SET007 Axioms: SET007+370.ax
%------------------------------------------------------------------------------
% File : SET007+370 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Remarks on Special 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_3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 90 ( 0 unt; 0 def)
% Number of atoms : 758 ( 96 equ)
% Maximal formula atoms : 15 ( 8 avg)
% Number of connectives : 762 ( 94 ~; 4 |; 283 &)
% ( 27 <=>; 354 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 10 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 16 usr; 0 prp; 1-2 aty)
% Number of functors : 13 ( 13 usr; 1 con; 0-3 aty)
% Number of variables : 286 ( 284 !; 2 ?)
% 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(t1_tops_3,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( B = k1_pre_topc(A)
=> k3_subset_1(u1_struct_0(A),B) = k2_pre_topc(A) )
& ( k3_subset_1(u1_struct_0(A),B) = k2_pre_topc(A)
=> B = k1_pre_topc(A) )
& ( B = k1_xboole_0
=> k3_subset_1(u1_struct_0(A),B) = u1_struct_0(A) )
& ( k3_subset_1(u1_struct_0(A),B) = u1_struct_0(A)
=> B = k1_xboole_0 ) ) ) ) ).
fof(t2_tops_3,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( B = k2_pre_topc(A)
=> k3_subset_1(u1_struct_0(A),B) = k1_pre_topc(A) )
& ( k3_subset_1(u1_struct_0(A),B) = k1_pre_topc(A)
=> B = k2_pre_topc(A) )
& ( B = u1_struct_0(A)
=> k3_subset_1(u1_struct_0(A),B) = k1_xboole_0 )
& ( k3_subset_1(u1_struct_0(A),B) = k1_xboole_0
=> B = u1_struct_0(A) ) ) ) ) ).
fof(t3_tops_3,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(k5_subset_1(u1_struct_0(A),k1_tops_1(A,B),k6_pre_topc(A,C)),k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C))) ) ) ) ).
fof(t4_tops_3,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,k4_subset_1(u1_struct_0(A),B,C)),k4_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k1_tops_1(A,C))) ) ) ) ).
fof(t5_tops_3,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(C,A)
=> r1_tarski(k1_tops_1(A,k4_subset_1(u1_struct_0(A),C,B)),k4_subset_1(u1_struct_0(A),C,k1_tops_1(A,B))) ) ) ) ) ).
fof(t6_tops_3,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(C,A)
=> k1_tops_1(A,k4_subset_1(u1_struct_0(A),C,B)) = k1_tops_1(A,k4_subset_1(u1_struct_0(A),C,k1_tops_1(A,B))) ) ) ) ) ).
fof(t7_tops_3,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_xboole_0(B,k1_tops_1(A,k6_pre_topc(A,B)))
=> k1_tops_1(A,k6_pre_topc(A,B)) = k1_xboole_0 ) ) ) ).
fof(t8_tops_3,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( k4_subset_1(u1_struct_0(A),B,k6_pre_topc(A,k1_tops_1(A,B))) = u1_struct_0(A)
=> k6_pre_topc(A,k1_tops_1(A,B)) = u1_struct_0(A) ) ) ) ).
fof(d1_tops_3,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(t9_tops_3,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> v2_tops_1(k1_pre_topc(A),A) ) ).
fof(t10_tops_3,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)))
=> ~ ( v2_tops_1(B,A)
& B = u1_struct_0(A) ) ) ) ).
fof(t11_tops_3,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)
& r1_tarski(C,B) )
=> v2_tops_1(C,A) ) ) ) ) ).
fof(t12_tops_3,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(k3_subset_1(u1_struct_0(A),B),C)
& v4_pre_topc(C,A) )
=> C = u1_struct_0(A) ) ) ) ) ) ).
fof(t13_tops_3,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)))
=> ~ ( C != k1_xboole_0
& v3_pre_topc(C,A)
& r1_xboole_0(k3_subset_1(u1_struct_0(A),B),C) ) ) ) ) ) ).
fof(t14_tops_3,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)))
=> ( v4_pre_topc(C,A)
=> k1_tops_1(A,C) = k1_tops_1(A,k4_subset_1(u1_struct_0(A),C,B)) ) ) ) ) ) ).
fof(t15_tops_3,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) )
=> v2_tops_1(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ).
fof(d2_tops_3,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) = u1_struct_0(A) ) ) ) ).
fof(t16_tops_3,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> v1_tops_1(k2_pre_topc(A),A) ) ).
fof(t17_tops_3,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_tops_1(B,A)
& B = k1_xboole_0 ) ) ) ).
fof(t18_tops_3,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_tops_1(B,A)
<=> v2_tops_1(k3_subset_1(u1_struct_0(A),B),A) ) ) ) ).
fof(t19_tops_3,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_tops_1(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r1_tarski(B,C)
& v4_pre_topc(C,A) )
=> C = u1_struct_0(A) ) ) ) ) ) ).
fof(t20_tops_3,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_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(t21_tops_3,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,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v1_tops_1(B,A)
| v1_tops_1(C,A) )
=> v1_tops_1(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ).
fof(d3_tops_3,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_tops_1(B,A)
<=> k1_tops_1(A,k6_pre_topc(A,B)) = k1_xboole_0 ) ) ) ).
fof(t22_tops_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> v3_tops_1(k1_pre_topc(A),A) ) ).
fof(t23_tops_3,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)))
=> ~ ( v3_tops_1(B,A)
& B = u1_struct_0(A) ) ) ) ).
fof(t24_tops_3,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)))
=> ( v3_tops_1(B,A)
=> v3_tops_1(k6_pre_topc(A,B),A) ) ) ) ).
fof(t25_tops_3,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)))
=> ~ ( v3_tops_1(B,A)
& v1_tops_1(B,A) ) ) ) ).
fof(t26_tops_3,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,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v3_tops_1(B,A)
& r1_tarski(C,B) )
=> v3_tops_1(C,A) ) ) ) ) ).
fof(t27_tops_3,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)))
=> ( v3_tops_1(B,A)
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& r1_tarski(B,C)
& v4_pre_topc(C,A)
& v2_tops_1(C,A) ) ) ) ) ).
fof(t28_tops_3,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)))
=> ( v3_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(t29_tops_3,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,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v3_tops_1(B,A)
| v3_tops_1(C,A) )
=> v3_tops_1(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ).
fof(t30_tops_3,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,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v3_tops_1(B,A)
& v2_tops_1(C,A) )
=> v2_tops_1(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ).
fof(d4_tops_3,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_tops_3(B,A)
<=> k6_pre_topc(A,k1_tops_1(A,B)) = k2_pre_topc(A) ) ) ) ).
fof(d5_tops_3,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_tops_3(B,A)
<=> k6_pre_topc(A,k1_tops_1(A,B)) = u1_struct_0(A) ) ) ) ).
fof(t31_tops_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> v1_tops_3(k2_pre_topc(A),A) ) ).
fof(t32_tops_3,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_tops_3(B,A)
=> v1_tops_3(k1_tops_1(A,B),A) ) ) ) ).
fof(t33_tops_3,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_tops_3(B,A)
=> v1_tops_1(B,A) ) ) ) ).
fof(t34_tops_3,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_tops_3(B,A)
& B = k1_xboole_0 ) ) ) ).
fof(t35_tops_3,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_tops_3(B,A)
<=> v1_tops_1(k1_tops_1(A,B),A) ) ) ) ).
fof(t36_tops_3,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)))
=> ( ( v3_pre_topc(B,A)
& v1_tops_1(B,A) )
=> v1_tops_3(B,A) ) ) ) ).
fof(t37_tops_3,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_tops_3(B,A)
& v2_tops_1(B,A) ) ) ) ).
fof(t38_tops_3,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,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v1_tops_3(B,A)
& r1_tarski(B,C) )
=> v1_tops_3(C,A) ) ) ) ) ).
fof(t39_tops_3,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_tops_3(B,A)
<=> v3_tops_1(k3_subset_1(u1_struct_0(A),B),A) ) ) ) ).
fof(t40_tops_3,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)))
=> ( v3_tops_1(B,A)
<=> v1_tops_3(k3_subset_1(u1_struct_0(A),B),A) ) ) ) ).
fof(t41_tops_3,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_tops_3(B,A)
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& r1_tarski(C,B)
& v3_pre_topc(C,A)
& v1_tops_1(C,A) ) ) ) ) ).
fof(t42_tops_3,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_tops_3(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( C != u1_struct_0(A)
& v4_pre_topc(C,A)
& ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( r1_tarski(C,D)
& D != u1_struct_0(A)
& v4_pre_topc(D,A)
& k4_subset_1(u1_struct_0(A),B,D) = u1_struct_0(A) ) ) ) ) ) ) ) ).
fof(t43_tops_3,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,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v1_tops_3(B,A)
| v1_tops_3(C,A) )
=> v1_tops_3(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ).
fof(t44_tops_3,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,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v1_tops_3(B,A)
& v1_tops_3(C,A) )
=> v1_tops_3(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ).
fof(t45_tops_3,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,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v1_tops_3(B,A)
& v1_tops_1(C,A) )
=> v1_tops_1(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ).
fof(t46_tops_3,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,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v1_tops_1(B,A)
& v3_tops_1(C,A) )
=> v1_tops_1(k6_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ).
fof(t47_tops_3,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,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v1_tops_3(B,A)
& v2_tops_1(C,A) )
=> v1_tops_1(k6_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ).
fof(t48_tops_3,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,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v1_tops_3(B,A)
& v3_tops_1(C,A) )
=> v1_tops_3(k6_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ).
fof(t49_tops_3,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_tops_3(B,A)
& ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( v3_pre_topc(C,A)
& v1_tops_1(C,A)
& v3_tops_1(D,A)
& k4_subset_1(u1_struct_0(A),C,D) = B
& r1_xboole_0(C,D) ) ) ) ) ) ) ).
fof(t50_tops_3,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_tops_3(B,A)
& ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( v3_pre_topc(C,A)
& v1_tops_1(C,A)
& v4_pre_topc(D,A)
& v2_tops_1(D,A)
& k4_subset_1(u1_struct_0(A),C,k5_subset_1(u1_struct_0(A),B,D)) = B
& r1_xboole_0(C,D)
& k4_subset_1(u1_struct_0(A),C,D) = u1_struct_0(A) ) ) ) ) ) ) ).
fof(t51_tops_3,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)))
=> ~ ( v3_tops_1(B,A)
& ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( v4_pre_topc(C,A)
& v2_tops_1(C,A)
& v1_tops_3(D,A)
& k5_subset_1(u1_struct_0(A),C,D) = B
& k4_subset_1(u1_struct_0(A),C,D) = u1_struct_0(A) ) ) ) ) ) ) ).
fof(t52_tops_3,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)))
=> ~ ( v3_tops_1(B,A)
& ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( v4_pre_topc(C,A)
& v2_tops_1(C,A)
& v3_pre_topc(D,A)
& v1_tops_1(D,A)
& k5_subset_1(u1_struct_0(A),C,k4_subset_1(u1_struct_0(A),B,D)) = B
& r1_xboole_0(C,D)
& k4_subset_1(u1_struct_0(A),C,D) = u1_struct_0(A) ) ) ) ) ) ) ).
fof(t53_tops_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( r1_tarski(D,C)
=> r1_tarski(k6_pre_topc(B,D),k6_pre_topc(A,C)) ) ) ) ) ) ).
fof(t54_tops_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( v4_pre_topc(C,A)
& r1_tarski(C,u1_struct_0(B))
& r1_tarski(D,C)
& D = E )
=> k6_pre_topc(A,D) = k6_pre_topc(B,E) ) ) ) ) ) ) ).
fof(t55_tops_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_borsuk_1(B,A)
& m1_pre_topc(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( C = D
=> k6_pre_topc(A,C) = k6_pre_topc(B,D) ) ) ) ) ) ).
fof(t56_tops_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( r1_tarski(C,D)
=> r1_tarski(k1_tops_1(A,C),k1_tops_1(B,D)) ) ) ) ) ) ).
fof(t57_tops_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( v3_pre_topc(C,A)
& r1_tarski(C,u1_struct_0(B))
& r1_tarski(D,C)
& D = E )
=> k1_tops_1(A,D) = k1_tops_1(B,E) ) ) ) ) ) ) ).
fof(t58_tops_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_tsep_1(B,A)
& m1_pre_topc(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( C = D
=> k1_tops_1(A,C) = k1_tops_1(B,D) ) ) ) ) ) ).
fof(t59_tops_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( r1_tarski(C,D)
& v1_tops_1(C,A) )
=> v1_tops_1(D,B) ) ) ) ) ) ).
fof(t60_tops_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( r1_tarski(C,u1_struct_0(B))
& r1_tarski(D,C)
& D = E )
=> ( ( v1_tops_1(C,A)
& v1_tops_1(E,B) )
<=> v1_tops_1(D,A) ) ) ) ) ) ) ) ).
fof(t61_tops_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( r1_tarski(C,D)
& v1_tops_3(C,A) )
=> v1_tops_3(D,B) ) ) ) ) ) ).
fof(t62_tops_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( v3_pre_topc(C,A)
& r1_tarski(C,u1_struct_0(B))
& r1_tarski(D,C)
& D = E )
=> ( ( v1_tops_1(C,A)
& v1_tops_3(E,B) )
<=> v1_tops_3(D,A) ) ) ) ) ) ) ) ).
fof(t63_tops_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_tsep_1(B,A)
& m1_pre_topc(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( D = u1_struct_0(B)
& C = E )
=> ( ( v1_tops_1(D,A)
& v1_tops_3(E,B) )
<=> v1_tops_3(C,A) ) ) ) ) ) ) ) ).
fof(t64_tops_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( r1_tarski(C,u1_struct_0(B))
& r1_tarski(D,C)
& D = E )
=> ( ( v1_tops_3(C,A)
& v1_tops_3(E,B) )
<=> v1_tops_3(D,A) ) ) ) ) ) ) ) ).
fof(t65_tops_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( r1_tarski(C,D)
& v2_tops_1(D,B) )
=> v2_tops_1(C,A) ) ) ) ) ) ).
fof(t66_tops_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( v3_pre_topc(C,A)
& r1_tarski(C,u1_struct_0(B))
& r1_tarski(D,C)
& D = E
& v2_tops_1(D,A) )
=> v2_tops_1(E,B) ) ) ) ) ) ) ).
fof(t67_tops_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_tsep_1(B,A)
& m1_pre_topc(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( C = D
=> ( v2_tops_1(C,A)
<=> v2_tops_1(D,B) ) ) ) ) ) ) ).
fof(t68_tops_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( r1_tarski(C,D)
& v3_tops_1(D,B) )
=> v3_tops_1(C,A) ) ) ) ) ) ).
fof(t69_tops_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( v3_pre_topc(C,A)
& r1_tarski(C,u1_struct_0(B))
& r1_tarski(D,C)
& D = E
& v3_tops_1(D,A) )
=> v3_tops_1(E,B) ) ) ) ) ) ) ).
fof(t70_tops_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_tsep_1(B,A)
& m1_pre_topc(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( C = D
=> ( v3_tops_1(C,A)
<=> v3_tops_1(D,B) ) ) ) ) ) ) ).
fof(t71_tops_3,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_struct_0(B)
=> ( u1_struct_0(A) = u1_struct_0(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)))
=> ( C = D
<=> k3_subset_1(u1_struct_0(A),C) = k3_subset_1(u1_struct_0(B),D) ) ) ) ) ) ) ).
fof(t72_tops_3,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( l1_pre_topc(B)
=> ( ( u1_struct_0(A) = u1_struct_0(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)))
=> ( C = D
=> ( v3_pre_topc(C,A)
<=> v3_pre_topc(D,B) ) ) ) ) )
=> g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) ) ) ) ).
fof(t73_tops_3,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( l1_pre_topc(B)
=> ( ( u1_struct_0(A) = u1_struct_0(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)))
=> ( C = D
=> ( v4_pre_topc(C,A)
<=> v4_pre_topc(D,B) ) ) ) ) )
=> g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) ) ) ) ).
fof(t74_tops_3,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( ( u1_struct_0(A) = u1_struct_0(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)))
=> ( C = D
=> k1_tops_1(A,C) = k1_tops_1(B,D) ) ) ) )
=> g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) ) ) ) ).
fof(t75_tops_3,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( ( u1_struct_0(A) = u1_struct_0(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)))
=> ( C = D
=> k6_pre_topc(A,C) = k6_pre_topc(B,D) ) ) ) )
=> g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) ) ) ) ).
fof(t76_tops_3,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_pre_topc(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)))
=> ( ( C = D
& g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
& v3_pre_topc(C,A) )
=> v3_pre_topc(D,B) ) ) ) ) ) ).
fof(t77_tops_3,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_pre_topc(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)))
=> ( ( C = D
& g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) )
=> k1_tops_1(A,C) = k1_tops_1(B,D) ) ) ) ) ) ).
fof(t78_tops_3,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_pre_topc(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)))
=> ( ( r1_tarski(C,D)
& g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) )
=> r1_tarski(k1_tops_1(A,C),k1_tops_1(B,D)) ) ) ) ) ) ).
fof(t79_tops_3,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_pre_topc(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)))
=> ( ( C = D
& g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
& v4_pre_topc(C,A) )
=> v4_pre_topc(D,B) ) ) ) ) ) ).
fof(t80_tops_3,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_pre_topc(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)))
=> ( ( C = D
& g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) )
=> k6_pre_topc(A,C) = k6_pre_topc(B,D) ) ) ) ) ) ).
fof(t81_tops_3,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_pre_topc(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)))
=> ( ( r1_tarski(C,D)
& g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) )
=> r1_tarski(k6_pre_topc(A,C),k6_pre_topc(B,D)) ) ) ) ) ) ).
fof(t82_tops_3,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_pre_topc(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)))
=> ( ( r1_tarski(D,C)
& g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
& v2_tops_1(C,A) )
=> v2_tops_1(D,B) ) ) ) ) ) ).
fof(t83_tops_3,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_pre_topc(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)))
=> ( ( r1_tarski(C,D)
& g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
& v1_tops_1(C,A) )
=> v1_tops_1(D,B) ) ) ) ) ) ).
fof(t84_tops_3,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_pre_topc(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)))
=> ( ( r1_tarski(D,C)
& g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
& v3_tops_1(C,A) )
=> v3_tops_1(D,B) ) ) ) ) ) ).
fof(t85_tops_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(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)))
=> ( ( r1_tarski(C,D)
& g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
& v1_tops_3(C,A) )
=> v1_tops_3(D,B) ) ) ) ) ) ).
%------------------------------------------------------------------------------