ITP001 Axioms: ITP124^4.ax
%------------------------------------------------------------------------------
% File : ITP124^4 : 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 : nets.ax [Gau19]
% : HL4124^4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 269 ( 93 unt; 143 typ; 0 def)
% Number of atoms : 287 ( 113 equ; 6 cnn)
% Maximal formula atoms : 11 ( 1 avg)
% Number of connectives : 6165 ( 6 ~; 1 |; 33 &;6047 @)
% ( 17 <=>; 61 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 8 avg;6047 nst)
% Number of types : 8 ( 7 usr)
% Number of type conns : 258 ( 258 >; 0 *; 0 +; 0 <<)
% Number of symbols : 138 ( 136 usr; 43 con; 0-3 aty)
% Number of variables : 412 ( 0 ^ 395 !; 17 ?; 412 :)
% 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_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29,type,
mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29: $tType ).
thf(mono_2Etyop_2Enum_2Enum,type,
mono_2Etyop_2Enum_2Enum: $tType ).
thf(mono_2Etyop_2Erealax_2Ereal,type,
mono_2Etyop_2Erealax_2Ereal: $tType ).
thf(mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29,type,
mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29: $tType ).
thf(tyop_2Emetric_2Emetric,type,
tyop_2Emetric_2Emetric: 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_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: d > d > d ).
thf(tyop_2Erealax_2Ereal,type,
tyop_2Erealax_2Ereal: d ).
thf(tyop_2Etopology_2Etopology,type,
tyop_2Etopology_2Etopology: 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_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_2Ereal_2E_2F_2E0,type,
c_2Ereal_2E_2F_2E0: u ).
thf(c_2Ereal_2E_2F_2E2,type,
c_2Ereal_2E_2F_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_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_2Earithmetic_2E_3E_3D_2E0,type,
c_2Earithmetic_2E_3E_3D_2E0: u ).
thf(c_2Earithmetic_2E_3E_3D_2E2,type,
c_2Earithmetic_2E_3E_3D_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_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: u ).
thf(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: u ).
thf(c_2Epred__set_2EUNIV_2E0,type,
c_2Epred__set_2EUNIV_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_2Ereal_2Eabs_2E0,type,
c_2Ereal_2Eabs_2E0: u ).
thf(c_2Ereal_2Eabs_2E1,type,
c_2Ereal_2Eabs_2E1: du > u ).
thf(c_2Enets_2Ebounded_2E0,type,
c_2Enets_2Ebounded_2E0: u ).
thf(c_2Enets_2Ebounded_2E2,type,
c_2Enets_2Ebounded_2E2: du > du > u ).
thf(c_2Emetric_2Edist_2E0,type,
c_2Emetric_2Edist_2E0: u ).
thf(c_2Emetric_2Edist_2E2,type,
c_2Emetric_2Edist_2E2: du > du > u ).
thf(c_2Enets_2Edorder_2E0,type,
c_2Enets_2Edorder_2E0: u ).
thf(c_2Enets_2Edorder_2E1,type,
c_2Enets_2Edorder_2E1: du > u ).
thf(c_2Erealax_2Einv_2E0,type,
c_2Erealax_2Einv_2E0: u ).
thf(c_2Erealax_2Einv_2E1,type,
c_2Erealax_2Einv_2E1: du > u ).
thf(c_2Etopology_2Elimpt_2E0,type,
c_2Etopology_2Elimpt_2E0: u ).
thf(c_2Etopology_2Elimpt_2E3,type,
c_2Etopology_2Elimpt_2E3: du > du > du > u ).
thf(c_2Emetric_2Emr1_2E0,type,
c_2Emetric_2Emr1_2E0: u ).
thf(c_2Emetric_2Emtop_2E0,type,
c_2Emetric_2Emtop_2E0: u ).
thf(c_2Emetric_2Emtop_2E1,type,
c_2Emetric_2Emtop_2E1: du > u ).
thf(c_2Etopology_2Eneigh_2E0,type,
c_2Etopology_2Eneigh_2E0: u ).
thf(c_2Etopology_2Eneigh_2E2,type,
c_2Etopology_2Eneigh_2E2: du > du > u ).
thf(c_2Erealax_2Ereal__add_2E0,type,
c_2Erealax_2Ereal__add_2E0: u ).
thf(c_2Erealax_2Ereal__add_2E2,type,
c_2Erealax_2Ereal__add_2E2: du > du > u ).
thf(c_2Erealax_2Ereal__lt_2E0,type,
c_2Erealax_2Ereal__lt_2E0: u ).
thf(c_2Erealax_2Ereal__lt_2E2,type,
c_2Erealax_2Ereal__lt_2E2: du > du > u ).
thf(c_2Ereal_2Ereal__lte_2E0,type,
c_2Ereal_2Ereal__lte_2E0: u ).
thf(c_2Ereal_2Ereal__lte_2E2,type,
c_2Ereal_2Ereal__lte_2E2: du > du > u ).
thf(c_2Erealax_2Ereal__mul_2E0,type,
c_2Erealax_2Ereal__mul_2E0: u ).
thf(c_2Erealax_2Ereal__mul_2E2,type,
c_2Erealax_2Ereal__mul_2E2: du > du > u ).
thf(c_2Erealax_2Ereal__neg_2E0,type,
c_2Erealax_2Ereal__neg_2E0: u ).
thf(c_2Erealax_2Ereal__neg_2E1,type,
c_2Erealax_2Ereal__neg_2E1: du > u ).
thf(c_2Ereal_2Ereal__of__num_2E0,type,
c_2Ereal_2Ereal__of__num_2E0: u ).
thf(c_2Ereal_2Ereal__of__num_2E1,type,
c_2Ereal_2Ereal__of__num_2E1: du > u ).
thf(c_2Ereal_2Ereal__sub_2E0,type,
c_2Ereal_2Ereal__sub_2E0: u ).
thf(c_2Ereal_2Ereal__sub_2E2,type,
c_2Ereal_2Ereal__sub_2E2: du > du > u ).
thf(c_2Enets_2Etends_2E0,type,
c_2Enets_2Etends_2E0: u ).
thf(c_2Enets_2Etends_2E3,type,
c_2Enets_2Etends_2E3: du > du > du > u ).
thf(c_2Enets_2Etendsto_2E0,type,
c_2Enets_2Etendsto_2E0: u ).
thf(c_2Enets_2Etendsto_2E1,type,
c_2Enets_2Etendsto_2E1: du > u ).
thf(c_2Enets_2Etendsto_2E3,type,
c_2Enets_2Etendsto_2E3: du > 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_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Ebool: ( ( 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_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_20mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29,type,
mono_2Eapp_2Emono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_20mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 > mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 ) > mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 > mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_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_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_2Erealax_2Ereal,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Erealax_2Ereal: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ).
thf(mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Erealax_2Ereal > $o ) > mono_2Etyop_2Erealax_2Ereal > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o ) > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
thf(mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,type,
mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
thf(mono_2Ec_2Ereal_2E_2F,type,
mono_2Ec_2Ereal_2E_2F: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
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_2Emin_2E_3D_3D_3E,type,
mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(mono_2Ec_2Earithmetic_2E_3E_3D,type,
mono_2Ec_2Earithmetic_2E_3E_3D: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Ebool_2EF,type,
mono_2Ec_2Ebool_2EF: $o ).
thf(mono_2Ec_2Ebool_2ET,type,
mono_2Ec_2Ebool_2ET: $o ).
thf(mono_2Ec_2Ebool_2E_5C_2F,type,
mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(mono_2Ec_2Ereal_2Eabs,type,
mono_2Ec_2Ereal_2Eabs: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
thf(mono_2Ec_2Enets_2Edorder_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Enets_2Edorder_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > $o ).
thf(mono_2Ec_2Erealax_2Einv,type,
mono_2Ec_2Erealax_2Einv: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
thf(mono_2Ec_2Emetric_2Emr1,type,
mono_2Ec_2Emetric_2Emr1: mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 ).
thf(mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal,type,
mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 > mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 ).
thf(mono_2Ec_2Erealax_2Ereal__add,type,
mono_2Ec_2Erealax_2Ereal__add: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
thf(mono_2Ec_2Erealax_2Ereal__lt,type,
mono_2Ec_2Erealax_2Ereal__lt: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o ).
thf(mono_2Ec_2Ereal_2Ereal__lte,type,
mono_2Ec_2Ereal_2Ereal__lte: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o ).
thf(mono_2Ec_2Erealax_2Ereal__mul,type,
mono_2Ec_2Erealax_2Ereal__mul: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
thf(mono_2Ec_2Erealax_2Ereal__neg,type,
mono_2Ec_2Erealax_2Ereal__neg: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
thf(mono_2Ec_2Ereal_2Ereal__of__num,type,
mono_2Ec_2Ereal_2Ereal__of__num: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ).
thf(mono_2Ec_2Ereal_2Ereal__sub,type,
mono_2Ec_2Ereal_2Ereal__sub: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
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_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_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_2Ebool_29: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29_29: ( mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 > mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_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_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_2Erealax_2Ereal_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Erealax_2Ereal > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > u ).
thf(i_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29,type,
i_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29: mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 > u ).
thf(i_mono_2Etyop_2Enum_2Enum,type,
i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).
thf(i_mono_2Etyop_2Erealax_2Ereal,type,
i_mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal > u ).
thf(i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29,type,
i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29: mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_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_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_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_2Ebool_29: du > ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29_29: du > mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 > mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_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_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_2Erealax_2Ereal_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Erealax_2Ereal > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: du > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: du > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
thf(j_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29,type,
j_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29: du > mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 ).
thf(j_mono_2Etyop_2Enum_2Enum,type,
j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).
thf(j_mono_2Etyop_2Erealax_2Ereal,type,
j_mono_2Etyop_2Erealax_2Ereal: du > mono_2Etyop_2Erealax_2Ereal ).
thf(j_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29,type,
j_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29: du > mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_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_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_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_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_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_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( 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_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) ) @ 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_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_2Erealax_2Ereal_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 @ ( j_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ 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_2Erealax_2Ereal,axiom,
! [V0_2E0: u] :
( ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ V0_2E0 ) ) ) )
= ( s @ tyop_2Erealax_2Ereal @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( j_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ 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_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( 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_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29_29,axiom,
! [V0: mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 > mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_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_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_2Erealax_2Ereal_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29,axiom,
! [V0: mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29] :
( ( j_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_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_2Erealax_2Ereal,axiom,
! [V0: mono_2Etyop_2Erealax_2Ereal] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29,axiom,
! [V0: mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29] :
( ( j_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_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_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27b @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ A_27a ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emetric_2Emetric_28A_27a_29_20mono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A_27a ) @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A_27a ) @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A_27a ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A_27a ) @ A_27a ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emetric_2Emetric @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emetric_2Emetric_28A_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emetric_2Emetric @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [A_27a: d,X0: mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 @ X0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( 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_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 @ X0 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Etopology_2Etopology_28A_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Etopology_2Etopology @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Etopology_2Etopology_28A_27a_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [A_27a: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ A_27a ) @ X0_2E0 ) @ ( 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 @ X1 ) ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( 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_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Etopology_2Etopology @ A_27a ) @ X0_2E0 ) ) ) @ ( 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 @ X1 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Etopology_2Etopology_28A_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27b ) @ ( 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_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etopology_2Etopology @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Etopology_2Etopology @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [A_27a: d,X0: mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ X0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( 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_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ X0 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ 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(arityeq2_2Ec_2Enets_2Ebounded_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Ebounded_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Enets_2Ebounded_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Enets_2Ebounded_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Ebounded_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ tyop_2Emin_2Ebool ) ) @ c_2Enets_2Ebounded_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Emetric_2Edist_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Erealax_2Ereal ) ) @ c_2Emetric_2Edist_2E0 ) @ ( s @ ( tyop_2Emetric_2Emetric @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Emetric_2Edist_2E2_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) @ tyop_2Erealax_2Ereal ) ) @ c_2Emetric_2Edist_2E0 ) @ ( s @ ( tyop_2Emetric_2Emetric @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Enets_2Edorder_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Edorder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( 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_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ c_2Enets_2Edorder_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Enets_2Edorder_2E1_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Edorder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ c_2Enets_2Edorder_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq3_2Ec_2Etopology_2Elimpt_2E3_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etopology_2Elimpt_2E3 @ ( s @ ( tyop_2Etopology_2Etopology @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X2_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 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Etopology_2Elimpt_2E0 ) @ ( s @ ( tyop_2Etopology_2Etopology @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X2_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Emetric_2Emtop_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( c_2Emetric_2Emtop_2E1 @ ( s @ ( tyop_2Emetric_2Emetric @ A_27a ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ A_27a ) @ ( tyop_2Etopology_2Etopology @ A_27a ) ) @ c_2Emetric_2Emtop_2E0 ) @ ( s @ ( tyop_2Emetric_2Emetric @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Emetric_2Emtop_2E1_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Etopology_2Etopology @ A_27b ) @ ( c_2Emetric_2Emtop_2E1 @ ( s @ ( tyop_2Emetric_2Emetric @ A_27b ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Etopology_2Etopology @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ A_27b ) @ ( tyop_2Etopology_2Etopology @ A_27b ) ) @ c_2Emetric_2Emtop_2E0 ) @ ( s @ ( tyop_2Emetric_2Emetric @ A_27b ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Etopology_2Eneigh_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etopology_2Eneigh_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ A_27a ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Etopology_2Eneigh_2E0 ) @ ( s @ ( tyop_2Etopology_2Etopology @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ A_27a ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq3_2Ec_2Enets_2Etends_2E3_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ X2_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Enets_2Etends_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ X2_2E0 ) ) ) ) ) ).
thf(arityeq3_2Ec_2Enets_2Etends_2E3_2Emono_2Etyop_2Erealax_2Ereal_20mono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1: mono_2Etyop_2Erealax_2Ereal,X2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ X0_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ X1 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ X2_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Enets_2Etends_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ X1 ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ X2_2E0 ) ) ) ) ) ).
thf(arityeq3_2Ec_2Enets_2Etends_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ X2_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Enets_2Etends_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ X2_2E0 ) ) ) ) ) ).
thf(arityeq3_2Ec_2Enets_2Etends_2E3_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ X2_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Enets_2Etends_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ X2_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Enets_2Etendsto_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( c_2Enets_2Etendsto_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A_27a ) @ A_27a ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A_27a ) @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Enets_2Etendsto_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A_27a ) @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Enets_2Etendsto_2E3_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etendsto_2E3 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A_27a ) @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ A_27a @ X2_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 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A_27a ) @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Enets_2Etendsto_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A_27a ) @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_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_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Enum_2Enum > 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_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_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_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_20mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29,axiom,
! [V0: mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 > mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29] :
( ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_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_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_2Erealax_2Ereal,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Erealax_2Ereal > $o,V1: mono_2Etyop_2Erealax_2Ereal] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o,V1: mono_2Etyop_2Erealax_2Ereal] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,V1: mono_2Etyop_2Erealax_2Ereal] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,
! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,V1: mono_2Etyop_2Erealax_2Ereal] :
( ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ V0 ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Enets_2Edorder_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_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Enets_2Edorder_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_2Ebool ) @ c_2Enets_2Edorder_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Enets_2Edorder_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Enets_2Edorder_2Emono_2Etyop_2Enum_2Enum @ V0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Edorder_2E1 @ ( 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 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Emetric_2Emtop_2E0_2Emono_2Etyop_2Erealax_2Ereal,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29_29 @ mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) ) @ c_2Emetric_2Emtop_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Emetric_2Emtop_2E1_2Emono_2Etyop_2Erealax_2Ereal,axiom,
! [V0: mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29] :
( ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ V0 ) ) )
= ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( c_2Emetric_2Emtop_2E1 @ ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 @ V0 ) ) ) ) ) ).
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_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_20mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29,axiom,
! [V0: mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 > mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_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_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_2Erealax_2Ereal,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Erealax_2Ereal > $o,V1: mono_2Etyop_2Erealax_2Ereal] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o,V1: mono_2Etyop_2Erealax_2Ereal] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,V1: mono_2Etyop_2Erealax_2Ereal] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,
! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,V1: mono_2Etyop_2Erealax_2Ereal] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(thm_2Enets_2Edorder,axiom,
! [A_27a: d,V0g_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Edorder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) )
<=> ! [V1x_2E0: u,V2y_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 @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ A_27a @ V1x_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 ) ) @ V0g_2E0 ) @ ( s @ A_27a @ V2y_2E0 ) ) ) @ ( s @ A_27a @ V2y_2E0 ) ) ) ) )
=> ? [V3z_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 @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) @ ( s @ A_27a @ V3z_2E0 ) ) ) @ ( s @ A_27a @ V3z_2E0 ) ) ) )
& ! [V4w_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 @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) @ ( s @ A_27a @ V4w_2E0 ) ) ) @ ( s @ A_27a @ V3z_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 ) ) @ V0g_2E0 ) @ ( s @ A_27a @ V4w_2E0 ) ) ) @ ( s @ A_27a @ V1x_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 ) ) @ V0g_2E0 ) @ ( s @ A_27a @ V4w_2E0 ) ) ) @ ( s @ A_27a @ V2y_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Enets_2Etends,axiom,
! [A_27a: d,A_27b: d,V0s_2E0: u,V1l_2E0: u,V2top_2E0: u,V3g_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V0s_2E0 ) @ ( s @ A_27a @ V1l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ A_27a ) @ V2top_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V3g_2E0 ) ) ) ) ) )
<=> ! [V4N_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etopology_2Eneigh_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ A_27a ) @ V2top_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V4N_2E0 ) @ ( s @ A_27a @ V1l_2E0 ) ) ) ) ) )
=> ? [V5n_2E0: u] :
( ( 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 @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V3g_2E0 ) @ ( s @ A_27b @ V5n_2E0 ) ) ) @ ( s @ A_27b @ V5n_2E0 ) ) ) )
& ! [V6m_2E0: u] :
( ( 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 @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V3g_2E0 ) @ ( s @ A_27b @ V6m_2E0 ) ) ) @ ( s @ A_27b @ V5n_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V4N_2E0 ) @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V0s_2E0 ) @ ( s @ A_27b @ V6m_2E0 ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Enets_2Ebounded,axiom,
! [A_27a: d,A_27b: d,V0m_2E0: u,V1g_2E0: u,V2f_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Ebounded_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A_27a ) @ V0m_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V1g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V2f_2E0 ) ) ) )
<=> ? [V3k: mono_2Etyop_2Erealax_2Ereal,V4x_2E0: u,V5N_2E0: u] :
( ( 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 @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V1g_2E0 ) @ ( s @ A_27b @ V5N_2E0 ) ) ) @ ( s @ A_27b @ V5N_2E0 ) ) ) )
& ! [V6n_2E0: u] :
( ( 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 @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V1g_2E0 ) @ ( s @ A_27b @ V6n_2E0 ) ) ) @ ( s @ A_27b @ V5N_2E0 ) ) ) )
=> ( mono_2Ec_2Erealax_2Ereal__lt @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A_27a ) @ V0m_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V2f_2E0 ) @ ( s @ A_27b @ V6n_2E0 ) ) ) @ ( s @ A_27a @ V4x_2E0 ) ) ) ) ) ) @ V3k ) ) ) ) ).
thf(thm_2Enets_2Etendsto,axiom,
! [A_27a: d,V0m_2E0: u,V1x_2E0: u,V2y_2E0: u,V3z_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etendsto_2E3 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A_27a ) @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A_27a ) @ V0m_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ A_27a @ V2y_2E0 ) @ ( s @ A_27a @ V3z_2E0 ) ) ) )
<=> ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A_27a ) @ V0m_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27a @ V2y_2E0 ) ) ) ) ) ) )
& ( mono_2Ec_2Ereal_2Ereal__lte @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A_27a ) @ V0m_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27a @ V2y_2E0 ) ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A_27a ) @ V0m_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27a @ V3z_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Enets_2EDORDER__LEMMA,axiom,
! [A_27a: d,V0g_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Edorder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) )
=> ! [V1P_2E0: u,V2Q_2E0: u] :
( ( ? [V3n_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 @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) @ ( s @ A_27a @ V3n_2E0 ) ) ) @ ( s @ A_27a @ V3n_2E0 ) ) ) )
& ! [V4m_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 @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) @ ( s @ A_27a @ V4m_2E0 ) ) ) @ ( s @ A_27a @ V3n_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) @ ( s @ A_27a @ V4m_2E0 ) ) ) ) ) )
& ? [V5n_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 @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) @ ( s @ A_27a @ V5n_2E0 ) ) ) @ ( s @ A_27a @ V5n_2E0 ) ) ) )
& ! [V6m_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 @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) @ ( s @ A_27a @ V6m_2E0 ) ) ) @ ( s @ A_27a @ V5n_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2Q_2E0 ) @ ( s @ A_27a @ V6m_2E0 ) ) ) ) ) ) )
=> ? [V7n_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 @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) @ ( s @ A_27a @ V7n_2E0 ) ) ) @ ( s @ A_27a @ V7n_2E0 ) ) ) )
& ! [V8m_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 @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) @ ( s @ A_27a @ V8m_2E0 ) ) ) @ ( s @ A_27a @ V7n_2E0 ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) @ ( s @ A_27a @ V8m_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2Q_2E0 ) @ ( s @ A_27a @ V8m_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Enets_2EDORDER__NGE,axiom,
mono_2Ec_2Enets_2Edorder_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Earithmetic_2E_3E_3D ).
thf(thm_2Enets_2EDORDER__TENDSTO,axiom,
! [A_27a: d,V0m_2E0: u,V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Edorder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( c_2Enets_2Etendsto_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A_27a ) @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A_27a ) @ V0m_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Enets_2EMTOP__TENDS,axiom,
! [A_27a: d,A_27b: d,V0d_2E0: u,V1g_2E0: u,V2x_2E0: u,V3x0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V2x_2E0 ) @ ( s @ A_27a @ V3x0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( c_2Emetric_2Emtop_2E1 @ ( s @ ( tyop_2Emetric_2Emetric @ A_27a ) @ V0d_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V1g_2E0 ) ) ) ) ) )
<=> ! [V4e: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ V4e )
=> ? [V5n_2E0: u] :
( ( 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 @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V1g_2E0 ) @ ( s @ A_27b @ V5n_2E0 ) ) ) @ ( s @ A_27b @ V5n_2E0 ) ) ) )
& ! [V6m_2E0: u] :
( ( 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 @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V1g_2E0 ) @ ( s @ A_27b @ V6m_2E0 ) ) ) @ ( s @ A_27b @ V5n_2E0 ) ) ) )
=> ( mono_2Ec_2Erealax_2Ereal__lt @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A_27a ) @ V0d_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V2x_2E0 ) @ ( s @ A_27b @ V6m_2E0 ) ) ) @ ( s @ A_27a @ V3x0_2E0 ) ) ) ) ) ) @ V4e ) ) ) ) ) ).
thf(thm_2Enets_2EMTOP__TENDS__UNIQ,axiom,
! [A_27a: d,A_27b: d,V0x1_2E0: u,V1x0_2E0: u,V2x_2E0: u,V3g_2E0: u,V4d_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Edorder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V3g_2E0 ) ) ) )
=> ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V2x_2E0 ) @ ( s @ A_27a @ V1x0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( c_2Emetric_2Emtop_2E1 @ ( s @ ( tyop_2Emetric_2Emetric @ A_27a ) @ V4d_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V3g_2E0 ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V2x_2E0 ) @ ( s @ A_27a @ V0x1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( c_2Emetric_2Emtop_2E1 @ ( s @ ( tyop_2Emetric_2Emetric @ A_27a ) @ V4d_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V3g_2E0 ) ) ) ) ) ) )
=> ( ( s @ A_27a @ V1x0_2E0 )
= ( s @ A_27a @ V0x1_2E0 ) ) ) ) ).
thf(thm_2Enets_2ESEQ__TENDS,axiom,
! [A_27a: d,V0d_2E0: u,V1x_2E0: u,V2x0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1x_2E0 ) @ ( s @ A_27a @ V2x0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( c_2Emetric_2Emtop_2E1 @ ( s @ ( tyop_2Emetric_2Emetric @ A_27a ) @ V0d_2E0 ) ) ) @ ( 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 @ mono_2Ec_2Earithmetic_2E_3E_3D ) ) ) ) ) ) )
<=> ! [V3e: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ V3e )
=> ? [V4N: mono_2Etyop_2Enum_2Enum] :
! [V5n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3E_3D @ V5n @ V4N )
=> ( mono_2Ec_2Erealax_2Ereal__lt @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A_27a ) @ V0d_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1x_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5n ) ) ) ) @ ( s @ A_27a @ V2x0_2E0 ) ) ) ) ) ) @ V3e ) ) ) ) ).
thf(thm_2Enets_2ELIM__TENDS,axiom,
! [A_27a: d,A_27b: d,V0m1_2E0: u,V1m2_2E0: u,V2f_2E0: u,V3x0_2E0: u,V4y0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etopology_2Elimpt_2E3 @ ( s @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( c_2Emetric_2Emtop_2E1 @ ( s @ ( tyop_2Emetric_2Emetric @ A_27a ) @ V0m1_2E0 ) ) ) @ ( s @ A_27a @ V3x0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ A_27b @ V4y0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ A_27b ) @ ( c_2Emetric_2Emtop_2E1 @ ( s @ ( tyop_2Emetric_2Emetric @ A_27b ) @ V1m2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( c_2Enets_2Etendsto_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A_27a ) @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A_27a ) @ V0m1_2E0 ) @ ( s @ A_27a @ V3x0_2E0 ) ) ) ) ) ) ) ) ) )
<=> ! [V5e: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ V5e )
=> ? [V6d: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ V6d )
& ! [V7x_2E0: u] :
( ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A_27a ) @ V0m1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V7x_2E0 ) @ ( s @ A_27a @ V3x0_2E0 ) ) ) ) ) ) )
& ( mono_2Ec_2Ereal_2Ereal__lte @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A_27a ) @ V0m1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V7x_2E0 ) @ ( s @ A_27a @ V3x0_2E0 ) ) ) ) ) ) @ V6d ) )
=> ( mono_2Ec_2Erealax_2Ereal__lt @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A_27b ) @ V1m2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ A_27a @ V7x_2E0 ) ) ) @ ( s @ A_27b @ V4y0_2E0 ) ) ) ) ) ) @ V5e ) ) ) ) ) ) ).
thf(thm_2Enets_2ELIM__TENDS2,axiom,
! [A_27a: d,A_27b: d,V0m1_2E0: u,V1m2_2E0: u,V2f_2E0: u,V3x0_2E0: u,V4y0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etopology_2Elimpt_2E3 @ ( s @ ( tyop_2Etopology_2Etopology @ A_27a ) @ ( c_2Emetric_2Emtop_2E1 @ ( s @ ( tyop_2Emetric_2Emetric @ A_27a ) @ V0m1_2E0 ) ) ) @ ( s @ A_27a @ V3x0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ A_27b @ V4y0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ A_27b ) @ ( c_2Emetric_2Emtop_2E1 @ ( s @ ( tyop_2Emetric_2Emetric @ A_27b ) @ V1m2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( c_2Enets_2Etendsto_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A_27a ) @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A_27a ) @ V0m1_2E0 ) @ ( s @ A_27a @ V3x0_2E0 ) ) ) ) ) ) ) ) ) )
<=> ! [V5e: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ V5e )
=> ? [V6d: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ V6d )
& ! [V7x_2E0: u] :
( ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A_27a ) @ V0m1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V7x_2E0 ) @ ( s @ A_27a @ V3x0_2E0 ) ) ) ) ) ) )
& ( mono_2Ec_2Erealax_2Ereal__lt @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A_27a ) @ V0m1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V7x_2E0 ) @ ( s @ A_27a @ V3x0_2E0 ) ) ) ) ) ) @ V6d ) )
=> ( mono_2Ec_2Erealax_2Ereal__lt @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A_27b ) @ V1m2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ A_27a @ V7x_2E0 ) ) ) @ ( s @ A_27b @ V4y0_2E0 ) ) ) ) ) ) @ V5e ) ) ) ) ) ) ).
thf(thm_2Enets_2EMR1__BOUNDED,axiom,
! [A_27a: d,V0g_2E0: u,V1f_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Ebounded_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 @ mono_2Ec_2Emetric_2Emr1 ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1f_2E0 ) ) ) )
<=> ? [V2k: mono_2Etyop_2Erealax_2Ereal,V3N_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 @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) @ ( s @ A_27a @ V3N_2E0 ) ) ) @ ( s @ A_27a @ V3N_2E0 ) ) ) )
& ! [V4n_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 @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) @ ( s @ A_27a @ V4n_2E0 ) ) ) @ ( s @ A_27a @ V3N_2E0 ) ) ) )
=> ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Eabs @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1f_2E0 ) @ ( s @ A_27a @ V4n_2E0 ) ) ) ) ) @ V2k ) ) ) ) ).
thf(thm_2Enets_2ENET__NULL,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V1x_2E0: u,V2x0: mono_2Etyop_2Erealax_2Ereal,V3n_2E0: u] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V2x0 ) ) ) ) @ ( s @ A_27a @ V3n_2E0 ) ) ) )
= ( mono_2Ec_2Ereal_2Ereal__sub @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) @ ( s @ A_27a @ V3n_2E0 ) ) ) ) @ V2x0 ) )
=> ! [V0g_2E0: u,V1x_2E0: u,V2x0: mono_2Etyop_2Erealax_2Ereal] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V2x0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V2x0 ) ) ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Enets_2ENET__CONV__BOUNDED,axiom,
! [A_27a: d,V0g_2E0: u,V1x_2E0: u,V2x0: mono_2Etyop_2Erealax_2Ereal] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V2x0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Ebounded_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 @ mono_2Ec_2Emetric_2Emr1 ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) ) ) ) ) ).
thf(thm_2Enets_2ENET__CONV__NZ,axiom,
! [A_27a: d,V0g_2E0: u,V1x_2E0: u,V2x0: mono_2Etyop_2Erealax_2Ereal] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V2x0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) )
& ( (~)
@ ( V2x0
= ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ) )
=> ? [V3N_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 @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) @ ( s @ A_27a @ V3N_2E0 ) ) ) @ ( s @ A_27a @ V3N_2E0 ) ) ) )
& ! [V4n_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 @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) @ ( s @ A_27a @ V4n_2E0 ) ) ) @ ( s @ A_27a @ V3N_2E0 ) ) ) )
=> ( (~)
@ ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) @ ( s @ A_27a @ V4n_2E0 ) ) ) )
= ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) ).
thf(thm_2Enets_2ENET__CONV__IBOUNDED,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V1x_2E0: u,V3n_2E0: u] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) ) ) @ ( s @ A_27a @ V3n_2E0 ) ) ) )
= ( mono_2Ec_2Erealax_2Einv @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) @ ( s @ A_27a @ V3n_2E0 ) ) ) ) ) )
=> ! [V0g_2E0: u,V1x_2E0: u,V2x0: mono_2Etyop_2Erealax_2Ereal] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V2x0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) )
& ( (~)
@ ( V2x0
= ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Ebounded_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 @ mono_2Ec_2Emetric_2Emr1 ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Enets_2ENET__NULL__ADD,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V1x_2E0: u,V2y_2E0: u,V3n_2E0: u] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V2y_2E0 ) ) ) @ ( s @ A_27a @ V3n_2E0 ) ) ) )
= ( mono_2Ec_2Erealax_2Ereal__add @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) @ ( s @ A_27a @ V3n_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V2y_2E0 ) @ ( s @ A_27a @ V3n_2E0 ) ) ) ) ) )
=> ! [V0g_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Edorder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) )
=> ! [V1x_2E0: u,V2y_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V2y_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V2y_2E0 ) ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Enets_2ENET__NULL__MUL,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V1x_2E0: u,V2y_2E0: u,V3n_2E0: u] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V2y_2E0 ) ) ) @ ( s @ A_27a @ V3n_2E0 ) ) ) )
= ( mono_2Ec_2Erealax_2Ereal__mul @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) @ ( s @ A_27a @ V3n_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V2y_2E0 ) @ ( s @ A_27a @ V3n_2E0 ) ) ) ) ) )
=> ! [V0g_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Edorder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) )
=> ! [V1x_2E0: u,V2y_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Ebounded_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 @ mono_2Ec_2Emetric_2Emr1 ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V2y_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V2y_2E0 ) ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Enets_2ENET__NULL__CMUL,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V1k: mono_2Etyop_2Erealax_2Ereal,V2x_2E0: u,V3n_2E0: u] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V1k ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V2x_2E0 ) ) ) @ ( s @ A_27a @ V3n_2E0 ) ) ) )
= ( mono_2Ec_2Erealax_2Ereal__mul @ V1k @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V2x_2E0 ) @ ( s @ A_27a @ V3n_2E0 ) ) ) ) ) )
=> ! [V0g_2E0: u,V1k: mono_2Etyop_2Erealax_2Ereal,V2x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V2x_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V1k ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V2x_2E0 ) ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Enets_2ENET__ADD,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V1x_2E0: u,V3y_2E0: u,V5n_2E0: u] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V3y_2E0 ) ) ) @ ( s @ A_27a @ V5n_2E0 ) ) ) )
= ( mono_2Ec_2Erealax_2Ereal__add @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) @ ( s @ A_27a @ V5n_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V3y_2E0 ) @ ( s @ A_27a @ V5n_2E0 ) ) ) ) ) )
=> ! [V0g_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Edorder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) )
=> ! [V1x_2E0: u,V2x0: mono_2Etyop_2Erealax_2Ereal,V3y_2E0: u,V4y0: mono_2Etyop_2Erealax_2Ereal] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V2x0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V3y_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V4y0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V3y_2E0 ) ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Erealax_2Ereal__add @ V2x0 @ V4y0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Enets_2ENET__NEG,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V1x_2E0: u,V3n_2E0: u] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) ) ) @ ( s @ A_27a @ V3n_2E0 ) ) ) )
= ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) @ ( s @ A_27a @ V3n_2E0 ) ) ) ) ) )
=> ! [V0g_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Edorder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) )
=> ! [V1x_2E0: u,V2x0: mono_2Etyop_2Erealax_2Ereal] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V2x0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Erealax_2Ereal__neg @ V2x0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Enets_2ENET__SUB,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V1x_2E0: u,V3y_2E0: u,V5n_2E0: u] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V3y_2E0 ) ) ) @ ( s @ A_27a @ V5n_2E0 ) ) ) )
= ( mono_2Ec_2Ereal_2Ereal__sub @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) @ ( s @ A_27a @ V5n_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V3y_2E0 ) @ ( s @ A_27a @ V5n_2E0 ) ) ) ) ) )
=> ! [V0g_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Edorder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) )
=> ! [V1x_2E0: u,V2x0: mono_2Etyop_2Erealax_2Ereal,V3y_2E0: u,V4y0: mono_2Etyop_2Erealax_2Ereal] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V2x0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V3y_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V4y0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V3y_2E0 ) ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal_2Ereal__sub @ V2x0 @ V4y0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Enets_2ENET__MUL,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V1x_2E0: u,V2y_2E0: u,V5n_2E0: u] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V2y_2E0 ) ) ) @ ( s @ A_27a @ V5n_2E0 ) ) ) )
= ( mono_2Ec_2Erealax_2Ereal__mul @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) @ ( s @ A_27a @ V5n_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V2y_2E0 ) @ ( s @ A_27a @ V5n_2E0 ) ) ) ) ) )
=> ! [V0g_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Edorder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) )
=> ! [V1x_2E0: u,V2y_2E0: u,V3x0: mono_2Etyop_2Erealax_2Ereal,V4y0: mono_2Etyop_2Erealax_2Ereal] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V3x0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V2y_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V4y0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V2y_2E0 ) ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Erealax_2Ereal__mul @ V3x0 @ V4y0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Enets_2ENET__INV,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V1x_2E0: u,V3n_2E0: u] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) ) ) @ ( s @ A_27a @ V3n_2E0 ) ) ) )
= ( mono_2Ec_2Erealax_2Einv @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) @ ( s @ A_27a @ V3n_2E0 ) ) ) ) ) )
=> ! [V0g_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Edorder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) )
=> ! [V1x_2E0: u,V2x0: mono_2Etyop_2Erealax_2Ereal] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V2x0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) )
& ( (~)
@ ( V2x0
= ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Erealax_2Einv @ V2x0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Enets_2ENET__DIV,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V1x_2E0: u,V3y_2E0: u,V5n_2E0: u] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V3y_2E0 ) ) ) @ ( s @ A_27a @ V5n_2E0 ) ) ) )
= ( mono_2Ec_2Ereal_2E_2F @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) @ ( s @ A_27a @ V5n_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V3y_2E0 ) @ ( s @ A_27a @ V5n_2E0 ) ) ) ) ) )
=> ! [V0g_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Edorder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) )
=> ! [V1x_2E0: u,V2x0: mono_2Etyop_2Erealax_2Ereal,V3y_2E0: u,V4y0: mono_2Etyop_2Erealax_2Ereal] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V2x0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V3y_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V4y0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) )
& ( (~)
@ ( V4y0
= ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V3y_2E0 ) ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal_2E_2F @ V2x0 @ V4y0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Enets_2ENET__ABS,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V1x_2E0: u,V3n_2E0: u] :
( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) ) ) @ ( s @ A_27a @ V3n_2E0 ) ) ) )
= ( mono_2Ec_2Ereal_2Eabs @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) @ ( s @ A_27a @ V3n_2E0 ) ) ) ) ) )
=> ! [V0g_2E0: u,V1x_2E0: u,V2x0: mono_2Etyop_2Erealax_2Ereal] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V2x0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal_2Eabs @ V2x0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Enets_2ENET__LE,axiom,
! [A_27a: d,V0g_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Edorder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) )
=> ! [V1x_2E0: u,V2x0: mono_2Etyop_2Erealax_2Ereal,V3y_2E0: u,V4y0: mono_2Etyop_2Erealax_2Ereal] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V2x0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etends_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V3y_2E0 ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V4y0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Etopology_2Etopology @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emtop_2Emono_2Etyop_2Erealax_2Ereal @ mono_2Ec_2Emetric_2Emr1 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) ) ) ) ) )
& ? [V5N_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 @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) @ ( s @ A_27a @ V5N_2E0 ) ) ) @ ( s @ A_27a @ V5N_2E0 ) ) ) )
& ! [V6n_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 @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0g_2E0 ) @ ( s @ A_27a @ V6n_2E0 ) ) ) @ ( s @ A_27a @ V5N_2E0 ) ) ) )
=> ( mono_2Ec_2Ereal_2Ereal__lte @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V1x_2E0 ) @ ( s @ A_27a @ V6n_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Erealax_2Ereal ) @ V3y_2E0 ) @ ( s @ A_27a @ V6n_2E0 ) ) ) ) ) ) ) )
=> ( mono_2Ec_2Ereal_2Ereal__lte @ V2x0 @ V4y0 ) ) ) ).
%------------------------------------------------------------------------------