ITP001 Axioms: ITP112^7.ax


%------------------------------------------------------------------------------
% File     : ITP112^7 : TPTP v9.0.0. 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    : patricia_casts.ax [Gau19]
%          : HL4112^7.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  178 (  49 unt; 114 typ;   0 def)
%            Number of atoms       :  116 (  67 equ;   1 cnn)
%            Maximal formula atoms :    8 (   0 avg)
%            Number of connectives : 1115 (   1   ~;   2   |;   7   &;1082   @)
%                                         (  15 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   31 (   6 avg;1082 nst)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :  275 ( 275   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  112 ( 110 usr;   4 con; 0-5 aty)
%            Number of variables   :  315 (  12   ^ 200   !;   7   ?; 315   :)
%                                         (  96  !>;   0  ?*;   0  @-;   0  @+)
% SPC      : TH1_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tyop_2Efcp_2Ecart,type,
    tyop_2Efcp_2Ecart: $tType > $tType > $tType ).

thf(tyop_2Eind__type_2Erecspace,type,
    tyop_2Eind__type_2Erecspace: $tType > $tType ).

thf(tyop_2Elist_2Elist,type,
    tyop_2Elist_2Elist: $tType > $tType ).

thf(tyop_2Emin_2Ebool,type,
    tyop_2Emin_2Ebool: $tType ).

thf(tyop_2Emin_2Efun,type,
    tyop_2Emin_2Efun: $tType > $tType > $tType ).

thf(tyop_2Enum_2Enum,type,
    tyop_2Enum_2Enum: $tType ).

thf(tyop_2Eone_2Eone,type,
    tyop_2Eone_2Eone: $tType ).

thf(tyop_2Eoption_2Eoption,type,
    tyop_2Eoption_2Eoption: $tType > $tType ).

thf(tyop_2Epair_2Eprod,type,
    tyop_2Epair_2Eprod: $tType > $tType > $tType ).

thf(tyop_2Epatricia_2Eptree,type,
    tyop_2Epatricia_2Eptree: $tType > $tType ).

thf(tyop_2Epatricia__casts_2Eword__ptree,type,
    tyop_2Epatricia__casts_2Eword__ptree: $tType > $tType > $tType ).

thf(tyop_2Estring_2Echar,type,
    tyop_2Estring_2Echar: $tType ).

thf(c_2Ebool_2E_21,type,
    c_2Ebool_2E_21: 
      !>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).

thf(c_2Earithmetic_2E_2A,type,
    c_2Earithmetic_2E_2A: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Earithmetic_2E_2B,type,
    c_2Earithmetic_2E_2B: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Epair_2E_2C,type,
    c_2Epair_2E_2C: 
      !>[A_27a: $tType,A_27b: $tType] : ( A_27a > A_27b > ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ).

thf(c_2Ebool_2E_2F_5C,type,
    c_2Ebool_2E_2F_5C: $o > $o > $o ).

thf(c_2Enum_2E0,type,
    c_2Enum_2E0: tyop_2Enum_2Enum ).

thf(c_2Eprim__rec_2E_3C,type,
    c_2Eprim__rec_2E_3C: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).

thf(c_2Earithmetic_2E_3C_3D,type,
    c_2Earithmetic_2E_3C_3D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).

thf(c_2Emin_2E_3D,type,
    c_2Emin_2E_3D: 
      !>[A_27a: $tType] : ( A_27a > A_27a > $o ) ).

thf(c_2Emin_2E_3D_3D_3E,type,
    c_2Emin_2E_3D_3D_3E: $o > $o > $o ).

thf(c_2Earithmetic_2E_3E,type,
    c_2Earithmetic_2E_3E: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).

thf(c_2Ebool_2E_3F,type,
    c_2Ebool_2E_3F: 
      !>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).

thf(c_2Epatricia_2EADD,type,
    c_2Epatricia_2EADD: 
      !>[A_27a: $tType] : ( ( tyop_2Epatricia_2Eptree @ A_27a ) > ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) > ( tyop_2Epatricia_2Eptree @ A_27a ) ) ).

thf(c_2Epatricia__casts_2EADD__LISTs,type,
    c_2Epatricia__casts_2EADD__LISTs: 
      !>[A_27a: $tType] : ( ( tyop_2Epatricia_2Eptree @ A_27a ) > ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ A_27a ) ) > ( tyop_2Epatricia_2Eptree @ A_27a ) ) ).

thf(c_2Epatricia__casts_2EADD__LISTw,type,
    c_2Epatricia__casts_2EADD__LISTw: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) > ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ A_27b ) ) > ( tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) ) ).

thf(c_2Epatricia__casts_2EADDs,type,
    c_2Epatricia__casts_2EADDs: 
      !>[A_27a: $tType] : ( ( tyop_2Epatricia_2Eptree @ A_27a ) > ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ A_27a ) > ( tyop_2Epatricia_2Eptree @ A_27a ) ) ).

thf(c_2Epatricia__casts_2EADDw,type,
    c_2Epatricia__casts_2EADDw: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) > ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ A_27b ) > ( tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) ) ).

thf(c_2Elist_2EAPPEND,type,
    c_2Elist_2EAPPEND: 
      !>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).

thf(c_2Earithmetic_2EBIT1,type,
    c_2Earithmetic_2EBIT1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Earithmetic_2EBIT2,type,
    c_2Earithmetic_2EBIT2: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Eind__type_2EBOTTOM,type,
    c_2Eind__type_2EBOTTOM: 
      !>[A_27a: $tType] : ( tyop_2Eind__type_2Erecspace @ A_27a ) ).

thf(c_2Estring_2ECHR,type,
    c_2Estring_2ECHR: tyop_2Enum_2Enum > tyop_2Estring_2Echar ).

thf(c_2Elist_2ECONS,type,
    c_2Elist_2ECONS: 
      !>[A_27a: $tType] : ( A_27a > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).

thf(c_2Eind__type_2ECONSTR,type,
    c_2Eind__type_2ECONSTR: 
      !>[A_27a: $tType] : ( tyop_2Enum_2Enum > A_27a > ( tyop_2Enum_2Enum > ( tyop_2Eind__type_2Erecspace @ A_27a ) ) > ( tyop_2Eind__type_2Erecspace @ A_27a ) ) ).

thf(c_2Ebool_2EDATATYPE,type,
    c_2Ebool_2EDATATYPE: 
      !>[A_27a: $tType] : ( A_27a > $o ) ).

thf(c_2Epatricia_2EDEPTH,type,
    c_2Epatricia_2EDEPTH: 
      !>[A_27a: $tType] : ( ( tyop_2Epatricia_2Eptree @ A_27a ) > tyop_2Enum_2Enum ) ).

thf(c_2Epatricia__casts_2EDEPTHw,type,
    c_2Epatricia__casts_2EDEPTHw: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) > tyop_2Enum_2Enum ) ).

thf(c_2Earithmetic_2EDIV,type,
    c_2Earithmetic_2EDIV: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Elist_2EEVERY,type,
    c_2Elist_2EEVERY: 
      !>[A_27a: $tType] : ( ( A_27a > $o ) > ( tyop_2Elist_2Elist @ A_27a ) > $o ) ).

thf(c_2Epatricia_2EEVERY__LEAF,type,
    c_2Epatricia_2EEVERY__LEAF: 
      !>[A_27a: $tType] : ( ( tyop_2Enum_2Enum > A_27a > $o ) > ( tyop_2Epatricia_2Eptree @ A_27a ) > $o ) ).

thf(c_2Epatricia__casts_2EEVERY__LEAFw,type,
    c_2Epatricia__casts_2EEVERY__LEAFw: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > A_27b > $o ) > ( tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) > $o ) ).

thf(c_2Epatricia_2EEXISTS__LEAF,type,
    c_2Epatricia_2EEXISTS__LEAF: 
      !>[A_27a: $tType] : ( ( tyop_2Enum_2Enum > A_27a > $o ) > ( tyop_2Epatricia_2Eptree @ A_27a ) > $o ) ).

thf(c_2Epatricia__casts_2EEXISTS__LEAFw,type,
    c_2Epatricia__casts_2EEXISTS__LEAFw: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > A_27b > $o ) > ( tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) > $o ) ).

thf(c_2Earithmetic_2EEXP,type,
    c_2Earithmetic_2EEXP: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Epatricia_2EEmpty,type,
    c_2Epatricia_2EEmpty: 
      !>[A_27a: $tType] : ( tyop_2Epatricia_2Eptree @ A_27a ) ).

thf(c_2Epatricia__casts_2EFINDs,type,
    c_2Epatricia__casts_2EFINDs: 
      !>[A_27a: $tType] : ( ( tyop_2Epatricia_2Eptree @ A_27a ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > A_27a ) ).

thf(c_2Epatricia__casts_2EFINDw,type,
    c_2Epatricia__casts_2EFINDw: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Epatricia__casts_2Eword__ptree @ A_27b @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27b ) > A_27a ) ).

thf(c_2Elist_2EFOLDL,type,
    c_2Elist_2EFOLDL: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27b > A_27a > A_27b ) > A_27b > ( tyop_2Elist_2Elist @ A_27a ) > A_27b ) ).

thf(c_2Epred__set_2EIMAGE,type,
    c_2Epred__set_2EIMAGE: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b ) > ( A_27a > $o ) > A_27b > $o ) ).

thf(c_2Ebool_2EIN,type,
    c_2Ebool_2EIN: 
      !>[A_27a: $tType] : ( A_27a > ( A_27a > $o ) > $o ) ).

thf(c_2Epatricia_2EINSERT__PTREE,type,
    c_2Epatricia_2EINSERT__PTREE: tyop_2Enum_2Enum > ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) > ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ).

thf(c_2Epatricia__casts_2EINSERT__PTREEs,type,
    c_2Epatricia__casts_2EINSERT__PTREEs: ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) > ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ).

thf(c_2Epatricia__casts_2EINSERT__PTREEw,type,
    c_2Epatricia__casts_2EINSERT__PTREEw: 
      !>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ tyop_2Eone_2Eone ) > ( tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ tyop_2Eone_2Eone ) ) ).

thf(c_2Epatricia_2EIN__PTREE,type,
    c_2Epatricia_2EIN__PTREE: tyop_2Enum_2Enum > ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) > $o ).

thf(c_2Epatricia__casts_2EIN__PTREEs,type,
    c_2Epatricia__casts_2EIN__PTREEs: ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) > $o ).

thf(c_2Epatricia__casts_2EIN__PTREEw,type,
    c_2Epatricia__casts_2EIN__PTREEw: 
      !>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ tyop_2Eone_2Eone ) > $o ) ).

thf(c_2Ecombin_2EK,type,
    c_2Ecombin_2EK: 
      !>[A_27a: $tType,A_27b: $tType] : ( A_27a > A_27b > A_27a ) ).

thf(c_2Epatricia__casts_2EKEYSs,type,
    c_2Epatricia__casts_2EKEYSs: 
      !>[A_27a: $tType] : ( ( tyop_2Epatricia_2Eptree @ A_27a ) > ( tyop_2Elist_2Elist @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) ) ).

thf(c_2Epatricia__casts_2EKEYSw,type,
    c_2Epatricia__casts_2EKEYSw: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) > ( tyop_2Elist_2Elist @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ) ).

thf(c_2Elist_2ELENGTH,type,
    c_2Elist_2ELENGTH: 
      !>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > tyop_2Enum_2Enum ) ).

thf(c_2Elist_2ELIST__TO__SET,type,
    c_2Elist_2ELIST__TO__SET: 
      !>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > A_27a > $o ) ).

thf(c_2Elogroot_2ELOG,type,
    c_2Elogroot_2ELOG: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Elist_2EMAP,type,
    c_2Elist_2EMAP: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > A_27b ) > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27b ) ) ).

thf(c_2Elist_2ENIL,type,
    c_2Elist_2ENIL: 
      !>[A_27a: $tType] : ( tyop_2Elist_2Elist @ A_27a ) ).

thf(c_2Earithmetic_2ENUMERAL,type,
    c_2Earithmetic_2ENUMERAL: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

thf(c_2Estring_2EORD,type,
    c_2Estring_2EORD: tyop_2Estring_2Echar > tyop_2Enum_2Enum ).

thf(c_2Epatricia_2EPEEK,type,
    c_2Epatricia_2EPEEK: 
      !>[A_27a: $tType] : ( ( tyop_2Epatricia_2Eptree @ A_27a ) > tyop_2Enum_2Enum > ( tyop_2Eoption_2Eoption @ A_27a ) ) ).

thf(c_2Epatricia__casts_2EPEEKs,type,
    c_2Epatricia__casts_2EPEEKs: 
      !>[A_27a: $tType] : ( ( tyop_2Epatricia_2Eptree @ A_27a ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > ( tyop_2Eoption_2Eoption @ A_27a ) ) ).

thf(c_2Epatricia__casts_2EPEEKw,type,
    c_2Epatricia__casts_2EPEEKw: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Eoption_2Eoption @ A_27b ) ) ).

thf(c_2Epatricia_2EPTREE__OF__NUMSET,type,
    c_2Epatricia_2EPTREE__OF__NUMSET: ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) > ( tyop_2Enum_2Enum > $o ) > ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ).

thf(c_2Epatricia__casts_2EPTREE__OF__STRINGSET,type,
    c_2Epatricia__casts_2EPTREE__OF__STRINGSET: ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) > ( ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > $o ) > ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ).

thf(c_2Epatricia__casts_2EPTREE__OF__WORDSET,type,
    c_2Epatricia__casts_2EPTREE__OF__WORDSET: 
      !>[A_27a: $tType] : ( ( tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ tyop_2Eone_2Eone ) > ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > $o ) > ( tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ tyop_2Eone_2Eone ) ) ).

thf(c_2Esorting_2EQSORT,type,
    c_2Esorting_2EQSORT: 
      !>[A_27a: $tType] : ( ( A_27a > A_27a > $o ) > ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).

thf(c_2Epatricia_2EREMOVE,type,
    c_2Epatricia_2EREMOVE: 
      !>[A_27a: $tType] : ( ( tyop_2Epatricia_2Eptree @ A_27a ) > tyop_2Enum_2Enum > ( tyop_2Epatricia_2Eptree @ A_27a ) ) ).

thf(c_2Epatricia__casts_2EREMOVEs,type,
    c_2Epatricia__casts_2EREMOVEs: 
      !>[A_27a: $tType] : ( ( tyop_2Epatricia_2Eptree @ A_27a ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > ( tyop_2Epatricia_2Eptree @ A_27a ) ) ).

thf(c_2Epatricia__casts_2EREMOVEw,type,
    c_2Epatricia__casts_2EREMOVEw: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) ) ).

thf(c_2Elist_2EREVERSE,type,
    c_2Elist_2EREVERSE: 
      !>[A_27a: $tType] : ( ( tyop_2Elist_2Elist @ A_27a ) > ( tyop_2Elist_2Elist @ A_27a ) ) ).

thf(c_2Epatricia_2ESIZE,type,
    c_2Epatricia_2ESIZE: 
      !>[A_27a: $tType] : ( ( tyop_2Epatricia_2Eptree @ A_27a ) > tyop_2Enum_2Enum ) ).

thf(c_2Epatricia__casts_2ESIZEw,type,
    c_2Epatricia__casts_2ESIZEw: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) > tyop_2Enum_2Enum ) ).

thf(c_2Epatricia__casts_2ESKIP1,type,
    c_2Epatricia__casts_2ESKIP1: ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ).

thf(c_2Epatricia__casts_2ESOME__PTREE,type,
    c_2Epatricia__casts_2ESOME__PTREE: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Epatricia_2Eptree @ A_27b ) > ( tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) ) ).

thf(c_2Epatricia__casts_2ESTRINGSET__OF__PTREE,type,
    c_2Epatricia__casts_2ESTRINGSET__OF__PTREE: ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > $o ).

thf(c_2Eoption_2ETHE,type,
    c_2Eoption_2ETHE: 
      !>[A_27a: $tType] : ( ( tyop_2Eoption_2Eoption @ A_27a ) > A_27a ) ).

thf(c_2Epatricia__casts_2ETHE__PTREE,type,
    c_2Epatricia__casts_2ETHE__PTREE: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Epatricia__casts_2Eword__ptree @ A_27b @ A_27a ) > ( tyop_2Epatricia_2Eptree @ A_27a ) ) ).

thf(c_2Epatricia_2ETRANSFORM,type,
    c_2Epatricia_2ETRANSFORM: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27b > A_27a ) > ( tyop_2Epatricia_2Eptree @ A_27b ) > ( tyop_2Epatricia_2Eptree @ A_27a ) ) ).

thf(c_2Epatricia__casts_2ETRANSFORMw,type,
    c_2Epatricia__casts_2ETRANSFORMw: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( A_27a > A_27b ) > ( tyop_2Epatricia__casts_2Eword__ptree @ A_27c @ A_27a ) > ( tyop_2Epatricia__casts_2Eword__ptree @ A_27c @ A_27b ) ) ).

thf(c_2Epatricia_2ETRAVERSE,type,
    c_2Epatricia_2ETRAVERSE: 
      !>[A_27a: $tType] : ( ( tyop_2Epatricia_2Eptree @ A_27a ) > ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ).

thf(c_2Epatricia__casts_2ETRAVERSEs,type,
    c_2Epatricia__casts_2ETRAVERSEs: 
      !>[A_27a: $tType] : ( ( tyop_2Epatricia_2Eptree @ A_27a ) > ( tyop_2Elist_2Elist @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) ) ).

thf(c_2Epatricia__casts_2ETRAVERSEw,type,
    c_2Epatricia__casts_2ETRAVERSEw: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) > ( tyop_2Elist_2Elist @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ) ).

thf(c_2Ebool_2ETYPE__DEFINITION,type,
    c_2Ebool_2ETYPE__DEFINITION: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > $o ) > ( A_27b > A_27a ) > $o ) ).

thf(c_2Epatricia_2EUNION__PTREE,type,
    c_2Epatricia_2EUNION__PTREE: ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) > ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) > ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ).

thf(c_2Epatricia__casts_2EUNION__PTREEw,type,
    c_2Epatricia__casts_2EUNION__PTREEw: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Epatricia__casts_2Eword__ptree @ A_27b @ tyop_2Eone_2Eone ) > ( tyop_2Epatricia__casts_2Eword__ptree @ A_27c @ tyop_2Eone_2Eone ) > ( tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ tyop_2Eone_2Eone ) ) ).

thf(c_2Epred__set_2EUNIV,type,
    c_2Epred__set_2EUNIV: 
      !>[A_27a: $tType] : ( A_27a > $o ) ).

thf(c_2Epatricia__casts_2EWORDSET__OF__PTREE,type,
    c_2Epatricia__casts_2EWORDSET__OF__PTREE: 
      !>[A_27a: $tType] : ( ( tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ tyop_2Eone_2Eone ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > $o ) ).

thf(c_2Epatricia__casts_2EWordEmpty,type,
    c_2Epatricia__casts_2EWordEmpty: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) ).

thf(c_2Epatricia__casts_2EWord__ptree,type,
    c_2Epatricia__casts_2EWord__ptree: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > tyop_2Eone_2Eone ) > ( tyop_2Epatricia_2Eptree @ A_27b ) > ( tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) ) ).

thf(c_2Earithmetic_2EZERO,type,
    c_2Earithmetic_2EZERO: tyop_2Enum_2Enum ).

thf(c_2Ebool_2E_5C_2F,type,
    c_2Ebool_2E_5C_2F: $o > $o > $o ).

thf(c_2Enumposrep_2El2n,type,
    c_2Enumposrep_2El2n: tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

thf(c_2EASCIInumbers_2En2s,type,
    c_2EASCIInumbers_2En2s: tyop_2Enum_2Enum > ( tyop_2Enum_2Enum > tyop_2Estring_2Echar ) > tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ).

thf(c_2Ewords_2En2w,type,
    c_2Ewords_2En2w: 
      !>[A_27a: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) ) ).

thf(c_2Epatricia__casts_2Enum__to__string,type,
    c_2Epatricia__casts_2Enum__to__string: tyop_2Enum_2Enum > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ).

thf(c_2Eone_2Eone,type,
    c_2Eone_2Eone: tyop_2Eone_2Eone ).

thf(c_2Epatricia_2Eptree__size,type,
    c_2Epatricia_2Eptree__size: 
      !>[A_27a: $tType] : ( ( A_27a > tyop_2Enum_2Enum ) > ( tyop_2Epatricia_2Eptree @ A_27a ) > tyop_2Enum_2Enum ) ).

thf(c_2EASCIInumbers_2Es2n,type,
    c_2EASCIInumbers_2Es2n: tyop_2Enum_2Enum > ( tyop_2Estring_2Echar > tyop_2Enum_2Enum ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > tyop_2Enum_2Enum ).

thf(c_2Estring_2Estring__lt,type,
    c_2Estring_2Estring__lt: ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > $o ).

thf(c_2Epatricia__casts_2Estring__to__num,type,
    c_2Epatricia__casts_2Estring__to__num: ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > tyop_2Enum_2Enum ).

thf(c_2Ewords_2Ew2n,type,
    c_2Ewords_2Ew2n: 
      !>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > tyop_2Enum_2Enum ) ).

thf(c_2Ewords_2Eword__lo,type,
    c_2Ewords_2Eword__lo: 
      !>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > $o ) ).

thf(c_2Epatricia__casts_2Eword__ptree__CASE,type,
    c_2Epatricia__casts_2Eword__ptree__CASE: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) > ( ( A_27a > tyop_2Eone_2Eone ) > ( tyop_2Epatricia_2Eptree @ A_27b ) > A_27c ) > A_27c ) ).

thf(c_2Epatricia__casts_2Eword__ptree__size,type,
    c_2Epatricia__casts_2Eword__ptree__size: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27a > tyop_2Enum_2Enum ) > ( A_27b > tyop_2Enum_2Enum ) > ( tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) > tyop_2Enum_2Enum ) ).

thf(c_2Ebool_2E_7E,type,
    c_2Ebool_2E_7E: $o > $o ).

thf(logicdef_2E_2F_5C,axiom,
    ! [V0: $o,V1: $o] :
      ( ( c_2Ebool_2E_2F_5C @ V0 @ V1 )
    <=> ( V0
        & V1 ) ) ).

thf(logicdef_2E_5C_2F,axiom,
    ! [V0: $o,V1: $o] :
      ( ( c_2Ebool_2E_5C_2F @ V0 @ V1 )
    <=> ( V0
        | V1 ) ) ).

thf(logicdef_2E_7E,axiom,
    ! [V0: $o] :
      ( ( c_2Ebool_2E_7E @ V0 )
    <=> ( (~) @ V0 ) ) ).

thf(logicdef_2E_3D_3D_3E,axiom,
    ! [V0: $o,V1: $o] :
      ( ( c_2Emin_2E_3D_3D_3E @ V0 @ V1 )
    <=> ( V0
       => V1 ) ) ).

thf(logicdef_2E_3D,axiom,
    ! [A_27a: $tType,V0: A_27a,V1: A_27a] :
      ( ( c_2Emin_2E_3D @ A_27a @ V0 @ V1 )
    <=> ( V0 = V1 ) ) ).

thf(quantdef_2E_21,axiom,
    ! [A_27a: $tType,V0f: A_27a > $o] :
      ( ( c_2Ebool_2E_21 @ A_27a @ V0f )
    <=> ! [V1x: A_27a] : ( V0f @ V1x ) ) ).

thf(quantdef_2E_3F,axiom,
    ! [A_27a: $tType,V0f: A_27a > $o] :
      ( ( c_2Ebool_2E_3F @ A_27a @ V0f )
    <=> ? [V1x: A_27a] : ( V0f @ V1x ) ) ).

thf(thm_2Epatricia__casts_2ESKIP1__def,axiom,
    ! [V0c: tyop_2Estring_2Echar,V1s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( c_2Epatricia__casts_2ESKIP1 @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ V0c @ V1s ) )
      = V1s ) ).

thf(thm_2Epatricia__casts_2Estring__to__num__def,axiom,
    ! [V0s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( c_2Epatricia__casts_2Estring__to__num @ V0s )
      = ( c_2EASCIInumbers_2Es2n @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ c_2Estring_2EORD @ ( c_2Elist_2ECONS @ tyop_2Estring_2Echar @ ( c_2Estring_2ECHR @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ V0s ) ) ) ).

thf(thm_2Epatricia__casts_2Enum__to__string__def,axiom,
    ! [V0n: tyop_2Enum_2Enum] :
      ( ( c_2Epatricia__casts_2Enum__to__string @ V0n )
      = ( c_2Epatricia__casts_2ESKIP1 @ ( c_2EASCIInumbers_2En2s @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ c_2Estring_2ECHR @ V0n ) ) ) ).

thf(thm_2Epatricia__casts_2EPEEKs__def,axiom,
    ! [A_27a: $tType,V0t: tyop_2Epatricia_2Eptree @ A_27a,V1w: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( c_2Epatricia__casts_2EPEEKs @ A_27a @ V0t @ V1w )
      = ( c_2Epatricia_2EPEEK @ A_27a @ V0t @ ( c_2Epatricia__casts_2Estring__to__num @ V1w ) ) ) ).

thf(thm_2Epatricia__casts_2EFINDs__def,axiom,
    ! [A_27a: $tType,V0t: tyop_2Epatricia_2Eptree @ A_27a,V1w: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( c_2Epatricia__casts_2EFINDs @ A_27a @ V0t @ V1w )
      = ( c_2Eoption_2ETHE @ A_27a @ ( c_2Epatricia__casts_2EPEEKs @ A_27a @ V0t @ V1w ) ) ) ).

thf(thm_2Epatricia__casts_2EADDs__def,axiom,
    ! [A_27a: $tType,V0t: tyop_2Epatricia_2Eptree @ A_27a,V1w: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V2d: A_27a] :
      ( ( c_2Epatricia__casts_2EADDs @ A_27a @ V0t @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ A_27a @ V1w @ V2d ) )
      = ( c_2Epatricia_2EADD @ A_27a @ V0t @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ A_27a @ ( c_2Epatricia__casts_2Estring__to__num @ V1w ) @ V2d ) ) ) ).

thf(thm_2Epatricia__casts_2EADD__LISTs__def,axiom,
    ! [A_27a: $tType] :
      ( ( c_2Epatricia__casts_2EADD__LISTs @ A_27a )
      = ( c_2Elist_2EFOLDL @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia__casts_2EADDs @ A_27a ) ) ) ).

thf(thm_2Epatricia__casts_2EREMOVEs__def,axiom,
    ! [A_27a: $tType,V0t: tyop_2Epatricia_2Eptree @ A_27a,V1w: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( c_2Epatricia__casts_2EREMOVEs @ A_27a @ V0t @ V1w )
      = ( c_2Epatricia_2EREMOVE @ A_27a @ V0t @ ( c_2Epatricia__casts_2Estring__to__num @ V1w ) ) ) ).

thf(thm_2Epatricia__casts_2ETRAVERSEs__def,axiom,
    ! [A_27a: $tType,V0t: tyop_2Epatricia_2Eptree @ A_27a] :
      ( ( c_2Epatricia__casts_2ETRAVERSEs @ A_27a @ V0t )
      = ( c_2Elist_2EMAP @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ c_2Epatricia__casts_2Enum__to__string @ ( c_2Epatricia_2ETRAVERSE @ A_27a @ V0t ) ) ) ).

thf(thm_2Epatricia__casts_2EKEYSs__def,axiom,
    ! [A_27a: $tType,V0t: tyop_2Epatricia_2Eptree @ A_27a] :
      ( ( c_2Epatricia__casts_2EKEYSs @ A_27a @ V0t )
      = ( c_2Esorting_2EQSORT @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ c_2Estring_2Estring__lt @ ( c_2Epatricia__casts_2ETRAVERSEs @ A_27a @ V0t ) ) ) ).

thf(thm_2Epatricia__casts_2EIN__PTREEs__def,axiom,
    ! [V0w: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V1t: tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone] :
      ( ( c_2Epatricia__casts_2EIN__PTREEs @ V0w @ V1t )
      = ( c_2Epatricia_2EIN__PTREE @ ( c_2Epatricia__casts_2Estring__to__num @ V0w ) @ V1t ) ) ).

thf(thm_2Epatricia__casts_2EINSERT__PTREEs__def,axiom,
    ! [V0w: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V1t: tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone] :
      ( ( c_2Epatricia__casts_2EINSERT__PTREEs @ V0w @ V1t )
      = ( c_2Epatricia_2EINSERT__PTREE @ ( c_2Epatricia__casts_2Estring__to__num @ V0w ) @ V1t ) ) ).

thf(thm_2Epatricia__casts_2ESTRINGSET__OF__PTREE__def,axiom,
    ! [V0t: tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone] :
      ( ( c_2Epatricia__casts_2ESTRINGSET__OF__PTREE @ V0t )
      = ( c_2Elist_2ELIST__TO__SET @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ ( c_2Epatricia__casts_2ETRAVERSEs @ tyop_2Eone_2Eone @ V0t ) ) ) ).

thf(thm_2Epatricia__casts_2EPTREE__OF__STRINGSET__def,axiom,
    ! [V0t: tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone,V1s: ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) > $o] :
      ( ( c_2Epatricia__casts_2EPTREE__OF__STRINGSET @ V0t @ V1s )
      = ( c_2Epatricia_2EPTREE__OF__NUMSET @ V0t @ ( c_2Epred__set_2EIMAGE @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2Enum_2Enum @ c_2Epatricia__casts_2Estring__to__num @ V1s ) ) ) ).

thf(thm_2Epatricia__casts_2Eword__ptree__TY__DEF,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
    ? [V0rep: ( tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) > ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ ( A_27a > tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) )] :
      ( c_2Ebool_2ETYPE__DEFINITION @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ ( A_27a > tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) ) @ ( tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b )
      @ ^ [V1a0_27: tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ ( A_27a > tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) )] :
          ( c_2Ebool_2E_21 @ ( ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ ( A_27a > tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) ) > $o )
          @ ^ [V2_27word__ptree_27: ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ ( A_27a > tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) ) > $o] :
              ( c_2Emin_2E_3D_3D_3E
              @ ( c_2Ebool_2E_21 @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ ( A_27a > tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) )
                @ ^ [V3a0_27: tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ ( A_27a > tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) )] :
                    ( c_2Emin_2E_3D_3D_3E
                    @ ( c_2Ebool_2E_3F @ ( A_27a > tyop_2Eone_2Eone )
                      @ ^ [V4a0: A_27a > tyop_2Eone_2Eone] :
                          ( c_2Ebool_2E_3F @ ( tyop_2Epatricia_2Eptree @ A_27b )
                          @ ^ [V5a1: tyop_2Epatricia_2Eptree @ A_27b] :
                              ( c_2Emin_2E_3D @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ ( A_27a > tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) ) @ V3a0_27
                              @ ( ^ [V6a0: A_27a > tyop_2Eone_2Eone,V7a1: tyop_2Epatricia_2Eptree @ A_27b] :
                                    ( c_2Eind__type_2ECONSTR @ ( tyop_2Epair_2Eprod @ ( A_27a > tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) @ c_2Enum_2E0 @ ( c_2Epair_2E_2C @ ( A_27a > tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ V6a0 @ V7a1 )
                                    @ ^ [V8n: tyop_2Enum_2Enum] : ( c_2Eind__type_2EBOTTOM @ ( tyop_2Epair_2Eprod @ ( A_27a > tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) ) )
                                @ V4a0
                                @ V5a1 ) ) ) )
                    @ ( V2_27word__ptree_27 @ V3a0_27 ) ) )
              @ ( V2_27word__ptree_27 @ V1a0_27 ) ) )
      @ V0rep ) ).

thf(thm_2Epatricia__casts_2Eword__ptree__case__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0a0: A_27a > tyop_2Eone_2Eone,V1a1: tyop_2Epatricia_2Eptree @ A_27b,V2f: ( A_27a > tyop_2Eone_2Eone ) > ( tyop_2Epatricia_2Eptree @ A_27b ) > A_27c] :
      ( ( c_2Epatricia__casts_2Eword__ptree__CASE @ A_27a @ A_27b @ A_27c @ ( c_2Epatricia__casts_2EWord__ptree @ A_27a @ A_27b @ V0a0 @ V1a1 ) @ V2f )
      = ( V2f @ V0a0 @ V1a1 ) ) ).

thf(thm_2Epatricia__casts_2Eword__ptree__size__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f: A_27a > tyop_2Enum_2Enum,V1f1: A_27b > tyop_2Enum_2Enum,V2a0: A_27a > tyop_2Eone_2Eone,V3a1: tyop_2Epatricia_2Eptree @ A_27b] :
      ( ( c_2Epatricia__casts_2Eword__ptree__size @ A_27a @ A_27b @ V0f @ V1f1 @ ( c_2Epatricia__casts_2EWord__ptree @ A_27a @ A_27b @ V2a0 @ V3a1 ) )
      = ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Epatricia_2Eptree__size @ A_27b @ V1f1 @ V3a1 ) ) ) ).

thf(thm_2Epatricia__casts_2ETHE__PTREE__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0a: A_27b > tyop_2Eone_2Eone,V1t: tyop_2Epatricia_2Eptree @ A_27a] :
      ( ( c_2Epatricia__casts_2ETHE__PTREE @ A_27a @ A_27b @ ( c_2Epatricia__casts_2EWord__ptree @ A_27b @ A_27a @ V0a @ V1t ) )
      = V1t ) ).

thf(thm_2Epatricia__casts_2ESOME__PTREE__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0t: tyop_2Epatricia_2Eptree @ A_27b] :
      ( ( c_2Epatricia__casts_2ESOME__PTREE @ A_27a @ A_27b @ V0t )
      = ( c_2Epatricia__casts_2EWord__ptree @ A_27a @ A_27b @ ( c_2Ecombin_2EK @ tyop_2Eone_2Eone @ A_27a @ c_2Eone_2Eone ) @ V0t ) ) ).

thf(thm_2Epatricia__casts_2EWordEmpty__def,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ( c_2Epatricia__casts_2EWordEmpty @ A_27a @ A_27b )
      = ( c_2Epatricia__casts_2ESOME__PTREE @ A_27a @ A_27b @ ( c_2Epatricia_2EEmpty @ A_27b ) ) ) ).

thf(thm_2Epatricia__casts_2EPEEKw__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0t: tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
      ( ( c_2Epatricia__casts_2EPEEKw @ A_27a @ A_27b @ V0t @ V1w )
      = ( c_2Epatricia_2EPEEK @ A_27b @ ( c_2Epatricia__casts_2ETHE__PTREE @ A_27b @ A_27a @ V0t ) @ ( c_2Ewords_2Ew2n @ A_27a @ V1w ) ) ) ).

thf(thm_2Epatricia__casts_2EFINDw__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0t: tyop_2Epatricia__casts_2Eword__ptree @ A_27b @ A_27a,V1w: tyop_2Efcp_2Ecart @ $o @ A_27b] :
      ( ( c_2Epatricia__casts_2EFINDw @ A_27a @ A_27b @ V0t @ V1w )
      = ( c_2Eoption_2ETHE @ A_27a @ ( c_2Epatricia__casts_2EPEEKw @ A_27b @ A_27a @ V0t @ V1w ) ) ) ).

thf(thm_2Epatricia__casts_2EADDw__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0t: tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a,V2d: A_27b] :
      ( ( c_2Epatricia__casts_2EADDw @ A_27a @ A_27b @ V0t @ ( c_2Epair_2E_2C @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ A_27b @ V1w @ V2d ) )
      = ( c_2Epatricia__casts_2ESOME__PTREE @ A_27a @ A_27b @ ( c_2Epatricia_2EADD @ A_27b @ ( c_2Epatricia__casts_2ETHE__PTREE @ A_27b @ A_27a @ V0t ) @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ A_27b @ ( c_2Ewords_2Ew2n @ A_27a @ V1w ) @ V2d ) ) ) ) ).

thf(thm_2Epatricia__casts_2EADD__LISTw__def,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ( c_2Epatricia__casts_2EADD__LISTw @ A_27a @ A_27b )
      = ( c_2Elist_2EFOLDL @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ A_27b ) @ ( tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) @ ( c_2Epatricia__casts_2EADDw @ A_27a @ A_27b ) ) ) ).

thf(thm_2Epatricia__casts_2EREMOVEw__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0t: tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b,V1w: tyop_2Efcp_2Ecart @ $o @ A_27a] :
      ( ( c_2Epatricia__casts_2EREMOVEw @ A_27a @ A_27b @ V0t @ V1w )
      = ( c_2Epatricia__casts_2ESOME__PTREE @ A_27a @ A_27b @ ( c_2Epatricia_2EREMOVE @ A_27b @ ( c_2Epatricia__casts_2ETHE__PTREE @ A_27b @ A_27a @ V0t ) @ ( c_2Ewords_2Ew2n @ A_27a @ V1w ) ) ) ) ).

thf(thm_2Epatricia__casts_2ETRAVERSEw__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0t: tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b] :
      ( ( c_2Epatricia__casts_2ETRAVERSEw @ A_27a @ A_27b @ V0t )
      = ( c_2Elist_2EMAP @ tyop_2Enum_2Enum @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Ewords_2En2w @ A_27a ) @ ( c_2Epatricia_2ETRAVERSE @ A_27b @ ( c_2Epatricia__casts_2ETHE__PTREE @ A_27b @ A_27a @ V0t ) ) ) ) ).

thf(thm_2Epatricia__casts_2EKEYSw__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0t: tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b] :
      ( ( c_2Epatricia__casts_2EKEYSw @ A_27a @ A_27b @ V0t )
      = ( c_2Esorting_2EQSORT @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Ewords_2Eword__lo @ A_27a ) @ ( c_2Epatricia__casts_2ETRAVERSEw @ A_27a @ A_27b @ V0t ) ) ) ).

thf(thm_2Epatricia__casts_2ETRANSFORMw__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f: A_27a > A_27b,V1t: tyop_2Epatricia__casts_2Eword__ptree @ A_27c @ A_27a] :
      ( ( c_2Epatricia__casts_2ETRANSFORMw @ A_27a @ A_27b @ A_27c @ V0f @ V1t )
      = ( c_2Epatricia__casts_2ESOME__PTREE @ A_27c @ A_27b @ ( c_2Epatricia_2ETRANSFORM @ A_27b @ A_27a @ V0f @ ( c_2Epatricia__casts_2ETHE__PTREE @ A_27a @ A_27c @ V1t ) ) ) ) ).

thf(thm_2Epatricia__casts_2EEVERY__LEAFw__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P: ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > A_27b > $o,V1t: tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b] :
      ( ( c_2Epatricia__casts_2EEVERY__LEAFw @ A_27a @ A_27b @ V0P @ V1t )
      = ( c_2Epatricia_2EEVERY__LEAF @ A_27b
        @ ^ [V2k: tyop_2Enum_2Enum,V3d: A_27b] : ( V0P @ ( c_2Ewords_2En2w @ A_27a @ V2k ) @ V3d )
        @ ( c_2Epatricia__casts_2ETHE__PTREE @ A_27b @ A_27a @ V1t ) ) ) ).

thf(thm_2Epatricia__casts_2EEXISTS__LEAFw__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P: ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > A_27b > $o,V1t: tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b] :
      ( ( c_2Epatricia__casts_2EEXISTS__LEAFw @ A_27a @ A_27b @ V0P @ V1t )
      = ( c_2Epatricia_2EEXISTS__LEAF @ A_27b
        @ ^ [V2k: tyop_2Enum_2Enum,V3d: A_27b] : ( V0P @ ( c_2Ewords_2En2w @ A_27a @ V2k ) @ V3d )
        @ ( c_2Epatricia__casts_2ETHE__PTREE @ A_27b @ A_27a @ V1t ) ) ) ).

thf(thm_2Epatricia__casts_2ESIZEw__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0t: tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b] :
      ( ( c_2Epatricia__casts_2ESIZEw @ A_27a @ A_27b @ V0t )
      = ( c_2Epatricia_2ESIZE @ A_27b @ ( c_2Epatricia__casts_2ETHE__PTREE @ A_27b @ A_27a @ V0t ) ) ) ).

thf(thm_2Epatricia__casts_2EDEPTHw__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0t: tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b] :
      ( ( c_2Epatricia__casts_2EDEPTHw @ A_27a @ A_27b @ V0t )
      = ( c_2Epatricia_2EDEPTH @ A_27b @ ( c_2Epatricia__casts_2ETHE__PTREE @ A_27b @ A_27a @ V0t ) ) ) ).

thf(thm_2Epatricia__casts_2EIN__PTREEw__def,axiom,
    ! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1t: tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ tyop_2Eone_2Eone] :
      ( ( c_2Epatricia__casts_2EIN__PTREEw @ A_27a @ V0w @ V1t )
      = ( c_2Epatricia_2EIN__PTREE @ ( c_2Ewords_2Ew2n @ A_27a @ V0w ) @ ( c_2Epatricia__casts_2ETHE__PTREE @ tyop_2Eone_2Eone @ A_27a @ V1t ) ) ) ).

thf(thm_2Epatricia__casts_2EINSERT__PTREEw__def,axiom,
    ! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1t: tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ tyop_2Eone_2Eone] :
      ( ( c_2Epatricia__casts_2EINSERT__PTREEw @ A_27a @ V0w @ V1t )
      = ( c_2Epatricia__casts_2ESOME__PTREE @ A_27a @ tyop_2Eone_2Eone @ ( c_2Epatricia_2EINSERT__PTREE @ ( c_2Ewords_2Ew2n @ A_27a @ V0w ) @ ( c_2Epatricia__casts_2ETHE__PTREE @ tyop_2Eone_2Eone @ A_27a @ V1t ) ) ) ) ).

thf(thm_2Epatricia__casts_2EWORDSET__OF__PTREE__def,axiom,
    ! [A_27a: $tType,V0t: tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ tyop_2Eone_2Eone] :
      ( ( c_2Epatricia__casts_2EWORDSET__OF__PTREE @ A_27a @ V0t )
      = ( c_2Elist_2ELIST__TO__SET @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ ( c_2Epatricia__casts_2ETRAVERSEw @ A_27a @ tyop_2Eone_2Eone @ V0t ) ) ) ).

thf(thm_2Epatricia__casts_2EUNION__PTREEw__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0t1: tyop_2Epatricia__casts_2Eword__ptree @ A_27b @ tyop_2Eone_2Eone,V1t2: tyop_2Epatricia__casts_2Eword__ptree @ A_27c @ tyop_2Eone_2Eone] :
      ( ( c_2Epatricia__casts_2EUNION__PTREEw @ A_27a @ A_27b @ A_27c @ V0t1 @ V1t2 )
      = ( c_2Epatricia__casts_2ESOME__PTREE @ A_27a @ tyop_2Eone_2Eone @ ( c_2Epatricia_2EUNION__PTREE @ ( c_2Epatricia__casts_2ETHE__PTREE @ tyop_2Eone_2Eone @ A_27b @ V0t1 ) @ ( c_2Epatricia__casts_2ETHE__PTREE @ tyop_2Eone_2Eone @ A_27c @ V1t2 ) ) ) ) ).

thf(thm_2Epatricia__casts_2EPTREE__OF__WORDSET__def,axiom,
    ! [A_27a: $tType,V0t: tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ tyop_2Eone_2Eone,V1s: ( tyop_2Efcp_2Ecart @ $o @ A_27a ) > $o] :
      ( ( c_2Epatricia__casts_2EPTREE__OF__WORDSET @ A_27a @ V0t @ V1s )
      = ( c_2Epatricia__casts_2ESOME__PTREE @ A_27a @ tyop_2Eone_2Eone @ ( c_2Epatricia_2EPTREE__OF__NUMSET @ ( c_2Epatricia__casts_2ETHE__PTREE @ tyop_2Eone_2Eone @ A_27a @ V0t ) @ ( c_2Epred__set_2EIMAGE @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ tyop_2Enum_2Enum @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1s ) ) ) ) ).

thf(thm_2Epatricia__casts_2Edatatype__word__ptree,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0word__ptree: ( ( A_27a > tyop_2Eone_2Eone ) > ( tyop_2Epatricia_2Eptree @ A_27b ) > ( tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) ) > $o] : ( c_2Ebool_2EDATATYPE @ $o @ ( V0word__ptree @ ( c_2Epatricia__casts_2EWord__ptree @ A_27a @ A_27b ) ) ) ).

thf(thm_2Epatricia__casts_2Eword__ptree__11,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0a0: A_27a > tyop_2Eone_2Eone,V1a1: tyop_2Epatricia_2Eptree @ A_27b,V2a0_27: A_27a > tyop_2Eone_2Eone,V3a1_27: tyop_2Epatricia_2Eptree @ A_27b] :
      ( ( ( c_2Epatricia__casts_2EWord__ptree @ A_27a @ A_27b @ V0a0 @ V1a1 )
        = ( c_2Epatricia__casts_2EWord__ptree @ A_27a @ A_27b @ V2a0_27 @ V3a1_27 ) )
    <=> ( ( V0a0 = V2a0_27 )
        & ( V1a1 = V3a1_27 ) ) ) ).

thf(thm_2Epatricia__casts_2Eword__ptree__nchotomy,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0ww: tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b] :
    ? [V1f: A_27a > tyop_2Eone_2Eone,V2p: tyop_2Epatricia_2Eptree @ A_27b] :
      ( V0ww
      = ( c_2Epatricia__casts_2EWord__ptree @ A_27a @ A_27b @ V1f @ V2p ) ) ).

thf(thm_2Epatricia__casts_2Eword__ptree__Axiom,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f: ( A_27a > tyop_2Eone_2Eone ) > ( tyop_2Epatricia_2Eptree @ A_27b ) > A_27c] :
    ? [V1fn: ( tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) > A_27c] :
    ! [V2a0: A_27a > tyop_2Eone_2Eone,V3a1: tyop_2Epatricia_2Eptree @ A_27b] :
      ( ( V1fn @ ( c_2Epatricia__casts_2EWord__ptree @ A_27a @ A_27b @ V2a0 @ V3a1 ) )
      = ( V0f @ V2a0 @ V3a1 ) ) ).

thf(thm_2Epatricia__casts_2Eword__ptree__induction,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P: ( tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) > $o] :
      ( ! [V1f: A_27a > tyop_2Eone_2Eone,V2p: tyop_2Epatricia_2Eptree @ A_27b] : ( V0P @ ( c_2Epatricia__casts_2EWord__ptree @ A_27a @ A_27b @ V1f @ V2p ) )
     => ! [V3w: tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b] : ( V0P @ V3w ) ) ).

thf(thm_2Epatricia__casts_2Eword__ptree__case__cong,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_27: ( A_27a > tyop_2Eone_2Eone ) > ( tyop_2Epatricia_2Eptree @ A_27b ) > A_27c,V1M: tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b,V2M_27: tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b,V3f: ( A_27a > tyop_2Eone_2Eone ) > ( tyop_2Epatricia_2Eptree @ A_27b ) > A_27c] :
      ( ( ( V1M = V2M_27 )
        & ! [V4a0: A_27a > tyop_2Eone_2Eone,V5a1: tyop_2Epatricia_2Eptree @ A_27b] :
            ( ( V2M_27
              = ( c_2Epatricia__casts_2EWord__ptree @ A_27a @ A_27b @ V4a0 @ V5a1 ) )
           => ( ( V3f @ V4a0 @ V5a1 )
              = ( V0f_27 @ V4a0 @ V5a1 ) ) ) )
     => ( ( c_2Epatricia__casts_2Eword__ptree__CASE @ A_27a @ A_27b @ A_27c @ V1M @ V3f )
        = ( c_2Epatricia__casts_2Eword__ptree__CASE @ A_27a @ A_27b @ A_27c @ V2M_27 @ V0f_27 ) ) ) ).

thf(thm_2Epatricia__casts_2Eword__ptree__case__eq,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0x: tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b,V1v: A_27c,V2f: ( A_27a > tyop_2Eone_2Eone ) > ( tyop_2Epatricia_2Eptree @ A_27b ) > A_27c] :
      ( ( ( c_2Epatricia__casts_2Eword__ptree__CASE @ A_27a @ A_27b @ A_27c @ V0x @ V2f )
        = V1v )
    <=> ? [V3f_27: A_27a > tyop_2Eone_2Eone,V4p: tyop_2Epatricia_2Eptree @ A_27b] :
          ( ( V0x
            = ( c_2Epatricia__casts_2EWord__ptree @ A_27a @ A_27b @ V3f_27 @ V4p ) )
          & ( ( V2f @ V3f_27 @ V4p )
            = V1v ) ) ) ).

thf(thm_2Epatricia__casts_2EADD__INSERT__STRING,axiom,
    ! [V0w: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V1v: tyop_2Eone_2Eone,V2t: tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone] :
      ( ( c_2Epatricia__casts_2EADDs @ tyop_2Eone_2Eone @ V2t @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2Eone_2Eone @ V0w @ V1v ) )
      = ( c_2Epatricia__casts_2EADDs @ tyop_2Eone_2Eone @ V2t @ ( c_2Epair_2E_2C @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2Eone_2Eone @ V0w @ c_2Eone_2Eone ) ) ) ).

thf(thm_2Epatricia__casts_2El2n__APPEND,axiom,
    ! [V0b: tyop_2Enum_2Enum,V1l1: tyop_2Elist_2Elist @ tyop_2Enum_2Enum,V2l2: tyop_2Elist_2Elist @ tyop_2Enum_2Enum] :
      ( ( c_2Enumposrep_2El2n @ V0b @ ( c_2Elist_2EAPPEND @ tyop_2Enum_2Enum @ V1l1 @ V2l2 ) )
      = ( c_2Earithmetic_2E_2B @ ( c_2Enumposrep_2El2n @ V0b @ V1l1 ) @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2EEXP @ V0b @ ( c_2Elist_2ELENGTH @ tyop_2Enum_2Enum @ V1l1 ) ) @ ( c_2Enumposrep_2El2n @ V0b @ V2l2 ) ) ) ) ).

thf(thm_2Epatricia__casts_2El2n__LENGTH,axiom,
    ! [V0b: tyop_2Enum_2Enum,V1l: tyop_2Elist_2Elist @ tyop_2Enum_2Enum] :
      ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0b )
     => ( c_2Eprim__rec_2E_3C @ ( c_2Enumposrep_2El2n @ V0b @ V1l ) @ ( c_2Earithmetic_2EEXP @ V0b @ ( c_2Elist_2ELENGTH @ tyop_2Enum_2Enum @ V1l ) ) ) ) ).

thf(thm_2Epatricia__casts_2El2n__11,axiom,
    ! [V0b: tyop_2Enum_2Enum,V1l1: tyop_2Elist_2Elist @ tyop_2Enum_2Enum,V2l2: tyop_2Elist_2Elist @ tyop_2Enum_2Enum] :
      ( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0b )
        & ( c_2Elist_2EEVERY @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2E_3E @ V0b ) @ V1l1 )
        & ( c_2Elist_2EEVERY @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2E_3E @ V0b ) @ V2l2 ) )
     => ( ( ( c_2Enumposrep_2El2n @ V0b @ ( c_2Elist_2EAPPEND @ tyop_2Enum_2Enum @ V1l1 @ ( c_2Elist_2ECONS @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Elist_2ENIL @ tyop_2Enum_2Enum ) ) ) )
          = ( c_2Enumposrep_2El2n @ V0b @ ( c_2Elist_2EAPPEND @ tyop_2Enum_2Enum @ V2l2 @ ( c_2Elist_2ECONS @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Elist_2ENIL @ tyop_2Enum_2Enum ) ) ) ) )
      <=> ( V1l1 = V2l2 ) ) ) ).

thf(thm_2Epatricia__casts_2EEVERY__MAP__ORD,axiom,
    ! [V0l: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] : ( c_2Elist_2EEVERY @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2E_3E @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) @ ( c_2Elist_2EMAP @ tyop_2Estring_2Echar @ tyop_2Enum_2Enum @ c_2Estring_2EORD @ V0l ) ) ).

thf(thm_2Epatricia__casts_2EMAP__11,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f: A_27a > A_27b,V1l1: tyop_2Elist_2Elist @ A_27a,V2l2: tyop_2Elist_2Elist @ A_27a] :
      ( ! [V3x: A_27a,V4y: A_27a] :
          ( ( ( V0f @ V3x )
            = ( V0f @ V4y ) )
        <=> ( V3x = V4y ) )
     => ( ( ( c_2Elist_2EMAP @ A_27a @ A_27b @ V0f @ V1l1 )
          = ( c_2Elist_2EMAP @ A_27a @ A_27b @ V0f @ V2l2 ) )
      <=> ( V1l1 = V2l2 ) ) ) ).

thf(thm_2Epatricia__casts_2EREVERSE__11,axiom,
    ! [A_27a: $tType,V0l1: tyop_2Elist_2Elist @ A_27a,V1l2: tyop_2Elist_2Elist @ A_27a] :
      ( ( ( c_2Elist_2EREVERSE @ A_27a @ V0l1 )
        = ( c_2Elist_2EREVERSE @ A_27a @ V1l2 ) )
    <=> ( V0l1 = V1l2 ) ) ).

thf(thm_2Epatricia__casts_2Estring__to__num__11,axiom,
    ! [V0s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar,V1t: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( ( c_2Epatricia__casts_2Estring__to__num @ V0s )
        = ( c_2Epatricia__casts_2Estring__to__num @ V1t ) )
    <=> ( V0s = V1t ) ) ).

thf(thm_2Epatricia__casts_2EIMAGE__string__to__num,axiom,
    ! [V0n: tyop_2Enum_2Enum] :
      ( ( ( V0n
          = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
        | ( ( c_2Earithmetic_2E_3C_3D @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ V0n )
          & ( ( c_2Earithmetic_2EDIV @ V0n @ ( c_2Earithmetic_2EEXP @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ ( c_2Elogroot_2ELOG @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) @ V0n ) ) )
            = ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
    <=> ( c_2Ebool_2EIN @ tyop_2Enum_2Enum @ V0n @ ( c_2Epred__set_2EIMAGE @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2Enum_2Enum @ c_2Epatricia__casts_2Estring__to__num @ ( c_2Epred__set_2EUNIV @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) ) ) ) ).

thf(thm_2Epatricia__casts_2Estring__to__num__num__to__string,axiom,
    ! [V0n: tyop_2Enum_2Enum] :
      ( ( c_2Ebool_2EIN @ tyop_2Enum_2Enum @ V0n @ ( c_2Epred__set_2EIMAGE @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) @ tyop_2Enum_2Enum @ c_2Epatricia__casts_2Estring__to__num @ ( c_2Epred__set_2EUNIV @ ( tyop_2Elist_2Elist @ tyop_2Estring_2Echar ) ) ) )
     => ( ( c_2Epatricia__casts_2Estring__to__num @ ( c_2Epatricia__casts_2Enum__to__string @ V0n ) )
        = V0n ) ) ).

thf(thm_2Epatricia__casts_2Enum__to__string__string__to__num,axiom,
    ! [V0s: tyop_2Elist_2Elist @ tyop_2Estring_2Echar] :
      ( ( c_2Epatricia__casts_2Enum__to__string @ ( c_2Epatricia__casts_2Estring__to__num @ V0s ) )
      = V0s ) ).

thf(thm_2Epatricia__casts_2EADD__INSERT__WORD,axiom,
    ! [A_27a: $tType,V0w: tyop_2Efcp_2Ecart @ $o @ A_27a,V1v: tyop_2Eone_2Eone,V2t: tyop_2Epatricia__casts_2Eword__ptree @ A_27a @ tyop_2Eone_2Eone] :
      ( ( c_2Epatricia__casts_2EADDw @ A_27a @ tyop_2Eone_2Eone @ V2t @ ( c_2Epair_2E_2C @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ tyop_2Eone_2Eone @ V0w @ V1v ) )
      = ( c_2Epatricia__casts_2EADDw @ A_27a @ tyop_2Eone_2Eone @ V2t @ ( c_2Epair_2E_2C @ ( tyop_2Efcp_2Ecart @ $o @ A_27a ) @ tyop_2Eone_2Eone @ V0w @ c_2Eone_2Eone ) ) ) ).

thf(thm_2Epatricia__casts_2ETHE__PTREE__SOME__PTREE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0t: tyop_2Epatricia_2Eptree @ A_27a] :
      ( ( c_2Epatricia__casts_2ETHE__PTREE @ A_27a @ A_27b @ ( c_2Epatricia__casts_2ESOME__PTREE @ A_27b @ A_27a @ V0t ) )
      = V0t ) ).

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