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 : 156 ( 54 unt; 50 typ; 0 def)
% Number of atoms : 1462 ( 74 equ)
% Maximal formula atoms : 10 ( 9 avg)
% Number of connectives : 118 ( 0 ~; 1 |; 12 &)
% ( 12 <=>; 93 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 1238 (1238 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 86 ( 43 >; 43 *; 0 +; 0 <<)
% Number of predicates : 97 ( 96 usr; 37 prp; 0-2 aty)
% Number of functors : 50 ( 50 usr; 7 con; 0-4 aty)
% Number of variables : 284 ( 278 !; 6 ?; 284 :)
% SPC : TF0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tp_ty_2Epatricia__casts_2Eword__ptree,type,
ty_2Epatricia__casts_2Eword__ptree: ( del * del ) > del ).
tff(tp_c_2Epatricia__casts_2EADD__LISTs,type,
c_2Epatricia__casts_2EADD__LISTs: del > $i ).
tff(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)))) ).
tff(tp_c_2Epatricia__casts_2EADD__LISTw,type,
c_2Epatricia__casts_2EADD__LISTw: ( del * del ) > $i ).
tff(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)))) ).
tff(tp_c_2Epatricia__casts_2EADDs,type,
c_2Epatricia__casts_2EADDs: del > $i ).
tff(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)))) ).
tff(tp_c_2Epatricia__casts_2EADDw,type,
c_2Epatricia__casts_2EADDw: ( del * del ) > $i ).
tff(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)))) ).
tff(tp_c_2Epatricia__casts_2EDEPTHw,type,
c_2Epatricia__casts_2EDEPTHw: ( del * del ) > $i ).
tff(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)) ).
tff(tp_c_2Epatricia__casts_2EEVERY__LEAFw,type,
c_2Epatricia__casts_2EEVERY__LEAFw: ( del * del ) > $i ).
tff(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))) ).
tff(tp_c_2Epatricia__casts_2EEXISTS__LEAFw,type,
c_2Epatricia__casts_2EEXISTS__LEAFw: ( del * del ) > $i ).
tff(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))) ).
tff(tp_c_2Epatricia__casts_2EFINDs,type,
c_2Epatricia__casts_2EFINDs: del > $i ).
tff(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))) ).
tff(tp_c_2Epatricia__casts_2EFINDw,type,
c_2Epatricia__casts_2EFINDw: ( del * del ) > $i ).
tff(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))) ).
tff(tp_c_2Epatricia__casts_2EINSERT__PTREEs,type,
c_2Epatricia__casts_2EINSERT__PTREEs: $i ).
tff(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)))) ).
tff(tp_c_2Epatricia__casts_2EINSERT__PTREEw,type,
c_2Epatricia__casts_2EINSERT__PTREEw: del > $i ).
tff(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)))) ).
tff(tp_c_2Epatricia__casts_2EIN__PTREEs,type,
c_2Epatricia__casts_2EIN__PTREEs: $i ).
tff(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))) ).
tff(stp_fo_c_2Epatricia__casts_2EIN__PTREEs,type,
fo__c_2Epatricia__casts_2EIN__PTREEs: ( tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar * tp__c_ty_2Epatricia_2Eptree_ty_2Eone_2Eone ) > tp__o ).
tff(stp_eq_fo_c_2Epatricia__casts_2EIN__PTREEs,axiom,
! [X0: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar,X1: tp__c_ty_2Epatricia_2Eptree_ty_2Eone_2Eone] : ( inj__o(fo__c_2Epatricia__casts_2EIN__PTREEs(X0,X1)) = ap(ap(c_2Epatricia__casts_2EIN__PTREEs,inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar(X0)),inj__c_ty_2Epatricia_2Eptree_ty_2Eone_2Eone(X1)) ) ).
tff(tp_c_2Epatricia__casts_2EIN__PTREEw,type,
c_2Epatricia__casts_2EIN__PTREEw: del > $i ).
tff(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))) ).
tff(tp_c_2Epatricia__casts_2EKEYSs,type,
c_2Epatricia__casts_2EKEYSs: del > $i ).
tff(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)))) ).
tff(tp_c_2Epatricia__casts_2EKEYSw,type,
c_2Epatricia__casts_2EKEYSw: ( del * del ) > $i ).
tff(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)))) ).
tff(tp_c_2Epatricia__casts_2EPEEKs,type,
c_2Epatricia__casts_2EPEEKs: del > $i ).
tff(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)))) ).
tff(tp_c_2Epatricia__casts_2EPEEKw,type,
c_2Epatricia__casts_2EPEEKw: ( del * del ) > $i ).
tff(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)))) ).
tff(tp_c_2Epatricia__casts_2EPTREE__OF__STRINGSET,type,
c_2Epatricia__casts_2EPTREE__OF__STRINGSET: $i ).
tff(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)))) ).
tff(tp_c_2Epatricia__casts_2EPTREE__OF__WORDSET,type,
c_2Epatricia__casts_2EPTREE__OF__WORDSET: del > $i ).
tff(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)))) ).
tff(tp_c_2Epatricia__casts_2EREMOVEs,type,
c_2Epatricia__casts_2EREMOVEs: del > $i ).
tff(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)))) ).
tff(tp_c_2Epatricia__casts_2EREMOVEw,type,
c_2Epatricia__casts_2EREMOVEw: ( del * del ) > $i ).
tff(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)))) ).
tff(tp_c_2Epatricia__casts_2ESIZEw,type,
c_2Epatricia__casts_2ESIZEw: ( del * del ) > $i ).
tff(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)) ).
tff(tp_c_2Epatricia__casts_2ESKIP1,type,
c_2Epatricia__casts_2ESKIP1: $i ).
tff(mem_c_2Epatricia__casts_2ESKIP1,axiom,
mem(c_2Epatricia__casts_2ESKIP1,arr(ty_2Elist_2Elist(ty_2Estring_2Echar),ty_2Elist_2Elist(ty_2Estring_2Echar))) ).
tff(tp_c_2Epatricia__casts_2ESOME__PTREE,type,
c_2Epatricia__casts_2ESOME__PTREE: ( del * del ) > $i ).
tff(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))) ).
tff(tp_c_2Epatricia__casts_2ESTRINGSET__OF__PTREE,type,
c_2Epatricia__casts_2ESTRINGSET__OF__PTREE: $i ).
tff(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))) ).
tff(stp_fo_c_2Epatricia__casts_2ESTRINGSET__OF__PTREE,type,
fo__c_2Epatricia__casts_2ESTRINGSET__OF__PTREE: ( tp__c_ty_2Epatricia_2Eptree_ty_2Eone_2Eone * tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar ) > tp__o ).
tff(stp_eq_fo_c_2Epatricia__casts_2ESTRINGSET__OF__PTREE,axiom,
! [X0: tp__c_ty_2Epatricia_2Eptree_ty_2Eone_2Eone,X1: tp__c_ty_2Elist_2Elist_ty_2Estring_2Echar] : ( inj__o(fo__c_2Epatricia__casts_2ESTRINGSET__OF__PTREE(X0,X1)) = ap(ap(c_2Epatricia__casts_2ESTRINGSET__OF__PTREE,inj__c_ty_2Epatricia_2Eptree_ty_2Eone_2Eone(X0)),inj__c_ty_2Elist_2Elist_ty_2Estring_2Echar(X1)) ) ).
tff(tp_c_2Epatricia__casts_2ETHE__PTREE,type,
c_2Epatricia__casts_2ETHE__PTREE: ( del * del ) > $i ).
tff(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))) ).
tff(tp_c_2Epatricia__casts_2ETRANSFORMw,type,
c_2Epatricia__casts_2ETRANSFORMw: ( del * del * del ) > $i ).
tff(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)))) ).
tff(tp_c_2Epatricia__casts_2ETRAVERSEs,type,
c_2Epatricia__casts_2ETRAVERSEs: del > $i ).
tff(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)))) ).
tff(tp_c_2Epatricia__casts_2ETRAVERSEw,type,
c_2Epatricia__casts_2ETRAVERSEw: ( del * del ) > $i ).
tff(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)))) ).
tff(tp_c_2Epatricia__casts_2EUNION__PTREEw,type,
c_2Epatricia__casts_2EUNION__PTREEw: ( del * del * del ) > $i ).
tff(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)))) ).
tff(tp_c_2Epatricia__casts_2EWORDSET__OF__PTREE,type,
c_2Epatricia__casts_2EWORDSET__OF__PTREE: del > $i ).
tff(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))) ).
tff(tp_c_2Epatricia__casts_2EWordEmpty,type,
c_2Epatricia__casts_2EWordEmpty: ( del * del ) > $i ).
tff(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)) ).
tff(tp_c_2Epatricia__casts_2EWord__ptree,type,
c_2Epatricia__casts_2EWord__ptree: ( del * del ) > $i ).
tff(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)))) ).
tff(tp_c_2Epatricia__casts_2Enum__to__string,type,
c_2Epatricia__casts_2Enum__to__string: $i ).
tff(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))) ).
tff(tp_c_2Epatricia__casts_2Estring__to__num,type,
c_2Epatricia__casts_2Estring__to__num: $i ).
tff(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)) ).
tff(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 ).
tff(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)) ) ).
tff(tp_c_2Epatricia__casts_2Eword__ptree__CASE,type,
c_2Epatricia__casts_2Eword__ptree__CASE: ( del * del * del ) > $i ).
tff(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))) ).
tff(tp_c_2Epatricia__casts_2Eword__ptree__size,type,
c_2Epatricia__casts_2Eword__ptree__size: ( del * del ) > $i ).
tff(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)))) ).
tff(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 ) ).
tff(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)))) ) ).
tff(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)))) ) ).
tff(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))) ) ) ).
tff(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))) ) ) ).
tff(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)) ) ) ) ).
tff(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)) ) ).
tff(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))) ) ) ).
tff(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))) ) ) ).
tff(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))) ) ) ).
tff(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))) ) ).
tff(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))) ) ).
tff(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))) ) ).
tff(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))) ) ) ).
tff(lamtp_f2696,type,
f2696: ( del * del * $i ) > $i ).
tff(lameq_f2696,axiom,
! [A_27a: del,A_27b: del,V6a0: $i] :
( mem(V6a0,arr(A_27a,ty_2Eone_2Eone))
=> ! [V7a1: $i] : ( ap(f2696(A_27a,A_27b,V6a0),V7a1) = 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)),k(ty_2Enum_2Enum,c_2Eind__type_2EBOTTOM(ty_2Epair_2Eprod(arr(A_27a,ty_2Eone_2Eone),ty_2Epatricia_2Eptree(A_27b))))) ) ) ).
tff(lamtp_f2697,type,
f2697: ( del * del ) > $i ).
tff(lameq_f2697,axiom,
! [A_27b: del,A_27a: del,V6a0: $i] : ( ap(f2697(A_27b,A_27a),V6a0) = f2696(A_27a,A_27b,V6a0) ) ).
tff(lamtp_f2698,type,
f2698: ( del * del * $i * $i ) > $i ).
tff(lameq_f2698,axiom,
! [A_27a: del,A_27b: del,V4a0: $i] :
( mem(V4a0,arr(A_27a,ty_2Eone_2Eone))
=> ! [V3a0_27: $i] :
( mem(V3a0_27,ty_2Eind__type_2Erecspace(ty_2Epair_2Eprod(arr(A_27a,ty_2Eone_2Eone),ty_2Epatricia_2Eptree(A_27b))))
=> ! [V5a1: $i] : ( ap(f2698(A_27a,A_27b,V4a0,V3a0_27),V5a1) = 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(f2697(A_27b,A_27a),V4a0),V5a1)) ) ) ) ).
tff(lamtp_f2699,type,
f2699: ( del * del * $i ) > $i ).
tff(lameq_f2699,axiom,
! [A_27b: del,A_27a: del,V3a0_27: $i] :
( mem(V3a0_27,ty_2Eind__type_2Erecspace(ty_2Epair_2Eprod(arr(A_27a,ty_2Eone_2Eone),ty_2Epatricia_2Eptree(A_27b))))
=> ! [V4a0: $i] : ( ap(f2699(A_27b,A_27a,V3a0_27),V4a0) = ap(c_2Ebool_2E_3F(ty_2Epatricia_2Eptree(A_27b)),f2698(A_27a,A_27b,V4a0,V3a0_27)) ) ) ).
tff(lamtp_f2700,type,
f2700: ( del * del * $i ) > $i ).
tff(lameq_f2700,axiom,
! [A_27b: del,A_27a: del,V2_27word__ptree_27: $i] :
( mem(V2_27word__ptree_27,arr(ty_2Eind__type_2Erecspace(ty_2Epair_2Eprod(arr(A_27a,ty_2Eone_2Eone),ty_2Epatricia_2Eptree(A_27b))),bool))
=> ! [V3a0_27: $i] : ( ap(f2700(A_27b,A_27a,V2_27word__ptree_27),V3a0_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_3F(arr(A_27a,ty_2Eone_2Eone)),f2699(A_27b,A_27a,V3a0_27))),ap(V2_27word__ptree_27,V3a0_27)) ) ) ).
tff(lamtp_f2701,type,
f2701: ( del * del * $i ) > $i ).
tff(lameq_f2701,axiom,
! [A_27b: del,A_27a: del,V1a0_27: $i] :
( mem(V1a0_27,ty_2Eind__type_2Erecspace(ty_2Epair_2Eprod(arr(A_27a,ty_2Eone_2Eone),ty_2Epatricia_2Eptree(A_27b))))
=> ! [V2_27word__ptree_27: $i] : ( ap(f2701(A_27b,A_27a,V1a0_27),V2_27word__ptree_27) = 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)))),f2700(A_27b,A_27a,V2_27word__ptree_27))),ap(V2_27word__ptree_27,V1a0_27)) ) ) ).
tff(lamtp_f2702,type,
f2702: ( del * del ) > $i ).
tff(lameq_f2702,axiom,
! [A_27b: del,A_27a: del,V1a0_27: $i] : ( ap(f2702(A_27b,A_27a),V1a0_27) = 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)),f2701(A_27b,A_27a,V1a0_27)) ) ).
tff(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)),f2702(A_27b,A_27a)),V0rep)) ) ).
tff(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) ) ) ) ) ).
tff(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))) ) ) ) ) ) ).
tff(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)))) ) ).
tff(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 ) ) ) ) ) ) ) ).
tff(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) ) ) ) ) ).
tff(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) ) ) ) ) ) ).
tff(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)) ) ) ) ).
tff(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) ) ) ) ) ) ) ).
tff(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 ) ) ) ) ) ) ) ).
tff(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 ) ) ) ).
tff(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) ) ) ).
tff(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)) ) ).
tff(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)) ) ) ) ).
tff(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)) ) ) ) ).
tff(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))) ) ) ) ) ).
tff(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)) ) ).
tff(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))) ) ) ) ).
tff(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))) ) ) ).
tff(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)) ) ) ).
tff(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))) ) ) ) ).
tff(lamtp_f2703,type,
f2703: ( del * del * tp__ty_2Enum_2Enum * $i ) > $i ).
tff(lameq_f2703,axiom,
! [A_27a: del,A_27b: del,V2k: tp__ty_2Enum_2Enum,V0P: $i] :
( mem(V0P,arr(ty_2Efcp_2Ecart(bool,A_27a),arr(A_27b,bool)))
=> ! [V3d: $i] : ( ap(f2703(A_27a,A_27b,V2k,V0P),V3d) = ap(ap(V0P,ap(c_2Ewords_2En2w(A_27a),inj__ty_2Enum_2Enum(V2k))),V3d) ) ) ).
tff(lamtp_f2704,type,
f2704: ( del * del * $i ) > $i ).
tff(lameq_f2704,axiom,
! [A_27b: del,A_27a: del,V0P: $i] :
( mem(V0P,arr(ty_2Efcp_2Ecart(bool,A_27a),arr(A_27b,bool)))
=> ! [V2k: tp__ty_2Enum_2Enum] : ( ap(f2704(A_27b,A_27a,V0P),inj__ty_2Enum_2Enum(V2k)) = f2703(A_27a,A_27b,V2k,V0P) ) ) ).
tff(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),f2704(A_27b,A_27a,V0P)),ap(c_2Epatricia__casts_2ETHE__PTREE(A_27b,A_27a),V1t))) ) ) ) ).
tff(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),f2704(A_27b,A_27a,V0P)),ap(c_2Epatricia__casts_2ETHE__PTREE(A_27b,A_27a),V1t))) ) ) ) ).
tff(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))) ) ) ).
tff(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))) ) ) ).
tff(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))) ) ) ) ).
tff(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))) ) ) ) ).
tff(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)) ) ) ).
tff(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))) ) ) ) ).
tff(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))) ) ) ) ).
tff(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)))) ) ).
tff(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))))) ) ).
tff(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))))) ) ).
tff(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 ) ) ) ).
tff(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)))) ).
tff(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 ) ) ) ) ) ) ).
tff(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 ) ) ) ) ).
tff(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 ) ) ).
tff(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))))) ) ).
tff(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 ) ) ).
tff(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 ) ).
tff(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))) ) ) ) ).
tff(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 ) ) ).
%------------------------------------------------------------------------------