TPTP Problem File: ITP025_1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ITP025_1 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Problem : HOL4 syntactic export of thm_2Elebesgue_2Epos__fn__integral__cmul.p, bushy 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 : thm_2Elebesgue_2Epos__fn__integral__cmul.p [Gau19]
% : HL412001_1.p [TPAP]
% Status : Theorem
% Rating : 0.89 v8.2.0, 1.00 v7.5.0
% Syntax : Number of formulae : 399 ( 121 unt; 215 typ; 0 def)
% Number of atoms : 394 ( 166 equ)
% Maximal formula atoms : 15 ( 0 avg)
% Number of connectives : 259 ( 49 ~; 34 |; 56 &)
% ( 59 <=>; 61 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 16 ( 2 avg)
% Number of types : 28 ( 27 usr)
% Number of type conns : 175 ( 122 >; 53 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 187 ( 187 usr; 66 con; 0-3 aty)
% Number of variables : 398 ( 394 !; 4 ?; 398 :)
% SPC : TF0_THM_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Bugfixes in axioms and export.
%------------------------------------------------------------------------------
tff(u,type,
u: $tType ).
tff(d,type,
d: $tType ).
tff(du,type,
du: $tType ).
tff(mono_2Etyop_2Emin_2Ebool,type,
mono_2Etyop_2Emin_2Ebool: $tType ).
tff(mono_2Etyop_2Eextreal_2Eextreal,type,
mono_2Etyop_2Eextreal_2Eextreal: $tType ).
tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: $tType ).
tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: $tType ).
tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29: $tType ).
tff(mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29: $tType ).
tff(mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29: $tType ).
tff(mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_29,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_29: $tType ).
tff(mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29: $tType ).
tff(mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29: $tType ).
tff(mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: $tType ).
tff(mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29: $tType ).
tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: $tType ).
tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eextreal_2Eextreal_29,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eextreal_2Eextreal_29: $tType ).
tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29: $tType ).
tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eextreal_2Eextreal_29,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eextreal_2Eextreal_29: $tType ).
tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29: $tType ).
tff(mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: $tType ).
tff(mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Eextreal_2Eextreal_29,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Eextreal_2Eextreal_29: $tType ).
tff(mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29: $tType ).
tff(mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $tType ).
tff(mono_2Etyop_2Enum_2Enum,type,
mono_2Etyop_2Enum_2Enum: $tType ).
tff(mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29: $tType ).
tff(mono_2Etyop_2Erealax_2Ereal,type,
mono_2Etyop_2Erealax_2Ereal: $tType ).
tff(tyop_2Eextreal_2Eextreal,type,
tyop_2Eextreal_2Eextreal: d ).
tff(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: d ).
tff(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: ( d * d ) > d ).
tff(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: d ).
tff(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: ( d * d ) > d ).
tff(tyop_2Erealax_2Ereal,type,
tyop_2Erealax_2Ereal: d ).
tff(s,type,
s: ( d * u ) > du ).
tff(app_2E2,type,
app_2E2: ( du * du ) > u ).
tff(p,type,
p: mono_2Etyop_2Emin_2Ebool > $o ).
tff(combin_i_2E0,type,
combin_i_2E0: u ).
tff(combin_k_2E0,type,
combin_k_2E0: u ).
tff(combin_s_2E0,type,
combin_s_2E0: u ).
tff(c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0: u ).
tff(c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1: du > u ).
tff(c_2Epair_2E_2C_2E0,type,
c_2Epair_2E_2C_2E0: u ).
tff(c_2Epair_2E_2C_2E2,type,
c_2Epair_2E_2C_2E2: ( du * du ) > u ).
tff(c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: u ).
tff(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: ( du * du ) > u ).
tff(c_2Enum_2E0_2E0,type,
c_2Enum_2E0_2E0: u ).
tff(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0: u ).
tff(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2: ( du * du ) > u ).
tff(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: u ).
tff(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: ( du * du ) > u ).
tff(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0: u ).
tff(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1: du > u ).
tff(c_2Ebool_2EBOUNDED_2E0,type,
c_2Ebool_2EBOUNDED_2E0: u ).
tff(c_2Ebool_2EBOUNDED_2E1,type,
c_2Ebool_2EBOUNDED_2E1: du > u ).
tff(c_2Ecombin_2EC_2E0,type,
c_2Ecombin_2EC_2E0: u ).
tff(c_2Ecombin_2EC_2E3,type,
c_2Ecombin_2EC_2E3: ( du * du * du ) > u ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: u ).
tff(c_2Epred__set_2EGSPEC_2E0,type,
c_2Epred__set_2EGSPEC_2E0: u ).
tff(c_2Epred__set_2EGSPEC_2E1,type,
c_2Epred__set_2EGSPEC_2E1: du > u ).
tff(c_2Ecombin_2EI_2E0,type,
c_2Ecombin_2EI_2E0: u ).
tff(c_2Ecombin_2EI_2E1,type,
c_2Ecombin_2EI_2E1: du > u ).
tff(c_2Ebool_2EIN_2E0,type,
c_2Ebool_2EIN_2E0: u ).
tff(c_2Ebool_2EIN_2E2,type,
c_2Ebool_2EIN_2E2: ( du * du ) > u ).
tff(c_2Eextreal_2ENegInf_2E0,type,
c_2Eextreal_2ENegInf_2E0: u ).
tff(c_2Eextreal_2ENormal_2E0,type,
c_2Eextreal_2ENormal_2E0: u ).
tff(c_2Eextreal_2ENormal_2E1,type,
c_2Eextreal_2ENormal_2E1: du > u ).
tff(c_2Eextreal_2EPosInf_2E0,type,
c_2Eextreal_2EPosInf_2E0: u ).
tff(c_2Ecombin_2ES_2E0,type,
c_2Ecombin_2ES_2E0: u ).
tff(c_2Ecombin_2ES_2E3,type,
c_2Ecombin_2ES_2E3: ( du * du * du ) > u ).
tff(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: u ).
tff(c_2Ebool_2E_5C_2F_2E0,type,
c_2Ebool_2E_5C_2F_2E0: u ).
tff(c_2Ebool_2E_5C_2F_2E2,type,
c_2Ebool_2E_5C_2F_2E2: ( du * du ) > u ).
tff(c_2Eextreal_2Eextreal__div_2E0,type,
c_2Eextreal_2Eextreal__div_2E0: u ).
tff(c_2Eextreal_2Eextreal__div_2E2,type,
c_2Eextreal_2Eextreal__div_2E2: ( du * du ) > u ).
tff(c_2Eextreal_2Eextreal__inv_2E0,type,
c_2Eextreal_2Eextreal__inv_2E0: u ).
tff(c_2Eextreal_2Eextreal__inv_2E1,type,
c_2Eextreal_2Eextreal__inv_2E1: du > u ).
tff(c_2Eextreal_2Eextreal__le_2E0,type,
c_2Eextreal_2Eextreal__le_2E0: u ).
tff(c_2Eextreal_2Eextreal__le_2E2,type,
c_2Eextreal_2Eextreal__le_2E2: ( du * du ) > u ).
tff(c_2Eextreal_2Eextreal__mul_2E0,type,
c_2Eextreal_2Eextreal__mul_2E0: u ).
tff(c_2Eextreal_2Eextreal__mul_2E2,type,
c_2Eextreal_2Eextreal__mul_2E2: ( du * du ) > u ).
tff(c_2Eextreal_2Eextreal__of__num_2E0,type,
c_2Eextreal_2Eextreal__of__num_2E0: u ).
tff(c_2Eextreal_2Eextreal__of__num_2E1,type,
c_2Eextreal_2Eextreal__of__num_2E1: du > u ).
tff(c_2Eextreal_2Eextreal__sup_2E0,type,
c_2Eextreal_2Eextreal__sup_2E0: u ).
tff(c_2Eextreal_2Eextreal__sup_2E1,type,
c_2Eextreal_2Eextreal__sup_2E1: du > u ).
tff(c_2Erealax_2Einv_2E0,type,
c_2Erealax_2Einv_2E0: u ).
tff(c_2Erealax_2Einv_2E1,type,
c_2Erealax_2Einv_2E1: du > u ).
tff(c_2Emeasure_2Em__space_2E0,type,
c_2Emeasure_2Em__space_2E0: u ).
tff(c_2Emeasure_2Em__space_2E1,type,
c_2Emeasure_2Em__space_2E1: du > u ).
tff(c_2Emeasure_2Emeasure__space_2E0,type,
c_2Emeasure_2Emeasure__space_2E0: u ).
tff(c_2Emeasure_2Emeasure__space_2E1,type,
c_2Emeasure_2Emeasure__space_2E1: du > u ).
tff(c_2Ecombin_2Eo_2E0,type,
c_2Ecombin_2Eo_2E0: u ).
tff(c_2Ecombin_2Eo_2E2,type,
c_2Ecombin_2Eo_2E2: ( du * du ) > u ).
tff(c_2Ecombin_2Eo_2E3,type,
c_2Ecombin_2Eo_2E3: ( du * du * du ) > u ).
tff(c_2Elebesgue_2Epos__fn__integral_2E0,type,
c_2Elebesgue_2Epos__fn__integral_2E0: u ).
tff(c_2Elebesgue_2Epos__fn__integral_2E2,type,
c_2Elebesgue_2Epos__fn__integral_2E2: ( du * du ) > u ).
tff(c_2Elebesgue_2Epsfis_2E0,type,
c_2Elebesgue_2Epsfis_2E0: u ).
tff(c_2Elebesgue_2Epsfis_2E2,type,
c_2Elebesgue_2Epsfis_2E2: ( du * du ) > u ).
tff(c_2Erealax_2Ereal__lt_2E0,type,
c_2Erealax_2Ereal__lt_2E0: u ).
tff(c_2Erealax_2Ereal__lt_2E2,type,
c_2Erealax_2Ereal__lt_2E2: ( du * du ) > u ).
tff(c_2Ereal_2Ereal__lte_2E0,type,
c_2Ereal_2Ereal__lte_2E0: u ).
tff(c_2Ereal_2Ereal__lte_2E2,type,
c_2Ereal_2Ereal__lte_2E2: ( du * du ) > u ).
tff(c_2Ereal_2Ereal__of__num_2E0,type,
c_2Ereal_2Ereal__of__num_2E0: u ).
tff(c_2Ereal_2Ereal__of__num_2E1,type,
c_2Ereal_2Ereal__of__num_2E1: du > u ).
tff(c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: u ).
tff(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: du > u ).
tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ).
tff(mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Eextreal_2Eextreal ) > mono_2Etyop_2Emin_2Ebool ).
tff(mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal: ( mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 * mono_2Etyop_2Eextreal_2Eextreal ) > mono_2Etyop_2Eextreal_2Eextreal ).
tff(mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_29 * mono_2Etyop_2Eextreal_2Eextreal ) > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 ).
tff(mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Eextreal_2Eextreal ) > mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ).
tff(mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 * mono_2Etyop_2Eextreal_2Eextreal ) > mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 ).
tff(mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Eextreal_2Eextreal ) > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 ).
tff(mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Eextreal_2Eextreal ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ).
tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Emin_2Ebool ).
tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Eextreal_2Eextreal,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Eextreal_2Eextreal: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eextreal_2Eextreal_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Eextreal_2Eextreal ).
tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ).
tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eextreal_2Eextreal,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eextreal_2Eextreal: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eextreal_2Eextreal_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Eextreal_2Eextreal ).
tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Erealax_2Ereal,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Erealax_2Ereal: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Erealax_2Ereal ).
tff(mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Emin_2Ebool ).
tff(mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Eextreal_2Eextreal,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Eextreal_2Eextreal: ( mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Eextreal_2Eextreal_29 * mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Eextreal_2Eextreal ).
tff(mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 ).
tff(mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal: ( mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 * mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Erealax_2Ereal ).
tff(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_29 ).
tff(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Eextreal_2Eextreal * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ).
tff(mono_2Ec_2Ebool_2E_2F_5C_2E0,type,
mono_2Ec_2Ebool_2E_2F_5C_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
tff(mono_2Ec_2Ebool_2E_2F_5C_2E2,type,
mono_2Ec_2Ebool_2E_2F_5C_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(mono_2Ec_2Enum_2E0_2E0,type,
mono_2Ec_2Enum_2E0_2E0: mono_2Etyop_2Enum_2Enum ).
tff(mono_2Ec_2Emin_2E_3D_3D_3E_2E0,type,
mono_2Ec_2Emin_2E_3D_3D_3E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
tff(mono_2Ec_2Emin_2E_3D_3D_3E_2E2,type,
mono_2Ec_2Emin_2E_3D_3D_3E_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(mono_2Ec_2Ebool_2EBOUNDED_2E0,type,
mono_2Ec_2Ebool_2EBOUNDED_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
tff(mono_2Ec_2Ebool_2EBOUNDED_2E1,type,
mono_2Ec_2Ebool_2EBOUNDED_2E1: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).
tff(mono_2Ec_2Ebool_2EF_2E0,type,
mono_2Ec_2Ebool_2EF_2E0: mono_2Etyop_2Emin_2Ebool ).
tff(mono_2Ec_2Epred__set_2EGSPEC_2E0_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal,type,
mono_2Ec_2Epred__set_2EGSPEC_2E0_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 ).
tff(mono_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal,type,
mono_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 > mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ).
tff(mono_2Ec_2Ebool_2EIN_2E0_2Emono_2Etyop_2Eextreal_2Eextreal,type,
mono_2Ec_2Ebool_2EIN_2E0_2Emono_2Etyop_2Eextreal_2Eextreal: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 ).
tff(mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Eextreal_2Eextreal,type,
mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Eextreal_2Eextreal: ( mono_2Etyop_2Eextreal_2Eextreal * mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Emin_2Ebool ).
tff(mono_2Ec_2Eextreal_2ENegInf_2E0,type,
mono_2Ec_2Eextreal_2ENegInf_2E0: mono_2Etyop_2Eextreal_2Eextreal ).
tff(mono_2Ec_2Eextreal_2ENormal_2E0,type,
mono_2Ec_2Eextreal_2ENormal_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Eextreal_2Eextreal_29 ).
tff(mono_2Ec_2Eextreal_2ENormal_2E1,type,
mono_2Ec_2Eextreal_2ENormal_2E1: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Eextreal_2Eextreal ).
tff(mono_2Ec_2Eextreal_2EPosInf_2E0,type,
mono_2Ec_2Eextreal_2EPosInf_2E0: mono_2Etyop_2Eextreal_2Eextreal ).
tff(mono_2Ec_2Ebool_2ET_2E0,type,
mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool ).
tff(mono_2Ec_2Ebool_2E_5C_2F_2E0,type,
mono_2Ec_2Ebool_2E_5C_2F_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
tff(mono_2Ec_2Ebool_2E_5C_2F_2E2,type,
mono_2Ec_2Ebool_2E_5C_2F_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).
tff(mono_2Ec_2Eextreal_2Eextreal__div_2E0,type,
mono_2Ec_2Eextreal_2Eextreal__div_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 ).
tff(mono_2Ec_2Eextreal_2Eextreal__div_2E2,type,
mono_2Ec_2Eextreal_2Eextreal__div_2E2: ( mono_2Etyop_2Eextreal_2Eextreal * mono_2Etyop_2Eextreal_2Eextreal ) > mono_2Etyop_2Eextreal_2Eextreal ).
tff(mono_2Ec_2Eextreal_2Eextreal__inv_2E0,type,
mono_2Ec_2Eextreal_2Eextreal__inv_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 ).
tff(mono_2Ec_2Eextreal_2Eextreal__inv_2E1,type,
mono_2Ec_2Eextreal_2Eextreal__inv_2E1: mono_2Etyop_2Eextreal_2Eextreal > mono_2Etyop_2Eextreal_2Eextreal ).
tff(mono_2Ec_2Eextreal_2Eextreal__le_2E0,type,
mono_2Ec_2Eextreal_2Eextreal__le_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 ).
tff(mono_2Ec_2Eextreal_2Eextreal__le_2E2,type,
mono_2Ec_2Eextreal_2Eextreal__le_2E2: ( mono_2Etyop_2Eextreal_2Eextreal * mono_2Etyop_2Eextreal_2Eextreal ) > mono_2Etyop_2Emin_2Ebool ).
tff(mono_2Ec_2Eextreal_2Eextreal__mul_2E0,type,
mono_2Ec_2Eextreal_2Eextreal__mul_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 ).
tff(mono_2Ec_2Eextreal_2Eextreal__mul_2E2,type,
mono_2Ec_2Eextreal_2Eextreal__mul_2E2: ( mono_2Etyop_2Eextreal_2Eextreal * mono_2Etyop_2Eextreal_2Eextreal ) > mono_2Etyop_2Eextreal_2Eextreal ).
tff(mono_2Ec_2Eextreal_2Eextreal__of__num_2E0,type,
mono_2Ec_2Eextreal_2Eextreal__of__num_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eextreal_2Eextreal_29 ).
tff(mono_2Ec_2Eextreal_2Eextreal__of__num_2E1,type,
mono_2Ec_2Eextreal_2Eextreal__of__num_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eextreal_2Eextreal ).
tff(mono_2Ec_2Eextreal_2Eextreal__sup_2E0,type,
mono_2Ec_2Eextreal_2Eextreal__sup_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eextreal_2Eextreal_29 ).
tff(mono_2Ec_2Eextreal_2Eextreal__sup_2E1,type,
mono_2Ec_2Eextreal_2Eextreal__sup_2E1: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 > mono_2Etyop_2Eextreal_2Eextreal ).
tff(mono_2Ec_2Erealax_2Einv_2E0,type,
mono_2Ec_2Erealax_2Einv_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
tff(mono_2Ec_2Erealax_2Einv_2E1,type,
mono_2Ec_2Erealax_2Einv_2E1: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
tff(mono_2Ec_2Erealax_2Ereal__lt_2E0,type,
mono_2Ec_2Erealax_2Ereal__lt_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 ).
tff(mono_2Ec_2Erealax_2Ereal__lt_2E2,type,
mono_2Ec_2Erealax_2Ereal__lt_2E2: ( mono_2Etyop_2Erealax_2Ereal * mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Emin_2Ebool ).
tff(mono_2Ec_2Ereal_2Ereal__lte_2E0,type,
mono_2Ec_2Ereal_2Ereal__lte_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 ).
tff(mono_2Ec_2Ereal_2Ereal__lte_2E2,type,
mono_2Ec_2Ereal_2Ereal__lte_2E2: ( mono_2Etyop_2Erealax_2Ereal * mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Emin_2Ebool ).
tff(mono_2Ec_2Ereal_2Ereal__of__num_2E0,type,
mono_2Ec_2Ereal_2Ereal__of__num_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29 ).
tff(mono_2Ec_2Ereal_2Ereal__of__num_2E1,type,
mono_2Ec_2Ereal_2Ereal__of__num_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ).
tff(mono_2Ec_2Ebool_2E_7E_2E0,type,
mono_2Ec_2Ebool_2E_7E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
tff(mono_2Ec_2Ebool_2E_7E_2E1,type,
mono_2Ec_2Ebool_2E_7E_2E1: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).
tff(i_mono_2Etyop_2Emin_2Ebool,type,
i_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool > u ).
tff(i_mono_2Etyop_2Eextreal_2Eextreal,type,
i_mono_2Etyop_2Eextreal_2Eextreal: mono_2Etyop_2Eextreal_2Eextreal > u ).
tff(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: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 > u ).
tff(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: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 > u ).
tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 > u ).
tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 > u ).
tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 > u ).
tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_29 > u ).
tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 > u ).
tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 > u ).
tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 > u ).
tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 > u ).
tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 > u ).
tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eextreal_2Eextreal_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eextreal_2Eextreal_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eextreal_2Eextreal_29 > u ).
tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 > u ).
tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eextreal_2Eextreal_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eextreal_2Eextreal_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eextreal_2Eextreal_29 > u ).
tff(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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29 > u ).
tff(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_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 > u ).
tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Eextreal_2Eextreal_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Eextreal_2Eextreal_29: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Eextreal_2Eextreal_29 > u ).
tff(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_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 > u ).
tff(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_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > u ).
tff(i_mono_2Etyop_2Enum_2Enum,type,
i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).
tff(i_mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 > u ).
tff(i_mono_2Etyop_2Erealax_2Ereal,type,
i_mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal > u ).
tff(j_mono_2Etyop_2Emin_2Ebool,type,
j_mono_2Etyop_2Emin_2Ebool: du > mono_2Etyop_2Emin_2Ebool ).
tff(j_mono_2Etyop_2Eextreal_2Eextreal,type,
j_mono_2Etyop_2Eextreal_2Eextreal: du > mono_2Etyop_2Eextreal_2Eextreal ).
tff(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 > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
tff(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 > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 ).
tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ).
tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29 ).
tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_29 ).
tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 ).
tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29 ).
tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 ).
tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 ).
tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 ).
tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eextreal_2Eextreal_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eextreal_2Eextreal_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eextreal_2Eextreal_29 ).
tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29 ).
tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eextreal_2Eextreal_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eextreal_2Eextreal_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eextreal_2Eextreal_29 ).
tff(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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29 ).
tff(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_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 ).
tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Eextreal_2Eextreal_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Eextreal_2Eextreal_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Eextreal_2Eextreal_29 ).
tff(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_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 ).
tff(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_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
tff(j_mono_2Etyop_2Enum_2Enum,type,
j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).
tff(j_mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29 ).
tff(j_mono_2Etyop_2Erealax_2Ereal,type,
j_mono_2Etyop_2Erealax_2Ereal: du > mono_2Etyop_2Erealax_2Ereal ).
tff(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) ) ) ).
tff(reserved_2Eho_2Eboolext,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
( ( p(V0_2E0)
<=> p(V1_2E0) )
=> ( V0_2E0 = V1_2E0 ) ) ).
tff(reserved_2Eho_2Etruth,axiom,
p(mono_2Ec_2Ebool_2ET_2E0) ).
tff(reserved_2Eho_2Enotfalse,axiom,
~ p(mono_2Ec_2Ebool_2EF_2E0) ).
tff(reserved_2Eho_2Ebool__cases__ax,axiom,
! [V0t_2E0: mono_2Etyop_2Emin_2Ebool] :
( ( V0t_2E0 = mono_2Ec_2Ebool_2ET_2E0 )
| ( V0t_2E0 = mono_2Ec_2Ebool_2EF_2E0 ) ) ).
tff(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) ).
tff(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) ).
tff(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))))) ).
tff(reserved_2Elogic_2E_2F_5C,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
( p(mono_2Ec_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
& p(V1_2E0) ) ) ).
tff(reserved_2Elogic_2E_5C_2F,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
( p(mono_2Ec_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
| p(V1_2E0) ) ) ).
tff(reserved_2Elogic_2E_7E,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Ebool] :
( p(mono_2Ec_2Ebool_2E_7E_2E1(V0_2E0))
<=> ~ p(V0_2E0) ) ).
tff(reserved_2Elogic_2E_3D_3D_3E,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
( p(mono_2Ec_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
=> p(V1_2E0) ) ) ).
tff(reserved_2Elogic_2E_3D,axiom,
! [A_27a: d,V0_2E0: u,V1_2E0: u] :
( p(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) ) ) ).
tff(reserved_2Equant_2E_21,axiom,
! [A_27a: d,V0f_2E0: u] :
( p(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] : p(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))))) ) ).
tff(reserved_2Equant_2E_3F,axiom,
! [A_27a: d,V0f_2E0: u] :
( p(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] : p(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))))) ) ).
tff(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) ).
tff(ij_2Emono_2Etyop_2Eextreal_2Eextreal,axiom,
! [V0_2E0: u] : s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(j_mono_2Etyop_2Eextreal_2Eextreal(s(tyop_2Eextreal_2Eextreal,V0_2E0)))) = s(tyop_2Eextreal_2Eextreal,V0_2E0) ).
tff(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) ).
tff(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) ).
tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] : s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),V0_2E0) ).
tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] : s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),V0_2E0) ).
tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29,axiom,
! [V0_2E0: u] : s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal),V0_2E0) ).
tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0_2E0: u] : s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_29(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),V0_2E0) ).
tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] : s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),V0_2E0) ).
tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29,axiom,
! [V0_2E0: u] : s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal)),V0_2E0) ).
tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] : s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),V0_2E0) ).
tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] : s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),V0_2E0) ).
tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0_2E0) ).
tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eextreal_2Eextreal_29,axiom,
! [V0_2E0: u] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eextreal_2Eextreal_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eextreal_2Eextreal_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal),V0_2E0) ).
tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),V0_2E0) ).
tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eextreal_2Eextreal_29,axiom,
! [V0_2E0: u] : s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eextreal_2Eextreal_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eextreal_2Eextreal_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal),V0_2E0) ).
tff(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) ).
tff(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) ).
tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Eextreal_2Eextreal_29,axiom,
! [V0_2E0: u] : s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Eextreal_2Eextreal),i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Eextreal_2Eextreal_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Eextreal_2Eextreal_29(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Eextreal_2Eextreal),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Eextreal_2Eextreal),V0_2E0) ).
tff(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) ).
tff(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) ).
tff(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) ).
tff(ij_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] : s(tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),i_mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29(j_mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29(s(tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),V0_2E0)))) = s(tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),V0_2E0) ).
tff(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) ).
tff(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Ebool] : j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V0_2E0))) = V0_2E0 ).
tff(ji_2Emono_2Etyop_2Eextreal_2Eextreal,axiom,
! [V0_2E0: mono_2Etyop_2Eextreal_2Eextreal] : j_mono_2Etyop_2Eextreal_2Eextreal(s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(V0_2E0))) = V0_2E0 ).
tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: 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),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(V0_2E0))) = V0_2E0 ).
tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: 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)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ).
tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29] : j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ).
tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29] : j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29(V0_2E0))) = V0_2E0 ).
tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29] : j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29(V0_2E0))) = V0_2E0 ).
tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_29] : j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_29(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_29(V0_2E0))) = V0_2E0 ).
tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29] : j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ).
tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29] : j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29(V0_2E0))) = V0_2E0 ).
tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29] : j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ).
tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29] : j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ).
tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29] : j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(V0_2E0))) = V0_2E0 ).
tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eextreal_2Eextreal_29,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eextreal_2Eextreal_29] : j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eextreal_2Eextreal_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eextreal_2Eextreal_29(V0_2E0))) = V0_2E0 ).
tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29] : j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ).
tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eextreal_2Eextreal_29,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eextreal_2Eextreal_29] : j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eextreal_2Eextreal_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eextreal_2Eextreal_29(V0_2E0))) = V0_2E0 ).
tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29,axiom,
! [V0_2E0: 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),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29(V0_2E0))) = V0_2E0 ).
tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: 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),i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(V0_2E0))) = V0_2E0 ).
tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Eextreal_2Eextreal_29,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Eextreal_2Eextreal_29] : j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Eextreal_2Eextreal_29(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Eextreal_2Eextreal),i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Eextreal_2Eextreal_29(V0_2E0))) = V0_2E0 ).
tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: 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)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ).
tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
! [V0_2E0: 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),i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29(V0_2E0))) = V0_2E0 ).
tff(ji_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0_2E0: mono_2Etyop_2Enum_2Enum] : j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0_2E0))) = V0_2E0 ).
tff(ji_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29] : j_mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29(s(tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),i_mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29(V0_2E0))) = V0_2E0 ).
tff(ji_2Emono_2Etyop_2Erealax_2Ereal,axiom,
! [V0_2E0: mono_2Etyop_2Erealax_2Ereal] : j_mono_2Etyop_2Erealax_2Ereal(s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(V0_2E0))) = V0_2E0 ).
tff(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)))) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Emin_2Ebool] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X1_2E0)))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X1_2E0)))) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: mono_2Etyop_2Eextreal_2Eextreal,X1_2E0: mono_2Etyop_2Emin_2Ebool] : mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool,X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Emin_2Ebool] :
( ( p(X0_2E0)
& p(X1_2E0) )
<=> p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).
tff(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) )
<=> p(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))))) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Emin_2Ebool] :
( ( p(X0_2E0)
=> p(X1_2E0) )
<=> p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).
tff(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)))) ).
tff(arityeq1_2Ec_2Ebool_2EBOUNDED_2E1,axiom,
! [X0_2E0: mono_2Etyop_2Emin_2Ebool] : mono_2Ec_2Ebool_2EBOUNDED_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EBOUNDED_2E0,X0_2E0) ).
tff(arityeq3_2Ec_2Ecombin_2EC_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : s(A_27c,c_2Ecombin_2EC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(A_27b,X1_2E0),s(A_27a,X2_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(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(A_27b,tyop_2Emin_2Efun(A_27a,A_27c))),c_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(A_27b,X1_2E0))),s(A_27a,X2_2E0))) ).
tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) ).
tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal,axiom,
! [X0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29] : mono_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Epred__set_2EGSPEC_2E0_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal,X0_2E0) ).
tff(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] : s(A_27a,c_2Ecombin_2EI_2E1(s(A_27a,X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EI_2E0),s(A_27a,X0_2E0))) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] : j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Eextreal_2Eextreal,axiom,
! [X0_2E0: mono_2Etyop_2Eextreal_2Eextreal,X1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29] : mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Eextreal_2Eextreal(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2EIN_2E0_2Emono_2Etyop_2Eextreal_2Eextreal,X0_2E0),X1_2E0) ).
tff(arityeq1_2Ec_2Eextreal_2ENormal_2E1,axiom,
! [X0_2E0: mono_2Etyop_2Erealax_2Ereal] : mono_2Ec_2Eextreal_2ENormal_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Eextreal_2Eextreal(mono_2Ec_2Eextreal_2ENormal_2E0,X0_2E0) ).
tff(arityeq3_2Ec_2Ecombin_2ES_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : s(A_27c,c_2Ecombin_2ES_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(A_27a,X2_2E0))) = 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))),c_2Ecombin_2ES_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(A_27a,X2_2E0))) ).
tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Emin_2Ebool] :
( ( p(X0_2E0)
| p(X1_2E0) )
<=> p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Eextreal_2Eextreal__div_2E2,axiom,
! [X0_2E0: mono_2Etyop_2Eextreal_2Eextreal,X1_2E0: mono_2Etyop_2Eextreal_2Eextreal] : mono_2Ec_2Eextreal_2Eextreal__div_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal(mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29(mono_2Ec_2Eextreal_2Eextreal__div_2E0,X0_2E0),X1_2E0) ).
tff(arityeq1_2Ec_2Eextreal_2Eextreal__inv_2E1,axiom,
! [X0_2E0: mono_2Etyop_2Eextreal_2Eextreal] : mono_2Ec_2Eextreal_2Eextreal__inv_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal(mono_2Ec_2Eextreal_2Eextreal__inv_2E0,X0_2E0) ).
tff(arityeq2_2Ec_2Eextreal_2Eextreal__le_2E2,axiom,
! [X0_2E0: mono_2Etyop_2Eextreal_2Eextreal,X1_2E0: mono_2Etyop_2Eextreal_2Eextreal] : mono_2Ec_2Eextreal_2Eextreal__le_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Eextreal_2Eextreal__le_2E0,X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Eextreal_2Eextreal__mul_2E2,axiom,
! [X0_2E0: mono_2Etyop_2Eextreal_2Eextreal,X1_2E0: mono_2Etyop_2Eextreal_2Eextreal] : mono_2Ec_2Eextreal_2Eextreal__mul_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal(mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29(mono_2Ec_2Eextreal_2Eextreal__mul_2E0,X0_2E0),X1_2E0) ).
tff(arityeq1_2Ec_2Eextreal_2Eextreal__of__num_2E1,axiom,
! [X0_2E0: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Eextreal_2Eextreal__of__num_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eextreal_2Eextreal(mono_2Ec_2Eextreal_2Eextreal__of__num_2E0,X0_2E0) ).
tff(arityeq1_2Ec_2Eextreal_2Eextreal__sup_2E1,axiom,
! [X0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29] : mono_2Ec_2Eextreal_2Eextreal__sup_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Eextreal_2Eextreal(mono_2Ec_2Eextreal_2Eextreal__sup_2E0,X0_2E0) ).
tff(arityeq1_2Ec_2Erealax_2Einv_2E1,axiom,
! [X0_2E0: mono_2Etyop_2Erealax_2Ereal] : mono_2Ec_2Erealax_2Einv_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Erealax_2Einv_2E0,X0_2E0) ).
tff(arityeq1_2Ec_2Emeasure_2Em__space_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emeasure_2Em__space_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),X0_2E0))) ).
tff(arityeq1_2Ec_2Emeasure_2Emeasure__space_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] : j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Emeasure_2Emeasure__space_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),X0_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),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Ebool),c_2Emeasure_2Emeasure__space_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),X0_2E0)))) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27b,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) ).
tff(arityeq3_2Ec_2Ecombin_2Eo_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : s(A_27b,c_2Ecombin_2Eo_2E3(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0),s(A_27a,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0))),s(A_27a,X2_2E0))) ).
tff(arityeq2_2Ec_2Elebesgue_2Epos__fn__integral_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] : j_mono_2Etyop_2Eextreal_2Eextreal(s(tyop_2Eextreal_2Eextreal,c_2Elebesgue_2Epos__fn__integral_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),X1_2E0)))) = j_mono_2Etyop_2Eextreal_2Eextreal(s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Eextreal_2Eextreal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Eextreal_2Eextreal)),c_2Elebesgue_2Epos__fn__integral_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),X1_2E0)))) ).
tff(arityeq2_2Ec_2Elebesgue_2Epsfis_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] : j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Elebesgue_2Epsfis_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),X1_2E0)))) = j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),c_2Elebesgue_2Epsfis_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),X1_2E0)))) ).
tff(arityeq2_2Ec_2Erealax_2Ereal__lt_2E2,axiom,
! [X0_2E0: mono_2Etyop_2Erealax_2Ereal,X1_2E0: mono_2Etyop_2Erealax_2Ereal] : mono_2Ec_2Erealax_2Ereal__lt_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Erealax_2Ereal__lt_2E0,X0_2E0),X1_2E0) ).
tff(arityeq2_2Ec_2Ereal_2Ereal__lte_2E2,axiom,
! [X0_2E0: mono_2Etyop_2Erealax_2Ereal,X1_2E0: mono_2Etyop_2Erealax_2Ereal] : mono_2Ec_2Ereal_2Ereal__lte_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal_2Ereal__lte_2E0,X0_2E0),X1_2E0) ).
tff(arityeq1_2Ec_2Ereal_2Ereal__of__num_2E1,axiom,
! [X0_2E0: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Ereal_2Ereal__of__num_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal_2Ereal__of__num_2E0,X0_2E0) ).
tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
! [X0_2E0: mono_2Etyop_2Emin_2Ebool] :
( ~ p(X0_2E0)
<=> p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,X0_2E0)) ) ).
tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Emin_2Ebool] : s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(V0_2E0,V1_2E0))) = 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_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)))) ).
tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: mono_2Etyop_2Emin_2Ebool] : s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(V0_2E0,V1_2E0))) = 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_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)))) ).
tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: mono_2Etyop_2Emin_2Ebool] : s(tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),i_mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29(V0_2E0,V1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29(V0_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)))) ).
tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Eextreal_2Eextreal] : s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29(V0_2E0)),s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(V1_2E0)))) ).
tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29,V1_2E0: mono_2Etyop_2Eextreal_2Eextreal] : s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal(V0_2E0,V1_2E0))) = s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29(V0_2E0)),s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(V1_2E0)))) ).
tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_29,V1_2E0: mono_2Etyop_2Eextreal_2Eextreal] : s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_29(V0_2E0)),s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(V1_2E0)))) ).
tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: mono_2Etyop_2Eextreal_2Eextreal] : s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29(V0_2E0)),s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(V1_2E0)))) ).
tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29,V1_2E0: mono_2Etyop_2Eextreal_2Eextreal] : s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29(mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Eextreal_2Eextreal)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_29(V0_2E0)),s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(V1_2E0)))) ).
tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: mono_2Etyop_2Eextreal_2Eextreal] : s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(V0_2E0)),s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(V1_2E0)))) ).
tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: mono_2Etyop_2Eextreal_2Eextreal] : s(tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),i_mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29(V0_2E0,V1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29(V0_2E0)),s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(V1_2E0)))) ).
tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29] : s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29(V1_2E0)))) ).
tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Eextreal_2Eextreal,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eextreal_2Eextreal_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29] : s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Eextreal_2Eextreal(V0_2E0,V1_2E0))) = s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Eextreal_2Eextreal),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Eextreal_2Eextreal_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29(V1_2E0)))) ).
tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29] : s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29(V1_2E0)))) ).
tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eextreal_2Eextreal,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eextreal_2Eextreal_29,V1_2E0: mono_2Etyop_2Enum_2Enum] : s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eextreal_2Eextreal(V0_2E0,V1_2E0))) = s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eextreal_2Eextreal),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eextreal_2Eextreal_29(V0_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ).
tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Erealax_2Ereal,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29,V1_2E0: mono_2Etyop_2Enum_2Enum] : s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Erealax_2Ereal(V0_2E0,V1_2E0))) = 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_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ).
tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Erealax_2Ereal] : s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool(V0_2E0,V1_2E0))) = 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_2E0)),s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(V1_2E0)))) ).
tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Eextreal_2Eextreal,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Eextreal_2Eextreal_29,V1_2E0: mono_2Etyop_2Erealax_2Ereal] : s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Eextreal_2Eextreal(V0_2E0,V1_2E0))) = s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Eextreal_2Eextreal),i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Eextreal_2Eextreal_29(V0_2E0)),s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(V1_2E0)))) ).
tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: 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(mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(V0_2E0,V1_2E0))) = 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_2E0)),s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(V1_2E0)))) ).
tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1_2E0: mono_2Etyop_2Erealax_2Ereal] : s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(mono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0_2E0,V1_2E0))) = 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_2E0)),s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(V1_2E0)))) ).
tff(monoeq_2Emono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool,axiom,
s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool)) = s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0) ).
tff(monoeq_2Emono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0_2E0: mono_2Etyop_2Eextreal_2Eextreal,V1_2E0: mono_2Etyop_2Emin_2Ebool] : s(tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),i_mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool(V0_2E0,V1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(V0_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)))) ).
tff(monoeq_2Emono_2Ec_2Epred__set_2EGSPEC_2E0_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal,axiom,
s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29(mono_2Ec_2Epred__set_2EGSPEC_2E0_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0) ).
tff(monoeq_2Emono_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal,axiom,
! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29] : s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal(V0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29(V0_2E0)))) ).
tff(monoeq_2Emono_2Ec_2Ebool_2EIN_2E0_2Emono_2Etyop_2Eextreal_2Eextreal,axiom,
s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29(mono_2Ec_2Ebool_2EIN_2E0_2Emono_2Etyop_2Eextreal_2Eextreal)) = s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0) ).
tff(monoeq_2Emono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Eextreal_2Eextreal,axiom,
! [V0_2E0: mono_2Etyop_2Eextreal_2Eextreal,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29] : s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Eextreal_2Eextreal(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29(V1_2E0)))) ).
tff(thm_2Ebool_2EETA__AX,axiom,
! [A_27a: d,A_27b: d,V0M_2E0: u,V1x_2E0: u] : s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0M_2E0),s(A_27a,V1x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0M_2E0),s(A_27a,V1x_2E0))) ).
tff(thm_2Ebool_2ETRUTH,axiom,
p(mono_2Ec_2Ebool_2ET_2E0) ).
tff(thm_2Ebool_2EIMP__ANTISYM__AX,axiom,
! [V0t1_2E0: mono_2Etyop_2Emin_2Ebool,V1t2_2E0: mono_2Etyop_2Emin_2Ebool] :
( ( p(V0t1_2E0)
=> p(V1t2_2E0) )
=> ( ( p(V1t2_2E0)
=> p(V0t1_2E0) )
=> ( V0t1_2E0 = V1t2_2E0 ) ) ) ).
tff(thm_2Ebool_2EFALSITY,axiom,
! [V0t_2E0: mono_2Etyop_2Emin_2Ebool] :
( p(mono_2Ec_2Ebool_2EF_2E0)
=> p(V0t_2E0) ) ).
tff(thm_2Ebool_2EEXCLUDED__MIDDLE,axiom,
! [V0t_2E0: mono_2Etyop_2Emin_2Ebool] :
( p(V0t_2E0)
| ~ p(V0t_2E0) ) ).
tff(thm_2Ebool_2EFORALL__SIMP,axiom,
! [A_27a: d,V0t_2E0: mono_2Etyop_2Emin_2Ebool] :
( ! [V1x_2E0: u] : p(V0t_2E0)
<=> p(V0t_2E0) ) ).
tff(thm_2Ebool_2EAND__CLAUSES,axiom,
! [V0t_2E0: mono_2Etyop_2Emin_2Ebool] :
( ( ( p(mono_2Ec_2Ebool_2ET_2E0)
& p(V0t_2E0) )
<=> p(V0t_2E0) )
& ( ( p(V0t_2E0)
& p(mono_2Ec_2Ebool_2ET_2E0) )
<=> p(V0t_2E0) )
& ( ( p(mono_2Ec_2Ebool_2EF_2E0)
& p(V0t_2E0) )
<=> p(mono_2Ec_2Ebool_2EF_2E0) )
& ( ( p(V0t_2E0)
& p(mono_2Ec_2Ebool_2EF_2E0) )
<=> p(mono_2Ec_2Ebool_2EF_2E0) )
& ( ( p(V0t_2E0)
& p(V0t_2E0) )
<=> p(V0t_2E0) ) ) ).
tff(thm_2Ebool_2EIMP__CLAUSES,axiom,
! [V0t_2E0: mono_2Etyop_2Emin_2Ebool] :
( ( ( p(mono_2Ec_2Ebool_2ET_2E0)
=> p(V0t_2E0) )
<=> p(V0t_2E0) )
& ( ( p(V0t_2E0)
=> p(mono_2Ec_2Ebool_2ET_2E0) )
<=> p(mono_2Ec_2Ebool_2ET_2E0) )
& ( ( p(mono_2Ec_2Ebool_2EF_2E0)
=> p(V0t_2E0) )
<=> p(mono_2Ec_2Ebool_2ET_2E0) )
& ( ( p(V0t_2E0)
=> p(V0t_2E0) )
<=> p(mono_2Ec_2Ebool_2ET_2E0) )
& ( ( p(V0t_2E0)
=> p(mono_2Ec_2Ebool_2EF_2E0) )
<=> ~ p(V0t_2E0) ) ) ).
tff(thm_2Ebool_2ENOT__CLAUSES,axiom,
( ! [V0t_2E0: mono_2Etyop_2Emin_2Ebool] :
( ~ ~ p(V0t_2E0)
<=> p(V0t_2E0) )
& ( ~ p(mono_2Ec_2Ebool_2ET_2E0)
<=> p(mono_2Ec_2Ebool_2EF_2E0) )
& ( ~ p(mono_2Ec_2Ebool_2EF_2E0)
<=> p(mono_2Ec_2Ebool_2ET_2E0) ) ) ).
tff(thm_2Ebool_2EREFL__CLAUSE,axiom,
! [A_27a: d,V0x_2E0: u] :
( ( s(A_27a,V0x_2E0) = s(A_27a,V0x_2E0) )
<=> p(mono_2Ec_2Ebool_2ET_2E0) ) ).
tff(thm_2Ebool_2EEQ__SYM__EQ,axiom,
! [A_27a: d,V0x_2E0: u,V1y_2E0: u] :
( ( s(A_27a,V0x_2E0) = s(A_27a,V1y_2E0) )
<=> ( s(A_27a,V1y_2E0) = s(A_27a,V0x_2E0) ) ) ).
tff(thm_2Ebool_2EFUN__EQ__THM,axiom,
! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
( ( s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) )
<=> ! [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))) ) ).
tff(thm_2Ebool_2EEQ__CLAUSES,axiom,
! [V0t_2E0: mono_2Etyop_2Emin_2Ebool] :
( ( ( mono_2Ec_2Ebool_2ET_2E0 = V0t_2E0 )
<=> p(V0t_2E0) )
& ( ( V0t_2E0 = mono_2Ec_2Ebool_2ET_2E0 )
<=> p(V0t_2E0) )
& ( ( mono_2Ec_2Ebool_2EF_2E0 = V0t_2E0 )
<=> ~ p(V0t_2E0) )
& ( ( V0t_2E0 = mono_2Ec_2Ebool_2EF_2E0 )
<=> ~ p(V0t_2E0) ) ) ).
tff(thm_2Ebool_2ERIGHT__AND__FORALL__THM,axiom,
! [A_27a: d,V0P_2E0: mono_2Etyop_2Emin_2Ebool,V1Q_2E0: u] :
( ( p(V0P_2E0)
& ! [V2x_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0))))) )
<=> ! [V3x_2E0: u] :
( p(V0P_2E0)
& p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0))))) ) ) ).
tff(thm_2Ebool_2ERIGHT__OR__OVER__AND,axiom,
! [V0A_2E0: mono_2Etyop_2Emin_2Ebool,V1B_2E0: mono_2Etyop_2Emin_2Ebool,V2C_2E0: mono_2Etyop_2Emin_2Ebool] :
( ( ( p(V1B_2E0)
& p(V2C_2E0) )
| p(V0A_2E0) )
<=> ( ( p(V1B_2E0)
| p(V0A_2E0) )
& ( p(V2C_2E0)
| p(V0A_2E0) ) ) ) ).
tff(thm_2Ebool_2EAND__IMP__INTRO,axiom,
! [V0t1_2E0: mono_2Etyop_2Emin_2Ebool,V1t2_2E0: mono_2Etyop_2Emin_2Ebool,V2t3_2E0: mono_2Etyop_2Emin_2Ebool] :
( ( p(V0t1_2E0)
=> ( p(V1t2_2E0)
=> p(V2t3_2E0) ) )
<=> ( ( p(V0t1_2E0)
& p(V1t2_2E0) )
=> p(V2t3_2E0) ) ) ).
tff(thm_2Ebool_2EIMP__CONG,axiom,
! [V0x_2E0: mono_2Etyop_2Emin_2Ebool,V1x_27_2E0: mono_2Etyop_2Emin_2Ebool,V2y_2E0: mono_2Etyop_2Emin_2Ebool,V3y_27_2E0: mono_2Etyop_2Emin_2Ebool] :
( ( ( V0x_2E0 = V1x_27_2E0 )
& ( p(V1x_27_2E0)
=> ( V2y_2E0 = V3y_27_2E0 ) ) )
=> ( ( p(V0x_2E0)
=> p(V2y_2E0) )
<=> ( p(V1x_27_2E0)
=> p(V3y_27_2E0) ) ) ) ).
tff(thm_2Ebool_2EUNWIND__THM2,axiom,
! [A_27a: d,V0P_2E0: u,V1a_2E0: u] :
( ? [V2x_2E0: u] :
( ( s(A_27a,V2x_2E0) = s(A_27a,V1a_2E0) )
& p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0))))) )
<=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1a_2E0))))) ) ).
tff(thm_2Ebool_2EBOUNDED__THM,axiom,
! [V0v_2E0: mono_2Etyop_2Emin_2Ebool] : mono_2Ec_2Ebool_2EBOUNDED_2E1(V0v_2E0) = mono_2Ec_2Ebool_2ET_2E0 ).
tff(thm_2Ecombin_2ES__DEF,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0x_2E0: u,V1x_27_2E0: u,V2x_27_27_2E0: u] : s(A_27c,c_2Ecombin_2ES_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1x_27_2E0),s(A_27a,V2x_27_27_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)),V0x_2E0),s(A_27a,V2x_27_27_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1x_27_2E0),s(A_27a,V2x_27_27_2E0))))) ).
tff(thm_2Ecombin_2EC__DEF,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0x_2E0: u,V1x_27_2E0: u,V2x_27_27_2E0: u] : s(A_27c,c_2Ecombin_2EC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0x_2E0),s(A_27b,V1x_27_2E0),s(A_27a,V2x_27_27_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)),V0x_2E0),s(A_27a,V2x_27_27_2E0))),s(A_27b,V1x_27_2E0))) ).
tff(thm_2Ecombin_2Eo__DEF,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] : s(A_27b,c_2Ecombin_2Eo_2E3(s(tyop_2Emin_2Efun(A_27c,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1g_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V0f_2E0),s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1g_2E0),s(A_27a,V2x_2E0))))) ).
tff(thm_2Ecombin_2EI__THM,axiom,
! [A_27a: d,V0x_2E0: u] : s(A_27a,c_2Ecombin_2EI_2E1(s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0) ).
tff(thm_2Ecombin_2EI__o__ID,axiom,
! [A_27a: d,A_27b: d,V0f_2E0: u] :
( ( s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),c_2Ecombin_2EI_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) )
& ( s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EI_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) ) ) ).
tff(thm_2Eextreal_2Eextreal__of__num__def,axiom,
! [V0n_2E0: mono_2Etyop_2Enum_2Enum] : mono_2Ec_2Eextreal_2Eextreal__of__num_2E1(V0n_2E0) = mono_2Ec_2Eextreal_2ENormal_2E1(mono_2Ec_2Ereal_2Ereal__of__num_2E1(V0n_2E0)) ).
tff(thm_2Eextreal_2Eextreal__le__def,axiom,
! [V0y_2E0: mono_2Etyop_2Erealax_2Ereal,V1x_2E0: mono_2Etyop_2Erealax_2Ereal,V2v5_2E0: mono_2Etyop_2Erealax_2Ereal,V3v3_2E0: mono_2Etyop_2Erealax_2Ereal,V4v2_2E0: mono_2Etyop_2Erealax_2Ereal,V5a_2E0: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Eextreal_2Eextreal__le_2E2(mono_2Ec_2Eextreal_2ENormal_2E1(V1x_2E0),mono_2Ec_2Eextreal_2ENormal_2E1(V0y_2E0)) = mono_2Ec_2Ereal_2Ereal__lte_2E2(V1x_2E0,V0y_2E0) )
& ( mono_2Ec_2Eextreal_2Eextreal__le_2E2(mono_2Ec_2Eextreal_2ENegInf_2E0,V5a_2E0) = mono_2Ec_2Ebool_2ET_2E0 )
& ( mono_2Ec_2Eextreal_2Eextreal__le_2E2(mono_2Ec_2Eextreal_2EPosInf_2E0,mono_2Ec_2Eextreal_2EPosInf_2E0) = mono_2Ec_2Ebool_2ET_2E0 )
& ( mono_2Ec_2Eextreal_2Eextreal__le_2E2(mono_2Ec_2Eextreal_2ENormal_2E1(V4v2_2E0),mono_2Ec_2Eextreal_2EPosInf_2E0) = mono_2Ec_2Ebool_2ET_2E0 )
& ( mono_2Ec_2Eextreal_2Eextreal__le_2E2(mono_2Ec_2Eextreal_2EPosInf_2E0,mono_2Ec_2Eextreal_2ENegInf_2E0) = mono_2Ec_2Ebool_2EF_2E0 )
& ( mono_2Ec_2Eextreal_2Eextreal__le_2E2(mono_2Ec_2Eextreal_2ENormal_2E1(V3v3_2E0),mono_2Ec_2Eextreal_2ENegInf_2E0) = mono_2Ec_2Ebool_2EF_2E0 )
& ( mono_2Ec_2Eextreal_2Eextreal__le_2E2(mono_2Ec_2Eextreal_2EPosInf_2E0,mono_2Ec_2Eextreal_2ENormal_2E1(V2v5_2E0)) = mono_2Ec_2Ebool_2EF_2E0 ) ) ).
tff(thm_2Eextreal_2Eextreal__inv__def,axiom,
( ( mono_2Ec_2Eextreal_2Eextreal__inv_2E1(mono_2Ec_2Eextreal_2ENegInf_2E0) = mono_2Ec_2Eextreal_2ENormal_2E1(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Enum_2E0_2E0)) )
& ( mono_2Ec_2Eextreal_2Eextreal__inv_2E1(mono_2Ec_2Eextreal_2EPosInf_2E0) = mono_2Ec_2Eextreal_2ENormal_2E1(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Enum_2E0_2E0)) )
& ! [V0x_2E0: mono_2Etyop_2Erealax_2Ereal] : mono_2Ec_2Eextreal_2Eextreal__inv_2E1(mono_2Ec_2Eextreal_2ENormal_2E1(V0x_2E0)) = mono_2Ec_2Eextreal_2ENormal_2E1(mono_2Ec_2Erealax_2Einv_2E1(V0x_2E0)) ) ).
tff(thm_2Eextreal_2Eextreal__div__def,axiom,
! [V0x_2E0: mono_2Etyop_2Eextreal_2Eextreal,V1y_2E0: mono_2Etyop_2Eextreal_2Eextreal] : mono_2Ec_2Eextreal_2Eextreal__div_2E2(V0x_2E0,V1y_2E0) = mono_2Ec_2Eextreal_2Eextreal__mul_2E2(V0x_2E0,mono_2Ec_2Eextreal_2Eextreal__inv_2E1(V1y_2E0)) ).
tff(thm_2Eextreal_2Emul__lzero,axiom,
! [V0x_2E0: mono_2Etyop_2Eextreal_2Eextreal] : mono_2Ec_2Eextreal_2Eextreal__mul_2E2(mono_2Ec_2Eextreal_2Eextreal__of__num_2E1(mono_2Ec_2Enum_2E0_2E0),V0x_2E0) = mono_2Ec_2Eextreal_2Eextreal__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) ).
tff(thm_2Eextreal_2Ele__lmul__imp,axiom,
! [V0x_2E0: mono_2Etyop_2Eextreal_2Eextreal,V1y_2E0: mono_2Etyop_2Eextreal_2Eextreal,V2z_2E0: mono_2Etyop_2Eextreal_2Eextreal] :
( ( p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(mono_2Ec_2Eextreal_2Eextreal__of__num_2E1(mono_2Ec_2Enum_2E0_2E0),V2z_2E0))
& p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(V0x_2E0,V1y_2E0)) )
=> p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(mono_2Ec_2Eextreal_2Eextreal__mul_2E2(V2z_2E0,V0x_2E0),mono_2Ec_2Eextreal_2Eextreal__mul_2E2(V2z_2E0,V1y_2E0))) ) ).
tff(thm_2Eextreal_2Emul__comm,axiom,
! [V0x_2E0: mono_2Etyop_2Eextreal_2Eextreal,V1y_2E0: mono_2Etyop_2Eextreal_2Eextreal] : mono_2Ec_2Eextreal_2Eextreal__mul_2E2(V0x_2E0,V1y_2E0) = mono_2Ec_2Eextreal_2Eextreal__mul_2E2(V1y_2E0,V0x_2E0) ).
tff(thm_2Eextreal_2Ele__rdiv,axiom,
! [V0x_2E0: mono_2Etyop_2Erealax_2Ereal,V1y_2E0: mono_2Etyop_2Eextreal_2Eextreal,V2z_2E0: mono_2Etyop_2Eextreal_2Eextreal] :
( p(mono_2Ec_2Erealax_2Ereal__lt_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Enum_2E0_2E0),V0x_2E0))
=> ( mono_2Ec_2Eextreal_2Eextreal__le_2E2(mono_2Ec_2Eextreal_2Eextreal__mul_2E2(V1y_2E0,mono_2Ec_2Eextreal_2ENormal_2E1(V0x_2E0)),V2z_2E0) = mono_2Ec_2Eextreal_2Eextreal__le_2E2(V1y_2E0,mono_2Ec_2Eextreal_2Eextreal__div_2E2(V2z_2E0,mono_2Ec_2Eextreal_2ENormal_2E1(V0x_2E0))) ) ) ).
tff(thm_2Eextreal_2Ele__ldiv,axiom,
! [V0x_2E0: mono_2Etyop_2Erealax_2Ereal,V1y_2E0: mono_2Etyop_2Eextreal_2Eextreal,V2z_2E0: mono_2Etyop_2Eextreal_2Eextreal] :
( p(mono_2Ec_2Erealax_2Ereal__lt_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Enum_2E0_2E0),V0x_2E0))
=> ( mono_2Ec_2Eextreal_2Eextreal__le_2E2(V1y_2E0,mono_2Ec_2Eextreal_2Eextreal__mul_2E2(V2z_2E0,mono_2Ec_2Eextreal_2ENormal_2E1(V0x_2E0))) = mono_2Ec_2Eextreal_2Eextreal__le_2E2(mono_2Ec_2Eextreal_2Eextreal__div_2E2(V1y_2E0,mono_2Ec_2Eextreal_2ENormal_2E1(V0x_2E0)),V2z_2E0) ) ) ).
tff(thm_2Eextreal_2Esup__le,axiom,
! [V0p_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,V1x_2E0: mono_2Etyop_2Eextreal_2Eextreal] :
( p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(mono_2Ec_2Eextreal_2Eextreal__sup_2E1(V0p_2E0),V1x_2E0))
<=> ! [V2y_2E0: mono_2Etyop_2Eextreal_2Eextreal] :
( p(mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool(V0p_2E0,V2y_2E0))
=> p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(V2y_2E0,V1x_2E0)) ) ) ).
tff(thm_2Eextreal_2Ele__sup,axiom,
! [V0p_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,V1x_2E0: mono_2Etyop_2Eextreal_2Eextreal] :
( p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(V1x_2E0,mono_2Ec_2Eextreal_2Eextreal__sup_2E1(V0p_2E0)))
<=> ! [V2y_2E0: mono_2Etyop_2Eextreal_2Eextreal] :
( ! [V3z_2E0: mono_2Etyop_2Eextreal_2Eextreal] :
( p(mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool(V0p_2E0,V3z_2E0))
=> p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(V3z_2E0,V2y_2E0)) )
=> p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(V1x_2E0,V2y_2E0)) ) ) ).
tff(thm_2Eextreal_2Esup__eq,axiom,
! [V0p_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29,V1x_2E0: mono_2Etyop_2Eextreal_2Eextreal] :
( ( mono_2Ec_2Eextreal_2Eextreal__sup_2E1(V0p_2E0) = V1x_2E0 )
<=> ( ! [V2y_2E0: mono_2Etyop_2Eextreal_2Eextreal] :
( p(mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool(V0p_2E0,V2y_2E0))
=> p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(V2y_2E0,V1x_2E0)) )
& ! [V3y_2E0: mono_2Etyop_2Eextreal_2Eextreal] :
( ! [V4z_2E0: mono_2Etyop_2Eextreal_2Eextreal] :
( p(mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool(V0p_2E0,V4z_2E0))
=> p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(V4z_2E0,V3y_2E0)) )
=> p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(V1x_2E0,V3y_2E0)) ) ) ) ).
tff(thm_2Elebesgue_2Epos__fn__integral__def,axiom,
! [A_27a: d,F1_2E0: u,F0_2E0: u] :
( ! [V2r_2E0: mono_2Etyop_2Eextreal_2Eextreal,V0m_2E0: u,V1f_2E0: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(V2r_2E0)))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V0m_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0)))))
<=> ? [V3g_2E0: u] :
( p(mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Eextreal_2Eextreal(V2r_2E0,j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Elebesgue_2Epsfis_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V0m_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V3g_2E0))))))
& ! [V4x_2E0: u] : p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(j_mono_2Etyop_2Eextreal_2Eextreal(s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V3g_2E0),s(A_27a,V4x_2E0)))),j_mono_2Etyop_2Eextreal_2Eextreal(s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0),s(A_27a,V4x_2E0)))))) ) )
=> ( ! [V0m_2E0: u,V1f_2E0: u,V2r_2E0: mono_2Etyop_2Eextreal_2Eextreal] : mono_2Eapp_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V0m_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0)))),V2r_2E0) = mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Emin_2Ebool(V2r_2E0,j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Eextreal_2Eextreal,i_mono_2Etyop_2Eextreal_2Eextreal(V2r_2E0)))),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V0m_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0)))))
=> ! [V0m_2E0: u,V1f_2E0: u] : j_mono_2Etyop_2Eextreal_2Eextreal(s(tyop_2Eextreal_2Eextreal,c_2Elebesgue_2Epos__fn__integral_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V0m_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0)))) = mono_2Ec_2Eextreal_2Eextreal__sup_2E1(mono_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Eextreal_2Eextreal_20mono_2Etyop_2Eextreal_2Eextreal(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Epair_2Eprod(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V0m_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0)))))) ) ) ).
tff(thm_2Elebesgue_2Epsfis__cmul,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V3z_2E0: mono_2Etyop_2Erealax_2Ereal,V1f_2E0: u,V4x_2E0: u] : j_mono_2Etyop_2Eextreal_2Eextreal(s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal))),F0_2E0),s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(V3z_2E0)))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0))),s(A_27a,V4x_2E0)))) = mono_2Ec_2Eextreal_2Eextreal__mul_2E2(mono_2Ec_2Eextreal_2ENormal_2E1(V3z_2E0),j_mono_2Etyop_2Eextreal_2Eextreal(s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0),s(A_27a,V4x_2E0)))))
=> ! [V0m_2E0: u,V1f_2E0: u,V2a_2E0: mono_2Etyop_2Eextreal_2Eextreal,V3z_2E0: mono_2Etyop_2Erealax_2Ereal] :
( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Emeasure_2Emeasure__space_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V0m_2E0)))))
& p(mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Eextreal_2Eextreal(V2a_2E0,j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Elebesgue_2Epsfis_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V0m_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0))))))
& p(mono_2Ec_2Ereal_2Ereal__lte_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Enum_2E0_2E0),V3z_2E0)) )
=> p(mono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Eextreal_2Eextreal(mono_2Ec_2Eextreal_2Eextreal__mul_2E2(mono_2Ec_2Eextreal_2ENormal_2E1(V3z_2E0),V2a_2E0),j_mono_2Etyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Eextreal_2Eextreal,tyop_2Emin_2Ebool),c_2Elebesgue_2Epsfis_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V0m_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal))),F0_2E0),s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(V3z_2E0)))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0)))))))) ) ) ).
tff(thm_2Elebesgue_2Epos__fn__integral__zero,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V1x_2E0: u] : j_mono_2Etyop_2Eextreal_2Eextreal(s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),F0_2E0),s(A_27a,V1x_2E0)))) = mono_2Ec_2Eextreal_2Eextreal__of__num_2E1(mono_2Ec_2Enum_2E0_2E0)
=> ! [V0m_2E0: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Emeasure_2Emeasure__space_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V0m_2E0)))))
=> ( j_mono_2Etyop_2Eextreal_2Eextreal(s(tyop_2Eextreal_2Eextreal,c_2Elebesgue_2Epos__fn__integral_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V0m_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),F0_2E0)))) = mono_2Ec_2Eextreal_2Eextreal__of__num_2E1(mono_2Ec_2Enum_2E0_2E0) ) ) ) ).
tff(thm_2Epair_2ECLOSED__PAIR__EQ,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u,V2a_2E0: u,V3b_2E0: u] :
( ( s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27b,V1y_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2a_2E0),s(A_27b,V3b_2E0))) )
<=> ( ( s(A_27a,V0x_2E0) = s(A_27a,V2a_2E0) )
& ( s(A_27b,V1y_2E0) = s(A_27b,V3b_2E0) ) ) ) ).
tff(thm_2Epred__set_2ESPECIFICATION,axiom,
! [A_27a: d,V0P_2E0: u,V1x_2E0: u] : j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0)))) ).
tff(thm_2Epred__set_2EGSPECIFICATION,axiom,
! [A_27a: d,A_27b: d,V0f_2E0: u,V1v_2E0: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),V0f_2E0)))))))
<=> ? [V2x_2E0: u] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V1v_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2ET_2E0)))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),V0f_2E0),s(A_27b,V2x_2E0))) ) ).
tff(thm_2Ereal_2EREAL__LT__LE,axiom,
! [V0x_2E0: mono_2Etyop_2Erealax_2Ereal,V1y_2E0: mono_2Etyop_2Erealax_2Ereal] :
( p(mono_2Ec_2Erealax_2Ereal__lt_2E2(V0x_2E0,V1y_2E0))
<=> ( p(mono_2Ec_2Ereal_2Ereal__lte_2E2(V0x_2E0,V1y_2E0))
& ( V0x_2E0 != V1y_2E0 ) ) ) ).
tff(thm_2Ereal_2EREAL__LE__INV,axiom,
! [V0x_2E0: mono_2Etyop_2Erealax_2Ereal] :
( p(mono_2Ec_2Ereal_2Ereal__lte_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Enum_2E0_2E0),V0x_2E0))
=> p(mono_2Ec_2Ereal_2Ereal__lte_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Enum_2E0_2E0),mono_2Ec_2Erealax_2Einv_2E1(V0x_2E0))) ) ).
tff(thm_2Esat_2ENOT__NOT,axiom,
! [V0t_2E0: mono_2Etyop_2Emin_2Ebool] :
( ~ ~ p(V0t_2E0)
<=> p(V0t_2E0) ) ).
tff(thm_2Esat_2EAND__INV__IMP,axiom,
! [V0A_2E0: mono_2Etyop_2Emin_2Ebool] :
( p(V0A_2E0)
=> ( ~ p(V0A_2E0)
=> p(mono_2Ec_2Ebool_2EF_2E0) ) ) ).
tff(thm_2Esat_2EOR__DUAL2,axiom,
! [V0B_2E0: mono_2Etyop_2Emin_2Ebool,V1A_2E0: mono_2Etyop_2Emin_2Ebool] :
( ( ~ ( p(V1A_2E0)
| p(V0B_2E0) )
=> p(mono_2Ec_2Ebool_2EF_2E0) )
<=> ( ( p(V1A_2E0)
=> p(mono_2Ec_2Ebool_2EF_2E0) )
=> ( ~ p(V0B_2E0)
=> p(mono_2Ec_2Ebool_2EF_2E0) ) ) ) ).
tff(thm_2Esat_2EOR__DUAL3,axiom,
! [V0B_2E0: mono_2Etyop_2Emin_2Ebool,V1A_2E0: mono_2Etyop_2Emin_2Ebool] :
( ( ~ ( ~ p(V1A_2E0)
| p(V0B_2E0) )
=> p(mono_2Ec_2Ebool_2EF_2E0) )
<=> ( p(V1A_2E0)
=> ( ~ p(V0B_2E0)
=> p(mono_2Ec_2Ebool_2EF_2E0) ) ) ) ).
tff(thm_2Esat_2EAND__INV2,axiom,
! [V0A_2E0: mono_2Etyop_2Emin_2Ebool] :
( ( ~ p(V0A_2E0)
=> p(mono_2Ec_2Ebool_2EF_2E0) )
=> ( ( p(V0A_2E0)
=> p(mono_2Ec_2Ebool_2EF_2E0) )
=> p(mono_2Ec_2Ebool_2EF_2E0) ) ) ).
tff(thm_2Esat_2Edc__eq,axiom,
! [V0r_2E0: mono_2Etyop_2Emin_2Ebool,V1q_2E0: mono_2Etyop_2Emin_2Ebool,V2p_2E0: mono_2Etyop_2Emin_2Ebool] :
( ( p(V2p_2E0)
<=> ( V1q_2E0 = V0r_2E0 ) )
<=> ( ( p(V2p_2E0)
| p(V1q_2E0)
| p(V0r_2E0) )
& ( p(V2p_2E0)
| ~ p(V0r_2E0)
| ~ p(V1q_2E0) )
& ( p(V1q_2E0)
| ~ p(V0r_2E0)
| ~ p(V2p_2E0) )
& ( p(V0r_2E0)
| ~ p(V1q_2E0)
| ~ p(V2p_2E0) ) ) ) ).
tff(thm_2Esat_2Edc__conj,axiom,
! [V0r_2E0: mono_2Etyop_2Emin_2Ebool,V1q_2E0: mono_2Etyop_2Emin_2Ebool,V2p_2E0: mono_2Etyop_2Emin_2Ebool] :
( ( p(V2p_2E0)
<=> ( p(V1q_2E0)
& p(V0r_2E0) ) )
<=> ( ( p(V2p_2E0)
| ~ p(V1q_2E0)
| ~ p(V0r_2E0) )
& ( p(V1q_2E0)
| ~ p(V2p_2E0) )
& ( p(V0r_2E0)
| ~ p(V2p_2E0) ) ) ) ).
tff(thm_2Esat_2Edc__disj,axiom,
! [V0r_2E0: mono_2Etyop_2Emin_2Ebool,V1q_2E0: mono_2Etyop_2Emin_2Ebool,V2p_2E0: mono_2Etyop_2Emin_2Ebool] :
( ( p(V2p_2E0)
<=> ( p(V1q_2E0)
| p(V0r_2E0) ) )
<=> ( ( p(V2p_2E0)
| ~ p(V1q_2E0) )
& ( p(V2p_2E0)
| ~ p(V0r_2E0) )
& ( p(V1q_2E0)
| p(V0r_2E0)
| ~ p(V2p_2E0) ) ) ) ).
tff(thm_2Esat_2Edc__imp,axiom,
! [V0r_2E0: mono_2Etyop_2Emin_2Ebool,V1q_2E0: mono_2Etyop_2Emin_2Ebool,V2p_2E0: mono_2Etyop_2Emin_2Ebool] :
( ( p(V2p_2E0)
<=> ( p(V1q_2E0)
=> p(V0r_2E0) ) )
<=> ( ( p(V2p_2E0)
| p(V1q_2E0) )
& ( p(V2p_2E0)
| ~ p(V0r_2E0) )
& ( ~ p(V1q_2E0)
| p(V0r_2E0)
| ~ p(V2p_2E0) ) ) ) ).
tff(thm_2Esat_2Edc__neg,axiom,
! [V0q_2E0: mono_2Etyop_2Emin_2Ebool,V1p_2E0: mono_2Etyop_2Emin_2Ebool] :
( ( p(V1p_2E0)
<=> ~ p(V0q_2E0) )
<=> ( ( p(V1p_2E0)
| p(V0q_2E0) )
& ( ~ p(V0q_2E0)
| ~ p(V1p_2E0) ) ) ) ).
tff(thm_2Esat_2Epth__ni1,axiom,
! [V0q_2E0: mono_2Etyop_2Emin_2Ebool,V1p_2E0: mono_2Etyop_2Emin_2Ebool] :
( ~ ( p(V1p_2E0)
=> p(V0q_2E0) )
=> p(V1p_2E0) ) ).
tff(thm_2Esat_2Epth__ni2,axiom,
! [V0q_2E0: mono_2Etyop_2Emin_2Ebool,V1p_2E0: mono_2Etyop_2Emin_2Ebool] :
( ~ ( p(V1p_2E0)
=> p(V0q_2E0) )
=> ~ p(V0q_2E0) ) ).
tff(thm_2Esat_2Epth__no1,axiom,
! [V0q_2E0: mono_2Etyop_2Emin_2Ebool,V1p_2E0: mono_2Etyop_2Emin_2Ebool] :
( ~ ( p(V1p_2E0)
| p(V0q_2E0) )
=> ~ p(V1p_2E0) ) ).
tff(thm_2Esat_2Epth__no2,axiom,
! [V0q_2E0: mono_2Etyop_2Emin_2Ebool,V1p_2E0: mono_2Etyop_2Emin_2Ebool] :
( ~ ( p(V1p_2E0)
| p(V0q_2E0) )
=> ~ p(V0q_2E0) ) ).
tff(thm_2Esat_2Epth__nn,axiom,
! [V0p_2E0: mono_2Etyop_2Emin_2Ebool] :
( ~ ~ p(V0p_2E0)
=> p(V0p_2E0) ) ).
tff(thm_2Elebesgue_2Epos__fn__integral__cmul,conjecture,
! [A_27a: d,F0_2E0: u] :
( ! [V2c_2E0: mono_2Etyop_2Erealax_2Ereal,V1f_2E0: u,V4x_2E0: u] : j_mono_2Etyop_2Eextreal_2Eextreal(s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal))),F0_2E0),s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(V2c_2E0)))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0))),s(A_27a,V4x_2E0)))) = mono_2Ec_2Eextreal_2Eextreal__mul_2E2(mono_2Ec_2Eextreal_2ENormal_2E1(V2c_2E0),j_mono_2Etyop_2Eextreal_2Eextreal(s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0),s(A_27a,V4x_2E0)))))
=> ! [V0m_2E0: u,V1f_2E0: u,V2c_2E0: mono_2Etyop_2Erealax_2Ereal] :
( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Emeasure_2Emeasure__space_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V0m_2E0)))))
& ! [V3x_2E0: u] :
( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emeasure_2Em__space_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V0m_2E0)))))))
=> p(mono_2Ec_2Eextreal_2Eextreal__le_2E2(mono_2Ec_2Eextreal_2Eextreal__of__num_2E1(mono_2Ec_2Enum_2E0_2E0),j_mono_2Etyop_2Eextreal_2Eextreal(s(tyop_2Eextreal_2Eextreal,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0),s(A_27a,V3x_2E0)))))) )
& p(mono_2Ec_2Ereal_2Ereal__lte_2E2(mono_2Ec_2Ereal_2Ereal__of__num_2E1(mono_2Ec_2Enum_2E0_2E0),V2c_2E0)) )
=> ( j_mono_2Etyop_2Eextreal_2Eextreal(s(tyop_2Eextreal_2Eextreal,c_2Elebesgue_2Epos__fn__integral_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V0m_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal))),F0_2E0),s(tyop_2Erealax_2Ereal,i_mono_2Etyop_2Erealax_2Ereal(V2c_2E0)))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0)))))) = mono_2Ec_2Eextreal_2Eextreal__mul_2E2(mono_2Ec_2Eextreal_2ENormal_2E1(V2c_2E0),j_mono_2Etyop_2Eextreal_2Eextreal(s(tyop_2Eextreal_2Eextreal,c_2Elebesgue_2Epos__fn__integral_2E2(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Erealax_2Ereal))),V0m_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eextreal_2Eextreal),V1f_2E0))))) ) ) ) ).
%------------------------------------------------------------------------------