SET007 Axioms: SET007+344.ax
%------------------------------------------------------------------------------
% File : SET007+344 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Completeness of the Lattices of Domains of a Topological Space
% 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 : tdlat_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 122 ( 0 unt; 0 def)
% Number of atoms : 827 ( 100 equ)
% Maximal formula atoms : 15 ( 6 avg)
% Number of connectives : 797 ( 92 ~; 3 |; 293 &)
% ( 23 <=>; 386 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 22 ( 21 usr; 0 prp; 1-3 aty)
% Number of functors : 33 ( 33 usr; 1 con; 0-3 aty)
% Number of variables : 328 ( 312 !; 16 ?)
% 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_tdlat_2,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_tarski(k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,B))),k1_tops_1(A,k6_pre_topc(A,B)))
& r1_tarski(k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,B))),k6_pre_topc(A,k1_tops_1(A,B))) ) ) ) ).
fof(t2_tdlat_2,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_tarski(k6_pre_topc(A,k1_tops_1(A,B)),k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,B))))
& r1_tarski(k1_tops_1(A,k6_pre_topc(A,B)),k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,B)))) ) ) ) ).
fof(t3_tdlat_2,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)
& k6_pre_topc(A,k1_tops_1(A,k5_subset_1(u1_struct_0(A),B,C))) = B )
=> r1_tarski(B,C) ) ) ) ) ).
fof(t4_tdlat_2,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)
& k1_tops_1(A,k6_pre_topc(A,k4_subset_1(u1_struct_0(A),B,C))) = C )
=> r1_tarski(B,C) ) ) ) ) ).
fof(t5_tdlat_2,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_tarski(B,k6_pre_topc(A,k1_tops_1(A,B)))
=> r1_tarski(k4_subset_1(u1_struct_0(A),B,k1_tops_1(A,k6_pre_topc(A,B))),k6_pre_topc(A,k1_tops_1(A,k4_subset_1(u1_struct_0(A),B,k1_tops_1(A,k6_pre_topc(A,B)))))) ) ) ) ).
fof(t6_tdlat_2,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_tarski(k1_tops_1(A,k6_pre_topc(A,B)),B)
=> r1_tarski(k1_tops_1(A,k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,k1_tops_1(A,B))))),k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,k1_tops_1(A,B)))) ) ) ) ).
fof(t8_tdlat_2,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> k3_pcomps_1(A,B) = k3_pcomps_1(A,k3_pcomps_1(A,B)) ) ) ).
fof(t9_tdlat_2,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( B = k1_xboole_0
<=> k3_pcomps_1(A,B) = k1_xboole_0 ) ) ) ).
fof(t10_tdlat_2,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k3_pcomps_1(A,k5_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C)),k5_subset_1(k1_zfmisc_1(u1_struct_0(A)),k3_pcomps_1(A,B),k3_pcomps_1(A,C))) ) ) ) ).
fof(t11_tdlat_2,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k6_subset_1(k1_zfmisc_1(u1_struct_0(A)),k3_pcomps_1(A,B),k3_pcomps_1(A,C)),k3_pcomps_1(A,k6_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C))) ) ) ) ).
fof(t12_tdlat_2,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(C,B)
=> ( r1_tarski(k6_setfam_1(u1_struct_0(A),k3_pcomps_1(A,B)),k6_pre_topc(A,C))
& r1_tarski(k6_pre_topc(A,C),k5_setfam_1(u1_struct_0(A),k3_pcomps_1(A,B))) ) ) ) ) ) ).
fof(t13_tdlat_2,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k6_setfam_1(u1_struct_0(A),B),k6_setfam_1(u1_struct_0(A),k3_pcomps_1(A,B))) ) ) ).
fof(t14_tdlat_2,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k6_pre_topc(A,k6_setfam_1(u1_struct_0(A),B)),k6_setfam_1(u1_struct_0(A),k3_pcomps_1(A,B))) ) ) ).
fof(t15_tdlat_2,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k5_setfam_1(u1_struct_0(A),k3_pcomps_1(A,B)),k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B))) ) ) ).
fof(d1_tdlat_2,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( C = k1_tdlat_2(A,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(D,C)
<=> ? [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
& D = k1_tops_1(A,E)
& r2_hidden(E,B) ) ) ) ) ) ) ) ).
fof(t17_tdlat_2,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> k1_tdlat_2(A,B) = k1_tdlat_2(A,k1_tdlat_2(A,B)) ) ) ).
fof(t18_tdlat_2,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> v1_tops_2(k1_tdlat_2(A,B),A) ) ) ).
fof(t19_tdlat_2,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( B = k1_xboole_0
<=> k1_tdlat_2(A,B) = k1_xboole_0 ) ) ) ).
fof(t20_tdlat_2,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(k1_zfmisc_1(u1_struct_0(A))))
=> ( C = k1_tarski(B)
=> k1_tdlat_2(A,C) = k1_tarski(k1_tops_1(A,B)) ) ) ) ) ).
fof(t21_tdlat_2,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( r1_tarski(B,C)
=> r1_tarski(k1_tdlat_2(A,B),k1_tdlat_2(A,C)) ) ) ) ) ).
fof(t22_tdlat_2,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> k1_tdlat_2(A,k4_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C)) = k4_subset_1(k1_zfmisc_1(u1_struct_0(A)),k1_tdlat_2(A,B),k1_tdlat_2(A,C)) ) ) ) ).
fof(t23_tdlat_2,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k1_tdlat_2(A,k5_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C)),k5_subset_1(k1_zfmisc_1(u1_struct_0(A)),k1_tdlat_2(A,B),k1_tdlat_2(A,C))) ) ) ) ).
fof(t24_tdlat_2,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k6_subset_1(k1_zfmisc_1(u1_struct_0(A)),k1_tdlat_2(A,B),k1_tdlat_2(A,C)),k1_tdlat_2(A,k6_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C))) ) ) ) ).
fof(t25_tdlat_2,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(C,B)
=> ( r1_tarski(k1_tops_1(A,C),k5_setfam_1(u1_struct_0(A),k1_tdlat_2(A,B)))
& r1_tarski(k6_setfam_1(u1_struct_0(A),k1_tdlat_2(A,B)),k1_tops_1(A,C)) ) ) ) ) ) ).
fof(t26_tdlat_2,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k5_setfam_1(u1_struct_0(A),k1_tdlat_2(A,B)),k5_setfam_1(u1_struct_0(A),B)) ) ) ).
fof(t27_tdlat_2,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k6_setfam_1(u1_struct_0(A),k1_tdlat_2(A,B)),k6_setfam_1(u1_struct_0(A),B)) ) ) ).
fof(t28_tdlat_2,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k5_setfam_1(u1_struct_0(A),k1_tdlat_2(A,B)),k1_tops_1(A,k5_setfam_1(u1_struct_0(A),B))) ) ) ).
fof(t29_tdlat_2,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B)),k6_setfam_1(u1_struct_0(A),k1_tdlat_2(A,B))) ) ) ).
fof(t30_tdlat_2,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v1_finset_1(B)
=> k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B)) = k6_setfam_1(u1_struct_0(A),k1_tdlat_2(A,B)) ) ) ) ).
fof(t35_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> k3_pcomps_1(A,k1_tdlat_2(A,k3_pcomps_1(A,k1_tdlat_2(A,B)))) = k3_pcomps_1(A,k1_tdlat_2(A,B)) ) ) ).
fof(t36_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> k1_tdlat_2(A,k3_pcomps_1(A,k1_tdlat_2(A,k3_pcomps_1(A,B)))) = k1_tdlat_2(A,k3_pcomps_1(A,B)) ) ) ).
fof(t37_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k5_setfam_1(u1_struct_0(A),k1_tdlat_2(A,k3_pcomps_1(A,B))),k5_setfam_1(u1_struct_0(A),k3_pcomps_1(A,k1_tdlat_2(A,k3_pcomps_1(A,B))))) ) ) ).
fof(t38_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k6_setfam_1(u1_struct_0(A),k1_tdlat_2(A,k3_pcomps_1(A,B))),k6_setfam_1(u1_struct_0(A),k3_pcomps_1(A,k1_tdlat_2(A,k3_pcomps_1(A,B))))) ) ) ).
fof(t39_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k5_setfam_1(u1_struct_0(A),k3_pcomps_1(A,k1_tdlat_2(A,B))),k5_setfam_1(u1_struct_0(A),k3_pcomps_1(A,k1_tdlat_2(A,k3_pcomps_1(A,B))))) ) ) ).
fof(t40_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k6_setfam_1(u1_struct_0(A),k3_pcomps_1(A,k1_tdlat_2(A,B))),k6_setfam_1(u1_struct_0(A),k3_pcomps_1(A,k1_tdlat_2(A,k3_pcomps_1(A,B))))) ) ) ).
fof(t41_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k5_setfam_1(u1_struct_0(A),k1_tdlat_2(A,k3_pcomps_1(A,k1_tdlat_2(A,B)))),k5_setfam_1(u1_struct_0(A),k1_tdlat_2(A,k3_pcomps_1(A,B)))) ) ) ).
fof(t42_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k6_setfam_1(u1_struct_0(A),k1_tdlat_2(A,k3_pcomps_1(A,k1_tdlat_2(A,B)))),k6_setfam_1(u1_struct_0(A),k1_tdlat_2(A,k3_pcomps_1(A,B)))) ) ) ).
fof(t43_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k5_setfam_1(u1_struct_0(A),k1_tdlat_2(A,k3_pcomps_1(A,k1_tdlat_2(A,B)))),k5_setfam_1(u1_struct_0(A),k3_pcomps_1(A,k1_tdlat_2(A,B)))) ) ) ).
fof(t44_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k6_setfam_1(u1_struct_0(A),k1_tdlat_2(A,k3_pcomps_1(A,k1_tdlat_2(A,B)))),k6_setfam_1(u1_struct_0(A),k3_pcomps_1(A,k1_tdlat_2(A,B)))) ) ) ).
fof(t45_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k5_setfam_1(u1_struct_0(A),k3_pcomps_1(A,k1_tdlat_2(A,k3_pcomps_1(A,B)))),k5_setfam_1(u1_struct_0(A),k3_pcomps_1(A,B))) ) ) ).
fof(t46_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k6_setfam_1(u1_struct_0(A),k3_pcomps_1(A,k1_tdlat_2(A,k3_pcomps_1(A,B)))),k6_setfam_1(u1_struct_0(A),k3_pcomps_1(A,B))) ) ) ).
fof(t47_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k5_setfam_1(u1_struct_0(A),k1_tdlat_2(A,B)),k5_setfam_1(u1_struct_0(A),k1_tdlat_2(A,k3_pcomps_1(A,k1_tdlat_2(A,B))))) ) ) ).
fof(t48_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k6_setfam_1(u1_struct_0(A),k1_tdlat_2(A,B)),k6_setfam_1(u1_struct_0(A),k1_tdlat_2(A,k3_pcomps_1(A,k1_tdlat_2(A,B))))) ) ) ).
fof(t49_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k5_setfam_1(u1_struct_0(A),k3_pcomps_1(A,k1_tdlat_2(A,B))),k6_pre_topc(A,k1_tops_1(A,k5_setfam_1(u1_struct_0(A),B)))) ) ) ).
fof(t50_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k6_pre_topc(A,k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B))),k6_setfam_1(u1_struct_0(A),k3_pcomps_1(A,k1_tdlat_2(A,B)))) ) ) ).
fof(t51_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k5_setfam_1(u1_struct_0(A),k1_tdlat_2(A,k3_pcomps_1(A,B))),k1_tops_1(A,k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B)))) ) ) ).
fof(t52_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k1_tops_1(A,k6_pre_topc(A,k6_setfam_1(u1_struct_0(A),B))),k6_setfam_1(u1_struct_0(A),k1_tdlat_2(A,k3_pcomps_1(A,B)))) ) ) ).
fof(t53_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k5_setfam_1(u1_struct_0(A),k3_pcomps_1(A,k1_tdlat_2(A,k3_pcomps_1(A,B)))),k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B))))) ) ) ).
fof(t54_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,k6_setfam_1(u1_struct_0(A),B)))),k6_setfam_1(u1_struct_0(A),k3_pcomps_1(A,k1_tdlat_2(A,k3_pcomps_1(A,B))))) ) ) ).
fof(t55_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k5_setfam_1(u1_struct_0(A),k1_tdlat_2(A,k3_pcomps_1(A,k1_tdlat_2(A,B)))),k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,k5_setfam_1(u1_struct_0(A),B))))) ) ) ).
fof(t56_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B)))),k6_setfam_1(u1_struct_0(A),k1_tdlat_2(A,k3_pcomps_1(A,k1_tdlat_2(A,B))))) ) ) ).
fof(t57_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(C,B)
=> r1_tarski(C,k6_pre_topc(A,k1_tops_1(A,C))) ) )
=> ( r1_tarski(k5_setfam_1(u1_struct_0(A),B),k6_pre_topc(A,k1_tops_1(A,k5_setfam_1(u1_struct_0(A),B))))
& k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B)) = k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B)))) ) ) ) ) ).
fof(t58_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(C,B)
=> r1_tarski(k1_tops_1(A,k6_pre_topc(A,C)),C) ) )
=> ( r1_tarski(k1_tops_1(A,k6_pre_topc(A,k6_setfam_1(u1_struct_0(A),B))),k6_setfam_1(u1_struct_0(A),B))
& k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B)))) = k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B)) ) ) ) ) ).
fof(t59_tdlat_2,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)))
=> ( v4_tops_1(C,A)
=> ( k4_subset_1(u1_struct_0(A),k1_tops_1(A,k6_pre_topc(A,k4_subset_1(u1_struct_0(A),B,C))),k4_subset_1(u1_struct_0(A),B,C)) = C
<=> r1_tarski(B,C) ) ) ) ) ) ).
fof(t60_tdlat_2,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)))
=> ( v4_tops_1(B,A)
=> ( k5_subset_1(u1_struct_0(A),k6_pre_topc(A,k1_tops_1(A,k5_subset_1(u1_struct_0(A),B,C))),k5_subset_1(u1_struct_0(A),B,C)) = B
<=> r1_tarski(B,C) ) ) ) ) ) ).
fof(t61_tdlat_2,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)))
=> ( ( v5_tops_1(B,A)
& v5_tops_1(C,A) )
=> ( r1_tarski(k1_tops_1(A,B),k1_tops_1(A,C))
<=> r1_tarski(B,C) ) ) ) ) ) ).
fof(t62_tdlat_2,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)))
=> ( ( v6_tops_1(B,A)
& v6_tops_1(C,A) )
=> ( r1_tarski(k6_pre_topc(A,B),k6_pre_topc(A,C))
<=> r1_tarski(B,C) ) ) ) ) ) ).
fof(t63_tdlat_2,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)))
=> ( ( v5_tops_1(B,A)
& r1_tarski(B,C) )
=> k6_pre_topc(A,k1_tops_1(A,k5_subset_1(u1_struct_0(A),B,C))) = B ) ) ) ) ).
fof(t64_tdlat_2,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)))
=> ( ( v6_tops_1(C,A)
& r1_tarski(B,C) )
=> k1_tops_1(A,k6_pre_topc(A,k4_subset_1(u1_struct_0(A),B,C))) = C ) ) ) ) ).
fof(d2_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v1_tdlat_2(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(C,B)
=> v4_tops_1(C,A) ) ) ) ) ) ).
fof(t65_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( r1_tarski(B,k1_tdlat_1(A))
<=> v1_tdlat_2(B,A) ) ) ) ).
fof(t66_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v1_tdlat_2(B,A)
=> ( r1_tarski(k5_setfam_1(u1_struct_0(A),B),k6_pre_topc(A,k1_tops_1(A,k5_setfam_1(u1_struct_0(A),B))))
& k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B)) = k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B)))) ) ) ) ) ).
fof(t67_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v1_tdlat_2(B,A)
=> ( r1_tarski(k1_tops_1(A,k6_pre_topc(A,k6_setfam_1(u1_struct_0(A),B))),k6_setfam_1(u1_struct_0(A),B))
& k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B)))) = k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B)) ) ) ) ) ).
fof(t68_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v1_tdlat_2(B,A)
=> v4_tops_1(k4_subset_1(u1_struct_0(A),k5_setfam_1(u1_struct_0(A),B),k1_tops_1(A,k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B)))),A) ) ) ) ).
fof(t69_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(C,B)
=> r1_tarski(C,k4_subset_1(u1_struct_0(A),k5_setfam_1(u1_struct_0(A),B),k1_tops_1(A,k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B))))) ) )
& ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v4_tops_1(C,A)
& ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(D,B)
=> r1_tarski(D,C) ) ) )
=> r1_tarski(k4_subset_1(u1_struct_0(A),k5_setfam_1(u1_struct_0(A),B),k1_tops_1(A,k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B)))),C) ) ) ) ) ) ).
fof(t70_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v1_tdlat_2(B,A)
=> v4_tops_1(k5_subset_1(u1_struct_0(A),k6_setfam_1(u1_struct_0(A),B),k6_pre_topc(A,k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B)))),A) ) ) ) ).
fof(t71_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(C,B)
=> r1_tarski(k5_subset_1(u1_struct_0(A),k6_setfam_1(u1_struct_0(A),B),k6_pre_topc(A,k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B)))),C) ) )
& ( B = k1_xboole_0
| ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v4_tops_1(C,A)
& ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(D,B)
=> r1_tarski(C,D) ) ) )
=> r1_tarski(C,k5_subset_1(u1_struct_0(A),k6_setfam_1(u1_struct_0(A),B),k6_pre_topc(A,k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B))))) ) ) ) ) ) ) ).
fof(d3_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v2_tdlat_2(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(C,B)
=> v5_tops_1(C,A) ) ) ) ) ) ).
fof(t72_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( r1_tarski(B,k5_tdlat_1(A))
<=> v2_tdlat_2(B,A) ) ) ) ).
fof(t73_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v2_tdlat_2(B,A)
=> v1_tdlat_2(B,A) ) ) ) ).
fof(t74_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v2_tdlat_2(B,A)
=> v2_tops_2(B,A) ) ) ) ).
fof(t75_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v1_tdlat_2(B,A)
=> v2_tdlat_2(k3_pcomps_1(A,B),A) ) ) ) ).
fof(t76_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v2_tdlat_2(B,A)
=> ( v5_tops_1(k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B)),A)
& v5_tops_1(k6_pre_topc(A,k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B))),A) ) ) ) ) ).
fof(t77_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(C,B)
=> r1_tarski(C,k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B))) ) )
& ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v5_tops_1(C,A)
& ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(D,B)
=> r1_tarski(D,C) ) ) )
=> r1_tarski(k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B)),C) ) ) ) ) ) ).
fof(t78_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( ( v2_tops_2(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(C,B)
=> r1_tarski(k6_pre_topc(A,k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B))),C) ) ) )
& ( B = k1_xboole_0
| ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v5_tops_1(C,A)
& ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(D,B)
=> r1_tarski(C,D) ) ) )
=> r1_tarski(C,k6_pre_topc(A,k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B)))) ) ) ) ) ) ) ).
fof(d4_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v3_tdlat_2(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(C,B)
=> v6_tops_1(C,A) ) ) ) ) ) ).
fof(t79_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( r1_tarski(B,k9_tdlat_1(A))
<=> v3_tdlat_2(B,A) ) ) ) ).
fof(t80_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v3_tdlat_2(B,A)
=> v1_tdlat_2(B,A) ) ) ) ).
fof(t81_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v3_tdlat_2(B,A)
=> v1_tops_2(B,A) ) ) ) ).
fof(t82_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v1_tdlat_2(B,A)
=> v3_tdlat_2(k1_tdlat_2(A,B),A) ) ) ) ).
fof(t83_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v3_tdlat_2(B,A)
=> ( v6_tops_1(k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B)),A)
& v6_tops_1(k1_tops_1(A,k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B))),A) ) ) ) ) ).
fof(t84_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( ( v1_tops_2(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(C,B)
=> r1_tarski(C,k1_tops_1(A,k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B)))) ) ) )
& ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v6_tops_1(C,A)
& ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(D,B)
=> r1_tarski(D,C) ) ) )
=> r1_tarski(k1_tops_1(A,k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B))),C) ) ) ) ) ) ).
fof(t85_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(C,B)
=> r1_tarski(k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B)),C) ) )
& ( B = k1_xboole_0
| ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v6_tops_1(C,A)
& ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(D,B)
=> r1_tarski(C,D) ) ) )
=> r1_tarski(C,k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B))) ) ) ) ) ) ) ).
fof(t86_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> u1_struct_0(k4_tdlat_1(A)) = k1_tdlat_1(A) ) ).
fof(t87_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k4_tdlat_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k4_tdlat_1(A)))
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k1_tdlat_1(A))
=> ! [E] :
( m2_subset_1(E,k1_zfmisc_1(u1_struct_0(A)),k1_tdlat_1(A))
=> ( ( B = D
& C = E )
=> ( k1_lattices(k4_tdlat_1(A),B,C) = k4_subset_1(u1_struct_0(A),k1_tops_1(A,k6_pre_topc(A,k4_subset_1(u1_struct_0(A),D,E))),k4_subset_1(u1_struct_0(A),D,E))
& k2_lattices(k4_tdlat_1(A),B,C) = k5_subset_1(u1_struct_0(A),k6_pre_topc(A,k1_tops_1(A,k5_subset_1(u1_struct_0(A),D,E))),k5_subset_1(u1_struct_0(A),D,E)) ) ) ) ) ) ) ) ).
fof(t88_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( k5_lattices(k4_tdlat_1(A)) = k1_pre_topc(A)
& k6_lattices(k4_tdlat_1(A)) = k2_pre_topc(A) ) ) ).
fof(t89_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k4_tdlat_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k4_tdlat_1(A)))
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k1_tdlat_1(A))
=> ! [E] :
( m2_subset_1(E,k1_zfmisc_1(u1_struct_0(A)),k1_tdlat_1(A))
=> ( ( B = D
& C = E )
=> ( r1_lattices(k4_tdlat_1(A),B,C)
<=> r1_tarski(D,E) ) ) ) ) ) ) ) ).
fof(t90_tdlat_2,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(k4_tdlat_1(A))))
=> ? [C] :
( m1_subset_1(C,u1_struct_0(k4_tdlat_1(A)))
& r4_lattice3(k4_tdlat_1(A),C,B)
& ! [D] :
( m1_subset_1(D,u1_struct_0(k4_tdlat_1(A)))
=> ( r4_lattice3(k4_tdlat_1(A),D,B)
=> r1_lattices(k4_tdlat_1(A),C,D) ) ) ) ) ) ).
fof(t91_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> v4_lattice3(k4_tdlat_1(A)) ) ).
fof(t92_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v1_tdlat_2(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_tdlat_1(A))))
=> ( C = B
=> k15_lattice3(k4_tdlat_1(A),C) = k4_subset_1(u1_struct_0(A),k5_setfam_1(u1_struct_0(A),B),k1_tops_1(A,k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B)))) ) ) ) ) ) ).
fof(t93_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v1_tdlat_2(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_tdlat_1(A))))
=> ( C = B
=> ( ( C != k1_xboole_0
=> k16_lattice3(k4_tdlat_1(A),C) = k5_subset_1(u1_struct_0(A),k6_setfam_1(u1_struct_0(A),B),k6_pre_topc(A,k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B)))) )
& ( C = k1_xboole_0
=> k16_lattice3(k4_tdlat_1(A),C) = k2_pre_topc(A) ) ) ) ) ) ) ) ).
fof(t94_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> u1_struct_0(k8_tdlat_1(A)) = k5_tdlat_1(A) ) ).
fof(t95_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k8_tdlat_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k8_tdlat_1(A)))
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k5_tdlat_1(A))
=> ! [E] :
( m2_subset_1(E,k1_zfmisc_1(u1_struct_0(A)),k5_tdlat_1(A))
=> ( ( B = D
& C = E )
=> ( k1_lattices(k8_tdlat_1(A),B,C) = k4_subset_1(u1_struct_0(A),D,E)
& k2_lattices(k8_tdlat_1(A),B,C) = k6_pre_topc(A,k1_tops_1(A,k5_subset_1(u1_struct_0(A),D,E))) ) ) ) ) ) ) ) ).
fof(t96_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( k5_lattices(k8_tdlat_1(A)) = k1_pre_topc(A)
& k6_lattices(k8_tdlat_1(A)) = k2_pre_topc(A) ) ) ).
fof(t97_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k8_tdlat_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k8_tdlat_1(A)))
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k5_tdlat_1(A))
=> ! [E] :
( m2_subset_1(E,k1_zfmisc_1(u1_struct_0(A)),k5_tdlat_1(A))
=> ( ( B = D
& C = E )
=> ( r1_lattices(k8_tdlat_1(A),B,C)
<=> r1_tarski(D,E) ) ) ) ) ) ) ) ).
fof(t98_tdlat_2,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(k8_tdlat_1(A))))
=> ? [C] :
( m1_subset_1(C,u1_struct_0(k8_tdlat_1(A)))
& r4_lattice3(k8_tdlat_1(A),C,B)
& ! [D] :
( m1_subset_1(D,u1_struct_0(k8_tdlat_1(A)))
=> ( r4_lattice3(k8_tdlat_1(A),D,B)
=> r1_lattices(k8_tdlat_1(A),C,D) ) ) ) ) ) ).
fof(t99_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> v4_lattice3(k8_tdlat_1(A)) ) ).
fof(t100_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v2_tdlat_2(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k8_tdlat_1(A))))
=> ( C = B
=> k15_lattice3(k8_tdlat_1(A),C) = k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B)) ) ) ) ) ) ).
fof(t101_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v2_tdlat_2(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k8_tdlat_1(A))))
=> ( C = B
=> ( ( C != k1_xboole_0
=> k16_lattice3(k8_tdlat_1(A),C) = k6_pre_topc(A,k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B))) )
& ( C = k1_xboole_0
=> k16_lattice3(k8_tdlat_1(A),C) = k2_pre_topc(A) ) ) ) ) ) ) ) ).
fof(t102_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v2_tdlat_2(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_tdlat_1(A))))
=> ( C = B
=> ( ( C != k1_xboole_0
=> k16_lattice3(k4_tdlat_1(A),C) = k6_pre_topc(A,k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B))) )
& ( C = k1_xboole_0
=> k16_lattice3(k4_tdlat_1(A),C) = k2_pre_topc(A) ) ) ) ) ) ) ) ).
fof(t103_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> u1_struct_0(k12_tdlat_1(A)) = k9_tdlat_1(A) ) ).
fof(t104_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k12_tdlat_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k12_tdlat_1(A)))
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k9_tdlat_1(A))
=> ! [E] :
( m2_subset_1(E,k1_zfmisc_1(u1_struct_0(A)),k9_tdlat_1(A))
=> ( ( B = D
& C = E )
=> ( k1_lattices(k12_tdlat_1(A),B,C) = k1_tops_1(A,k6_pre_topc(A,k4_subset_1(u1_struct_0(A),D,E)))
& k2_lattices(k12_tdlat_1(A),B,C) = k5_subset_1(u1_struct_0(A),D,E) ) ) ) ) ) ) ) ).
fof(t105_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( k5_lattices(k12_tdlat_1(A)) = k1_pre_topc(A)
& k6_lattices(k12_tdlat_1(A)) = k2_pre_topc(A) ) ) ).
fof(t106_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k12_tdlat_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k12_tdlat_1(A)))
=> ! [D] :
( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k9_tdlat_1(A))
=> ! [E] :
( m2_subset_1(E,k1_zfmisc_1(u1_struct_0(A)),k9_tdlat_1(A))
=> ( ( B = D
& C = E )
=> ( r1_lattices(k12_tdlat_1(A),B,C)
<=> r1_tarski(D,E) ) ) ) ) ) ) ) ).
fof(t107_tdlat_2,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(k12_tdlat_1(A))))
=> ? [C] :
( m1_subset_1(C,u1_struct_0(k12_tdlat_1(A)))
& r4_lattice3(k12_tdlat_1(A),C,B)
& ! [D] :
( m1_subset_1(D,u1_struct_0(k12_tdlat_1(A)))
=> ( r4_lattice3(k12_tdlat_1(A),D,B)
=> r1_lattices(k12_tdlat_1(A),C,D) ) ) ) ) ) ).
fof(t108_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> v4_lattice3(k12_tdlat_1(A)) ) ).
fof(t109_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v3_tdlat_2(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k12_tdlat_1(A))))
=> ( C = B
=> k15_lattice3(k12_tdlat_1(A),C) = k1_tops_1(A,k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B))) ) ) ) ) ) ).
fof(t110_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v3_tdlat_2(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k12_tdlat_1(A))))
=> ( C = B
=> ( ( C != k1_xboole_0
=> k16_lattice3(k12_tdlat_1(A),C) = k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B)) )
& ( C = k1_xboole_0
=> k16_lattice3(k12_tdlat_1(A),C) = k2_pre_topc(A) ) ) ) ) ) ) ) ).
fof(t111_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v3_tdlat_2(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_tdlat_1(A))))
=> ( C = B
=> k15_lattice3(k4_tdlat_1(A),C) = k1_tops_1(A,k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B))) ) ) ) ) ) ).
fof(dt_k1_tdlat_2,axiom,
! [A,B] :
( ( v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) )
=> m1_subset_1(k1_tdlat_2(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(t7_tdlat_2,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> k3_pcomps_1(A,B) = a_2_0_tdlat_2(A,B) ) ) ).
fof(t16_tdlat_2,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> k1_tdlat_2(A,B) = a_2_1_tdlat_2(A,B) ) ) ).
fof(t31_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> k3_pcomps_1(A,k1_tdlat_2(A,B)) = a_2_2_tdlat_2(A,B) ) ) ).
fof(t32_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> k1_tdlat_2(A,k3_pcomps_1(A,B)) = a_2_3_tdlat_2(A,B) ) ) ).
fof(t33_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> k3_pcomps_1(A,k1_tdlat_2(A,k3_pcomps_1(A,B))) = a_2_4_tdlat_2(A,B) ) ) ).
fof(t34_tdlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> k1_tdlat_2(A,k3_pcomps_1(A,k1_tdlat_2(A,B))) = a_2_5_tdlat_2(A,B) ) ) ).
fof(fraenkel_a_2_0_tdlat_2,axiom,
! [A,B,C] :
( ( v2_pre_topc(B)
& l1_pre_topc(B)
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) )
=> ( r2_hidden(A,a_2_0_tdlat_2(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
& A = D
& ? [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
& D = k6_pre_topc(B,E)
& r2_hidden(E,C) ) ) ) ) ).
fof(fraenkel_a_2_1_tdlat_2,axiom,
! [A,B,C] :
( ( v2_pre_topc(B)
& l1_pre_topc(B)
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) )
=> ( r2_hidden(A,a_2_1_tdlat_2(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
& A = D
& ? [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
& D = k1_tops_1(B,E)
& r2_hidden(E,C) ) ) ) ) ).
fof(fraenkel_a_2_2_tdlat_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) )
=> ( r2_hidden(A,a_2_2_tdlat_2(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
& A = D
& ? [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
& D = k6_pre_topc(B,k1_tops_1(B,E))
& r2_hidden(E,C) ) ) ) ) ).
fof(fraenkel_a_2_3_tdlat_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) )
=> ( r2_hidden(A,a_2_3_tdlat_2(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
& A = D
& ? [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
& D = k1_tops_1(B,k6_pre_topc(B,E))
& r2_hidden(E,C) ) ) ) ) ).
fof(fraenkel_a_2_4_tdlat_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) )
=> ( r2_hidden(A,a_2_4_tdlat_2(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
& A = D
& ? [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
& D = k6_pre_topc(B,k1_tops_1(B,k6_pre_topc(B,E)))
& r2_hidden(E,C) ) ) ) ) ).
fof(fraenkel_a_2_5_tdlat_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) )
=> ( r2_hidden(A,a_2_5_tdlat_2(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
& A = D
& ? [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
& D = k1_tops_1(B,k6_pre_topc(B,k1_tops_1(B,E)))
& r2_hidden(E,C) ) ) ) ) ).
%------------------------------------------------------------------------------