ITP001 Axioms: ITP087^5.ax


%------------------------------------------------------------------------------
% File     : ITP087^5 : TPTP v9.0.0. 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 ) ) ) ) ).

%------------------------------------------------------------------------------