ITP001 Axioms: ITP041^5.ax


%------------------------------------------------------------------------------
% File     : ITP041^5 : 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    : numposrep^2.ax [Gau20]
%          : HL4041^5.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   72 (  20 unt;  18 typ;   0 def)
%            Number of atoms       : 1285 (  47 equ;   0 cnn)
%            Maximal formula atoms :   42 (  17 avg)
%            Number of connectives : 1437 (   3   ~;   1   |;  19   &;1390   @)
%                                         (   2 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   6 avg;1390 nst)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   81 (  80 usr;  74 con; 0-2 aty)
%            Number of variables   :   70 (   3   ^  67   !;   0   ?;  70   :)
% SPC      : TH0_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tp_c_2Enumposrep_2EBOOLIFY,type,
    c_2Enumposrep_2EBOOLIFY: $i ).

thf(mem_c_2Enumposrep_2EBOOLIFY,axiom,
    mem @ c_2Enumposrep_2EBOOLIFY @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Elist_2Elist @ bool ) @ ( ty_2Elist_2Elist @ bool ) ) ) ) ).

thf(tp_c_2Enumposrep_2El2n,type,
    c_2Enumposrep_2El2n: $i ).

thf(mem_c_2Enumposrep_2El2n,axiom,
    mem @ c_2Enumposrep_2El2n @ ( arr @ ty_2Enum_2Enum @ ( arr @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) ) ).

thf(stp_fo_c_2Enumposrep_2El2n,type,
    fo__c_2Enumposrep_2El2n: tp__ty_2Enum_2Enum > tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).

thf(stp_eq_fo_c_2Enumposrep_2El2n,axiom,
    ! [X0: tp__ty_2Enum_2Enum,X1: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
      ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Enumposrep_2El2n @ X0 @ X1 ) )
      = ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( inj__ty_2Enum_2Enum @ X0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ X1 ) ) ) ).

thf(tp_c_2Enumposrep_2El2n2,type,
    c_2Enumposrep_2El2n2: $i ).

thf(mem_c_2Enumposrep_2El2n2,axiom,
    mem @ c_2Enumposrep_2El2n2 @ ( arr @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) ).

thf(stp_fo_c_2Enumposrep_2El2n2,type,
    fo__c_2Enumposrep_2El2n2: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).

thf(stp_eq_fo_c_2Enumposrep_2El2n2,axiom,
    ! [X0: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
      ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Enumposrep_2El2n2 @ X0 ) )
      = ( ap @ c_2Enumposrep_2El2n2 @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ X0 ) ) ) ).

thf(tp_c_2Enumposrep_2En2l,type,
    c_2Enumposrep_2En2l: $i ).

thf(mem_c_2Enumposrep_2En2l,axiom,
    mem @ c_2Enumposrep_2En2l @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) ) ) ).

thf(tp_c_2Enumposrep_2Enum__from__bin__list,type,
    c_2Enumposrep_2Enum__from__bin__list: $i ).

thf(mem_c_2Enumposrep_2Enum__from__bin__list,axiom,
    mem @ c_2Enumposrep_2Enum__from__bin__list @ ( arr @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) ).

thf(stp_fo_c_2Enumposrep_2Enum__from__bin__list,type,
    fo__c_2Enumposrep_2Enum__from__bin__list: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).

thf(stp_eq_fo_c_2Enumposrep_2Enum__from__bin__list,axiom,
    ! [X0: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
      ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Enumposrep_2Enum__from__bin__list @ X0 ) )
      = ( ap @ c_2Enumposrep_2Enum__from__bin__list @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ X0 ) ) ) ).

thf(tp_c_2Enumposrep_2Enum__from__dec__list,type,
    c_2Enumposrep_2Enum__from__dec__list: $i ).

thf(mem_c_2Enumposrep_2Enum__from__dec__list,axiom,
    mem @ c_2Enumposrep_2Enum__from__dec__list @ ( arr @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) ).

thf(stp_fo_c_2Enumposrep_2Enum__from__dec__list,type,
    fo__c_2Enumposrep_2Enum__from__dec__list: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).

thf(stp_eq_fo_c_2Enumposrep_2Enum__from__dec__list,axiom,
    ! [X0: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
      ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Enumposrep_2Enum__from__dec__list @ X0 ) )
      = ( ap @ c_2Enumposrep_2Enum__from__dec__list @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ X0 ) ) ) ).

thf(tp_c_2Enumposrep_2Enum__from__hex__list,type,
    c_2Enumposrep_2Enum__from__hex__list: $i ).

thf(mem_c_2Enumposrep_2Enum__from__hex__list,axiom,
    mem @ c_2Enumposrep_2Enum__from__hex__list @ ( arr @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) ).

thf(stp_fo_c_2Enumposrep_2Enum__from__hex__list,type,
    fo__c_2Enumposrep_2Enum__from__hex__list: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).

thf(stp_eq_fo_c_2Enumposrep_2Enum__from__hex__list,axiom,
    ! [X0: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
      ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Enumposrep_2Enum__from__hex__list @ X0 ) )
      = ( ap @ c_2Enumposrep_2Enum__from__hex__list @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ X0 ) ) ) ).

thf(tp_c_2Enumposrep_2Enum__from__oct__list,type,
    c_2Enumposrep_2Enum__from__oct__list: $i ).

thf(mem_c_2Enumposrep_2Enum__from__oct__list,axiom,
    mem @ c_2Enumposrep_2Enum__from__oct__list @ ( arr @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) ).

thf(stp_fo_c_2Enumposrep_2Enum__from__oct__list,type,
    fo__c_2Enumposrep_2Enum__from__oct__list: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum > tp__ty_2Enum_2Enum ).

thf(stp_eq_fo_c_2Enumposrep_2Enum__from__oct__list,axiom,
    ! [X0: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
      ( ( inj__ty_2Enum_2Enum @ ( fo__c_2Enumposrep_2Enum__from__oct__list @ X0 ) )
      = ( ap @ c_2Enumposrep_2Enum__from__oct__list @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ X0 ) ) ) ).

thf(tp_c_2Enumposrep_2Enum__to__bin__list,type,
    c_2Enumposrep_2Enum__to__bin__list: $i ).

thf(mem_c_2Enumposrep_2Enum__to__bin__list,axiom,
    mem @ c_2Enumposrep_2Enum__to__bin__list @ ( arr @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) ) ).

thf(tp_c_2Enumposrep_2Enum__to__dec__list,type,
    c_2Enumposrep_2Enum__to__dec__list: $i ).

thf(mem_c_2Enumposrep_2Enum__to__dec__list,axiom,
    mem @ c_2Enumposrep_2Enum__to__dec__list @ ( arr @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) ) ).

thf(tp_c_2Enumposrep_2Enum__to__hex__list,type,
    c_2Enumposrep_2Enum__to__hex__list: $i ).

thf(mem_c_2Enumposrep_2Enum__to__hex__list,axiom,
    mem @ c_2Enumposrep_2Enum__to__hex__list @ ( arr @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) ) ).

thf(tp_c_2Enumposrep_2Enum__to__oct__list,type,
    c_2Enumposrep_2Enum__to__oct__list: $i ).

thf(mem_c_2Enumposrep_2Enum__to__oct__list,axiom,
    mem @ c_2Enumposrep_2Enum__to__oct__list @ ( arr @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) ) ).

thf(ax_thm_2Enumposrep_2El2n__def,axiom,
    ( ! [V0b: tp__ty_2Enum_2Enum] :
        ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( c_2Elist_2ENIL @ ty_2Enum_2Enum ) ) )
        = fo__c_2Enum_2E0 )
    & ! [V1b: tp__ty_2Enum_2Enum,V2h: tp__ty_2Enum_2Enum,V3t: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
        ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V2h ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V3t ) ) ) )
        = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V2h ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V3t ) ) ) ) ) ) ) ).

thf(conj_thm_2Enumposrep_2En2l__ind,axiom,
    ! [V0P: $i] :
      ( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) )
     => ( ! [V1b: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
            ( ( ~ ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
                  | ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) )
             => ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) ) )
           => ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
       => ! [V3v: tp__ty_2Enum_2Enum,V4v1: tp__ty_2Enum_2Enum] : ( p @ ( ap @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V3v ) ) @ ( inj__ty_2Enum_2Enum @ V4v1 ) ) ) ) ) ).

thf(conj_thm_2Enumposrep_2En2l__def,axiom,
    ! [V0n: tp__ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
      ( ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumposrep_2En2l @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
      = ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) @ ( c_2Elist_2ENIL @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) @ ( ap @ ( ap @ c_2Enumposrep_2En2l @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) ) ) ) ) ).

thf(ax_thm_2Enumposrep_2Enum__from__bin__list__def,axiom,
    ( c_2Enumposrep_2Enum__from__bin__list
    = ( ap @ c_2Enumposrep_2El2n @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ).

thf(ax_thm_2Enumposrep_2Enum__from__oct__list__def,axiom,
    ( c_2Enumposrep_2Enum__from__oct__list
    = ( ap @ c_2Enumposrep_2El2n @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).

thf(ax_thm_2Enumposrep_2Enum__from__dec__list__def,axiom,
    ( c_2Enumposrep_2Enum__from__dec__list
    = ( ap @ c_2Enumposrep_2El2n @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).

thf(ax_thm_2Enumposrep_2Enum__from__hex__list__def,axiom,
    ( c_2Enumposrep_2Enum__from__hex__list
    = ( ap @ c_2Enumposrep_2El2n @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).

thf(ax_thm_2Enumposrep_2Enum__to__bin__list__def,axiom,
    ( c_2Enumposrep_2Enum__to__bin__list
    = ( ap @ c_2Enumposrep_2En2l @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ).

thf(ax_thm_2Enumposrep_2Enum__to__oct__list__def,axiom,
    ( c_2Enumposrep_2Enum__to__oct__list
    = ( ap @ c_2Enumposrep_2En2l @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).

thf(ax_thm_2Enumposrep_2Enum__to__dec__list__def,axiom,
    ( c_2Enumposrep_2Enum__to__dec__list
    = ( ap @ c_2Enumposrep_2En2l @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).

thf(ax_thm_2Enumposrep_2Enum__to__hex__list__def,axiom,
    ( c_2Enumposrep_2Enum__to__hex__list
    = ( ap @ c_2Enumposrep_2En2l @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).

thf(ax_thm_2Enumposrep_2EBOOLIFY__def,axiom,
    ( ! [V0m: tp__ty_2Enum_2Enum,V1a: tp__c_ty_2Elist_2Elist_o] :
        ( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ c_2Enumposrep_2EBOOLIFY @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V1a ) ) )
        = V1a )
    & ! [V2n: tp__ty_2Enum_2Enum,V3m: tp__ty_2Enum_2Enum,V4a: tp__c_ty_2Elist_2Elist_o] :
        ( ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ c_2Enumposrep_2EBOOLIFY @ ( ap @ c_2Enum_2ESUC @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) @ ( inj__ty_2Enum_2Enum @ V3m ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V4a ) ) )
        = ( surj__c_ty_2Elist_2Elist_o @ ( ap @ ( ap @ ( ap @ c_2Enumposrep_2EBOOLIFY @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ c_2Earithmetic_2EDIV2 @ ( inj__ty_2Enum_2Enum @ V3m ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ bool ) @ ( ap @ c_2Earithmetic_2EODD @ ( inj__ty_2Enum_2Enum @ V3m ) ) ) @ ( inj__c_ty_2Elist_2Elist_o @ V4a ) ) ) ) ) ) ).

thf(conj_thm_2Enumposrep_2ELENGTH__n2l,axiom,
    ! [V0b: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
      ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) )
     => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Enumposrep_2En2l @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
        = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ) ).

thf(conj_thm_2Enumposrep_2El2n__n2l,axiom,
    ! [V0b: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
      ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) )
     => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( ap @ ( ap @ c_2Enumposrep_2En2l @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
        = V1n ) ) ).

thf(conj_thm_2Enumposrep_2El2n__lt,axiom,
    ! [V0l: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum,V1b: tp__ty_2Enum_2Enum] :
      ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) )
     => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V0l ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V0l ) ) ) ) ) ) ).

thf(conj_thm_2Enumposrep_2ELENGTH__l2n,axiom,
    ! [V0b: tp__ty_2Enum_2Enum,V1l: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
      ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) )
        & ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2E_3E @ ( inj__ty_2Enum_2Enum @ V0b ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) )
        & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) )
         != fo__c_2Enum_2E0 ) )
     => ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) ) ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) ) ) ) ).

thf(conj_thm_2Enumposrep_2El2n__DIGIT,axiom,
    ! [V0b: tp__ty_2Enum_2Enum,V1l: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum,V2x: tp__ty_2Enum_2Enum] :
      ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) )
        & ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2E_3E @ ( inj__ty_2Enum_2Enum @ V0b ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) )
        & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V2x ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) ) ) )
     => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V2x ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) )
        = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Elist_2EEL @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V2x ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) ) ) ) ).

thf(conj_thm_2Enumposrep_2EDIV__0__IMP__LT,axiom,
    ! [V0b: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
      ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) )
        & ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) )
          = fo__c_2Enum_2E0 ) )
     => ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) ) ) ).

thf(conj_thm_2Enumposrep_2EEL__n2l,axiom,
    ! [V0b: tp__ty_2Enum_2Enum,V1x: tp__ty_2Enum_2Enum,V2n: tp__ty_2Enum_2Enum] :
      ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) )
        & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Enumposrep_2En2l @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) ) ) )
     => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Elist_2EEL @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) @ ( ap @ ( ap @ c_2Enumposrep_2En2l @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V2n ) ) ) )
        = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EMOD @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V2n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V1x ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) ) ) ) ).

thf(conj_thm_2Enumposrep_2En2l__l2n,axiom,
    ! [V0b: tp__ty_2Enum_2Enum,V1l: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
      ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) )
        & ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2E_3E @ ( inj__ty_2Enum_2Enum @ V0b ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) ) )
     => ( ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumposrep_2En2l @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) ) )
        = ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( c_2Elist_2ENIL @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ETAKE @ ty_2Enum_2Enum ) @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) ) ) ) ) ).

thf(conj_thm_2Enumposrep_2El2n__eq__0,axiom,
    ! [V0b: tp__ty_2Enum_2Enum] :
      ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) )
     => ! [V1l: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
          ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) )
            = fo__c_2Enum_2E0 )
        <=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ty_2Enum_2Enum @ bool @ ty_2Enum_2Enum ) @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ ( c_2Ecombin_2EC @ ty_2Enum_2Enum @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ c_2Earithmetic_2EMOD ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) ) ) ) ).

thf(conj_thm_2Enumposrep_2El2n__SNOC__0,axiom,
    ! [V0b: tp__ty_2Enum_2Enum,V1ls: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
      ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) )
     => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( ap @ ( ap @ ( c_2Elist_2ESNOC @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1ls ) ) ) )
        = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1ls ) ) ) ) ) ).

thf(conj_thm_2Enumposrep_2ELOG__l2n,axiom,
    ! [V0b: tp__ty_2Enum_2Enum] :
      ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) )
     => ! [V1l: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
          ( ( ( V1l
             != ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( c_2Elist_2ENIL @ ty_2Enum_2Enum ) ) )
            & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( c_2Elist_2ELAST @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) ) )
            & ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2E_3E @ ( inj__ty_2Enum_2Enum @ V0b ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) ) )
         => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) ) )
            = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eprim__rec_2EPRE @ ( ap @ ( c_2Elist_2ELENGTH @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) ) ) ) ) ) ).

thf(conj_thm_2Enumposrep_2El2n__dropWhile__0,axiom,
    ! [V0b: tp__ty_2Enum_2Enum,V1ls: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
      ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) )
     => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( ap @ ( c_2Elist_2EREVERSE @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Elist_2EdropWhile @ ty_2Enum_2Enum ) @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Elist_2EREVERSE @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1ls ) ) ) ) ) )
        = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1ls ) ) ) ) ) ).

thf(conj_thm_2Enumposrep_2ELOG__l2n__dropWhile,axiom,
    ! [V0b: tp__ty_2Enum_2Enum,V1l: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
      ( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) )
        & ( p
          @ ( ap
            @ ( ap @ ( c_2Elist_2EEXISTS @ ty_2Enum_2Enum )
              @ ( lam @ ty_2Enum_2Enum
                @ ^ [V2y: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ V2y ) ) ) )
            @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) )
        & ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2E_3E @ ( inj__ty_2Enum_2Enum @ V0b ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) ) )
     => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) ) )
        = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Eprim__rec_2EPRE @ ( ap @ ( c_2Elist_2ELENGTH @ ty_2Enum_2Enum ) @ ( ap @ ( ap @ ( c_2Elist_2EdropWhile @ ty_2Enum_2Enum ) @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( c_2Elist_2EREVERSE @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) ) ) ) ) ) ) ).

thf(conj_thm_2Enumposrep_2En2l__BOUND,axiom,
    ! [V0b: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
      ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) )
     => ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2E_3E @ ( inj__ty_2Enum_2Enum @ V0b ) ) ) @ ( ap @ ( ap @ c_2Enumposrep_2En2l @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ).

thf(conj_thm_2Enumposrep_2El2n__pow2__compute,axiom,
    ( ! [V0p: tp__ty_2Enum_2Enum] :
        ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0p ) ) ) @ ( c_2Elist_2ENIL @ ty_2Enum_2Enum ) ) )
        = fo__c_2Enum_2E0 )
    & ! [V1p: tp__ty_2Enum_2Enum,V2h: tp__ty_2Enum_2Enum,V3t: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
        ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1p ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V2h ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V3t ) ) ) )
        = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Ebit_2EMOD__2EXP @ ( inj__ty_2Enum_2Enum @ V1p ) ) @ ( inj__ty_2Enum_2Enum @ V2h ) ) ) @ ( ap @ ( ap @ c_2Ebit_2ETIMES__2EXP @ ( inj__ty_2Enum_2Enum @ V1p ) ) @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V1p ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V3t ) ) ) ) ) ) ) ).

thf(conj_thm_2Enumposrep_2En2l__pow2__compute,axiom,
    ! [V0p: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
      ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__ty_2Enum_2Enum @ V0p ) ) )
     => ( ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumposrep_2En2l @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0p ) ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
        = ( surj__c_ty_2Elist_2Elist_ty_2Enum_2Enum
          @ ( ap
            @ ( ap @ ( c_2Ebool_2ELET @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) )
              @ ( ap @ ( c_2Epair_2EUNCURRY @ ty_2Enum_2Enum @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) )
                @ ( lam @ ty_2Enum_2Enum
                  @ ^ [V2q: $i] :
                      ( lam @ ty_2Enum_2Enum
                      @ ^ [V3r: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ ty_2Enum_2Enum ) @ V2q ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Enum_2Enum ) @ V3r ) @ ( c_2Elist_2ENIL @ ty_2Enum_2Enum ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Enum_2Enum ) @ V3r ) @ ( ap @ ( ap @ c_2Enumposrep_2En2l @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0p ) ) ) @ V2q ) ) ) ) ) ) )
            @ ( ap @ ( ap @ c_2Ebit_2EDIVMOD__2EXP @ ( inj__ty_2Enum_2Enum @ V0p ) ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) ).

thf(ax_thm_2Enumposrep_2El2n2,axiom,
    ( c_2Enumposrep_2El2n2
    = ( ap @ c_2Enumposrep_2El2n @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ).

thf(conj_thm_2Enumposrep_2El2n__2__thms,axiom,
    ( ! [V0t: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
        ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V0t ) ) ) )
        = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Enumposrep_2El2n2 @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V0t ) ) ) ) ) )
    & ! [V1t: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
        ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1t ) ) ) )
        = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Enumposrep_2El2n2 @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1t ) ) ) ) ) )
    & ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumposrep_2El2n2 @ ( c_2Elist_2ENIL @ ty_2Enum_2Enum ) ) )
      = fo__c_2Earithmetic_2EZERO )
    & ! [V2t: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
        ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumposrep_2El2n2 @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V2t ) ) ) )
        = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumeral_2EiDUB @ ( ap @ c_2Enumposrep_2El2n2 @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V2t ) ) ) ) )
    & ! [V3t: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
        ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Enumposrep_2El2n2 @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V3t ) ) ) )
        = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Enumposrep_2El2n2 @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V3t ) ) ) ) ) ) ).

thf(conj_thm_2Enumposrep_2EBIT__num__from__bin__list,axiom,
    ! [V0x: tp__ty_2Enum_2Enum,V1l: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
      ( ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2E_3E @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) )
        & ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) ) ) )
     => ( ( p @ ( ap @ ( ap @ c_2Ebit_2EBIT @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ c_2Enumposrep_2Enum__from__bin__list @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) ) )
      <=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Elist_2EEL @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) )
          = ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).

thf(conj_thm_2Enumposrep_2EEL__num__to__bin__list,axiom,
    ! [V0x: tp__ty_2Enum_2Enum,V1n: tp__ty_2Enum_2Enum] :
      ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ ty_2Enum_2Enum ) @ ( ap @ c_2Enumposrep_2Enum__to__bin__list @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) )
     => ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Elist_2EEL @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) @ ( ap @ c_2Enumposrep_2Enum__to__bin__list @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) )
        = ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Ebit_2EBITV @ ( inj__ty_2Enum_2Enum @ V1n ) ) @ ( inj__ty_2Enum_2Enum @ V0x ) ) ) ) ) ).

thf(conj_thm_2Enumposrep_2Enum__bin__list,axiom,
    ( ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ty_2Enum_2Enum @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) ) @ c_2Enumposrep_2Enum__from__bin__list ) @ c_2Enumposrep_2Enum__to__bin__list )
    = ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) ) ).

thf(conj_thm_2Enumposrep_2Enum__oct__list,axiom,
    ( ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ty_2Enum_2Enum @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) ) @ c_2Enumposrep_2Enum__from__oct__list ) @ c_2Enumposrep_2Enum__to__oct__list )
    = ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) ) ).

thf(conj_thm_2Enumposrep_2Enum__dec__list,axiom,
    ( ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ty_2Enum_2Enum @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) ) @ c_2Enumposrep_2Enum__from__dec__list ) @ c_2Enumposrep_2Enum__to__dec__list )
    = ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) ) ).

thf(conj_thm_2Enumposrep_2Enum__hex__list,axiom,
    ( ( ap @ ( ap @ ( c_2Ecombin_2Eo @ ty_2Enum_2Enum @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ ty_2Enum_2Enum ) ) @ c_2Enumposrep_2Enum__from__hex__list ) @ c_2Enumposrep_2Enum__to__hex__list )
    = ( c_2Ecombin_2EI @ ty_2Enum_2Enum ) ) ).

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