ITP001 Axioms: ITP112^7.ax
%------------------------------------------------------------------------------
% File : ITP112^7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : 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 ) ).
%------------------------------------------------------------------------------