SET007 Axioms: SET007+874.ax
%------------------------------------------------------------------------------
% File : SET007+874 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Introduction to Real Linear 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 : rltopsp1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 124 ( 2 unt; 0 def)
% Number of atoms : 1370 ( 46 equ)
% Maximal formula atoms : 23 ( 11 avg)
% Number of connectives : 1401 ( 155 ~; 0 |; 906 &)
% ( 19 <=>; 321 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 11 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 55 ( 53 usr; 1 prp; 0-3 aty)
% Number of functors : 50 ( 50 usr; 3 con; 0-5 aty)
% Number of variables : 368 ( 340 !; 28 ?)
% 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(rc1_rltopsp1,axiom,
? [A] :
( m1_subset_1(A,k1_numbers)
& ~ v1_xboole_0(A)
& v1_xcmplx_0(A)
& v1_xreal_0(A) ) ).
fof(fc1_rltopsp1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A)
& v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_xboole_0(k3_convex1(A,B))
& v1_convex1(k3_convex1(A,B),A) ) ) ).
fof(fc2_rltopsp1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( ~ v1_xboole_0(k1_rltopsp1(A,B,C))
& v1_convex1(k1_rltopsp1(A,B,C),A) ) ) ).
fof(rc2_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_rlvect_1(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
& ~ v1_xboole_0(B)
& v1_rltopsp1(B,A) ) ) ).
fof(rc3_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v2_rltopsp1(B,A) ) ) ).
fof(fc3_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_rlvect_1(A) )
=> ( v1_xboole_0(k1_pre_topc(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))
& v3_rltopsp1(k1_pre_topc(A),A) ) ) ).
fof(rc4_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v3_rltopsp1(B,A) ) ) ).
fof(fc4_rltopsp1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A)
& v3_rltopsp1(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v3_rltopsp1(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> v3_rltopsp1(k6_rusub_4(A,B,C),A) ) ).
fof(cc1_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_rltopsp1(B,A)
=> v2_rltopsp1(B,A) ) ) ) ).
fof(fc5_rltopsp1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A)
& v3_rltopsp1(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_convex1(k3_convex1(A,B),A)
& v2_rltopsp1(k3_convex1(A,B),A)
& v3_rltopsp1(k3_convex1(A,B),A) ) ) ).
fof(rc5_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_rlvect_1(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
& ~ v1_xboole_0(B)
& v4_rltopsp1(B,A) ) ) ).
fof(rc6_rltopsp1,axiom,
? [A] :
( l1_rltopsp1(A)
& v5_rltopsp1(A) ) ).
fof(fc6_rltopsp1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A)
& m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A)
& m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ( ~ v3_struct_0(g1_rltopsp1(A,B,C,D,E))
& v5_rltopsp1(g1_rltopsp1(A,B,C,D,E)) ) ) ).
fof(rc7_rltopsp1,axiom,
? [A] :
( l1_rltopsp1(A)
& ~ v3_struct_0(A)
& v5_rltopsp1(A) ) ).
fof(rc8_rltopsp1,axiom,
? [A] :
( l1_rltopsp1(A)
& ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v5_rltopsp1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A) ) ).
fof(fc7_rltopsp1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v1_relat_1(k3_rltopsp1(A,B))
& v1_funct_1(k3_rltopsp1(A,B))
& v1_funct_2(k3_rltopsp1(A,B),u1_struct_0(A),u1_struct_0(A))
& v3_tops_2(k3_rltopsp1(A,B),A,A) ) ) ).
fof(fc8_rltopsp1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A)
& v3_pre_topc(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& m1_subset_1(C,u1_struct_0(A)) )
=> v3_pre_topc(k5_rusub_4(A,B,C),A) ) ).
fof(fc9_rltopsp1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A)
& v3_pre_topc(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> v3_pre_topc(k6_rusub_4(A,C,B),A) ) ).
fof(fc10_rltopsp1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A)
& v4_pre_topc(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& m1_subset_1(C,u1_struct_0(A)) )
=> v4_pre_topc(k5_rusub_4(A,B,C),A) ) ).
fof(fc11_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ( v1_xboole_0(k1_pre_topc(A))
& v3_pre_topc(k1_pre_topc(A),A)
& v4_pre_topc(k1_pre_topc(A),A)
& v2_tops_1(k1_pre_topc(A),A)
& v3_tops_1(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))
& v2_rltopsp1(k1_pre_topc(A),A)
& v3_rltopsp1(k1_pre_topc(A),A)
& v9_rltopsp1(k1_pre_topc(A),A) ) ) ).
fof(rc9_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v9_rltopsp1(B,A) ) ) ).
fof(fc12_rltopsp1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_numbers) )
=> ( v1_relat_1(k4_rltopsp1(A,B))
& v1_funct_1(k4_rltopsp1(A,B))
& v1_funct_2(k4_rltopsp1(A,B),u1_struct_0(A),u1_struct_0(A))
& v3_tops_2(k4_rltopsp1(A,B),A,A) ) ) ).
fof(fc13_rltopsp1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A)
& v9_rltopsp1(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& m1_subset_1(C,k1_numbers) )
=> v9_rltopsp1(k1_convex1(A,B,C),A) ) ).
fof(cc2_rltopsp1,axiom,
! [A] :
( l1_rltopsp1(A)
=> ( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_urysohn1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A) )
=> ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_compts_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A) ) ) ) ).
fof(fc14_rltopsp1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A)
& v1_convex1(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v4_pre_topc(k6_pre_topc(A,B),A)
& v1_convex1(k6_pre_topc(A,B),A) ) ) ).
fof(fc15_rltopsp1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A)
& v1_convex1(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v3_pre_topc(k1_tops_1(A,B),A)
& v1_convex1(k1_tops_1(A,B),A) ) ) ).
fof(fc16_rltopsp1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A)
& v3_rltopsp1(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v4_pre_topc(k6_pre_topc(A,B),A)
& v2_rltopsp1(k6_pre_topc(A,B),A)
& v3_rltopsp1(k6_pre_topc(A,B),A) ) ) ).
fof(fc17_rltopsp1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A)
& v9_rltopsp1(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v4_pre_topc(k6_pre_topc(A,B),A)
& v9_rltopsp1(k6_pre_topc(A,B),A) ) ) ).
fof(t1_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(C,B)
=> r2_hidden(k3_rlvect_1(A,C,D),k1_convex1(A,B,D)) ) ) ) ) ) ).
fof(t2_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v1_xboole_0(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))))
=> ( r1_compts_1(A,C,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,B)
& ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( r2_hidden(D,E)
& r2_hidden(E,C) ) ) ) ) ) ) ) ) ).
fof(t3_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(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)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r2_hidden(D,B)
& r2_hidden(E,C) )
=> r2_hidden(k2_rlvect_1(A,D,E),k6_rusub_4(A,B,C)) ) ) ) ) ) ) ).
fof(t5_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k5_rusub_4(A,B,k1_rlvect_1(A)) = B ) ) ).
fof(t6_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> k5_rusub_4(A,D,k2_rlvect_1(A,B,C)) = k5_rusub_4(A,k5_rusub_4(A,D,C),B) ) ) ) ) ).
fof(t7_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(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)))
=> k6_rusub_4(A,k5_rusub_4(A,C,B),D) = k5_rusub_4(A,k6_rusub_4(A,C,D),B) ) ) ) ) ).
fof(t8_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(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)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_tarski(B,C)
=> r1_tarski(k5_rusub_4(A,B,D),k5_rusub_4(A,C,D)) ) ) ) ) ) ).
fof(t9_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(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,B)
=> r2_hidden(k1_rlvect_1(A),k5_rusub_4(A,B,k5_rlvect_1(A,C))) ) ) ) ) ).
fof(t10_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(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)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_tarski(B,C)
=> r1_tarski(k6_rusub_4(A,B,D),k6_rusub_4(A,C,D)) ) ) ) ) ) ).
fof(t11_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(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)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r1_tarski(B,D)
& r1_tarski(C,E) )
=> r1_tarski(k6_rusub_4(A,B,C),k6_rusub_4(A,D,E)) ) ) ) ) ) ) ).
fof(t12_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v5_rlvect_1(A)
& l1_rlvect_1(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)))
=> ( r2_hidden(k1_rlvect_1(A),C)
=> r1_tarski(B,k6_rusub_4(A,B,C)) ) ) ) ) ).
fof(t13_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> k1_convex1(A,k1_struct_0(A,k1_rlvect_1(A)),B) = k1_struct_0(A,k1_rlvect_1(A)) ) ) ).
fof(t14_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_numbers) )
=> ( r2_hidden(k1_rlvect_1(A),k1_convex1(A,B,C))
=> r2_hidden(k1_rlvect_1(A),B) ) ) ) ) ).
fof(t15_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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)))
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_numbers) )
=> k5_subset_1(u1_struct_0(A),k1_convex1(A,B,D),k1_convex1(A,C,D)) = k1_convex1(A,k5_subset_1(u1_struct_0(A),B,C),D) ) ) ) ) ).
fof(t16_rltopsp1,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_connsp_2(C,A,B)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_tarski(C,D)
=> m1_connsp_2(D,A,B) ) ) ) ) ) ).
fof(d1_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_convex1(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( ( r1_xreal_0(np__0,E)
& r1_xreal_0(E,np__1)
& r2_hidden(C,B)
& r2_hidden(D,B) )
=> r2_hidden(k4_rlvect_1(A,k3_rlvect_1(A,C,E),k3_rlvect_1(A,D,k5_real_1(np__1,E))),B) ) ) ) ) ) ) ) ).
fof(t17_rltopsp1,axiom,
$true ).
fof(t18_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( v1_convex1(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> k3_convex1(A,B) = B ) ) ).
fof(t19_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> k1_convex1(A,k3_convex1(A,B),C) = k3_convex1(A,k1_convex1(A,B,C)) ) ) ) ).
fof(t20_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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(k2_convex1(A,C),k2_convex1(A,B)) ) ) ) ) ).
fof(t21_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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(k3_convex1(A,B),k3_convex1(A,C)) ) ) ) ) ).
fof(t22_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( v1_convex1(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( ( r1_xreal_0(np__0,C)
& r1_xreal_0(C,np__1)
& r2_hidden(k1_rlvect_1(A),B) )
=> r1_tarski(k1_convex1(A,B,C),B) ) ) ) ) ).
fof(t23_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_convex1(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(C,B)
& r2_hidden(D,B) )
=> r1_tarski(k1_rltopsp1(A,C,D),B) ) ) ) ) ) ) ).
fof(d3_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v1_rltopsp1(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(C,B)
=> v1_convex1(C,A) ) ) ) ) ) ).
fof(t24_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( v1_rltopsp1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) )
=> v1_convex1(k6_setfam_1(u1_struct_0(A),B),A) ) ) ).
fof(d4_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k2_rltopsp1(A,B) = k1_convex1(A,B,k1_real_1(np__1)) ) ) ).
fof(t25_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ~ r1_xboole_0(k5_rusub_4(A,B,D),C)
<=> r2_hidden(D,k7_rusub_4(A,C,k2_rltopsp1(A,B))) ) ) ) ) ) ).
fof(d5_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v2_rltopsp1(B,A)
<=> B = k2_rltopsp1(A,B) ) ) ) ).
fof(t26_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( v2_rltopsp1(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,B)
=> r2_hidden(k5_rlvect_1(A,C),B) ) ) ) ) ).
fof(d6_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_rltopsp1(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r1_xreal_0(k18_complex1(C),np__1)
=> r1_tarski(k1_convex1(A,B,C),B) ) ) ) ) ) ).
fof(t27_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> v3_rltopsp1(k1_struct_0(A,k1_rlvect_1(A)),A) ) ).
fof(t28_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v3_rltopsp1(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> r2_hidden(k1_rlvect_1(A),B) ) ) ).
fof(t29_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( v3_rltopsp1(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( k18_complex1(C) = np__1
=> k1_convex1(A,B,C) = B ) ) ) ) ).
fof(d7_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v4_rltopsp1(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(C,B)
=> v3_rltopsp1(C,A) ) ) ) ) ) ).
fof(t30_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( v4_rltopsp1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) )
=> v3_rltopsp1(k5_setfam_1(u1_struct_0(A),B),A) ) ) ).
fof(t31_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( v4_rltopsp1(B,A)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) )
=> v3_rltopsp1(k6_setfam_1(u1_struct_0(A),B),A) ) ) ).
fof(d8_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rltopsp1(A) )
=> ( v6_rltopsp1(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( v3_pre_topc(D,A)
& r2_hidden(k2_rlvect_1(A,B,C),D)
& ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( v3_pre_topc(E,A)
& v3_pre_topc(F,A)
& r2_hidden(B,E)
& r2_hidden(C,F)
& r1_tarski(k6_rusub_4(A,E,F),D) ) ) ) ) ) ) ) ) ) ).
fof(d9_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rltopsp1(A) )
=> ( v7_rltopsp1(A)
<=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( v3_pre_topc(D,A)
& r2_hidden(k3_rlvect_1(A,C,B),D)
& ! [E] :
( ( v2_xreal_0(E)
& m1_subset_1(E,k1_numbers) )
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( v3_pre_topc(F,A)
& r2_hidden(C,F)
& ! [G] :
( m1_subset_1(G,k1_numbers)
=> ( ~ r1_xreal_0(E,k18_complex1(k5_real_1(G,B)))
=> r1_tarski(k1_convex1(A,F,G),D) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t32_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_connsp_2(D,A,k4_rlvect_1(A,B,C))
=> ? [E] :
( m1_connsp_2(E,A,B)
& ? [F] :
( m1_connsp_2(F,A,C)
& r1_tarski(k7_rusub_4(A,E,F),D) ) ) ) ) ) ) ).
fof(t33_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_connsp_2(D,A,k3_rlvect_1(A,C,B))
=> ? [E] :
( v2_xreal_0(E)
& m1_subset_1(E,k1_numbers)
& ? [F] :
( m1_connsp_2(F,A,C)
& ! [G] :
( m1_subset_1(G,k1_numbers)
=> ( ~ r1_xreal_0(E,k18_complex1(k5_real_1(G,B)))
=> r1_tarski(k1_convex1(A,F,G),D) ) ) ) ) ) ) ) ) ).
fof(d10_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rltopsp1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( C = k3_rltopsp1(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,D) = k2_rlvect_1(A,B,D) ) ) ) ) ) ).
fof(t34_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rltopsp1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> k4_pre_topc(A,A,k3_rltopsp1(A,B),C) = k5_rusub_4(A,C,B) ) ) ) ).
fof(t35_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k2_relat_1(k3_rltopsp1(A,B)) = k2_pre_topc(A) ) ) ).
fof(t36_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k2_tops_2(A,A,k3_rltopsp1(A,B)) = k3_rltopsp1(A,k5_rlvect_1(A,B)) ) ) ).
fof(t37_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(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)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_tarski(k7_rusub_4(A,B,C),D)
=> r1_tarski(k7_rusub_4(A,k1_tops_1(A,B),k1_tops_1(A,C)),k1_tops_1(A,D)) ) ) ) ) ) ).
fof(t38_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> k5_rusub_4(A,k1_tops_1(A,C),B) = k1_tops_1(A,k5_rusub_4(A,C,B)) ) ) ) ).
fof(t39_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> k5_rusub_4(A,k6_pre_topc(A,C),B) = k6_pre_topc(A,k5_rusub_4(A,C,B)) ) ) ) ).
fof(t40_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_connsp_2(D,A,B)
=> m1_connsp_2(k5_rusub_4(A,D,C),A,k4_rlvect_1(A,C,B)) ) ) ) ) ).
fof(t41_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_connsp_2(C,A,B)
=> m1_connsp_2(k5_rusub_4(A,C,k5_rlvect_1(A,B)),A,k1_rlvect_1(A)) ) ) ) ).
fof(d11_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rltopsp1(A) )
=> ( v8_rltopsp1(A)
<=> ? [B] :
( m1_yellow13(B,A,k1_rlvect_1(A))
& v1_rltopsp1(B,A) ) ) ) ).
fof(d12_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v9_rltopsp1(B,A)
<=> ! [C] :
( m1_connsp_2(C,A,k1_rlvect_1(A))
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( ~ r1_xreal_0(E,D)
=> r1_tarski(B,k1_convex1(A,C,E)) ) ) ) ) ) ) ) ).
fof(t42_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ! [B] :
( ( v9_rltopsp1(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v9_rltopsp1(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> v9_rltopsp1(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ).
fof(t43_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ! [B] :
( ( v9_rltopsp1(B,A)
& 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(C,B)
=> v9_rltopsp1(C,A) ) ) ) ) ).
fof(d13_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rltopsp1(A) )
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( C = k4_rltopsp1(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,D) = k3_rlvect_1(A,D,B) ) ) ) ) ) ).
fof(t47_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rltopsp1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_numbers) )
=> k4_pre_topc(A,A,k4_rltopsp1(A,C),B) = k1_convex1(A,B,C) ) ) ) ).
fof(t48_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_numbers) )
=> k2_relat_1(k4_rltopsp1(A,B)) = k2_pre_topc(A) ) ) ).
fof(t49_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_numbers) )
=> k2_tops_2(A,A,k4_rltopsp1(A,B)) = k4_rltopsp1(A,k2_real_1(B)) ) ) ).
fof(t50_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ! [B] :
( ( v3_pre_topc(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_numbers) )
=> v3_pre_topc(k1_convex1(A,B,C),A) ) ) ) ).
fof(t51_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ! [B] :
( ( v4_pre_topc(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_numbers) )
=> v4_pre_topc(k1_convex1(A,B,C),A) ) ) ) ).
fof(t52_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_numbers) )
=> k1_convex1(A,k1_tops_1(A,B),C) = k1_tops_1(A,k1_convex1(A,B,C)) ) ) ) ).
fof(t53_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_numbers) )
=> k1_convex1(A,k6_pre_topc(A,B),C) = k6_pre_topc(A,k1_convex1(A,B,C)) ) ) ) ).
fof(t54_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_urysohn1(A)
=> k1_convex1(A,k6_pre_topc(A,B),np__0) = k6_pre_topc(A,k1_convex1(A,B,np__0)) ) ) ) ).
fof(t55_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_connsp_2(C,A,B)
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_numbers) )
=> m1_connsp_2(k1_convex1(A,C,D),A,k3_rlvect_1(A,B,D)) ) ) ) ) ).
fof(t56_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ! [B] :
( m1_connsp_2(B,A,k1_rlvect_1(A))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_numbers) )
=> m1_connsp_2(k1_convex1(A,B,C),A,k1_rlvect_1(A)) ) ) ) ).
fof(t57_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ! [B] :
( m1_connsp_2(B,A,k1_rlvect_1(A))
=> ? [C] :
( v3_pre_topc(C,A)
& m1_connsp_2(C,A,k1_rlvect_1(A))
& v2_rltopsp1(C,A)
& r1_tarski(k7_rusub_4(A,C,C),B) ) ) ) ).
fof(t58_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ! [B] :
( ( v6_compts_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v4_pre_topc(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( r1_xboole_0(B,C)
& ! [D] :
( m1_connsp_2(D,A,k1_rlvect_1(A))
=> ~ r1_xboole_0(k7_rusub_4(A,B,D),k7_rusub_4(A,C,D)) ) ) ) ) ) ).
fof(t59_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ! [B] :
( m1_yellow13(B,A,k1_rlvect_1(A))
=> ! [C] :
( m1_connsp_2(C,A,k1_rlvect_1(A))
=> ? [D] :
( m1_connsp_2(D,A,k1_rlvect_1(A))
& r2_hidden(D,B)
& r1_tarski(k6_pre_topc(A,D),C) ) ) ) ) ).
fof(t60_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ! [B] :
( m1_connsp_2(B,A,k1_rlvect_1(A))
=> ? [C] :
( m1_connsp_2(C,A,k1_rlvect_1(A))
& r1_tarski(k6_pre_topc(A,C),B) ) ) ) ).
fof(t62_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(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(k7_rusub_4(A,k1_tops_1(A,B),k1_tops_1(A,C)),k1_tops_1(A,k7_rusub_4(A,B,C))) ) ) ) ).
fof(t63_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(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(k7_rusub_4(A,k6_pre_topc(A,B),k6_pre_topc(A,C)),k6_pre_topc(A,k7_rusub_4(A,B,C))) ) ) ) ).
fof(t64_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ! [B] :
( ( v3_rltopsp1(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r2_hidden(k1_rlvect_1(A),k1_tops_1(A,B))
=> v3_rltopsp1(k1_tops_1(A,B),A) ) ) ) ).
fof(t65_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ! [B] :
( m1_connsp_2(B,A,k1_rlvect_1(A))
=> ? [C] :
( m1_connsp_2(C,A,k1_rlvect_1(A))
& v3_rltopsp1(C,A)
& r1_tarski(C,B) ) ) ) ).
fof(t66_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ! [B] :
( m1_connsp_2(B,A,k1_rlvect_1(A))
=> ~ ( v1_convex1(B,A)
& ! [C] :
( m1_connsp_2(C,A,k1_rlvect_1(A))
=> ~ ( v3_rltopsp1(C,A)
& v1_convex1(C,A)
& r1_tarski(C,B) ) ) ) ) ) ).
fof(t67_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ? [B] :
( m1_yellow13(B,A,k1_rlvect_1(A))
& v4_rltopsp1(B,A) ) ) ).
fof(t68_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ~ ( v8_rltopsp1(A)
& ! [B] :
( m1_yellow13(B,A,k1_rlvect_1(A))
=> ~ v1_rltopsp1(B,A) ) ) ) ).
fof(dt_l1_rltopsp1,axiom,
! [A] :
( l1_rltopsp1(A)
=> ( l2_rlvect_1(A)
& l1_pre_topc(A) ) ) ).
fof(existence_l1_rltopsp1,axiom,
? [A] : l1_rltopsp1(A) ).
fof(abstractness_v5_rltopsp1,axiom,
! [A] :
( l1_rltopsp1(A)
=> ( v5_rltopsp1(A)
=> A = g1_rltopsp1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A),u1_pre_topc(A)) ) ) ).
fof(dt_k1_rltopsp1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k1_rltopsp1(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k2_rltopsp1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l2_rlvect_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k2_rltopsp1(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k3_rltopsp1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_rltopsp1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v1_funct_1(k3_rltopsp1(A,B))
& v1_funct_2(k3_rltopsp1(A,B),u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(k3_rltopsp1(A,B),u1_struct_0(A),u1_struct_0(A)) ) ) ).
fof(dt_k4_rltopsp1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_rltopsp1(A)
& m1_subset_1(B,k1_numbers) )
=> ( v1_funct_1(k4_rltopsp1(A,B))
& v1_funct_2(k4_rltopsp1(A,B),u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(k4_rltopsp1(A,B),u1_struct_0(A),u1_struct_0(A)) ) ) ).
fof(dt_g1_rltopsp1,axiom,
! [A,B,C,D,E] :
( ( m1_subset_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A)
& m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A)
& m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ( v5_rltopsp1(g1_rltopsp1(A,B,C,D,E))
& l1_rltopsp1(g1_rltopsp1(A,B,C,D,E)) ) ) ).
fof(free_g1_rltopsp1,axiom,
! [A,B,C,D,E] :
( ( m1_subset_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A)
& m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A)
& m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(A))) )
=> ! [F,G,H,I,J] :
( g1_rltopsp1(A,B,C,D,E) = g1_rltopsp1(F,G,H,I,J)
=> ( A = F
& B = G
& C = H
& D = I
& E = J ) ) ) ).
fof(t4_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(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)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( D = a_3_0_rltopsp1(A,B,C)
=> k6_rusub_4(A,B,C) = k5_setfam_1(u1_struct_0(A),D) ) ) ) ) ) ).
fof(d2_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k1_rltopsp1(A,B,C) = a_3_1_rltopsp1(A,B,C) ) ) ) ).
fof(t44_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( ( v1_finset_1(B)
& B = a_1_0_rltopsp1(A) )
=> v9_rltopsp1(k5_setfam_1(u1_struct_0(A),B),A) ) ) ) ).
fof(t45_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( B = a_1_1_rltopsp1(A)
=> m1_yellow13(B,A,k1_rlvect_1(A)) ) ) ) ).
fof(t46_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ! [B] :
( m1_yellow13(B,A,k1_rlvect_1(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( C = a_2_0_rltopsp1(A,B)
=> m2_yellow13(C,A) ) ) ) ) ).
fof(t61_rltopsp1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v6_rltopsp1(A)
& v7_rltopsp1(A)
& l1_rltopsp1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k6_pre_topc(A,B) = k1_setfam_1(a_2_1_rltopsp1(A,B)) ) ) ).
fof(fraenkel_a_3_0_rltopsp1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& l1_rlvect_1(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_3_0_rltopsp1(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = k5_rusub_4(B,D,E)
& r2_hidden(E,C) ) ) ) ).
fof(fraenkel_a_3_1_rltopsp1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& l2_rlvect_1(B)
& m1_subset_1(C,u1_struct_0(B))
& m1_subset_1(D,u1_struct_0(B)) )
=> ( r2_hidden(A,a_3_1_rltopsp1(B,C,D))
<=> ? [E] :
( m1_subset_1(E,k1_numbers)
& A = k4_rlvect_1(B,k3_rlvect_1(B,C,k5_real_1(np__1,E)),k3_rlvect_1(B,D,E))
& r1_xreal_0(np__0,E)
& r1_xreal_0(E,np__1) ) ) ) ).
fof(fraenkel_a_1_0_rltopsp1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v6_rltopsp1(B)
& v7_rltopsp1(B)
& l1_rltopsp1(B) )
=> ( r2_hidden(A,a_1_0_rltopsp1(B))
<=> ? [C] :
( v9_rltopsp1(C,B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& A = C ) ) ) ).
fof(fraenkel_a_1_1_rltopsp1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v6_rltopsp1(B)
& v7_rltopsp1(B)
& l1_rltopsp1(B) )
=> ( r2_hidden(A,a_1_1_rltopsp1(B))
<=> ? [C] :
( m1_connsp_2(C,B,k1_rlvect_1(B))
& A = C ) ) ) ).
fof(fraenkel_a_2_0_rltopsp1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v6_rltopsp1(B)
& v7_rltopsp1(B)
& l1_rltopsp1(B)
& m1_yellow13(C,B,k1_rlvect_1(B)) )
=> ( r2_hidden(A,a_2_0_rltopsp1(B,C))
<=> ? [D,E] :
( m1_subset_1(D,u1_struct_0(B))
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
& A = k5_rusub_4(B,E,D)
& r2_hidden(E,C) ) ) ) ).
fof(fraenkel_a_2_1_rltopsp1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v6_rltopsp1(B)
& v7_rltopsp1(B)
& l1_rltopsp1(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_2_1_rltopsp1(B,C))
<=> ? [D] :
( m1_connsp_2(D,B,k1_rlvect_1(B))
& A = k7_rusub_4(B,C,D) ) ) ) ).
%------------------------------------------------------------------------------