ITP001 Axioms: ITP087_7.ax
%------------------------------------------------------------------------------
% File : ITP087_7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : quote.ax [Gau19]
% : HL4087_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 152 ( 33 unt; 78 typ; 0 def)
% Number of atoms : 199 ( 122 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 132 ( 7 ~; 12 |; 56 &)
% ( 23 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 57 ( 33 >; 24 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 73 ( 73 usr; 21 con; 0-5 aty)
% Number of variables : 363 ( 298 !; 20 ?; 363 :)
% ( 45 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Eind__type_2Erecspace,type,
tyop_2Eind__type_2Erecspace: $tType > $tType ).
tff(tyop_2Elist_2Elist,type,
tyop_2Elist_2Elist: $tType > $tType ).
tff(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
tff(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: $tType ).
tff(tyop_2Equote_2Eindex,type,
tyop_2Equote_2Eindex: $tType ).
tff(tyop_2Equote_2Evarmap,type,
tyop_2Equote_2Evarmap: $tType > $tType ).
tff(tyop_2EternaryComparisons_2Eordering,type,
tyop_2EternaryComparisons_2Eordering: $tType ).
tff(app_2E2,type,
app_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(p,type,
p: tyop_2Emin_2Ebool > $o ).
tff(combin_i_2E0,type,
combin_i_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(combin_k_2E0,type,
combin_k_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(combin_s_2E0,type,
combin_s_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))) ).
tff(c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Earithmetic_2E_2B_2E0,type,
c_2Earithmetic_2E_2B_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2B_2E2,type,
c_2Earithmetic_2E_2B_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Enum_2E0_2E0,type,
c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).
tff(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2:
!>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_40_2E0,type,
c_2Emin_2E_40_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a) ).
tff(c_2Emin_2E_40_2E1,type,
c_2Emin_2E_40_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > A_27a ) ).
tff(c_2Ebool_2EARB_2E0,type,
c_2Ebool_2EARB_2E0:
!>[A_27a: $tType] : A_27a ).
tff(c_2Earithmetic_2EBIT1_2E0,type,
c_2Earithmetic_2EBIT1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EBIT1_2E1,type,
c_2Earithmetic_2EBIT1_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Eind__type_2EBOTTOM_2E0,type,
c_2Eind__type_2EBOTTOM_2E0:
!>[A_27a: $tType] : tyop_2Eind__type_2Erecspace(A_27a) ).
tff(c_2Eind__type_2ECONSTR_2E0,type,
c_2Eind__type_2ECONSTR_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a)))) ).
tff(c_2Eind__type_2ECONSTR_2E3,type,
c_2Eind__type_2ECONSTR_2E3:
!>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * A_27a * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)) ) > tyop_2Eind__type_2Erecspace(A_27a) ) ).
tff(c_2Ebool_2EDATATYPE_2E0,type,
c_2Ebool_2EDATATYPE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2EDATATYPE_2E1,type,
c_2Ebool_2EDATATYPE_2E1:
!>[A_27a: $tType] : ( A_27a > tyop_2Emin_2Ebool ) ).
tff(c_2EternaryComparisons_2EEQUAL_2E0,type,
c_2EternaryComparisons_2EEQUAL_2E0: tyop_2EternaryComparisons_2Eordering ).
tff(c_2Equote_2EEmpty__vm_2E0,type,
c_2Equote_2EEmpty__vm_2E0:
!>[A_27a: $tType] : tyop_2Equote_2Evarmap(A_27a) ).
tff(c_2Equote_2EEnd__idx_2E0,type,
c_2Equote_2EEnd__idx_2E0: tyop_2Equote_2Eindex ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(c_2Eind__type_2EFCONS_2E0,type,
c_2Eind__type_2EFCONS_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))) ).
tff(c_2Eind__type_2EFCONS_2E2,type,
c_2Eind__type_2EFCONS_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a) ) > tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a) ) ).
tff(c_2EternaryComparisons_2EGREATER_2E0,type,
c_2EternaryComparisons_2EGREATER_2E0: tyop_2EternaryComparisons_2Eordering ).
tff(c_2EternaryComparisons_2ELESS_2E0,type,
c_2EternaryComparisons_2ELESS_2E0: tyop_2EternaryComparisons_2Eordering ).
tff(c_2Equote_2ELeft__idx_2E0,type,
c_2Equote_2ELeft__idx_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex) ).
tff(c_2Equote_2ELeft__idx_2E1,type,
c_2Equote_2ELeft__idx_2E1: tyop_2Equote_2Eindex > tyop_2Equote_2Eindex ).
tff(c_2Earithmetic_2ENUMERAL_2E0,type,
c_2Earithmetic_2ENUMERAL_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2ENUMERAL_2E1,type,
c_2Earithmetic_2ENUMERAL_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Equote_2ENode__vm_2E0,type,
c_2Equote_2ENode__vm_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Equote_2Evarmap(A_27a)))) ).
tff(c_2Equote_2ENode__vm_2E3,type,
c_2Equote_2ENode__vm_2E3:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Equote_2Evarmap(A_27a) * tyop_2Equote_2Evarmap(A_27a) ) > tyop_2Equote_2Evarmap(A_27a) ) ).
tff(c_2Equote_2ERight__idx_2E0,type,
c_2Equote_2ERight__idx_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex) ).
tff(c_2Equote_2ERight__idx_2E1,type,
c_2Equote_2ERight__idx_2E1: tyop_2Equote_2Eindex > tyop_2Equote_2Eindex ).
tff(c_2Enum_2ESUC_2E0,type,
c_2Enum_2ESUC_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Enum_2ESUC_2E1,type,
c_2Enum_2ESUC_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(c_2Ebool_2ETYPE__DEFINITION_2E0,type,
c_2Ebool_2ETYPE__DEFINITION_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2ETYPE__DEFINITION_2E2,type,
c_2Ebool_2ETYPE__DEFINITION_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Earithmetic_2EZERO_2E0,type,
c_2Earithmetic_2EZERO_2E0: tyop_2Enum_2Enum ).
tff(c_2Ebool_2E_5C_2F_2E0,type,
c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_5C_2F_2E2,type,
c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Equote_2Eindex__CASE_2E0,type,
c_2Equote_2Eindex__CASE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)))) ).
tff(c_2Equote_2Eindex__CASE_2E4,type,
c_2Equote_2Eindex__CASE_2E4:
!>[A_27a: $tType] : ( ( tyop_2Equote_2Eindex * tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27a) * tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27a) * A_27a ) > A_27a ) ).
tff(c_2Equote_2Eindex__compare_2E0,type,
c_2Equote_2Eindex__compare_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2EternaryComparisons_2Eordering)) ).
tff(c_2Equote_2Eindex__compare_2E2,type,
c_2Equote_2Eindex__compare_2E2: ( tyop_2Equote_2Eindex * tyop_2Equote_2Eindex ) > tyop_2EternaryComparisons_2Eordering ).
tff(c_2Equote_2Eindex__lt_2E0,type,
c_2Equote_2Eindex__lt_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool)) ).
tff(c_2Equote_2Eindex__lt_2E2,type,
c_2Equote_2Eindex__lt_2E2: ( tyop_2Equote_2Eindex * tyop_2Equote_2Eindex ) > tyop_2Emin_2Ebool ).
tff(c_2Equote_2Eindex__size_2E0,type,
c_2Equote_2Eindex__size_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Enum_2Enum) ).
tff(c_2Equote_2Eindex__size_2E1,type,
c_2Equote_2Eindex__size_2E1: tyop_2Equote_2Eindex > tyop_2Enum_2Enum ).
tff(c_2EternaryComparisons_2Elist__compare_2E0,type,
c_2EternaryComparisons_2Elist__compare_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2EternaryComparisons_2Eordering))) ).
tff(c_2EternaryComparisons_2Elist__compare_2E3,type,
c_2EternaryComparisons_2Elist__compare_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2EternaryComparisons_2Eordering)) * tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27b) ) > tyop_2EternaryComparisons_2Eordering ) ).
tff(c_2Equote_2Evarmap__CASE_2E0,type,
c_2Equote_2Evarmap__CASE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),A_27b))),A_27b))) ).
tff(c_2Equote_2Evarmap__CASE_2E3,type,
c_2Equote_2Evarmap__CASE_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Equote_2Evarmap(A_27a) * A_27b * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),A_27b))) ) > A_27b ) ).
tff(c_2Equote_2Evarmap__find_2E0,type,
c_2Equote_2Evarmap__find_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),A_27a)) ).
tff(c_2Equote_2Evarmap__find_2E2,type,
c_2Equote_2Evarmap__find_2E2:
!>[A_27a: $tType] : ( ( tyop_2Equote_2Eindex * tyop_2Equote_2Evarmap(A_27a) ) > A_27a ) ).
tff(c_2Equote_2Evarmap__size_2E0,type,
c_2Equote_2Evarmap__size_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Enum_2Enum)) ).
tff(c_2Equote_2Evarmap__size_2E2,type,
c_2Equote_2Evarmap__size_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Equote_2Evarmap(A_27a) ) > tyop_2Enum_2Enum ) ).
tff(c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(thm_2Eextra_2Dho_2Eeq__ext,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0) )
=> ( V0f_2E0 = V1g_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Eboolext,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( ( p(V0_2E0)
<=> p(V1_2E0) )
=> ( V0_2E0 = V1_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Etruth,axiom,
p(c_2Ebool_2ET_2E0) ).
tff(thm_2Eextra_2Dho_2Enotfalse,axiom,
~ p(c_2Ebool_2EF_2E0) ).
tff(thm_2Eextra_2Dho_2Ebool__cases__ax,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
| ( V0t_2E0 = c_2Ebool_2EF_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Ei__thm,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,combin_i_2E0(A_27a),V0x_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Ek__thm,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : ( app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),combin_k_2E0(A_27a,A_27b),V0x_2E0),V1y_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Es__thm,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),combin_s_2E0(A_27a,A_27b,A_27c),V0f_2E0),V1g_2E0),V2x_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V2x_2E0),app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)) ) ).
tff(logicdef_2E_2F_5C,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
& p(V1_2E0) ) ) ).
tff(logicdef_2E_5C_2F,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
| p(V1_2E0) ) ) ).
tff(logicdef_2E_7E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(V0_2E0))
<=> ~ p(V0_2E0) ) ).
tff(logicdef_2E_3D_3D_3E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
=> p(V1_2E0) ) ) ).
tff(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0_2E0: A_27a,V1_2E0: A_27a] :
( p(c_2Emin_2E_3D_2E2(A_27a,V0_2E0,V1_2E0))
<=> ( V0_2E0 = V1_2E0 ) ) ).
tff(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(A_27a,V0f_2E0))
<=> ! [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_2E1(A_27a,V0f_2E0))
<=> ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
& p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] :
( ( X0_2E0 = X1_2E0 )
<=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
=> p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a,c_2Emin_2E_40_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT1_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E0,X0_2E0) ) ).
tff(arityeq3_2Ec_2Eind__type_2ECONSTR_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: A_27a,X2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a))] : ( c_2Eind__type_2ECONSTR_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a))),c_2Eind__type_2ECONSTR_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Eind__type_2ECONSTR_2E3_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Ebool,X2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool))] : ( c_2Eind__type_2ECONSTR_2E3(tyop_2Emin_2Ebool,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)),tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)),tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)),tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool))),c_2Eind__type_2ECONSTR_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] : ( c_2Ebool_2EDATATYPE_2E1(tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E0(tyop_2Emin_2Ebool),X0_2E0) ) ).
tff(arityeq2_2Ec_2Eind__type_2EFCONS_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eind__type_2Erecspace(A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a))] : ( c_2Eind__type_2EFCONS_2E2(tyop_2Eind__type_2Erecspace(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a))),c_2Eind__type_2EFCONS_2E0(tyop_2Eind__type_2Erecspace(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eind__type_2EFCONS_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28tyop_2Emin_2Ebool_29,axiom,
! [X0_2E0: tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool))] : ( c_2Eind__type_2EFCONS_2E2(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)),app_2E2(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool))),c_2Eind__type_2EFCONS_2E0(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Equote_2ELeft__idx_2E1,axiom,
! [X0_2E0: tyop_2Equote_2Eindex] : ( c_2Equote_2ELeft__idx_2E1(X0_2E0) = app_2E2(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex,c_2Equote_2ELeft__idx_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2ENUMERAL_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E0,X0_2E0) ) ).
tff(arityeq3_2Ec_2Equote_2ENode__vm_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Equote_2Evarmap(A_27a),X2_2E0: tyop_2Equote_2Evarmap(A_27a)] : ( c_2Equote_2ENode__vm_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Equote_2Evarmap(A_27a),tyop_2Equote_2Evarmap(A_27a),app_2E2(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Equote_2Evarmap(A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Equote_2Evarmap(A_27a))),c_2Equote_2ENode__vm_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Equote_2ERight__idx_2E1,axiom,
! [X0_2E0: tyop_2Equote_2Eindex] : ( c_2Equote_2ERight__idx_2E1(X0_2E0) = app_2E2(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex,c_2Equote_2ERight__idx_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Enum_2ESUC_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28A_27a_29_20mono_2Etyop_2Equote_2Evarmap_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Eind__type_2Erecspace(A_27a))] : ( c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Equote_2Evarmap(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Ebool),c_2Ebool_2ETYPE__DEFINITION_2E0(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Equote_2Evarmap(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28tyop_2Emin_2Ebool_29_20mono_2Etyop_2Equote_2Eindex,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool))] : ( c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),tyop_2Equote_2Eindex,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Ebool_2ETYPE__DEFINITION_2E0(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),tyop_2Equote_2Eindex),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
| p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq4_2Ec_2Equote_2Eindex__CASE_2E4_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Equote_2Eindex,X1_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27a),X2_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27a),X3_2E0: A_27a] : ( c_2Equote_2Eindex__CASE_2E4(A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27a),tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27a),tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27a),tyop_2Emin_2Efun(A_27a,A_27a))),c_2Equote_2Eindex__CASE_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq2_2Ec_2Equote_2Eindex__compare_2E2,axiom,
! [X0_2E0: tyop_2Equote_2Eindex,X1_2E0: tyop_2Equote_2Eindex] : ( c_2Equote_2Eindex__compare_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Equote_2Eindex,tyop_2EternaryComparisons_2Eordering,app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2EternaryComparisons_2Eordering),c_2Equote_2Eindex__compare_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Equote_2Eindex__lt_2E2,axiom,
! [X0_2E0: tyop_2Equote_2Eindex,X1_2E0: tyop_2Equote_2Eindex] : ( c_2Equote_2Eindex__lt_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool,app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool),c_2Equote_2Eindex__lt_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Equote_2Eindex__size_2E1,axiom,
! [X0_2E0: tyop_2Equote_2Eindex] : ( c_2Equote_2Eindex__size_2E1(X0_2E0) = app_2E2(tyop_2Equote_2Eindex,tyop_2Enum_2Enum,c_2Equote_2Eindex__size_2E0,X0_2E0) ) ).
tff(arityeq3_2Ec_2EternaryComparisons_2Elist__compare_2E3_2Emono_2Etyop_2Equote_2Eindex_20mono_2Etyop_2Equote_2Eindex,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2EternaryComparisons_2Eordering)),X1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),X2_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex)] : ( c_2EternaryComparisons_2Elist__compare_2E3(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2EternaryComparisons_2Eordering,app_2E2(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2EternaryComparisons_2Eordering),app_2E2(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2EternaryComparisons_2Eordering)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Equote_2Eindex),tyop_2EternaryComparisons_2Eordering)),c_2EternaryComparisons_2Elist__compare_2E0(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Equote_2Evarmap__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Equote_2Evarmap(A_27a),X1_2E0: A_27b,X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),A_27b)))] : ( c_2Equote_2Evarmap__CASE_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),A_27b))),A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),A_27b))),A_27b),app_2E2(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),A_27b))),A_27b)),c_2Equote_2Evarmap__CASE_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Equote_2Evarmap__find_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Equote_2Eindex,X1_2E0: tyop_2Equote_2Evarmap(A_27a)] : ( c_2Equote_2Evarmap__find_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Equote_2Evarmap(A_27a),A_27a,app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),A_27a),c_2Equote_2Evarmap__find_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Equote_2Evarmap__size_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Equote_2Evarmap(A_27a)] : ( c_2Equote_2Evarmap__size_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Equote_2Evarmap(A_27a),tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Enum_2Enum),c_2Equote_2Evarmap__size_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] :
( ~ p(X0_2E0)
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0_2E0)) ) ).
tff(thm_2Equote_2Eindex__TY__DEF,axiom,
! [F3_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)),F2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)),F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ! [V8n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),F3_2E0,V8n_2E0) = c_2Eind__type_2EBOTTOM_2E0(tyop_2Emin_2Ebool) )
=> ( ! [V7n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),F2_2E0,V7n_2E0) = c_2Eind__type_2EBOTTOM_2E0(tyop_2Emin_2Ebool) )
=> ( ! [V5n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),F1_2E0,V5n_2E0) = c_2Eind__type_2EBOTTOM_2E0(tyop_2Emin_2Ebool) )
=> ( ! [V1a0_2E0: tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)] :
( p(app_2E2(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,F0_2E0,V1a0_2E0))
<=> ! [V2_27index_27_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
( ! [V3a0_2E0: tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)] :
( ( ? [V4a_2E0: tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)] :
( ( V3a0_2E0 = c_2Eind__type_2ECONSTR_2E3(tyop_2Emin_2Ebool,c_2Enum_2E0_2E0,c_2Ebool_2EARB_2E0(tyop_2Emin_2Ebool),c_2Eind__type_2EFCONS_2E2(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),V4a_2E0,F1_2E0)) )
& p(app_2E2(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V2_27index_27_2E0,V4a_2E0)) )
| ? [V6a_2E0: tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool)] :
( ( V3a0_2E0 = c_2Eind__type_2ECONSTR_2E3(tyop_2Emin_2Ebool,c_2Enum_2ESUC_2E1(c_2Enum_2E0_2E0),c_2Ebool_2EARB_2E0(tyop_2Emin_2Ebool),c_2Eind__type_2EFCONS_2E2(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),V6a_2E0,F2_2E0)) )
& p(app_2E2(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V2_27index_27_2E0,V6a_2E0)) )
| ( V3a0_2E0 = c_2Eind__type_2ECONSTR_2E3(tyop_2Emin_2Ebool,c_2Enum_2ESUC_2E1(c_2Enum_2ESUC_2E1(c_2Enum_2E0_2E0)),c_2Ebool_2EARB_2E0(tyop_2Emin_2Ebool),F3_2E0) ) )
=> p(app_2E2(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V2_27index_27_2E0,V3a0_2E0)) )
=> p(app_2E2(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V2_27index_27_2E0,V1a0_2E0)) ) )
=> ? [V0rep_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool))] : p(c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Eind__type_2Erecspace(tyop_2Emin_2Ebool),tyop_2Equote_2Eindex,F0_2E0,V0rep_2E0)) ) ) ) ) ).
tff(thm_2Equote_2Eindex__case__def,axiom,
! [A_27a: $tType] :
( ! [V0a_2E0: tyop_2Equote_2Eindex,V1f_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27a),V2f1_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27a),V3v_2E0: A_27a] : ( c_2Equote_2Eindex__CASE_2E4(A_27a,c_2Equote_2ELeft__idx_2E1(V0a_2E0),V1f_2E0,V2f1_2E0,V3v_2E0) = app_2E2(tyop_2Equote_2Eindex,A_27a,V1f_2E0,V0a_2E0) )
& ! [V4a_2E0: tyop_2Equote_2Eindex,V5f_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27a),V6f1_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27a),V7v_2E0: A_27a] : ( c_2Equote_2Eindex__CASE_2E4(A_27a,c_2Equote_2ERight__idx_2E1(V4a_2E0),V5f_2E0,V6f1_2E0,V7v_2E0) = app_2E2(tyop_2Equote_2Eindex,A_27a,V6f1_2E0,V4a_2E0) )
& ! [V8f_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27a),V9f1_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27a),V10v_2E0: A_27a] : ( c_2Equote_2Eindex__CASE_2E4(A_27a,c_2Equote_2EEnd__idx_2E0,V8f_2E0,V9f1_2E0,V10v_2E0) = V10v_2E0 ) ) ).
tff(thm_2Equote_2Eindex__size__def,axiom,
( ! [V0a_2E0: tyop_2Equote_2Eindex] : ( c_2Equote_2Eindex__size_2E1(c_2Equote_2ELeft__idx_2E1(V0a_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Equote_2Eindex__size_2E1(V0a_2E0)) )
& ! [V1a_2E0: tyop_2Equote_2Eindex] : ( c_2Equote_2Eindex__size_2E1(c_2Equote_2ERight__idx_2E1(V1a_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Equote_2Eindex__size_2E1(V1a_2E0)) )
& ( c_2Equote_2Eindex__size_2E1(c_2Equote_2EEnd__idx_2E0) = c_2Enum_2E0_2E0 ) ) ).
tff(thm_2Equote_2Eindex__lt__def,axiom,
! [V0i1_2E0: tyop_2Equote_2Eindex,V1i2_2E0: tyop_2Equote_2Eindex] :
( p(c_2Equote_2Eindex__lt_2E2(V0i1_2E0,V1i2_2E0))
<=> ( c_2Equote_2Eindex__compare_2E2(V0i1_2E0,V1i2_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) ).
tff(thm_2Equote_2Evarmap__TY__DEF,axiom,
! [A_27a: $tType,F2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F0_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool)] :
( ! [V8n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a),F2_2E0,V8n_2E0) = c_2Eind__type_2EBOTTOM_2E0(A_27a) )
=> ( ! [V4n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a),F1_2E0,V4n_2E0) = c_2Eind__type_2EBOTTOM_2E0(A_27a) )
=> ( ! [V1a0_27_2E0: tyop_2Eind__type_2Erecspace(A_27a)] :
( p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,F0_2E0,V1a0_27_2E0))
<=> ! [V2_27varmap_27_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool)] :
( ! [V3a0_27_2E0: tyop_2Eind__type_2Erecspace(A_27a)] :
( ( ( V3a0_27_2E0 = c_2Eind__type_2ECONSTR_2E3(A_27a,c_2Enum_2E0_2E0,c_2Ebool_2EARB_2E0(A_27a),F1_2E0) )
| ? [V5a0_2E0: A_27a,V6a1_2E0: tyop_2Eind__type_2Erecspace(A_27a),V7a2_2E0: tyop_2Eind__type_2Erecspace(A_27a)] :
( ( V3a0_27_2E0 = c_2Eind__type_2ECONSTR_2E3(A_27a,c_2Enum_2ESUC_2E1(c_2Enum_2E0_2E0),V5a0_2E0,c_2Eind__type_2EFCONS_2E2(tyop_2Eind__type_2Erecspace(A_27a),V6a1_2E0,c_2Eind__type_2EFCONS_2E2(tyop_2Eind__type_2Erecspace(A_27a),V7a2_2E0,F2_2E0))) )
& p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,V2_27varmap_27_2E0,V6a1_2E0))
& p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,V2_27varmap_27_2E0,V7a2_2E0)) ) )
=> p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,V2_27varmap_27_2E0,V3a0_27_2E0)) )
=> p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,V2_27varmap_27_2E0,V1a0_27_2E0)) ) )
=> ? [V0rep_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Eind__type_2Erecspace(A_27a))] : p(c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Equote_2Evarmap(A_27a),F0_2E0,V0rep_2E0)) ) ) ) ).
tff(thm_2Equote_2Evarmap__case__def,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0v_2E0: A_27b,V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),A_27b)))] : ( c_2Equote_2Evarmap__CASE_2E3(A_27a,A_27b,c_2Equote_2EEmpty__vm_2E0(A_27a),V0v_2E0,V1f_2E0) = V0v_2E0 )
& ! [V2a0_2E0: A_27a,V3a1_2E0: tyop_2Equote_2Evarmap(A_27a),V4a2_2E0: tyop_2Equote_2Evarmap(A_27a),V5v_2E0: A_27b,V6f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),A_27b)))] : ( c_2Equote_2Evarmap__CASE_2E3(A_27a,A_27b,c_2Equote_2ENode__vm_2E3(A_27a,V2a0_2E0,V3a1_2E0,V4a2_2E0),V5v_2E0,V6f_2E0) = app_2E2(tyop_2Equote_2Evarmap(A_27a),A_27b,app_2E2(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),A_27b)),V6f_2E0,V2a0_2E0),V3a1_2E0),V4a2_2E0) ) ) ).
tff(thm_2Equote_2Evarmap__size__def,axiom,
! [A_27a: $tType] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Equote_2Evarmap__size_2E2(A_27a,V0f_2E0,c_2Equote_2EEmpty__vm_2E0(A_27a)) = c_2Enum_2E0_2E0 )
& ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2a0_2E0: A_27a,V3a1_2E0: tyop_2Equote_2Evarmap(A_27a),V4a2_2E0: tyop_2Equote_2Evarmap(A_27a)] : ( c_2Equote_2Evarmap__size_2E2(A_27a,V1f_2E0,c_2Equote_2ENode__vm_2E3(A_27a,V2a0_2E0,V3a1_2E0,V4a2_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2B_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V1f_2E0,V2a0_2E0),c_2Earithmetic_2E_2B_2E2(c_2Equote_2Evarmap__size_2E2(A_27a,V1f_2E0,V3a1_2E0),c_2Equote_2Evarmap__size_2E2(A_27a,V1f_2E0,V4a2_2E0)))) ) ) ).
tff(thm_2Equote_2Edatatype__index,axiom,
! [V0index_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool)))] : p(c_2Ebool_2EDATATYPE_2E1(tyop_2Emin_2Ebool,app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex),tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool)),V0index_2E0,c_2Equote_2ELeft__idx_2E0),c_2Equote_2ERight__idx_2E0),c_2Equote_2EEnd__idx_2E0))) ).
tff(thm_2Equote_2Eindex__11,axiom,
( ! [V0a_2E0: tyop_2Equote_2Eindex,V1a_27_2E0: tyop_2Equote_2Eindex] :
( ( c_2Equote_2ELeft__idx_2E1(V0a_2E0) = c_2Equote_2ELeft__idx_2E1(V1a_27_2E0) )
<=> ( V0a_2E0 = V1a_27_2E0 ) )
& ! [V2a_2E0: tyop_2Equote_2Eindex,V3a_27_2E0: tyop_2Equote_2Eindex] :
( ( c_2Equote_2ERight__idx_2E1(V2a_2E0) = c_2Equote_2ERight__idx_2E1(V3a_27_2E0) )
<=> ( V2a_2E0 = V3a_27_2E0 ) ) ) ).
tff(thm_2Equote_2Eindex__distinct,axiom,
( ! [V0a_27_2E0: tyop_2Equote_2Eindex,V1a_2E0: tyop_2Equote_2Eindex] : ( c_2Equote_2ELeft__idx_2E1(V1a_2E0) != c_2Equote_2ERight__idx_2E1(V0a_27_2E0) )
& ! [V2a_2E0: tyop_2Equote_2Eindex] : ( c_2Equote_2ELeft__idx_2E1(V2a_2E0) != c_2Equote_2EEnd__idx_2E0 )
& ! [V3a_2E0: tyop_2Equote_2Eindex] : ( c_2Equote_2ERight__idx_2E1(V3a_2E0) != c_2Equote_2EEnd__idx_2E0 ) ) ).
tff(thm_2Equote_2Eindex__nchotomy,axiom,
! [V0ii_2E0: tyop_2Equote_2Eindex] :
( ? [V1i_2E0: tyop_2Equote_2Eindex] : ( V0ii_2E0 = c_2Equote_2ELeft__idx_2E1(V1i_2E0) )
| ? [V2i_2E0: tyop_2Equote_2Eindex] : ( V0ii_2E0 = c_2Equote_2ERight__idx_2E1(V2i_2E0) )
| ( V0ii_2E0 = c_2Equote_2EEnd__idx_2E0 ) ) ).
tff(thm_2Equote_2Eindex__Axiom,axiom,
! [A_27a: $tType,V0f0_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(A_27a,A_27a)),V1f1_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(A_27a,A_27a)),V2f2_2E0: A_27a] :
? [V3fn_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27a)] :
( ! [V4a_2E0: tyop_2Equote_2Eindex] : ( app_2E2(tyop_2Equote_2Eindex,A_27a,V3fn_2E0,c_2Equote_2ELeft__idx_2E1(V4a_2E0)) = app_2E2(A_27a,A_27a,app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(A_27a,A_27a),V0f0_2E0,V4a_2E0),app_2E2(tyop_2Equote_2Eindex,A_27a,V3fn_2E0,V4a_2E0)) )
& ! [V5a_2E0: tyop_2Equote_2Eindex] : ( app_2E2(tyop_2Equote_2Eindex,A_27a,V3fn_2E0,c_2Equote_2ERight__idx_2E1(V5a_2E0)) = app_2E2(A_27a,A_27a,app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(A_27a,A_27a),V1f1_2E0,V5a_2E0),app_2E2(tyop_2Equote_2Eindex,A_27a,V3fn_2E0,V5a_2E0)) )
& ( app_2E2(tyop_2Equote_2Eindex,A_27a,V3fn_2E0,c_2Equote_2EEnd__idx_2E0) = V2f2_2E0 ) ) ).
tff(thm_2Equote_2Eindex__induction,axiom,
! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool)] :
( ( ! [V1i_2E0: tyop_2Equote_2Eindex] :
( p(app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool,V0P_2E0,V1i_2E0))
=> p(app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool,V0P_2E0,c_2Equote_2ELeft__idx_2E1(V1i_2E0))) )
& ! [V2i_2E0: tyop_2Equote_2Eindex] :
( p(app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool,V0P_2E0,V2i_2E0))
=> p(app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool,V0P_2E0,c_2Equote_2ERight__idx_2E1(V2i_2E0))) )
& p(app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool,V0P_2E0,c_2Equote_2EEnd__idx_2E0)) )
=> ! [V3i_2E0: tyop_2Equote_2Eindex] : p(app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool,V0P_2E0,V3i_2E0)) ) ).
tff(thm_2Equote_2Eindex__case__cong,axiom,
! [A_27a: $tType,V0v_27_2E0: A_27a,V1f1_27_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27a),V2f_27_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27a),V3M_2E0: tyop_2Equote_2Eindex,V4M_27_2E0: tyop_2Equote_2Eindex,V5f_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27a),V6f1_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27a),V7v_2E0: A_27a] :
( ( ( V3M_2E0 = V4M_27_2E0 )
& ! [V8a_2E0: tyop_2Equote_2Eindex] :
( ( V4M_27_2E0 = c_2Equote_2ELeft__idx_2E1(V8a_2E0) )
=> ( app_2E2(tyop_2Equote_2Eindex,A_27a,V5f_2E0,V8a_2E0) = app_2E2(tyop_2Equote_2Eindex,A_27a,V2f_27_2E0,V8a_2E0) ) )
& ! [V9a_2E0: tyop_2Equote_2Eindex] :
( ( V4M_27_2E0 = c_2Equote_2ERight__idx_2E1(V9a_2E0) )
=> ( app_2E2(tyop_2Equote_2Eindex,A_27a,V6f1_2E0,V9a_2E0) = app_2E2(tyop_2Equote_2Eindex,A_27a,V1f1_27_2E0,V9a_2E0) ) )
& ( ( V4M_27_2E0 = c_2Equote_2EEnd__idx_2E0 )
=> ( V7v_2E0 = V0v_27_2E0 ) ) )
=> ( c_2Equote_2Eindex__CASE_2E4(A_27a,V3M_2E0,V5f_2E0,V6f1_2E0,V7v_2E0) = c_2Equote_2Eindex__CASE_2E4(A_27a,V4M_27_2E0,V2f_27_2E0,V1f1_27_2E0,V0v_27_2E0) ) ) ).
tff(thm_2Equote_2Eindex__case__eq,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Equote_2Eindex,V1v_27_2E0: A_27a,V2v_2E0: A_27a,V3f1_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27a),V4f_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,A_27a)] :
( ( c_2Equote_2Eindex__CASE_2E4(A_27a,V0x_2E0,V4f_2E0,V3f1_2E0,V2v_2E0) = V1v_27_2E0 )
<=> ( ? [V5i_2E0: tyop_2Equote_2Eindex] :
( ( V0x_2E0 = c_2Equote_2ELeft__idx_2E1(V5i_2E0) )
& ( app_2E2(tyop_2Equote_2Eindex,A_27a,V4f_2E0,V5i_2E0) = V1v_27_2E0 ) )
| ? [V6i_2E0: tyop_2Equote_2Eindex] :
( ( V0x_2E0 = c_2Equote_2ERight__idx_2E1(V6i_2E0) )
& ( app_2E2(tyop_2Equote_2Eindex,A_27a,V3f1_2E0,V6i_2E0) = V1v_27_2E0 ) )
| ( ( V0x_2E0 = c_2Equote_2EEnd__idx_2E0 )
& ( V2v_2E0 = V1v_27_2E0 ) ) ) ) ).
tff(thm_2Equote_2Eindex__compare__ind,axiom,
! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool))] :
( ( p(app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool,app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool),V0P_2E0,c_2Equote_2EEnd__idx_2E0),c_2Equote_2EEnd__idx_2E0))
& ! [V1v10_2E0: tyop_2Equote_2Eindex] : p(app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool,app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool),V0P_2E0,c_2Equote_2EEnd__idx_2E0),c_2Equote_2ELeft__idx_2E1(V1v10_2E0)))
& ! [V2v11_2E0: tyop_2Equote_2Eindex] : p(app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool,app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool),V0P_2E0,c_2Equote_2EEnd__idx_2E0),c_2Equote_2ERight__idx_2E1(V2v11_2E0)))
& ! [V3v2_2E0: tyop_2Equote_2Eindex] : p(app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool,app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool),V0P_2E0,c_2Equote_2ELeft__idx_2E1(V3v2_2E0)),c_2Equote_2EEnd__idx_2E0))
& ! [V4v3_2E0: tyop_2Equote_2Eindex] : p(app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool,app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool),V0P_2E0,c_2Equote_2ERight__idx_2E1(V4v3_2E0)),c_2Equote_2EEnd__idx_2E0))
& ! [V5n_27_2E0: tyop_2Equote_2Eindex,V6m_27_2E0: tyop_2Equote_2Eindex] :
( p(app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool,app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool),V0P_2E0,V5n_27_2E0),V6m_27_2E0))
=> p(app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool,app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool),V0P_2E0,c_2Equote_2ELeft__idx_2E1(V5n_27_2E0)),c_2Equote_2ELeft__idx_2E1(V6m_27_2E0))) )
& ! [V7n_27_2E0: tyop_2Equote_2Eindex,V8m_27_2E0: tyop_2Equote_2Eindex] : p(app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool,app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool),V0P_2E0,c_2Equote_2ELeft__idx_2E1(V7n_27_2E0)),c_2Equote_2ERight__idx_2E1(V8m_27_2E0)))
& ! [V9n_27_2E0: tyop_2Equote_2Eindex,V10m_27_2E0: tyop_2Equote_2Eindex] :
( p(app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool,app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool),V0P_2E0,V9n_27_2E0),V10m_27_2E0))
=> p(app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool,app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool),V0P_2E0,c_2Equote_2ERight__idx_2E1(V9n_27_2E0)),c_2Equote_2ERight__idx_2E1(V10m_27_2E0))) )
& ! [V11n_27_2E0: tyop_2Equote_2Eindex,V12m_27_2E0: tyop_2Equote_2Eindex] : p(app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool,app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool),V0P_2E0,c_2Equote_2ERight__idx_2E1(V11n_27_2E0)),c_2Equote_2ELeft__idx_2E1(V12m_27_2E0))) )
=> ! [V13v_2E0: tyop_2Equote_2Eindex,V14v1_2E0: tyop_2Equote_2Eindex] : p(app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool,app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Ebool),V0P_2E0,V13v_2E0),V14v1_2E0)) ) ).
tff(thm_2Equote_2Eindex__compare__def,axiom,
( ( c_2Equote_2Eindex__compare_2E2(c_2Equote_2EEnd__idx_2E0,c_2Equote_2EEnd__idx_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
& ! [V0v10_2E0: tyop_2Equote_2Eindex] : ( c_2Equote_2Eindex__compare_2E2(c_2Equote_2EEnd__idx_2E0,c_2Equote_2ELeft__idx_2E1(V0v10_2E0)) = c_2EternaryComparisons_2ELESS_2E0 )
& ! [V1v11_2E0: tyop_2Equote_2Eindex] : ( c_2Equote_2Eindex__compare_2E2(c_2Equote_2EEnd__idx_2E0,c_2Equote_2ERight__idx_2E1(V1v11_2E0)) = c_2EternaryComparisons_2ELESS_2E0 )
& ! [V2v2_2E0: tyop_2Equote_2Eindex] : ( c_2Equote_2Eindex__compare_2E2(c_2Equote_2ELeft__idx_2E1(V2v2_2E0),c_2Equote_2EEnd__idx_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
& ! [V3v3_2E0: tyop_2Equote_2Eindex] : ( c_2Equote_2Eindex__compare_2E2(c_2Equote_2ERight__idx_2E1(V3v3_2E0),c_2Equote_2EEnd__idx_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
& ! [V4n_27_2E0: tyop_2Equote_2Eindex,V5m_27_2E0: tyop_2Equote_2Eindex] : ( c_2Equote_2Eindex__compare_2E2(c_2Equote_2ELeft__idx_2E1(V4n_27_2E0),c_2Equote_2ELeft__idx_2E1(V5m_27_2E0)) = c_2Equote_2Eindex__compare_2E2(V4n_27_2E0,V5m_27_2E0) )
& ! [V6n_27_2E0: tyop_2Equote_2Eindex,V7m_27_2E0: tyop_2Equote_2Eindex] : ( c_2Equote_2Eindex__compare_2E2(c_2Equote_2ELeft__idx_2E1(V6n_27_2E0),c_2Equote_2ERight__idx_2E1(V7m_27_2E0)) = c_2EternaryComparisons_2ELESS_2E0 )
& ! [V8n_27_2E0: tyop_2Equote_2Eindex,V9m_27_2E0: tyop_2Equote_2Eindex] : ( c_2Equote_2Eindex__compare_2E2(c_2Equote_2ERight__idx_2E1(V8n_27_2E0),c_2Equote_2ERight__idx_2E1(V9m_27_2E0)) = c_2Equote_2Eindex__compare_2E2(V8n_27_2E0,V9m_27_2E0) )
& ! [V10n_27_2E0: tyop_2Equote_2Eindex,V11m_27_2E0: tyop_2Equote_2Eindex] : ( c_2Equote_2Eindex__compare_2E2(c_2Equote_2ERight__idx_2E1(V10n_27_2E0),c_2Equote_2ELeft__idx_2E1(V11m_27_2E0)) = c_2EternaryComparisons_2EGREATER_2E0 ) ) ).
tff(thm_2Equote_2Ecompare__index__equal,axiom,
! [V0i1_2E0: tyop_2Equote_2Eindex,V1i2_2E0: tyop_2Equote_2Eindex] :
( ( c_2Equote_2Eindex__compare_2E2(V0i1_2E0,V1i2_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
<=> ( V0i1_2E0 = V1i2_2E0 ) ) ).
tff(thm_2Equote_2Ecompare__list__index,axiom,
! [V0l1_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex),V1l2_2E0: tyop_2Elist_2Elist(tyop_2Equote_2Eindex)] :
( ( c_2EternaryComparisons_2Elist__compare_2E3(tyop_2Equote_2Eindex,tyop_2Equote_2Eindex,c_2Equote_2Eindex__compare_2E0,V0l1_2E0,V1l2_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
<=> ( V0l1_2E0 = V1l2_2E0 ) ) ).
tff(thm_2Equote_2Edatatype__varmap,axiom,
! [A_27a: $tType,V0varmap_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Equote_2Evarmap(A_27a)))),tyop_2Emin_2Ebool))] : p(c_2Ebool_2EDATATYPE_2E1(tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Equote_2Evarmap(A_27a)))),tyop_2Emin_2Ebool,app_2E2(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Equote_2Evarmap(A_27a)))),tyop_2Emin_2Ebool),V0varmap_2E0,c_2Equote_2EEmpty__vm_2E0(A_27a)),c_2Equote_2ENode__vm_2E0(A_27a)))) ).
tff(thm_2Equote_2Evarmap__11,axiom,
! [A_27a: $tType,V0a0_2E0: A_27a,V1a1_2E0: tyop_2Equote_2Evarmap(A_27a),V2a2_2E0: tyop_2Equote_2Evarmap(A_27a),V3a0_27_2E0: A_27a,V4a1_27_2E0: tyop_2Equote_2Evarmap(A_27a),V5a2_27_2E0: tyop_2Equote_2Evarmap(A_27a)] :
( ( c_2Equote_2ENode__vm_2E3(A_27a,V0a0_2E0,V1a1_2E0,V2a2_2E0) = c_2Equote_2ENode__vm_2E3(A_27a,V3a0_27_2E0,V4a1_27_2E0,V5a2_27_2E0) )
<=> ( ( V0a0_2E0 = V3a0_27_2E0 )
& ( V1a1_2E0 = V4a1_27_2E0 )
& ( V2a2_2E0 = V5a2_27_2E0 ) ) ) ).
tff(thm_2Equote_2Evarmap__distinct,axiom,
! [A_27a: $tType,V0a2_2E0: tyop_2Equote_2Evarmap(A_27a),V1a1_2E0: tyop_2Equote_2Evarmap(A_27a),V2a0_2E0: A_27a] : ( c_2Equote_2EEmpty__vm_2E0(A_27a) != c_2Equote_2ENode__vm_2E3(A_27a,V2a0_2E0,V1a1_2E0,V0a2_2E0) ) ).
tff(thm_2Equote_2Evarmap__nchotomy,axiom,
! [A_27a: $tType,V0vv_2E0: tyop_2Equote_2Evarmap(A_27a)] :
( ( V0vv_2E0 = c_2Equote_2EEmpty__vm_2E0(A_27a) )
| ? [V1a_2E0: A_27a,V2v_2E0: tyop_2Equote_2Evarmap(A_27a),V3v0_2E0: tyop_2Equote_2Evarmap(A_27a)] : ( V0vv_2E0 = c_2Equote_2ENode__vm_2E3(A_27a,V1a_2E0,V2v_2E0,V3v0_2E0) ) ) ).
tff(thm_2Equote_2Evarmap__Axiom,axiom,
! [A_27a: $tType,A_27b: $tType,V0f0_2E0: A_27b,V1f1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)))))] :
? [V2fn_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),A_27b)] :
( ( app_2E2(tyop_2Equote_2Evarmap(A_27a),A_27b,V2fn_2E0,c_2Equote_2EEmpty__vm_2E0(A_27a)) = V0f0_2E0 )
& ! [V3a0_2E0: A_27a,V4a1_2E0: tyop_2Equote_2Evarmap(A_27a),V5a2_2E0: tyop_2Equote_2Evarmap(A_27a)] : ( app_2E2(tyop_2Equote_2Evarmap(A_27a),A_27b,V2fn_2E0,c_2Equote_2ENode__vm_2E3(A_27a,V3a0_2E0,V4a1_2E0,V5a2_2E0)) = app_2E2(A_27b,A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)))),V1f1_2E0,V3a0_2E0),V4a1_2E0),V5a2_2E0),app_2E2(tyop_2Equote_2Evarmap(A_27a),A_27b,V2fn_2E0,V4a1_2E0)),app_2E2(tyop_2Equote_2Evarmap(A_27a),A_27b,V2fn_2E0,V5a2_2E0)) ) ) ).
tff(thm_2Equote_2Evarmap__induction,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Ebool)] :
( ( p(app_2E2(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Equote_2EEmpty__vm_2E0(A_27a)))
& ! [V1v_2E0: tyop_2Equote_2Evarmap(A_27a),V2v0_2E0: tyop_2Equote_2Evarmap(A_27a)] :
( ( p(app_2E2(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V1v_2E0))
& p(app_2E2(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V2v0_2E0)) )
=> ! [V3a_2E0: A_27a] : p(app_2E2(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Equote_2ENode__vm_2E3(A_27a,V3a_2E0,V1v_2E0,V2v0_2E0))) ) )
=> ! [V4v_2E0: tyop_2Equote_2Evarmap(A_27a)] : p(app_2E2(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V4v_2E0)) ) ).
tff(thm_2Equote_2Evarmap__case__cong,axiom,
! [A_27a: $tType,A_27b: $tType,V0v_27_2E0: A_27b,V1f_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),A_27b))),V2M_2E0: tyop_2Equote_2Evarmap(A_27a),V3M_27_2E0: tyop_2Equote_2Evarmap(A_27a),V4v_2E0: A_27b,V5f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),A_27b)))] :
( ( ( V2M_2E0 = V3M_27_2E0 )
& ( ( V3M_27_2E0 = c_2Equote_2EEmpty__vm_2E0(A_27a) )
=> ( V4v_2E0 = V0v_27_2E0 ) )
& ! [V6a0_2E0: A_27a,V7a1_2E0: tyop_2Equote_2Evarmap(A_27a),V8a2_2E0: tyop_2Equote_2Evarmap(A_27a)] :
( ( V3M_27_2E0 = c_2Equote_2ENode__vm_2E3(A_27a,V6a0_2E0,V7a1_2E0,V8a2_2E0) )
=> ( app_2E2(tyop_2Equote_2Evarmap(A_27a),A_27b,app_2E2(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),A_27b)),V5f_2E0,V6a0_2E0),V7a1_2E0),V8a2_2E0) = app_2E2(tyop_2Equote_2Evarmap(A_27a),A_27b,app_2E2(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),A_27b)),V1f_27_2E0,V6a0_2E0),V7a1_2E0),V8a2_2E0) ) ) )
=> ( c_2Equote_2Evarmap__CASE_2E3(A_27a,A_27b,V2M_2E0,V4v_2E0,V5f_2E0) = c_2Equote_2Evarmap__CASE_2E3(A_27a,A_27b,V3M_27_2E0,V0v_27_2E0,V1f_27_2E0) ) ) ).
tff(thm_2Equote_2Evarmap__case__eq,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Equote_2Evarmap(A_27a),V1v_27_2E0: A_27b,V2v_2E0: A_27b,V3f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),A_27b)))] :
( ( c_2Equote_2Evarmap__CASE_2E3(A_27a,A_27b,V0x_2E0,V2v_2E0,V3f_2E0) = V1v_27_2E0 )
<=> ( ( ( V0x_2E0 = c_2Equote_2EEmpty__vm_2E0(A_27a) )
& ( V2v_2E0 = V1v_27_2E0 ) )
| ? [V4a_2E0: A_27a,V5v_27_27_2E0: tyop_2Equote_2Evarmap(A_27a),V6v0_2E0: tyop_2Equote_2Evarmap(A_27a)] :
( ( V0x_2E0 = c_2Equote_2ENode__vm_2E3(A_27a,V4a_2E0,V5v_27_27_2E0,V6v0_2E0) )
& ( app_2E2(tyop_2Equote_2Evarmap(A_27a),A_27b,app_2E2(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),A_27b)),V3f_2E0,V4a_2E0),V5v_27_27_2E0),V6v0_2E0) = V1v_27_2E0 ) ) ) ) ).
tff(thm_2Equote_2Evarmap__find__ind,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Ebool))] :
( ( ! [V1x_2E0: A_27a,V2v1_2E0: tyop_2Equote_2Evarmap(A_27a),V3v2_2E0: tyop_2Equote_2Evarmap(A_27a)] : p(app_2E2(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Ebool),V0P_2E0,c_2Equote_2EEnd__idx_2E0),c_2Equote_2ENode__vm_2E3(A_27a,V1x_2E0,V2v1_2E0,V3v2_2E0)))
& ! [V4i1_2E0: tyop_2Equote_2Eindex,V5x_2E0: A_27a,V6v1_2E0: tyop_2Equote_2Evarmap(A_27a),V7v2_2E0: tyop_2Equote_2Evarmap(A_27a)] :
( p(app_2E2(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Ebool),V0P_2E0,V4i1_2E0),V7v2_2E0))
=> p(app_2E2(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Ebool),V0P_2E0,c_2Equote_2ERight__idx_2E1(V4i1_2E0)),c_2Equote_2ENode__vm_2E3(A_27a,V5x_2E0,V6v1_2E0,V7v2_2E0))) )
& ! [V8i1_2E0: tyop_2Equote_2Eindex,V9x_2E0: A_27a,V10v1_2E0: tyop_2Equote_2Evarmap(A_27a),V11v2_2E0: tyop_2Equote_2Evarmap(A_27a)] :
( p(app_2E2(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Ebool),V0P_2E0,V8i1_2E0),V10v1_2E0))
=> p(app_2E2(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Ebool),V0P_2E0,c_2Equote_2ELeft__idx_2E1(V8i1_2E0)),c_2Equote_2ENode__vm_2E3(A_27a,V9x_2E0,V10v1_2E0,V11v2_2E0))) )
& ! [V12i_2E0: tyop_2Equote_2Eindex] : p(app_2E2(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Ebool),V0P_2E0,V12i_2E0),c_2Equote_2EEmpty__vm_2E0(A_27a))) )
=> ! [V13v_2E0: tyop_2Equote_2Eindex,V14v1_2E0: tyop_2Equote_2Evarmap(A_27a)] : p(app_2E2(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Equote_2Eindex,tyop_2Emin_2Efun(tyop_2Equote_2Evarmap(A_27a),tyop_2Emin_2Ebool),V0P_2E0,V13v_2E0),V14v1_2E0)) ) ).
tff(thm_2Equote_2Evarmap__find__def,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ! [V12x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Ebool,F0_2E0,V12x_2E0) = c_2Ebool_2ET_2E0 )
=> ( ! [V0x_2E0: A_27a,V1v2_2E0: tyop_2Equote_2Evarmap(A_27a),V2v1_2E0: tyop_2Equote_2Evarmap(A_27a)] : ( c_2Equote_2Evarmap__find_2E2(A_27a,c_2Equote_2EEnd__idx_2E0,c_2Equote_2ENode__vm_2E3(A_27a,V0x_2E0,V2v1_2E0,V1v2_2E0)) = V0x_2E0 )
& ! [V3x_2E0: A_27a,V4v2_2E0: tyop_2Equote_2Evarmap(A_27a),V5v1_2E0: tyop_2Equote_2Evarmap(A_27a),V6i1_2E0: tyop_2Equote_2Eindex] : ( c_2Equote_2Evarmap__find_2E2(A_27a,c_2Equote_2ERight__idx_2E1(V6i1_2E0),c_2Equote_2ENode__vm_2E3(A_27a,V3x_2E0,V5v1_2E0,V4v2_2E0)) = c_2Equote_2Evarmap__find_2E2(A_27a,V6i1_2E0,V4v2_2E0) )
& ! [V7x_2E0: A_27a,V8v2_2E0: tyop_2Equote_2Evarmap(A_27a),V9v1_2E0: tyop_2Equote_2Evarmap(A_27a),V10i1_2E0: tyop_2Equote_2Eindex] : ( c_2Equote_2Evarmap__find_2E2(A_27a,c_2Equote_2ELeft__idx_2E1(V10i1_2E0),c_2Equote_2ENode__vm_2E3(A_27a,V7x_2E0,V9v1_2E0,V8v2_2E0)) = c_2Equote_2Evarmap__find_2E2(A_27a,V10i1_2E0,V9v1_2E0) )
& ! [V11i_2E0: tyop_2Equote_2Eindex] : ( c_2Equote_2Evarmap__find_2E2(A_27a,V11i_2E0,c_2Equote_2EEmpty__vm_2E0(A_27a)) = c_2Emin_2E_40_2E1(A_27a,F0_2E0) ) ) ) ).
%------------------------------------------------------------------------------