SET007 Axioms: SET007+177.ax
%------------------------------------------------------------------------------
% File : SET007+177 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Definitions and Basic Properties of Measurable Functions
% Version : [Urb08] axioms.
% English :
% Refs : [Mat90] Matuszewski (1990), Formalized Mathematics
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : mesfunc1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 85 ( 10 unt; 0 def)
% Number of atoms : 630 ( 73 equ)
% Maximal formula atoms : 15 ( 7 avg)
% Number of connectives : 637 ( 92 ~; 0 |; 251 &)
% ( 27 <=>; 267 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 1 prp; 0-4 aty)
% Number of functors : 59 ( 59 usr; 14 con; 0-4 aty)
% Number of variables : 296 ( 287 !; 9 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_mesfunc1,axiom,
( ~ v1_xboole_0(k1_mesfunc1)
& v1_membered(k1_mesfunc1)
& v2_membered(k1_mesfunc1) ) ).
fof(fc2_mesfunc1,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ( ~ v1_xboole_0(k3_mesfunc1(k1_nat_1(A,np__1)))
& v1_membered(k3_mesfunc1(k1_nat_1(A,np__1)))
& v2_membered(k3_mesfunc1(k1_nat_1(A,np__1)))
& v3_membered(k3_mesfunc1(k1_nat_1(A,np__1))) ) ) ).
fof(d1_mesfunc1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k6_supinf_1))
=> ( A = k1_mesfunc1
<=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ( r2_hidden(B,A)
<=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& B = k1_real_1(C) ) ) ) ) ) ).
fof(t1_mesfunc1,axiom,
r2_tarski(k5_numbers,k1_mesfunc1) ).
fof(t2_mesfunc1,axiom,
k4_numbers = k4_subset_1(k1_numbers,k1_mesfunc1,k5_numbers) ).
fof(t3_mesfunc1,axiom,
r2_tarski(k5_numbers,k4_numbers) ).
fof(d2_mesfunc1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k3_numbers))
=> ( B = k3_mesfunc1(A)
<=> ! [C] :
( v1_rat_1(C)
=> ( r2_hidden(C,B)
<=> ? [D] :
( v1_int_1(D)
& C = k7_xcmplx_0(D,A) ) ) ) ) ) ) ).
fof(t4_mesfunc1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> r2_tarski(k2_mesfunc1,k3_mesfunc1(k1_nat_1(A,np__1))) ) ).
fof(t5_mesfunc1,axiom,
r2_tarski(k5_numbers,k3_numbers) ).
fof(d3_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k3_supinf_1) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k3_supinf_1) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k3_supinf_1) )
=> ( D = k5_mesfunc1(A,B,C)
<=> ( k1_relat_1(D) = k4_xboole_0(k3_xboole_0(k1_relat_1(B),k1_relat_1(C)),k4_subset_1(A,k5_subset_1(A,k3_funct_2(A,k3_supinf_1,B,k11_supinf_1(k5_supinf_1)),k3_funct_2(A,k3_supinf_1,C,k11_supinf_1(k4_supinf_1))),k5_subset_1(A,k3_funct_2(A,k3_supinf_1,B,k11_supinf_1(k4_supinf_1)),k3_funct_2(A,k3_supinf_1,C,k11_supinf_1(k5_supinf_1)))))
& ! [E] :
( m1_subset_1(E,A)
=> ( r2_hidden(E,k1_relat_1(D))
=> k4_mesfunc1(A,D,E) = k2_supinf_2(k4_mesfunc1(A,B,E),k4_mesfunc1(A,C,E)) ) ) ) ) ) ) ) ) ).
fof(d4_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k3_supinf_1) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k3_supinf_1) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k3_supinf_1) )
=> ( D = k6_mesfunc1(A,B,C)
<=> ( k1_relat_1(D) = k4_xboole_0(k3_xboole_0(k1_relat_1(B),k1_relat_1(C)),k4_subset_1(A,k5_subset_1(A,k3_funct_2(A,k3_supinf_1,B,k11_supinf_1(k4_supinf_1)),k3_funct_2(A,k3_supinf_1,C,k11_supinf_1(k4_supinf_1))),k5_subset_1(A,k3_funct_2(A,k3_supinf_1,B,k11_supinf_1(k5_supinf_1)),k3_funct_2(A,k3_supinf_1,C,k11_supinf_1(k5_supinf_1)))))
& ! [E] :
( m1_subset_1(E,A)
=> ( r2_hidden(E,k1_relat_1(D))
=> k4_mesfunc1(A,D,E) = k4_supinf_2(k4_mesfunc1(A,B,E),k4_mesfunc1(A,C,E)) ) ) ) ) ) ) ) ) ).
fof(d5_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k3_supinf_1) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k3_supinf_1) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k3_supinf_1) )
=> ( D = k7_mesfunc1(A,B,C)
<=> ( k1_relat_1(D) = k3_xboole_0(k1_relat_1(B),k1_relat_1(C))
& ! [E] :
( m1_subset_1(E,A)
=> ( r2_hidden(E,k1_relat_1(D))
=> k4_mesfunc1(A,D,E) = k2_extreal1(k4_mesfunc1(A,B,E),k4_mesfunc1(A,C,E)) ) ) ) ) ) ) ) ) ).
fof(d6_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k3_supinf_1) )
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k3_supinf_1) )
=> ( D = k8_mesfunc1(A,B,C)
<=> ( k1_relat_1(D) = k1_relat_1(B)
& ! [E] :
( m1_subset_1(E,A)
=> ( r2_hidden(E,k1_relat_1(D))
=> k4_mesfunc1(A,D,E) = k2_extreal1(k1_measure6(C),k4_mesfunc1(A,B,E)) ) ) ) ) ) ) ) ) ).
fof(t6_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k3_supinf_1) )
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( C != np__0
=> ! [D] :
( m1_subset_1(D,A)
=> ( r2_hidden(D,k1_relat_1(k8_mesfunc1(A,B,C)))
=> k4_mesfunc1(A,B,D) = k3_extreal1(k4_mesfunc1(A,k8_mesfunc1(A,B,C),D),k1_measure6(C)) ) ) ) ) ) ) ).
fof(d7_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k3_supinf_1) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k3_supinf_1) )
=> ( C = k9_mesfunc1(A,B)
<=> ( k1_relat_1(C) = k1_relat_1(B)
& ! [D] :
( m1_subset_1(D,A)
=> ( r2_hidden(D,k1_relat_1(C))
=> k4_mesfunc1(A,C,D) = k3_supinf_2(k4_mesfunc1(A,B,D)) ) ) ) ) ) ) ) ).
fof(d8_mesfunc1,axiom,
k10_mesfunc1 = np__1 ).
fof(d9_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k3_supinf_1) )
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k3_supinf_1) )
=> ( D = k11_mesfunc1(A,B,C)
<=> ( k1_relat_1(D) = k4_xboole_0(k1_relat_1(B),k3_funct_2(A,k3_supinf_1,B,k11_supinf_1(k1_supinf_2)))
& ! [E] :
( m1_subset_1(E,A)
=> ( r2_hidden(E,k1_relat_1(D))
=> k4_mesfunc1(A,D,E) = k3_extreal1(k1_measure6(C),k4_mesfunc1(A,B,E)) ) ) ) ) ) ) ) ) ).
fof(t7_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k3_supinf_1) )
=> ( k1_relat_1(k11_mesfunc1(A,B,np__1)) = k4_xboole_0(k1_relat_1(B),k3_funct_2(A,k3_supinf_1,B,k11_supinf_1(k1_supinf_2)))
& ! [C] :
( m1_subset_1(C,A)
=> ( r2_hidden(C,k1_relat_1(k11_mesfunc1(A,B,np__1)))
=> k4_mesfunc1(A,k11_mesfunc1(A,B,np__1),C) = k3_extreal1(k10_mesfunc1,k4_mesfunc1(A,B,C)) ) ) ) ) ) ).
fof(d10_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k3_supinf_1) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k3_supinf_1) )
=> ( C = k12_mesfunc1(A,B)
<=> ( k1_relat_1(C) = k1_relat_1(B)
& ! [D] :
( m1_subset_1(D,A)
=> ( r2_hidden(D,k1_relat_1(C))
=> k4_mesfunc1(A,C,D) = k4_extreal1(k4_mesfunc1(A,B,D)) ) ) ) ) ) ) ) ).
fof(t8_mesfunc1,axiom,
$true ).
fof(t9_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k3_supinf_1) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k3_supinf_1) )
=> k5_mesfunc1(A,B,C) = k5_mesfunc1(A,C,B) ) ) ) ).
fof(t10_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k3_supinf_1) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k3_supinf_1) )
=> k7_mesfunc1(A,B,C) = k7_mesfunc1(A,C,B) ) ) ) ).
fof(t11_mesfunc1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& r1_xreal_0(A,B) ) ) ).
fof(t12_mesfunc1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& r1_xreal_0(k1_real_1(B),A) ) ) ).
fof(t13_mesfunc1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(B,A)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_xreal_0(k6_xcmplx_0(B,A),k6_real_1(np__1,k1_nat_1(C,np__1))) ) ) ) ) ).
fof(t14_mesfunc1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_xreal_0(k6_xcmplx_0(A,k6_real_1(np__1,k1_nat_1(C,np__1))),B) )
=> r1_xreal_0(A,B) ) ) ) ).
fof(t15_mesfunc1,axiom,
! [A] :
( m1_subset_1(A,k3_supinf_1)
=> ( ! [B] :
( m1_subset_1(B,k1_numbers)
=> ~ r1_supinf_1(A,k1_measure6(B)) )
=> A = k4_supinf_1 ) ) ).
fof(t16_mesfunc1,axiom,
! [A] :
( m1_subset_1(A,k3_supinf_1)
=> ( ! [B] :
( m1_subset_1(B,k1_numbers)
=> ~ r1_supinf_1(k1_measure6(B),A) )
=> A = k5_supinf_1 ) ) ).
fof(d11_mesfunc1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( r1_mesfunc1(A,B,C)
<=> r2_hidden(C,B) ) ) ).
fof(t17_mesfunc1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(C)
& v1_prob_1(C,A)
& v1_measure1(C,A)
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ( r1_mesfunc1(A,C,B)
<=> ! [D] :
( m3_measure1(D,A,C)
=> r2_measure1(A,C,D,B) ) ) ) ).
fof(d12_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k3_supinf_1) )
=> ! [C] :
( m1_subset_1(C,k3_supinf_1)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(A))
=> ( D = k15_mesfunc1(A,B,C)
<=> ! [E] :
( m1_subset_1(E,A)
=> ( r2_hidden(E,D)
<=> ( r2_hidden(E,k1_relat_1(B))
& ? [F] :
( m1_subset_1(F,k3_supinf_1)
& F = k4_mesfunc1(A,B,E)
& ~ r1_supinf_1(C,F) ) ) ) ) ) ) ) ) ) ).
fof(d13_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k3_supinf_1) )
=> ! [C] :
( m1_subset_1(C,k3_supinf_1)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(A))
=> ( D = k16_mesfunc1(A,B,C)
<=> ! [E] :
( m1_subset_1(E,A)
=> ( r2_hidden(E,D)
<=> ( r2_hidden(E,k1_relat_1(B))
& ? [F] :
( m1_subset_1(F,k3_supinf_1)
& F = k4_mesfunc1(A,B,E)
& r1_supinf_1(F,C) ) ) ) ) ) ) ) ) ) ).
fof(d14_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k3_supinf_1) )
=> ! [C] :
( m1_subset_1(C,k3_supinf_1)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(A))
=> ( D = k17_mesfunc1(A,B,C)
<=> ! [E] :
( m1_subset_1(E,A)
=> ( r2_hidden(E,D)
<=> ( r2_hidden(E,k1_relat_1(B))
& ? [F] :
( m1_subset_1(F,k3_supinf_1)
& F = k4_mesfunc1(A,B,E)
& ~ r1_supinf_1(F,C) ) ) ) ) ) ) ) ) ) ).
fof(d15_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k3_supinf_1) )
=> ! [C] :
( m1_subset_1(C,k3_supinf_1)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(A))
=> ( D = k18_mesfunc1(A,B,C)
<=> ! [E] :
( m1_subset_1(E,A)
=> ( r2_hidden(E,D)
<=> ( r2_hidden(E,k1_relat_1(B))
& ? [F] :
( m1_subset_1(F,k3_supinf_1)
& F = k4_mesfunc1(A,B,E)
& r1_supinf_1(C,F) ) ) ) ) ) ) ) ) ) ).
fof(d16_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k3_supinf_1) )
=> ! [C] :
( m1_subset_1(C,k3_supinf_1)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(A))
=> ( D = k19_mesfunc1(A,B,C)
<=> ! [E] :
( m1_subset_1(E,A)
=> ( r2_hidden(E,D)
<=> ( r2_hidden(E,k1_relat_1(B))
& ? [F] :
( m1_subset_1(F,k3_supinf_1)
& F = k4_mesfunc1(A,B,E)
& C = F ) ) ) ) ) ) ) ) ) ).
fof(t18_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k3_supinf_1) )
=> ! [C,D] :
( m1_subset_1(D,k3_supinf_1)
=> ( r1_tarski(C,k1_relat_1(B))
=> k3_xboole_0(C,k18_mesfunc1(A,B,D)) = k4_xboole_0(C,k3_xboole_0(C,k15_mesfunc1(A,B,D))) ) ) ) ) ).
fof(t19_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k3_supinf_1) )
=> ! [C,D] :
( m1_subset_1(D,k3_supinf_1)
=> ( r1_tarski(C,k1_relat_1(B))
=> k3_xboole_0(C,k17_mesfunc1(A,B,D)) = k4_xboole_0(C,k3_xboole_0(C,k16_mesfunc1(A,B,D))) ) ) ) ) ).
fof(t20_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k3_supinf_1) )
=> ! [C,D] :
( m1_subset_1(D,k3_supinf_1)
=> ( r1_tarski(C,k1_relat_1(B))
=> k3_xboole_0(C,k16_mesfunc1(A,B,D)) = k4_xboole_0(C,k3_xboole_0(C,k17_mesfunc1(A,B,D))) ) ) ) ) ).
fof(t21_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k3_supinf_1) )
=> ! [C,D] :
( m1_subset_1(D,k3_supinf_1)
=> ( r1_tarski(C,k1_relat_1(B))
=> k3_xboole_0(C,k15_mesfunc1(A,B,D)) = k4_xboole_0(C,k3_xboole_0(C,k18_mesfunc1(A,B,D))) ) ) ) ) ).
fof(t22_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k3_supinf_1) )
=> ! [C,D] :
( m1_subset_1(D,k3_supinf_1)
=> k3_xboole_0(C,k19_mesfunc1(A,B,D)) = k3_xboole_0(k3_xboole_0(C,k18_mesfunc1(A,B,D)),k16_mesfunc1(A,B,D)) ) ) ) ).
fof(t23_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,B)
& m2_relset_1(C,k5_numbers,B) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k3_supinf_1) )
=> ! [E,F] :
( m1_subset_1(F,k1_numbers)
=> ( ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,B,C,G) = k3_xboole_0(E,k17_mesfunc1(A,D,k1_measure6(k5_real_1(F,k6_real_1(np__1,k1_nat_1(G,np__1)))))) )
=> k3_xboole_0(E,k18_mesfunc1(A,D,k1_measure6(F))) = k1_measure2(A,B,k1_measure3(A,B,C)) ) ) ) ) ) ) ).
fof(t24_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k3_supinf_1) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_prob_1(C,A)
& v1_measure1(C,A)
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,C)
& m2_relset_1(D,k5_numbers,C) )
=> ! [E,F] :
( v1_xreal_0(F)
=> ( ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,C,D,G) = k3_xboole_0(E,k15_mesfunc1(A,B,k1_measure6(k2_xcmplx_0(F,k6_real_1(np__1,k1_nat_1(G,np__1)))))) )
=> k3_xboole_0(E,k16_mesfunc1(A,B,k1_measure6(F))) = k1_measure2(A,C,k1_measure3(A,C,D)) ) ) ) ) ) ) ).
fof(t25_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,A,k3_supinf_1) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_prob_1(C,A)
& v1_measure1(C,A)
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,C)
& m2_relset_1(D,k5_numbers,C) )
=> ! [E,F] :
( v1_xreal_0(F)
=> ( ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,C,D,G) = k3_xboole_0(E,k16_mesfunc1(A,B,k1_measure6(k6_xcmplx_0(F,k6_real_1(np__1,k1_nat_1(G,np__1)))))) )
=> k3_xboole_0(E,k15_mesfunc1(A,B,k1_measure6(F))) = k2_measure2(A,C,k1_measure3(A,C,D)) ) ) ) ) ) ) ).
fof(t26_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,B)
& m2_relset_1(C,k5_numbers,B) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k3_supinf_1) )
=> ! [E,F] :
( m1_subset_1(F,k1_numbers)
=> ( ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,B,C,G) = k3_xboole_0(E,k18_mesfunc1(A,D,k1_measure6(k3_real_1(F,k6_real_1(np__1,k1_nat_1(G,np__1)))))) )
=> k3_xboole_0(E,k17_mesfunc1(A,D,k1_measure6(F))) = k2_measure2(A,B,k1_measure3(A,B,C)) ) ) ) ) ) ) ).
fof(t27_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,B)
& m2_relset_1(C,k5_numbers,B) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k3_supinf_1) )
=> ! [E] :
( ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,B,C,F) = k3_xboole_0(E,k17_mesfunc1(A,D,k1_measure6(F))) )
=> k3_xboole_0(E,k19_mesfunc1(A,D,k4_supinf_1)) = k1_measure2(A,B,k1_measure3(A,B,C)) ) ) ) ) ) ).
fof(t28_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,B)
& m2_relset_1(C,k5_numbers,B) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k3_supinf_1) )
=> ! [E] :
( ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,B,C,F) = k3_xboole_0(E,k15_mesfunc1(A,D,k1_measure6(F))) )
=> k3_xboole_0(E,k15_mesfunc1(A,D,k4_supinf_1)) = k2_measure2(A,B,k1_measure3(A,B,C)) ) ) ) ) ) ).
fof(t29_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,B)
& m2_relset_1(C,k5_numbers,B) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k3_supinf_1) )
=> ! [E] :
( ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,B,C,F) = k3_xboole_0(E,k15_mesfunc1(A,D,k1_measure6(k1_real_1(F)))) )
=> k3_xboole_0(E,k19_mesfunc1(A,D,k5_supinf_1)) = k1_measure2(A,B,k1_measure3(A,B,C)) ) ) ) ) ) ).
fof(t30_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,B)
& m2_relset_1(C,k5_numbers,B) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k3_supinf_1) )
=> ! [E] :
( ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,B,C,F) = k3_xboole_0(E,k17_mesfunc1(A,D,k1_measure6(k1_real_1(F)))) )
=> k3_xboole_0(E,k17_mesfunc1(A,D,k5_supinf_1)) = k2_measure2(A,B,k1_measure3(A,B,C)) ) ) ) ) ) ).
fof(d17_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k3_supinf_1) )
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(A),B)
=> ( r2_mesfunc1(A,B,C,D)
<=> ! [E] :
( v1_xreal_0(E)
=> r1_mesfunc1(A,B,k5_subset_1(A,D,k15_mesfunc1(A,C,k1_measure6(E)))) ) ) ) ) ) ) ).
fof(t31_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k3_supinf_1) )
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(A),B)
=> ( r1_tarski(D,k1_relat_1(C))
=> ( r2_mesfunc1(A,B,C,D)
<=> ! [E] :
( v1_xreal_0(E)
=> r1_mesfunc1(A,B,k5_subset_1(A,D,k18_mesfunc1(A,C,k1_measure6(E)))) ) ) ) ) ) ) ) ).
fof(t32_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k3_supinf_1) )
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(A),B)
=> ( r2_mesfunc1(A,B,C,D)
<=> ! [E] :
( v1_xreal_0(E)
=> r1_mesfunc1(A,B,k5_subset_1(A,D,k16_mesfunc1(A,C,k1_measure6(E)))) ) ) ) ) ) ) ).
fof(t33_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k3_supinf_1) )
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(A),B)
=> ( r1_tarski(D,k1_relat_1(C))
=> ( r2_mesfunc1(A,B,C,D)
<=> ! [E] :
( v1_xreal_0(E)
=> r1_mesfunc1(A,B,k5_subset_1(A,D,k17_mesfunc1(A,C,k1_measure6(E)))) ) ) ) ) ) ) ) ).
fof(t34_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k3_supinf_1) )
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(A),B)
=> ! [E] :
( m2_subset_1(E,k1_zfmisc_1(A),B)
=> ( ( r1_tarski(E,D)
& r2_mesfunc1(A,B,C,D) )
=> r2_mesfunc1(A,B,C,E) ) ) ) ) ) ) ).
fof(t35_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k3_supinf_1) )
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(A),B)
=> ! [E] :
( m2_subset_1(E,k1_zfmisc_1(A),B)
=> ( ( r2_mesfunc1(A,B,C,D)
& r2_mesfunc1(A,B,C,E) )
=> r2_mesfunc1(A,B,C,k2_measure1(A,B,D,E)) ) ) ) ) ) ) ).
fof(t36_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k3_supinf_1) )
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(A),B)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ( ( r2_mesfunc1(A,B,C,D)
& r1_tarski(D,k1_relat_1(C)) )
=> r1_mesfunc1(A,B,k5_subset_1(A,k5_subset_1(A,D,k17_mesfunc1(A,C,k1_measure6(E))),k15_mesfunc1(A,C,k1_measure6(F)))) ) ) ) ) ) ) ) ).
fof(t37_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k3_supinf_1) )
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(A),B)
=> ( ( r2_mesfunc1(A,B,C,D)
& r1_tarski(D,k1_relat_1(C)) )
=> r1_mesfunc1(A,B,k5_subset_1(A,D,k19_mesfunc1(A,C,k4_supinf_1))) ) ) ) ) ) ).
fof(t38_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k3_supinf_1) )
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(A),B)
=> ( r2_mesfunc1(A,B,C,D)
=> r1_mesfunc1(A,B,k5_subset_1(A,D,k19_mesfunc1(A,C,k5_supinf_1))) ) ) ) ) ) ).
fof(t39_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k3_supinf_1) )
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(A),B)
=> ( ( r2_mesfunc1(A,B,C,D)
& r1_tarski(D,k1_relat_1(C)) )
=> r1_mesfunc1(A,B,k5_subset_1(A,k5_subset_1(A,D,k17_mesfunc1(A,C,k5_supinf_1)),k15_mesfunc1(A,C,k4_supinf_1))) ) ) ) ) ) ).
fof(t40_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k3_supinf_1) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,A,k3_supinf_1) )
=> ! [E] :
( m2_subset_1(E,k1_zfmisc_1(A),B)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ( ( r2_mesfunc1(A,B,C,E)
& r2_mesfunc1(A,B,D,E)
& r1_tarski(E,k1_relat_1(D)) )
=> r1_mesfunc1(A,B,k5_subset_1(A,k5_subset_1(A,E,k15_mesfunc1(A,C,k1_measure6(F))),k17_mesfunc1(A,D,k1_measure6(F)))) ) ) ) ) ) ) ) ).
fof(t41_mesfunc1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_prob_1(B,A)
& v1_measure1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,A,k3_supinf_1) )
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(A),B)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( ( r2_mesfunc1(A,B,C,D)
& r1_tarski(D,k1_relat_1(C)) )
=> r2_mesfunc1(A,B,k8_mesfunc1(A,C,E),D) ) ) ) ) ) ) ).
fof(dt_k1_mesfunc1,axiom,
m1_subset_1(k1_mesfunc1,k1_zfmisc_1(k6_supinf_1)) ).
fof(dt_k2_mesfunc1,axiom,
m1_subset_1(k2_mesfunc1,k1_zfmisc_1(k6_supinf_1)) ).
fof(redefinition_k2_mesfunc1,axiom,
k2_mesfunc1 = k4_numbers ).
fof(dt_k3_mesfunc1,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> m1_subset_1(k3_mesfunc1(A),k1_zfmisc_1(k3_numbers)) ) ).
fof(dt_k4_mesfunc1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,A,k3_supinf_1) )
=> m1_subset_1(k4_mesfunc1(A,B,C),k3_supinf_1) ) ).
fof(redefinition_k4_mesfunc1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,A,k3_supinf_1) )
=> k4_mesfunc1(A,B,C) = k1_funct_1(B,C) ) ).
fof(dt_k5_mesfunc1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,A,k3_supinf_1)
& v1_funct_1(C)
& m1_relset_1(C,A,k3_supinf_1) )
=> ( v1_funct_1(k5_mesfunc1(A,B,C))
& m2_relset_1(k5_mesfunc1(A,B,C),A,k3_supinf_1) ) ) ).
fof(dt_k6_mesfunc1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,A,k3_supinf_1)
& v1_funct_1(C)
& m1_relset_1(C,A,k3_supinf_1) )
=> ( v1_funct_1(k6_mesfunc1(A,B,C))
& m2_relset_1(k6_mesfunc1(A,B,C),A,k3_supinf_1) ) ) ).
fof(dt_k7_mesfunc1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,A,k3_supinf_1)
& v1_funct_1(C)
& m1_relset_1(C,A,k3_supinf_1) )
=> ( v1_funct_1(k7_mesfunc1(A,B,C))
& m2_relset_1(k7_mesfunc1(A,B,C),A,k3_supinf_1) ) ) ).
fof(dt_k8_mesfunc1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,A,k3_supinf_1)
& m1_subset_1(C,k1_numbers) )
=> ( v1_funct_1(k8_mesfunc1(A,B,C))
& m2_relset_1(k8_mesfunc1(A,B,C),A,k3_supinf_1) ) ) ).
fof(dt_k9_mesfunc1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,A,k3_supinf_1) )
=> ( v1_funct_1(k9_mesfunc1(A,B))
& m2_relset_1(k9_mesfunc1(A,B),A,k3_supinf_1) ) ) ).
fof(dt_k10_mesfunc1,axiom,
m1_subset_1(k10_mesfunc1,k3_supinf_1) ).
fof(dt_k11_mesfunc1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,A,k3_supinf_1)
& m1_subset_1(C,k1_numbers) )
=> ( v1_funct_1(k11_mesfunc1(A,B,C))
& m2_relset_1(k11_mesfunc1(A,B,C),A,k3_supinf_1) ) ) ).
fof(dt_k12_mesfunc1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,A,k3_supinf_1) )
=> ( v1_funct_1(k12_mesfunc1(A,B))
& m2_relset_1(k12_mesfunc1(A,B),A,k3_supinf_1) ) ) ).
fof(dt_k13_mesfunc1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,A,k3_supinf_1)
& v1_funct_1(C)
& m1_relset_1(C,A,k3_supinf_1) )
=> ( v1_funct_1(k13_mesfunc1(A,B,C))
& m2_relset_1(k13_mesfunc1(A,B,C),A,k3_supinf_1) ) ) ).
fof(commutativity_k13_mesfunc1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,A,k3_supinf_1)
& v1_funct_1(C)
& m1_relset_1(C,A,k3_supinf_1) )
=> k13_mesfunc1(A,B,C) = k13_mesfunc1(A,C,B) ) ).
fof(redefinition_k13_mesfunc1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,A,k3_supinf_1)
& v1_funct_1(C)
& m1_relset_1(C,A,k3_supinf_1) )
=> k13_mesfunc1(A,B,C) = k5_mesfunc1(A,B,C) ) ).
fof(dt_k14_mesfunc1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,A,k3_supinf_1)
& v1_funct_1(C)
& m1_relset_1(C,A,k3_supinf_1) )
=> ( v1_funct_1(k14_mesfunc1(A,B,C))
& m2_relset_1(k14_mesfunc1(A,B,C),A,k3_supinf_1) ) ) ).
fof(commutativity_k14_mesfunc1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,A,k3_supinf_1)
& v1_funct_1(C)
& m1_relset_1(C,A,k3_supinf_1) )
=> k14_mesfunc1(A,B,C) = k14_mesfunc1(A,C,B) ) ).
fof(redefinition_k14_mesfunc1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,A,k3_supinf_1)
& v1_funct_1(C)
& m1_relset_1(C,A,k3_supinf_1) )
=> k14_mesfunc1(A,B,C) = k7_mesfunc1(A,B,C) ) ).
fof(dt_k15_mesfunc1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,A,k3_supinf_1)
& m1_subset_1(C,k3_supinf_1) )
=> m1_subset_1(k15_mesfunc1(A,B,C),k1_zfmisc_1(A)) ) ).
fof(dt_k16_mesfunc1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,A,k3_supinf_1)
& m1_subset_1(C,k3_supinf_1) )
=> m1_subset_1(k16_mesfunc1(A,B,C),k1_zfmisc_1(A)) ) ).
fof(dt_k17_mesfunc1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,A,k3_supinf_1)
& m1_subset_1(C,k3_supinf_1) )
=> m1_subset_1(k17_mesfunc1(A,B,C),k1_zfmisc_1(A)) ) ).
fof(dt_k18_mesfunc1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,A,k3_supinf_1)
& m1_subset_1(C,k3_supinf_1) )
=> m1_subset_1(k18_mesfunc1(A,B,C),k1_zfmisc_1(A)) ) ).
fof(dt_k19_mesfunc1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& m1_relset_1(B,A,k3_supinf_1)
& m1_subset_1(C,k3_supinf_1) )
=> m1_subset_1(k19_mesfunc1(A,B,C),k1_zfmisc_1(A)) ) ).
%------------------------------------------------------------------------------