ITP001 Axioms: ITP112_7.ax
%------------------------------------------------------------------------------
% File : ITP112_7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : patricia_casts.ax [Gau19]
% : HL4112_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 403 ( 164 unt; 210 typ; 0 def)
% Number of atoms : 244 ( 196 equ)
% Maximal formula atoms : 6 ( 0 avg)
% Number of connectives : 54 ( 3 ~; 4 |; 8 &)
% ( 22 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 164 ( 99 >; 65 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 205 ( 205 usr; 37 con; 0-5 aty)
% Number of variables : 742 ( 543 !; 9 ?; 742 :)
% ( 190 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Efcp_2Ecart,type,
tyop_2Efcp_2Ecart: ( $tType * $tType ) > $tType ).
tff(tyop_2Eind__type_2Erecspace,type,
tyop_2Eind__type_2Erecspace: $tType > $tType ).
tff(tyop_2Elist_2Elist,type,
tyop_2Elist_2Elist: $tType > $tType ).
tff(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
tff(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: $tType ).
tff(tyop_2Eone_2Eone,type,
tyop_2Eone_2Eone: $tType ).
tff(tyop_2Eoption_2Eoption,type,
tyop_2Eoption_2Eoption: $tType > $tType ).
tff(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).
tff(tyop_2Epatricia_2Eptree,type,
tyop_2Epatricia_2Eptree: $tType > $tType ).
tff(tyop_2Epatricia__casts_2Eword__ptree,type,
tyop_2Epatricia__casts_2Eword__ptree: ( $tType * $tType ) > $tType ).
tff(tyop_2Estring_2Echar,type,
tyop_2Estring_2Echar: $tType ).
tff(app_2E2,type,
app_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(p,type,
p: tyop_2Emin_2Ebool > $o ).
tff(combin_i_2E0,type,
combin_i_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(combin_k_2E0,type,
combin_k_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(combin_s_2E0,type,
combin_s_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))) ).
tff(c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Earithmetic_2E_2A_2E0,type,
c_2Earithmetic_2E_2A_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2A_2E2,type,
c_2Earithmetic_2E_2A_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2E_2B_2E0,type,
c_2Earithmetic_2E_2B_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2B_2E2,type,
c_2Earithmetic_2E_2B_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Epair_2E_2C_2E0,type,
c_2Epair_2E_2C_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))) ).
tff(c_2Epair_2E_2C_2E2,type,
c_2Epair_2E_2C_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > tyop_2Epair_2Eprod(A_27a,A_27b) ) ).
tff(c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Enum_2E0_2E0,type,
c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).
tff(c_2Eprim__rec_2E_3C_2E0,type,
c_2Eprim__rec_2E_3C_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Eprim__rec_2E_3C_2E2,type,
c_2Eprim__rec_2E_3C_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(c_2Earithmetic_2E_3C_3D_2E0,type,
c_2Earithmetic_2E_3C_3D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Earithmetic_2E_3C_3D_2E2,type,
c_2Earithmetic_2E_3C_3D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2:
!>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Earithmetic_2E_3E_2E0,type,
c_2Earithmetic_2E_3E_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Earithmetic_2E_3E_2E1,type,
c_2Earithmetic_2E_3E_2E1: tyop_2Enum_2Enum > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Epatricia_2EADD_2E0,type,
c_2Epatricia_2EADD_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Epatricia_2Eptree(A_27a))) ).
tff(c_2Epatricia_2EADD_2E2,type,
c_2Epatricia_2EADD_2E2:
!>[A_27a: $tType] : ( ( tyop_2Epatricia_2Eptree(A_27a) * tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a) ) > tyop_2Epatricia_2Eptree(A_27a) ) ).
tff(c_2Epatricia__casts_2EADD__LISTs_2E0,type,
c_2Epatricia__casts_2EADD__LISTs_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a)),tyop_2Epatricia_2Eptree(A_27a))) ).
tff(c_2Epatricia__casts_2EADD__LISTw_2E0,type,
c_2Epatricia__casts_2EADD__LISTw_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b)),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))) ).
tff(c_2Epatricia__casts_2EADDs_2E0,type,
c_2Epatricia__casts_2EADDs_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a),tyop_2Epatricia_2Eptree(A_27a))) ).
tff(c_2Epatricia__casts_2EADDs_2E2,type,
c_2Epatricia__casts_2EADDs_2E2:
!>[A_27a: $tType] : ( ( tyop_2Epatricia_2Eptree(A_27a) * tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a) ) > tyop_2Epatricia_2Eptree(A_27a) ) ).
tff(c_2Epatricia__casts_2EADDw_2E0,type,
c_2Epatricia__casts_2EADDw_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))) ).
tff(c_2Epatricia__casts_2EADDw_2E2,type,
c_2Epatricia__casts_2EADDw_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b) * tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b) ) > tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b) ) ).
tff(c_2Elist_2EAPPEND_2E0,type,
c_2Elist_2EAPPEND_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Elist_2EAPPEND_2E2,type,
c_2Elist_2EAPPEND_2E2:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Earithmetic_2EBIT1_2E0,type,
c_2Earithmetic_2EBIT1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EBIT1_2E1,type,
c_2Earithmetic_2EBIT1_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2EBIT2_2E0,type,
c_2Earithmetic_2EBIT2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EBIT2_2E1,type,
c_2Earithmetic_2EBIT2_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Eind__type_2EBOTTOM_2E0,type,
c_2Eind__type_2EBOTTOM_2E0:
!>[A_27a: $tType] : tyop_2Eind__type_2Erecspace(A_27a) ).
tff(c_2Estring_2ECHR_2E0,type,
c_2Estring_2ECHR_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar) ).
tff(c_2Estring_2ECHR_2E1,type,
c_2Estring_2ECHR_2E1: tyop_2Enum_2Enum > tyop_2Estring_2Echar ).
tff(c_2Elist_2ECONS_2E0,type,
c_2Elist_2ECONS_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Elist_2ECONS_2E2,type,
c_2Elist_2ECONS_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Eind__type_2ECONSTR_2E0,type,
c_2Eind__type_2ECONSTR_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a)))) ).
tff(c_2Eind__type_2ECONSTR_2E3,type,
c_2Eind__type_2ECONSTR_2E3:
!>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * A_27a * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)) ) > tyop_2Eind__type_2Erecspace(A_27a) ) ).
tff(c_2Ebool_2EDATATYPE_2E0,type,
c_2Ebool_2EDATATYPE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2EDATATYPE_2E1,type,
c_2Ebool_2EDATATYPE_2E1:
!>[A_27a: $tType] : ( A_27a > tyop_2Emin_2Ebool ) ).
tff(c_2Epatricia_2EDEPTH_2E0,type,
c_2Epatricia_2EDEPTH_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Enum_2Enum) ).
tff(c_2Epatricia_2EDEPTH_2E1,type,
c_2Epatricia_2EDEPTH_2E1:
!>[A_27a: $tType] : ( tyop_2Epatricia_2Eptree(A_27a) > tyop_2Enum_2Enum ) ).
tff(c_2Epatricia__casts_2EDEPTHw_2E0,type,
c_2Epatricia__casts_2EDEPTHw_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Enum_2Enum) ).
tff(c_2Epatricia__casts_2EDEPTHw_2E1,type,
c_2Epatricia__casts_2EDEPTHw_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b) > tyop_2Enum_2Enum ) ).
tff(c_2Earithmetic_2EDIV_2E0,type,
c_2Earithmetic_2EDIV_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2EDIV_2E2,type,
c_2Earithmetic_2EDIV_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Elist_2EEVERY_2E0,type,
c_2Elist_2EEVERY_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Elist_2EEVERY_2E2,type,
c_2Elist_2EEVERY_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epatricia_2EEVERY__LEAF_2E0,type,
c_2Epatricia_2EEVERY__LEAF_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Epatricia_2EEVERY__LEAF_2E2,type,
c_2Epatricia_2EEVERY__LEAF_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Epatricia_2Eptree(A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epatricia__casts_2EEVERY__LEAFw_2E0,type,
c_2Epatricia__casts_2EEVERY__LEAFw_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Ebool)) ).
tff(c_2Epatricia__casts_2EEVERY__LEAFw_2E2,type,
c_2Epatricia__casts_2EEVERY__LEAFw_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epatricia_2EEXISTS__LEAF_2E0,type,
c_2Epatricia_2EEXISTS__LEAF_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Epatricia_2EEXISTS__LEAF_2E2,type,
c_2Epatricia_2EEXISTS__LEAF_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Epatricia_2Eptree(A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epatricia__casts_2EEXISTS__LEAFw_2E0,type,
c_2Epatricia__casts_2EEXISTS__LEAFw_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Ebool)) ).
tff(c_2Epatricia__casts_2EEXISTS__LEAFw_2E2,type,
c_2Epatricia__casts_2EEXISTS__LEAFw_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Earithmetic_2EEXP_2E0,type,
c_2Earithmetic_2EEXP_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2EEXP_2E2,type,
c_2Earithmetic_2EEXP_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Epatricia_2EEmpty_2E0,type,
c_2Epatricia_2EEmpty_2E0:
!>[A_27a: $tType] : tyop_2Epatricia_2Eptree(A_27a) ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(c_2Epatricia__casts_2EFINDs_2E0,type,
c_2Epatricia__casts_2EFINDs_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a)) ).
tff(c_2Epatricia__casts_2EFINDs_2E2,type,
c_2Epatricia__casts_2EFINDs_2E2:
!>[A_27a: $tType] : ( ( tyop_2Epatricia_2Eptree(A_27a) * tyop_2Elist_2Elist(tyop_2Estring_2Echar) ) > A_27a ) ).
tff(c_2Epatricia__casts_2EFINDw_2E0,type,
c_2Epatricia__casts_2EFINDw_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),A_27a)) ).
tff(c_2Epatricia__casts_2EFINDw_2E2,type,
c_2Epatricia__casts_2EFINDw_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a) * tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b) ) > A_27a ) ).
tff(c_2Elist_2EFOLDL_2E0,type,
c_2Elist_2EFOLDL_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))) ).
tff(c_2Elist_2EFOLDL_2E1,type,
c_2Elist_2EFOLDL_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)) > tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)) ) ).
tff(c_2Epred__set_2EIMAGE_2E0,type,
c_2Epred__set_2EIMAGE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EIMAGE_2E2,type,
c_2Epred__set_2EIMAGE_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) ).
tff(c_2Ebool_2EIN_2E0,type,
c_2Ebool_2EIN_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2EIN_2E2,type,
c_2Ebool_2EIN_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epatricia_2EINSERT__PTREE_2E0,type,
c_2Epatricia_2EINSERT__PTREE_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone))) ).
tff(c_2Epatricia_2EINSERT__PTREE_2E2,type,
c_2Epatricia_2EINSERT__PTREE_2E2: ( tyop_2Enum_2Enum * tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone) ) > tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone) ).
tff(c_2Epatricia__casts_2EINSERT__PTREEs_2E0,type,
c_2Epatricia__casts_2EINSERT__PTREEs_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone))) ).
tff(c_2Epatricia__casts_2EINSERT__PTREEs_2E2,type,
c_2Epatricia__casts_2EINSERT__PTREEs_2E2: ( tyop_2Elist_2Elist(tyop_2Estring_2Echar) * tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone) ) > tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone) ).
tff(c_2Epatricia__casts_2EINSERT__PTREEw_2E0,type,
c_2Epatricia__casts_2EINSERT__PTREEw_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone))) ).
tff(c_2Epatricia__casts_2EINSERT__PTREEw_2E2,type,
c_2Epatricia__casts_2EINSERT__PTREEw_2E2:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) * tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone) ) > tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone) ) ).
tff(c_2Epatricia_2EIN__PTREE_2E0,type,
c_2Epatricia_2EIN__PTREE_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Emin_2Ebool)) ).
tff(c_2Epatricia_2EIN__PTREE_2E2,type,
c_2Epatricia_2EIN__PTREE_2E2: ( tyop_2Enum_2Enum * tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone) ) > tyop_2Emin_2Ebool ).
tff(c_2Epatricia__casts_2EIN__PTREEs_2E0,type,
c_2Epatricia__casts_2EIN__PTREEs_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Emin_2Ebool)) ).
tff(c_2Epatricia__casts_2EIN__PTREEs_2E2,type,
c_2Epatricia__casts_2EIN__PTREEs_2E2: ( tyop_2Elist_2Elist(tyop_2Estring_2Echar) * tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone) ) > tyop_2Emin_2Ebool ).
tff(c_2Epatricia__casts_2EIN__PTREEw_2E0,type,
c_2Epatricia__casts_2EIN__PTREEw_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Ebool)) ).
tff(c_2Epatricia__casts_2EIN__PTREEw_2E2,type,
c_2Epatricia__casts_2EIN__PTREEw_2E2:
!>[A_27a: $tType] : ( ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) * tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ecombin_2EK_2E0,type,
c_2Ecombin_2EK_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(c_2Ecombin_2EK_2E1,type,
c_2Ecombin_2EK_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( A_27a > tyop_2Emin_2Efun(A_27b,A_27a) ) ).
tff(c_2Epatricia__casts_2EKEYSs_2E0,type,
c_2Epatricia__casts_2EKEYSs_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar))) ).
tff(c_2Epatricia__casts_2EKEYSs_2E1,type,
c_2Epatricia__casts_2EKEYSs_2E1:
!>[A_27a: $tType] : ( tyop_2Epatricia_2Eptree(A_27a) > tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)) ) ).
tff(c_2Epatricia__casts_2EKEYSw_2E0,type,
c_2Epatricia__casts_2EKEYSw_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a))) ).
tff(c_2Epatricia__casts_2EKEYSw_2E1,type,
c_2Epatricia__casts_2EKEYSw_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b) > tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)) ) ).
tff(c_2Elist_2ELENGTH_2E0,type,
c_2Elist_2ELENGTH_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum) ).
tff(c_2Elist_2ELENGTH_2E1,type,
c_2Elist_2ELENGTH_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Enum_2Enum ) ).
tff(c_2Elist_2ELIST__TO__SET_2E0,type,
c_2Elist_2ELIST__TO__SET_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Elist_2ELIST__TO__SET_2E1,type,
c_2Elist_2ELIST__TO__SET_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Elogroot_2ELOG_2E0,type,
c_2Elogroot_2ELOG_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Elogroot_2ELOG_2E2,type,
c_2Elogroot_2ELOG_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Elist_2EMAP_2E0,type,
c_2Elist_2EMAP_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))) ).
tff(c_2Elist_2EMAP_2E2,type,
c_2Elist_2EMAP_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27b) ) ).
tff(c_2Elist_2ENIL_2E0,type,
c_2Elist_2ENIL_2E0:
!>[A_27a: $tType] : tyop_2Elist_2Elist(A_27a) ).
tff(c_2Earithmetic_2ENUMERAL_2E0,type,
c_2Earithmetic_2ENUMERAL_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2ENUMERAL_2E1,type,
c_2Earithmetic_2ENUMERAL_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Estring_2EORD_2E0,type,
c_2Estring_2EORD_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum) ).
tff(c_2Epatricia_2EPEEK_2E0,type,
c_2Epatricia_2EPEEK_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))) ).
tff(c_2Epatricia_2EPEEK_2E2,type,
c_2Epatricia_2EPEEK_2E2:
!>[A_27a: $tType] : ( ( tyop_2Epatricia_2Eptree(A_27a) * tyop_2Enum_2Enum ) > tyop_2Eoption_2Eoption(A_27a) ) ).
tff(c_2Epatricia__casts_2EPEEKs_2E0,type,
c_2Epatricia__casts_2EPEEKs_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eoption_2Eoption(A_27a))) ).
tff(c_2Epatricia__casts_2EPEEKs_2E2,type,
c_2Epatricia__casts_2EPEEKs_2E2:
!>[A_27a: $tType] : ( ( tyop_2Epatricia_2Eptree(A_27a) * tyop_2Elist_2Elist(tyop_2Estring_2Echar) ) > tyop_2Eoption_2Eoption(A_27a) ) ).
tff(c_2Epatricia__casts_2EPEEKw_2E0,type,
c_2Epatricia__casts_2EPEEKw_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Eoption_2Eoption(A_27b))) ).
tff(c_2Epatricia__casts_2EPEEKw_2E2,type,
c_2Epatricia__casts_2EPEEKw_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b) * tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) > tyop_2Eoption_2Eoption(A_27b) ) ).
tff(c_2Epatricia_2EPTREE__OF__NUMSET_2E0,type,
c_2Epatricia_2EPTREE__OF__NUMSET_2E0: tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone))) ).
tff(c_2Epatricia_2EPTREE__OF__NUMSET_2E2,type,
c_2Epatricia_2EPTREE__OF__NUMSET_2E2: ( tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone) * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ) > tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone) ).
tff(c_2Epatricia__casts_2EPTREE__OF__STRINGSET_2E0,type,
c_2Epatricia__casts_2EPTREE__OF__STRINGSET_2E0: tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone))) ).
tff(c_2Epatricia__casts_2EPTREE__OF__STRINGSET_2E2,type,
c_2Epatricia__casts_2EPTREE__OF__STRINGSET_2E2: ( tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone) * tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool) ) > tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone) ).
tff(c_2Epatricia__casts_2EPTREE__OF__WORDSET_2E0,type,
c_2Epatricia__casts_2EPTREE__OF__WORDSET_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone))) ).
tff(c_2Epatricia__casts_2EPTREE__OF__WORDSET_2E2,type,
c_2Epatricia__casts_2EPTREE__OF__WORDSET_2E2:
!>[A_27a: $tType] : ( ( tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone) * tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool) ) > tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone) ) ).
tff(c_2Esorting_2EQSORT_2E0,type,
c_2Esorting_2EQSORT_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Esorting_2EQSORT_2E2,type,
c_2Esorting_2EQSORT_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Epatricia_2EREMOVE_2E0,type,
c_2Epatricia_2EREMOVE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epatricia_2Eptree(A_27a))) ).
tff(c_2Epatricia_2EREMOVE_2E2,type,
c_2Epatricia_2EREMOVE_2E2:
!>[A_27a: $tType] : ( ( tyop_2Epatricia_2Eptree(A_27a) * tyop_2Enum_2Enum ) > tyop_2Epatricia_2Eptree(A_27a) ) ).
tff(c_2Epatricia__casts_2EREMOVEs_2E0,type,
c_2Epatricia__casts_2EREMOVEs_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epatricia_2Eptree(A_27a))) ).
tff(c_2Epatricia__casts_2EREMOVEs_2E2,type,
c_2Epatricia__casts_2EREMOVEs_2E2:
!>[A_27a: $tType] : ( ( tyop_2Epatricia_2Eptree(A_27a) * tyop_2Elist_2Elist(tyop_2Estring_2Echar) ) > tyop_2Epatricia_2Eptree(A_27a) ) ).
tff(c_2Epatricia__casts_2EREMOVEw_2E0,type,
c_2Epatricia__casts_2EREMOVEw_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))) ).
tff(c_2Epatricia__casts_2EREMOVEw_2E2,type,
c_2Epatricia__casts_2EREMOVEw_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b) * tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) > tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b) ) ).
tff(c_2Elist_2EREVERSE_2E0,type,
c_2Elist_2EREVERSE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)) ).
tff(c_2Elist_2EREVERSE_2E1,type,
c_2Elist_2EREVERSE_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Epatricia_2ESIZE_2E0,type,
c_2Epatricia_2ESIZE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Enum_2Enum) ).
tff(c_2Epatricia_2ESIZE_2E1,type,
c_2Epatricia_2ESIZE_2E1:
!>[A_27a: $tType] : ( tyop_2Epatricia_2Eptree(A_27a) > tyop_2Enum_2Enum ) ).
tff(c_2Epatricia__casts_2ESIZEw_2E0,type,
c_2Epatricia__casts_2ESIZEw_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Enum_2Enum) ).
tff(c_2Epatricia__casts_2ESIZEw_2E1,type,
c_2Epatricia__casts_2ESIZEw_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b) > tyop_2Enum_2Enum ) ).
tff(c_2Epatricia__casts_2ESKIP1_2E0,type,
c_2Epatricia__casts_2ESKIP1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)) ).
tff(c_2Epatricia__casts_2ESKIP1_2E1,type,
c_2Epatricia__casts_2ESKIP1_2E1: tyop_2Elist_2Elist(tyop_2Estring_2Echar) > tyop_2Elist_2Elist(tyop_2Estring_2Echar) ).
tff(c_2Epatricia__casts_2ESOME__PTREE_2E0,type,
c_2Epatricia__casts_2ESOME__PTREE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)) ).
tff(c_2Epatricia__casts_2ESOME__PTREE_2E1,type,
c_2Epatricia__casts_2ESOME__PTREE_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epatricia_2Eptree(A_27b) > tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b) ) ).
tff(c_2Epatricia__casts_2ESTRINGSET__OF__PTREE_2E0,type,
c_2Epatricia__casts_2ESTRINGSET__OF__PTREE_2E0: tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)) ).
tff(c_2Epatricia__casts_2ESTRINGSET__OF__PTREE_2E1,type,
c_2Epatricia__casts_2ESTRINGSET__OF__PTREE_2E1: tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(c_2Eoption_2ETHE_2E0,type,
c_2Eoption_2ETHE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),A_27a) ).
tff(c_2Eoption_2ETHE_2E1,type,
c_2Eoption_2ETHE_2E1:
!>[A_27a: $tType] : ( tyop_2Eoption_2Eoption(A_27a) > A_27a ) ).
tff(c_2Epatricia__casts_2ETHE__PTREE_2E0,type,
c_2Epatricia__casts_2ETHE__PTREE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a),tyop_2Epatricia_2Eptree(A_27a)) ).
tff(c_2Epatricia__casts_2ETHE__PTREE_2E1,type,
c_2Epatricia__casts_2ETHE__PTREE_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a) > tyop_2Epatricia_2Eptree(A_27a) ) ).
tff(c_2Epatricia_2ETRANSFORM_2E0,type,
c_2Epatricia_2ETRANSFORM_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),tyop_2Epatricia_2Eptree(A_27a))) ).
tff(c_2Epatricia_2ETRANSFORM_2E2,type,
c_2Epatricia_2ETRANSFORM_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27b,A_27a) * tyop_2Epatricia_2Eptree(A_27b) ) > tyop_2Epatricia_2Eptree(A_27a) ) ).
tff(c_2Epatricia__casts_2ETRANSFORMw_2E0,type,
c_2Epatricia__casts_2ETRANSFORMw_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27c,A_27a),tyop_2Epatricia__casts_2Eword__ptree(A_27c,A_27b))) ).
tff(c_2Epatricia__casts_2ETRANSFORMw_2E2,type,
c_2Epatricia__casts_2ETRANSFORMw_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Epatricia__casts_2Eword__ptree(A_27c,A_27a) ) > tyop_2Epatricia__casts_2Eword__ptree(A_27c,A_27b) ) ).
tff(c_2Epatricia_2ETRAVERSE_2E0,type,
c_2Epatricia_2ETRAVERSE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Elist_2Elist(tyop_2Enum_2Enum)) ).
tff(c_2Epatricia_2ETRAVERSE_2E1,type,
c_2Epatricia_2ETRAVERSE_2E1:
!>[A_27a: $tType] : ( tyop_2Epatricia_2Eptree(A_27a) > tyop_2Elist_2Elist(tyop_2Enum_2Enum) ) ).
tff(c_2Epatricia__casts_2ETRAVERSEs_2E0,type,
c_2Epatricia__casts_2ETRAVERSEs_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar))) ).
tff(c_2Epatricia__casts_2ETRAVERSEs_2E1,type,
c_2Epatricia__casts_2ETRAVERSEs_2E1:
!>[A_27a: $tType] : ( tyop_2Epatricia_2Eptree(A_27a) > tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)) ) ).
tff(c_2Epatricia__casts_2ETRAVERSEw_2E0,type,
c_2Epatricia__casts_2ETRAVERSEw_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a))) ).
tff(c_2Epatricia__casts_2ETRAVERSEw_2E1,type,
c_2Epatricia__casts_2ETRAVERSEw_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b) > tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)) ) ).
tff(c_2Ebool_2ETYPE__DEFINITION_2E0,type,
c_2Ebool_2ETYPE__DEFINITION_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2ETYPE__DEFINITION_2E2,type,
c_2Ebool_2ETYPE__DEFINITION_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epatricia_2EUNION__PTREE_2E0,type,
c_2Epatricia_2EUNION__PTREE_2E0: tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone))) ).
tff(c_2Epatricia_2EUNION__PTREE_2E2,type,
c_2Epatricia_2EUNION__PTREE_2E2: ( tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone) * tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone) ) > tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone) ).
tff(c_2Epatricia__casts_2EUNION__PTREEw_2E0,type,
c_2Epatricia__casts_2EUNION__PTREEw_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27c,tyop_2Eone_2Eone),tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone))) ).
tff(c_2Epatricia__casts_2EUNION__PTREEw_2E2,type,
c_2Epatricia__casts_2EUNION__PTREEw_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Epatricia__casts_2Eword__ptree(A_27b,tyop_2Eone_2Eone) * tyop_2Epatricia__casts_2Eword__ptree(A_27c,tyop_2Eone_2Eone) ) > tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone) ) ).
tff(c_2Epred__set_2EUNIV_2E0,type,
c_2Epred__set_2EUNIV_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).
tff(c_2Epatricia__casts_2EWORDSET__OF__PTREE_2E0,type,
c_2Epatricia__casts_2EWORDSET__OF__PTREE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Epatricia__casts_2EWORDSET__OF__PTREE_2E1,type,
c_2Epatricia__casts_2EWORDSET__OF__PTREE_2E1:
!>[A_27a: $tType] : ( tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone) > tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool) ) ).
tff(c_2Epatricia__casts_2EWordEmpty_2E0,type,
c_2Epatricia__casts_2EWordEmpty_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b) ).
tff(c_2Epatricia__casts_2EWord__ptree_2E0,type,
c_2Epatricia__casts_2EWord__ptree_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))) ).
tff(c_2Epatricia__casts_2EWord__ptree_2E2,type,
c_2Epatricia__casts_2EWord__ptree_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone) * tyop_2Epatricia_2Eptree(A_27b) ) > tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b) ) ).
tff(c_2Earithmetic_2EZERO_2E0,type,
c_2Earithmetic_2EZERO_2E0: tyop_2Enum_2Enum ).
tff(c_2Ebool_2E_5C_2F_2E0,type,
c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_5C_2F_2E2,type,
c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Enumposrep_2El2n_2E0,type,
c_2Enumposrep_2El2n_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum)) ).
tff(c_2Enumposrep_2El2n_2E2,type,
c_2Enumposrep_2El2n_2E2: ( tyop_2Enum_2Enum * tyop_2Elist_2Elist(tyop_2Enum_2Enum) ) > tyop_2Enum_2Enum ).
tff(c_2EASCIInumbers_2En2s_2E0,type,
c_2EASCIInumbers_2En2s_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)))) ).
tff(c_2EASCIInumbers_2En2s_2E3,type,
c_2EASCIInumbers_2En2s_2E3: ( tyop_2Enum_2Enum * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar) * tyop_2Enum_2Enum ) > tyop_2Elist_2Elist(tyop_2Estring_2Echar) ).
tff(c_2Ewords_2En2w_2E0,type,
c_2Ewords_2En2w_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)) ).
tff(c_2Ewords_2En2w_2E1,type,
c_2Ewords_2En2w_2E1:
!>[A_27a: $tType] : ( tyop_2Enum_2Enum > tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) ) ).
tff(c_2Epatricia__casts_2Enum__to__string_2E0,type,
c_2Epatricia__casts_2Enum__to__string_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)) ).
tff(c_2Epatricia__casts_2Enum__to__string_2E1,type,
c_2Epatricia__casts_2Enum__to__string_2E1: tyop_2Enum_2Enum > tyop_2Elist_2Elist(tyop_2Estring_2Echar) ).
tff(c_2Eone_2Eone_2E0,type,
c_2Eone_2Eone_2E0: tyop_2Eone_2Eone ).
tff(c_2Epatricia_2Eptree__size_2E0,type,
c_2Epatricia_2Eptree__size_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Enum_2Enum)) ).
tff(c_2Epatricia_2Eptree__size_2E2,type,
c_2Epatricia_2Eptree__size_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Epatricia_2Eptree(A_27a) ) > tyop_2Enum_2Enum ) ).
tff(c_2EASCIInumbers_2Es2n_2E0,type,
c_2EASCIInumbers_2Es2n_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum))) ).
tff(c_2EASCIInumbers_2Es2n_2E3,type,
c_2EASCIInumbers_2Es2n_2E3: ( tyop_2Enum_2Enum * tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum) * tyop_2Elist_2Elist(tyop_2Estring_2Echar) ) > tyop_2Enum_2Enum ).
tff(c_2Estring_2Estring__lt_2E0,type,
c_2Estring_2Estring__lt_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)) ).
tff(c_2Epatricia__casts_2Estring__to__num_2E0,type,
c_2Epatricia__casts_2Estring__to__num_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum) ).
tff(c_2Epatricia__casts_2Estring__to__num_2E1,type,
c_2Epatricia__casts_2Estring__to__num_2E1: tyop_2Elist_2Elist(tyop_2Estring_2Echar) > tyop_2Enum_2Enum ).
tff(c_2Ewords_2Ew2n_2E0,type,
c_2Ewords_2Ew2n_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Enum_2Enum) ).
tff(c_2Ewords_2Ew2n_2E1,type,
c_2Ewords_2Ew2n_2E1:
!>[A_27a: $tType] : ( tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a) > tyop_2Enum_2Enum ) ).
tff(c_2Ewords_2Eword__lo_2E0,type,
c_2Ewords_2Eword__lo_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Epatricia__casts_2Eword__ptree__CASE_2E0,type,
c_2Epatricia__casts_2Eword__ptree__CASE_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c)),A_27c)) ).
tff(c_2Epatricia__casts_2Eword__ptree__CASE_2E2,type,
c_2Epatricia__casts_2Eword__ptree__CASE_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b) * tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c)) ) > A_27c ) ).
tff(c_2Epatricia__casts_2Eword__ptree__size_2E0,type,
c_2Epatricia__casts_2Eword__ptree__size_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Enum_2Enum))) ).
tff(c_2Epatricia__casts_2Eword__ptree__size_2E3,type,
c_2Epatricia__casts_2Eword__ptree__size_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum) * tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b) ) > tyop_2Enum_2Enum ) ).
tff(c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(thm_2Eextra_2Dho_2Eeq__ext,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0) )
=> ( V0f_2E0 = V1g_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Eboolext,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( ( p(V0_2E0)
<=> p(V1_2E0) )
=> ( V0_2E0 = V1_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Etruth,axiom,
p(c_2Ebool_2ET_2E0) ).
tff(thm_2Eextra_2Dho_2Enotfalse,axiom,
~ p(c_2Ebool_2EF_2E0) ).
tff(thm_2Eextra_2Dho_2Ebool__cases__ax,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
| ( V0t_2E0 = c_2Ebool_2EF_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Ei__thm,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,combin_i_2E0(A_27a),V0x_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Ek__thm,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : ( app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),combin_k_2E0(A_27a,A_27b),V0x_2E0),V1y_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Es__thm,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),combin_s_2E0(A_27a,A_27b,A_27c),V0f_2E0),V1g_2E0),V2x_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V2x_2E0),app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)) ) ).
tff(logicdef_2E_2F_5C,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
& p(V1_2E0) ) ) ).
tff(logicdef_2E_5C_2F,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
| p(V1_2E0) ) ) ).
tff(logicdef_2E_7E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(V0_2E0))
<=> ~ p(V0_2E0) ) ).
tff(logicdef_2E_3D_3D_3E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
=> p(V1_2E0) ) ) ).
tff(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0_2E0: A_27a,V1_2E0: A_27a] :
( p(c_2Emin_2E_3D_2E2(A_27a,V0_2E0,V1_2E0))
<=> ( V0_2E0 = V1_2E0 ) ) ).
tff(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(A_27a,V0f_2E0))
<=> ! [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_2E1(A_27a,V0f_2E0))
<=> ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_2A_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2A_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0: A_27b] : ( c_2Epair_2E_2C_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b)),c_2Epair_2E_2C_2E0(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29_20mono_2Etyop_2Eone_2Eone,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0: tyop_2Eone_2Eone] : ( c_2Epair_2E_2C_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Eone_2Eone,X0_2E0,X1_2E0) = app_2E2(tyop_2Eone_2Eone,tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Eone_2Eone),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Eone_2Eone)),c_2Epair_2E_2C_2E0(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Eone_2Eone),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eone_2Eone_29_20mono_2Etyop_2Epatricia_2Eptree_28A_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),X1_2E0: tyop_2Epatricia_2Eptree(A_27b)] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Epatricia_2Eptree(A_27b),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0: A_27a] : ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a),app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a)),c_2Epair_2E_2C_2E0(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_20mono_2Etyop_2Eone_2Eone,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0: tyop_2Eone_2Eone] : ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eone_2Eone,X0_2E0,X1_2E0) = app_2E2(tyop_2Eone_2Eone,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eone_2Eone),app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eone_2Eone)),c_2Epair_2E_2C_2E0(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eone_2Eone),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: A_27a] : ( c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Epair_2E_2C_2E0(tyop_2Enum_2Enum,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: A_27b] : ( c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b)),c_2Epair_2E_2C_2E0(tyop_2Enum_2Enum,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
& p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3C_3D_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] :
( ( X0_2E0 = X1_2E0 )
<=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
=> p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Earithmetic_2E_3E_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3E_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3E_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia_2EADD_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epatricia_2Eptree(A_27a),X1_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)] : ( c_2Epatricia_2EADD_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Epatricia_2Eptree(A_27a),app_2E2(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Epatricia_2Eptree(A_27a)),c_2Epatricia_2EADD_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia_2EADD_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Epatricia_2Eptree(A_27b),X1_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b)] : ( c_2Epatricia_2EADD_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),tyop_2Epatricia_2Eptree(A_27b),app_2E2(tyop_2Epatricia_2Eptree(A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),tyop_2Epatricia_2Eptree(A_27b)),c_2Epatricia_2EADD_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia__casts_2EADDs_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epatricia_2Eptree(A_27a),X1_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a)] : ( c_2Epatricia__casts_2EADDs_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a),tyop_2Epatricia_2Eptree(A_27a),app_2E2(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a),tyop_2Epatricia_2Eptree(A_27a)),c_2Epatricia__casts_2EADDs_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia__casts_2EADDs_2E2_2Emono_2Etyop_2Eone_2Eone,axiom,
! [X0_2E0: tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),X1_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eone_2Eone)] : ( c_2Epatricia__casts_2EADDs_2E2(tyop_2Eone_2Eone,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),app_2E2(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone)),c_2Epatricia__casts_2EADDs_2E0(tyop_2Eone_2Eone),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia__casts_2EADDw_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),X1_2E0: tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b)] : ( c_2Epatricia__casts_2EADDw_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),app_2E2(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)),c_2Epatricia__casts_2EADDw_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia__casts_2EADDw_2E2_2Emono_2EA_27a_20mono_2Etyop_2Eone_2Eone,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),X1_2E0: tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Eone_2Eone)] : ( c_2Epatricia__casts_2EADDw_2E2(A_27a,tyop_2Eone_2Eone,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Eone_2Eone),tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),app_2E2(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Eone_2Eone),tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone)),c_2Epatricia__casts_2EADDw_2E0(A_27a,tyop_2Eone_2Eone),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2EAPPEND_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),c_2Elist_2EAPPEND_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT1_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT2_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Estring_2ECHR_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Estring_2ECHR_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Estring_2Echar,c_2Estring_2ECHR_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Estring_2Echar,axiom,
! [X0_2E0: tyop_2Estring_2Echar,X1_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2Elist_2ECONS_2E2(tyop_2Estring_2Echar,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(tyop_2Estring_2Echar,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Elist_2ECONS_2E0(tyop_2Estring_2Echar),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2ECONS_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),c_2Elist_2ECONS_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Eind__type_2ECONSTR_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28A_27b_29_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)),X2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))))] : ( c_2Eind__type_2ECONSTR_2E3(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)))),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))),app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)))),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)))),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))))),c_2Eind__type_2ECONSTR_2E0(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] : ( c_2Ebool_2EDATATYPE_2E1(tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E0(tyop_2Emin_2Ebool),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epatricia_2EDEPTH_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Epatricia_2Eptree(A_27b)] : ( c_2Epatricia_2EDEPTH_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Epatricia_2Eptree(A_27b),tyop_2Enum_2Enum,c_2Epatricia_2EDEPTH_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epatricia__casts_2EDEPTHw_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)] : ( c_2Epatricia__casts_2EDEPTHw_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Enum_2Enum,c_2Epatricia__casts_2EDEPTHw_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2EDIV_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EDIV_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2EEVERY_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Elist_2EEVERY_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia_2EEVERY__LEAF_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Epatricia_2Eptree(A_27b)] : ( c_2Epatricia_2EEVERY__LEAF_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Epatricia_2Eptree(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),tyop_2Emin_2Ebool),c_2Epatricia_2EEVERY__LEAF_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia__casts_2EEVERY__LEAFw_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)] : ( c_2Epatricia__casts_2EEVERY__LEAFw_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epatricia__casts_2EEVERY__LEAFw_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia_2EEXISTS__LEAF_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Epatricia_2Eptree(A_27b)] : ( c_2Epatricia_2EEXISTS__LEAF_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Epatricia_2Eptree(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),tyop_2Emin_2Ebool),c_2Epatricia_2EEXISTS__LEAF_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia__casts_2EEXISTS__LEAFw_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)] : ( c_2Epatricia__casts_2EEXISTS__LEAFw_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epatricia__casts_2EEXISTS__LEAFw_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2EEXP_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEXP_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia__casts_2EFINDs_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epatricia_2Eptree(A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2Epatricia__casts_2EFINDs_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a,app_2E2(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a),c_2Epatricia__casts_2EFINDs_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia__casts_2EFINDw_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a),X1_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)] : ( c_2Epatricia__casts_2EFINDw_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),A_27a,app_2E2(tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),A_27a),c_2Epatricia__casts_2EFINDw_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EFOLDL_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2CA_27a_29_20mono_2Etyop_2Epatricia_2Eptree_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a),tyop_2Epatricia_2Eptree(A_27a)))] : ( c_2Elist_2EFOLDL_2E1(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a),tyop_2Epatricia_2Eptree(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a),tyop_2Epatricia_2Eptree(A_27a))),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a)),tyop_2Epatricia_2Eptree(A_27a))),c_2Elist_2EFOLDL_2E0(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a),tyop_2Epatricia_2Eptree(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EFOLDL_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29_2CA_27b_29_20mono_2Etyop_2Epatricia__casts_2Eword__ptree_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)))] : ( c_2Elist_2EFOLDL_2E1(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b)),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))),c_2Elist_2EFOLDL_2E0(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)),X0_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia_2EINSERT__PTREE_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone)] : ( c_2Epatricia_2EINSERT__PTREE_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone)),c_2Epatricia_2EINSERT__PTREE_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia__casts_2EINSERT__PTREEs_2E2,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0: tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone)] : ( c_2Epatricia__casts_2EINSERT__PTREEs_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone)),c_2Epatricia__casts_2EINSERT__PTREEs_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia__casts_2EINSERT__PTREEw_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone)] : ( c_2Epatricia__casts_2EINSERT__PTREEw_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone)),c_2Epatricia__casts_2EINSERT__PTREEw_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia_2EIN__PTREE_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone)] : ( c_2Epatricia_2EIN__PTREE_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Emin_2Ebool),c_2Epatricia_2EIN__PTREE_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia__casts_2EIN__PTREEs_2E2,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar),X1_2E0: tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone)] : ( c_2Epatricia__casts_2EIN__PTREEs_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Emin_2Ebool),c_2Epatricia__casts_2EIN__PTREEs_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia__casts_2EIN__PTREEw_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X1_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone)] : ( c_2Epatricia__casts_2EIN__PTREEw_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Ebool,app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),c_2Epatricia__casts_2EIN__PTREEw_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Eone_2Eone_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eone_2Eone] : ( c_2Ecombin_2EK_2E1(tyop_2Eone_2Eone,A_27a,X0_2E0) = app_2E2(tyop_2Eone_2Eone,tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),c_2Ecombin_2EK_2E0(tyop_2Eone_2Eone,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epatricia__casts_2EKEYSs_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epatricia_2Eptree(A_27a)] : ( c_2Epatricia__casts_2EKEYSs_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Epatricia_2Eptree(A_27a),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Epatricia__casts_2EKEYSs_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epatricia__casts_2EKEYSw_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)] : ( c_2Epatricia__casts_2EKEYSw_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Epatricia__casts_2EKEYSw_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2ELENGTH_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a))] : ( c_2Elist_2ELIST__TO__SET_2E1(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar))] : ( c_2Elist_2ELIST__TO__SET_2E1(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X0_2E0) ) ).
tff(arityeq2_2Ec_2Elogroot_2ELOG_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Elogroot_2ELOG_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Elogroot_2ELOG_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EMAP_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EMAP_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Estring_2Echar_20mono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),X1_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2Elist_2EMAP_2E2(tyop_2Estring_2Echar,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),c_2Elist_2EMAP_2E0(tyop_2Estring_2Echar,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),X1_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2EMAP_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a))),c_2Elist_2EMAP_2E0(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X1_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2EMAP_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Elist_2EMAP_2E0(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2ENUMERAL_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia_2EPEEK_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epatricia_2Eptree(A_27a),X1_2E0: tyop_2Enum_2Enum] : ( c_2Epatricia_2EPEEK_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),c_2Epatricia_2EPEEK_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia_2EPEEK_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Epatricia_2Eptree(A_27b),X1_2E0: tyop_2Enum_2Enum] : ( c_2Epatricia_2EPEEK_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Epatricia_2Eptree(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27b)),c_2Epatricia_2EPEEK_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia__casts_2EPEEKs_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epatricia_2Eptree(A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2Epatricia__casts_2EPEEKs_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eoption_2Eoption(A_27a)),c_2Epatricia__casts_2EPEEKs_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia__casts_2EPEEKw_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),X1_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : ( c_2Epatricia__casts_2EPEEKw_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Eoption_2Eoption(A_27b)),c_2Epatricia__casts_2EPEEKw_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia__casts_2EPEEKw_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a),X1_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)] : ( c_2Epatricia__casts_2EPEEKw_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b),tyop_2Eoption_2Eoption(A_27a)),c_2Epatricia__casts_2EPEEKw_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia_2EPTREE__OF__NUMSET_2E2,axiom,
! [X0_2E0: tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epatricia_2EPTREE__OF__NUMSET_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),app_2E2(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone)),c_2Epatricia_2EPTREE__OF__NUMSET_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia__casts_2EPTREE__OF__STRINGSET_2E2,axiom,
! [X0_2E0: tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)] : ( c_2Epatricia__casts_2EPTREE__OF__STRINGSET_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),app_2E2(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone)),c_2Epatricia__casts_2EPTREE__OF__STRINGSET_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia__casts_2EPTREE__OF__WORDSET_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),X1_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool)] : ( c_2Epatricia__casts_2EPTREE__OF__WORDSET_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),app_2E2(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone)),c_2Epatricia__casts_2EPTREE__OF__WORDSET_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Esorting_2EQSORT_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a))] : ( c_2Esorting_2EQSORT_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a))),c_2Esorting_2EQSORT_2E0(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Esorting_2EQSORT_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar))] : ( c_2Esorting_2EQSORT_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2Esorting_2EQSORT_2E0(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia_2EREMOVE_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epatricia_2Eptree(A_27a),X1_2E0: tyop_2Enum_2Enum] : ( c_2Epatricia_2EREMOVE_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Epatricia_2Eptree(A_27a),app_2E2(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epatricia_2Eptree(A_27a)),c_2Epatricia_2EREMOVE_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia_2EREMOVE_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Epatricia_2Eptree(A_27b),X1_2E0: tyop_2Enum_2Enum] : ( c_2Epatricia_2EREMOVE_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Epatricia_2Eptree(A_27b),app_2E2(tyop_2Epatricia_2Eptree(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epatricia_2Eptree(A_27b)),c_2Epatricia_2EREMOVE_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia__casts_2EREMOVEs_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epatricia_2Eptree(A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2Epatricia__casts_2EREMOVEs_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epatricia_2Eptree(A_27a),app_2E2(tyop_2Epatricia_2Eptree(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Epatricia_2Eptree(A_27a)),c_2Epatricia__casts_2EREMOVEs_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia__casts_2EREMOVEw_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),X1_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : ( c_2Epatricia__casts_2EREMOVEw_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),app_2E2(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)),c_2Epatricia__casts_2EREMOVEw_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EREVERSE_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EREVERSE_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epatricia_2ESIZE_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Epatricia_2Eptree(A_27b)] : ( c_2Epatricia_2ESIZE_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Epatricia_2Eptree(A_27b),tyop_2Enum_2Enum,c_2Epatricia_2ESIZE_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epatricia__casts_2ESIZEw_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)] : ( c_2Epatricia__casts_2ESIZEw_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Enum_2Enum,c_2Epatricia__casts_2ESIZEw_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epatricia__casts_2ESKIP1_2E1,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2Epatricia__casts_2ESKIP1_2E1(X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Epatricia__casts_2ESKIP1_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Epatricia__casts_2ESOME__PTREE_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epatricia_2Eptree(A_27a)] : ( c_2Epatricia__casts_2ESOME__PTREE_2E1(A_27b,A_27a,X0_2E0) = app_2E2(tyop_2Epatricia_2Eptree(A_27a),tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a),c_2Epatricia__casts_2ESOME__PTREE_2E0(A_27b,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epatricia__casts_2ESOME__PTREE_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epatricia_2Eptree(A_27b)] : ( c_2Epatricia__casts_2ESOME__PTREE_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epatricia_2Eptree(A_27b),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),c_2Epatricia__casts_2ESOME__PTREE_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epatricia__casts_2ESOME__PTREE_2E1_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Epatricia_2Eptree(A_27b)] : ( c_2Epatricia__casts_2ESOME__PTREE_2E1(A_27c,A_27b,X0_2E0) = app_2E2(tyop_2Epatricia_2Eptree(A_27b),tyop_2Epatricia__casts_2Eword__ptree(A_27c,A_27b),c_2Epatricia__casts_2ESOME__PTREE_2E0(A_27c,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epatricia__casts_2ESOME__PTREE_2E1_2Emono_2EA_27a_20mono_2Etyop_2Eone_2Eone,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone)] : ( c_2Epatricia__casts_2ESOME__PTREE_2E1(A_27a,tyop_2Eone_2Eone,X0_2E0) = app_2E2(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),c_2Epatricia__casts_2ESOME__PTREE_2E0(A_27a,tyop_2Eone_2Eone),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epatricia__casts_2ESTRINGSET__OF__PTREE_2E1,axiom,
! [X0_2E0: tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone)] : ( c_2Epatricia__casts_2ESTRINGSET__OF__PTREE_2E1(X0_2E0) = app_2E2(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool),c_2Epatricia__casts_2ESTRINGSET__OF__PTREE_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27a)] : ( c_2Eoption_2ETHE_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27a),A_27a,c_2Eoption_2ETHE_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epatricia__casts_2ETHE__PTREE_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)] : ( c_2Epatricia__casts_2ETHE__PTREE_2E1(A_27b,A_27a,X0_2E0) = app_2E2(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Epatricia_2Eptree(A_27b),c_2Epatricia__casts_2ETHE__PTREE_2E0(A_27b,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epatricia__casts_2ETHE__PTREE_2E1_2Emono_2Etyop_2Eone_2Eone_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone)] : ( c_2Epatricia__casts_2ETHE__PTREE_2E1(tyop_2Eone_2Eone,A_27a,X0_2E0) = app_2E2(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),c_2Epatricia__casts_2ETHE__PTREE_2E0(tyop_2Eone_2Eone,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epatricia__casts_2ETHE__PTREE_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a)] : ( c_2Epatricia__casts_2ETHE__PTREE_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a),tyop_2Epatricia_2Eptree(A_27a),c_2Epatricia__casts_2ETHE__PTREE_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epatricia__casts_2ETHE__PTREE_2E1_2Emono_2Etyop_2Eone_2Eone_20mono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27b,tyop_2Eone_2Eone)] : ( c_2Epatricia__casts_2ETHE__PTREE_2E1(tyop_2Eone_2Eone,A_27b,X0_2E0) = app_2E2(tyop_2Epatricia__casts_2Eword__ptree(A_27b,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),c_2Epatricia__casts_2ETHE__PTREE_2E0(tyop_2Eone_2Eone,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epatricia__casts_2ETHE__PTREE_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27c,A_27a)] : ( c_2Epatricia__casts_2ETHE__PTREE_2E1(A_27a,A_27c,X0_2E0) = app_2E2(tyop_2Epatricia__casts_2Eword__ptree(A_27c,A_27a),tyop_2Epatricia_2Eptree(A_27a),c_2Epatricia__casts_2ETHE__PTREE_2E0(A_27a,A_27c),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epatricia__casts_2ETHE__PTREE_2E1_2Emono_2Etyop_2Eone_2Eone_20mono_2EA_27c,axiom,
! [A_27c: $tType,X0_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27c,tyop_2Eone_2Eone)] : ( c_2Epatricia__casts_2ETHE__PTREE_2E1(tyop_2Eone_2Eone,A_27c,X0_2E0) = app_2E2(tyop_2Epatricia__casts_2Eword__ptree(A_27c,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),c_2Epatricia__casts_2ETHE__PTREE_2E0(tyop_2Eone_2Eone,A_27c),X0_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia_2ETRANSFORM_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Epatricia_2Eptree(A_27a)] : ( c_2Epatricia_2ETRANSFORM_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Epatricia_2Eptree(A_27a),tyop_2Epatricia_2Eptree(A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Epatricia_2Eptree(A_27b)),c_2Epatricia_2ETRANSFORM_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia__casts_2ETRANSFORMw_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27c,A_27a)] : ( c_2Epatricia__casts_2ETRANSFORMw_2E2(A_27a,A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Epatricia__casts_2Eword__ptree(A_27c,A_27a),tyop_2Epatricia__casts_2Eword__ptree(A_27c,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27c,A_27a),tyop_2Epatricia__casts_2Eword__ptree(A_27c,A_27b)),c_2Epatricia__casts_2ETRANSFORMw_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epatricia_2ETRAVERSE_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epatricia_2Eptree(A_27a)] : ( c_2Epatricia_2ETRAVERSE_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Epatricia_2Eptree(A_27a),tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Epatricia_2ETRAVERSE_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epatricia_2ETRAVERSE_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Epatricia_2Eptree(A_27b)] : ( c_2Epatricia_2ETRAVERSE_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Epatricia_2Eptree(A_27b),tyop_2Elist_2Elist(tyop_2Enum_2Enum),c_2Epatricia_2ETRAVERSE_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epatricia__casts_2ETRAVERSEs_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epatricia_2Eptree(A_27a)] : ( c_2Epatricia__casts_2ETRAVERSEs_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Epatricia_2Eptree(A_27a),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Epatricia__casts_2ETRAVERSEs_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epatricia__casts_2ETRAVERSEs_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
! [X0_2E0: tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone)] : ( c_2Epatricia__casts_2ETRAVERSEs_2E1(tyop_2Eone_2Eone,X0_2E0) = app_2E2(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Elist_2Elist(tyop_2Estring_2Echar)),c_2Epatricia__casts_2ETRAVERSEs_2E0(tyop_2Eone_2Eone),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epatricia__casts_2ETRAVERSEw_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)] : ( c_2Epatricia__casts_2ETRAVERSEw_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Epatricia__casts_2ETRAVERSEw_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epatricia__casts_2ETRAVERSEw_2E1_2Emono_2EA_27a_20mono_2Etyop_2Eone_2Eone,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone)] : ( c_2Epatricia__casts_2ETRAVERSEw_2E1(A_27a,tyop_2Eone_2Eone,X0_2E0) = app_2E2(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),tyop_2Elist_2Elist(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)),c_2Epatricia__casts_2ETRAVERSEw_2E0(A_27a,tyop_2Eone_2Eone),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28tyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28A_27b_29_29_29_20mono_2Etyop_2Epatricia__casts_2Eword__ptree_28A_27a_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))))] : ( c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)))),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)))),tyop_2Emin_2Ebool),c_2Ebool_2ETYPE__DEFINITION_2E0(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia_2EUNION__PTREE_2E2,axiom,
! [X0_2E0: tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),X1_2E0: tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone)] : ( c_2Epatricia_2EUNION__PTREE_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),app_2E2(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone)),c_2Epatricia_2EUNION__PTREE_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia__casts_2EUNION__PTREEw_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27b,tyop_2Eone_2Eone),X1_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27c,tyop_2Eone_2Eone)] : ( c_2Epatricia__casts_2EUNION__PTREEw_2E2(A_27a,A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Epatricia__casts_2Eword__ptree(A_27c,tyop_2Eone_2Eone),tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),app_2E2(tyop_2Epatricia__casts_2Eword__ptree(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27c,tyop_2Eone_2Eone),tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone)),c_2Epatricia__casts_2EUNION__PTREEw_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epatricia__casts_2EWORDSET__OF__PTREE_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone)] : ( c_2Epatricia__casts_2EWORDSET__OF__PTREE_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),c_2Epatricia__casts_2EWORDSET__OF__PTREE_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia__casts_2EWord__ptree_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),X1_2E0: tyop_2Epatricia_2Eptree(A_27b)] : ( c_2Epatricia__casts_2EWord__ptree_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Epatricia_2Eptree(A_27b),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)),c_2Epatricia__casts_2EWord__ptree_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia__casts_2EWord__ptree_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),X1_2E0: tyop_2Epatricia_2Eptree(A_27a)] : ( c_2Epatricia__casts_2EWord__ptree_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Epatricia_2Eptree(A_27a),tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27a),tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a)),c_2Epatricia__casts_2EWord__ptree_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
| p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Enumposrep_2El2n_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Enumposrep_2El2n_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Enumposrep_2El2n_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2EASCIInumbers_2En2s_2E3,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),X2_2E0: tyop_2Enum_2Enum] : ( c_2EASCIInumbers_2En2s_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Estring_2Echar),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar))),c_2EASCIInumbers_2En2s_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum] : ( c_2Ewords_2En2w_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epatricia__casts_2Enum__to__string_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Epatricia__casts_2Enum__to__string_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Epatricia__casts_2Enum__to__string_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia_2Eptree__size_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0: tyop_2Epatricia_2Eptree(A_27b)] : ( c_2Epatricia_2Eptree__size_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Epatricia_2Eptree(A_27b),tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),tyop_2Enum_2Enum),c_2Epatricia_2Eptree__size_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2EASCIInumbers_2Es2n_2E3,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),X2_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2EASCIInumbers_2Es2n_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Estring_2Echar,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum)),c_2EASCIInumbers_2Es2n_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Epatricia__casts_2Estring__to__num_2E1,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2Epatricia__casts_2Estring__to__num_2E1(X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum,c_2Epatricia__casts_2Estring__to__num_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Ewords_2Ew2n_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : ( c_2Ewords_2Ew2n_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Enum_2Enum,c_2Ewords_2Ew2n_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Epatricia__casts_2Eword__ptree__CASE_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c))] : ( c_2Epatricia__casts_2Eword__ptree__CASE_2E2(A_27a,A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c)),A_27c,app_2E2(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c)),A_27c),c_2Epatricia__casts_2Eword__ptree__CASE_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Epatricia__casts_2Eword__ptree__size_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X2_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)] : ( c_2Epatricia__casts_2Eword__ptree__size_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Enum_2Enum)),c_2Epatricia__casts_2Eword__ptree__size_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] :
( ~ p(X0_2E0)
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0_2E0)) ) ).
tff(thm_2Epatricia__casts_2ESKIP1__def,axiom,
! [V0c_2E0: tyop_2Estring_2Echar,V1s_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2Epatricia__casts_2ESKIP1_2E1(c_2Elist_2ECONS_2E2(tyop_2Estring_2Echar,V0c_2E0,V1s_2E0)) = V1s_2E0 ) ).
tff(thm_2Epatricia__casts_2Estring__to__num__def,axiom,
! [V0s_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2Epatricia__casts_2Estring__to__num_2E1(V0s_2E0) = c_2EASCIInumbers_2Es2n_2E3(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))))),c_2Estring_2EORD_2E0,c_2Elist_2ECONS_2E2(tyop_2Estring_2Echar,c_2Estring_2ECHR_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V0s_2E0)) ) ).
tff(thm_2Epatricia__casts_2Enum__to__string__def,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Epatricia__casts_2Enum__to__string_2E1(V0n_2E0) = c_2Epatricia__casts_2ESKIP1_2E1(c_2EASCIInumbers_2En2s_2E3(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))))),c_2Estring_2ECHR_2E0,V0n_2E0)) ) ).
tff(thm_2Epatricia__casts_2EPEEKs__def,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Epatricia_2Eptree(A_27a),V1w_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2Epatricia__casts_2EPEEKs_2E2(A_27a,V0t_2E0,V1w_2E0) = c_2Epatricia_2EPEEK_2E2(A_27a,V0t_2E0,c_2Epatricia__casts_2Estring__to__num_2E1(V1w_2E0)) ) ).
tff(thm_2Epatricia__casts_2EFINDs__def,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Epatricia_2Eptree(A_27a),V1w_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2Epatricia__casts_2EFINDs_2E2(A_27a,V0t_2E0,V1w_2E0) = c_2Eoption_2ETHE_2E1(A_27a,c_2Epatricia__casts_2EPEEKs_2E2(A_27a,V0t_2E0,V1w_2E0)) ) ).
tff(thm_2Epatricia__casts_2EADDs__def,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Epatricia_2Eptree(A_27a),V1w_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar),V2d_2E0: A_27a] : ( c_2Epatricia__casts_2EADDs_2E2(A_27a,V0t_2E0,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a,V1w_2E0,V2d_2E0)) = c_2Epatricia_2EADD_2E2(A_27a,V0t_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,A_27a,c_2Epatricia__casts_2Estring__to__num_2E1(V1w_2E0),V2d_2E0)) ) ).
tff(thm_2Epatricia__casts_2EADD__LISTs__def,axiom,
! [A_27a: $tType] : ( c_2Epatricia__casts_2EADD__LISTs_2E0(A_27a) = c_2Elist_2EFOLDL_2E1(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Estring_2Echar),A_27a),tyop_2Epatricia_2Eptree(A_27a),c_2Epatricia__casts_2EADDs_2E0(A_27a)) ) ).
tff(thm_2Epatricia__casts_2EREMOVEs__def,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Epatricia_2Eptree(A_27a),V1w_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2Epatricia__casts_2EREMOVEs_2E2(A_27a,V0t_2E0,V1w_2E0) = c_2Epatricia_2EREMOVE_2E2(A_27a,V0t_2E0,c_2Epatricia__casts_2Estring__to__num_2E1(V1w_2E0)) ) ).
tff(thm_2Epatricia__casts_2ETRAVERSEs__def,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Epatricia_2Eptree(A_27a)] : ( c_2Epatricia__casts_2ETRAVERSEs_2E1(A_27a,V0t_2E0) = c_2Elist_2EMAP_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Epatricia__casts_2Enum__to__string_2E0,c_2Epatricia_2ETRAVERSE_2E1(A_27a,V0t_2E0)) ) ).
tff(thm_2Epatricia__casts_2EKEYSs__def,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Epatricia_2Eptree(A_27a)] : ( c_2Epatricia__casts_2EKEYSs_2E1(A_27a,V0t_2E0) = c_2Esorting_2EQSORT_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Estring_2Estring__lt_2E0,c_2Epatricia__casts_2ETRAVERSEs_2E1(A_27a,V0t_2E0)) ) ).
tff(thm_2Epatricia__casts_2EIN__PTREEs__def,axiom,
! [V0w_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1t_2E0: tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone)] : ( c_2Epatricia__casts_2EIN__PTREEs_2E2(V0w_2E0,V1t_2E0) = c_2Epatricia_2EIN__PTREE_2E2(c_2Epatricia__casts_2Estring__to__num_2E1(V0w_2E0),V1t_2E0) ) ).
tff(thm_2Epatricia__casts_2EINSERT__PTREEs__def,axiom,
! [V0w_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1t_2E0: tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone)] : ( c_2Epatricia__casts_2EINSERT__PTREEs_2E2(V0w_2E0,V1t_2E0) = c_2Epatricia_2EINSERT__PTREE_2E2(c_2Epatricia__casts_2Estring__to__num_2E1(V0w_2E0),V1t_2E0) ) ).
tff(thm_2Epatricia__casts_2ESTRINGSET__OF__PTREE__def,axiom,
! [V0t_2E0: tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone)] : ( c_2Epatricia__casts_2ESTRINGSET__OF__PTREE_2E1(V0t_2E0) = c_2Elist_2ELIST__TO__SET_2E1(tyop_2Elist_2Elist(tyop_2Estring_2Echar),c_2Epatricia__casts_2ETRAVERSEs_2E1(tyop_2Eone_2Eone,V0t_2E0)) ) ).
tff(thm_2Epatricia__casts_2EPTREE__OF__STRINGSET__def,axiom,
! [V0t_2E0: tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone),V1s_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Emin_2Ebool)] : ( c_2Epatricia__casts_2EPTREE__OF__STRINGSET_2E2(V0t_2E0,V1s_2E0) = c_2Epatricia_2EPTREE__OF__NUMSET_2E2(V0t_2E0,c_2Epred__set_2EIMAGE_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum,c_2Epatricia__casts_2Estring__to__num_2E0,V1s_2E0)) ) ).
tff(thm_2Epatricia__casts_2Eword__ptree__TY__DEF,axiom,
! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))),tyop_2Emin_2Ebool)] :
( ! [V6n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))),F1_2E0,V6n_2E0) = c_2Eind__type_2EBOTTOM_2E0(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))) )
=> ( ! [V1a0_27_2E0: tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)))] :
( p(app_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))),tyop_2Emin_2Ebool,F0_2E0,V1a0_27_2E0))
<=> ! [V2_27word__ptree_27_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))),tyop_2Emin_2Ebool)] :
( ! [V3a0_27_2E0: tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)))] :
( ? [V4a0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),V5a1_2E0: tyop_2Epatricia_2Eptree(A_27b)] : ( V3a0_27_2E0 = c_2Eind__type_2ECONSTR_2E3(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b)),c_2Enum_2E0_2E0,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b),V4a0_2E0,V5a1_2E0),F1_2E0) )
=> p(app_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))),tyop_2Emin_2Ebool,V2_27word__ptree_27_2E0,V3a0_27_2E0)) )
=> p(app_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))),tyop_2Emin_2Ebool,V2_27word__ptree_27_2E0,V1a0_27_2E0)) ) )
=> ? [V0rep_2E0: tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))))] : p(c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Eind__type_2Erecspace(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Epatricia_2Eptree(A_27b))),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),F0_2E0,V0rep_2E0)) ) ) ).
tff(thm_2Epatricia__casts_2Eword__ptree__case__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0a0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),V1a1_2E0: tyop_2Epatricia_2Eptree(A_27b),V2f_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c))] : ( c_2Epatricia__casts_2Eword__ptree__CASE_2E2(A_27a,A_27b,A_27c,c_2Epatricia__casts_2EWord__ptree_2E2(A_27a,A_27b,V0a0_2E0,V1a1_2E0),V2f_2E0) = app_2E2(tyop_2Epatricia_2Eptree(A_27b),A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c),V2f_2E0,V0a0_2E0),V1a1_2E0) ) ).
tff(thm_2Epatricia__casts_2Eword__ptree__size__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V1f1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V2a0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),V3a1_2E0: tyop_2Epatricia_2Eptree(A_27b)] : ( c_2Epatricia__casts_2Eword__ptree__size_2E3(A_27a,A_27b,V0f_2E0,V1f1_2E0,c_2Epatricia__casts_2EWord__ptree_2E2(A_27a,A_27b,V2a0_2E0,V3a1_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Epatricia_2Eptree__size_2E2(A_27b,V1f1_2E0,V3a1_2E0)) ) ).
tff(thm_2Epatricia__casts_2ETHE__PTREE__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0a_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eone_2Eone),V1t_2E0: tyop_2Epatricia_2Eptree(A_27a)] : ( c_2Epatricia__casts_2ETHE__PTREE_2E1(A_27a,A_27b,c_2Epatricia__casts_2EWord__ptree_2E2(A_27b,A_27a,V0a_2E0,V1t_2E0)) = V1t_2E0 ) ).
tff(thm_2Epatricia__casts_2ESOME__PTREE__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Epatricia_2Eptree(A_27b)] : ( c_2Epatricia__casts_2ESOME__PTREE_2E1(A_27a,A_27b,V0t_2E0) = c_2Epatricia__casts_2EWord__ptree_2E2(A_27a,A_27b,c_2Ecombin_2EK_2E1(tyop_2Eone_2Eone,A_27a,c_2Eone_2Eone_2E0),V0t_2E0) ) ).
tff(thm_2Epatricia__casts_2EWordEmpty__def,axiom,
! [A_27a: $tType,A_27b: $tType] : ( c_2Epatricia__casts_2EWordEmpty_2E0(A_27a,A_27b) = c_2Epatricia__casts_2ESOME__PTREE_2E1(A_27a,A_27b,c_2Epatricia_2EEmpty_2E0(A_27b)) ) ).
tff(thm_2Epatricia__casts_2EPEEKw__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V1w_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : ( c_2Epatricia__casts_2EPEEKw_2E2(A_27a,A_27b,V0t_2E0,V1w_2E0) = c_2Epatricia_2EPEEK_2E2(A_27b,c_2Epatricia__casts_2ETHE__PTREE_2E1(A_27b,A_27a,V0t_2E0),c_2Ewords_2Ew2n_2E1(A_27a,V1w_2E0)) ) ).
tff(thm_2Epatricia__casts_2EFINDw__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27b,A_27a),V1w_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27b)] : ( c_2Epatricia__casts_2EFINDw_2E2(A_27a,A_27b,V0t_2E0,V1w_2E0) = c_2Eoption_2ETHE_2E1(A_27a,c_2Epatricia__casts_2EPEEKw_2E2(A_27b,A_27a,V0t_2E0,V1w_2E0)) ) ).
tff(thm_2Epatricia__casts_2EADDw__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V1w_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V2d_2E0: A_27b] : ( c_2Epatricia__casts_2EADDw_2E2(A_27a,A_27b,V0t_2E0,c_2Epair_2E_2C_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b,V1w_2E0,V2d_2E0)) = c_2Epatricia__casts_2ESOME__PTREE_2E1(A_27a,A_27b,c_2Epatricia_2EADD_2E2(A_27b,c_2Epatricia__casts_2ETHE__PTREE_2E1(A_27b,A_27a,V0t_2E0),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,A_27b,c_2Ewords_2Ew2n_2E1(A_27a,V1w_2E0),V2d_2E0))) ) ).
tff(thm_2Epatricia__casts_2EADD__LISTw__def,axiom,
! [A_27a: $tType,A_27b: $tType] : ( c_2Epatricia__casts_2EADD__LISTw_2E0(A_27a,A_27b) = c_2Elist_2EFOLDL_2E1(tyop_2Epair_2Eprod(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),A_27b),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),c_2Epatricia__casts_2EADDw_2E0(A_27a,A_27b)) ) ).
tff(thm_2Epatricia__casts_2EREMOVEw__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V1w_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a)] : ( c_2Epatricia__casts_2EREMOVEw_2E2(A_27a,A_27b,V0t_2E0,V1w_2E0) = c_2Epatricia__casts_2ESOME__PTREE_2E1(A_27a,A_27b,c_2Epatricia_2EREMOVE_2E2(A_27b,c_2Epatricia__casts_2ETHE__PTREE_2E1(A_27b,A_27a,V0t_2E0),c_2Ewords_2Ew2n_2E1(A_27a,V1w_2E0))) ) ).
tff(thm_2Epatricia__casts_2ETRAVERSEw__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)] : ( c_2Epatricia__casts_2ETRAVERSEw_2E1(A_27a,A_27b,V0t_2E0) = c_2Elist_2EMAP_2E2(tyop_2Enum_2Enum,tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2En2w_2E0(A_27a),c_2Epatricia_2ETRAVERSE_2E1(A_27b,c_2Epatricia__casts_2ETHE__PTREE_2E1(A_27b,A_27a,V0t_2E0))) ) ).
tff(thm_2Epatricia__casts_2EKEYSw__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)] : ( c_2Epatricia__casts_2EKEYSw_2E1(A_27a,A_27b,V0t_2E0) = c_2Esorting_2EQSORT_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Ewords_2Eword__lo_2E0(A_27a),c_2Epatricia__casts_2ETRAVERSEw_2E1(A_27a,A_27b,V0t_2E0)) ) ).
tff(thm_2Epatricia__casts_2ETRANSFORMw__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1t_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27c,A_27a)] : ( c_2Epatricia__casts_2ETRANSFORMw_2E2(A_27a,A_27b,A_27c,V0f_2E0,V1t_2E0) = c_2Epatricia__casts_2ESOME__PTREE_2E1(A_27c,A_27b,c_2Epatricia_2ETRANSFORM_2E2(A_27b,A_27a,V0f_2E0,c_2Epatricia__casts_2ETHE__PTREE_2E1(A_27a,A_27c,V1t_2E0))) ) ).
tff(thm_2Epatricia__casts_2EEVERY__LEAFw__def,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))] :
( ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2k_2E0: tyop_2Enum_2Enum,V3d_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F0_2E0,V0P_2E0),V2k_2E0),V3d_2E0) = app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0,c_2Ewords_2En2w_2E1(A_27a,V2k_2E0)),V3d_2E0) )
=> ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1t_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)] : ( c_2Epatricia__casts_2EEVERY__LEAFw_2E2(A_27a,A_27b,V0P_2E0,V1t_2E0) = c_2Epatricia_2EEVERY__LEAF_2E2(A_27b,app_2E2(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F0_2E0,V0P_2E0),c_2Epatricia__casts_2ETHE__PTREE_2E1(A_27b,A_27a,V1t_2E0)) ) ) ).
tff(thm_2Epatricia__casts_2EEXISTS__LEAFw__def,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))] :
( ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2k_2E0: tyop_2Enum_2Enum,V3d_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F0_2E0,V0P_2E0),V2k_2E0),V3d_2E0) = app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0,c_2Ewords_2En2w_2E1(A_27a,V2k_2E0)),V3d_2E0) )
=> ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1t_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)] : ( c_2Epatricia__casts_2EEXISTS__LEAFw_2E2(A_27a,A_27b,V0P_2E0,V1t_2E0) = c_2Epatricia_2EEXISTS__LEAF_2E2(A_27b,app_2E2(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F0_2E0,V0P_2E0),c_2Epatricia__casts_2ETHE__PTREE_2E1(A_27b,A_27a,V1t_2E0)) ) ) ).
tff(thm_2Epatricia__casts_2ESIZEw__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)] : ( c_2Epatricia__casts_2ESIZEw_2E1(A_27a,A_27b,V0t_2E0) = c_2Epatricia_2ESIZE_2E1(A_27b,c_2Epatricia__casts_2ETHE__PTREE_2E1(A_27b,A_27a,V0t_2E0)) ) ).
tff(thm_2Epatricia__casts_2EDEPTHw__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)] : ( c_2Epatricia__casts_2EDEPTHw_2E1(A_27a,A_27b,V0t_2E0) = c_2Epatricia_2EDEPTH_2E1(A_27b,c_2Epatricia__casts_2ETHE__PTREE_2E1(A_27b,A_27a,V0t_2E0)) ) ).
tff(thm_2Epatricia__casts_2EIN__PTREEw__def,axiom,
! [A_27a: $tType,V0w_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1t_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone)] : ( c_2Epatricia__casts_2EIN__PTREEw_2E2(A_27a,V0w_2E0,V1t_2E0) = c_2Epatricia_2EIN__PTREE_2E2(c_2Ewords_2Ew2n_2E1(A_27a,V0w_2E0),c_2Epatricia__casts_2ETHE__PTREE_2E1(tyop_2Eone_2Eone,A_27a,V1t_2E0)) ) ).
tff(thm_2Epatricia__casts_2EINSERT__PTREEw__def,axiom,
! [A_27a: $tType,V0w_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1t_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone)] : ( c_2Epatricia__casts_2EINSERT__PTREEw_2E2(A_27a,V0w_2E0,V1t_2E0) = c_2Epatricia__casts_2ESOME__PTREE_2E1(A_27a,tyop_2Eone_2Eone,c_2Epatricia_2EINSERT__PTREE_2E2(c_2Ewords_2Ew2n_2E1(A_27a,V0w_2E0),c_2Epatricia__casts_2ETHE__PTREE_2E1(tyop_2Eone_2Eone,A_27a,V1t_2E0))) ) ).
tff(thm_2Epatricia__casts_2EWORDSET__OF__PTREE__def,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone)] : ( c_2Epatricia__casts_2EWORDSET__OF__PTREE_2E1(A_27a,V0t_2E0) = c_2Elist_2ELIST__TO__SET_2E1(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),c_2Epatricia__casts_2ETRAVERSEw_2E1(A_27a,tyop_2Eone_2Eone,V0t_2E0)) ) ).
tff(thm_2Epatricia__casts_2EUNION__PTREEw__def,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0t1_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27b,tyop_2Eone_2Eone),V1t2_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27c,tyop_2Eone_2Eone)] : ( c_2Epatricia__casts_2EUNION__PTREEw_2E2(A_27a,A_27b,A_27c,V0t1_2E0,V1t2_2E0) = c_2Epatricia__casts_2ESOME__PTREE_2E1(A_27a,tyop_2Eone_2Eone,c_2Epatricia_2EUNION__PTREE_2E2(c_2Epatricia__casts_2ETHE__PTREE_2E1(tyop_2Eone_2Eone,A_27b,V0t1_2E0),c_2Epatricia__casts_2ETHE__PTREE_2E1(tyop_2Eone_2Eone,A_27c,V1t2_2E0))) ) ).
tff(thm_2Epatricia__casts_2EPTREE__OF__WORDSET__def,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone),V1s_2E0: tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool)] : ( c_2Epatricia__casts_2EPTREE__OF__WORDSET_2E2(A_27a,V0t_2E0,V1s_2E0) = c_2Epatricia__casts_2ESOME__PTREE_2E1(A_27a,tyop_2Eone_2Eone,c_2Epatricia_2EPTREE__OF__NUMSET_2E2(c_2Epatricia__casts_2ETHE__PTREE_2E1(tyop_2Eone_2Eone,A_27a,V0t_2E0),c_2Epred__set_2EIMAGE_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Enum_2Enum,c_2Ewords_2Ew2n_2E0(A_27a),V1s_2E0))) ) ).
tff(thm_2Epatricia__casts_2Edatatype__word__ptree,axiom,
! [A_27a: $tType,A_27b: $tType,V0word__ptree_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))),tyop_2Emin_2Ebool)] : p(c_2Ebool_2EDATATYPE_2E1(tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b))),tyop_2Emin_2Ebool,V0word__ptree_2E0,c_2Epatricia__casts_2EWord__ptree_2E0(A_27a,A_27b)))) ).
tff(thm_2Epatricia__casts_2Eword__ptree__11,axiom,
! [A_27a: $tType,A_27b: $tType,V0a0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),V1a1_2E0: tyop_2Epatricia_2Eptree(A_27b),V2a0_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),V3a1_27_2E0: tyop_2Epatricia_2Eptree(A_27b)] :
( ( c_2Epatricia__casts_2EWord__ptree_2E2(A_27a,A_27b,V0a0_2E0,V1a1_2E0) = c_2Epatricia__casts_2EWord__ptree_2E2(A_27a,A_27b,V2a0_27_2E0,V3a1_27_2E0) )
<=> ( ( V0a0_2E0 = V2a0_27_2E0 )
& ( V1a1_2E0 = V3a1_27_2E0 ) ) ) ).
tff(thm_2Epatricia__casts_2Eword__ptree__nchotomy,axiom,
! [A_27a: $tType,A_27b: $tType,V0ww_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)] :
? [V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),V2p_2E0: tyop_2Epatricia_2Eptree(A_27b)] : ( V0ww_2E0 = c_2Epatricia__casts_2EWord__ptree_2E2(A_27a,A_27b,V1f_2E0,V2p_2E0) ) ).
tff(thm_2Epatricia__casts_2Eword__ptree__Axiom,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c))] :
? [V1fn_2E0: tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),A_27c)] :
! [V2a0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),V3a1_2E0: tyop_2Epatricia_2Eptree(A_27b)] : ( app_2E2(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),A_27c,V1fn_2E0,c_2Epatricia__casts_2EWord__ptree_2E2(A_27a,A_27b,V2a0_2E0,V3a1_2E0)) = app_2E2(tyop_2Epatricia_2Eptree(A_27b),A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c),V0f_2E0,V2a0_2E0),V3a1_2E0) ) ).
tff(thm_2Epatricia__casts_2Eword__ptree__induction,axiom,
! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Ebool)] :
( ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),V2p_2E0: tyop_2Epatricia_2Eptree(A_27b)] : p(app_2E2(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,c_2Epatricia__casts_2EWord__ptree_2E2(A_27a,A_27b,V1f_2E0,V2p_2E0)))
=> ! [V3w_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b)] : p(app_2E2(tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,V3w_2E0)) ) ).
tff(thm_2Epatricia__casts_2Eword__ptree__case__cong,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_27_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c)),V1M_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V2M_27_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V3f_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c))] :
( ( ( V1M_2E0 = V2M_27_2E0 )
& ! [V4a0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),V5a1_2E0: tyop_2Epatricia_2Eptree(A_27b)] :
( ( V2M_27_2E0 = c_2Epatricia__casts_2EWord__ptree_2E2(A_27a,A_27b,V4a0_2E0,V5a1_2E0) )
=> ( app_2E2(tyop_2Epatricia_2Eptree(A_27b),A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c),V3f_2E0,V4a0_2E0),V5a1_2E0) = app_2E2(tyop_2Epatricia_2Eptree(A_27b),A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c),V0f_27_2E0,V4a0_2E0),V5a1_2E0) ) ) )
=> ( c_2Epatricia__casts_2Eword__ptree__CASE_2E2(A_27a,A_27b,A_27c,V1M_2E0,V3f_2E0) = c_2Epatricia__casts_2Eword__ptree__CASE_2E2(A_27a,A_27b,A_27c,V2M_27_2E0,V0f_27_2E0) ) ) ).
tff(thm_2Epatricia__casts_2Eword__ptree__case__eq,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0x_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,A_27b),V1v_2E0: A_27c,V2f_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c))] :
( ( c_2Epatricia__casts_2Eword__ptree__CASE_2E2(A_27a,A_27b,A_27c,V0x_2E0,V2f_2E0) = V1v_2E0 )
<=> ? [V3f_27_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),V4p_2E0: tyop_2Epatricia_2Eptree(A_27b)] :
( ( V0x_2E0 = c_2Epatricia__casts_2EWord__ptree_2E2(A_27a,A_27b,V3f_27_2E0,V4p_2E0) )
& ( app_2E2(tyop_2Epatricia_2Eptree(A_27b),A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Epatricia_2Eptree(A_27b),A_27c),V2f_2E0,V3f_27_2E0),V4p_2E0) = V1v_2E0 ) ) ) ).
tff(thm_2Epatricia__casts_2EADD__INSERT__STRING,axiom,
! [V0w_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1v_2E0: tyop_2Eone_2Eone,V2t_2E0: tyop_2Epatricia_2Eptree(tyop_2Eone_2Eone)] : ( c_2Epatricia__casts_2EADDs_2E2(tyop_2Eone_2Eone,V2t_2E0,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eone_2Eone,V0w_2E0,V1v_2E0)) = c_2Epatricia__casts_2EADDs_2E2(tyop_2Eone_2Eone,V2t_2E0,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Eone_2Eone,V0w_2E0,c_2Eone_2Eone_2E0)) ) ).
tff(thm_2Epatricia__casts_2El2n__APPEND,axiom,
! [V0b_2E0: tyop_2Enum_2Enum,V1l1_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum),V2l2_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Enumposrep_2El2n_2E2(V0b_2E0,c_2Elist_2EAPPEND_2E2(tyop_2Enum_2Enum,V1l1_2E0,V2l2_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Enumposrep_2El2n_2E2(V0b_2E0,V1l1_2E0),c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2EEXP_2E2(V0b_2E0,c_2Elist_2ELENGTH_2E1(tyop_2Enum_2Enum,V1l1_2E0)),c_2Enumposrep_2El2n_2E2(V0b_2E0,V2l2_2E0))) ) ).
tff(thm_2Epatricia__casts_2El2n__LENGTH,axiom,
! [V0b_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] :
( p(c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0b_2E0))
=> p(c_2Eprim__rec_2E_3C_2E2(c_2Enumposrep_2El2n_2E2(V0b_2E0,V1l_2E0),c_2Earithmetic_2EEXP_2E2(V0b_2E0,c_2Elist_2ELENGTH_2E1(tyop_2Enum_2Enum,V1l_2E0)))) ) ).
tff(thm_2Epatricia__casts_2El2n__11,axiom,
! [V0b_2E0: tyop_2Enum_2Enum,V1l1_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum),V2l2_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] :
( ( p(c_2Eprim__rec_2E_3C_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V0b_2E0))
& p(c_2Elist_2EEVERY_2E2(tyop_2Enum_2Enum,c_2Earithmetic_2E_3E_2E1(V0b_2E0),V1l1_2E0))
& p(c_2Elist_2EEVERY_2E2(tyop_2Enum_2Enum,c_2Earithmetic_2E_3E_2E1(V0b_2E0),V2l2_2E0)) )
=> ( ( c_2Enumposrep_2El2n_2E2(V0b_2E0,c_2Elist_2EAPPEND_2E2(tyop_2Enum_2Enum,V1l1_2E0,c_2Elist_2ECONS_2E2(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Elist_2ENIL_2E0(tyop_2Enum_2Enum)))) = c_2Enumposrep_2El2n_2E2(V0b_2E0,c_2Elist_2EAPPEND_2E2(tyop_2Enum_2Enum,V2l2_2E0,c_2Elist_2ECONS_2E2(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Elist_2ENIL_2E0(tyop_2Enum_2Enum)))) )
<=> ( V1l1_2E0 = V2l2_2E0 ) ) ) ).
tff(thm_2Epatricia__casts_2EEVERY__MAP__ORD,axiom,
! [V0l_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : p(c_2Elist_2EEVERY_2E2(tyop_2Enum_2Enum,c_2Earithmetic_2E_3E_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))))))),c_2Elist_2EMAP_2E2(tyop_2Estring_2Echar,tyop_2Enum_2Enum,c_2Estring_2EORD_2E0,V0l_2E0))) ).
tff(thm_2Epatricia__casts_2EMAP__11,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1l1_2E0: tyop_2Elist_2Elist(A_27a),V2l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
( ( app_2E2(A_27a,A_27b,V0f_2E0,V3x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V4y_2E0) )
<=> ( V3x_2E0 = V4y_2E0 ) )
=> ( ( c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f_2E0,V1l1_2E0) = c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f_2E0,V2l2_2E0) )
<=> ( V1l1_2E0 = V2l2_2E0 ) ) ) ).
tff(thm_2Epatricia__casts_2EREVERSE__11,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(A_27a),V1l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( c_2Elist_2EREVERSE_2E1(A_27a,V0l1_2E0) = c_2Elist_2EREVERSE_2E1(A_27a,V1l2_2E0) )
<=> ( V0l1_2E0 = V1l2_2E0 ) ) ).
tff(thm_2Epatricia__casts_2Estring__to__num__11,axiom,
! [V0s_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar),V1t_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] :
( ( c_2Epatricia__casts_2Estring__to__num_2E1(V0s_2E0) = c_2Epatricia__casts_2Estring__to__num_2E1(V1t_2E0) )
<=> ( V0s_2E0 = V1t_2E0 ) ) ).
tff(thm_2Epatricia__casts_2EIMAGE__string__to__num,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] :
( ( ( V0n_2E0 = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) )
| ( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))))),V0n_2E0))
& ( c_2Earithmetic_2EDIV_2E2(V0n_2E0,c_2Earithmetic_2EEXP_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))))),c_2Elogroot_2ELOG_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))))))),V0n_2E0))) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) ) ) )
<=> p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V0n_2E0,c_2Epred__set_2EIMAGE_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum,c_2Epatricia__casts_2Estring__to__num_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Elist_2Elist(tyop_2Estring_2Echar))))) ) ).
tff(thm_2Epatricia__casts_2Estring__to__num__num__to__string,axiom,
! [V0n_2E0: tyop_2Enum_2Enum] :
( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V0n_2E0,c_2Epred__set_2EIMAGE_2E2(tyop_2Elist_2Elist(tyop_2Estring_2Echar),tyop_2Enum_2Enum,c_2Epatricia__casts_2Estring__to__num_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Elist_2Elist(tyop_2Estring_2Echar)))))
=> ( c_2Epatricia__casts_2Estring__to__num_2E1(c_2Epatricia__casts_2Enum__to__string_2E1(V0n_2E0)) = V0n_2E0 ) ) ).
tff(thm_2Epatricia__casts_2Enum__to__string__string__to__num,axiom,
! [V0s_2E0: tyop_2Elist_2Elist(tyop_2Estring_2Echar)] : ( c_2Epatricia__casts_2Enum__to__string_2E1(c_2Epatricia__casts_2Estring__to__num_2E1(V0s_2E0)) = V0s_2E0 ) ).
tff(thm_2Epatricia__casts_2EADD__INSERT__WORD,axiom,
! [A_27a: $tType,V0w_2E0: tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),V1v_2E0: tyop_2Eone_2Eone,V2t_2E0: tyop_2Epatricia__casts_2Eword__ptree(A_27a,tyop_2Eone_2Eone)] : ( c_2Epatricia__casts_2EADDw_2E2(A_27a,tyop_2Eone_2Eone,V2t_2E0,c_2Epair_2E_2C_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Eone_2Eone,V0w_2E0,V1v_2E0)) = c_2Epatricia__casts_2EADDw_2E2(A_27a,tyop_2Eone_2Eone,V2t_2E0,c_2Epair_2E_2C_2E2(tyop_2Efcp_2Ecart(tyop_2Emin_2Ebool,A_27a),tyop_2Eone_2Eone,V0w_2E0,c_2Eone_2Eone_2E0)) ) ).
tff(thm_2Epatricia__casts_2ETHE__PTREE__SOME__PTREE,axiom,
! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Epatricia_2Eptree(A_27a)] : ( c_2Epatricia__casts_2ETHE__PTREE_2E1(A_27a,A_27b,c_2Epatricia__casts_2ESOME__PTREE_2E1(A_27b,A_27a,V0t_2E0)) = V0t_2E0 ) ).
%------------------------------------------------------------------------------