ITP001 Axioms: ITP112^5.ax
%------------------------------------------------------------------------------
% File : ITP112^5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 set theory export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : patricia_casts^2.ax [Gau20]
% : HL4112^5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 134 ( 13 unt; 39 typ; 0 def)
% Number of atoms : 1426 ( 63 equ; 0 cnn)
% Maximal formula atoms : 110 ( 10 avg)
% Number of connectives : 2225 ( 0 ~; 1 |; 12 &;2115 @)
% ( 12 <=>; 85 =>; 0 <=; 0 <~>)
% Maximal formula depth : 49 ( 9 avg;2115 nst)
% Number of types : 1 ( 0 usr)
% Number of type conns : 55 ( 55 >; 0 *; 0 +; 0 <<)
% Number of symbols : 134 ( 133 usr; 101 con; 0-3 aty)
% Number of variables : 256 ( 12 ^ 238 !; 6 ?; 256 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tp_ty_2Epatricia__casts_2Eword__ptree,type,
ty_2Epatricia__casts_2Eword__ptree: del > del > del ).
thf(tp_c_2Epatricia__casts_2EADD__LISTs,type,
c_2Epatricia__casts_2EADD__LISTs: del > $i ).
thf(mem_c_2Epatricia__casts_2EADD__LISTs,axiom,
! [A_27a: del] : ( mem @ ( c_2Epatricia__casts_2EADD__LISTs @ A_27a ) @ ( arr @ ( ty_2Epatricia_2Eptree @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ A_27a ) ) @ ( ty_2Epatricia_2Eptree @ A_27a ) ) ) ) ).
thf(tp_c_2Epatricia__casts_2EADD__LISTw,type,
c_2Epatricia__casts_2EADD__LISTw: del > del > $i ).
thf(mem_c_2Epatricia__casts_2EADD__LISTw,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epatricia__casts_2EADD__LISTw @ A_27a @ A_27b ) @ ( arr @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) @ ( arr @ ( ty_2Elist_2Elist @ ( ty_2Epair_2Eprod @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ A_27b ) ) @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) ) ) ) ).
thf(tp_c_2Epatricia__casts_2EADDs,type,
c_2Epatricia__casts_2EADDs: del > $i ).
thf(mem_c_2Epatricia__casts_2EADDs,axiom,
! [A_27a: del] : ( mem @ ( c_2Epatricia__casts_2EADDs @ A_27a ) @ ( arr @ ( ty_2Epatricia_2Eptree @ A_27a ) @ ( arr @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ A_27a ) @ ( ty_2Epatricia_2Eptree @ A_27a ) ) ) ) ).
thf(tp_c_2Epatricia__casts_2EADDw,type,
c_2Epatricia__casts_2EADDw: del > del > $i ).
thf(mem_c_2Epatricia__casts_2EADDw,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epatricia__casts_2EADDw @ A_27a @ A_27b ) @ ( arr @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) @ ( arr @ ( ty_2Epair_2Eprod @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ A_27b ) @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) ) ) ) ).
thf(tp_c_2Epatricia__casts_2EDEPTHw,type,
c_2Epatricia__casts_2EDEPTHw: del > del > $i ).
thf(mem_c_2Epatricia__casts_2EDEPTHw,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epatricia__casts_2EDEPTHw @ A_27a @ A_27b ) @ ( arr @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) @ ty_2Enum_2Enum ) ) ).
thf(tp_c_2Epatricia__casts_2EEVERY__LEAFw,type,
c_2Epatricia__casts_2EEVERY__LEAFw: del > del > $i ).
thf(mem_c_2Epatricia__casts_2EEVERY__LEAFw,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epatricia__casts_2EEVERY__LEAFw @ A_27a @ A_27b ) @ ( arr @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ A_27b @ bool ) ) @ ( arr @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) @ bool ) ) ) ).
thf(tp_c_2Epatricia__casts_2EEXISTS__LEAFw,type,
c_2Epatricia__casts_2EEXISTS__LEAFw: del > del > $i ).
thf(mem_c_2Epatricia__casts_2EEXISTS__LEAFw,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epatricia__casts_2EEXISTS__LEAFw @ A_27a @ A_27b ) @ ( arr @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ A_27b @ bool ) ) @ ( arr @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) @ bool ) ) ) ).
thf(tp_c_2Epatricia__casts_2EFINDs,type,
c_2Epatricia__casts_2EFINDs: del > $i ).
thf(mem_c_2Epatricia__casts_2EFINDs,axiom,
! [A_27a: del] : ( mem @ ( c_2Epatricia__casts_2EFINDs @ A_27a ) @ ( arr @ ( ty_2Epatricia_2Eptree @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ A_27a ) ) ) ).
thf(tp_c_2Epatricia__casts_2EFINDw,type,
c_2Epatricia__casts_2EFINDw: del > del > $i ).
thf(mem_c_2Epatricia__casts_2EFINDw,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epatricia__casts_2EFINDw @ A_27a @ A_27b ) @ ( arr @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27b @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) @ A_27a ) ) ) ).
thf(tp_c_2Epatricia__casts_2EINSERT__PTREEs,type,
c_2Epatricia__casts_2EINSERT__PTREEs: $i ).
thf(mem_c_2Epatricia__casts_2EINSERT__PTREEs,axiom,
mem @ c_2Epatricia__casts_2EINSERT__PTREEs @ ( arr @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ( arr @ ( ty_2Epatricia_2Eptree @ ty_2Eone_2Eone ) @ ( ty_2Epatricia_2Eptree @ ty_2Eone_2Eone ) ) ) ).
thf(tp_c_2Epatricia__casts_2EINSERT__PTREEw,type,
c_2Epatricia__casts_2EINSERT__PTREEw: del > $i ).
thf(mem_c_2Epatricia__casts_2EINSERT__PTREEw,axiom,
! [A_27a: del] : ( mem @ ( c_2Epatricia__casts_2EINSERT__PTREEw @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ ty_2Eone_2Eone ) @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ ty_2Eone_2Eone ) ) ) ) ).
thf(tp_c_2Epatricia__casts_2EIN__PTREEs,type,
c_2Epatricia__casts_2EIN__PTREEs: $i ).
thf(mem_c_2Epatricia__casts_2EIN__PTREEs,axiom,
mem @ c_2Epatricia__casts_2EIN__PTREEs @ ( arr @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ( arr @ ( ty_2Epatricia_2Eptree @ ty_2Eone_2Eone ) @ bool ) ) ).
thf(tp_c_2Epatricia__casts_2EIN__PTREEw,type,
c_2Epatricia__casts_2EIN__PTREEw: del > $i ).
thf(mem_c_2Epatricia__casts_2EIN__PTREEw,axiom,
! [A_27a: del] : ( mem @ ( c_2Epatricia__casts_2EIN__PTREEw @ A_27a ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ ty_2Eone_2Eone ) @ bool ) ) ) ).
thf(tp_c_2Epatricia__casts_2EKEYSs,type,
c_2Epatricia__casts_2EKEYSs: del > $i ).
thf(mem_c_2Epatricia__casts_2EKEYSs,axiom,
! [A_27a: del] : ( mem @ ( c_2Epatricia__casts_2EKEYSs @ A_27a ) @ ( arr @ ( ty_2Epatricia_2Eptree @ A_27a ) @ ( ty_2Elist_2Elist @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) ) ) ).
thf(tp_c_2Epatricia__casts_2EKEYSw,type,
c_2Epatricia__casts_2EKEYSw: del > del > $i ).
thf(mem_c_2Epatricia__casts_2EKEYSw,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epatricia__casts_2EKEYSw @ A_27a @ A_27b ) @ ( arr @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) @ ( ty_2Elist_2Elist @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Epatricia__casts_2EPEEKs,type,
c_2Epatricia__casts_2EPEEKs: del > $i ).
thf(mem_c_2Epatricia__casts_2EPEEKs,axiom,
! [A_27a: del] : ( mem @ ( c_2Epatricia__casts_2EPEEKs @ A_27a ) @ ( arr @ ( ty_2Epatricia_2Eptree @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ( ty_2Eoption_2Eoption @ A_27a ) ) ) ) ).
thf(tp_c_2Epatricia__casts_2EPEEKw,type,
c_2Epatricia__casts_2EPEEKw: del > del > $i ).
thf(mem_c_2Epatricia__casts_2EPEEKw,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epatricia__casts_2EPEEKw @ A_27a @ A_27b ) @ ( arr @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Eoption_2Eoption @ A_27b ) ) ) ) ).
thf(tp_c_2Epatricia__casts_2EPTREE__OF__STRINGSET,type,
c_2Epatricia__casts_2EPTREE__OF__STRINGSET: $i ).
thf(mem_c_2Epatricia__casts_2EPTREE__OF__STRINGSET,axiom,
mem @ c_2Epatricia__casts_2EPTREE__OF__STRINGSET @ ( arr @ ( ty_2Epatricia_2Eptree @ ty_2Eone_2Eone ) @ ( arr @ ( arr @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ bool ) @ ( ty_2Epatricia_2Eptree @ ty_2Eone_2Eone ) ) ) ).
thf(tp_c_2Epatricia__casts_2EPTREE__OF__WORDSET,type,
c_2Epatricia__casts_2EPTREE__OF__WORDSET: del > $i ).
thf(mem_c_2Epatricia__casts_2EPTREE__OF__WORDSET,axiom,
! [A_27a: del] : ( mem @ ( c_2Epatricia__casts_2EPTREE__OF__WORDSET @ A_27a ) @ ( arr @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ ty_2Eone_2Eone ) @ ( arr @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool ) @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ ty_2Eone_2Eone ) ) ) ) ).
thf(tp_c_2Epatricia__casts_2EREMOVEs,type,
c_2Epatricia__casts_2EREMOVEs: del > $i ).
thf(mem_c_2Epatricia__casts_2EREMOVEs,axiom,
! [A_27a: del] : ( mem @ ( c_2Epatricia__casts_2EREMOVEs @ A_27a ) @ ( arr @ ( ty_2Epatricia_2Eptree @ A_27a ) @ ( arr @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ( ty_2Epatricia_2Eptree @ A_27a ) ) ) ) ).
thf(tp_c_2Epatricia__casts_2EREMOVEw,type,
c_2Epatricia__casts_2EREMOVEw: del > del > $i ).
thf(mem_c_2Epatricia__casts_2EREMOVEw,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epatricia__casts_2EREMOVEw @ A_27a @ A_27b ) @ ( arr @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) ) ) ) ).
thf(tp_c_2Epatricia__casts_2ESIZEw,type,
c_2Epatricia__casts_2ESIZEw: del > del > $i ).
thf(mem_c_2Epatricia__casts_2ESIZEw,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epatricia__casts_2ESIZEw @ A_27a @ A_27b ) @ ( arr @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) @ ty_2Enum_2Enum ) ) ).
thf(tp_c_2Epatricia__casts_2ESKIP1,type,
c_2Epatricia__casts_2ESKIP1: $i ).
thf(mem_c_2Epatricia__casts_2ESKIP1,axiom,
mem @ c_2Epatricia__casts_2ESKIP1 @ ( arr @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) ).
thf(tp_c_2Epatricia__casts_2ESOME__PTREE,type,
c_2Epatricia__casts_2ESOME__PTREE: del > del > $i ).
thf(mem_c_2Epatricia__casts_2ESOME__PTREE,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epatricia__casts_2ESOME__PTREE @ A_27a @ A_27b ) @ ( arr @ ( ty_2Epatricia_2Eptree @ A_27b ) @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) ) ) ).
thf(tp_c_2Epatricia__casts_2ESTRINGSET__OF__PTREE,type,
c_2Epatricia__casts_2ESTRINGSET__OF__PTREE: $i ).
thf(mem_c_2Epatricia__casts_2ESTRINGSET__OF__PTREE,axiom,
mem @ c_2Epatricia__casts_2ESTRINGSET__OF__PTREE @ ( arr @ ( ty_2Epatricia_2Eptree @ ty_2Eone_2Eone ) @ ( arr @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ bool ) ) ).
thf(tp_c_2Epatricia__casts_2ETHE__PTREE,type,
c_2Epatricia__casts_2ETHE__PTREE: del > del > $i ).
thf(mem_c_2Epatricia__casts_2ETHE__PTREE,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epatricia__casts_2ETHE__PTREE @ A_27a @ A_27b ) @ ( arr @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27b @ A_27a ) @ ( ty_2Epatricia_2Eptree @ A_27a ) ) ) ).
thf(tp_c_2Epatricia__casts_2ETRANSFORMw,type,
c_2Epatricia__casts_2ETRANSFORMw: del > del > del > $i ).
thf(mem_c_2Epatricia__casts_2ETRANSFORMw,axiom,
! [A_27a: del,A_27b: del,A_27c: del] : ( mem @ ( c_2Epatricia__casts_2ETRANSFORMw @ A_27a @ A_27b @ A_27c ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27c @ A_27a ) @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27c @ A_27b ) ) ) ) ).
thf(tp_c_2Epatricia__casts_2ETRAVERSEs,type,
c_2Epatricia__casts_2ETRAVERSEs: del > $i ).
thf(mem_c_2Epatricia__casts_2ETRAVERSEs,axiom,
! [A_27a: del] : ( mem @ ( c_2Epatricia__casts_2ETRAVERSEs @ A_27a ) @ ( arr @ ( ty_2Epatricia_2Eptree @ A_27a ) @ ( ty_2Elist_2Elist @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) ) ) ).
thf(tp_c_2Epatricia__casts_2ETRAVERSEw,type,
c_2Epatricia__casts_2ETRAVERSEw: del > del > $i ).
thf(mem_c_2Epatricia__casts_2ETRAVERSEw,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epatricia__casts_2ETRAVERSEw @ A_27a @ A_27b ) @ ( arr @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) @ ( ty_2Elist_2Elist @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ) ) ).
thf(tp_c_2Epatricia__casts_2EUNION__PTREEw,type,
c_2Epatricia__casts_2EUNION__PTREEw: del > del > del > $i ).
thf(mem_c_2Epatricia__casts_2EUNION__PTREEw,axiom,
! [A_27a: del,A_27b: del,A_27c: del] : ( mem @ ( c_2Epatricia__casts_2EUNION__PTREEw @ A_27a @ A_27b @ A_27c ) @ ( arr @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27b @ ty_2Eone_2Eone ) @ ( arr @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27c @ ty_2Eone_2Eone ) @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ ty_2Eone_2Eone ) ) ) ) ).
thf(tp_c_2Epatricia__casts_2EWORDSET__OF__PTREE,type,
c_2Epatricia__casts_2EWORDSET__OF__PTREE: del > $i ).
thf(mem_c_2Epatricia__casts_2EWORDSET__OF__PTREE,axiom,
! [A_27a: del] : ( mem @ ( c_2Epatricia__casts_2EWORDSET__OF__PTREE @ A_27a ) @ ( arr @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ ty_2Eone_2Eone ) @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool ) ) ) ).
thf(tp_c_2Epatricia__casts_2EWordEmpty,type,
c_2Epatricia__casts_2EWordEmpty: del > del > $i ).
thf(mem_c_2Epatricia__casts_2EWordEmpty,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epatricia__casts_2EWordEmpty @ A_27a @ A_27b ) @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) ) ).
thf(tp_c_2Epatricia__casts_2EWord__ptree,type,
c_2Epatricia__casts_2EWord__ptree: del > del > $i ).
thf(mem_c_2Epatricia__casts_2EWord__ptree,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epatricia__casts_2EWord__ptree @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ty_2Eone_2Eone ) @ ( arr @ ( ty_2Epatricia_2Eptree @ A_27b ) @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) ) ) ) ).
thf(tp_c_2Epatricia__casts_2Enum__to__string,type,
c_2Epatricia__casts_2Enum__to__string: $i ).
thf(mem_c_2Epatricia__casts_2Enum__to__string,axiom,
mem @ c_2Epatricia__casts_2Enum__to__string @ ( arr @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) ).
thf(tp_c_2Epatricia__casts_2Estring__to__num,type,
c_2Epatricia__casts_2Estring__to__num: $i ).
thf(mem_c_2Epatricia__casts_2Estring__to__num,axiom,
mem @ c_2Epatricia__casts_2Estring__to__num @ ( arr @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ty_2Enum_2Enum ) ).
thf(stp_fo_c_2Epatricia__casts_2Estring__to__num,type,
fo__c_2Epatricia__casts_2Estring__to__num: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar > tp__ty_2Enum_2Enum ).
thf(stp_eq_fo_c_2Epatricia__casts_2Estring__to__num,axiom,
! [X0: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar] :
( ( inj__ty_2Enum_2Enum @ ( fo__c_2Epatricia__casts_2Estring__to__num @ X0 ) )
= ( ap @ c_2Epatricia__casts_2Estring__to__num @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ X0 ) ) ) ).
thf(tp_c_2Epatricia__casts_2Eword__ptree__CASE,type,
c_2Epatricia__casts_2Eword__ptree__CASE: del > del > del > $i ).
thf(mem_c_2Epatricia__casts_2Eword__ptree__CASE,axiom,
! [A_27a: del,A_27b: del,A_27c: del] : ( mem @ ( c_2Epatricia__casts_2Eword__ptree__CASE @ A_27a @ A_27b @ A_27c ) @ ( arr @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) @ ( arr @ ( arr @ ( arr @ A_27a @ ty_2Eone_2Eone ) @ ( arr @ ( ty_2Epatricia_2Eptree @ A_27b ) @ A_27c ) ) @ A_27c ) ) ) ).
thf(tp_c_2Epatricia__casts_2Eword__ptree__size,type,
c_2Epatricia__casts_2Eword__ptree__size: del > del > $i ).
thf(mem_c_2Epatricia__casts_2Eword__ptree__size,axiom,
! [A_27a: del,A_27b: del] : ( mem @ ( c_2Epatricia__casts_2Eword__ptree__size @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ ty_2Enum_2Enum ) @ ( arr @ ( arr @ A_27b @ ty_2Enum_2Enum ) @ ( arr @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) @ ty_2Enum_2Enum ) ) ) ) ).
thf(ax_thm_2Epatricia__casts_2ESKIP1__def,axiom,
! [V0c: tp__ty_2Estring_2Echar,V1s: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar] :
( ( surj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ ( ap @ c_2Epatricia__casts_2ESKIP1 @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Estring_2Echar ) @ ( inj__ty_2Estring_2Echar @ V0c ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V1s ) ) ) )
= V1s ) ).
thf(ax_thm_2Epatricia__casts_2Estring__to__num__def,axiom,
! [V0s: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar] :
( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Epatricia__casts_2Estring__to__num @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V0s ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ c_2EASCIInumbers_2Es2n @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) @ c_2Estring_2EORD ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Estring_2Echar ) @ ( ap @ c_2Estring_2ECHR @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V0s ) ) ) ) ) ).
thf(ax_thm_2Epatricia__casts_2Enum__to__string__def,axiom,
! [V0n: tp__ty_2Enum_2Enum] :
( ( surj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ ( ap @ c_2Epatricia__casts_2Enum__to__string @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
= ( surj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ ( ap @ c_2Epatricia__casts_2ESKIP1 @ ( ap @ ( ap @ ( ap @ c_2EASCIInumbers_2En2s @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) @ c_2Estring_2ECHR ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) ) ).
thf(ax_thm_2Epatricia__casts_2EPEEKs__def,axiom,
! [A_27a: del,V0t: $i] :
( ( mem @ V0t @ ( ty_2Epatricia_2Eptree @ A_27a ) )
=> ! [V1w: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar] :
( ( ap @ ( ap @ ( c_2Epatricia__casts_2EPEEKs @ A_27a ) @ V0t ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V1w ) )
= ( ap @ ( ap @ ( c_2Epatricia_2EPEEK @ A_27a ) @ V0t ) @ ( ap @ c_2Epatricia__casts_2Estring__to__num @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V1w ) ) ) ) ) ).
thf(ax_thm_2Epatricia__casts_2EFINDs__def,axiom,
! [A_27a: del,V0t: $i] :
( ( mem @ V0t @ ( ty_2Epatricia_2Eptree @ A_27a ) )
=> ! [V1w: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar] :
( ( ap @ ( ap @ ( c_2Epatricia__casts_2EFINDs @ A_27a ) @ V0t ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V1w ) )
= ( ap @ ( c_2Eoption_2ETHE @ A_27a ) @ ( ap @ ( ap @ ( c_2Epatricia__casts_2EPEEKs @ A_27a ) @ V0t ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V1w ) ) ) ) ) ).
thf(ax_thm_2Epatricia__casts_2EADDs__def,axiom,
! [A_27a: del,V0t: $i] :
( ( mem @ V0t @ ( ty_2Epatricia_2Eptree @ A_27a ) )
=> ! [V1w: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar,V2d: $i] :
( ( mem @ V2d @ A_27a )
=> ( ( ap @ ( ap @ ( c_2Epatricia__casts_2EADDs @ A_27a ) @ V0t ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ A_27a ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V1w ) ) @ V2d ) )
= ( ap @ ( ap @ ( c_2Epatricia_2EADD @ A_27a ) @ V0t ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ A_27a ) @ ( ap @ c_2Epatricia__casts_2Estring__to__num @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V1w ) ) ) @ V2d ) ) ) ) ) ).
thf(ax_thm_2Epatricia__casts_2EADD__LISTs__def,axiom,
! [A_27a: del] :
( ( c_2Epatricia__casts_2EADD__LISTs @ A_27a )
= ( ap @ ( c_2Elist_2EFOLDL @ ( ty_2Epair_2Eprod @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ A_27a ) @ ( ty_2Epatricia_2Eptree @ A_27a ) ) @ ( c_2Epatricia__casts_2EADDs @ A_27a ) ) ) ).
thf(ax_thm_2Epatricia__casts_2EREMOVEs__def,axiom,
! [A_27a: del,V0t: $i] :
( ( mem @ V0t @ ( ty_2Epatricia_2Eptree @ A_27a ) )
=> ! [V1w: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar] :
( ( ap @ ( ap @ ( c_2Epatricia__casts_2EREMOVEs @ A_27a ) @ V0t ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V1w ) )
= ( ap @ ( ap @ ( c_2Epatricia_2EREMOVE @ A_27a ) @ V0t ) @ ( ap @ c_2Epatricia__casts_2Estring__to__num @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V1w ) ) ) ) ) ).
thf(ax_thm_2Epatricia__casts_2ETRAVERSEs__def,axiom,
! [A_27a: del,V0t: $i] :
( ( mem @ V0t @ ( ty_2Epatricia_2Eptree @ A_27a ) )
=> ( ( surj__c_ty_2Elist_2Elist_c_ty_2Elist_2Elist_ty_2Estring_2Echar @ ( ap @ ( c_2Epatricia__casts_2ETRAVERSEs @ A_27a ) @ V0t ) )
= ( surj__c_ty_2Elist_2Elist_c_ty_2Elist_2Elist_ty_2Estring_2Echar @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ ty_2Enum_2Enum @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) @ c_2Epatricia__casts_2Enum__to__string ) @ ( ap @ ( c_2Epatricia_2ETRAVERSE @ A_27a ) @ V0t ) ) ) ) ) ).
thf(ax_thm_2Epatricia__casts_2EKEYSs__def,axiom,
! [A_27a: del,V0t: $i] :
( ( mem @ V0t @ ( ty_2Epatricia_2Eptree @ A_27a ) )
=> ( ( surj__c_ty_2Elist_2Elist_c_ty_2Elist_2Elist_ty_2Estring_2Echar @ ( ap @ ( c_2Epatricia__casts_2EKEYSs @ A_27a ) @ V0t ) )
= ( surj__c_ty_2Elist_2Elist_c_ty_2Elist_2Elist_ty_2Estring_2Echar @ ( ap @ ( ap @ ( c_2Esorting_2EQSORT @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) @ c_2Estring_2Estring__lt ) @ ( ap @ ( c_2Epatricia__casts_2ETRAVERSEs @ A_27a ) @ V0t ) ) ) ) ) ).
thf(ax_thm_2Epatricia__casts_2EIN__PTREEs__def,axiom,
! [V0w: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar,V1t: tp__c_ty_2Epatricia_2Eptree_ty_2Eone_2Eone] :
( ( p @ ( ap @ ( ap @ c_2Epatricia__casts_2EIN__PTREEs @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V0w ) ) @ ( inj__c_ty_2Epatricia_2Eptree_ty_2Eone_2Eone @ V1t ) ) )
<=> ( p @ ( ap @ ( ap @ c_2Epatricia_2EIN__PTREE @ ( ap @ c_2Epatricia__casts_2Estring__to__num @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V0w ) ) ) @ ( inj__c_ty_2Epatricia_2Eptree_ty_2Eone_2Eone @ V1t ) ) ) ) ).
thf(ax_thm_2Epatricia__casts_2EINSERT__PTREEs__def,axiom,
! [V0w: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar,V1t: tp__c_ty_2Epatricia_2Eptree_ty_2Eone_2Eone] :
( ( surj__c_ty_2Epatricia_2Eptree_ty_2Eone_2Eone @ ( ap @ ( ap @ c_2Epatricia__casts_2EINSERT__PTREEs @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V0w ) ) @ ( inj__c_ty_2Epatricia_2Eptree_ty_2Eone_2Eone @ V1t ) ) )
= ( surj__c_ty_2Epatricia_2Eptree_ty_2Eone_2Eone @ ( ap @ ( ap @ c_2Epatricia_2EINSERT__PTREE @ ( ap @ c_2Epatricia__casts_2Estring__to__num @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V0w ) ) ) @ ( inj__c_ty_2Epatricia_2Eptree_ty_2Eone_2Eone @ V1t ) ) ) ) ).
thf(ax_thm_2Epatricia__casts_2ESTRINGSET__OF__PTREE__def,axiom,
! [V0t: tp__c_ty_2Epatricia_2Eptree_ty_2Eone_2Eone] :
( ( ap @ c_2Epatricia__casts_2ESTRINGSET__OF__PTREE @ ( inj__c_ty_2Epatricia_2Eptree_ty_2Eone_2Eone @ V0t ) )
= ( ap @ ( c_2Elist_2ELIST__TO__SET @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) @ ( ap @ ( c_2Epatricia__casts_2ETRAVERSEs @ ty_2Eone_2Eone ) @ ( inj__c_ty_2Epatricia_2Eptree_ty_2Eone_2Eone @ V0t ) ) ) ) ).
thf(ax_thm_2Epatricia__casts_2EPTREE__OF__STRINGSET__def,axiom,
! [V0t: tp__c_ty_2Epatricia_2Eptree_ty_2Eone_2Eone,V1s: $i] :
( ( mem @ V1s @ ( arr @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ bool ) )
=> ( ( surj__c_ty_2Epatricia_2Eptree_ty_2Eone_2Eone @ ( ap @ ( ap @ c_2Epatricia__casts_2EPTREE__OF__STRINGSET @ ( inj__c_ty_2Epatricia_2Eptree_ty_2Eone_2Eone @ V0t ) ) @ V1s ) )
= ( surj__c_ty_2Epatricia_2Eptree_ty_2Eone_2Eone @ ( ap @ ( ap @ c_2Epatricia_2EPTREE__OF__NUMSET @ ( inj__c_ty_2Epatricia_2Eptree_ty_2Eone_2Eone @ V0t ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ty_2Enum_2Enum ) @ c_2Epatricia__casts_2Estring__to__num ) @ V1s ) ) ) ) ) ).
thf(ax_thm_2Epatricia__casts_2Eword__ptree__TY__DEF,axiom,
! [A_27a: del,A_27b: del] :
? [V0rep: $i] :
( ( mem @ V0rep @ ( arr @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ ty_2Eone_2Eone ) @ ( ty_2Epatricia_2Eptree @ A_27b ) ) ) ) )
& ( p
@ ( ap
@ ( ap @ ( c_2Ebool_2ETYPE__DEFINITION @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ ty_2Eone_2Eone ) @ ( ty_2Epatricia_2Eptree @ A_27b ) ) ) @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) )
@ ( lam @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ ty_2Eone_2Eone ) @ ( ty_2Epatricia_2Eptree @ A_27b ) ) )
@ ^ [V1a0_27: $i] :
( ap @ ( c_2Ebool_2E_21 @ ( arr @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ ty_2Eone_2Eone ) @ ( ty_2Epatricia_2Eptree @ A_27b ) ) ) @ bool ) )
@ ( lam @ ( arr @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ ty_2Eone_2Eone ) @ ( ty_2Epatricia_2Eptree @ A_27b ) ) ) @ bool )
@ ^ [V2_27word__ptree_27: $i] :
( ap
@ ( ap @ c_2Emin_2E_3D_3D_3E
@ ( ap @ ( c_2Ebool_2E_21 @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ ty_2Eone_2Eone ) @ ( ty_2Epatricia_2Eptree @ A_27b ) ) ) )
@ ( lam @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ ty_2Eone_2Eone ) @ ( ty_2Epatricia_2Eptree @ A_27b ) ) )
@ ^ [V3a0_27: $i] :
( ap
@ ( ap @ c_2Emin_2E_3D_3D_3E
@ ( ap @ ( c_2Ebool_2E_3F @ ( arr @ A_27a @ ty_2Eone_2Eone ) )
@ ( lam @ ( arr @ A_27a @ ty_2Eone_2Eone )
@ ^ [V4a0: $i] :
( ap @ ( c_2Ebool_2E_3F @ ( ty_2Epatricia_2Eptree @ A_27b ) )
@ ( lam @ ( ty_2Epatricia_2Eptree @ A_27b )
@ ^ [V5a1: $i] :
( ap @ ( ap @ ( c_2Emin_2E_3D @ ( ty_2Eind__type_2Erecspace @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ ty_2Eone_2Eone ) @ ( ty_2Epatricia_2Eptree @ A_27b ) ) ) ) @ V3a0_27 )
@ ( ap
@ ( ap
@ ( lam @ ( arr @ A_27a @ ty_2Eone_2Eone )
@ ^ [V6a0: $i] :
( lam @ ( ty_2Epatricia_2Eptree @ A_27b )
@ ^ [V7a1: $i] :
( ap @ ( ap @ ( ap @ ( c_2Eind__type_2ECONSTR @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ ty_2Eone_2Eone ) @ ( ty_2Epatricia_2Eptree @ A_27b ) ) ) @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( arr @ A_27a @ ty_2Eone_2Eone ) @ ( ty_2Epatricia_2Eptree @ A_27b ) ) @ V6a0 ) @ V7a1 ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V8n: $i] : ( c_2Eind__type_2EBOTTOM @ ( ty_2Epair_2Eprod @ ( arr @ A_27a @ ty_2Eone_2Eone ) @ ( ty_2Epatricia_2Eptree @ A_27b ) ) ) ) ) ) )
@ V4a0 )
@ V5a1 ) ) ) ) ) ) )
@ ( ap @ V2_27word__ptree_27 @ V3a0_27 ) ) ) ) )
@ ( ap @ V2_27word__ptree_27 @ V1a0_27 ) ) ) ) ) )
@ V0rep ) ) ) ).
thf(ax_thm_2Epatricia__casts_2Eword__ptree__case__def,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0a0: $i] :
( ( mem @ V0a0 @ ( arr @ A_27a @ ty_2Eone_2Eone ) )
=> ! [V1a1: $i] :
( ( mem @ V1a1 @ ( ty_2Epatricia_2Eptree @ A_27b ) )
=> ! [V2f: $i] :
( ( mem @ V2f @ ( arr @ ( arr @ A_27a @ ty_2Eone_2Eone ) @ ( arr @ ( ty_2Epatricia_2Eptree @ A_27b ) @ A_27c ) ) )
=> ( ( ap @ ( ap @ ( c_2Epatricia__casts_2Eword__ptree__CASE @ A_27a @ A_27b @ A_27c ) @ ( ap @ ( ap @ ( c_2Epatricia__casts_2EWord__ptree @ A_27a @ A_27b ) @ V0a0 ) @ V1a1 ) ) @ V2f )
= ( ap @ ( ap @ V2f @ V0a0 ) @ V1a1 ) ) ) ) ) ).
thf(ax_thm_2Epatricia__casts_2Eword__ptree__size__def,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ ty_2Enum_2Enum ) )
=> ! [V1f1: $i] :
( ( mem @ V1f1 @ ( arr @ A_27b @ ty_2Enum_2Enum ) )
=> ! [V2a0: $i] :
( ( mem @ V2a0 @ ( arr @ A_27a @ ty_2Eone_2Eone ) )
=> ! [V3a1: $i] :
( ( mem @ V3a1 @ ( ty_2Epatricia_2Eptree @ A_27b ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ ( ap @ ( c_2Epatricia__casts_2Eword__ptree__size @ A_27a @ A_27b ) @ V0f ) @ V1f1 ) @ ( ap @ ( ap @ ( c_2Epatricia__casts_2EWord__ptree @ A_27a @ A_27b ) @ V2a0 ) @ V3a1 ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( ap @ ( ap @ ( c_2Epatricia_2Eptree__size @ A_27b ) @ V1f1 ) @ V3a1 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Epatricia__casts_2Edatatype__word__ptree,axiom,
! [A_27a: del,A_27b: del,V0word__ptree: $i] :
( ( mem @ V0word__ptree @ ( arr @ ( arr @ ( arr @ A_27a @ ty_2Eone_2Eone ) @ ( arr @ ( ty_2Epatricia_2Eptree @ A_27b ) @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) ) ) @ bool ) )
=> ( p @ ( ap @ ( c_2Ebool_2EDATATYPE @ bool ) @ ( ap @ V0word__ptree @ ( c_2Epatricia__casts_2EWord__ptree @ A_27a @ A_27b ) ) ) ) ) ).
thf(conj_thm_2Epatricia__casts_2Eword__ptree__11,axiom,
! [A_27a: del,A_27b: del,V0a0: $i] :
( ( mem @ V0a0 @ ( arr @ A_27a @ ty_2Eone_2Eone ) )
=> ! [V1a1: $i] :
( ( mem @ V1a1 @ ( ty_2Epatricia_2Eptree @ A_27b ) )
=> ! [V2a0_27: $i] :
( ( mem @ V2a0_27 @ ( arr @ A_27a @ ty_2Eone_2Eone ) )
=> ! [V3a1_27: $i] :
( ( mem @ V3a1_27 @ ( ty_2Epatricia_2Eptree @ A_27b ) )
=> ( ( ( ap @ ( ap @ ( c_2Epatricia__casts_2EWord__ptree @ A_27a @ A_27b ) @ V0a0 ) @ V1a1 )
= ( ap @ ( ap @ ( c_2Epatricia__casts_2EWord__ptree @ A_27a @ A_27b ) @ V2a0_27 ) @ V3a1_27 ) )
<=> ( ( V0a0 = V2a0_27 )
& ( V1a1 = V3a1_27 ) ) ) ) ) ) ) ).
thf(conj_thm_2Epatricia__casts_2Eword__ptree__nchotomy,axiom,
! [A_27a: del,A_27b: del,V0ww: $i] :
( ( mem @ V0ww @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) )
=> ? [V1f: $i] :
( ( mem @ V1f @ ( arr @ A_27a @ ty_2Eone_2Eone ) )
& ? [V2p: $i] :
( ( mem @ V2p @ ( ty_2Epatricia_2Eptree @ A_27b ) )
& ( V0ww
= ( ap @ ( ap @ ( c_2Epatricia__casts_2EWord__ptree @ A_27a @ A_27b ) @ V1f ) @ V2p ) ) ) ) ) ).
thf(conj_thm_2Epatricia__casts_2Eword__ptree__Axiom,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ ( arr @ A_27a @ ty_2Eone_2Eone ) @ ( arr @ ( ty_2Epatricia_2Eptree @ A_27b ) @ A_27c ) ) )
=> ? [V1fn: $i] :
( ( mem @ V1fn @ ( arr @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) @ A_27c ) )
& ! [V2a0: $i] :
( ( mem @ V2a0 @ ( arr @ A_27a @ ty_2Eone_2Eone ) )
=> ! [V3a1: $i] :
( ( mem @ V3a1 @ ( ty_2Epatricia_2Eptree @ A_27b ) )
=> ( ( ap @ V1fn @ ( ap @ ( ap @ ( c_2Epatricia__casts_2EWord__ptree @ A_27a @ A_27b ) @ V2a0 ) @ V3a1 ) )
= ( ap @ ( ap @ V0f @ V2a0 ) @ V3a1 ) ) ) ) ) ) ).
thf(conj_thm_2Epatricia__casts_2Eword__ptree__induction,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) @ bool ) )
=> ( ! [V1f: $i] :
( ( mem @ V1f @ ( arr @ A_27a @ ty_2Eone_2Eone ) )
=> ! [V2p: $i] :
( ( mem @ V2p @ ( ty_2Epatricia_2Eptree @ A_27b ) )
=> ( p @ ( ap @ V0P @ ( ap @ ( ap @ ( c_2Epatricia__casts_2EWord__ptree @ A_27a @ A_27b ) @ V1f ) @ V2p ) ) ) ) )
=> ! [V3w: $i] :
( ( mem @ V3w @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) )
=> ( p @ ( ap @ V0P @ V3w ) ) ) ) ) ).
thf(conj_thm_2Epatricia__casts_2Eword__ptree__case__cong,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f_27: $i] :
( ( mem @ V0f_27 @ ( arr @ ( arr @ A_27a @ ty_2Eone_2Eone ) @ ( arr @ ( ty_2Epatricia_2Eptree @ A_27b ) @ A_27c ) ) )
=> ! [V1M: $i] :
( ( mem @ V1M @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) )
=> ! [V2M_27: $i] :
( ( mem @ V2M_27 @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) )
=> ! [V3f: $i] :
( ( mem @ V3f @ ( arr @ ( arr @ A_27a @ ty_2Eone_2Eone ) @ ( arr @ ( ty_2Epatricia_2Eptree @ A_27b ) @ A_27c ) ) )
=> ( ( ( V1M = V2M_27 )
& ! [V4a0: $i] :
( ( mem @ V4a0 @ ( arr @ A_27a @ ty_2Eone_2Eone ) )
=> ! [V5a1: $i] :
( ( mem @ V5a1 @ ( ty_2Epatricia_2Eptree @ A_27b ) )
=> ( ( V2M_27
= ( ap @ ( ap @ ( c_2Epatricia__casts_2EWord__ptree @ A_27a @ A_27b ) @ V4a0 ) @ V5a1 ) )
=> ( ( ap @ ( ap @ V3f @ V4a0 ) @ V5a1 )
= ( ap @ ( ap @ V0f_27 @ V4a0 ) @ V5a1 ) ) ) ) ) )
=> ( ( ap @ ( ap @ ( c_2Epatricia__casts_2Eword__ptree__CASE @ A_27a @ A_27b @ A_27c ) @ V1M ) @ V3f )
= ( ap @ ( ap @ ( c_2Epatricia__casts_2Eword__ptree__CASE @ A_27a @ A_27b @ A_27c ) @ V2M_27 ) @ V0f_27 ) ) ) ) ) ) ) ).
thf(conj_thm_2Epatricia__casts_2Eword__ptree__case__eq,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0x: $i] :
( ( mem @ V0x @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) )
=> ! [V1f: $i] :
( ( mem @ V1f @ ( arr @ ( arr @ A_27a @ ty_2Eone_2Eone ) @ ( arr @ ( ty_2Epatricia_2Eptree @ A_27b ) @ A_27c ) ) )
=> ! [V2v: $i] :
( ( mem @ V2v @ A_27c )
=> ( ( ( ap @ ( ap @ ( c_2Epatricia__casts_2Eword__ptree__CASE @ A_27a @ A_27b @ A_27c ) @ V0x ) @ V1f )
= V2v )
<=> ? [V3f_27: $i] :
( ( mem @ V3f_27 @ ( arr @ A_27a @ ty_2Eone_2Eone ) )
& ? [V4p: $i] :
( ( mem @ V4p @ ( ty_2Epatricia_2Eptree @ A_27b ) )
& ( V0x
= ( ap @ ( ap @ ( c_2Epatricia__casts_2EWord__ptree @ A_27a @ A_27b ) @ V3f_27 ) @ V4p ) )
& ( ( ap @ ( ap @ V1f @ V3f_27 ) @ V4p )
= V2v ) ) ) ) ) ) ) ).
thf(ax_thm_2Epatricia__casts_2ETHE__PTREE__def,axiom,
! [A_27a: del,A_27b: del,V0a: $i] :
( ( mem @ V0a @ ( arr @ A_27b @ ty_2Eone_2Eone ) )
=> ! [V1t: $i] :
( ( mem @ V1t @ ( ty_2Epatricia_2Eptree @ A_27a ) )
=> ( ( ap @ ( c_2Epatricia__casts_2ETHE__PTREE @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Epatricia__casts_2EWord__ptree @ A_27b @ A_27a ) @ V0a ) @ V1t ) )
= V1t ) ) ) ).
thf(ax_thm_2Epatricia__casts_2ESOME__PTREE__def,axiom,
! [A_27a: del,A_27b: del,V0t: $i] :
( ( mem @ V0t @ ( ty_2Epatricia_2Eptree @ A_27b ) )
=> ( ( ap @ ( c_2Epatricia__casts_2ESOME__PTREE @ A_27a @ A_27b ) @ V0t )
= ( ap @ ( ap @ ( c_2Epatricia__casts_2EWord__ptree @ A_27a @ A_27b ) @ ( ap @ ( c_2Ecombin_2EK @ ty_2Eone_2Eone @ A_27a ) @ ( inj__ty_2Eone_2Eone @ fo__c_2Eone_2Eone ) ) ) @ V0t ) ) ) ).
thf(ax_thm_2Epatricia__casts_2EWordEmpty__def,axiom,
! [A_27a: del,A_27b: del] :
( ( c_2Epatricia__casts_2EWordEmpty @ A_27a @ A_27b )
= ( ap @ ( c_2Epatricia__casts_2ESOME__PTREE @ A_27a @ A_27b ) @ ( c_2Epatricia_2EEmpty @ A_27b ) ) ) ).
thf(ax_thm_2Epatricia__casts_2EPEEKw__def,axiom,
! [A_27a: del,A_27b: del,V0t: $i] :
( ( mem @ V0t @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Epatricia__casts_2EPEEKw @ A_27a @ A_27b ) @ V0t ) @ V1w )
= ( ap @ ( ap @ ( c_2Epatricia_2EPEEK @ A_27b ) @ ( ap @ ( c_2Epatricia__casts_2ETHE__PTREE @ A_27b @ A_27a ) @ V0t ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1w ) ) ) ) ) ).
thf(ax_thm_2Epatricia__casts_2EFINDw__def,axiom,
! [A_27a: del,A_27b: del,V0t: $i] :
( ( mem @ V0t @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27b @ A_27a ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) )
=> ( ( ap @ ( ap @ ( c_2Epatricia__casts_2EFINDw @ A_27a @ A_27b ) @ V0t ) @ V1w )
= ( ap @ ( c_2Eoption_2ETHE @ A_27a ) @ ( ap @ ( ap @ ( c_2Epatricia__casts_2EPEEKw @ A_27b @ A_27a ) @ V0t ) @ V1w ) ) ) ) ) ).
thf(ax_thm_2Epatricia__casts_2EADDw__def,axiom,
! [A_27a: del,A_27b: del,V0t: $i] :
( ( mem @ V0t @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V2d: $i] :
( ( mem @ V2d @ A_27b )
=> ( ( ap @ ( ap @ ( c_2Epatricia__casts_2EADDw @ A_27a @ A_27b ) @ V0t ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ A_27b ) @ V1w ) @ V2d ) )
= ( ap @ ( c_2Epatricia__casts_2ESOME__PTREE @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Epatricia_2EADD @ A_27b ) @ ( ap @ ( c_2Epatricia__casts_2ETHE__PTREE @ A_27b @ A_27a ) @ V0t ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ A_27b ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1w ) ) @ V2d ) ) ) ) ) ) ) ).
thf(ax_thm_2Epatricia__casts_2EADD__LISTw__def,axiom,
! [A_27a: del,A_27b: del] :
( ( c_2Epatricia__casts_2EADD__LISTw @ A_27a @ A_27b )
= ( ap @ ( c_2Elist_2EFOLDL @ ( ty_2Epair_2Eprod @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ A_27b ) @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) ) @ ( c_2Epatricia__casts_2EADDw @ A_27a @ A_27b ) ) ) ).
thf(ax_thm_2Epatricia__casts_2EREMOVEw__def,axiom,
! [A_27a: del,A_27b: del,V0t: $i] :
( ( mem @ V0t @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) )
=> ! [V1w: $i] :
( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Epatricia__casts_2EREMOVEw @ A_27a @ A_27b ) @ V0t ) @ V1w )
= ( ap @ ( c_2Epatricia__casts_2ESOME__PTREE @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( c_2Epatricia_2EREMOVE @ A_27b ) @ ( ap @ ( c_2Epatricia__casts_2ETHE__PTREE @ A_27b @ A_27a ) @ V0t ) ) @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V1w ) ) ) ) ) ) ).
thf(ax_thm_2Epatricia__casts_2ETRAVERSEw__def,axiom,
! [A_27a: del,A_27b: del,V0t: $i] :
( ( mem @ V0t @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) )
=> ( ( ap @ ( c_2Epatricia__casts_2ETRAVERSEw @ A_27a @ A_27b ) @ V0t )
= ( ap @ ( ap @ ( c_2Elist_2EMAP @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( c_2Ewords_2En2w @ A_27a ) ) @ ( ap @ ( c_2Epatricia_2ETRAVERSE @ A_27b ) @ ( ap @ ( c_2Epatricia__casts_2ETHE__PTREE @ A_27b @ A_27a ) @ V0t ) ) ) ) ) ).
thf(ax_thm_2Epatricia__casts_2EKEYSw__def,axiom,
! [A_27a: del,A_27b: del,V0t: $i] :
( ( mem @ V0t @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) )
=> ( ( ap @ ( c_2Epatricia__casts_2EKEYSw @ A_27a @ A_27b ) @ V0t )
= ( ap @ ( ap @ ( c_2Esorting_2EQSORT @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( c_2Ewords_2Eword__lo @ A_27a ) ) @ ( ap @ ( c_2Epatricia__casts_2ETRAVERSEw @ A_27a @ A_27b ) @ V0t ) ) ) ) ).
thf(ax_thm_2Epatricia__casts_2ETRANSFORMw__def,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
=> ! [V1t: $i] :
( ( mem @ V1t @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27c @ A_27a ) )
=> ( ( ap @ ( ap @ ( c_2Epatricia__casts_2ETRANSFORMw @ A_27a @ A_27b @ A_27c ) @ V0f ) @ V1t )
= ( ap @ ( c_2Epatricia__casts_2ESOME__PTREE @ A_27c @ A_27b ) @ ( ap @ ( ap @ ( c_2Epatricia_2ETRANSFORM @ A_27b @ A_27a ) @ V0f ) @ ( ap @ ( c_2Epatricia__casts_2ETHE__PTREE @ A_27a @ A_27c ) @ V1t ) ) ) ) ) ) ).
thf(ax_thm_2Epatricia__casts_2EEVERY__LEAFw__def,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ A_27b @ bool ) ) )
=> ! [V1t: $i] :
( ( mem @ V1t @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Epatricia__casts_2EEVERY__LEAFw @ A_27a @ A_27b ) @ V0P ) @ V1t ) )
<=> ( p
@ ( ap
@ ( ap @ ( c_2Epatricia_2EEVERY__LEAF @ A_27b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2k: $i] :
( lam @ A_27b
@ ^ [V3d: $i] : ( ap @ ( ap @ V0P @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ V2k ) ) @ V3d ) ) ) )
@ ( ap @ ( c_2Epatricia__casts_2ETHE__PTREE @ A_27b @ A_27a ) @ V1t ) ) ) ) ) ) ).
thf(ax_thm_2Epatricia__casts_2EEXISTS__LEAFw__def,axiom,
! [A_27a: del,A_27b: del,V0P: $i] :
( ( mem @ V0P @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ( arr @ A_27b @ bool ) ) )
=> ! [V1t: $i] :
( ( mem @ V1t @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Epatricia__casts_2EEXISTS__LEAFw @ A_27a @ A_27b ) @ V0P ) @ V1t ) )
<=> ( p
@ ( ap
@ ( ap @ ( c_2Epatricia_2EEXISTS__LEAF @ A_27b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2k: $i] :
( lam @ A_27b
@ ^ [V3d: $i] : ( ap @ ( ap @ V0P @ ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ V2k ) ) @ V3d ) ) ) )
@ ( ap @ ( c_2Epatricia__casts_2ETHE__PTREE @ A_27b @ A_27a ) @ V1t ) ) ) ) ) ) ).
thf(ax_thm_2Epatricia__casts_2ESIZEw__def,axiom,
! [A_27a: del,A_27b: del,V0t: $i] :
( ( mem @ V0t @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epatricia__casts_2ESIZEw @ A_27a @ A_27b ) @ V0t ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epatricia_2ESIZE @ A_27b ) @ ( ap @ ( c_2Epatricia__casts_2ETHE__PTREE @ A_27b @ A_27a ) @ V0t ) ) ) ) ) ).
thf(ax_thm_2Epatricia__casts_2EDEPTHw__def,axiom,
! [A_27a: del,A_27b: del,V0t: $i] :
( ( mem @ V0t @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ A_27b ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epatricia__casts_2EDEPTHw @ A_27a @ A_27b ) @ V0t ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Epatricia_2EDEPTH @ A_27b ) @ ( ap @ ( c_2Epatricia__casts_2ETHE__PTREE @ A_27b @ A_27a ) @ V0t ) ) ) ) ) ).
thf(ax_thm_2Epatricia__casts_2EIN__PTREEw__def,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1t: $i] :
( ( mem @ V1t @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ ty_2Eone_2Eone ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Epatricia__casts_2EIN__PTREEw @ A_27a ) @ V0w ) @ V1t ) )
<=> ( p @ ( ap @ ( ap @ c_2Epatricia_2EIN__PTREE @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0w ) ) @ ( ap @ ( c_2Epatricia__casts_2ETHE__PTREE @ ty_2Eone_2Eone @ A_27a ) @ V1t ) ) ) ) ) ) ).
thf(ax_thm_2Epatricia__casts_2EINSERT__PTREEw__def,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1t: $i] :
( ( mem @ V1t @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ ty_2Eone_2Eone ) )
=> ( ( ap @ ( ap @ ( c_2Epatricia__casts_2EINSERT__PTREEw @ A_27a ) @ V0w ) @ V1t )
= ( ap @ ( c_2Epatricia__casts_2ESOME__PTREE @ A_27a @ ty_2Eone_2Eone ) @ ( ap @ ( ap @ c_2Epatricia_2EINSERT__PTREE @ ( ap @ ( c_2Ewords_2Ew2n @ A_27a ) @ V0w ) ) @ ( ap @ ( c_2Epatricia__casts_2ETHE__PTREE @ ty_2Eone_2Eone @ A_27a ) @ V1t ) ) ) ) ) ) ).
thf(ax_thm_2Epatricia__casts_2EWORDSET__OF__PTREE__def,axiom,
! [A_27a: del,V0t: $i] :
( ( mem @ V0t @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ ty_2Eone_2Eone ) )
=> ( ( ap @ ( c_2Epatricia__casts_2EWORDSET__OF__PTREE @ A_27a ) @ V0t )
= ( ap @ ( c_2Elist_2ELIST__TO__SET @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ ( ap @ ( c_2Epatricia__casts_2ETRAVERSEw @ A_27a @ ty_2Eone_2Eone ) @ V0t ) ) ) ) ).
thf(ax_thm_2Epatricia__casts_2EUNION__PTREEw__def,axiom,
! [A_27a: del,A_27b: del,A_27c: del,V0t1: $i] :
( ( mem @ V0t1 @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27b @ ty_2Eone_2Eone ) )
=> ! [V1t2: $i] :
( ( mem @ V1t2 @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27c @ ty_2Eone_2Eone ) )
=> ( ( ap @ ( ap @ ( c_2Epatricia__casts_2EUNION__PTREEw @ A_27a @ A_27b @ A_27c ) @ V0t1 ) @ V1t2 )
= ( ap @ ( c_2Epatricia__casts_2ESOME__PTREE @ A_27a @ ty_2Eone_2Eone ) @ ( ap @ ( ap @ c_2Epatricia_2EUNION__PTREE @ ( ap @ ( c_2Epatricia__casts_2ETHE__PTREE @ ty_2Eone_2Eone @ A_27b ) @ V0t1 ) ) @ ( ap @ ( c_2Epatricia__casts_2ETHE__PTREE @ ty_2Eone_2Eone @ A_27c ) @ V1t2 ) ) ) ) ) ) ).
thf(ax_thm_2Epatricia__casts_2EPTREE__OF__WORDSET__def,axiom,
! [A_27a: del,V0t: $i] :
( ( mem @ V0t @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ ty_2Eone_2Eone ) )
=> ! [V1s: $i] :
( ( mem @ V1s @ ( arr @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ bool ) )
=> ( ( ap @ ( ap @ ( c_2Epatricia__casts_2EPTREE__OF__WORDSET @ A_27a ) @ V0t ) @ V1s )
= ( ap @ ( c_2Epatricia__casts_2ESOME__PTREE @ A_27a @ ty_2Eone_2Eone ) @ ( ap @ ( ap @ c_2Epatricia_2EPTREE__OF__NUMSET @ ( ap @ ( c_2Epatricia__casts_2ETHE__PTREE @ ty_2Eone_2Eone @ A_27a ) @ V0t ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ty_2Enum_2Enum ) @ ( c_2Ewords_2Ew2n @ A_27a ) ) @ V1s ) ) ) ) ) ) ).
thf(conj_thm_2Epatricia__casts_2EADD__INSERT__STRING,axiom,
! [V0w: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar,V1v: tp__ty_2Eone_2Eone,V2t: tp__c_ty_2Epatricia_2Eptree_ty_2Eone_2Eone] :
( ( surj__c_ty_2Epatricia_2Eptree_ty_2Eone_2Eone @ ( ap @ ( ap @ ( c_2Epatricia__casts_2EADDs @ ty_2Eone_2Eone ) @ ( inj__c_ty_2Epatricia_2Eptree_ty_2Eone_2Eone @ V2t ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ty_2Eone_2Eone ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V0w ) ) @ ( inj__ty_2Eone_2Eone @ V1v ) ) ) )
= ( surj__c_ty_2Epatricia_2Eptree_ty_2Eone_2Eone @ ( ap @ ( ap @ ( c_2Epatricia__casts_2EADDs @ ty_2Eone_2Eone ) @ ( inj__c_ty_2Epatricia_2Eptree_ty_2Eone_2Eone @ V2t ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ty_2Eone_2Eone ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V0w ) ) @ ( inj__ty_2Eone_2Eone @ fo__c_2Eone_2Eone ) ) ) ) ) ).
thf(conj_thm_2Epatricia__casts_2El2n__APPEND,axiom,
! [V0b: tp__ty_2Enum_2Enum,V1l1: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum,V2l2: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l1 ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V2l2 ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l1 ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2A @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l1 ) ) ) ) @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V2l2 ) ) ) ) ) ) ).
thf(conj_thm_2Epatricia__casts_2El2n__LENGTH,axiom,
! [V0b: tp__ty_2Enum_2Enum,V1l: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) )
=> ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( ap @ ( c_2Elist_2ELENGTH @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l ) ) ) ) ) ) ).
thf(conj_thm_2Epatricia__casts_2El2n__11,axiom,
! [V0b: tp__ty_2Enum_2Enum,V1l1: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum,V2l2: tp__c_ty_2Elist_2Elist_ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0b ) ) )
& ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2E_3E @ ( inj__ty_2Enum_2Enum @ V0b ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l1 ) ) )
& ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2E_3E @ ( inj__ty_2Enum_2Enum @ V0b ) ) ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V2l2 ) ) ) )
=> ( ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V1l1 ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( c_2Elist_2ENIL @ ty_2Enum_2Enum ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Enumposrep_2El2n @ ( inj__ty_2Enum_2Enum @ V0b ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ ty_2Enum_2Enum ) @ ( inj__c_ty_2Elist_2Elist_ty_2Enum_2Enum @ V2l2 ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) @ ( c_2Elist_2ENIL @ ty_2Enum_2Enum ) ) ) ) ) )
<=> ( V1l1 = V2l2 ) ) ) ).
thf(conj_thm_2Epatricia__casts_2EEVERY__MAP__ORD,axiom,
! [V0l: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar] : ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ ty_2Enum_2Enum ) @ ( ap @ c_2Earithmetic_2E_3E @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ ty_2Estring_2Echar @ ty_2Enum_2Enum ) @ c_2Estring_2EORD ) @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V0l ) ) ) ) ).
thf(conj_thm_2Epatricia__casts_2EMAP__11,axiom,
! [A_27a: del,A_27b: del,V0f: $i] :
( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
=> ! [V1l1: $i] :
( ( mem @ V1l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V2l2: $i] :
( ( mem @ V2l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ! [V3x: $i] :
( ( mem @ V3x @ A_27a )
=> ! [V4y: $i] :
( ( mem @ V4y @ A_27a )
=> ( ( ( ap @ V0f @ V3x )
= ( ap @ V0f @ V4y ) )
<=> ( V3x = V4y ) ) ) )
=> ( ( ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ A_27b ) @ V0f ) @ V1l1 )
= ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ A_27b ) @ V0f ) @ V2l2 ) )
<=> ( V1l1 = V2l2 ) ) ) ) ) ) ).
thf(conj_thm_2Epatricia__casts_2EREVERSE__11,axiom,
! [A_27a: del,V0l1: $i] :
( ( mem @ V0l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V1l2: $i] :
( ( mem @ V1l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V0l1 )
= ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V1l2 ) )
<=> ( V0l1 = V1l2 ) ) ) ) ).
thf(conj_thm_2Epatricia__casts_2Estring__to__num__11,axiom,
! [V0s: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar,V1t: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar] :
( ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Epatricia__casts_2Estring__to__num @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V0s ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Epatricia__casts_2Estring__to__num @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V1t ) ) ) )
<=> ( V0s = V1t ) ) ).
thf(conj_thm_2Epatricia__casts_2EIMAGE__string__to__num,axiom,
! [V0n: tp__ty_2Enum_2Enum] :
( ( ( V0n
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) )
| ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ ( ap @ c_2Earithmetic_2EDIV @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ c_2Earithmetic_2EEXP @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) @ ( ap @ ( ap @ c_2Elogroot_2ELOG @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT2 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ty_2Enum_2Enum ) @ c_2Epatricia__casts_2Estring__to__num ) @ ( c_2Epred__set_2EUNIV @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) ) ) ) ) ).
thf(conj_thm_2Epatricia__casts_2Estring__to__num__num__to__string,axiom,
! [V0n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ ty_2Enum_2Enum ) @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2EIMAGE @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) @ ty_2Enum_2Enum ) @ c_2Epatricia__casts_2Estring__to__num ) @ ( c_2Epred__set_2EUNIV @ ( ty_2Elist_2Elist @ ty_2Estring_2Echar ) ) ) ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ c_2Epatricia__casts_2Estring__to__num @ ( ap @ c_2Epatricia__casts_2Enum__to__string @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) )
= V0n ) ) ).
thf(conj_thm_2Epatricia__casts_2Enum__to__string__string__to__num,axiom,
! [V0s: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar] :
( ( surj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ ( ap @ c_2Epatricia__casts_2Enum__to__string @ ( ap @ c_2Epatricia__casts_2Estring__to__num @ ( inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar @ V0s ) ) ) )
= V0s ) ).
thf(conj_thm_2Epatricia__casts_2EADD__INSERT__WORD,axiom,
! [A_27a: del,V0w: $i] :
( ( mem @ V0w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) )
=> ! [V1v: tp__ty_2Eone_2Eone,V2t: $i] :
( ( mem @ V2t @ ( ty_2Epatricia__casts_2Eword__ptree @ A_27a @ ty_2Eone_2Eone ) )
=> ( ( ap @ ( ap @ ( c_2Epatricia__casts_2EADDw @ A_27a @ ty_2Eone_2Eone ) @ V2t ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ty_2Eone_2Eone ) @ V0w ) @ ( inj__ty_2Eone_2Eone @ V1v ) ) )
= ( ap @ ( ap @ ( c_2Epatricia__casts_2EADDw @ A_27a @ ty_2Eone_2Eone ) @ V2t ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ ty_2Eone_2Eone ) @ V0w ) @ ( inj__ty_2Eone_2Eone @ fo__c_2Eone_2Eone ) ) ) ) ) ) ).
thf(conj_thm_2Epatricia__casts_2ETHE__PTREE__SOME__PTREE,axiom,
! [A_27a: del,A_27b: del,V0t: $i] :
( ( mem @ V0t @ ( ty_2Epatricia_2Eptree @ A_27a ) )
=> ( ( ap @ ( c_2Epatricia__casts_2ETHE__PTREE @ A_27a @ A_27b ) @ ( ap @ ( c_2Epatricia__casts_2ESOME__PTREE @ A_27b @ A_27a ) @ V0t ) )
= V0t ) ) ).
%------------------------------------------------------------------------------