1a0_27),V2_27varmap_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_21(ty_2Eind__type_2Erecspace(A_27a)),f2131(A_27a,V2_27varmap_27))),ap(V2_27varmap_27,V1a0_27)) ) ).
fof(lameq_f2133,axiom,
! [A_27a,V1a0_27] : ap(f2133(A_27a),V1a0_27) = ap(c_2Ebool_2E_21(arr(ty_2Eind__type_2Erecspace(A_27a),bool)),f2132(A_27a,V1a0_27)) ).
fof(ax_thm_2Equote_2Evarmap__TY__DEF,axiom,
! [A_27a] :
( ne(A_27a)
=> ? [V0rep] :
( 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)),f2133(A_27a)),V0rep)) ) ) ).
fof(ax_thm_2Equote_2Evarmap__case__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ( ! [V0v] :
( mem(V0v,A_27b)
=> ! [V1f] :
( 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] :
( mem(V2a0,A_27a)
=> ! [V3a1] :
( mem(V3a1,ty_2Equote_2Evarmap(A_27a))
=> ! [V4a2] :
( mem(V4a2,ty_2Equote_2Evarmap(A_27a))
=> ! [V5v] :
( mem(V5v,A_27b)
=> ! [V6f] :
( 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) ) ) ) ) ) ) ) ) ).
fof(ax_thm_2Equote_2Evarmap__size__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0f] :
( mem(V0f,arr(A_27a,ty_2Enum_2Enum))
=> ap(ap(c_2Equote_2Evarmap__size(A_27a),V0f),c_2Equote_2EEmpty__vm(A_27a)) = c_2Enum_2E0 )
& ! [V1f] :
( mem(V1f,arr(A_27a,ty_2Enum_2Enum))
=> ! [V2a0] :
( mem(V2a0,A_27a)
=> ! [V3a1] :
( mem(V3a1,ty_2Equote_2Evarmap(A_27a))
=> ! [V4a2] :
( mem(V4a2,ty_2Equote_2Evarmap(A_27a))
=> ap(ap(c_2Equote_2Evarmap__size(A_27a),V1f),ap(ap(ap(c_2Equote_2ENode__vm(A_27a),V2a0),V3a1),V4a2)) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,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)))) ) ) ) ) ) ) ).
fof(conj_thm_2Equote_2Edatatype__varmap,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0varmap] :
( 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)))) ) ) ).
fof(conj_thm_2Equote_2Evarmap__11,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a0] :
( mem(V0a0,A_27a)
=> ! [V1a1] :
( mem(V1a1,ty_2Equote_2Evarmap(A_27a))
=> ! [V2a2] :
( mem(V2a2,ty_2Equote_2Evarmap(A_27a))
=> ! [V3a0_27] :
( mem(V3a0_27,A_27a)
=> ! [V4a1_27] :
( mem(V4a1_27,ty_2Equote_2Evarmap(A_27a))
=> ! [V5a2_27] :
( 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 ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equote_2Evarmap__distinct,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0a2] :
( mem(V0a2,ty_2Equote_2Evarmap(A_27a))
=> ! [V1a1] :
( mem(V1a1,ty_2Equote_2Evarmap(A_27a))
=> ! [V2a0] :
( mem(V2a0,A_27a)
=> c_2Equote_2EEmpty__vm(A_27a) != ap(ap(ap(c_2Equote_2ENode__vm(A_27a),V2a0),V1a1),V0a2) ) ) ) ) ).
fof(conj_thm_2Equote_2Evarmap__nchotomy,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0vv] :
( mem(V0vv,ty_2Equote_2Evarmap(A_27a))
=> ( V0vv = c_2Equote_2EEmpty__vm(A_27a)
| ? [V1a] :
( mem(V1a,A_27a)
& ? [V2v] :
( mem(V2v,ty_2Equote_2Evarmap(A_27a))
& ? [V3v0] :
( mem(V3v0,ty_2Equote_2Evarmap(A_27a))
& V0vv = ap(ap(ap(c_2Equote_2ENode__vm(A_27a),V1a),V2v),V3v0) ) ) ) ) ) ) ).
fof(conj_thm_2Equote_2Evarmap__Axiom,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0f0] :
( mem(V0f0,A_27b)
=> ! [V1f1] :
( 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] :
( mem(V2fn,arr(ty_2Equote_2Evarmap(A_27a),A_27b))
& ap(V2fn,c_2Equote_2EEmpty__vm(A_27a)) = V0f0
& ! [V3a0] :
( mem(V3a0,A_27a)
=> ! [V4a1] :
( mem(V4a1,ty_2Equote_2Evarmap(A_27a))
=> ! [V5a2] :
( 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)) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equote_2Evarmap__induction,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(ty_2Equote_2Evarmap(A_27a),bool))
=> ( ( p(ap(V0P,c_2Equote_2EEmpty__vm(A_27a)))
& ! [V1v] :
( mem(V1v,ty_2Equote_2Evarmap(A_27a))
=> ! [V2v0] :
( mem(V2v0,ty_2Equote_2Evarmap(A_27a))
=> ( ( p(ap(V0P,V1v))
& p(ap(V0P,V2v0)) )
=> ! [V3a] :
( mem(V3a,A_27a)
=> p(ap(V0P,ap(ap(ap(c_2Equote_2ENode__vm(A_27a),V3a),V1v),V2v0))) ) ) ) ) )
=> ! [V4v] :
( mem(V4v,ty_2Equote_2Evarmap(A_27a))
=> p(ap(V0P,V4v)) ) ) ) ) ).
fof(conj_thm_2Equote_2Evarmap__case__cong,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0v_27] :
( mem(V0v_27,A_27b)
=> ! [V1f_27] :
( mem(V1f_27,arr(A_27a,arr(ty_2Equote_2Evarmap(A_27a),arr(ty_2Equote_2Evarmap(A_27a),A_27b))))
=> ! [V2M] :
( mem(V2M,ty_2Equote_2Evarmap(A_27a))
=> ! [V3M_27] :
( mem(V3M_27,ty_2Equote_2Evarmap(A_27a))
=> ! [V4v] :
( mem(V4v,A_27b)
=> ! [V5f] :
( 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] :
( mem(V6a0,A_27a)
=> ! [V7a1] :
( mem(V7a1,ty_2Equote_2Evarmap(A_27a))
=> ! [V8a2] :
( 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) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equote_2Evarmap__case__eq,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0x] :
( mem(V0x,ty_2Equote_2Evarmap(A_27a))
=> ! [V1v] :
( mem(V1v,A_27b)
=> ! [V2f] :
( mem(V2f,arr(A_27a,arr(ty_2Equote_2Evarmap(A_27a),arr(ty_2Equote_2Evarmap(A_27a),A_27b))))
=> ! [V3v_27] :
( 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] :
( mem(V4a,A_27a)
& ? [V5v_27_27] :
( mem(V5v_27_27,ty_2Equote_2Evarmap(A_27a))
& ? [V6v0] :
( 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 ) ) ) ) ) ) ) ) ) ) ) ).
fof(conj_thm_2Equote_2Evarmap__find__ind,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0P] :
( mem(V0P,arr(ty_2Equote_2Eindex,arr(ty_2Equote_2Evarmap(A_27a),bool)))
=> ( ( ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2v1] :
( mem(V2v1,ty_2Equote_2Evarmap(A_27a))
=> ! [V3v2] :
( mem(V3v2,ty_2Equote_2Evarmap(A_27a))
=> p(ap(ap(V0P,c_2Equote_2EEnd__idx),ap(ap(ap(c_2Equote_2ENode__vm(A_27a),V1x),V2v1),V3v2))) ) ) )
& ! [V4i1] :
( mem(V4i1,ty_2Equote_2Eindex)
=> ! [V5x] :
( mem(V5x,A_27a)
=> ! [V6v1] :
( mem(V6v1,ty_2Equote_2Evarmap(A_27a))
=> ! [V7v2] :
( mem(V7v2,ty_2Equote_2Evarmap(A_27a))
=> ( p(ap(ap(V0P,V4i1),V7v2))
=> p(ap(ap(V0P,ap(c_2Equote_2ERight__idx,V4i1)),ap(ap(ap(c_2Equote_2ENode__vm(A_27a),V5x),V6v1),V7v2))) ) ) ) ) )
& ! [V8i1] :
( mem(V8i1,ty_2Equote_2Eindex)
=> ! [V9x] :
( mem(V9x,A_27a)
=> ! [V10v1] :
( mem(V10v1,ty_2Equote_2Evarmap(A_27a))
=> ! [V11v2] :
( mem(V11v2,ty_2Equote_2Evarmap(A_27a))
=> ( p(ap(ap(V0P,V8i1),V10v1))
=> p(ap(ap(V0P,ap(c_2Equote_2ELeft__idx,V8i1)),ap(ap(ap(c_2Equote_2ENode__vm(A_27a),V9x),V10v1),V11v2))) ) ) ) ) )
& ! [V12i] :
( mem(V12i,ty_2Equote_2Eindex)
=> p(ap(ap(V0P,V12i),c_2Equote_2EEmpty__vm(A_27a))) ) )
=> ! [V13v] :
( mem(V13v,ty_2Equote_2Eindex)
=> ! [V14v1] :
( mem(V14v1,ty_2Equote_2Evarmap(A_27a))
=> p(ap(ap(V0P,V13v),V14v1)) ) ) ) ) ) ).
fof(conj_thm_2Equote_2Evarmap__find__def,axiom,
! [A_27a] :
( ne(A_27a)
=> ( ! [V0x] :
( mem(V0x,A_27a)
=> ! [V1v2] :
( mem(V1v2,ty_2Equote_2Evarmap(A_27a))
=> ! [V2v1] :
( mem(V2v1,ty_2Equote_2Evarmap(A_27a))
=> ap(ap(c_2Equote_2Evarmap__find(A_27a),c_2Equote_2EEnd__idx),ap(ap(ap(c_2Equote_2ENode__vm(A_27a),V0x),V2v1),V1v2)) = V0x ) ) )
& ! [V3x] :
( mem(V3x,A_27a)
=> ! [V4v2] :
( mem(V4v2,ty_2Equote_2Evarmap(A_27a))
=> ! [V5v1] :
( mem(V5v1,ty_2Equote_2Evarmap(A_27a))
=> ! [V6i1] :
( mem(V6i1,ty_2Equote_2Eindex)
=> ap(ap(c_2Equote_2Evarmap__find(A_27a),ap(c_2Equote_2ERight__idx,V6i1)),ap(ap(ap(c_2Equote_2ENode__vm(A_27a),V3x),V5v1),V4v2)) = ap(ap(c_2Equote_2Evarmap__find(A_27a),V6i1),V4v2) ) ) ) )
& ! [V7x] :
( mem(V7x,A_27a)
=> ! [V8v2] :
( mem(V8v2,ty_2Equote_2Evarmap(A_27a))
=> ! [V9v1] :
( mem(V9v1,ty_2Equote_2Evarmap(A_27a))
=> ! [V10i1] :
( mem(V10i1,ty_2Equote_2Eindex)
=> ap(ap(c_2Equote_2Evarmap__find(A_27a),ap(c_2Equote_2ELeft__idx,V10i1)),ap(ap(ap(c_2Equote_2ENode__vm(A_27a),V7x),V9v1),V8v2)) = ap(ap(c_2Equote_2Evarmap__find(A_27a),V10i1),V9v1) ) ) ) )
& ! [V11i] :
( mem(V11i,ty_2Equote_2Eindex)
=> ap(ap(c_2Equote_2Evarmap__find(A_27a),V11i),c_2Equote_2EEmpty__vm(A_27a)) = ap(c_2Emin_2E_40(A_27a),k(A_27a,c_2Ebool_2ET)) ) ) ) ).
%------------------------------------------------------------------------------