SET007 Axioms: SET007+572.ax
%------------------------------------------------------------------------------
% File : SET007+572 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Introduction to Meet-Continuous Topological Lattices
% 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 : yellow13 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 69 ( 0 unt; 0 def)
% Number of atoms : 461 ( 6 equ)
% Maximal formula atoms : 33 ( 6 avg)
% Number of connectives : 449 ( 57 ~; 0 |; 252 &)
% ( 10 <=>; 130 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 68 ( 67 usr; 0 prp; 1-4 aty)
% Number of functors : 20 ( 20 usr; 0 con; 1-4 aty)
% Number of variables : 145 ( 130 !; 15 ?)
% 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_yellow13,axiom,
! [A] :
( ( v6_group_1(A)
& l1_struct_0(A) )
=> v1_finset_1(u1_struct_0(A)) ) ).
fof(fc2_yellow13,axiom,
! [A] :
( ( v3_realset2(A)
& l1_struct_0(A) )
=> v1_realset1(u1_struct_0(A)) ) ).
fof(cc1_yellow13,axiom,
! [A] :
( v1_realset1(A)
=> v1_finset_1(A) ) ).
fof(cc2_yellow13,axiom,
! [A] :
( l1_struct_0(A)
=> ( v3_realset2(A)
=> v6_group_1(A) ) ) ).
fof(cc3_yellow13,axiom,
! [A] :
( l1_struct_0(A)
=> ( ~ v3_realset2(A)
=> ~ v3_struct_0(A) ) ) ).
fof(rc1_yellow13,axiom,
? [A] :
( l1_struct_0(A)
& v1_struct_0(A)
& ~ v3_struct_0(A)
& v6_group_1(A)
& v3_realset2(A) ) ).
fof(rc2_yellow13,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v1_orders_2(A)
& v6_group_1(A)
& v3_realset2(A) ) ).
fof(rc3_yellow13,axiom,
? [A] :
( l1_waybel_9(A)
& ~ v3_struct_0(A)
& v1_waybel_9(A)
& v6_group_1(A)
& v3_realset2(A) ) ).
fof(cc4_yellow13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_urysohn1(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_finset_1(B)
=> v4_pre_topc(B,A) ) ) ) ).
fof(fc3_yellow13,axiom,
! [A] :
( ( v2_compts_1(A)
& l1_pre_topc(A) )
=> ( v1_tops_1(k2_pre_topc(A),A)
& v6_compts_1(k2_pre_topc(A),A) ) ) ).
fof(rc4_yellow13,axiom,
? [A] :
( l1_pre_topc(A)
& ~ v3_struct_0(A)
& v1_pre_topc(A)
& v2_pre_topc(A)
& v1_tdlat_3(A)
& v2_tdlat_3(A)
& v3_tdlat_3(A)
& v4_tdlat_3(A)
& v5_tdlat_3(A)
& v6_group_1(A)
& v3_realset2(A) ) ).
fof(cc5_yellow13,axiom,
! [A] :
( l1_pre_topc(A)
=> ( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_urysohn1(A)
& v6_group_1(A) )
=> ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_tdlat_3(A)
& v3_tdlat_3(A)
& v4_tdlat_3(A)
& v5_tdlat_3(A) ) ) ) ).
fof(cc6_yellow13,axiom,
! [A] :
( l1_pre_topc(A)
=> ( ( v2_pre_topc(A)
& v6_group_1(A) )
=> ( v2_pre_topc(A)
& v2_compts_1(A) ) ) ) ).
fof(cc7_yellow13,axiom,
! [A] :
( l1_pre_topc(A)
=> ( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_tdlat_3(A) )
=> ( v2_pre_topc(A)
& v1_urysohn1(A)
& v3_compts_1(A)
& v4_compts_1(A)
& v5_compts_1(A) ) ) ) ).
fof(cc8_yellow13,axiom,
! [A] :
( l1_pre_topc(A)
=> ( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_urysohn1(A)
& v5_compts_1(A) )
=> ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v4_compts_1(A) ) ) ) ).
fof(cc9_yellow13,axiom,
! [A] :
( l1_pre_topc(A)
=> ( ( v2_pre_topc(A)
& v1_urysohn1(A)
& v4_compts_1(A) )
=> ( v2_pre_topc(A)
& v3_compts_1(A) ) ) ) ).
fof(cc10_yellow13,axiom,
! [A] :
( l1_pre_topc(A)
=> ( ( v2_pre_topc(A)
& v3_compts_1(A) )
=> ( v2_pre_topc(A)
& v1_urysohn1(A) ) ) ) ).
fof(cc11_yellow13,axiom,
! [A] :
( l1_pre_topc(A)
=> ( ( v2_pre_topc(A)
& v1_urysohn1(A) )
=> ( v2_pre_topc(A)
& v2_t_0topsp(A) ) ) ) ).
fof(fc4_yellow13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ( v1_relat_1(k4_yellow_2(A))
& v1_funct_1(k4_yellow_2(A))
& v2_funct_1(k4_yellow_2(A))
& v1_funct_2(k4_yellow_2(A),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
& v5_orders_3(k4_yellow_2(A),A,k2_yellow_1(k8_waybel_0(A))) ) ) ).
fof(fc5_yellow13,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v6_group_1(A)
& l1_orders_2(A) )
=> ( v1_relat_1(k3_yellow_2(A))
& v1_funct_1(k3_yellow_2(A))
& v2_funct_1(k3_yellow_2(A))
& v1_funct_2(k3_yellow_2(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A))
& v5_orders_3(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A) ) ) ).
fof(fc6_yellow13,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( ~ v1_xboole_0(k4_waybel_1(A,B))
& v1_relat_1(k4_waybel_1(A,B))
& v1_funct_1(k4_waybel_1(A,B))
& v1_funct_2(k4_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A))
& v1_partfun1(k4_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A))
& v19_waybel_0(k4_waybel_1(A,B),A,A)
& v5_orders_3(k4_waybel_1(A,B),A,A) ) ) ).
fof(cc12_yellow13,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ! [C] :
( m1_yellow13(C,A,B)
=> ~ v1_xboole_0(C) ) ) ).
fof(rc5_yellow13,axiom,
! [A,B] :
( ( l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ? [C] :
( m1_yellow13(C,A,B)
& ~ v1_xboole_0(C) ) ) ).
fof(rc6_yellow13,axiom,
! [A,B] :
( ( l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ? [C] :
( m1_yellow13(C,A,B)
& v1_yellow13(C,A,B) ) ) ).
fof(rc7_yellow13,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ? [C] :
( m1_yellow13(C,A,B)
& ~ v1_xboole_0(C)
& v1_yellow13(C,A,B) ) ) ).
fof(cc13_yellow13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m2_yellow13(B,A)
=> ~ v1_xboole_0(B) ) ) ).
fof(rc8_yellow13,axiom,
! [A] :
( l1_pre_topc(A)
=> ? [B] :
( m2_yellow13(B,A)
& ~ v1_xboole_0(B) ) ) ).
fof(cc14_yellow13,axiom,
! [A] :
( l1_waybel_9(A)
=> ( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_orders_2(A)
& v3_realset2(A) )
=> ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_yellow13(A) ) ) ) ).
fof(rc9_yellow13,axiom,
? [A] :
( l1_waybel_9(A)
& ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_tdlat_3(A)
& v2_tdlat_3(A)
& v3_tdlat_3(A)
& v4_tdlat_3(A)
& v5_tdlat_3(A)
& v2_t_0topsp(A)
& v1_urysohn1(A)
& v3_yellow_8(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v16_waybel_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v2_waybel_3(A)
& v3_waybel_3(A)
& v6_waybel_3(A)
& v2_compts_1(A)
& v3_compts_1(A)
& v4_compts_1(A)
& v5_compts_1(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v6_group_1(A)
& v3_realset2(A)
& v2_yellow13(A) ) ).
fof(fc7_yellow13,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_yellow13(A)
& l1_waybel_9(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v1_relat_1(k4_waybel_1(A,B))
& v1_funct_1(k4_waybel_1(A,B))
& v1_funct_2(k4_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A))
& v5_pre_topc(k4_waybel_1(A,B),A,A) ) ) ).
fof(t1_yellow13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_urysohn1(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v4_pre_topc(B,A) ) ) ).
fof(t2_yellow13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_tdlat_3(A)
& l1_pre_topc(A) )
=> v5_compts_1(A) ) ).
fof(t3_yellow13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_tdlat_3(A)
& l1_pre_topc(A) )
=> v4_compts_1(A) ) ).
fof(t4_yellow13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_tdlat_3(A)
& l1_pre_topc(A) )
=> v3_compts_1(A) ) ).
fof(t5_yellow13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_tdlat_3(A)
& l1_pre_topc(A) )
=> v1_urysohn1(A) ) ).
fof(t6_yellow13,axiom,
! [A] :
( ( v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> r1_tarski(k4_waybel_0(B,k4_pre_topc(A,B,C,D)),k4_waybel_0(B,k4_pre_topc(A,B,C,k4_waybel_0(A,D)))) ) ) ) ) ).
fof(t7_yellow13,axiom,
! [A] :
( ( v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( v5_orders_3(C,A,B)
=> k4_waybel_0(B,k4_pre_topc(A,B,C,D)) = k4_waybel_0(B,k4_pre_topc(A,B,C,k4_waybel_0(A,D))) ) ) ) ) ) ).
fof(t8_yellow13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> v2_funct_1(k4_yellow_2(A)) ) ).
fof(t9_yellow13,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v6_group_1(A)
& l1_orders_2(A) )
=> v2_funct_1(k3_yellow_2(A)) ) ).
fof(t10_yellow13,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v6_group_1(A)
& l1_orders_2(A) )
=> r5_waybel_1(A,k2_yellow_1(k8_waybel_0(A))) ) ).
fof(t11_yellow13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> r3_waybel_0(A,A,k4_waybel_1(A,B),C) ) ) ) ).
fof(t12_yellow13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> v19_waybel_0(k4_waybel_1(A,B),A,A) ) ) ).
fof(t13_yellow13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> m1_yellow_8(k1_tarski(u1_struct_0(A)),A,B) ) ) ).
fof(t14_yellow13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_yellow_8(C,A,B)
=> C = k1_tarski(u1_struct_0(A)) ) ) ) ).
fof(t16_yellow13,axiom,
! [A] :
( ( ~ v3_struct_0(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_yellow_8(D,A,C)
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( r2_hidden(E,D)
& r1_xboole_0(B,E) ) ) ) ) ) ) ) ).
fof(t17_yellow13,axiom,
! [A] :
( ( ~ v3_struct_0(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_yellow_8(D,A,C)
& ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( r2_hidden(E,D)
& r1_xboole_0(B,E) ) ) ) ) ) ) ) ).
fof(d1_yellow13,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( m1_yellow13(C,A,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( r2_hidden(B,k1_tops_1(A,D))
& ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( r2_hidden(E,C)
& r2_hidden(B,k1_tops_1(A,E))
& r1_tarski(E,D) ) ) ) ) ) ) ) ) ).
fof(d2_yellow13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( m1_yellow13(C,A,B)
<=> ! [D] :
( m1_connsp_2(D,A,B)
=> ? [E] :
( m1_connsp_2(E,A,B)
& r2_hidden(E,C)
& r1_tarski(E,D) ) ) ) ) ) ) ).
fof(t18_yellow13,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> m1_yellow13(k1_zfmisc_1(u1_struct_0(A)),A,B) ) ) ).
fof(t19_yellow13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_yellow13(C,A,B)
=> ~ v1_xboole_0(C) ) ) ) ).
fof(d3_yellow13,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_yellow13(C,A,B)
=> ( v1_yellow13(C,A,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(D,C)
<=> r2_hidden(B,k1_tops_1(A,D)) ) ) ) ) ) ) ).
fof(t21_yellow13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v1_yellow13(k1_tarski(u1_struct_0(A)),A,B)
& m1_yellow13(k1_tarski(u1_struct_0(A)),A,B) ) ) ) ).
fof(t22_yellow13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_yellow13(C,A,B)
& m1_yellow13(C,A,B) )
=> C = k1_tarski(u1_struct_0(A)) ) ) ) ).
fof(t23_yellow13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_yellow_8(C,A,B)
=> m1_yellow13(C,A,B) ) ) ) ).
fof(d4_yellow13,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( m2_yellow13(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> m1_yellow13(B,A,C) ) ) ) ) ).
fof(t24_yellow13,axiom,
! [A] :
( l1_pre_topc(A)
=> m2_yellow13(k1_zfmisc_1(u1_struct_0(A)),A) ) ).
fof(t25_yellow13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m2_yellow13(B,A)
=> ~ v1_xboole_0(B) ) ) ).
fof(t26_yellow13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m2_yellow13(B,A)
=> r1_tarski(u1_pre_topc(A),k1_cantor_1(u1_struct_0(A),k1_tdlat_2(A,B))) ) ) ).
fof(t27_yellow13,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_cantor_1(B,A)
=> m2_yellow13(B,A) ) ) ).
fof(d5_yellow13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_waybel_9(A) )
=> ( v2_yellow13(A)
<=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k6_borsuk_1(A,A)),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(k6_borsuk_1(A,A)),u1_struct_0(A)) )
=> ( B = k4_waybel_2(A)
=> v5_pre_topc(B,k6_borsuk_1(A,A),A) ) ) ) ) ).
fof(t28_yellow13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_yellow13(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> v5_pre_topc(k4_waybel_1(A,B),A,A) ) ) ).
fof(dt_m1_yellow13,axiom,
! [A,B] :
( ( l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ! [C] :
( m1_yellow13(C,A,B)
=> m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) ).
fof(existence_m1_yellow13,axiom,
! [A,B] :
( ( l1_pre_topc(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ? [C] : m1_yellow13(C,A,B) ) ).
fof(dt_m2_yellow13,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m2_yellow13(B,A)
=> m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) ).
fof(existence_m2_yellow13,axiom,
! [A] :
( l1_pre_topc(A)
=> ? [B] : m2_yellow13(B,A) ) ).
fof(t15_yellow13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_cantor_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> m1_yellow_8(a_3_0_yellow13(A,B,C),A,C) ) ) ) ).
fof(t20_yellow13,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v1_yellow13(a_2_0_yellow13(A,B),A,B)
& m1_yellow13(a_2_0_yellow13(A,B),A,B) ) ) ) ).
fof(fraenkel_a_3_0_yellow13,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& m1_cantor_1(C,B)
& m1_subset_1(D,u1_struct_0(B)) )
=> ( r2_hidden(A,a_3_0_yellow13(B,C,D))
<=> ? [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
& A = E
& r2_hidden(E,C)
& r2_hidden(D,E) ) ) ) ).
fof(fraenkel_a_2_0_yellow13,axiom,
! [A,B,C] :
( ( l1_pre_topc(B)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( r2_hidden(A,a_2_0_yellow13(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
& A = D
& r2_hidden(C,k1_tops_1(B,D)) ) ) ) ).
%------------------------------------------------------------------------------