ITP001 Axioms: ITP101^4.ax
%------------------------------------------------------------------------------
% File : ITP101^4 : 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.ax [Gau19]
% : HL4101^4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 949 ( 403 unt; 435 typ; 0 def)
% Number of atoms : 1049 ( 586 equ; 31 cnn)
% Maximal formula atoms : 19 ( 1 avg)
% Number of connectives : 20383 ( 31 ~; 16 |; 130 &;20035 @)
% ( 44 <=>; 127 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 5 avg;20035 nst)
% Number of types : 10 ( 9 usr)
% Number of type conns : 1277 (1277 >; 0 *; 0 +; 0 <<)
% Number of symbols : 428 ( 426 usr; 109 con; 0-4 aty)
% Number of variables : 1484 ( 0 ^1461 !; 23 ?;1484 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(u,type,
u: $tType ).
thf(d,type,
d: $tType ).
thf(du,type,
du: $tType ).
thf(mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,type,
mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29: $tType ).
thf(mono_2Etyop_2Enum_2Enum,type,
mono_2Etyop_2Enum_2Enum: $tType ).
thf(mono_2Etyop_2Eone_2Eone,type,
mono_2Etyop_2Eone_2Eone: $tType ).
thf(mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,type,
mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29: $tType ).
thf(mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,type,
mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29: $tType ).
thf(tyop_2Eind__type_2Erecspace,type,
tyop_2Eind__type_2Erecspace: d > d ).
thf(tyop_2Elist_2Elist,type,
tyop_2Elist_2Elist: d > d ).
thf(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: d ).
thf(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: d > d > d ).
thf(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: d ).
thf(tyop_2Eone_2Eone,type,
tyop_2Eone_2Eone: d ).
thf(tyop_2Eoption_2Eoption,type,
tyop_2Eoption_2Eoption: d > d ).
thf(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: d > d > d ).
thf(tyop_2Epatricia_2Eptree,type,
tyop_2Epatricia_2Eptree: d > d ).
thf(s,type,
s: d > u > du ).
thf(app_2E2,type,
app_2E2: du > du > u ).
thf(combin_i_2E0,type,
combin_i_2E0: u ).
thf(combin_k_2E0,type,
combin_k_2E0: u ).
thf(combin_s_2E0,type,
combin_s_2E0: u ).
thf(c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0: u ).
thf(c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1: du > u ).
thf(c_2Earithmetic_2E_2B_2E0,type,
c_2Earithmetic_2E_2B_2E0: u ).
thf(c_2Earithmetic_2E_2B_2E2,type,
c_2Earithmetic_2E_2B_2E2: du > du > u ).
thf(c_2Epair_2E_2C_2E0,type,
c_2Epair_2E_2C_2E0: u ).
thf(c_2Epair_2E_2C_2E2,type,
c_2Epair_2E_2C_2E2: du > du > u ).
thf(c_2Earithmetic_2E_2D_2E0,type,
c_2Earithmetic_2E_2D_2E0: u ).
thf(c_2Earithmetic_2E_2D_2E2,type,
c_2Earithmetic_2E_2D_2E2: du > du > u ).
thf(c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: u ).
thf(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: du > du > u ).
thf(c_2Enum_2E0_2E0,type,
c_2Enum_2E0_2E0: u ).
thf(c_2Eprim__rec_2E_3C_2E0,type,
c_2Eprim__rec_2E_3C_2E0: u ).
thf(c_2Eprim__rec_2E_3C_2E2,type,
c_2Eprim__rec_2E_3C_2E2: du > du > u ).
thf(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0: u ).
thf(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2: du > du > u ).
thf(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: u ).
thf(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
thf(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0: u ).
thf(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1: du > u ).
thf(c_2Emin_2E_40_2E0,type,
c_2Emin_2E_40_2E0: u ).
thf(c_2Emin_2E_40_2E1,type,
c_2Emin_2E_40_2E1: du > u ).
thf(c_2Epatricia_2EADD_2E0,type,
c_2Epatricia_2EADD_2E0: u ).
thf(c_2Epatricia_2EADD_2E2,type,
c_2Epatricia_2EADD_2E2: du > du > u ).
thf(c_2Epatricia_2EADD__LIST_2E0,type,
c_2Epatricia_2EADD__LIST_2E0: u ).
thf(c_2Epatricia_2EADD__LIST_2E2,type,
c_2Epatricia_2EADD__LIST_2E2: du > du > u ).
thf(c_2Elist_2EALL__DISTINCT_2E0,type,
c_2Elist_2EALL__DISTINCT_2E0: u ).
thf(c_2Elist_2EALL__DISTINCT_2E1,type,
c_2Elist_2EALL__DISTINCT_2E1: du > u ).
thf(c_2Elist_2EAPPEND_2E0,type,
c_2Elist_2EAPPEND_2E0: u ).
thf(c_2Elist_2EAPPEND_2E2,type,
c_2Elist_2EAPPEND_2E2: du > du > u ).
thf(c_2Ebool_2EARB_2E0,type,
c_2Ebool_2EARB_2E0: u ).
thf(c_2Ebit_2EBIT_2E0,type,
c_2Ebit_2EBIT_2E0: u ).
thf(c_2Ebit_2EBIT_2E2,type,
c_2Ebit_2EBIT_2E2: du > du > u ).
thf(c_2Earithmetic_2EBIT1_2E0,type,
c_2Earithmetic_2EBIT1_2E0: u ).
thf(c_2Earithmetic_2EBIT1_2E1,type,
c_2Earithmetic_2EBIT1_2E1: du > u ).
thf(c_2Earithmetic_2EBIT2_2E0,type,
c_2Earithmetic_2EBIT2_2E0: u ).
thf(c_2Earithmetic_2EBIT2_2E1,type,
c_2Earithmetic_2EBIT2_2E1: du > u ).
thf(c_2Eind__type_2EBOTTOM_2E0,type,
c_2Eind__type_2EBOTTOM_2E0: u ).
thf(c_2Epatricia_2EBRANCH_2E0,type,
c_2Epatricia_2EBRANCH_2E0: u ).
thf(c_2Epatricia_2EBRANCH_2E1,type,
c_2Epatricia_2EBRANCH_2E1: du > u ).
thf(c_2Epatricia_2EBRANCHING__BIT_2E0,type,
c_2Epatricia_2EBRANCHING__BIT_2E0: u ).
thf(c_2Epatricia_2EBRANCHING__BIT_2E2,type,
c_2Epatricia_2EBRANCHING__BIT_2E2: du > du > u ).
thf(c_2Epatricia_2EBranch_2E0,type,
c_2Epatricia_2EBranch_2E0: u ).
thf(c_2Epatricia_2EBranch_2E4,type,
c_2Epatricia_2EBranch_2E4: du > du > du > du > u ).
thf(c_2Ecombin_2EC_2E0,type,
c_2Ecombin_2EC_2E0: u ).
thf(c_2Ecombin_2EC_2E1,type,
c_2Ecombin_2EC_2E1: du > u ).
thf(c_2Epred__set_2ECARD_2E0,type,
c_2Epred__set_2ECARD_2E0: u ).
thf(c_2Epred__set_2ECARD_2E1,type,
c_2Epred__set_2ECARD_2E1: du > u ).
thf(c_2Ebool_2ECOND_2E0,type,
c_2Ebool_2ECOND_2E0: u ).
thf(c_2Ebool_2ECOND_2E3,type,
c_2Ebool_2ECOND_2E3: du > du > du > u ).
thf(c_2Elist_2ECONS_2E0,type,
c_2Elist_2ECONS_2E0: u ).
thf(c_2Elist_2ECONS_2E2,type,
c_2Elist_2ECONS_2E2: du > du > u ).
thf(c_2Eind__type_2ECONSTR_2E0,type,
c_2Eind__type_2ECONSTR_2E0: u ).
thf(c_2Eind__type_2ECONSTR_2E3,type,
c_2Eind__type_2ECONSTR_2E3: du > du > du > u ).
thf(c_2Ebool_2EDATATYPE_2E0,type,
c_2Ebool_2EDATATYPE_2E0: u ).
thf(c_2Ebool_2EDATATYPE_2E1,type,
c_2Ebool_2EDATATYPE_2E1: du > u ).
thf(c_2Epred__set_2EDELETE_2E0,type,
c_2Epred__set_2EDELETE_2E0: u ).
thf(c_2Epred__set_2EDELETE_2E2,type,
c_2Epred__set_2EDELETE_2E2: du > du > u ).
thf(c_2Epatricia_2EDEPTH_2E0,type,
c_2Epatricia_2EDEPTH_2E0: u ).
thf(c_2Epatricia_2EDEPTH_2E1,type,
c_2Epatricia_2EDEPTH_2E1: du > u ).
thf(c_2Earithmetic_2EDIV2_2E0,type,
c_2Earithmetic_2EDIV2_2E0: u ).
thf(c_2Earithmetic_2EDIV2_2E1,type,
c_2Earithmetic_2EDIV2_2E1: du > u ).
thf(c_2Elist_2EEL_2E0,type,
c_2Elist_2EEL_2E0: u ).
thf(c_2Elist_2EEL_2E2,type,
c_2Elist_2EEL_2E2: du > du > u ).
thf(c_2Epred__set_2EEMPTY_2E0,type,
c_2Epred__set_2EEMPTY_2E0: u ).
thf(c_2Earithmetic_2EEVEN_2E0,type,
c_2Earithmetic_2EEVEN_2E0: u ).
thf(c_2Earithmetic_2EEVEN_2E1,type,
c_2Earithmetic_2EEVEN_2E1: du > u ).
thf(c_2Epatricia_2EEVERY__LEAF_2E0,type,
c_2Epatricia_2EEVERY__LEAF_2E0: u ).
thf(c_2Epatricia_2EEVERY__LEAF_2E2,type,
c_2Epatricia_2EEVERY__LEAF_2E2: du > du > u ).
thf(c_2Epatricia_2EEXISTS__LEAF_2E0,type,
c_2Epatricia_2EEXISTS__LEAF_2E0: u ).
thf(c_2Epatricia_2EEXISTS__LEAF_2E2,type,
c_2Epatricia_2EEXISTS__LEAF_2E2: du > du > u ).
thf(c_2Earithmetic_2EEXP_2E0,type,
c_2Earithmetic_2EEXP_2E0: u ).
thf(c_2Earithmetic_2EEXP_2E2,type,
c_2Earithmetic_2EEXP_2E2: du > du > u ).
thf(c_2Epatricia_2EEmpty_2E0,type,
c_2Epatricia_2EEmpty_2E0: u ).
thf(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: u ).
thf(c_2Eind__type_2EFCONS_2E0,type,
c_2Eind__type_2EFCONS_2E0: u ).
thf(c_2Eind__type_2EFCONS_2E2,type,
c_2Eind__type_2EFCONS_2E2: du > du > u ).
thf(c_2Elist_2EFILTER_2E0,type,
c_2Elist_2EFILTER_2E0: u ).
thf(c_2Elist_2EFILTER_2E2,type,
c_2Elist_2EFILTER_2E2: du > du > u ).
thf(c_2Epatricia_2EFIND_2E0,type,
c_2Epatricia_2EFIND_2E0: u ).
thf(c_2Epatricia_2EFIND_2E2,type,
c_2Epatricia_2EFIND_2E2: du > du > u ).
thf(c_2Epred__set_2EFINITE_2E0,type,
c_2Epred__set_2EFINITE_2E0: u ).
thf(c_2Epred__set_2EFINITE_2E1,type,
c_2Epred__set_2EFINITE_2E1: du > u ).
thf(c_2Elist_2EFOLDL_2E0,type,
c_2Elist_2EFOLDL_2E0: u ).
thf(c_2Elist_2EFOLDL_2E1,type,
c_2Elist_2EFOLDL_2E1: du > u ).
thf(c_2Elist_2EFOLDL_2E3,type,
c_2Elist_2EFOLDL_2E3: du > du > du > u ).
thf(c_2Ecombin_2EI_2E0,type,
c_2Ecombin_2EI_2E0: u ).
thf(c_2Ecombin_2EI_2E1,type,
c_2Ecombin_2EI_2E1: du > u ).
thf(c_2Ebool_2EIN_2E0,type,
c_2Ebool_2EIN_2E0: u ).
thf(c_2Ebool_2EIN_2E2,type,
c_2Ebool_2EIN_2E2: du > du > u ).
thf(c_2Epred__set_2EINSERT_2E0,type,
c_2Epred__set_2EINSERT_2E0: u ).
thf(c_2Epred__set_2EINSERT_2E2,type,
c_2Epred__set_2EINSERT_2E2: du > du > u ).
thf(c_2Epatricia_2EINSERT__PTREE_2E0,type,
c_2Epatricia_2EINSERT__PTREE_2E0: u ).
thf(c_2Epatricia_2EINSERT__PTREE_2E2,type,
c_2Epatricia_2EINSERT__PTREE_2E2: du > du > u ).
thf(c_2Epatricia_2EIN__PTREE_2E0,type,
c_2Epatricia_2EIN__PTREE_2E0: u ).
thf(c_2Epatricia_2EIN__PTREE_2E2,type,
c_2Epatricia_2EIN__PTREE_2E2: du > du > u ).
thf(c_2Epatricia_2EIS__EMPTY_2E0,type,
c_2Epatricia_2EIS__EMPTY_2E0: u ).
thf(c_2Epatricia_2EIS__EMPTY_2E1,type,
c_2Epatricia_2EIS__EMPTY_2E1: du > u ).
thf(c_2Epatricia_2EIS__PTREE_2E0,type,
c_2Epatricia_2EIS__PTREE_2E0: u ).
thf(c_2Epatricia_2EIS__PTREE_2E1,type,
c_2Epatricia_2EIS__PTREE_2E1: du > u ).
thf(c_2Eoption_2EIS__SOME_2E0,type,
c_2Eoption_2EIS__SOME_2E0: u ).
thf(c_2Eoption_2EIS__SOME_2E1,type,
c_2Eoption_2EIS__SOME_2E1: du > u ).
thf(c_2Epatricia_2EJOIN_2E0,type,
c_2Epatricia_2EJOIN_2E0: u ).
thf(c_2Epatricia_2EJOIN_2E1,type,
c_2Epatricia_2EJOIN_2E1: du > u ).
thf(c_2Epatricia_2EKEYS_2E0,type,
c_2Epatricia_2EKEYS_2E0: u ).
thf(c_2Epatricia_2EKEYS_2E1,type,
c_2Epatricia_2EKEYS_2E1: du > u ).
thf(c_2Elist_2ELENGTH_2E0,type,
c_2Elist_2ELENGTH_2E0: u ).
thf(c_2Elist_2ELENGTH_2E1,type,
c_2Elist_2ELENGTH_2E1: du > u ).
thf(c_2Ebool_2ELET_2E0,type,
c_2Ebool_2ELET_2E0: u ).
thf(c_2Ebool_2ELET_2E2,type,
c_2Ebool_2ELET_2E2: du > du > u ).
thf(c_2Elist_2ELIST__TO__SET_2E0,type,
c_2Elist_2ELIST__TO__SET_2E0: u ).
thf(c_2Elist_2ELIST__TO__SET_2E1,type,
c_2Elist_2ELIST__TO__SET_2E1: du > u ).
thf(c_2Epatricia_2ELeaf_2E0,type,
c_2Epatricia_2ELeaf_2E0: u ).
thf(c_2Epatricia_2ELeaf_2E2,type,
c_2Epatricia_2ELeaf_2E2: du > du > u ).
thf(c_2Earithmetic_2EMAX_2E0,type,
c_2Earithmetic_2EMAX_2E0: u ).
thf(c_2Earithmetic_2EMAX_2E2,type,
c_2Earithmetic_2EMAX_2E2: du > du > u ).
thf(c_2Ebit_2EMOD__2EXP_2E0,type,
c_2Ebit_2EMOD__2EXP_2E0: u ).
thf(c_2Ebit_2EMOD__2EXP_2E2,type,
c_2Ebit_2EMOD__2EXP_2E2: du > du > u ).
thf(c_2Ebit_2EMOD__2EXP__EQ_2E0,type,
c_2Ebit_2EMOD__2EXP__EQ_2E0: u ).
thf(c_2Ebit_2EMOD__2EXP__EQ_2E3,type,
c_2Ebit_2EMOD__2EXP__EQ_2E3: du > du > du > u ).
thf(c_2Elist_2ENIL_2E0,type,
c_2Elist_2ENIL_2E0: u ).
thf(c_2Eoption_2ENONE_2E0,type,
c_2Eoption_2ENONE_2E0: u ).
thf(c_2Earithmetic_2ENUMERAL_2E0,type,
c_2Earithmetic_2ENUMERAL_2E0: u ).
thf(c_2Earithmetic_2ENUMERAL_2E1,type,
c_2Earithmetic_2ENUMERAL_2E1: du > u ).
thf(c_2Epatricia_2ENUMSET__OF__PTREE_2E0,type,
c_2Epatricia_2ENUMSET__OF__PTREE_2E0: u ).
thf(c_2Epatricia_2ENUMSET__OF__PTREE_2E1,type,
c_2Epatricia_2ENUMSET__OF__PTREE_2E1: du > u ).
thf(c_2Earithmetic_2EODD_2E0,type,
c_2Earithmetic_2EODD_2E0: u ).
thf(c_2Earithmetic_2EODD_2E1,type,
c_2Earithmetic_2EODD_2E1: du > u ).
thf(c_2Epatricia_2EPEEK_2E0,type,
c_2Epatricia_2EPEEK_2E0: u ).
thf(c_2Epatricia_2EPEEK_2E2,type,
c_2Epatricia_2EPEEK_2E2: du > du > u ).
thf(c_2Esorting_2EPERM_2E0,type,
c_2Esorting_2EPERM_2E0: u ).
thf(c_2Esorting_2EPERM_2E2,type,
c_2Esorting_2EPERM_2E2: du > du > u ).
thf(c_2Epatricia_2EPTREE__OF__NUMSET_2E0,type,
c_2Epatricia_2EPTREE__OF__NUMSET_2E0: u ).
thf(c_2Epatricia_2EPTREE__OF__NUMSET_2E2,type,
c_2Epatricia_2EPTREE__OF__NUMSET_2E2: du > du > u ).
thf(c_2Esorting_2EQSORT_2E0,type,
c_2Esorting_2EQSORT_2E0: u ).
thf(c_2Esorting_2EQSORT_2E2,type,
c_2Esorting_2EQSORT_2E2: du > du > u ).
thf(c_2Epatricia_2EREMOVE_2E0,type,
c_2Epatricia_2EREMOVE_2E0: u ).
thf(c_2Epatricia_2EREMOVE_2E2,type,
c_2Epatricia_2EREMOVE_2E2: du > du > u ).
thf(c_2Elist_2ESET__TO__LIST_2E0,type,
c_2Elist_2ESET__TO__LIST_2E0: u ).
thf(c_2Elist_2ESET__TO__LIST_2E1,type,
c_2Elist_2ESET__TO__LIST_2E1: du > u ).
thf(c_2Epatricia_2ESIZE_2E0,type,
c_2Epatricia_2ESIZE_2E0: u ).
thf(c_2Epatricia_2ESIZE_2E1,type,
c_2Epatricia_2ESIZE_2E1: du > u ).
thf(c_2Eoption_2ESOME_2E0,type,
c_2Eoption_2ESOME_2E0: u ).
thf(c_2Eoption_2ESOME_2E1,type,
c_2Eoption_2ESOME_2E1: du > u ).
thf(c_2Enum_2ESUC_2E0,type,
c_2Enum_2ESUC_2E0: u ).
thf(c_2Enum_2ESUC_2E1,type,
c_2Enum_2ESUC_2E1: du > u ).
thf(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: u ).
thf(c_2Eoption_2ETHE_2E0,type,
c_2Eoption_2ETHE_2E0: u ).
thf(c_2Eoption_2ETHE_2E1,type,
c_2Eoption_2ETHE_2E1: du > u ).
thf(c_2Epatricia_2ETRANSFORM_2E0,type,
c_2Epatricia_2ETRANSFORM_2E0: u ).
thf(c_2Epatricia_2ETRANSFORM_2E2,type,
c_2Epatricia_2ETRANSFORM_2E2: du > du > u ).
thf(c_2Epatricia_2ETRAVERSE_2E0,type,
c_2Epatricia_2ETRAVERSE_2E0: u ).
thf(c_2Epatricia_2ETRAVERSE_2E1,type,
c_2Epatricia_2ETRAVERSE_2E1: du > u ).
thf(c_2Epatricia_2ETRAVERSE__AUX_2E0,type,
c_2Epatricia_2ETRAVERSE__AUX_2E0: u ).
thf(c_2Epatricia_2ETRAVERSE__AUX_2E2,type,
c_2Epatricia_2ETRAVERSE__AUX_2E2: du > du > u ).
thf(c_2Ebool_2ETYPE__DEFINITION_2E0,type,
c_2Ebool_2ETYPE__DEFINITION_2E0: u ).
thf(c_2Ebool_2ETYPE__DEFINITION_2E2,type,
c_2Ebool_2ETYPE__DEFINITION_2E2: du > du > u ).
thf(c_2Epred__set_2EUNION_2E0,type,
c_2Epred__set_2EUNION_2E0: u ).
thf(c_2Epred__set_2EUNION_2E2,type,
c_2Epred__set_2EUNION_2E2: du > du > u ).
thf(c_2Epatricia_2EUNION__PTREE_2E0,type,
c_2Epatricia_2EUNION__PTREE_2E0: u ).
thf(c_2Epatricia_2EUNION__PTREE_2E2,type,
c_2Epatricia_2EUNION__PTREE_2E2: du > du > u ).
thf(c_2Erelation_2EWF_2E0,type,
c_2Erelation_2EWF_2E0: u ).
thf(c_2Erelation_2EWF_2E1,type,
c_2Erelation_2EWF_2E1: du > u ).
thf(c_2Erelation_2EWFREC_2E0,type,
c_2Erelation_2EWFREC_2E0: u ).
thf(c_2Erelation_2EWFREC_2E2,type,
c_2Erelation_2EWFREC_2E2: du > du > u ).
thf(c_2Earithmetic_2EZERO_2E0,type,
c_2Earithmetic_2EZERO_2E0: u ).
thf(c_2Ebool_2E_5C_2F_2E0,type,
c_2Ebool_2E_5C_2F_2E0: u ).
thf(c_2Ebool_2E_5C_2F_2E2,type,
c_2Ebool_2E_5C_2F_2E2: du > du > u ).
thf(c_2Eone_2Eone_2E0,type,
c_2Eone_2Eone_2E0: u ).
thf(c_2Eoption_2Eoption__CASE_2E0,type,
c_2Eoption_2Eoption__CASE_2E0: u ).
thf(c_2Eoption_2Eoption__CASE_2E3,type,
c_2Eoption_2Eoption__CASE_2E3: du > du > du > u ).
thf(c_2Epair_2Epair__CASE_2E0,type,
c_2Epair_2Epair__CASE_2E0: u ).
thf(c_2Epair_2Epair__CASE_2E2,type,
c_2Epair_2Epair__CASE_2E2: du > du > u ).
thf(c_2Epatricia_2Eptree__CASE_2E0,type,
c_2Epatricia_2Eptree__CASE_2E0: u ).
thf(c_2Epatricia_2Eptree__CASE_2E4,type,
c_2Epatricia_2Eptree__CASE_2E4: du > du > du > du > u ).
thf(c_2Epatricia_2Eptree__size_2E0,type,
c_2Epatricia_2Eptree__size_2E0: u ).
thf(c_2Epatricia_2Eptree__size_2E2,type,
c_2Epatricia_2Eptree__size_2E2: du > du > u ).
thf(c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: u ).
thf(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: du > u ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29: ( $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool: ( ( mono_2Etyop_2Enum_2Enum > $o ) > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum: ( ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29: ( ( mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > ( mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,type,
mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum,type,
mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,type,
mono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ) > mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,type,
mono_2Eapp_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: ( mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29,type,
mono_2Eapp_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29: ( mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 ) > mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > $o ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,type,
mono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,type,
mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > $o ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,type,
mono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29: ( mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Enum_2Enum,type,
mono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,type,
mono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29: ( mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(mono_2Ec_2Earithmetic_2E_2B,type,
mono_2Ec_2Earithmetic_2E_2B: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eone_2Eone,type,
mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eone_2Eone: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 ).
thf(mono_2Ec_2Earithmetic_2E_2D,type,
mono_2Ec_2Earithmetic_2E_2D: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebool_2E_2F_5C,type,
mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(mono_2Ec_2Enum_2E0,type,
mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Eprim__rec_2E_3C,type,
mono_2Ec_2Eprim__rec_2E_3C: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(mono_2Ec_2Epatricia_2EADD_2Emono_2Etyop_2Eone_2Eone,type,
mono_2Ec_2Epatricia_2EADD_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(mono_2Ec_2Elist_2EALL__DISTINCT_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Elist_2EALL__DISTINCT_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > $o ).
thf(mono_2Ec_2Elist_2EAPPEND_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Elist_2EAPPEND_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).
thf(mono_2Ec_2Ebool_2EARB_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Ebool_2EARB_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebit_2EBIT,type,
mono_2Ec_2Ebit_2EBIT: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Earithmetic_2EBIT1,type,
mono_2Ec_2Earithmetic_2EBIT1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Earithmetic_2EBIT2,type,
mono_2Ec_2Earithmetic_2EBIT2: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Epatricia_2EBRANCHING__BIT,type,
mono_2Ec_2Epatricia_2EBRANCHING__BIT: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ecombin_2EC_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,type,
mono_2Ec_2Ecombin_2EC_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(mono_2Ec_2Epred__set_2ECARD_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Epred__set_2ECARD_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum: $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,type,
mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).
thf(mono_2Ec_2Elist_2ECONS_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Elist_2ECONS_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).
thf(mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool,type,
mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool: $o > $o ).
thf(mono_2Ec_2Epred__set_2EDELETE_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Epred__set_2EDELETE_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Earithmetic_2EDIV2,type,
mono_2Ec_2Earithmetic_2EDIV2: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Earithmetic_2EEVEN,type,
mono_2Ec_2Earithmetic_2EEVEN: mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Earithmetic_2EEXP,type,
mono_2Ec_2Earithmetic_2EEXP: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Epatricia_2EEmpty_2Emono_2Etyop_2Eone_2Eone,type,
mono_2Ec_2Epatricia_2EEmpty_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(mono_2Ec_2Ebool_2EF,type,
mono_2Ec_2Ebool_2EF: $o ).
thf(mono_2Ec_2Elist_2EFILTER_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Elist_2EFILTER_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).
thf(mono_2Ec_2Epred__set_2EFINITE_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Epred__set_2EFINITE_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).
thf(mono_2Ec_2Elist_2EFOLDL_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,type,
mono_2Ec_2Elist_2EFOLDL_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29: ( mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(mono_2Ec_2Ecombin_2EI_2Emono_2Etyop_2Emin_2Ebool,type,
mono_2Ec_2Ecombin_2EI_2Emono_2Etyop_2Emin_2Ebool: $o > $o ).
thf(mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).
thf(mono_2Ec_2Epred__set_2EINSERT_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Epred__set_2EINSERT_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Epatricia_2EINSERT__PTREE,type,
mono_2Ec_2Epatricia_2EINSERT__PTREE: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(mono_2Ec_2Epatricia_2EIN__PTREE,type,
mono_2Ec_2Epatricia_2EIN__PTREE: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > $o ).
thf(mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone,type,
mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > $o ).
thf(mono_2Ec_2Eoption_2EIS__SOME_2Emono_2Etyop_2Eone_2Eone,type,
mono_2Ec_2Eoption_2EIS__SOME_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > $o ).
thf(mono_2Ec_2Elist_2ELENGTH_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Elist_2ELENGTH_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Elist_2ELIST__TO__SET_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Elist_2ELIST__TO__SET_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Earithmetic_2EMAX,type,
mono_2Ec_2Earithmetic_2EMAX: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebit_2EMOD__2EXP,type,
mono_2Ec_2Ebit_2EMOD__2EXP: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebit_2EMOD__2EXP__EQ,type,
mono_2Ec_2Ebit_2EMOD__2EXP__EQ: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Elist_2ENIL_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Elist_2ENIL_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).
thf(mono_2Ec_2Earithmetic_2ENUMERAL,type,
mono_2Ec_2Earithmetic_2ENUMERAL: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Epatricia_2ENUMSET__OF__PTREE,type,
mono_2Ec_2Epatricia_2ENUMSET__OF__PTREE: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Earithmetic_2EODD,type,
mono_2Ec_2Earithmetic_2EODD: mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Epatricia_2EPEEK_2Emono_2Etyop_2Eone_2Eone,type,
mono_2Ec_2Epatricia_2EPEEK_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).
thf(mono_2Ec_2Esorting_2EPERM_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Esorting_2EPERM_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > $o ).
thf(mono_2Ec_2Epatricia_2EPTREE__OF__NUMSET,type,
mono_2Ec_2Epatricia_2EPTREE__OF__NUMSET: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(mono_2Ec_2Esorting_2EQSORT_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Esorting_2EQSORT_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).
thf(mono_2Ec_2Epatricia_2EREMOVE_2Emono_2Etyop_2Eone_2Eone,type,
mono_2Ec_2Epatricia_2EREMOVE_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(mono_2Ec_2Elist_2ESET__TO__LIST_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Elist_2ESET__TO__LIST_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).
thf(mono_2Ec_2Epatricia_2ESIZE_2Emono_2Etyop_2Eone_2Eone,type,
mono_2Ec_2Epatricia_2ESIZE_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Eone_2Eone,type,
mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).
thf(mono_2Ec_2Enum_2ESUC,type,
mono_2Ec_2Enum_2ESUC: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebool_2ET,type,
mono_2Ec_2Ebool_2ET: $o ).
thf(mono_2Ec_2Epatricia_2ETRAVERSE_2Emono_2Etyop_2Eone_2Eone,type,
mono_2Ec_2Epatricia_2ETRAVERSE_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).
thf(mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Epatricia_2EUNION__PTREE,type,
mono_2Ec_2Epatricia_2EUNION__PTREE: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(mono_2Ec_2Earithmetic_2EZERO,type,
mono_2Ec_2Earithmetic_2EZERO: mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebool_2E_5C_2F,type,
mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(mono_2Ec_2Eone_2Eone,type,
mono_2Ec_2Eone_2Eone: mono_2Etyop_2Eone_2Eone ).
thf(mono_2Ec_2Ebool_2E_7E,type,
mono_2Ec_2Ebool_2E_7E: $o > $o ).
thf(i_mono_2Etyop_2Emin_2Ebool,type,
i_mono_2Etyop_2Emin_2Ebool: $o > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29: ( $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29: ( $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_29: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_29: ( ( mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: ( mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29: ( mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29: ( mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29: ( mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29: ( mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29: ( mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29: ( mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29: ( mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > u ).
thf(i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,type,
i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > u ).
thf(i_mono_2Etyop_2Enum_2Enum,type,
i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).
thf(i_mono_2Etyop_2Eone_2Eone,type,
i_mono_2Etyop_2Eone_2Eone: mono_2Etyop_2Eone_2Eone > u ).
thf(i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,type,
i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > u ).
thf(i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29,type,
i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 > u ).
thf(i_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,type,
i_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > u ).
thf(j_mono_2Etyop_2Emin_2Ebool,type,
j_mono_2Etyop_2Emin_2Ebool: du > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29: du > $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29: du > $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: du > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: du > ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29: du > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: du > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29: du > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29: du > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29: du > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29: du > ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_29: du > ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_29: du > ( mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29: du > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29: du > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Enum_2Enum > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: du > mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: du > mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_29: du > mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29: du > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29: du > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29: du > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29: du > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29: du > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29: du > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29: du > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29: du > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29: du > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,type,
j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29: du > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 ).
thf(j_mono_2Etyop_2Enum_2Enum,type,
j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).
thf(j_mono_2Etyop_2Eone_2Eone,type,
j_mono_2Etyop_2Eone_2Eone: du > mono_2Etyop_2Eone_2Eone ).
thf(j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,type,
j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: du > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ).
thf(j_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29,type,
j_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 ).
thf(j_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,type,
j_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29: du > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ).
thf(reserved_2Eho_2Eeq__ext,axiom,
! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
( ! [V2x_2E0: u] :
( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
=> ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).
thf(reserved_2Eho_2Ei__thm,axiom,
! [A_27a: d,V0x_2E0: u] :
( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
= ( s @ A_27a @ V0x_2E0 ) ) ).
thf(reserved_2Eho_2Ek__thm,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ combin_k_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) )
= ( s @ A_27a @ V0x_2E0 ) ) ).
thf(reserved_2Eho_2Es__thm,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
= ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ).
thf(reserved_2Elogic_2E_2F_5C,axiom,
! [V0: $o,V1: $o] :
( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
<=> ( V0
& V1 ) ) ).
thf(reserved_2Elogic_2E_5C_2F,axiom,
! [V0: $o,V1: $o] :
( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
<=> ( V0
| V1 ) ) ).
thf(reserved_2Elogic_2E_7E,axiom,
! [V0: $o] :
( ( mono_2Ec_2Ebool_2E_7E @ V0 )
<=> ( (~) @ V0 ) ) ).
thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
! [V0: $o,V1: $o] :
( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
<=> ( V0
=> V1 ) ) ).
thf(reserved_2Elogic_2E_3D,axiom,
! [A_27a: d,V0_2E0: u,V1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
<=> ( ( s @ A_27a @ V0_2E0 )
= ( s @ A_27a @ V1_2E0 ) ) ) ).
thf(reserved_2Equant_2E_21,axiom,
! [A_27a: d,V0f_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
<=> ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
thf(reserved_2Equant_2E_3F,axiom,
! [A_27a: d,V0f_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
<=> ? [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [V0_2E0: u] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( 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 ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ ( s @ ( 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 ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( 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 ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0_2E0: u] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ V0_2E0 ) ) ) )
= ( s @ tyop_2Enum_2Enum @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Eone_2Eone,axiom,
! [V0_2E0: u] :
( ( s @ tyop_2Eone_2Eone @ ( i_mono_2Etyop_2Eone_2Eone @ ( j_mono_2Etyop_2Eone_2Eone @ ( s @ tyop_2Eone_2Eone @ V0_2E0 ) ) ) )
= ( s @ tyop_2Eone_2Eone @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 @ ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ ( j_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ V0_2E0 ) ) ).
thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [V0: $o] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: $o > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: $o > $o > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,axiom,
! [V0: $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29,axiom,
! [V0: $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_29,axiom,
! [V0: ( mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
! [V0: mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_29,axiom,
! [V0: mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ ( s @ ( 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 ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Eone_2Eone,axiom,
! [V0: mono_2Etyop_2Eone_2Eone] :
( ( j_mono_2Etyop_2Eone_2Eone @ ( s @ tyop_2Eone_2Eone @ ( i_mono_2Etyop_2Eone_2Eone @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] :
( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29] :
( ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( j_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ V0 ) ) )
= V0 ) ).
thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ A_27a @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27b,axiom,
! [A_27b: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ A_27b @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Enum_2Enum_29,axiom,
! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Epatricia_2Eptree_28A_27a_29_2Ctyop_2Epatricia_2Eptree_28A_27a_29_29_29,axiom,
! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Epatricia_2Eptree_28A_27b_29_2Ctyop_2Epatricia_2Eptree_28A_27b_29_29_29,axiom,
! [A_27b: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Epatricia_2Eptree_28A_27a_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28A_27a_29_29_29,axiom,
! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Epatricia_2Eptree_28A_27a_29_2Ctyop_2Epatricia_2Eptree_28A_27a_29_29,axiom,
! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Epatricia_2Eptree_28A_27b_29_2Ctyop_2Epatricia_2Eptree_28A_27b_29_29,axiom,
! [A_27b: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epatricia_2Eptree_28A_27a_29,axiom,
! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epatricia_2Eptree_28A_27a_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28A_27a_29_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epatricia_2Eptree_28A_27a_29_20mono_2Etyop_2Epatricia_2Eptree_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epatricia_2Eptree_28A_27b_29_20mono_2Etyop_2Epatricia_2Eptree_28A_27b_29,axiom,
! [A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( ( s @ A_27a @ X0_2E0 )
= ( s @ A_27a @ X1_2E0 ) )
<=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Epatricia_2Eptree_28A_27a_29_2Ctyop_2Epatricia_2Eptree_28A_27a_29_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Epatricia_2Eptree_28A_27a_29_2Ctyop_2Epatricia_2Eptree_28A_27a_29_29_29_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Emin_2E_40_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Emin_2E_40_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28A_27a_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28A_27a_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Emin_2E_40_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Emin_2E_40_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epatricia_2EADD_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EADD_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epatricia_2EADD_2E2_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( c_2Epatricia_2EADD_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epatricia_2EADD__LIST_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EADD__LIST_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ c_2Epatricia_2EADD__LIST_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EALL__DISTINCT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Elist_2EALL__DISTINCT_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Epatricia_2EBRANCH_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBRANCH_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ c_2Epatricia_2EBRANCH_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epatricia_2EBRANCH_2E1_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( c_2Epatricia_2EBRANCH_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) @ c_2Epatricia_2EBRANCH_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq4_2Ec_2Epatricia_2EBranch_2E4_2Emono_2EA_27a,axiom,
! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum,X1: mono_2Etyop_2Enum_2Enum,X2_2E0: u,X3_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X2_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X3_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ c_2Epatricia_2EBranch_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X3_2E0 ) ) ) ) ).
thf(arityeq4_2Ec_2Epatricia_2EBranch_2E4_2Emono_2EA_27b,axiom,
! [A_27b: d,X0: mono_2Etyop_2Enum_2Enum,X1: mono_2Etyop_2Enum_2Enum,X2_2E0: u,X3_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ X2_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ X3_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) ) ) ) @ c_2Epatricia_2EBranch_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ X3_2E0 ) ) ) ) ).
thf(arityeq4_2Ec_2Epatricia_2EBranch_2E4_2Emono_2EA_27c,axiom,
! [A_27c: d,X0: mono_2Etyop_2Enum_2Enum,X1: mono_2Etyop_2Enum_2Enum,X2_2E0: u,X3_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27c ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27c ) @ X2_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27c ) @ X3_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27c ) @ ( tyop_2Epatricia_2Eptree @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27c ) @ ( tyop_2Epatricia_2Eptree @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27c ) @ ( tyop_2Epatricia_2Eptree @ A_27c ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27c ) @ ( tyop_2Epatricia_2Eptree @ A_27c ) ) ) ) ) @ c_2Epatricia_2EBranch_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27c ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27c ) @ X3_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epred__set_2ECARD_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ c_2Epred__set_2ECARD_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a: d,X0: $o,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Epatricia_2Eptree_28A_27a_29,axiom,
! [A_27a: d,X0: $o,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Eind__type_2ECONSTR_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28A_27a_2Ctyop_2Enum_2Enum_29_29,axiom,
! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ ( c_2Eind__type_2ECONSTR_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) ) ) ) @ c_2Eind__type_2ECONSTR_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) ) @ X2_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EDELETE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epatricia_2EDEPTH_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epatricia_2EDEPTH_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Enum_2Enum ) @ c_2Epatricia_2EDEPTH_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ A_27a @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ A_27a ) ) @ c_2Elist_2EEL_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epatricia_2EEVERY__LEAF_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EEVERY__LEAF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ c_2Epatricia_2EEVERY__LEAF_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Epatricia_2EEVERY__LEAF_2E2_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EEVERY__LEAF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Epatricia_2EEXISTS__LEAF_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EEXISTS__LEAF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ c_2Epatricia_2EEXISTS__LEAF_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Eind__type_2EFCONS_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28A_27a_2Ctyop_2Enum_2Enum_29_29_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) ) @ ( c_2Eind__type_2EFCONS_2E2 @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) ) ) ) @ c_2Eind__type_2EFCONS_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Elist_2EFILTER_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EFILTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2EFILTER_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epatricia_2EFIND_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum] :
( ( s @ A_27a @ ( c_2Epatricia_2EFIND_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) @ c_2Epatricia_2EFIND_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Elist_2EFOLDL_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_20mono_2Etyop_2Epatricia_2Eptree_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( c_2Elist_2EFOLDL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ 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_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ c_2Elist_2EFOLDL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Epatricia_2Eptree_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Ecombin_2EI_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ c_2Ecombin_2EI_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Epatricia_2EIS__EMPTY_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__EMPTY_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epatricia_2EIS__EMPTY_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Epatricia_2EIS__PTREE_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epatricia_2EIS__PTREE_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Epatricia_2EIS__PTREE_2E1_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ tyop_2Emin_2Ebool ) @ c_2Epatricia_2EIS__PTREE_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Epatricia_2EIS__PTREE_2E1_2Emono_2EA_27c,axiom,
! [A_27c: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27c ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27c ) @ tyop_2Emin_2Ebool ) @ c_2Epatricia_2EIS__PTREE_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27c ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Eoption_2EIS__SOME_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) @ c_2Eoption_2EIS__SOME_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2EA_27c,axiom,
! [A_27c: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27c ) @ tyop_2Emin_2Ebool ) @ c_2Eoption_2EIS__SOME_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Epatricia_2EJOIN_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EJOIN_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ c_2Epatricia_2EJOIN_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epatricia_2EKEYS_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2EKEYS_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ c_2Epatricia_2EKEYS_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Epatricia_2EKEYS_2E1_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2EKEYS_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ c_2Epatricia_2EKEYS_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Enum_2Enum ) @ c_2Elist_2ELENGTH_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epatricia_2Eptree_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Ebool_2ELET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ X0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ c_2Ebool_2ELET_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Elist_2ELIST__TO__SET_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epatricia_2ELeaf_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ A_27a @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ c_2Epatricia_2ELeaf_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epatricia_2ELeaf_2E2_2Emono_2EA_27b,axiom,
! [A_27b: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ A_27b @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) ) @ c_2Epatricia_2ELeaf_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epatricia_2EPEEK_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Epatricia_2EPEEK_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ c_2Epatricia_2EPEEK_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Epatricia_2EPEEK_2E2_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Epatricia_2EPEEK_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ X0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ c_2Epatricia_2EPEEK_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Epatricia_2EPEEK_2E2_2Emono_2EA_27c,axiom,
! [A_27c: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ ( c_2Epatricia_2EPEEK_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27c ) @ X0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27c ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27c ) ) ) @ c_2Epatricia_2EPEEK_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Esorting_2EPERM_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esorting_2EPERM_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Esorting_2EPERM_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Esorting_2EQSORT_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Esorting_2EQSORT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ c_2Esorting_2EQSORT_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epatricia_2EREMOVE_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EREMOVE_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ c_2Epatricia_2EREMOVE_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Epatricia_2EREMOVE_2E2_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( c_2Epatricia_2EREMOVE_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ X0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) ) @ c_2Epatricia_2EREMOVE_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Epatricia_2ESIZE_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epatricia_2ESIZE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Enum_2Enum ) @ c_2Epatricia_2ESIZE_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ X0_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ X0_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ A_27a @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ A_27a ) @ c_2Eoption_2ETHE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epatricia_2ETRANSFORM_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( c_2Epatricia_2ETRANSFORM_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) ) @ c_2Epatricia_2ETRANSFORM_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epatricia_2ETRANSFORM_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ETRANSFORM_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ c_2Epatricia_2ETRANSFORM_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epatricia_2ETRAVERSE_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ c_2Epatricia_2ETRAVERSE_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Epatricia_2ETRAVERSE_2E1_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ c_2Epatricia_2ETRAVERSE_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Epatricia_2ETRAVERSE__AUX_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE__AUX_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ X1 ) ) ) ) )
= ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ c_2Epatricia_2ETRAVERSE__AUX_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) ) ) @ X1 ) ) ).
thf(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28A_27a_2Ctyop_2Enum_2Enum_29_29_29_20mono_2Etyop_2Epatricia_2Eptree_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ETYPE__DEFINITION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2ETYPE__DEFINITION_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EUNION_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Epatricia_2Eptree_28A_27a_29_2Ctyop_2Epatricia_2Eptree_28A_27a_29_29_29_29,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2EWF_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ c_2Erelation_2EWF_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Epatricia_2Eptree_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2EWF_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ c_2Erelation_2EWF_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Epatricia_2Eptree_28A_27a_29_2Ctyop_2Epatricia_2Eptree_28A_27a_29_29_29_29_20mono_2Etyop_2Epatricia_2Eptree_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( c_2Erelation_2EWFREC_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ c_2Erelation_2EWFREC_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Epatricia_2Eptree_28A_27a_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Erelation_2EWFREC_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Erelation_2EWFREC_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ X2_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Epatricia_2Eptree_28A_27a_29_20mono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Epatricia_2Eptree_28A_27a_29_2Ctyop_2Epatricia_2Eptree_28A_27a_29_29_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Epatricia_2Eptree_28A_27a_29_20mono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Epatricia_2Eptree_28A_27a_29_2Ctyop_2Epatricia_2Eptree_28A_27a_29_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Epatricia_2Eptree_28A_27a_29_20mono_2Etyop_2Epatricia_2Eptree_28A_27a_29_20mono_2Etyop_2Epatricia_2Eptree_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq4_2Ec_2Epatricia_2Eptree__CASE_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
( ( s @ A_27b @ ( c_2Epatricia_2Eptree__CASE_2E4 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ X2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) ) ) ) @ X3_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) ) ) ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) ) ) ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) ) ) ) @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) ) ) ) @ A_27b ) ) ) ) @ c_2Epatricia_2Eptree__CASE_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) ) ) ) @ X3_2E0 ) ) ) ) ).
thf(arityeq4_2Ec_2Epatricia_2Eptree__CASE_2E4_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: d,X0_2E0: u,X1: $o,X2_2E0: u,X3_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2Eptree__CASE_2E4 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) ) @ X3_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Epatricia_2Eptree__CASE_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) ) @ X3_2E0 ) ) ) ) ) ).
thf(arityeq4_2Ec_2Epatricia_2Eptree__CASE_2E4_2Emono_2EA_27a_20mono_2Etyop_2Epatricia_2Eptree_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2Eptree__CASE_2E4 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ X2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ X3_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ c_2Epatricia_2Eptree__CASE_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ X3_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epatricia_2Eptree__size_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epatricia_2Eptree__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ X0_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Enum_2Enum ) ) @ c_2Epatricia_2Eptree__size_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ X1_2E0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: $o > $o,V1: $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: $o > $o > $o,V1: $o] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0: $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: $o] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,axiom,
! [V0: $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V1: $o] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29,axiom,
! [V0: ( mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > $o,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > $o,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 @ V0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29 @ V0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
! [V0: mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Eone_2Eone] :
( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ V0 ) ) @ ( s @ tyop_2Eone_2Eone @ ( i_mono_2Etyop_2Eone_2Eone @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29,axiom,
! [V0: mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29,V1: mono_2Etyop_2Eone_2Eone] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_29 @ V0 ) ) @ ( s @ tyop_2Eone_2Eone @ ( i_mono_2Etyop_2Eone_2Eone @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > $o,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] :
( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ V0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29] :
( ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29 @ V0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > $o,V1: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 @ V0 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29 @ V0 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eone_2Eone,axiom,
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_29_29 @ mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eone_2Eone ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) ) ) @ c_2Epair_2E_2C_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eone_2Eone,axiom,
! [V0: mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Eone_2Eone] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eone_2Eone @ V0 @ V1 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0 ) ) @ ( s @ tyop_2Eone_2Eone @ ( i_mono_2Etyop_2Eone_2Eone @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Epatricia_2EADD_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ mono_2Ec_2Epatricia_2EADD_2Emono_2Etyop_2Eone_2Eone ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ c_2Epatricia_2EADD_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Epatricia_2EADD_2E2_2Emono_2Etyop_2Eone_2Eone,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29] :
( ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ ( mono_2Ec_2Epatricia_2EADD_2Emono_2Etyop_2Eone_2Eone @ V0 @ V1 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( c_2Epatricia_2EADD_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ V0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Elist_2EALL__DISTINCT_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Elist_2EALL__DISTINCT_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ c_2Elist_2EALL__DISTINCT_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Elist_2EALL__DISTINCT_2Emono_2Etyop_2Enum_2Enum @ V0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EALL__DISTINCT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Elist_2EAPPEND_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ mono_2Ec_2Elist_2EAPPEND_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ ( 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 ) ) ).
thf(monoeq_2Emono_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( mono_2Ec_2Elist_2EAPPEND_2Emono_2Etyop_2Enum_2Enum @ V0 @ V1 ) ) )
= ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2EARB_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Ebool_2EARB_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ tyop_2Enum_2Enum @ c_2Ebool_2EARB_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Ecombin_2EC_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_29 @ mono_2Ec_2Ecombin_2EC_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) ) @ c_2Ecombin_2EC_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Ecombin_2EC_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ ( mono_2Ec_2Ecombin_2EC_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ V0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( c_2Ecombin_2EC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Epred__set_2ECARD_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 @ mono_2Ec_2Epred__set_2ECARD_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ c_2Epred__set_2ECARD_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Epred__set_2ECARD_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Epred__set_2ECARD_2Emono_2Etyop_2Enum_2Enum @ V0 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( c_2Epred__set_2ECARD_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ c_2Ebool_2ECOND_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: $o,V1: mono_2Etyop_2Enum_2Enum,V2: mono_2Etyop_2Enum_2Enum] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ V0 @ V1 @ V2 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29_29 @ mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
! [V0: $o,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V2: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] :
( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ V0 @ V1 @ V2 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ V1 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ V2 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Elist_2ECONS_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ mono_2Ec_2Elist_2ECONS_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ c_2Elist_2ECONS_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( mono_2Ec_2Elist_2ECONS_2Emono_2Etyop_2Enum_2Enum @ V0 @ V1 ) ) )
= ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2EDATATYPE_2E0_2Emono_2Etyop_2Emin_2Ebool,axiom,
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2EDATATYPE_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [V0: $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool @ V0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EDATATYPE_2E1 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Epred__set_2EDELETE_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ mono_2Ec_2Epred__set_2EDELETE_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EDELETE_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( mono_2Ec_2Epred__set_2EDELETE_2Emono_2Etyop_2Enum_2Enum @ V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Epred__set_2EEMPTY_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Epatricia_2EEmpty_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
( ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ mono_2Ec_2Epatricia_2EEmpty_2Emono_2Etyop_2Eone_2Eone ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ c_2Epatricia_2EEmpty_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Elist_2EFILTER_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ mono_2Ec_2Elist_2EFILTER_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ c_2Elist_2EFILTER_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Elist_2EFILTER_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( mono_2Ec_2Elist_2EFILTER_2Emono_2Etyop_2Enum_2Enum @ V0 @ V1 ) ) )
= ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Elist_2EFILTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Epred__set_2EFINITE_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Epred__set_2EFINITE_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EFINITE_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Epred__set_2EFINITE_2Emono_2Etyop_2Enum_2Enum @ V0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Elist_2EFOLDL_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_29 @ mono_2Ec_2Elist_2EFOLDL_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) ) @ c_2Elist_2EFOLDL_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Elist_2EFOLDL_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V2: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ ( mono_2Ec_2Elist_2EFOLDL_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ V0 @ V1 @ V2 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( c_2Elist_2EFOLDL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ V1 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V2 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Ecombin_2EI_2E0_2Emono_2Etyop_2Emin_2Ebool,axiom,
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Ecombin_2EI_2Emono_2Etyop_2Emin_2Ebool ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ecombin_2EI_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [V0: $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ecombin_2EI_2Emono_2Etyop_2Emin_2Ebool @ V0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Ecombin_2EI_2E1 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2EIN_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Epred__set_2EINSERT_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ mono_2Ec_2Epred__set_2EINSERT_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EINSERT_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( mono_2Ec_2Epred__set_2EINSERT_2Emono_2Etyop_2Enum_2Enum @ V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Epatricia_2EIS__PTREE_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ c_2Epatricia_2EIS__PTREE_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Epatricia_2EIS__PTREE_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ V0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Eoption_2EIS__SOME_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Eoption_2EIS__SOME_2Emono_2Etyop_2Eone_2Eone ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ c_2Eoption_2EIS__SOME_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Eoption_2EIS__SOME_2Emono_2Etyop_2Eone_2Eone @ V0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Elist_2ELENGTH_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 @ mono_2Ec_2Elist_2ELENGTH_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum ) @ c_2Elist_2ELENGTH_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Elist_2ELENGTH_2Emono_2Etyop_2Enum_2Enum @ V0 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Elist_2ELIST__TO__SET_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ mono_2Ec_2Elist_2ELIST__TO__SET_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ c_2Elist_2ELIST__TO__SET_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( mono_2Ec_2Elist_2ELIST__TO__SET_2Emono_2Etyop_2Enum_2Enum @ V0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Elist_2ENIL_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ mono_2Ec_2Elist_2ENIL_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ c_2Elist_2ENIL_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Epatricia_2EPEEK_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29 @ mono_2Ec_2Epatricia_2EPEEK_2Emono_2Etyop_2Eone_2Eone ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) ) @ c_2Epatricia_2EPEEK_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Epatricia_2EPEEK_2E2_2Emono_2Etyop_2Eone_2Eone,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ ( mono_2Ec_2Epatricia_2EPEEK_2Emono_2Etyop_2Eone_2Eone @ V0 @ V1 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( c_2Epatricia_2EPEEK_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Esorting_2EPERM_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ mono_2Ec_2Esorting_2EPERM_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ c_2Esorting_2EPERM_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Esorting_2EPERM_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Esorting_2EPERM_2Emono_2Etyop_2Enum_2Enum @ V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Esorting_2EPERM_2E2 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Esorting_2EQSORT_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_29 @ mono_2Ec_2Esorting_2EQSORT_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) ) @ c_2Esorting_2EQSORT_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Esorting_2EQSORT_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( mono_2Ec_2Esorting_2EQSORT_2Emono_2Etyop_2Enum_2Enum @ V0 @ V1 ) ) )
= ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Esorting_2EQSORT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Epatricia_2EREMOVE_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29 @ mono_2Ec_2Epatricia_2EREMOVE_2Emono_2Etyop_2Eone_2Eone ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) ) ) @ c_2Epatricia_2EREMOVE_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Epatricia_2EREMOVE_2E2_2Emono_2Etyop_2Eone_2Eone,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ ( mono_2Ec_2Epatricia_2EREMOVE_2Emono_2Etyop_2Eone_2Eone @ V0 @ V1 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( c_2Epatricia_2EREMOVE_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Elist_2ESET__TO__LIST_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 @ mono_2Ec_2Elist_2ESET__TO__LIST_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ c_2Elist_2ESET__TO__LIST_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Elist_2ESET__TO__LIST_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( mono_2Ec_2Elist_2ESET__TO__LIST_2Emono_2Etyop_2Enum_2Enum @ V0 ) ) )
= ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Elist_2ESET__TO__LIST_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Epatricia_2ESIZE_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29 @ mono_2Ec_2Epatricia_2ESIZE_2Emono_2Etyop_2Eone_2Eone ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ tyop_2Enum_2Enum ) @ c_2Epatricia_2ESIZE_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Epatricia_2ESIZE_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Epatricia_2ESIZE_2Emono_2Etyop_2Eone_2Eone @ V0 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( c_2Epatricia_2ESIZE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Eoption_2ESOME_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29 @ mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Eone_2Eone ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) ) @ c_2Eoption_2ESOME_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
! [V0: mono_2Etyop_2Eone_2Eone] :
( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Eone_2Eone @ V0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Eone_2Eone ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ tyop_2Eone_2Eone @ ( i_mono_2Etyop_2Eone_2Eone @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Epatricia_2ETRAVERSE_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29 @ mono_2Ec_2Epatricia_2ETRAVERSE_2Emono_2Etyop_2Eone_2Eone ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) ) @ c_2Epatricia_2ETRAVERSE_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Epatricia_2ETRAVERSE_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( mono_2Ec_2Epatricia_2ETRAVERSE_2Emono_2Etyop_2Eone_2Eone @ V0 ) ) )
= ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Epred__set_2EUNION_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EUNION_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Enum_2Enum @ V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: $o > $o,V1: $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: $o > $o > $o,V1: $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0: $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29_29,axiom,
! [V0: $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V1: $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29_29,axiom,
! [V0: ( mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > $o,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > $o,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,axiom,
! [V0: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
! [V0: mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Eone_2Eone] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29,axiom,
! [V0: mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29,V1: mono_2Etyop_2Eone_2Eone] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > $o,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > $o,V1: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_29,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_2Ctyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_29,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,axiom,
! [V0: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(thm_2Epatricia_2Eptree__TY__DEF,axiom,
! [A_27a: d,F3_2E0: u,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
( ! [V12n: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) ) @ F3_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V12n ) ) ) )
= ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ c_2Eind__type_2EBOTTOM_2E0 ) )
=> ( ! [V7n: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) ) @ F2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V7n ) ) ) )
= ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ c_2Eind__type_2EBOTTOM_2E0 ) )
=> ( ! [V4n: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) ) @ F1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4n ) ) ) )
= ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ c_2Eind__type_2EBOTTOM_2E0 ) )
=> ( ! [V1a0_27_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ V1a0_27_2E0 ) ) ) )
<=> ! [V2_27ptree_27_2E0: u] :
( ! [V3a0_27_2E0: u] :
( ( ( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ V3a0_27_2E0 )
= ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ ( c_2Eind__type_2ECONSTR_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Ebool_2EARB_2Emono_2Etyop_2Enum_2Enum ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ c_2Ebool_2EARB_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Ebool_2EARB_2Emono_2Etyop_2Enum_2Enum ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) ) @ F1_2E0 ) ) ) )
| ? [V5a0: mono_2Etyop_2Enum_2Enum,V6a1_2E0: u] :
( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ V3a0_27_2E0 )
= ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ ( c_2Eind__type_2ECONSTR_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5a0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V6a1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Ebool_2EARB_2Emono_2Etyop_2Enum_2Enum ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) ) @ F2_2E0 ) ) ) )
| ? [V8a0: mono_2Etyop_2Enum_2Enum,V9a1: mono_2Etyop_2Enum_2Enum,V10a2_2E0: u,V11a3_2E0: u] :
( ( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ V3a0_27_2E0 )
= ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ ( c_2Eind__type_2ECONSTR_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8a0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ c_2Ebool_2EARB_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V9a1 ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) ) @ ( c_2Eind__type_2EFCONS_2E2 @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ V10a2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) ) @ ( c_2Eind__type_2EFCONS_2E2 @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ V11a3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) ) @ F3_2E0 ) ) ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ tyop_2Emin_2Ebool ) @ V2_27ptree_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ V10a2_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ tyop_2Emin_2Ebool ) @ V2_27ptree_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ V11a3_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ tyop_2Emin_2Ebool ) @ V2_27ptree_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ V3a0_27_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ tyop_2Emin_2Ebool ) @ V2_27ptree_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ V1a0_27_2E0 ) ) ) ) ) )
=> ? [V0rep_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ETYPE__DEFINITION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Enum_2Enum ) ) ) ) @ V0rep_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2Eptree__case__def,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0v_2E0: u,V1f_2E0: u,V2f1_2E0: u] :
( ( s @ A_27b @ ( c_2Epatricia_2Eptree__CASE_2E4 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) @ ( s @ A_27b @ V0v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ V1f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) ) ) ) @ V2f1_2E0 ) ) )
= ( s @ A_27b @ V0v_2E0 ) )
& ! [V3a0: mono_2Etyop_2Enum_2Enum,V4a1_2E0: u,V5v_2E0: u,V6f_2E0: u,V7f1_2E0: u] :
( ( s @ A_27b @ ( c_2Epatricia_2Eptree__CASE_2E4 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3a0 ) ) @ ( s @ A_27a @ V4a1_2E0 ) ) ) @ ( s @ A_27b @ V5v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ V6f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) ) ) ) @ V7f1_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ V6f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3a0 ) ) ) ) @ ( s @ A_27a @ V4a1_2E0 ) ) ) )
& ! [V8a0: mono_2Etyop_2Enum_2Enum,V9a1: mono_2Etyop_2Enum_2Enum,V10a2_2E0: u,V11a3_2E0: u,V12v_2E0: u,V13f_2E0: u,V14f1_2E0: u] :
( ( s @ A_27b @ ( c_2Epatricia_2Eptree__CASE_2E4 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8a0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V9a1 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V10a2_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V11a3_2E0 ) ) ) @ ( s @ A_27b @ V12v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ V13f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) ) ) ) @ V14f1_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) ) ) ) @ V14f1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8a0 ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V9a1 ) ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V10a2_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V11a3_2E0 ) ) ) ) ) ).
thf(thm_2Epatricia_2Eptree__size__def,axiom,
! [A_27a: d] :
( ! [V0f_2E0: u] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epatricia_2Eptree__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) ) ) )
= mono_2Ec_2Enum_2E0 )
& ! [V1f_2E0: u,V2a0: mono_2Etyop_2Enum_2Enum,V3a1_2E0: u] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epatricia_2Eptree__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V1f_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2a0 ) ) @ ( s @ A_27a @ V3a1_2E0 ) ) ) ) ) )
= ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( mono_2Ec_2Earithmetic_2E_2B @ V2a0 @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V1f_2E0 ) @ ( s @ A_27a @ V3a1_2E0 ) ) ) ) ) ) )
& ! [V4f_2E0: u,V5a0: mono_2Etyop_2Enum_2Enum,V6a1: mono_2Etyop_2Enum_2Enum,V7a2_2E0: u,V8a3_2E0: u] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epatricia_2Eptree__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V4f_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5a0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6a1 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V7a2_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V8a3_2E0 ) ) ) ) ) )
= ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( mono_2Ec_2Earithmetic_2E_2B @ V5a0 @ ( mono_2Ec_2Earithmetic_2E_2B @ V6a1 @ ( mono_2Ec_2Earithmetic_2E_2B @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epatricia_2Eptree__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V4f_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V7a2_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epatricia_2Eptree__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V4f_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V8a3_2E0 ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EJOIN__def,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V0p0: mono_2Etyop_2Enum_2Enum,V1t0_2E0: u,V3t1_2E0: u,V4m: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0p0 ) ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V1t0_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V3t1_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4m ) ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebit_2EBIT @ V4m @ V0p0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Ebit_2EMOD__2EXP @ V4m @ V0p0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4m ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V1t0_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V3t1_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Ebit_2EMOD__2EXP @ V4m @ V0p0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4m ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V3t1_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V1t0_2E0 ) ) ) ) ) )
=> ! [V0p0: mono_2Etyop_2Enum_2Enum,V1t0_2E0: u,V2p1: mono_2Etyop_2Enum_2Enum,V3t1_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EJOIN_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0p0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V1t0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2p1 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V3t1_2E0 ) ) ) ) ) ) ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Ebool_2ELET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0p0 ) ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V1t0_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V3t1_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Epatricia_2EBRANCHING__BIT @ V0p0 @ V2p1 ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EBRANCH__primitive__def,axiom,
! [A_27a: d,F10_2E0: u,F9_2E0: u,F6_2E0: u,F8_2E0: u,F7_2E0: u,F5_2E0: u,F4_2E0: u,F3_2E0: u,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
( ! [V3p: mono_2Etyop_2Enum_2Enum,V5m: mono_2Etyop_2Enum_2Enum,V17v20: mono_2Etyop_2Enum_2Enum,V18v21: mono_2Etyop_2Enum_2Enum,V19v22_2E0: u,V20v23_2E0: u,V23v44: mono_2Etyop_2Enum_2Enum,V24v45: mono_2Etyop_2Enum_2Enum,V25v46_2E0: u,V26v47_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) ) ) ) ) ) @ F10_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3p ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5m ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V17v20 ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V18v21 ) ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V19v22_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V20v23_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V23v44 ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V24v45 ) ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V25v46_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V26v47_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Ecombin_2EI_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3p ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5m ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V17v20 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V18v21 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V19v22_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V20v23_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V23v44 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V24v45 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V25v46_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V26v47_2E0 ) ) ) ) ) ) ) )
=> ( ! [V3p: mono_2Etyop_2Enum_2Enum,V5m: mono_2Etyop_2Enum_2Enum,V17v20: mono_2Etyop_2Enum_2Enum,V18v21: mono_2Etyop_2Enum_2Enum,V19v22_2E0: u,V20v23_2E0: u,V21v42: mono_2Etyop_2Enum_2Enum,V22v43_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) ) ) ) @ F9_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3p ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5m ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V17v20 ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V18v21 ) ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V19v22_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V20v23_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V21v42 ) ) ) ) @ ( s @ A_27a @ V22v43_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Ecombin_2EI_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3p ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5m ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V17v20 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V18v21 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V19v22_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V20v23_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V21v42 ) ) @ ( s @ A_27a @ V22v43_2E0 ) ) ) ) ) ) ) )
=> ( ! [V8t_2E0: u,V3p: mono_2Etyop_2Enum_2Enum,V5m: mono_2Etyop_2Enum_2Enum,V17v20: mono_2Etyop_2Enum_2Enum,V18v21: mono_2Etyop_2Enum_2Enum,V19v22_2E0: u,V20v23_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) ) ) @ F6_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V8t_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3p ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5m ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V17v20 ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V18v21 ) ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V19v22_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V20v23_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2Eptree__CASE_2E4 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V8t_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Ecombin_2EI_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V17v20 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V18v21 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V19v22_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V20v23_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) ) ) ) @ F9_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3p ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5m ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V17v20 ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V18v21 ) ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V19v22_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V20v23_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) ) ) ) ) ) @ F10_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3p ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5m ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V17v20 ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V18v21 ) ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V19v22_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V20v23_2E0 ) ) ) ) ) )
=> ( ! [V3p: mono_2Etyop_2Enum_2Enum,V5m: mono_2Etyop_2Enum_2Enum,V9v18: mono_2Etyop_2Enum_2Enum,V10v19_2E0: u,V13v32: mono_2Etyop_2Enum_2Enum,V14v33: mono_2Etyop_2Enum_2Enum,V15v34_2E0: u,V16v35_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) ) ) ) @ F8_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3p ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5m ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V9v18 ) ) ) ) @ ( s @ A_27a @ V10v19_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V13v32 ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V14v33 ) ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V15v34_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V16v35_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Ecombin_2EI_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3p ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5m ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V9v18 ) ) @ ( s @ A_27a @ V10v19_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V13v32 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V14v33 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V15v34_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V16v35_2E0 ) ) ) ) ) ) ) )
=> ( ! [V3p: mono_2Etyop_2Enum_2Enum,V5m: mono_2Etyop_2Enum_2Enum,V9v18: mono_2Etyop_2Enum_2Enum,V10v19_2E0: u,V11v30: mono_2Etyop_2Enum_2Enum,V12v31_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) ) @ F7_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3p ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5m ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V9v18 ) ) ) ) @ ( s @ A_27a @ V10v19_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V11v30 ) ) ) ) @ ( s @ A_27a @ V12v31_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Ecombin_2EI_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3p ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5m ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V9v18 ) ) @ ( s @ A_27a @ V10v19_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V11v30 ) ) @ ( s @ A_27a @ V12v31_2E0 ) ) ) ) ) ) ) )
=> ( ! [V8t_2E0: u,V3p: mono_2Etyop_2Enum_2Enum,V5m: mono_2Etyop_2Enum_2Enum,V9v18: mono_2Etyop_2Enum_2Enum,V10v19_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) @ F5_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V8t_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3p ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5m ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V9v18 ) ) ) ) @ ( s @ A_27a @ V10v19_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2Eptree__CASE_2E4 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V8t_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Ecombin_2EI_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V9v18 ) ) @ ( s @ A_27a @ V10v19_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) ) @ F7_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3p ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5m ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V9v18 ) ) ) ) @ ( s @ A_27a @ V10v19_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) ) ) ) @ F8_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3p ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5m ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V9v18 ) ) ) ) @ ( s @ A_27a @ V10v19_2E0 ) ) ) ) ) )
=> ( ! [V3p: mono_2Etyop_2Enum_2Enum,V5m: mono_2Etyop_2Enum_2Enum,V7v4_2E0: u,V8t_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ F4_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3p ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5m ) ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V7v4_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V8t_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2Eptree__CASE_2E4 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V7v4_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Ecombin_2EI_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V8t_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) @ F5_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V8t_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3p ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5m ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) ) ) ) @ F6_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V8t_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3p ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5m ) ) ) ) ) ) )
=> ( ! [V3p: mono_2Etyop_2Enum_2Enum,V5m: mono_2Etyop_2Enum_2Enum,V6v3_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ F3_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3p ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5m ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ V6v3_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ V6v3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ F4_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3p ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5m ) ) ) ) ) ) )
=> ( ! [V3p: mono_2Etyop_2Enum_2Enum,V4v1_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ F2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3p ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ V4v1_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ V4v1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ F3_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3p ) ) ) ) ) ) )
=> ( ! [V1BRANCH_2E0: u,V2a_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ V1BRANCH_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ V2a_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ V2a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ F2_2E0 ) ) ) )
=> ( ! [V0R_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2EWF_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) ) ) ) )
=> ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ c_2Epatricia_2EBRANCH_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( c_2Erelation_2EWFREC_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Emin_2E_40_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ F1_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EREMOVE__def,axiom,
! [A_27a: d,F0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ! [V1j: mono_2Etyop_2Enum_2Enum,V3k: mono_2Etyop_2Enum_2Enum] :
( ( F0 @ V1j @ V3k )
<=> ( V1j = V3k ) )
=> ( ! [V0k: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EREMOVE_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0k ) ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) )
& ! [V1j: mono_2Etyop_2Enum_2Enum,V2d_2E0: u,V3k: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EREMOVE_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1j ) ) @ ( s @ A_27a @ V2d_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3k ) ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F0 @ V1j @ V3k ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1j ) ) @ ( s @ A_27a @ V2d_2E0 ) ) ) ) ) )
& ! [V4p: mono_2Etyop_2Enum_2Enum,V5m: mono_2Etyop_2Enum_2Enum,V6l_2E0: u,V7r_2E0: u,V8k: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EREMOVE_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4p ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5m ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V6l_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V7r_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8k ) ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebit_2EMOD__2EXP__EQ @ V5m @ V8k @ V4p ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebit_2EBIT @ V5m @ V8k ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBRANCH_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4p ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5m ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EREMOVE_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V6l_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8k ) ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V7r_2E0 ) ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBRANCH_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4p ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5m ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V6l_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EREMOVE_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V7r_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8k ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4p ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5m ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V6l_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V7r_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2ETRAVERSE__AUX__def,axiom,
! [A_27a: d] :
( ! [V0a: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE__AUX_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V0a ) ) ) ) )
= V0a )
& ! [V1k: mono_2Etyop_2Enum_2Enum,V2d_2E0: u,V3a: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE__AUX_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) @ ( s @ A_27a @ V2d_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V3a ) ) ) ) )
= ( mono_2Ec_2Elist_2ECONS_2Emono_2Etyop_2Enum_2Enum @ V1k @ V3a ) )
& ! [V4p: mono_2Etyop_2Enum_2Enum,V5m: mono_2Etyop_2Enum_2Enum,V6l_2E0: u,V7r_2E0: u,V8a: mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29] :
( ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE__AUX_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4p ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5m ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V6l_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V7r_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V8a ) ) ) ) )
= ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE__AUX_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V6l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE__AUX_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V7r_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ V8a ) ) ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2ETRAVERSE__def,axiom,
! [A_27a: d] :
( ( ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) ) ) )
= mono_2Ec_2Elist_2ENIL_2Emono_2Etyop_2Enum_2Enum )
& ! [V0j: mono_2Etyop_2Enum_2Enum,V1d_2E0: u] :
( ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0j ) ) @ ( s @ A_27a @ V1d_2E0 ) ) ) ) ) )
= ( mono_2Ec_2Elist_2ECONS_2Emono_2Etyop_2Enum_2Enum @ V0j @ mono_2Ec_2Elist_2ENIL_2Emono_2Etyop_2Enum_2Enum ) )
& ! [V2p: mono_2Etyop_2Enum_2Enum,V3m: mono_2Etyop_2Enum_2Enum,V4l_2E0: u,V5r_2E0: u] :
( ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2p ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3m ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V4l_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V5r_2E0 ) ) ) ) ) )
= ( mono_2Ec_2Elist_2EAPPEND_2Emono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V4l_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V5r_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EKEYS__def,axiom,
! [A_27a: d,V0t_2E0: u] :
( ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2EKEYS_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) )
= ( mono_2Ec_2Esorting_2EQSORT_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Eprim__rec_2E_3C @ ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) ) ) ) ).
thf(thm_2Epatricia_2ETRANSFORM__def,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0f_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ETRANSFORM_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ c_2Epatricia_2EEmpty_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) )
& ! [V1f_2E0: u,V2j: mono_2Etyop_2Enum_2Enum,V3d_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ETRANSFORM_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V1f_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2j ) ) @ ( s @ A_27b @ V3d_2E0 ) ) ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2j ) ) @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V1f_2E0 ) @ ( s @ A_27b @ V3d_2E0 ) ) ) ) ) )
& ! [V4f_2E0: u,V5p: mono_2Etyop_2Enum_2Enum,V6m: mono_2Etyop_2Enum_2Enum,V7l_2E0: u,V8r_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ETRANSFORM_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V4f_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5p ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6m ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ V7l_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ V8r_2E0 ) ) ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5p ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6m ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ETRANSFORM_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V4f_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ V7l_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ETRANSFORM_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V4f_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ V8r_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EEVERY__LEAF__def,axiom,
! [A_27a: d] :
( ! [V0P_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EEVERY__LEAF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) ) ) )
= mono_2Ec_2Ebool_2ET )
& ! [V1P_2E0: u,V2j: mono_2Etyop_2Enum_2Enum,V3d_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EEVERY__LEAF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V1P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2j ) ) @ ( s @ A_27a @ V3d_2E0 ) ) ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V1P_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2j ) ) ) ) @ ( s @ A_27a @ V3d_2E0 ) ) ) ) )
& ! [V4P_2E0: u,V5p: mono_2Etyop_2Enum_2Enum,V6m: mono_2Etyop_2Enum_2Enum,V7l_2E0: u,V8r_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EEVERY__LEAF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V4P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5p ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6m ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V7l_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V8r_2E0 ) ) ) ) ) )
<=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EEVERY__LEAF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V4P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V7l_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EEVERY__LEAF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V4P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V8r_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EEXISTS__LEAF__def,axiom,
! [A_27a: d] :
( ! [V0P_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EEXISTS__LEAF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) ) ) )
= mono_2Ec_2Ebool_2EF )
& ! [V1P_2E0: u,V2j: mono_2Etyop_2Enum_2Enum,V3d_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EEXISTS__LEAF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V1P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2j ) ) @ ( s @ A_27a @ V3d_2E0 ) ) ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V1P_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2j ) ) ) ) @ ( s @ A_27a @ V3d_2E0 ) ) ) ) )
& ! [V4P_2E0: u,V5p: mono_2Etyop_2Enum_2Enum,V6m: mono_2Etyop_2Enum_2Enum,V7l_2E0: u,V8r_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EEXISTS__LEAF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V4P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5p ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6m ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V7l_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V8r_2E0 ) ) ) ) ) )
<=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EEXISTS__LEAF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V4P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V7l_2E0 ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EEXISTS__LEAF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V4P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V8r_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2ESIZE__def,axiom,
! [A_27a: d,V0t_2E0: u] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epatricia_2ESIZE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) )
= ( mono_2Ec_2Elist_2ELENGTH_2Emono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EDEPTH__def,axiom,
! [A_27a: d] :
( ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epatricia_2EDEPTH_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) ) ) )
= mono_2Ec_2Enum_2E0 )
& ! [V0j: mono_2Etyop_2Enum_2Enum,V1d_2E0: u] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epatricia_2EDEPTH_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0j ) ) @ ( s @ A_27a @ V1d_2E0 ) ) ) ) ) )
= ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
& ! [V2p: mono_2Etyop_2Enum_2Enum,V3m: mono_2Etyop_2Enum_2Enum,V4l_2E0: u,V5r_2E0: u] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epatricia_2EDEPTH_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2p ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3m ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V4l_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V5r_2E0 ) ) ) ) ) )
= ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( mono_2Ec_2Earithmetic_2EMAX @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epatricia_2EDEPTH_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V4l_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epatricia_2EDEPTH_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V5r_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EIS__PTREE__def,axiom,
! [A_27a: d,F0_2E0: u,F1_2E0: u] :
( ! [V3m: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum,V6k: mono_2Etyop_2Enum_2Enum,V7d_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3m ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2p ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6k ) ) ) ) @ ( s @ A_27a @ V7d_2E0 ) ) ) )
<=> ( ( mono_2Ec_2Ebit_2EMOD__2EXP__EQ @ V3m @ V6k @ V2p )
& ( mono_2Ec_2Ebit_2EBIT @ V3m @ V6k ) ) )
=> ( ! [V3m: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum,V8k: mono_2Etyop_2Enum_2Enum,V9d_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3m ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2p ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8k ) ) ) ) @ ( s @ A_27a @ V9d_2E0 ) ) ) )
<=> ( ( mono_2Ec_2Ebit_2EMOD__2EXP__EQ @ V3m @ V8k @ V2p )
& ( (~) @ ( mono_2Ec_2Ebit_2EBIT @ V3m @ V8k ) ) ) )
=> ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) ) ) )
= mono_2Ec_2Ebool_2ET )
& ! [V0k: mono_2Etyop_2Enum_2Enum,V1d_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0k ) ) @ ( s @ A_27a @ V1d_2E0 ) ) ) ) ) )
= mono_2Ec_2Ebool_2ET )
& ! [V2p: mono_2Etyop_2Enum_2Enum,V3m: mono_2Etyop_2Enum_2Enum,V4l_2E0: u,V5r_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2p ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3m ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V4l_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V5r_2E0 ) ) ) ) ) )
<=> ( ( mono_2Ec_2Eprim__rec_2E_3C @ V2p @ ( mono_2Ec_2Earithmetic_2EEXP @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V3m ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V4l_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V5r_2E0 ) ) ) )
& ( (~)
@ ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V4l_2E0 )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) ) )
& ( (~)
@ ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V5r_2E0 )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EEVERY__LEAF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3m ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2p ) ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V4l_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EEVERY__LEAF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3m ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2p ) ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V5r_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EIN__PTREE__def,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1t: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( mono_2Ec_2Epatricia_2EIN__PTREE @ V0n @ V1t )
= ( mono_2Ec_2Eoption_2EIS__SOME_2Emono_2Etyop_2Eone_2Eone @ ( mono_2Ec_2Epatricia_2EPEEK_2Emono_2Etyop_2Eone_2Eone @ V1t @ V0n ) ) ) ).
thf(thm_2Epatricia_2EINSERT__PTREE__def,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1t: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( mono_2Ec_2Epatricia_2EINSERT__PTREE @ V0n @ V1t )
= ( mono_2Ec_2Epatricia_2EADD_2Emono_2Etyop_2Eone_2Eone @ V1t @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eone_2Eone @ V0n @ mono_2Ec_2Eone_2Eone ) ) ) ).
thf(thm_2Epatricia_2EPTREE__OF__NUMSET__def,axiom,
! [V0t: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1s: mono_2Etyop_2Enum_2Enum > $o] :
( ( mono_2Ec_2Epatricia_2EPTREE__OF__NUMSET @ V0t @ V1s )
= ( mono_2Ec_2Elist_2EFOLDL_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ ( mono_2Ec_2Ecombin_2EC_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ mono_2Ec_2Epatricia_2EINSERT__PTREE ) @ V0t @ ( mono_2Ec_2Elist_2ESET__TO__LIST_2Emono_2Etyop_2Enum_2Enum @ V1s ) ) ) ).
thf(thm_2Epatricia_2ENUMSET__OF__PTREE__def,axiom,
! [V0t: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( mono_2Ec_2Epatricia_2ENUMSET__OF__PTREE @ V0t )
= ( mono_2Ec_2Elist_2ELIST__TO__SET_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Epatricia_2ETRAVERSE_2Emono_2Etyop_2Eone_2Eone @ V0t ) ) ) ).
thf(thm_2Epatricia_2EUNION__PTREE__def,axiom,
! [V0t1: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1t2: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( mono_2Ec_2Epatricia_2EUNION__PTREE @ V0t1 @ V1t2 )
= ( mono_2Ec_2Epatricia_2EPTREE__OF__NUMSET @ V0t1 @ ( mono_2Ec_2Epatricia_2ENUMSET__OF__PTREE @ V1t2 ) ) ) ).
thf(thm_2Epatricia_2EIS__EMPTY__primitive__def,axiom,
! [A_27a: d,F0_2E0: u,F3_2E0: u,F2_2E0: u,F1_2E0: u] :
( ! [V0R_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2EWF_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) ) ) ) )
=> ( ! [V5v8: mono_2Etyop_2Enum_2Enum,V6v9: mono_2Etyop_2Enum_2Enum,V7v10_2E0: u,V8v11_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) ) @ F3_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5v8 ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6v9 ) ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V7v10_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V8v11_2E0 ) ) ) )
= ( mono_2Ec_2Ecombin_2EI_2Emono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF ) )
=> ( ! [V3v6: mono_2Etyop_2Enum_2Enum,V4v7_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ F2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3v6 ) ) ) ) @ ( s @ A_27a @ V4v7_2E0 ) ) ) )
= ( mono_2Ec_2Ecombin_2EI_2Emono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF ) )
=> ( ! [V1IS__EMPTY_2E0: u,V2a_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1IS__EMPTY_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V2a_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2Eptree__CASE_2E4 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V2a_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ecombin_2EI_2Emono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) ) @ F3_2E0 ) ) ) ) )
=> ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Epatricia_2EIS__EMPTY_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Erelation_2EWFREC_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Emin_2E_40_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F1_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EFIND__def,axiom,
! [A_27a: d,V0t_2E0: u,V1k: mono_2Etyop_2Enum_2Enum] :
( ( s @ A_27a @ ( c_2Epatricia_2EFIND_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) ) )
= ( s @ A_27a @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Epatricia_2EPEEK_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EADD__LIST__def,axiom,
! [A_27a: d] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ c_2Epatricia_2EADD__LIST_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( c_2Elist_2EFOLDL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) ) ) ) ).
thf(thm_2Epatricia_2Edatatype__ptree,axiom,
! [A_27a: d,V0ptree_2E0: u] : ( mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ tyop_2Emin_2Ebool ) ) ) @ V0ptree_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ c_2Epatricia_2ELeaf_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) ) @ c_2Epatricia_2EBranch_2E0 ) ) ) ) ) ).
thf(thm_2Epatricia_2Eptree__11,axiom,
! [A_27a: d] :
( ! [V0a0: mono_2Etyop_2Enum_2Enum,V1a1_2E0: u,V2a0_27: mono_2Etyop_2Enum_2Enum,V3a1_27_2E0: u] :
( ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0a0 ) ) @ ( s @ A_27a @ V1a1_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2a0_27 ) ) @ ( s @ A_27a @ V3a1_27_2E0 ) ) ) )
<=> ( ( V0a0 = V2a0_27 )
& ( ( s @ A_27a @ V1a1_2E0 )
= ( s @ A_27a @ V3a1_27_2E0 ) ) ) )
& ! [V4a0: mono_2Etyop_2Enum_2Enum,V5a1: mono_2Etyop_2Enum_2Enum,V6a2_2E0: u,V7a3_2E0: u,V8a0_27: mono_2Etyop_2Enum_2Enum,V9a1_27: mono_2Etyop_2Enum_2Enum,V10a2_27_2E0: u,V11a3_27_2E0: u] :
( ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4a0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5a1 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V6a2_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V7a3_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8a0_27 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V9a1_27 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V10a2_27_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V11a3_27_2E0 ) ) ) )
<=> ( ( V4a0 = V8a0_27 )
& ( V5a1 = V9a1_27 )
& ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V6a2_2E0 )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V10a2_27_2E0 ) )
& ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V7a3_2E0 )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V11a3_27_2E0 ) ) ) ) ) ).
thf(thm_2Epatricia_2Eptree__distinct,axiom,
! [A_27a: d] :
( ! [V0a1_2E0: u,V1a0: mono_2Etyop_2Enum_2Enum] :
( (~)
@ ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1a0 ) ) @ ( s @ A_27a @ V0a1_2E0 ) ) ) ) )
& ! [V2a3_2E0: u,V3a2_2E0: u,V4a1: mono_2Etyop_2Enum_2Enum,V5a0: mono_2Etyop_2Enum_2Enum] :
( (~)
@ ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5a0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4a1 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V3a2_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V2a3_2E0 ) ) ) ) )
& ! [V6a3_2E0: u,V7a2_2E0: u,V8a1_27: mono_2Etyop_2Enum_2Enum,V9a1_2E0: u,V10a0_27: mono_2Etyop_2Enum_2Enum,V11a0: mono_2Etyop_2Enum_2Enum] :
( (~)
@ ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V11a0 ) ) @ ( s @ A_27a @ V9a1_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V10a0_27 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8a1_27 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V7a2_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V6a3_2E0 ) ) ) ) ) ) ).
thf(thm_2Epatricia_2Eptree__nchotomy,axiom,
! [A_27a: d,V0pp_2E0: u] :
( ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0pp_2E0 )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) )
| ? [V1n: mono_2Etyop_2Enum_2Enum,V2a_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0pp_2E0 )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) @ ( s @ A_27a @ V2a_2E0 ) ) ) )
| ? [V3n0: mono_2Etyop_2Enum_2Enum,V4n: mono_2Etyop_2Enum_2Enum,V5p_2E0: u,V6p0_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0pp_2E0 )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4n ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V5p_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V6p0_2E0 ) ) ) ) ) ).
thf(thm_2Epatricia_2Eptree__Axiom,axiom,
! [A_27a: d,A_27b: d,V0f0_2E0: u,V1f1_2E0: u,V2f2_2E0: u] :
? [V3fn_2E0: u] :
( ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) @ V3fn_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) ) )
= ( s @ A_27b @ V0f0_2E0 ) )
& ! [V4a0: mono_2Etyop_2Enum_2Enum,V5a1_2E0: u] :
( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) @ V3fn_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4a0 ) ) @ ( s @ A_27a @ V5a1_2E0 ) ) ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ V1f1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4a0 ) ) ) ) @ ( s @ A_27a @ V5a1_2E0 ) ) ) )
& ! [V6a0: mono_2Etyop_2Enum_2Enum,V7a1: mono_2Etyop_2Enum_2Enum,V8a2_2E0: u,V9a3_2E0: u] :
( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) @ V3fn_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6a0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V7a1 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V8a2_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V9a3_2E0 ) ) ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) ) ) ) @ V2f2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6a0 ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V7a1 ) ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V8a2_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V9a3_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) @ V3fn_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V8a2_2E0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) @ V3fn_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V9a3_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2Eptree__induction,axiom,
! [A_27a: d,V0P_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) ) ) )
& ! [V1n: mono_2Etyop_2Enum_2Enum,V2a_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) @ ( s @ A_27a @ V2a_2E0 ) ) ) ) ) )
& ! [V3p_2E0: u,V4p0_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V3p_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V4p0_2E0 ) ) ) ) )
=> ! [V5n: mono_2Etyop_2Enum_2Enum,V6n0: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6n0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5n ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V3p_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V4p0_2E0 ) ) ) ) ) ) ) )
=> ! [V7p_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V7p_2E0 ) ) ) ) ) ).
thf(thm_2Epatricia_2Eptree__case__cong,axiom,
! [A_27a: d,A_27b: d,V0v_27_2E0: u,V1f1_27_2E0: u,V2f_27_2E0: u,V3M_2E0: u,V4M_27_2E0: u,V5v_2E0: u,V6f_2E0: u,V7f1_2E0: u] :
( ( ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V3M_2E0 )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V4M_27_2E0 ) )
& ( ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V4M_27_2E0 )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) )
=> ( ( s @ A_27b @ V5v_2E0 )
= ( s @ A_27b @ V0v_27_2E0 ) ) )
& ! [V8a0: mono_2Etyop_2Enum_2Enum,V9a1_2E0: u] :
( ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V4M_27_2E0 )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8a0 ) ) @ ( s @ A_27a @ V9a1_2E0 ) ) ) )
=> ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ V6f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8a0 ) ) ) ) @ ( s @ A_27a @ V9a1_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ V2f_27_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8a0 ) ) ) ) @ ( s @ A_27a @ V9a1_2E0 ) ) ) ) )
& ! [V10a0: mono_2Etyop_2Enum_2Enum,V11a1: mono_2Etyop_2Enum_2Enum,V12a2_2E0: u,V13a3_2E0: u] :
( ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V4M_27_2E0 )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V10a0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V11a1 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V12a2_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V13a3_2E0 ) ) ) )
=> ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) ) ) ) @ V7f1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V10a0 ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V11a1 ) ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V12a2_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V13a3_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) ) ) ) @ V1f1_27_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V10a0 ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V11a1 ) ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V12a2_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V13a3_2E0 ) ) ) ) ) )
=> ( ( s @ A_27b @ ( c_2Epatricia_2Eptree__CASE_2E4 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V3M_2E0 ) @ ( s @ A_27b @ V5v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ V6f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) ) ) ) @ V7f1_2E0 ) ) )
= ( s @ A_27b @ ( c_2Epatricia_2Eptree__CASE_2E4 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V4M_27_2E0 ) @ ( s @ A_27b @ V0v_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ V2f_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) ) ) ) @ V1f1_27_2E0 ) ) ) ) ) ).
thf(thm_2Epatricia_2Eptree__case__eq,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u,V1v_27_2E0: u,V2v_2E0: u,V3f1_2E0: u,V4f_2E0: u] :
( ( ( s @ A_27b @ ( c_2Epatricia_2Eptree__CASE_2E4 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0x_2E0 ) @ ( s @ A_27b @ V2v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ V4f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) ) ) ) @ V3f1_2E0 ) ) )
= ( s @ A_27b @ V1v_27_2E0 ) )
<=> ( ( ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0x_2E0 )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) )
& ( ( s @ A_27b @ V2v_2E0 )
= ( s @ A_27b @ V1v_27_2E0 ) ) )
| ? [V5n: mono_2Etyop_2Enum_2Enum,V6a_2E0: u] :
( ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0x_2E0 )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5n ) ) @ ( s @ A_27a @ V6a_2E0 ) ) ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ V4f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5n ) ) ) ) @ ( s @ A_27a @ V6a_2E0 ) ) )
= ( s @ A_27b @ V1v_27_2E0 ) ) )
| ? [V7n0: mono_2Etyop_2Enum_2Enum,V8n: mono_2Etyop_2Enum_2Enum,V9p_2E0: u,V10p0_2E0: u] :
( ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0x_2E0 )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V7n0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8n ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V9p_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V10p0_2E0 ) ) ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ A_27b ) ) ) ) @ V3f1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V7n0 ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8n ) ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V9p_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V10p0_2E0 ) ) )
= ( s @ A_27b @ V1v_27_2E0 ) ) ) ) ) ).
thf(thm_2Epatricia_2EBRANCHING__BIT__ind,axiom,
! [V0P: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ! [V1p0: mono_2Etyop_2Enum_2Enum,V2p1: mono_2Etyop_2Enum_2Enum] :
( ( ( (~)
@ ( ( ( mono_2Ec_2Earithmetic_2EODD @ V1p0 )
= ( mono_2Ec_2Earithmetic_2EEVEN @ V2p1 ) )
| ( V1p0 = V2p1 ) ) )
=> ( V0P @ ( mono_2Ec_2Earithmetic_2EDIV2 @ V1p0 ) @ ( mono_2Ec_2Earithmetic_2EDIV2 @ V2p1 ) ) )
=> ( V0P @ V1p0 @ V2p1 ) )
=> ! [V3v: mono_2Etyop_2Enum_2Enum,V4v1: mono_2Etyop_2Enum_2Enum] : ( V0P @ V3v @ V4v1 ) ) ).
thf(thm_2Epatricia_2EBRANCHING__BIT__def,axiom,
! [F0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ! [V1p0: mono_2Etyop_2Enum_2Enum,V0p1: mono_2Etyop_2Enum_2Enum] :
( ( F0 @ V1p0 @ V0p1 )
<=> ( ( ( mono_2Ec_2Earithmetic_2EODD @ V1p0 )
= ( mono_2Ec_2Earithmetic_2EEVEN @ V0p1 ) )
| ( V1p0 = V0p1 ) ) )
=> ! [V0p1: mono_2Etyop_2Enum_2Enum,V1p0: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Epatricia_2EBRANCHING__BIT @ V1p0 @ V0p1 )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ ( F0 @ V1p0 @ V0p1 ) @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Epatricia_2EBRANCHING__BIT @ ( mono_2Ec_2Earithmetic_2EDIV2 @ V1p0 ) @ ( mono_2Ec_2Earithmetic_2EDIV2 @ V0p1 ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EPEEK__ind,axiom,
! [A_27a: d,V0P_2E0: u] :
( ( ! [V1k: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) ) ) @ V1k )
& ! [V2j: mono_2Etyop_2Enum_2Enum,V3d_2E0: u,V4k: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2j ) ) @ ( s @ A_27a @ V3d_2E0 ) ) ) ) ) @ V4k )
& ! [V5p: mono_2Etyop_2Enum_2Enum,V6m: mono_2Etyop_2Enum_2Enum,V7l_2E0: u,V8r_2E0: u,V9k: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebit_2EBIT @ V6m @ V9k ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V7l_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V8r_2E0 ) ) ) ) ) @ V9k )
=> ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5p ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6m ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V7l_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V8r_2E0 ) ) ) ) ) @ V9k ) ) )
=> ! [V10v_2E0: u,V11v1: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V10v_2E0 ) ) ) @ V11v1 ) ) ).
thf(thm_2Epatricia_2EPEEK__def,axiom,
! [A_27a: d,F0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ! [V1k: mono_2Etyop_2Enum_2Enum,V2j: mono_2Etyop_2Enum_2Enum] :
( ( F0 @ V1k @ V2j )
<=> ( V1k = V2j ) )
=> ( ! [V0k: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Epatricia_2EPEEK_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0k ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
& ! [V1k: mono_2Etyop_2Enum_2Enum,V2j: mono_2Etyop_2Enum_2Enum,V3d_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Epatricia_2EPEEK_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2j ) ) @ ( s @ A_27a @ V3d_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F0 @ V1k @ V2j ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V3d_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
& ! [V4r_2E0: u,V5p: mono_2Etyop_2Enum_2Enum,V6m: mono_2Etyop_2Enum_2Enum,V7l_2E0: u,V8k: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Epatricia_2EPEEK_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5p ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6m ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V7l_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V4r_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8k ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Epatricia_2EPEEK_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebit_2EBIT @ V6m @ V8k ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V7l_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V4r_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8k ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EADD__ind,axiom,
! [A_27a: d,V0P_2E0: u] :
( ( ! [V1k: mono_2Etyop_2Enum_2Enum,V2e_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) @ ( s @ A_27a @ V2e_2E0 ) ) ) ) ) )
& ! [V3j: mono_2Etyop_2Enum_2Enum,V4d_2E0: u,V5k: mono_2Etyop_2Enum_2Enum,V6e_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3j ) ) @ ( s @ A_27a @ V4d_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5k ) ) @ ( s @ A_27a @ V6e_2E0 ) ) ) ) ) )
& ! [V7p: mono_2Etyop_2Enum_2Enum,V8m: mono_2Etyop_2Enum_2Enum,V9l_2E0: u,V10r_2E0: u,V11k: mono_2Etyop_2Enum_2Enum,V12e_2E0: u] :
( ( ( ( ( mono_2Ec_2Ebit_2EMOD__2EXP__EQ @ V8m @ V11k @ V7p )
& ( (~) @ ( mono_2Ec_2Ebit_2EBIT @ V8m @ V11k ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V10r_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V11k ) ) @ ( s @ A_27a @ V12e_2E0 ) ) ) ) ) ) )
& ( ( ( mono_2Ec_2Ebit_2EMOD__2EXP__EQ @ V8m @ V11k @ V7p )
& ( mono_2Ec_2Ebit_2EBIT @ V8m @ V11k ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V9l_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V11k ) ) @ ( s @ A_27a @ V12e_2E0 ) ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V7p ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8m ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V9l_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V10r_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V11k ) ) @ ( s @ A_27a @ V12e_2E0 ) ) ) ) ) ) ) )
=> ! [V13v_2E0: u,V14v1: mono_2Etyop_2Enum_2Enum,V15v2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V13v_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V14v1 ) ) @ ( s @ A_27a @ V15v2_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EADD__def,axiom,
! [A_27a: d,F0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ! [V3j: mono_2Etyop_2Enum_2Enum,V2k: mono_2Etyop_2Enum_2Enum] :
( ( F0 @ V3j @ V2k )
<=> ( V3j = V2k ) )
=> ( ! [V0k: mono_2Etyop_2Enum_2Enum,V1e_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EADD_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0k ) ) @ ( s @ A_27a @ V1e_2E0 ) ) ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0k ) ) @ ( s @ A_27a @ V1e_2E0 ) ) ) )
& ! [V2k: mono_2Etyop_2Enum_2Enum,V3j: mono_2Etyop_2Enum_2Enum,V4e_2E0: u,V5d_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EADD_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3j ) ) @ ( s @ A_27a @ V5d_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) @ ( s @ A_27a @ V4e_2E0 ) ) ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F0 @ V3j @ V2k ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) @ ( s @ A_27a @ V4e_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EJOIN_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) @ ( s @ A_27a @ V4e_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3j ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3j ) ) @ ( s @ A_27a @ V5d_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ! [V6r_2E0: u,V7p: mono_2Etyop_2Enum_2Enum,V8m: mono_2Etyop_2Enum_2Enum,V9l_2E0: u,V10k: mono_2Etyop_2Enum_2Enum,V11e_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EADD_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V7p ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8m ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V9l_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V6r_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V10k ) ) @ ( s @ A_27a @ V11e_2E0 ) ) ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebit_2EMOD__2EXP__EQ @ V8m @ V10k @ V7p ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebit_2EBIT @ V8m @ V10k ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V7p ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8m ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EADD_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V9l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V10k ) ) @ ( s @ A_27a @ V11e_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V6r_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V7p ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8m ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V9l_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EADD_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V6r_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V10k ) ) @ ( s @ A_27a @ V11e_2E0 ) ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EJOIN_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V10k ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V10k ) ) @ ( s @ A_27a @ V11e_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V7p ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V7p ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8m ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V9l_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V6r_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EBRANCH__ind,axiom,
! [A_27a: d,V0P_2E0: u] :
( ( ! [V1p: mono_2Etyop_2Enum_2Enum,V2m: mono_2Etyop_2Enum_2Enum,V3t_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1p ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2m ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V3t_2E0 ) ) ) ) ) ) ) ) ) )
& ! [V4p: mono_2Etyop_2Enum_2Enum,V5m: mono_2Etyop_2Enum_2Enum,V6v6: mono_2Etyop_2Enum_2Enum,V7v7_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4p ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5m ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6v6 ) ) @ ( s @ A_27a @ V7v7_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) ) ) ) ) ) ) ) ) )
& ! [V8p: mono_2Etyop_2Enum_2Enum,V9m: mono_2Etyop_2Enum_2Enum,V10v8: mono_2Etyop_2Enum_2Enum,V11v9: mono_2Etyop_2Enum_2Enum,V12v10_2E0: u,V13v11_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8p ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V9m ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V10v8 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V11v9 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V12v10_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V13v11_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) ) ) ) ) ) ) ) ) )
& ! [V14p: mono_2Etyop_2Enum_2Enum,V15m: mono_2Etyop_2Enum_2Enum,V16v12: mono_2Etyop_2Enum_2Enum,V17v13_2E0: u,V18v24: mono_2Etyop_2Enum_2Enum,V19v25_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V14p ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V15m ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V16v12 ) ) @ ( s @ A_27a @ V17v13_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V18v24 ) ) @ ( s @ A_27a @ V19v25_2E0 ) ) ) ) ) ) ) ) ) ) ) )
& ! [V20p: mono_2Etyop_2Enum_2Enum,V21m: mono_2Etyop_2Enum_2Enum,V22v12: mono_2Etyop_2Enum_2Enum,V23v13_2E0: u,V24v26: mono_2Etyop_2Enum_2Enum,V25v27: mono_2Etyop_2Enum_2Enum,V26v28_2E0: u,V27v29_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V20p ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V21m ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V22v12 ) ) @ ( s @ A_27a @ V23v13_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V24v26 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V25v27 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V26v28_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V27v29_2E0 ) ) ) ) ) ) ) ) ) ) ) )
& ! [V28p: mono_2Etyop_2Enum_2Enum,V29m: mono_2Etyop_2Enum_2Enum,V30v14: mono_2Etyop_2Enum_2Enum,V31v15: mono_2Etyop_2Enum_2Enum,V32v16_2E0: u,V33v17_2E0: u,V34v36: mono_2Etyop_2Enum_2Enum,V35v37_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V28p ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V29m ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V30v14 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V31v15 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V32v16_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V33v17_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V34v36 ) ) @ ( s @ A_27a @ V35v37_2E0 ) ) ) ) ) ) ) ) ) ) ) )
& ! [V36p: mono_2Etyop_2Enum_2Enum,V37m: mono_2Etyop_2Enum_2Enum,V38v14: mono_2Etyop_2Enum_2Enum,V39v15: mono_2Etyop_2Enum_2Enum,V40v16_2E0: u,V41v17_2E0: u,V42v38: mono_2Etyop_2Enum_2Enum,V43v39: mono_2Etyop_2Enum_2Enum,V44v40_2E0: u,V45v41_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V36p ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V37m ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V38v14 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V39v15 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V40v16_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V41v17_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V42v38 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V43v39 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V44v40_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V45v41_2E0 ) ) ) ) ) ) ) ) ) ) ) ) )
=> ! [V46v: mono_2Etyop_2Enum_2Enum,V47v1: mono_2Etyop_2Enum_2Enum,V48v2_2E0: u,V49v3_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V46v ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V47v1 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V48v2_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V49v3_2E0 ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EBRANCH__def,axiom,
! [A_27a: d,V0v9: mono_2Etyop_2Enum_2Enum,V1v8: mono_2Etyop_2Enum_2Enum,V2v7_2E0: u,V3v6: mono_2Etyop_2Enum_2Enum,V4v41_2E0: u,V5v40_2E0: u,V6v39: mono_2Etyop_2Enum_2Enum,V7v38: mono_2Etyop_2Enum_2Enum,V8v37_2E0: u,V9v36: mono_2Etyop_2Enum_2Enum,V10v29_2E0: u,V11v28_2E0: u,V12v27: mono_2Etyop_2Enum_2Enum,V13v26: mono_2Etyop_2Enum_2Enum,V14v25_2E0: u,V15v24: mono_2Etyop_2Enum_2Enum,V16v17_2E0: u,V17v16_2E0: u,V18v15: mono_2Etyop_2Enum_2Enum,V19v14: mono_2Etyop_2Enum_2Enum,V20v13_2E0: u,V21v12: mono_2Etyop_2Enum_2Enum,V22v11_2E0: u,V23v10_2E0: u,V24t_2E0: u,V25p: mono_2Etyop_2Enum_2Enum,V26m: mono_2Etyop_2Enum_2Enum] :
( ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBRANCH_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V25p ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V26m ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V24t_2E0 ) ) ) ) ) ) ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V24t_2E0 ) )
& ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBRANCH_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V25p ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V26m ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3v6 ) ) @ ( s @ A_27a @ V2v7_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) ) ) ) ) ) ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3v6 ) ) @ ( s @ A_27a @ V2v7_2E0 ) ) ) )
& ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBRANCH_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V25p ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V26m ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1v8 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0v9 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V23v10_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V22v11_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) ) ) ) ) ) ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1v8 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0v9 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V23v10_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V22v11_2E0 ) ) ) )
& ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBRANCH_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V25p ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V26m ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V21v12 ) ) @ ( s @ A_27a @ V20v13_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V15v24 ) ) @ ( s @ A_27a @ V14v25_2E0 ) ) ) ) ) ) ) ) ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V25p ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V26m ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V21v12 ) ) @ ( s @ A_27a @ V20v13_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V15v24 ) ) @ ( s @ A_27a @ V14v25_2E0 ) ) ) ) ) )
& ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBRANCH_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V25p ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V26m ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V21v12 ) ) @ ( s @ A_27a @ V20v13_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V13v26 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V12v27 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V11v28_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V10v29_2E0 ) ) ) ) ) ) ) ) ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V25p ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V26m ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V21v12 ) ) @ ( s @ A_27a @ V20v13_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V13v26 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V12v27 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V11v28_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V10v29_2E0 ) ) ) ) ) )
& ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBRANCH_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V25p ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V26m ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V19v14 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V18v15 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V17v16_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V16v17_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V9v36 ) ) @ ( s @ A_27a @ V8v37_2E0 ) ) ) ) ) ) ) ) ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V25p ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V26m ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V19v14 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V18v15 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V17v16_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V16v17_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V9v36 ) ) @ ( s @ A_27a @ V8v37_2E0 ) ) ) ) ) )
& ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBRANCH_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V25p ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V26m ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V19v14 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V18v15 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V17v16_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V16v17_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V7v38 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6v39 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V5v40_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V4v41_2E0 ) ) ) ) ) ) ) ) ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V25p ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V26m ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V19v14 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V18v15 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V17v16_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V16v17_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V7v38 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6v39 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V5v40_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V4v41_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EIS__EMPTY__ind,axiom,
! [A_27a: d,V0P_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) ) ) )
& ! [V1v: mono_2Etyop_2Enum_2Enum,V2v1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1v ) ) @ ( s @ A_27a @ V2v1_2E0 ) ) ) ) ) )
& ! [V3v2: mono_2Etyop_2Enum_2Enum,V4v3: mono_2Etyop_2Enum_2Enum,V5v4_2E0: u,V6v5_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3v2 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4v3 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V5v4_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V6v5_2E0 ) ) ) ) ) ) )
=> ! [V7v_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V7v_2E0 ) ) ) ) ) ).
thf(thm_2Epatricia_2EIS__EMPTY__def,axiom,
! [A_27a: d,V0v5_2E0: u,V1v4_2E0: u,V2v3: mono_2Etyop_2Enum_2Enum,V3v2: mono_2Etyop_2Enum_2Enum,V4v1_2E0: u,V5v: mono_2Etyop_2Enum_2Enum] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__EMPTY_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) ) ) )
= mono_2Ec_2Ebool_2ET )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__EMPTY_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5v ) ) @ ( s @ A_27a @ V4v1_2E0 ) ) ) ) ) )
= mono_2Ec_2Ebool_2EF )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__EMPTY_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3v2 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2v3 ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V1v4_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0v5_2E0 ) ) ) ) ) )
= mono_2Ec_2Ebool_2EF ) ) ).
thf(thm_2Epatricia_2EBRANCHING__BIT,axiom,
! [V0a: mono_2Etyop_2Enum_2Enum,V1b: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( V0a = V1b ) )
=> ( (~)
@ ( ( mono_2Ec_2Ebit_2EBIT @ ( mono_2Ec_2Epatricia_2EBRANCHING__BIT @ V0a @ V1b ) @ V0a )
= ( mono_2Ec_2Ebit_2EBIT @ ( mono_2Ec_2Epatricia_2EBRANCHING__BIT @ V0a @ V1b ) @ V1b ) ) ) ) ).
thf(thm_2Epatricia_2EBRANCHING__BIT__ZERO,axiom,
! [V0a: mono_2Etyop_2Enum_2Enum,V1b: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Epatricia_2EBRANCHING__BIT @ V0a @ V1b )
= mono_2Ec_2Enum_2E0 )
<=> ( ( ( mono_2Ec_2Earithmetic_2EODD @ V0a )
= ( mono_2Ec_2Earithmetic_2EEVEN @ V1b ) )
| ( V0a = V1b ) ) ) ).
thf(thm_2Epatricia_2EBRANCHING__BIT__SYM,axiom,
! [V0a: mono_2Etyop_2Enum_2Enum,V1b: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Epatricia_2EBRANCHING__BIT @ V0a @ V1b )
= ( mono_2Ec_2Epatricia_2EBRANCHING__BIT @ V1b @ V0a ) ) ).
thf(thm_2Epatricia_2EEVERY__LEAF__ADD,axiom,
! [A_27a: d,V0P_2E0: u,V1t_2E0: u,V2k: mono_2Etyop_2Enum_2Enum,V3d_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) ) ) @ ( s @ A_27a @ V3d_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EEVERY__LEAF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V1t_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EEVERY__LEAF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EADD_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V1t_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) @ ( s @ A_27a @ V3d_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EMONO__EVERY__LEAF,axiom,
! [A_27a: d,V0P_2E0: u,V1Q_2E0: u,V2t_2E0: u] :
( ( ! [V3k: mono_2Etyop_2Enum_2Enum,V4d_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3k ) ) ) ) @ ( s @ A_27a @ V4d_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V1Q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3k ) ) ) ) @ ( s @ A_27a @ V4d_2E0 ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EEVERY__LEAF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V2t_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EEVERY__LEAF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V1Q_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V2t_2E0 ) ) ) ) ) ).
thf(thm_2Epatricia_2ENOT__ADD__EMPTY,axiom,
! [A_27a: d,V0t_2E0: u,V1k: mono_2Etyop_2Enum_2Enum,V2d_2E0: u] :
( (~)
@ ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EADD_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) @ ( s @ A_27a @ V2d_2E0 ) ) ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) ) ) ).
thf(thm_2Epatricia_2EEMPTY__IS__PTREE,axiom,
! [A_27a: d] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) ) ) ) ).
thf(thm_2Epatricia_2EADD__IS__PTREE,axiom,
! [A_27a: d,V0t_2E0: u,V1x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EADD_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ V1x_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EEVERY__LEAF__BRANCH,axiom,
! [A_27a: d,V0P_2E0: u,V1p: mono_2Etyop_2Enum_2Enum,V2m: mono_2Etyop_2Enum_2Enum,V3l_2E0: u,V4r_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EEVERY__LEAF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBRANCH_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1p ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2m ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V3l_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V4r_2E0 ) ) ) ) ) ) ) ) ) ) ) )
<=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EEVERY__LEAF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V3l_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EEVERY__LEAF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V4r_2E0 ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EEVERY__LEAF__REMOVE,axiom,
! [A_27a: d,V0P_2E0: u,V1t_2E0: u,V2k: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EEVERY__LEAF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V1t_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EEVERY__LEAF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EREMOVE_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V1t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EIS__PTREE__BRANCH,axiom,
! [A_27a: d,F0_2E0: u,F1_2E0: u] :
( ! [V1m: mono_2Etyop_2Enum_2Enum,V0p: mono_2Etyop_2Enum_2Enum,V4k: mono_2Etyop_2Enum_2Enum,V5d_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1m ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0p ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4k ) ) ) ) @ ( s @ A_27a @ V5d_2E0 ) ) ) )
<=> ( ( mono_2Ec_2Ebit_2EMOD__2EXP__EQ @ V1m @ V4k @ V0p )
& ( mono_2Ec_2Ebit_2EBIT @ V1m @ V4k ) ) )
=> ( ! [V1m: mono_2Etyop_2Enum_2Enum,V0p: mono_2Etyop_2Enum_2Enum,V6k: mono_2Etyop_2Enum_2Enum,V7d_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1m ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0p ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6k ) ) ) ) @ ( s @ A_27a @ V7d_2E0 ) ) ) )
<=> ( ( mono_2Ec_2Ebit_2EMOD__2EXP__EQ @ V1m @ V6k @ V0p )
& ( (~) @ ( mono_2Ec_2Ebit_2EBIT @ V1m @ V6k ) ) ) )
=> ! [V0p: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum,V2l_2E0: u,V3r_2E0: u] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ V0p @ ( mono_2Ec_2Earithmetic_2EEXP @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V1m ) )
& ( (~)
@ ( ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V2l_2E0 )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) )
& ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V3r_2E0 )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EEVERY__LEAF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1m ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0p ) ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V2l_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EEVERY__LEAF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1m ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0p ) ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V3r_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V2l_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V3r_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBRANCH_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0p ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1m ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V2l_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V3r_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EREMOVE__IS__PTREE,axiom,
! [A_27a: d,V0t_2E0: u,V1k: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EREMOVE_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EPEEK__NONE,axiom,
! [A_27a: d,V0P_2E0: u,V1t_2E0: u,V2k: mono_2Etyop_2Enum_2Enum] :
( ( ! [V3d_2E0: u] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) ) ) @ ( s @ A_27a @ V3d_2E0 ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EEVERY__LEAF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V1t_2E0 ) ) ) ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Epatricia_2EPEEK_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V1t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) ).
thf(thm_2Epatricia_2EPEEK__ADD,axiom,
! [A_27a: d,F0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ! [V1k: mono_2Etyop_2Enum_2Enum,V3j: mono_2Etyop_2Enum_2Enum] :
( ( F0 @ V1k @ V3j )
<=> ( V1k = V3j ) )
=> ! [V0t_2E0: u,V1k: mono_2Etyop_2Enum_2Enum,V2d_2E0: u,V3j: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Epatricia_2EPEEK_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EADD_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) @ ( s @ A_27a @ V2d_2E0 ) ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3j ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F0 @ V1k @ V3j ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V2d_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Epatricia_2EPEEK_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3j ) ) ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EBRANCH,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V2l_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V2l_2E0 ) ) ) )
<=> ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V2l_2E0 )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) ) )
=> ! [V0p: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum,V2l_2E0: u,V3r_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBRANCH_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0p ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1m ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V2l_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V3r_2E0 ) ) ) ) ) ) ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V2l_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V3r_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V3r_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V2l_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0p ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1m ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V2l_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V3r_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EPEEK__REMOVE,axiom,
! [A_27a: d,F0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ! [V1k: mono_2Etyop_2Enum_2Enum,V2j: mono_2Etyop_2Enum_2Enum] :
( ( F0 @ V1k @ V2j )
<=> ( V1k = V2j ) )
=> ! [V0t_2E0: u,V1k: mono_2Etyop_2Enum_2Enum,V2j: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Epatricia_2EPEEK_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EREMOVE_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2j ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F0 @ V1k @ V2j ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Epatricia_2EPEEK_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2j ) ) ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EEVERY__LEAF__TRANSFORM,axiom,
! [A_27a: d,A_27b: d,V0P_2E0: u,V1Q_2E0: u,V2f_2E0: u,V3t_2E0: u] :
( ( ! [V4k: mono_2Etyop_2Enum_2Enum,V5d_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4k ) ) ) ) @ ( s @ A_27a @ V5d_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V1Q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4k ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ A_27a @ V5d_2E0 ) ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EEVERY__LEAF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V3t_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EEVERY__LEAF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V1Q_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( c_2Epatricia_2ETRANSFORM_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V3t_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2ETRANSFORM__EMPTY,axiom,
! [A_27a: d,A_27b: d,V0f_2E0: u,V1t_2E0: u] :
( ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( c_2Epatricia_2ETRANSFORM_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V1t_2E0 ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ c_2Epatricia_2EEmpty_2E0 ) )
<=> ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V1t_2E0 )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) ) ) ).
thf(thm_2Epatricia_2ETRANSFORM__IS__PTREE,axiom,
! [A_27a: d,A_27b: d,V0f_2E0: u,V1t_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V1t_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( c_2Epatricia_2ETRANSFORM_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V1t_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EPEEK__TRANSFORM,axiom,
! [A_27a: d,A_27b: d,F0_2E0: u] :
( ! [V0f_2E0: u,V3x_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) ) ) )
=> ! [V0f_2E0: u,V1t_2E0: u,V2k: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Epatricia_2EPEEK_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( c_2Epatricia_2ETRANSFORM_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V1t_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Epatricia_2EPEEK_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V1t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EADD__TRANSFORM,axiom,
! [A_27a: d,A_27b: d,V0f_2E0: u,V1t_2E0: u,V2k: mono_2Etyop_2Enum_2Enum,V3d_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( c_2Epatricia_2ETRANSFORM_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EADD_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V1t_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) @ ( s @ A_27a @ V3d_2E0 ) ) ) ) ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( c_2Epatricia_2EADD_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( c_2Epatricia_2ETRANSFORM_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V1t_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V3d_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2ETRANSFORM__BRANCH,axiom,
! [A_27a: d,A_27b: d,V0f_2E0: u,V1p: mono_2Etyop_2Enum_2Enum,V2m: mono_2Etyop_2Enum_2Enum,V3l_2E0: u,V4r_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( c_2Epatricia_2ETRANSFORM_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBRANCH_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1p ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2m ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( tyop_2Epatricia_2Eptree @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V3l_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V4r_2E0 ) ) ) ) ) ) ) ) ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( c_2Epatricia_2EBRANCH_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1p ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2m ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( tyop_2Epatricia_2Eptree @ A_27b ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( c_2Epatricia_2ETRANSFORM_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V3l_2E0 ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( c_2Epatricia_2ETRANSFORM_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V4r_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EREMOVE__TRANSFORM,axiom,
! [A_27a: d,A_27b: d,V0f_2E0: u,V1t_2E0: u,V2k: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( c_2Epatricia_2ETRANSFORM_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EREMOVE_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V1t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) ) ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( c_2Epatricia_2EREMOVE_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( c_2Epatricia_2ETRANSFORM_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V1t_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) ) ) ) ).
thf(thm_2Epatricia_2EREMOVE__ADD__EQ,axiom,
! [A_27a: d,V0t_2E0: u,V1k: mono_2Etyop_2Enum_2Enum,V2d_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EREMOVE_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EADD_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) @ ( s @ A_27a @ V2d_2E0 ) ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EREMOVE_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) ) ) ) ).
thf(thm_2Epatricia_2EADD__ADD,axiom,
! [A_27a: d,V0t_2E0: u,V1k: mono_2Etyop_2Enum_2Enum,V2d_2E0: u,V3e_2E0: u] :
( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EADD_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EADD_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) @ ( s @ A_27a @ V2d_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) @ ( s @ A_27a @ V3e_2E0 ) ) ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EADD_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) @ ( s @ A_27a @ V3e_2E0 ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EEVERY__LEAF__PEEK,axiom,
! [A_27a: d,V0P_2E0: u,V1t_2E0: u,V2k: mono_2Etyop_2Enum_2Enum] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EEVERY__LEAF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V1t_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Epatricia_2EPEEK_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V1t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) ) ) @ ( s @ A_27a @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Epatricia_2EPEEK_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V1t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EIS__PTREE__PEEK,axiom,
! [A_27a: d,A_27b: d,A_27c: d] :
( ! [V0k: mono_2Etyop_2Enum_2Enum] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Epatricia_2EPEEK_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0k ) ) ) ) ) ) ) )
& ! [V1k: mono_2Etyop_2Enum_2Enum,V2j: mono_2Etyop_2Enum_2Enum,V3b_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Epatricia_2EPEEK_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2j ) ) @ ( s @ A_27b @ V3b_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) ) ) ) ) )
<=> ( V2j = V1k ) )
& ! [V4p: mono_2Etyop_2Enum_2Enum,V5m: mono_2Etyop_2Enum_2Enum,V6l_2E0: u,V7r_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27c ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4p ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5m ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27c ) @ V6l_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27c ) @ V7r_2E0 ) ) ) ) ) )
=> ( ? [V8k: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Ebit_2EBIT @ V5m @ V8k )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ ( c_2Epatricia_2EPEEK_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27c ) @ V6l_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8k ) ) ) ) ) ) ) )
& ? [V9k: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( mono_2Ec_2Ebit_2EBIT @ V5m @ V9k ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ ( c_2Epatricia_2EPEEK_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27c ) @ V7r_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V9k ) ) ) ) ) ) ) )
& ! [V10k: mono_2Etyop_2Enum_2Enum,V11n: mono_2Etyop_2Enum_2Enum] :
( ( ( (~) @ ( mono_2Ec_2Ebit_2EMOD__2EXP__EQ @ V5m @ V10k @ V4p ) )
| ( ( mono_2Ec_2Eprim__rec_2E_3C @ V11n @ V5m )
& ( (~)
@ ( ( mono_2Ec_2Ebit_2EBIT @ V11n @ V4p )
= ( mono_2Ec_2Ebit_2EBIT @ V11n @ V10k ) ) ) ) )
=> ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ ( c_2Epatricia_2EPEEK_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27c ) @ V6l_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V10k ) ) ) ) ) ) ) )
& ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ ( c_2Epatricia_2EPEEK_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27c ) @ V7r_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V10k ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EPTREE__EQ,axiom,
! [A_27a: d,V0t1_2E0: u,V1t2_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t1_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V1t2_2E0 ) ) ) ) )
=> ( ! [V2k: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Epatricia_2EPEEK_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Epatricia_2EPEEK_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V1t2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2k ) ) ) ) )
<=> ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t1_2E0 )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V1t2_2E0 ) ) ) ) ).
thf(thm_2Epatricia_2EREMOVE__REMOVE,axiom,
! [A_27a: d,V0t_2E0: u,V1k: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) )
=> ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EREMOVE_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EREMOVE_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EREMOVE_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EREMOVE__ADD,axiom,
! [A_27a: d,F0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ! [V1k: mono_2Etyop_2Enum_2Enum,V3j: mono_2Etyop_2Enum_2Enum] :
( ( F0 @ V1k @ V3j )
<=> ( V1k = V3j ) )
=> ! [V0t_2E0: u,V1k: mono_2Etyop_2Enum_2Enum,V2d_2E0: u,V3j: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) )
=> ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EREMOVE_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EADD_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) @ ( s @ A_27a @ V2d_2E0 ) ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3j ) ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F0 @ V1k @ V3j ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EREMOVE_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3j ) ) ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EADD_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EREMOVE_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3j ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) @ ( s @ A_27a @ V2d_2E0 ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EADD__ADD__SYM,axiom,
! [A_27a: d,V0t_2E0: u,V1k: mono_2Etyop_2Enum_2Enum,V2j: mono_2Etyop_2Enum_2Enum,V3d_2E0: u,V4e_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) )
& ( (~) @ ( V1k = V2j ) ) )
=> ( ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EADD_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EADD_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) @ ( s @ A_27a @ V3d_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2j ) ) @ ( s @ A_27a @ V4e_2E0 ) ) ) ) )
= ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EADD_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EADD_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2j ) ) @ ( s @ A_27a @ V4e_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) @ ( s @ A_27a @ V3d_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EFILTER__ALL,axiom,
! [A_27a: d,V0P_2E0: u,V1l_2E0: u] :
( ! [V2n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V2n @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ) )
=> ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ) ) ) ) )
<=> ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EFILTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) )
= ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) ).
thf(thm_2Epatricia_2ETRAVERSE__TRANSFORM,axiom,
! [A_27a: d,A_27b: d,V0f_2E0: u,V1t_2E0: u] :
( ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ ( c_2Epatricia_2ETRANSFORM_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V1t_2E0 ) ) ) ) ) )
= ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V1t_2E0 ) ) ) ) ) ).
thf(thm_2Epatricia_2EMEM__TRAVERSE__PEEK,axiom,
! [A_27a: d,V0t_2E0: u,V1k: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) )
=> ( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V1k @ ( mono_2Ec_2Elist_2ELIST__TO__SET_2Emono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Epatricia_2EPEEK_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EIN__NUMSET__OF__PTREE,axiom,
! [V0t: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ V0t )
=> ( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V1n @ ( mono_2Ec_2Epatricia_2ENUMSET__OF__PTREE @ V0t ) )
= ( mono_2Ec_2Epatricia_2EIN__PTREE @ V1n @ V0t ) ) ) ).
thf(thm_2Epatricia_2EADD__LIST__IS__PTREE,axiom,
! [A_27a: d,V0t_2E0: u,V1l_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EADD__LIST_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ V1l_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EADD__LIST__TO__EMPTY__IS__PTREE,axiom,
! [A_27a: d,V0l_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EADD__LIST_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ V0l_2E0 ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EPTREE__OF__NUMSET__IS__PTREE,axiom,
! [V0t: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1s: mono_2Etyop_2Enum_2Enum > $o] :
( ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ V0t )
=> ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ ( mono_2Ec_2Epatricia_2EPTREE__OF__NUMSET @ V0t @ V1s ) ) ) ).
thf(thm_2Epatricia_2EPTREE__OF__NUMSET__IS__PTREE__EMPTY,axiom,
! [V0s: mono_2Etyop_2Enum_2Enum > $o] : ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ ( mono_2Ec_2Epatricia_2EPTREE__OF__NUMSET @ mono_2Ec_2Epatricia_2EEmpty_2Emono_2Etyop_2Eone_2Eone @ V0s ) ) ).
thf(thm_2Epatricia_2ENOT__KEY__LEFT__AND__RIGHT,axiom,
! [A_27a: d,V0p: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum,V2l_2E0: u,V3r_2E0: u,V4k: mono_2Etyop_2Enum_2Enum,V5j: mono_2Etyop_2Enum_2Enum] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0p ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1m ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V2l_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V3r_2E0 ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Epatricia_2EPEEK_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V2l_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4k ) ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Epatricia_2EPEEK_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V3r_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5j ) ) ) ) ) ) ) )
=> ( (~) @ ( V4k = V5j ) ) ) ).
thf(thm_2Epatricia_2EALL__DISTINCT__TRAVERSE,axiom,
! [A_27a: d,V0t_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) )
=> ( mono_2Ec_2Elist_2EALL__DISTINCT_2Emono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EMEM__ALL__DISTINCT__IMP__PERM,axiom,
! [A_27a: d,V0l1_2E0: u,V1l2_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EALL__DISTINCT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l1_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EALL__DISTINCT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l2_2E0 ) ) ) )
& ! [V2x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l1_2E0 ) ) ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l2_2E0 ) ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esorting_2EPERM_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l2_2E0 ) ) ) ) ) ).
thf(thm_2Epatricia_2EMEM__TRAVERSE,axiom,
! [V0t: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1k: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ V0t )
=> ( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V1k @ ( mono_2Ec_2Elist_2ELIST__TO__SET_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Epatricia_2ETRAVERSE_2Emono_2Etyop_2Eone_2Eone @ V0t ) ) )
= ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V1k @ ( mono_2Ec_2Epatricia_2ENUMSET__OF__PTREE @ V0t ) ) ) ) ).
thf(thm_2Epatricia_2EINSERT__PTREE__IS__PTREE,axiom,
! [V0t: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1x: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ V0t )
=> ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ ( mono_2Ec_2Epatricia_2EINSERT__PTREE @ V1x @ V0t ) ) ) ).
thf(thm_2Epatricia_2EFINITE__NUMSET__OF__PTREE,axiom,
! [V0t: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] : ( mono_2Ec_2Epred__set_2EFINITE_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Epatricia_2ENUMSET__OF__PTREE @ V0t ) ) ).
thf(thm_2Epatricia_2EADD__INSERT,axiom,
! [V0v: mono_2Etyop_2Eone_2Eone,V1t: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V2n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Epatricia_2EADD_2Emono_2Etyop_2Eone_2Eone @ V1t @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eone_2Eone @ V2n @ V0v ) )
= ( mono_2Ec_2Epatricia_2EINSERT__PTREE @ V2n @ V1t ) ) ).
thf(thm_2Epatricia_2EPEEK__INSERT__PTREE,axiom,
! [F0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ! [V1k: mono_2Etyop_2Enum_2Enum,V2j: mono_2Etyop_2Enum_2Enum] :
( ( F0 @ V1k @ V2j )
<=> ( V1k = V2j ) )
=> ! [V0t: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1k: mono_2Etyop_2Enum_2Enum,V2j: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ V0t )
=> ( ( mono_2Ec_2Epatricia_2EPEEK_2Emono_2Etyop_2Eone_2Eone @ ( mono_2Ec_2Epatricia_2EINSERT__PTREE @ V1k @ V0t ) @ V2j )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29 @ ( F0 @ V1k @ V2j ) @ ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Eone_2Eone @ mono_2Ec_2Eone_2Eone ) @ ( mono_2Ec_2Epatricia_2EPEEK_2Emono_2Etyop_2Eone_2Eone @ V0t @ V2j ) ) ) ) ) ).
thf(thm_2Epatricia_2EMEM__TRAVERSE__INSERT__PTREE,axiom,
! [V0t: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1x: mono_2Etyop_2Enum_2Enum,V2h: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ V0t )
=> ( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V1x @ ( mono_2Ec_2Elist_2ELIST__TO__SET_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Epatricia_2ETRAVERSE_2Emono_2Etyop_2Eone_2Eone @ ( mono_2Ec_2Epatricia_2EINSERT__PTREE @ V2h @ V0t ) ) ) )
<=> ( ( V1x = V2h )
| ( ( (~) @ ( V1x = V2h ) )
& ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V1x @ ( mono_2Ec_2Elist_2ELIST__TO__SET_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Epatricia_2ETRAVERSE_2Emono_2Etyop_2Eone_2Eone @ V0t ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EPERM__INSERT__PTREE,axiom,
! [V0t: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1s: mono_2Etyop_2Enum_2Enum > $o] :
( ( mono_2Ec_2Epred__set_2EFINITE_2Emono_2Etyop_2Enum_2Enum @ V1s )
=> ( ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ V0t )
=> ( mono_2Ec_2Esorting_2EPERM_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Epatricia_2ETRAVERSE_2Emono_2Etyop_2Eone_2Eone @ ( mono_2Ec_2Elist_2EFOLDL_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ ( mono_2Ec_2Ecombin_2EC_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29 @ mono_2Ec_2Epatricia_2EINSERT__PTREE ) @ V0t @ ( mono_2Ec_2Elist_2ESET__TO__LIST_2Emono_2Etyop_2Enum_2Enum @ V1s ) ) ) @ ( mono_2Ec_2Elist_2ESET__TO__LIST_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Epatricia_2ENUMSET__OF__PTREE @ V0t ) @ V1s ) ) ) ) ) ).
thf(thm_2Epatricia_2EIN__PTREE__OF__NUMSET,axiom,
! [V0t: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1s: mono_2Etyop_2Enum_2Enum > $o,V2n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ V0t )
& ( mono_2Ec_2Epred__set_2EFINITE_2Emono_2Etyop_2Enum_2Enum @ V1s ) )
=> ( ( mono_2Ec_2Epatricia_2EIN__PTREE @ V2n @ ( mono_2Ec_2Epatricia_2EPTREE__OF__NUMSET @ V0t @ V1s ) )
<=> ( ( mono_2Ec_2Epatricia_2EIN__PTREE @ V2n @ V0t )
| ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V2n @ V1s ) ) ) ) ).
thf(thm_2Epatricia_2EIN__PTREE__EMPTY,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] : ( (~) @ ( mono_2Ec_2Epatricia_2EIN__PTREE @ V0n @ mono_2Ec_2Epatricia_2EEmpty_2Emono_2Etyop_2Eone_2Eone ) ) ).
thf(thm_2Epatricia_2EIN__PTREE__OF__NUMSET__EMPTY,axiom,
! [V0s: mono_2Etyop_2Enum_2Enum > $o,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Epred__set_2EFINITE_2Emono_2Etyop_2Enum_2Enum @ V0s )
=> ( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V1n @ V0s )
= ( mono_2Ec_2Epatricia_2EIN__PTREE @ V1n @ ( mono_2Ec_2Epatricia_2EPTREE__OF__NUMSET @ mono_2Ec_2Epatricia_2EEmpty_2Emono_2Etyop_2Eone_2Eone @ V0s ) ) ) ) ).
thf(thm_2Epatricia_2EPTREE__EXTENSION,axiom,
! [V0t1: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1t2: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ V0t1 )
& ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ V1t2 ) )
=> ( ( V0t1 = V1t2 )
<=> ! [V2x: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Epatricia_2EIN__PTREE @ V2x @ V0t1 )
= ( mono_2Ec_2Epatricia_2EIN__PTREE @ V2x @ V1t2 ) ) ) ) ).
thf(thm_2Epatricia_2EPTREE__OF__NUMSET__NUMSET__OF__PTREE,axiom,
! [V0t: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1s: mono_2Etyop_2Enum_2Enum > $o] :
( ( ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ V0t )
& ( mono_2Ec_2Epred__set_2EFINITE_2Emono_2Etyop_2Enum_2Enum @ V1s ) )
=> ( ( mono_2Ec_2Epatricia_2EPTREE__OF__NUMSET @ mono_2Ec_2Epatricia_2EEmpty_2Emono_2Etyop_2Eone_2Eone @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Epatricia_2ENUMSET__OF__PTREE @ V0t ) @ V1s ) )
= ( mono_2Ec_2Epatricia_2EPTREE__OF__NUMSET @ V0t @ V1s ) ) ) ).
thf(thm_2Epatricia_2ENUMSET__OF__PTREE__PTREE__OF__NUMSET,axiom,
! [V0t: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1s: mono_2Etyop_2Enum_2Enum > $o] :
( ( ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ V0t )
& ( mono_2Ec_2Epred__set_2EFINITE_2Emono_2Etyop_2Enum_2Enum @ V1s ) )
=> ( ( mono_2Ec_2Epatricia_2ENUMSET__OF__PTREE @ ( mono_2Ec_2Epatricia_2EPTREE__OF__NUMSET @ V0t @ V1s ) )
= ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Epatricia_2ENUMSET__OF__PTREE @ V0t ) @ V1s ) ) ) ).
thf(thm_2Epatricia_2ENUMSET__OF__PTREE__EMPTY,axiom,
( ( mono_2Ec_2Epatricia_2ENUMSET__OF__PTREE @ mono_2Ec_2Epatricia_2EEmpty_2Emono_2Etyop_2Eone_2Eone )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Enum_2Enum ) ).
thf(thm_2Epatricia_2EPTREE__OF__NUMSET__EMPTY,axiom,
! [V0t: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( mono_2Ec_2Epatricia_2EPTREE__OF__NUMSET @ V0t @ mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Enum_2Enum )
= V0t ) ).
thf(thm_2Epatricia_2ENUMSET__OF__PTREE__PTREE__OF__NUMSET__EMPTY,axiom,
! [V0s: mono_2Etyop_2Enum_2Enum > $o] :
( ( mono_2Ec_2Epred__set_2EFINITE_2Emono_2Etyop_2Enum_2Enum @ V0s )
=> ( ( mono_2Ec_2Epatricia_2ENUMSET__OF__PTREE @ ( mono_2Ec_2Epatricia_2EPTREE__OF__NUMSET @ mono_2Ec_2Epatricia_2EEmpty_2Emono_2Etyop_2Eone_2Eone @ V0s ) )
= V0s ) ) ).
thf(thm_2Epatricia_2EIN__PTREE__INSERT__PTREE,axiom,
! [V0t: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1m: mono_2Etyop_2Enum_2Enum,V2n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ V0t )
=> ( ( mono_2Ec_2Epatricia_2EIN__PTREE @ V2n @ ( mono_2Ec_2Epatricia_2EINSERT__PTREE @ V1m @ V0t ) )
<=> ( ( V1m = V2n )
| ( mono_2Ec_2Epatricia_2EIN__PTREE @ V2n @ V0t ) ) ) ) ).
thf(thm_2Epatricia_2EIN__PTREE__REMOVE,axiom,
! [V0t: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1m: mono_2Etyop_2Enum_2Enum,V2n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ V0t )
=> ( ( mono_2Ec_2Epatricia_2EIN__PTREE @ V2n @ ( mono_2Ec_2Epatricia_2EREMOVE_2Emono_2Etyop_2Eone_2Eone @ V0t @ V1m ) )
<=> ( ( (~) @ ( V2n = V1m ) )
& ( mono_2Ec_2Epatricia_2EIN__PTREE @ V2n @ V0t ) ) ) ) ).
thf(thm_2Epatricia_2EIN__PTREE__UNION__PTREE,axiom,
! [V0t1: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1t2: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V2n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ V0t1 )
& ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ V1t2 ) )
=> ( ( mono_2Ec_2Epatricia_2EIN__PTREE @ V2n @ ( mono_2Ec_2Epatricia_2EUNION__PTREE @ V0t1 @ V1t2 ) )
<=> ( ( mono_2Ec_2Epatricia_2EIN__PTREE @ V2n @ V0t1 )
| ( mono_2Ec_2Epatricia_2EIN__PTREE @ V2n @ V1t2 ) ) ) ) ).
thf(thm_2Epatricia_2EUNION__PTREE__IS__PTREE,axiom,
! [V0t1: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1t2: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ V0t1 )
& ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ V1t2 ) )
=> ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ ( mono_2Ec_2Epatricia_2EUNION__PTREE @ V0t1 @ V1t2 ) ) ) ).
thf(thm_2Epatricia_2EUNION__PTREE__COMM,axiom,
! [V0t1: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1t2: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ V0t1 )
& ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ V1t2 ) )
=> ( ( mono_2Ec_2Epatricia_2EUNION__PTREE @ V0t1 @ V1t2 )
= ( mono_2Ec_2Epatricia_2EUNION__PTREE @ V1t2 @ V0t1 ) ) ) ).
thf(thm_2Epatricia_2EUNION__PTREE__COMM__EMPTY,axiom,
! [V0t: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ V0t )
=> ( ( mono_2Ec_2Epatricia_2EUNION__PTREE @ mono_2Ec_2Epatricia_2EEmpty_2Emono_2Etyop_2Eone_2Eone @ V0t )
= ( mono_2Ec_2Epatricia_2EUNION__PTREE @ V0t @ mono_2Ec_2Epatricia_2EEmpty_2Emono_2Etyop_2Eone_2Eone ) ) ) ).
thf(thm_2Epatricia_2EUNION__PTREE__EMPTY,axiom,
( ! [V0t: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( mono_2Ec_2Epatricia_2EUNION__PTREE @ V0t @ mono_2Ec_2Epatricia_2EEmpty_2Emono_2Etyop_2Eone_2Eone )
= V0t )
& ! [V1t: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ V1t )
=> ( ( mono_2Ec_2Epatricia_2EUNION__PTREE @ mono_2Ec_2Epatricia_2EEmpty_2Emono_2Etyop_2Eone_2Eone @ V1t )
= V1t ) ) ) ).
thf(thm_2Epatricia_2EUNION__PTREE__ASSOC,axiom,
! [V0t1: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1t2: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V2t3: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ V0t1 )
& ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ V1t2 )
& ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ V2t3 ) )
=> ( ( mono_2Ec_2Epatricia_2EUNION__PTREE @ V0t1 @ ( mono_2Ec_2Epatricia_2EUNION__PTREE @ V1t2 @ V2t3 ) )
= ( mono_2Ec_2Epatricia_2EUNION__PTREE @ ( mono_2Ec_2Epatricia_2EUNION__PTREE @ V0t1 @ V1t2 ) @ V2t3 ) ) ) ).
thf(thm_2Epatricia_2EPTREE__OF__NUMSET__UNION,axiom,
! [V0t: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1s1: mono_2Etyop_2Enum_2Enum > $o,V2s2: mono_2Etyop_2Enum_2Enum > $o] :
( ( ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ V0t )
& ( mono_2Ec_2Epred__set_2EFINITE_2Emono_2Etyop_2Enum_2Enum @ V1s1 )
& ( mono_2Ec_2Epred__set_2EFINITE_2Emono_2Etyop_2Enum_2Enum @ V2s2 ) )
=> ( ( mono_2Ec_2Epatricia_2EPTREE__OF__NUMSET @ V0t @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Enum_2Enum @ V1s1 @ V2s2 ) )
= ( mono_2Ec_2Epatricia_2EPTREE__OF__NUMSET @ ( mono_2Ec_2Epatricia_2EPTREE__OF__NUMSET @ V0t @ V1s1 ) @ V2s2 ) ) ) ).
thf(thm_2Epatricia_2EPTREE__OF__NUMSET__INSERT,axiom,
! [V0t: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1s: mono_2Etyop_2Enum_2Enum > $o,V2x: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ V0t )
& ( mono_2Ec_2Epred__set_2EFINITE_2Emono_2Etyop_2Enum_2Enum @ V1s ) )
=> ( ( mono_2Ec_2Epatricia_2EPTREE__OF__NUMSET @ V0t @ ( mono_2Ec_2Epred__set_2EINSERT_2Emono_2Etyop_2Enum_2Enum @ V2x @ V1s ) )
= ( mono_2Ec_2Epatricia_2EINSERT__PTREE @ V2x @ ( mono_2Ec_2Epatricia_2EPTREE__OF__NUMSET @ V0t @ V1s ) ) ) ) ).
thf(thm_2Epatricia_2EPTREE__OF__NUMSET__INSERT__EMPTY,axiom,
! [V0s: mono_2Etyop_2Enum_2Enum > $o,V1x: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Epred__set_2EFINITE_2Emono_2Etyop_2Enum_2Enum @ V0s )
=> ( ( mono_2Ec_2Epatricia_2EPTREE__OF__NUMSET @ mono_2Ec_2Epatricia_2EEmpty_2Emono_2Etyop_2Eone_2Eone @ ( mono_2Ec_2Epred__set_2EINSERT_2Emono_2Etyop_2Enum_2Enum @ V1x @ V0s ) )
= ( mono_2Ec_2Epatricia_2EINSERT__PTREE @ V1x @ ( mono_2Ec_2Epatricia_2EPTREE__OF__NUMSET @ mono_2Ec_2Epatricia_2EEmpty_2Emono_2Etyop_2Eone_2Eone @ V0s ) ) ) ) ).
thf(thm_2Epatricia_2EPTREE__OF__NUMSET__DELETE,axiom,
! [V0s: mono_2Etyop_2Enum_2Enum > $o,V1x: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Epred__set_2EFINITE_2Emono_2Etyop_2Enum_2Enum @ V0s )
=> ( ( mono_2Ec_2Epatricia_2EPTREE__OF__NUMSET @ mono_2Ec_2Epatricia_2EEmpty_2Emono_2Etyop_2Eone_2Eone @ ( mono_2Ec_2Epred__set_2EDELETE_2Emono_2Etyop_2Enum_2Enum @ V0s @ V1x ) )
= ( mono_2Ec_2Epatricia_2EREMOVE_2Emono_2Etyop_2Eone_2Eone @ ( mono_2Ec_2Epatricia_2EPTREE__OF__NUMSET @ mono_2Ec_2Epatricia_2EEmpty_2Emono_2Etyop_2Eone_2Eone @ V0s ) @ V1x ) ) ) ).
thf(thm_2Epatricia_2ETRAVERSE__AUX,axiom,
! [A_27a: d,V0t_2E0: u] :
( ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) )
= ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE__AUX_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ mono_2Ec_2Elist_2ENIL_2Emono_2Etyop_2Enum_2Enum ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EPTREE__TRAVERSE__EQ,axiom,
! [A_27a: d,A_27b: d,V0t1_2E0: u,V1t2_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t1_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ V1t2_2E0 ) ) ) ) )
=> ( ! [V2k: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V2k @ ( mono_2Ec_2Elist_2ELIST__TO__SET_2Emono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t1_2E0 ) ) ) ) ) )
= ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V2k @ ( mono_2Ec_2Elist_2ELIST__TO__SET_2Emono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ V1t2_2E0 ) ) ) ) ) ) )
<=> ( ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ V1t2_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EQSORT__MEM__EQ,axiom,
! [A_27a: d,V0l2_2E0: u,V1l1_2E0: u,V2R_2E0: u] :
( ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Esorting_2EQSORT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l1_2E0 ) ) )
= ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Esorting_2EQSORT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l2_2E0 ) ) ) )
=> ! [V3x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l1_2E0 ) ) ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l2_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EKEYS__PEEK,axiom,
! [A_27a: d,A_27b: d,V0t1_2E0: u,V1t2_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t1_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ V1t2_2E0 ) ) ) ) )
=> ( ( ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2EKEYS_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2EKEYS_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ V1t2_2E0 ) ) ) ) )
<=> ( ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27b ) @ V1t2_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EPERM__ADD,axiom,
! [A_27a: d,V0t_2E0: u,V1k: mono_2Etyop_2Enum_2Enum,V2d_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) )
& ( (~) @ ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V1k @ ( mono_2Ec_2Elist_2ELIST__TO__SET_2Emono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) ) ) ) ) )
=> ( mono_2Ec_2Esorting_2EPERM_2Emono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EADD_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) @ ( s @ A_27a @ V2d_2E0 ) ) ) ) ) ) ) ) @ ( mono_2Ec_2Elist_2ECONS_2Emono_2Etyop_2Enum_2Enum @ V1k @ ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EPERM__NOT__ADD,axiom,
! [A_27a: d,V0t_2E0: u,V1k: mono_2Etyop_2Enum_2Enum,V2d_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) )
& ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V1k @ ( mono_2Ec_2Elist_2ELIST__TO__SET_2Emono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EADD_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) @ ( s @ A_27a @ V2d_2E0 ) ) ) ) ) ) ) )
= ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EPERM__NOT__REMOVE,axiom,
! [A_27a: d,V0t_2E0: u,V1k: mono_2Etyop_2Enum_2Enum] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) )
& ( (~) @ ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V1k @ ( mono_2Ec_2Elist_2ELIST__TO__SET_2Emono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EREMOVE_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) ) ) ) ) )
= ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) ) ) ) ).
thf(thm_2Epatricia_2EPERM__DELETE__PTREE,axiom,
! [F0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ! [V1k: mono_2Etyop_2Enum_2Enum,V2x: mono_2Etyop_2Enum_2Enum] :
( ( F0 @ V1k @ V2x )
<=> ( (~) @ ( V2x = V1k ) ) )
=> ! [V0t: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1k: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ V0t )
& ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V1k @ ( mono_2Ec_2Elist_2ELIST__TO__SET_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Epatricia_2ETRAVERSE_2Emono_2Etyop_2Eone_2Eone @ V0t ) ) ) )
=> ( mono_2Ec_2Esorting_2EPERM_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Epatricia_2ETRAVERSE_2Emono_2Etyop_2Eone_2Eone @ ( mono_2Ec_2Epatricia_2EREMOVE_2Emono_2Etyop_2Eone_2Eone @ V0t @ V1k ) ) @ ( mono_2Ec_2Elist_2EFILTER_2Emono_2Etyop_2Enum_2Enum @ ( F0 @ V1k ) @ ( mono_2Ec_2Epatricia_2ETRAVERSE_2Emono_2Etyop_2Eone_2Eone @ V0t ) ) ) ) ) ).
thf(thm_2Epatricia_2EFILTER__NONE,axiom,
! [A_27a: d,V0P_2E0: u,V1l_2E0: u] :
( ! [V2n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V2n @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ) ) ) )
=> ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EFILTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) )
= ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ).
thf(thm_2Epatricia_2EPERM__REMOVE,axiom,
! [A_27a: d,F0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ! [V1k: mono_2Etyop_2Enum_2Enum,V2x: mono_2Etyop_2Enum_2Enum] :
( ( F0 @ V1k @ V2x )
<=> ( (~) @ ( V2x = V1k ) ) )
=> ! [V0t_2E0: u,V1k: mono_2Etyop_2Enum_2Enum] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) )
& ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V1k @ ( mono_2Ec_2Elist_2ELIST__TO__SET_2Emono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) ) ) ) )
=> ( mono_2Ec_2Esorting_2EPERM_2Emono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EREMOVE_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) ) ) ) ) ) @ ( mono_2Ec_2Elist_2EFILTER_2Emono_2Etyop_2Enum_2Enum @ ( F0 @ V1k ) @ ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2ESIZE__ADD,axiom,
! [A_27a: d,V0t_2E0: u,V1k: mono_2Etyop_2Enum_2Enum,V2d_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) )
=> ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epatricia_2ESIZE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EADD_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) @ ( s @ A_27a @ V2d_2E0 ) ) ) ) ) ) ) )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V1k @ ( mono_2Ec_2Elist_2ELIST__TO__SET_2Emono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) ) ) ) @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epatricia_2ESIZE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) ) @ ( mono_2Ec_2Earithmetic_2E_2B @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epatricia_2ESIZE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(thm_2Epatricia_2ESIZE__REMOVE,axiom,
! [A_27a: d,V0t_2E0: u,V1k: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epatricia_2EIS__PTREE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) )
=> ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epatricia_2ESIZE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EREMOVE_2E2 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k ) ) ) ) ) ) )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V1k @ ( mono_2Ec_2Elist_2ELIST__TO__SET_2Emono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Elist_2Elist @ tyop_2Enum_2Enum ) @ ( c_2Epatricia_2ETRAVERSE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) ) ) ) @ ( mono_2Ec_2Earithmetic_2E_2D @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epatricia_2ESIZE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epatricia_2ESIZE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V0t_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2ESIZE,axiom,
! [A_27a: d] :
( ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epatricia_2ESIZE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ c_2Epatricia_2EEmpty_2E0 ) ) ) )
= mono_2Ec_2Enum_2E0 )
& ! [V0k: mono_2Etyop_2Enum_2Enum,V1d_2E0: u] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epatricia_2ESIZE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2ELeaf_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0k ) ) @ ( s @ A_27a @ V1d_2E0 ) ) ) ) ) )
= ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) )
& ! [V2p: mono_2Etyop_2Enum_2Enum,V3m: mono_2Etyop_2Enum_2Enum,V4l_2E0: u,V5r_2E0: u] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epatricia_2ESIZE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ ( c_2Epatricia_2EBranch_2E4 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2p ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3m ) ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V4l_2E0 ) @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V5r_2E0 ) ) ) ) ) )
= ( mono_2Ec_2Earithmetic_2E_2B @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epatricia_2ESIZE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V4l_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epatricia_2ESIZE_2E1 @ ( s @ ( tyop_2Epatricia_2Eptree @ A_27a ) @ V5r_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epatricia_2ESIZE__PTREE__OF__NUMSET,axiom,
! [V0t: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29,V1s: mono_2Etyop_2Enum_2Enum > $o] :
( ( mono_2Ec_2Epred__set_2EFINITE_2Emono_2Etyop_2Enum_2Enum @ V1s )
=> ( ( ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ V0t )
& ( mono_2Ec_2Elist_2EALL__DISTINCT_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Elist_2EAPPEND_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Epatricia_2ETRAVERSE_2Emono_2Etyop_2Eone_2Eone @ V0t ) @ ( mono_2Ec_2Elist_2ESET__TO__LIST_2Emono_2Etyop_2Enum_2Enum @ V1s ) ) ) )
=> ( ( mono_2Ec_2Epatricia_2ESIZE_2Emono_2Etyop_2Eone_2Eone @ ( mono_2Ec_2Epatricia_2EPTREE__OF__NUMSET @ V0t @ V1s ) )
= ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Epatricia_2ESIZE_2Emono_2Etyop_2Eone_2Eone @ V0t ) @ ( mono_2Ec_2Epred__set_2ECARD_2Emono_2Etyop_2Enum_2Enum @ V1s ) ) ) ) ) ).
thf(thm_2Epatricia_2ESIZE__PTREE__OF__NUMSET__EMPTY,axiom,
! [V0s: mono_2Etyop_2Enum_2Enum > $o] :
( ( mono_2Ec_2Epred__set_2EFINITE_2Emono_2Etyop_2Enum_2Enum @ V0s )
=> ( ( mono_2Ec_2Epatricia_2ESIZE_2Emono_2Etyop_2Eone_2Eone @ ( mono_2Ec_2Epatricia_2EPTREE__OF__NUMSET @ mono_2Ec_2Epatricia_2EEmpty_2Emono_2Etyop_2Eone_2Eone @ V0s ) )
= ( mono_2Ec_2Epred__set_2ECARD_2Emono_2Etyop_2Enum_2Enum @ V0s ) ) ) ).
thf(thm_2Epatricia_2ECARD__LIST__TO__SET,axiom,
! [A_27a: d,V0ls_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EALL__DISTINCT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0ls_2E0 ) ) ) )
=> ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epred__set_2ECARD_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0ls_2E0 ) ) ) ) ) )
= ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0ls_2E0 ) ) ) ) ) ) ).
thf(thm_2Epatricia_2ECARD__NUMSET__OF__PTREE,axiom,
! [V0t: mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29] :
( ( mono_2Ec_2Epatricia_2EIS__PTREE_2Emono_2Etyop_2Eone_2Eone @ V0t )
=> ( ( mono_2Ec_2Epred__set_2ECARD_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Epatricia_2ENUMSET__OF__PTREE @ V0t ) )
= ( mono_2Ec_2Epatricia_2ESIZE_2Emono_2Etyop_2Eone_2Eone @ V0t ) ) ) ).
thf(thm_2Epatricia_2EDELETE__UNION,axiom,
! [A_27a: d,V0x_2E0: u,V1s1_2E0: u,V2s2_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2s2_2E0 ) ) ) @ ( s @ A_27a @ V0x_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s1_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2s2_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) ) ) ) ).
%------------------------------------------------------------------------------