SET007 Axioms: SET007+207.ax
%------------------------------------------------------------------------------
% File : SET007+207 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Subsets of Topological Spaces
% 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 : tops_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 145 ( 30 unt; 0 def)
% Number of atoms : 648 ( 41 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 516 ( 13 ~; 0 |; 187 &)
% ( 24 <=>; 292 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 1 con; 0-3 aty)
% Number of variables : 262 ( 255 !; 7 ?)
% 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_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v1_xboole_0(k1_pre_topc(A))
& v4_pre_topc(k1_pre_topc(A),A)
& v1_membered(k1_pre_topc(A))
& v2_membered(k1_pre_topc(A))
& v3_membered(k1_pre_topc(A))
& v4_membered(k1_pre_topc(A))
& v5_membered(k1_pre_topc(A)) ) ) ).
fof(fc2_tops_1,axiom,
! [A,B] :
( ( v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v4_pre_topc(k6_pre_topc(A,B),A) ) ).
fof(fc3_tops_1,axiom,
! [A,B] :
( ( v2_pre_topc(A)
& l1_pre_topc(A)
& v4_pre_topc(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v3_pre_topc(k3_subset_1(u1_struct_0(A),B),A) ) ).
fof(rc1_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v3_pre_topc(B,A) ) ) ).
fof(fc4_tops_1,axiom,
! [A,B] :
( ( v2_pre_topc(A)
& l1_pre_topc(A)
& v3_pre_topc(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v4_pre_topc(k3_subset_1(u1_struct_0(A),B),A) ) ).
fof(fc5_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ( v1_xboole_0(k1_tops_1(A,k1_pre_topc(A)))
& v1_membered(k1_tops_1(A,k1_pre_topc(A)))
& v2_membered(k1_tops_1(A,k1_pre_topc(A)))
& v3_membered(k1_tops_1(A,k1_pre_topc(A)))
& v4_membered(k1_tops_1(A,k1_pre_topc(A)))
& v5_membered(k1_tops_1(A,k1_pre_topc(A))) ) ) ).
fof(fc6_tops_1,axiom,
! [A,B] :
( ( v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v3_pre_topc(k1_tops_1(A,B),A) ) ).
fof(fc7_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v1_xboole_0(k1_pre_topc(A))
& v3_pre_topc(k1_pre_topc(A),A)
& v4_pre_topc(k1_pre_topc(A),A)
& v1_membered(k1_pre_topc(A))
& v2_membered(k1_pre_topc(A))
& v3_membered(k1_pre_topc(A))
& v4_membered(k1_pre_topc(A))
& v5_membered(k1_pre_topc(A)) ) ) ).
fof(fc8_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v3_pre_topc(k2_pre_topc(A),A)
& v4_pre_topc(k2_pre_topc(A),A) ) ) ).
fof(cc1_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_xboole_0(B)
=> ( v3_pre_topc(B,A)
& v4_pre_topc(B,A) ) ) ) ) ).
fof(rc2_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v3_pre_topc(B,A)
& v4_pre_topc(B,A) ) ) ).
fof(rc3_tops_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v3_pre_topc(B,A)
& v4_pre_topc(B,A) ) ) ).
fof(fc9_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> v1_tops_1(k2_pre_topc(A),A) ) ).
fof(cc2_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_xboole_0(B)
=> v2_tops_1(B,A) ) ) ) ).
fof(rc4_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_xboole_0(B)
& v1_membered(B)
& v2_membered(B)
& v3_membered(B)
& v4_membered(B)
& v5_membered(B)
& v2_tops_1(B,A) ) ) ).
fof(fc10_tops_1,axiom,
! [A,B] :
( ( l1_pre_topc(A)
& v2_tops_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_xboole_0(k1_tops_1(A,B))
& v1_membered(k1_tops_1(A,B))
& v2_membered(k1_tops_1(A,B))
& v3_membered(k1_tops_1(A,B))
& v4_membered(k1_tops_1(A,B))
& v5_membered(k1_tops_1(A,B))
& v2_tops_1(k1_tops_1(A,B),A) ) ) ).
fof(cc3_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_xboole_0(B)
=> v3_tops_1(B,A) ) ) ) ).
fof(rc5_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_xboole_0(B)
& v3_pre_topc(B,A)
& v4_pre_topc(B,A)
& v1_membered(B)
& v2_membered(B)
& v3_membered(B)
& v4_membered(B)
& v5_membered(B)
& v2_tops_1(B,A)
& v3_tops_1(B,A) ) ) ).
fof(fc11_tops_1,axiom,
! [A,B] :
( ( v2_pre_topc(A)
& l1_pre_topc(A)
& v3_tops_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v1_tops_1(k3_subset_1(u1_struct_0(A),B),A) ) ).
fof(cc4_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_tops_1(B,A)
=> v2_tops_1(B,A) ) ) ) ).
fof(cc5_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v4_pre_topc(B,A)
& v2_tops_1(B,A) )
=> ( v2_tops_1(B,A)
& v3_tops_1(B,A) ) ) ) ) ).
fof(fc12_tops_1,axiom,
! [A,B] :
( ( v2_pre_topc(A)
& l1_pre_topc(A)
& v3_pre_topc(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v2_tops_1(k2_tops_1(A,B),A)
& v3_tops_1(k2_tops_1(A,B),A) ) ) ).
fof(fc13_tops_1,axiom,
! [A,B] :
( ( v2_pre_topc(A)
& l1_pre_topc(A)
& v4_pre_topc(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v2_tops_1(k2_tops_1(A,B),A)
& v3_tops_1(k2_tops_1(A,B),A) ) ) ).
fof(cc6_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v3_pre_topc(B,A)
& v3_tops_1(B,A) )
=> ( v1_xboole_0(B)
& v3_pre_topc(B,A)
& v4_pre_topc(B,A)
& v1_membered(B)
& v2_membered(B)
& v3_membered(B)
& v4_membered(B)
& v5_membered(B)
& v2_tops_1(B,A)
& v3_tops_1(B,A) ) ) ) ) ).
fof(t1_tops_1,axiom,
$true ).
fof(t2_tops_1,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k4_subset_1(u1_struct_0(A),B,k2_pre_topc(A)) = k2_pre_topc(A) ) ) ).
fof(t3_tops_1,axiom,
$true ).
fof(t4_tops_1,axiom,
$true ).
fof(t5_tops_1,axiom,
$true ).
fof(t6_tops_1,axiom,
$true ).
fof(t7_tops_1,axiom,
$true ).
fof(t8_tops_1,axiom,
! [A] :
( l1_struct_0(A)
=> k3_subset_1(u1_struct_0(A),k2_pre_topc(A)) = k1_pre_topc(A) ) ).
fof(t9_tops_1,axiom,
$true ).
fof(t10_tops_1,axiom,
$true ).
fof(t11_tops_1,axiom,
$true ).
fof(t12_tops_1,axiom,
$true ).
fof(t13_tops_1,axiom,
$true ).
fof(t14_tops_1,axiom,
$true ).
fof(t15_tops_1,axiom,
$true ).
fof(t16_tops_1,axiom,
$true ).
fof(t17_tops_1,axiom,
$true ).
fof(t18_tops_1,axiom,
$true ).
fof(t19_tops_1,axiom,
$true ).
fof(t20_tops_1,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_tarski(B,C)
<=> r1_xboole_0(B,k3_subset_1(u1_struct_0(A),C)) ) ) ) ) ).
fof(t21_tops_1,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( k3_subset_1(u1_struct_0(A),B) = k3_subset_1(u1_struct_0(A),C)
=> B = C ) ) ) ) ).
fof(t22_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> v4_pre_topc(k1_pre_topc(A),A) ) ).
fof(t23_tops_1,axiom,
$true ).
fof(t24_tops_1,axiom,
$true ).
fof(t25_tops_1,axiom,
$true ).
fof(t26_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k6_pre_topc(A,k6_pre_topc(A,B)) = k6_pre_topc(A,B) ) ) ).
fof(t27_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> k6_pre_topc(A,k2_pre_topc(A)) = k2_pre_topc(A) ) ).
fof(t28_tops_1,axiom,
$true ).
fof(t29_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_pre_topc(B,A)
<=> v3_pre_topc(k3_subset_1(u1_struct_0(A),B),A) ) ) ) ).
fof(t30_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(B,A)
<=> v4_pre_topc(k3_subset_1(u1_struct_0(A),B),A) ) ) ) ).
fof(t31_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v4_pre_topc(B,A)
& r1_tarski(C,B) )
=> r1_tarski(k6_pre_topc(A,C),B) ) ) ) ) ).
fof(t32_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> r1_tarski(k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,C)),k6_pre_topc(A,k6_subset_1(u1_struct_0(A),B,C))) ) ) ) ).
fof(t33_tops_1,axiom,
$true ).
fof(t34_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v4_pre_topc(B,A)
& v4_pre_topc(C,A) )
=> k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C)) = k5_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,C)) ) ) ) ) ).
fof(t35_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v4_pre_topc(B,A)
& v4_pre_topc(C,A) )
=> v4_pre_topc(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ).
fof(t36_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v4_pre_topc(B,A)
& v4_pre_topc(C,A) )
=> v4_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ).
fof(t37_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v3_pre_topc(B,A)
& v3_pre_topc(C,A) )
=> v3_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ).
fof(t38_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v3_pre_topc(B,A)
& v3_pre_topc(C,A) )
=> v3_pre_topc(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ).
fof(t39_tops_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,k6_pre_topc(A,B))
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( v3_pre_topc(D,A)
& r2_hidden(C,D)
& r1_xboole_0(B,D) ) ) ) ) ) ) ).
fof(t40_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(B,A)
=> r1_tarski(k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,C)),k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C))) ) ) ) ) ).
fof(t41_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(B,A)
=> k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,C))) = k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C)) ) ) ) ) ).
fof(d1_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k1_tops_1(A,B) = k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))) ) ) ).
fof(t42_tops_1,axiom,
$true ).
fof(t43_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> k1_tops_1(A,k2_pre_topc(A)) = k2_pre_topc(A) ) ).
fof(t44_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> r1_tarski(k1_tops_1(A,B),B) ) ) ).
fof(t45_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k1_tops_1(A,k1_tops_1(A,B)) = k1_tops_1(A,B) ) ) ).
fof(t46_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> k5_subset_1(u1_struct_0(A),k1_tops_1(A,B),k1_tops_1(A,C)) = k1_tops_1(A,k5_subset_1(u1_struct_0(A),B,C)) ) ) ) ).
fof(t47_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> k1_tops_1(A,k1_pre_topc(A)) = k1_pre_topc(A) ) ).
fof(t48_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_tarski(B,C)
=> r1_tarski(k1_tops_1(A,B),k1_tops_1(A,C)) ) ) ) ) ).
fof(t49_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> r1_tarski(k4_subset_1(u1_struct_0(A),k1_tops_1(A,B),k1_tops_1(A,C)),k1_tops_1(A,k4_subset_1(u1_struct_0(A),B,C))) ) ) ) ).
fof(t50_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> r1_tarski(k1_tops_1(A,k6_subset_1(u1_struct_0(A),B,C)),k6_subset_1(u1_struct_0(A),k1_tops_1(A,B),k1_tops_1(A,C))) ) ) ) ).
fof(t51_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> v3_pre_topc(k1_tops_1(A,B),A) ) ) ).
fof(t52_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> v3_pre_topc(k1_pre_topc(A),A) ) ).
fof(t53_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> v3_pre_topc(k2_pre_topc(A),A) ) ).
fof(t54_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B,C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(B,k1_tops_1(A,C))
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
& v3_pre_topc(D,A)
& r1_tarski(D,C)
& r2_hidden(B,D) ) ) ) ) ).
fof(t55_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( l1_pre_topc(B)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( v3_pre_topc(D,B)
=> k1_tops_1(B,D) = D )
& ( k1_tops_1(A,C) = C
=> v3_pre_topc(C,A) ) ) ) ) ) ) ).
fof(t56_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v3_pre_topc(B,A)
& r1_tarski(B,C) )
=> r1_tarski(B,k1_tops_1(A,C)) ) ) ) ) ).
fof(t57_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(B,A)
<=> ! [C] :
( r2_hidden(C,B)
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
& v3_pre_topc(D,A)
& r1_tarski(D,B)
& r2_hidden(C,D) ) ) ) ) ) ).
fof(t58_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k6_pre_topc(A,k1_tops_1(A,B)) = k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,B)))) ) ) ).
fof(t59_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(B,A)
=> k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,B))) = k6_pre_topc(A,B) ) ) ) ).
fof(d2_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k2_tops_1(A,B) = k5_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))) ) ) ).
fof(t60_tops_1,axiom,
$true ).
fof(t61_tops_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,k2_tops_1(A,B))
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v3_pre_topc(D,A)
& r2_hidden(C,D) )
=> ( ~ r1_xboole_0(B,D)
& ~ r1_xboole_0(k3_subset_1(u1_struct_0(A),B),D) ) ) ) ) ) ) ) ).
fof(t62_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k2_tops_1(A,B) = k2_tops_1(A,k3_subset_1(u1_struct_0(A),B)) ) ) ).
fof(t63_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> r1_tarski(k2_tops_1(A,B),k6_pre_topc(A,B)) ) ) ).
fof(t64_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k2_tops_1(A,B) = k4_subset_1(u1_struct_0(A),k5_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)),B),k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),B)) ) ) ).
fof(t65_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k6_pre_topc(A,B) = k4_subset_1(u1_struct_0(A),B,k2_tops_1(A,B)) ) ) ).
fof(t66_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> r1_tarski(k2_tops_1(A,k5_subset_1(u1_struct_0(A),B,C)),k4_subset_1(u1_struct_0(A),k2_tops_1(A,B),k2_tops_1(A,C))) ) ) ) ).
fof(t67_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> r1_tarski(k2_tops_1(A,k4_subset_1(u1_struct_0(A),B,C)),k4_subset_1(u1_struct_0(A),k2_tops_1(A,B),k2_tops_1(A,C))) ) ) ) ).
fof(t68_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> r1_tarski(k2_tops_1(A,k2_tops_1(A,B)),k2_tops_1(A,B)) ) ) ).
fof(t69_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_pre_topc(B,A)
=> r1_tarski(k2_tops_1(A,B),B) ) ) ) ).
fof(t70_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> k4_subset_1(u1_struct_0(A),k2_tops_1(A,B),k2_tops_1(A,C)) = k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),k2_tops_1(A,k4_subset_1(u1_struct_0(A),B,C)),k2_tops_1(A,k5_subset_1(u1_struct_0(A),B,C))),k5_subset_1(u1_struct_0(A),k2_tops_1(A,B),k2_tops_1(A,C))) ) ) ) ).
fof(t71_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> r1_tarski(k2_tops_1(A,k1_tops_1(A,B)),k2_tops_1(A,B)) ) ) ).
fof(t72_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> r1_tarski(k2_tops_1(A,k6_pre_topc(A,B)),k2_tops_1(A,B)) ) ) ).
fof(t73_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> r1_xboole_0(k1_tops_1(A,B),k2_tops_1(A,B)) ) ) ).
fof(t74_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k1_tops_1(A,B) = k6_subset_1(u1_struct_0(A),B,k2_tops_1(A,B)) ) ) ).
fof(t75_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k2_tops_1(A,k2_tops_1(A,k2_tops_1(A,B))) = k2_tops_1(A,k2_tops_1(A,B)) ) ) ).
fof(t76_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(B,A)
<=> k2_tops_1(A,B) = k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),B) ) ) ) ).
fof(t77_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_pre_topc(B,A)
<=> k2_tops_1(A,B) = k6_subset_1(u1_struct_0(A),B,k1_tops_1(A,B)) ) ) ) ).
fof(d3_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_tops_1(B,A)
<=> k6_pre_topc(A,B) = k2_pre_topc(A) ) ) ) ).
fof(t78_tops_1,axiom,
$true ).
fof(t79_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v1_tops_1(B,A)
& r1_tarski(B,C) )
=> v1_tops_1(C,A) ) ) ) ) ).
fof(t80_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_tops_1(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( C != k1_xboole_0
& v3_pre_topc(C,A)
& r1_xboole_0(B,C) ) ) ) ) ) ).
fof(t81_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_tops_1(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(C,A)
=> k6_pre_topc(A,C) = k6_pre_topc(A,k5_subset_1(u1_struct_0(A),C,B)) ) ) ) ) ) ).
fof(t82_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v1_tops_1(B,A)
& v1_tops_1(C,A)
& v3_pre_topc(C,A) )
=> v1_tops_1(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ).
fof(d4_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v2_tops_1(B,A)
<=> v1_tops_1(k3_subset_1(u1_struct_0(A),B),A) ) ) ) ).
fof(t83_tops_1,axiom,
$true ).
fof(t84_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v2_tops_1(B,A)
<=> k1_tops_1(A,B) = k1_xboole_0 ) ) ) ).
fof(t85_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v2_tops_1(B,A)
& v2_tops_1(C,A)
& v4_pre_topc(C,A) )
=> v2_tops_1(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ).
fof(t86_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v2_tops_1(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r1_tarski(C,B)
& v3_pre_topc(C,A) )
=> C = k1_xboole_0 ) ) ) ) ) ).
fof(t87_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_pre_topc(B,A)
=> ( v2_tops_1(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( C != k1_xboole_0
& v3_pre_topc(C,A)
& ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( r1_tarski(D,C)
& D != k1_xboole_0
& v3_pre_topc(D,A)
& r1_xboole_0(B,D) ) ) ) ) ) ) ) ) ).
fof(t88_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v2_tops_1(B,A)
<=> r1_tarski(B,k2_tops_1(A,B)) ) ) ) ).
fof(d5_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_tops_1(B,A)
<=> v2_tops_1(k6_pre_topc(A,B),A) ) ) ) ).
fof(t89_tops_1,axiom,
$true ).
fof(t90_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v3_tops_1(B,A)
& v3_tops_1(C,A) )
=> v3_tops_1(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ).
fof(t91_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_tops_1(B,A)
=> v1_tops_1(k3_subset_1(u1_struct_0(A),B),A) ) ) ) ).
fof(t92_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_tops_1(B,A)
=> v2_tops_1(B,A) ) ) ) ).
fof(t93_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v2_tops_1(B,A)
& v4_pre_topc(B,A) )
=> v3_tops_1(B,A) ) ) ) ).
fof(t94_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_pre_topc(B,A)
=> ( v3_tops_1(B,A)
<=> B = k2_tops_1(A,B) ) ) ) ) ).
fof(t95_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(B,A)
=> v3_tops_1(k2_tops_1(A,B),A) ) ) ) ).
fof(t96_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_pre_topc(B,A)
=> v3_tops_1(k2_tops_1(A,B),A) ) ) ) ).
fof(t97_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v3_pre_topc(B,A)
& v3_tops_1(B,A) )
=> B = k1_xboole_0 ) ) ) ).
fof(d6_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_tops_1(B,A)
<=> ( r1_tarski(k1_tops_1(A,k6_pre_topc(A,B)),B)
& r1_tarski(B,k6_pre_topc(A,k1_tops_1(A,B))) ) ) ) ) ).
fof(d7_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v5_tops_1(B,A)
<=> B = k6_pre_topc(A,k1_tops_1(A,B)) ) ) ) ).
fof(d8_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v6_tops_1(B,A)
<=> B = k1_tops_1(A,k6_pre_topc(A,B)) ) ) ) ).
fof(t98_tops_1,axiom,
$true ).
fof(t99_tops_1,axiom,
$true ).
fof(t100_tops_1,axiom,
$true ).
fof(t101_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v6_tops_1(B,A)
<=> v5_tops_1(k3_subset_1(u1_struct_0(A),B),A) ) ) ) ).
fof(t102_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v5_tops_1(B,A)
=> k2_tops_1(A,k1_tops_1(A,B)) = k2_tops_1(A,B) ) ) ) ).
fof(t103_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v5_tops_1(B,A)
=> r1_tarski(k2_tops_1(A,B),k6_pre_topc(A,k1_tops_1(A,B))) ) ) ) ).
fof(t104_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v6_tops_1(B,A)
=> ( k2_tops_1(A,B) = k2_tops_1(A,k6_pre_topc(A,B))
& k2_tops_1(A,k6_pre_topc(A,B)) = k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),B) ) ) ) ) ).
fof(t105_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v3_pre_topc(B,A)
& v4_pre_topc(B,A) )
=> ( v5_tops_1(B,A)
<=> v6_tops_1(B,A) ) ) ) ) ).
fof(t106_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( l1_pre_topc(B)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( ( v4_pre_topc(D,B)
& v4_tops_1(D,B) )
=> v5_tops_1(D,B) )
& ( v5_tops_1(C,A)
=> ( v4_pre_topc(C,A)
& v4_tops_1(C,A) ) ) ) ) ) ) ) ).
fof(t107_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( l1_pre_topc(B)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( ( v3_pre_topc(D,B)
& v4_tops_1(D,B) )
=> v6_tops_1(D,B) )
& ( v6_tops_1(C,A)
=> ( v3_pre_topc(C,A)
& v4_tops_1(C,A) ) ) ) ) ) ) ) ).
fof(t108_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v5_tops_1(B,A)
& v5_tops_1(C,A) )
=> v5_tops_1(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ).
fof(t109_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v6_tops_1(B,A)
& v6_tops_1(C,A) )
=> v6_tops_1(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ).
fof(t110_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_tops_1(B,A)
=> k1_tops_1(A,k2_tops_1(A,B)) = k1_xboole_0 ) ) ) ).
fof(t111_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_tops_1(B,A)
=> ( v4_tops_1(k1_tops_1(A,B),A)
& v4_tops_1(k6_pre_topc(A,B),A) ) ) ) ) ).
fof(dt_k1_tops_1,axiom,
! [A,B] :
( ( l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k1_tops_1(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k2_tops_1,axiom,
! [A,B] :
( ( l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k2_tops_1(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
%------------------------------------------------------------------------------