SET007 Axioms: SET007+875.ax
%------------------------------------------------------------------------------
% File : SET007+875 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Some Properties of Rectangles on the Plane
% 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 : topreala [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 88 ( 2 unt; 0 def)
% Number of atoms : 674 ( 32 equ)
% Maximal formula atoms : 19 ( 7 avg)
% Number of connectives : 650 ( 64 ~; 11 |; 275 &)
% ( 4 <=>; 296 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 9 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 48 ( 47 usr; 0 prp; 1-4 aty)
% Number of functors : 44 ( 44 usr; 6 con; 0-5 aty)
% Number of variables : 280 ( 278 !; 2 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_topreala,axiom,
! [A,B] :
( ( v1_xreal_0(A)
& v1_xreal_0(B)
& v2_xreal_0(B) )
=> ~ v1_xboole_0(k2_rcomp_1(A,k2_xcmplx_0(A,B))) ) ).
fof(fc2_topreala,axiom,
! [A,B] :
( ( v1_xreal_0(A)
& v1_xreal_0(B)
& v2_xreal_0(B) )
=> ~ v1_xboole_0(k1_rcomp_2(A,k2_xcmplx_0(A,B))) ) ).
fof(fc3_topreala,axiom,
! [A,B] :
( ( v1_xreal_0(A)
& v1_xreal_0(B)
& v2_xreal_0(B) )
=> ~ v1_xboole_0(k2_rcomp_2(A,k2_xcmplx_0(A,B))) ) ).
fof(fc4_topreala,axiom,
! [A,B] :
( ( v1_xreal_0(A)
& v1_xreal_0(B)
& v2_xreal_0(B) )
=> ( ~ v1_xboole_0(k1_rcomp_1(A,k2_xcmplx_0(A,B)))
& v1_rcomp_1(k1_rcomp_1(A,k2_xcmplx_0(A,B)))
& v2_rcomp_1(k1_rcomp_1(A,k2_xcmplx_0(A,B)))
& v1_membered(k1_rcomp_1(A,k2_xcmplx_0(A,B)))
& v2_membered(k1_rcomp_1(A,k2_xcmplx_0(A,B)))
& v1_seq_4(k1_rcomp_1(A,k2_xcmplx_0(A,B)))
& v2_seq_4(k1_rcomp_1(A,k2_xcmplx_0(A,B)))
& v3_seq_4(k1_rcomp_1(A,k2_xcmplx_0(A,B))) ) ) ).
fof(fc5_topreala,axiom,
! [A,B] :
( ( v1_xreal_0(A)
& v1_xreal_0(B)
& v2_xreal_0(B) )
=> ~ v1_xboole_0(k2_rcomp_1(k6_xcmplx_0(A,B),A)) ) ).
fof(fc6_topreala,axiom,
! [A,B] :
( ( v1_xreal_0(A)
& v1_xreal_0(B)
& v2_xreal_0(B) )
=> ~ v1_xboole_0(k1_rcomp_2(k6_xcmplx_0(A,B),A)) ) ).
fof(fc7_topreala,axiom,
! [A,B] :
( ( v1_xreal_0(A)
& v1_xreal_0(B)
& v2_xreal_0(B) )
=> ~ v1_xboole_0(k2_rcomp_2(k6_xcmplx_0(A,B),A)) ) ).
fof(fc8_topreala,axiom,
! [A,B] :
( ( v1_xreal_0(A)
& v1_xreal_0(B)
& v2_xreal_0(B) )
=> ( ~ v1_xboole_0(k1_rcomp_1(k6_xcmplx_0(A,B),A))
& v1_rcomp_1(k1_rcomp_1(k6_xcmplx_0(A,B),A))
& v2_rcomp_1(k1_rcomp_1(k6_xcmplx_0(A,B),A))
& v1_membered(k1_rcomp_1(k6_xcmplx_0(A,B),A))
& v2_membered(k1_rcomp_1(k6_xcmplx_0(A,B),A))
& v1_seq_4(k1_rcomp_1(k6_xcmplx_0(A,B),A))
& v2_seq_4(k1_rcomp_1(k6_xcmplx_0(A,B),A))
& v3_seq_4(k1_rcomp_1(k6_xcmplx_0(A,B),A)) ) ) ).
fof(fc9_topreala,axiom,
! [A,B] :
( ( v1_xreal_0(A)
& ~ v2_xreal_0(A)
& v1_xreal_0(B)
& v2_xreal_0(B) )
=> ~ v1_xboole_0(k2_rcomp_1(A,B)) ) ).
fof(fc10_topreala,axiom,
! [A,B] :
( ( v1_xreal_0(A)
& ~ v2_xreal_0(A)
& v1_xreal_0(B)
& v2_xreal_0(B) )
=> ~ v1_xboole_0(k1_rcomp_2(A,B)) ) ).
fof(fc11_topreala,axiom,
! [A,B] :
( ( v1_xreal_0(A)
& ~ v2_xreal_0(A)
& v1_xreal_0(B)
& v2_xreal_0(B) )
=> ~ v1_xboole_0(k2_rcomp_2(A,B)) ) ).
fof(fc12_topreala,axiom,
! [A,B] :
( ( v1_xreal_0(A)
& ~ v2_xreal_0(A)
& v1_xreal_0(B)
& v2_xreal_0(B) )
=> ( ~ v1_xboole_0(k1_rcomp_1(A,B))
& v1_rcomp_1(k1_rcomp_1(A,B))
& v2_rcomp_1(k1_rcomp_1(A,B))
& v1_membered(k1_rcomp_1(A,B))
& v2_membered(k1_rcomp_1(A,B))
& v1_seq_4(k1_rcomp_1(A,B))
& v2_seq_4(k1_rcomp_1(A,B))
& v3_seq_4(k1_rcomp_1(A,B)) ) ) ).
fof(fc13_topreala,axiom,
! [A,B] :
( ( v1_xreal_0(A)
& v3_xreal_0(A)
& v1_xreal_0(B)
& ~ v3_xreal_0(B) )
=> ~ v1_xboole_0(k2_rcomp_1(A,B)) ) ).
fof(fc14_topreala,axiom,
! [A,B] :
( ( v1_xreal_0(A)
& v3_xreal_0(A)
& v1_xreal_0(B)
& ~ v3_xreal_0(B) )
=> ~ v1_xboole_0(k1_rcomp_2(A,B)) ) ).
fof(fc15_topreala,axiom,
! [A,B] :
( ( v1_xreal_0(A)
& v3_xreal_0(A)
& v1_xreal_0(B)
& ~ v3_xreal_0(B) )
=> ~ v1_xboole_0(k2_rcomp_2(A,B)) ) ).
fof(fc16_topreala,axiom,
! [A,B] :
( ( v1_xreal_0(A)
& v3_xreal_0(A)
& v1_xreal_0(B)
& ~ v3_xreal_0(B) )
=> ( ~ v1_xboole_0(k1_rcomp_1(A,B))
& v1_rcomp_1(k1_rcomp_1(A,B))
& v2_rcomp_1(k1_rcomp_1(A,B))
& v1_membered(k1_rcomp_1(A,B))
& v2_membered(k1_rcomp_1(A,B))
& v1_seq_4(k1_rcomp_1(A,B))
& v2_seq_4(k1_rcomp_1(A,B))
& v3_seq_4(k1_rcomp_1(A,B)) ) ) ).
fof(rc1_topreala,axiom,
? [A] :
( l1_pre_topc(A)
& ~ v3_struct_0(A)
& v1_pre_topc(A)
& v2_pre_topc(A)
& v1_monoid_0(A)
& v2_monoid_0(A) ) ).
fof(cc1_topreala,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_monoid_0(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( v2_pre_topc(B)
& v1_monoid_0(B)
& v2_monoid_0(B) ) ) ) ).
fof(cc2_topreala,axiom,
! [A] :
( l1_pre_topc(A)
=> ( ( v3_struct_0(A)
& v2_pre_topc(A) )
=> ( v2_pre_topc(A)
& v1_tdlat_3(A)
& v2_tdlat_3(A) ) ) ) ).
fof(cc3_topreala,axiom,
! [A,B] :
( ( v2_pre_topc(A)
& v1_tdlat_3(A)
& l1_pre_topc(A)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
=> ( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(C,A,B) ) ) ) ) ).
fof(cc4_topreala,axiom,
! [A,B] :
( ( v2_pre_topc(A)
& l1_pre_topc(A)
& l1_pre_topc(B) )
=> ! [C] :
( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
=> ( ( v1_funct_1(C)
& v1_xboole_0(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(C,A,B) ) ) ) ) ).
fof(fc17_topreala,axiom,
! [A,B,C,D] :
( ( v1_xreal_0(A)
& ~ v2_xreal_0(A)
& v1_xreal_0(B)
& ~ v2_xreal_0(B)
& v1_xreal_0(C)
& ~ v3_xreal_0(C)
& v1_xreal_0(D)
& ~ v3_xreal_0(D) )
=> ( ~ v3_struct_0(k1_topreala(A,C,B,D))
& v2_pre_topc(k1_topreala(A,C,B,D))
& v1_monoid_0(k1_topreala(A,C,B,D))
& v2_monoid_0(k1_topreala(A,C,B,D)) ) ) ).
fof(t1_topreala,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_xreal_0(B)
=> k4_int_1(k2_xcmplx_0(B,A)) = k4_int_1(B) ) ) ).
fof(t2_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(A,B)
=> ( r1_xreal_0(k2_xcmplx_0(k1_int_1(A),np__1),B)
| k1_int_1(B) = k1_int_1(A) ) ) ) ) ).
fof(t3_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(A,B)
=> ( r1_xreal_0(k2_xcmplx_0(k1_int_1(A),np__1),B)
| r1_xreal_0(k4_int_1(A),k4_int_1(B)) ) ) ) ) ).
fof(t4_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(B,A)
& ~ r1_xreal_0(k2_xcmplx_0(k1_int_1(A),np__1),B)
& r1_xreal_0(k4_int_1(B),k4_int_1(A)) ) ) ) ).
fof(t5_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(k2_xcmplx_0(k1_int_1(B),np__1),A)
& r1_xreal_0(A,k2_xcmplx_0(B,np__1)) )
=> k1_int_1(A) = k2_xcmplx_0(k1_int_1(B),np__1) ) ) ) ).
fof(t6_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( r1_xreal_0(k2_xcmplx_0(k1_int_1(B),np__1),A)
& ~ r1_xreal_0(k2_xcmplx_0(B,np__1),A)
& r1_xreal_0(k4_int_1(B),k4_int_1(A)) ) ) ) ).
fof(t7_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(A,C)
& k4_int_1(B) = k4_int_1(C) )
=> ( r1_xreal_0(k2_xcmplx_0(A,np__1),B)
| r1_xreal_0(k2_xcmplx_0(A,np__1),C)
| B = C ) ) ) ) ) ).
fof(t8_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( r1_xreal_0(A,B)
=> ( r1_xreal_0(D,C)
| r1_tarski(k1_rcomp_1(B,C),k1_rcomp_2(A,D)) ) ) ) ) ) ) ).
fof(t9_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( r1_xreal_0(C,D)
=> ( r1_xreal_0(B,A)
| r1_tarski(k1_rcomp_1(B,C),k2_rcomp_2(A,D)) ) ) ) ) ) ) ).
fof(t10_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ~ ( ~ r1_xreal_0(B,A)
& ~ r1_xreal_0(D,C)
& ~ r1_tarski(k1_rcomp_1(B,C),k2_rcomp_1(A,D)) ) ) ) ) ) ).
fof(t11_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> r1_tarski(k1_rcomp_2(B,C),k1_rcomp_1(A,D)) ) ) ) ) ) ).
fof(t12_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> r1_tarski(k1_rcomp_2(B,C),k1_rcomp_2(A,D)) ) ) ) ) ) ).
fof(t13_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( r1_xreal_0(C,D)
=> ( r1_xreal_0(B,A)
| r1_tarski(k1_rcomp_2(B,C),k2_rcomp_2(A,D)) ) ) ) ) ) ) ).
fof(t14_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( r1_xreal_0(C,D)
=> ( r1_xreal_0(B,A)
| r1_tarski(k1_rcomp_2(B,C),k2_rcomp_1(A,D)) ) ) ) ) ) ) ).
fof(t15_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> r1_tarski(k2_rcomp_2(B,C),k1_rcomp_1(A,D)) ) ) ) ) ) ).
fof(t16_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( r1_xreal_0(A,B)
=> ( r1_xreal_0(D,C)
| r1_tarski(k2_rcomp_2(B,C),k1_rcomp_2(A,D)) ) ) ) ) ) ) ).
fof(t17_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> r1_tarski(k2_rcomp_2(B,C),k2_rcomp_2(A,D)) ) ) ) ) ) ).
fof(t18_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( r1_xreal_0(A,B)
=> ( r1_xreal_0(D,C)
| r1_tarski(k2_rcomp_2(B,C),k2_rcomp_1(A,D)) ) ) ) ) ) ) ).
fof(t19_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> r1_tarski(k2_rcomp_1(B,C),k1_rcomp_1(A,D)) ) ) ) ) ) ).
fof(t20_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> r1_tarski(k2_rcomp_1(B,C),k1_rcomp_2(A,D)) ) ) ) ) ) ).
fof(t21_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> r1_tarski(k2_rcomp_1(B,C),k2_rcomp_2(A,D)) ) ) ) ) ) ).
fof(t22_topreala,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C] :
( ( r2_hidden(B,k1_relat_1(A))
& r2_hidden(k1_funct_1(A,B),k9_relat_1(A,C))
& v2_funct_1(A) )
=> r2_hidden(B,C) ) ) ).
fof(t23_topreala,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [B] :
( v4_ordinal2(B)
=> ~ ( r2_hidden(k2_xcmplx_0(B,np__1),k4_finseq_1(A))
& ~ r2_hidden(B,k4_finseq_1(A))
& B != np__0 ) ) ) ).
fof(t24_topreala,axiom,
! [A,B,C,D,E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( r2_hidden(E,k4_card_3(k4_funct_4(A,B,C,D)))
=> ( A = B
| ( r2_hidden(k1_funct_1(E,A),C)
& r2_hidden(k1_funct_1(E,B),D) ) ) ) ) ).
fof(t25_topreala,axiom,
! [A,B] : k10_finseq_1(A,B) = k4_funct_4(np__1,np__2,A,B) ).
fof(t26_topreala,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( ( v3_pre_topc(E,A)
& m1_connsp_2(E,A,C) )
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( C = D
& F = k3_xboole_0(E,k2_pre_topc(B)) )
=> ( v3_pre_topc(F,B)
& m1_connsp_2(F,B,D) ) ) ) ) ) ) ) ) ).
fof(t27_topreala,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( l1_pre_topc(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)) )
=> ( v1_xboole_0(C)
=> v5_pre_topc(C,A,B) ) ) ) ) ).
fof(t28_topreala,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)) )
=> ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ) ).
fof(t29_topreala,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(E,A,B)
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(k3_pre_topc(A,C)),u1_struct_0(k3_pre_topc(B,D)))
& m2_relset_1(F,u1_struct_0(k3_pre_topc(A,C)),u1_struct_0(k3_pre_topc(B,D))) )
=> ( F = k2_partfun1(u1_struct_0(A),u1_struct_0(B),E,C)
=> v5_pre_topc(F,k3_pre_topc(A,C),k3_pre_topc(B,D)) ) ) ) ) ) ) ) ).
fof(t30_topreala,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
=> ( ( D = E
& v1_t_0topsp(D,A,B) )
=> v1_t_0topsp(E,A,C) ) ) ) ) ) ) ).
fof(t31_topreala,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(k3_pre_topc(A,C)),u1_struct_0(k3_pre_topc(B,D)))
& m2_relset_1(F,u1_struct_0(k3_pre_topc(A,C)),u1_struct_0(k3_pre_topc(B,D))) )
=> ( ( F = k2_partfun1(u1_struct_0(A),u1_struct_0(B),E,C)
& v2_funct_2(F,u1_struct_0(k3_pre_topc(A,C)),u1_struct_0(k3_pre_topc(B,D)))
& v1_t_0topsp(E,A,B)
& v2_funct_1(E) )
=> v1_t_0topsp(F,k3_pre_topc(A,C),k3_pre_topc(B,D)) ) ) ) ) ) ) ) ).
fof(t32_topreala,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_pre_topc(C)
& l1_pre_topc(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( ( v1_t_0topsp(D,A,B)
& v1_t_0topsp(E,B,C) )
=> v1_t_0topsp(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C) ) ) ) ) ) ) ).
fof(t33_topreala,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v1_tsep_1(C,B)
& m1_pre_topc(C,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
=> ( ( D = E
& v1_t_0topsp(E,A,C) )
=> v1_t_0topsp(D,A,B) ) ) ) ) ) ) ).
fof(t34_topreala,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( 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)) )
=> ( ( v2_funct_1(C)
& v2_funct_2(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v5_pre_topc(C,A,B)
<=> v1_t_0topsp(k2_tops_2(A,B,C),B,A) ) ) ) ) ) ).
fof(t35_topreala,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( 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)) )
=> ( ( v2_funct_1(C)
& v2_funct_2(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_t_0topsp(C,A,B)
<=> v5_pre_topc(k2_tops_2(A,B,C),B,A) ) ) ) ) ) ).
fof(t36_topreala,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( r1_t_0topsp(A,B)
<=> r1_t_0topsp(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)),g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))) ) ) ) ).
fof(t37_topreala,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( 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)) )
=> ( ( v2_funct_1(C)
& v2_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(C,A,B)
& v1_t_0topsp(C,A,B) )
=> v3_tops_2(C,A,B) ) ) ) ) ).
fof(t38_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( B = k2_funcop_1(k1_numbers,A)
=> r2_fcont_1(B,k1_numbers) ) ) ) ).
fof(t39_topreala,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k1_numbers,k1_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( k4_relset_1(k1_numbers,k1_numbers,A) = k4_subset_1(k1_numbers,k4_relset_1(k1_numbers,k1_numbers,B),k4_relset_1(k1_numbers,k1_numbers,C))
& v3_rcomp_1(k4_relset_1(k1_numbers,k1_numbers,B))
& v3_rcomp_1(k4_relset_1(k1_numbers,k1_numbers,C))
& r2_fcont_1(B,k4_relset_1(k1_numbers,k1_numbers,B))
& r2_fcont_1(C,k4_relset_1(k1_numbers,k1_numbers,C))
& ! [D] :
( r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,B))
=> k2_seq_1(k1_numbers,k1_numbers,A,D) = k2_seq_1(k1_numbers,k1_numbers,B,D) )
& ! [D] :
( r2_hidden(D,k4_relset_1(k1_numbers,k1_numbers,C))
=> k2_seq_1(k1_numbers,k1_numbers,A,D) = k2_seq_1(k1_numbers,k1_numbers,C,D) ) )
=> r2_fcont_1(A,k4_relset_1(k1_numbers,k1_numbers,A)) ) ) ) ) ).
fof(t40_topreala,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k3_topalg_2))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_topalg_2)))
=> ( ( C = B
& m1_rcomp_1(B,A) )
=> m1_connsp_2(C,k3_topalg_2,A) ) ) ) ) ).
fof(t41_topreala,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k3_topalg_2))
=> ! [B] :
( m1_connsp_2(B,k3_topalg_2,A)
=> ? [C] :
( m1_rcomp_1(C,A)
& r1_tarski(C,B) ) ) ) ).
fof(t42_topreala,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k3_topalg_2),u1_struct_0(k3_topalg_2))
& m2_relset_1(A,u1_struct_0(k3_topalg_2),u1_struct_0(k3_topalg_2)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_topalg_2))
=> ( ( A = B
& r1_fcont_1(B,C) )
=> r1_tmap_1(k3_topalg_2,k3_topalg_2,A,C) ) ) ) ) ).
fof(t43_topreala,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k3_topalg_2),u1_struct_0(k3_topalg_2))
& m2_relset_1(A,u1_struct_0(k3_topalg_2),u1_struct_0(k3_topalg_2)) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k1_numbers,k1_numbers)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( A = B
& r2_fcont_1(B,k1_numbers) )
=> v5_pre_topc(A,k3_topalg_2,k3_topalg_2) ) ) ) ).
fof(t44_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> ( v4_pre_topc(k1_rcomp_1(B,C),k4_topmetr(A,D))
& m1_subset_1(k1_rcomp_1(B,C),k1_zfmisc_1(u1_struct_0(k4_topmetr(A,D)))) ) ) ) ) ) ) ).
fof(t45_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> ( v3_pre_topc(k2_rcomp_1(B,C),k4_topmetr(A,D))
& m1_subset_1(k2_rcomp_1(B,C),k1_zfmisc_1(u1_struct_0(k4_topmetr(A,D)))) ) ) ) ) ) ) ).
fof(t46_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(A,C) )
=> ( v3_pre_topc(k2_rcomp_2(C,B),k4_topmetr(A,B))
& m1_subset_1(k2_rcomp_2(C,B),k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B)))) ) ) ) ) ) ).
fof(t47_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,B) )
=> ( v3_pre_topc(k1_rcomp_2(A,C),k4_topmetr(A,B))
& m1_subset_1(k1_rcomp_2(A,C),k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B)))) ) ) ) ) ) ).
fof(t48_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> u1_struct_0(k6_borsuk_1(k4_topmetr(A,B),k4_topmetr(C,D))) = k2_zfmisc_1(k1_rcomp_1(A,B),k1_rcomp_1(C,D)) ) ) ) ) ) ).
fof(t49_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> k23_euclid(A,B) = k4_funct_4(np__1,np__2,A,B) ) ) ).
fof(t50_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( k1_funct_1(k23_euclid(A,B),np__1) = A
& k1_funct_1(k23_euclid(A,B),np__2) = B ) ) ) ).
fof(t51_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> k2_jgraph_6(A,B,C,D) = k4_card_3(k4_funct_4(np__1,np__2,k1_rcomp_1(A,B),k1_rcomp_1(C,D))) ) ) ) ) ).
fof(t52_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> r2_hidden(k23_euclid(A,C),k2_jgraph_6(A,B,C,D)) ) ) ) ) ) ).
fof(d1_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> k1_topreala(A,B,C,D) = k3_pre_topc(k15_euclid(np__2),k2_jgraph_6(A,B,C,D)) ) ) ) ) ).
fof(t53_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> u1_struct_0(k1_topreala(A,B,C,D)) = k2_jgraph_6(A,B,C,D) ) ) ) ) ).
fof(t54_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ~ ( r1_xreal_0(A,B)
& r1_xreal_0(C,D)
& v3_struct_0(k1_topreala(A,B,C,D)) ) ) ) ) ) ).
fof(d2_topreala,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k6_borsuk_1(k3_topalg_2,k3_topalg_2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(A,u1_struct_0(k6_borsuk_1(k3_topalg_2,k3_topalg_2)),u1_struct_0(k15_euclid(np__2))) )
=> ( A = k2_topreala
<=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> k1_funct_1(A,k4_tarski(B,C)) = k10_finseq_1(B,C) ) ) ) ) ).
fof(t55_topreala,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_numbers))
=> k4_pre_topc(k6_borsuk_1(k3_topalg_2,k3_topalg_2),k15_euclid(np__2),k2_topreala,k2_zfmisc_1(A,B)) = k4_card_3(k4_funct_4(np__1,np__2,A,B)) ) ) ).
fof(t56_topreala,axiom,
v3_tops_2(k2_topreala,k6_borsuk_1(k3_topalg_2,k3_topalg_2),k15_euclid(np__2)) ).
fof(t57_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> ( v1_funct_1(k2_partfun1(u1_struct_0(k6_borsuk_1(k3_topalg_2,k3_topalg_2)),u1_struct_0(k15_euclid(np__2)),k2_topreala,u1_struct_0(k6_borsuk_1(k4_topmetr(A,B),k4_topmetr(C,D)))))
& v1_funct_2(k2_partfun1(u1_struct_0(k6_borsuk_1(k3_topalg_2,k3_topalg_2)),u1_struct_0(k15_euclid(np__2)),k2_topreala,u1_struct_0(k6_borsuk_1(k4_topmetr(A,B),k4_topmetr(C,D)))),u1_struct_0(k6_borsuk_1(k4_topmetr(A,B),k4_topmetr(C,D))),u1_struct_0(k1_topreala(A,B,C,D)))
& m2_relset_1(k2_partfun1(u1_struct_0(k6_borsuk_1(k3_topalg_2,k3_topalg_2)),u1_struct_0(k15_euclid(np__2)),k2_topreala,u1_struct_0(k6_borsuk_1(k4_topmetr(A,B),k4_topmetr(C,D)))),u1_struct_0(k6_borsuk_1(k4_topmetr(A,B),k4_topmetr(C,D))),u1_struct_0(k1_topreala(A,B,C,D))) ) ) ) ) ) ) ).
fof(t58_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k6_borsuk_1(k4_topmetr(A,B),k4_topmetr(C,D))),u1_struct_0(k1_topreala(A,B,C,D)))
& m2_relset_1(E,u1_struct_0(k6_borsuk_1(k4_topmetr(A,B),k4_topmetr(C,D))),u1_struct_0(k1_topreala(A,B,C,D))) )
=> ( E = k2_partfun1(u1_struct_0(k6_borsuk_1(k3_topalg_2,k3_topalg_2)),u1_struct_0(k15_euclid(np__2)),k2_topreala,u1_struct_0(k6_borsuk_1(k4_topmetr(A,B),k4_topmetr(C,D))))
=> v3_tops_2(E,k6_borsuk_1(k4_topmetr(A,B),k4_topmetr(C,D)),k1_topreala(A,B,C,D)) ) ) ) ) ) ) ) ).
fof(t59_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> r1_t_0topsp(k6_borsuk_1(k4_topmetr(A,B),k4_topmetr(C,D)),k1_topreala(A,B,C,D)) ) ) ) ) ) ).
fof(t60_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B))))
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k4_topmetr(C,D))))
=> m1_subset_1(k4_card_3(k4_funct_4(np__1,np__2,E,F)),k1_zfmisc_1(u1_struct_0(k1_topreala(A,B,C,D)))) ) ) ) ) ) ) ) ).
fof(t61_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> ! [E] :
( ( v3_pre_topc(E,k4_topmetr(A,B))
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B)))) )
=> ! [F] :
( ( v3_pre_topc(F,k4_topmetr(C,D))
& m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k4_topmetr(C,D)))) )
=> ( v3_pre_topc(k4_card_3(k4_funct_4(np__1,np__2,E,F)),k1_topreala(A,B,C,D))
& m1_subset_1(k4_card_3(k4_funct_4(np__1,np__2,E,F)),k1_zfmisc_1(u1_struct_0(k1_topreala(A,B,C,D)))) ) ) ) ) ) ) ) ) ).
fof(t62_topreala,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> ! [E] :
( ( v4_pre_topc(E,k4_topmetr(A,B))
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B)))) )
=> ! [F] :
( ( v4_pre_topc(F,k4_topmetr(C,D))
& m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k4_topmetr(C,D)))) )
=> ( v4_pre_topc(k4_card_3(k4_funct_4(np__1,np__2,E,F)),k1_topreala(A,B,C,D))
& m1_subset_1(k4_card_3(k4_funct_4(np__1,np__2,E,F)),k1_zfmisc_1(u1_struct_0(k1_topreala(A,B,C,D)))) ) ) ) ) ) ) ) ) ).
fof(dt_k1_topreala,axiom,
! [A,B,C,D] :
( ( v1_xreal_0(A)
& v1_xreal_0(B)
& v1_xreal_0(C)
& v1_xreal_0(D) )
=> m1_pre_topc(k1_topreala(A,B,C,D),k15_euclid(np__2)) ) ).
fof(dt_k2_topreala,axiom,
( v1_funct_1(k2_topreala)
& v1_funct_2(k2_topreala,u1_struct_0(k6_borsuk_1(k3_topalg_2,k3_topalg_2)),u1_struct_0(k15_euclid(np__2)))
& m2_relset_1(k2_topreala,u1_struct_0(k6_borsuk_1(k3_topalg_2,k3_topalg_2)),u1_struct_0(k15_euclid(np__2))) ) ).
%------------------------------------------------------------------------------