SET007 Axioms: SET007+336.ax
%------------------------------------------------------------------------------
% File : SET007+336 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Continuity of Mappings over the Union of Subspaces
% 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 : tmap_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 180 ( 2 unt; 0 def)
% Number of atoms : 2758 ( 176 equ)
% Maximal formula atoms : 35 ( 15 avg)
% Number of connectives : 3167 ( 589 ~; 24 |;1551 &)
% ( 46 <=>; 957 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 13 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 29 ( 27 usr; 1 prp; 0-4 aty)
% Number of functors : 35 ( 35 usr; 0 con; 1-6 aty)
% Number of variables : 836 ( 826 !; 10 ?)
% 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_tmap_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& m1_pre_topc(B,A)
& ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ( ~ v3_struct_0(k1_tsep_1(A,B,C))
& v1_pre_topc(k1_tsep_1(A,B,C))
& v2_pre_topc(k1_tsep_1(A,B,C)) ) ) ).
fof(fc2_tmap_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v3_struct_0(k6_tmap_1(A,B))
& v1_pre_topc(k6_tmap_1(A,B))
& v2_pre_topc(k6_tmap_1(A,B)) ) ) ).
fof(fc3_tmap_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_pre_topc(B,A) )
=> ( ~ v3_struct_0(k8_tmap_1(A,B))
& v1_pre_topc(k8_tmap_1(A,B))
& v2_pre_topc(k8_tmap_1(A,B)) ) ) ).
fof(t1_tmap_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(A))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(B))
=> ( r1_tarski(k2_funct_2(A,B,C,D),E)
<=> r1_tarski(D,k3_funct_2(A,B,C,E)) ) ) ) ) ) ) ).
fof(t2_tmap_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,D,B)
& m2_relset_1(E,D,B) )
=> ( ! [F] :
( m1_subset_1(F,A)
=> ( r2_hidden(F,D)
=> k8_funct_2(A,B,C,F) = k1_funct_1(E,F) ) )
=> k2_partfun1(A,B,C,D) = E ) ) ) ) ) ) ).
fof(t3_tmap_1,axiom,
$true ).
fof(t4_tmap_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C] :
( r1_tarski(C,B)
=> k9_relat_1(A,C) = k9_relat_1(k7_relat_1(A,B),C) ) ) ).
fof(t5_tmap_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C] :
( r1_tarski(k10_relat_1(A,C),B)
=> k10_relat_1(A,C) = k10_relat_1(k7_relat_1(A,B),C) ) ) ).
fof(d1_tmap_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(A)) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,C,B)
& m2_relset_1(E,C,B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,D,B)
& m2_relset_1(F,D,B) )
=> ( k2_partfun1(C,B,E,k5_subset_1(A,C,D)) = k2_partfun1(D,B,F,k5_subset_1(A,C,D))
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k4_subset_1(A,C,D),B)
& m2_relset_1(G,k4_subset_1(A,C,D),B) )
=> ( G = k1_tmap_1(A,B,C,D,E,F)
<=> ( k2_partfun1(k4_subset_1(A,C,D),B,G,C) = E
& k2_partfun1(k4_subset_1(A,C,D),B,G,D) = F ) ) ) ) ) ) ) ) ) ) ).
fof(t6_tmap_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(A)) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(A)) )
=> ( r1_subset_1(C,D)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,C,B)
& m2_relset_1(E,C,B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,D,B)
& m2_relset_1(F,D,B) )
=> ( k2_partfun1(C,B,E,k5_subset_1(A,C,D)) = k2_partfun1(D,B,F,k5_subset_1(A,C,D))
& k2_partfun1(k4_subset_1(A,C,D),B,k1_tmap_1(A,B,C,D,E,F),C) = E
& k2_partfun1(k4_subset_1(A,C,D),B,k1_tmap_1(A,B,C,D,E,F),D) = F ) ) ) ) ) ) ) ) ).
fof(t7_tmap_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(A)) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k4_subset_1(A,C,D),B)
& m2_relset_1(E,k4_subset_1(A,C,D),B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,C,B)
& m2_relset_1(F,C,B) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,D,B)
& m2_relset_1(G,D,B) )
=> ( ( k2_partfun1(k4_subset_1(A,C,D),B,E,C) = F
& k2_partfun1(k4_subset_1(A,C,D),B,E,D) = G )
=> E = k1_tmap_1(A,B,C,D,F,G) ) ) ) ) ) ) ) ) ).
fof(t8_tmap_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(A)) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,C,B)
& m2_relset_1(E,C,B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,D,B)
& m2_relset_1(F,D,B) )
=> ( k2_partfun1(C,B,E,k5_subset_1(A,C,D)) = k2_partfun1(D,B,F,k5_subset_1(A,C,D))
=> k1_tmap_1(A,B,C,D,E,F) = k1_tmap_1(A,B,D,C,F,E) ) ) ) ) ) ) ) ).
fof(t9_tmap_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(A)) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(A)) )
=> ! [E] :
( ( ~ v1_xboole_0(E)
& m1_subset_1(E,k1_zfmisc_1(A)) )
=> ! [F] :
( ( ~ v1_xboole_0(F)
& m1_subset_1(F,k1_zfmisc_1(A)) )
=> ! [G] :
( ( ~ v1_xboole_0(G)
& m1_subset_1(G,k1_zfmisc_1(A)) )
=> ( ( F = k4_subset_1(A,C,D)
& G = k4_subset_1(A,D,E) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,C,B)
& m2_relset_1(H,C,B) )
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,D,B)
& m2_relset_1(I,D,B) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,E,B)
& m2_relset_1(J,E,B) )
=> ( ( k2_partfun1(C,B,H,k5_subset_1(A,C,D)) = k2_partfun1(D,B,I,k5_subset_1(A,C,D))
& k2_partfun1(D,B,I,k5_subset_1(A,D,E)) = k2_partfun1(E,B,J,k5_subset_1(A,D,E))
& k2_partfun1(C,B,H,k5_subset_1(A,C,E)) = k2_partfun1(E,B,J,k5_subset_1(A,C,E)) )
=> ! [K] :
( ( v1_funct_1(K)
& v1_funct_2(K,F,B)
& m2_relset_1(K,F,B) )
=> ! [L] :
( ( v1_funct_1(L)
& v1_funct_2(L,G,B)
& m2_relset_1(L,G,B) )
=> ( ( K = k1_tmap_1(A,B,C,D,H,I)
& L = k1_tmap_1(A,B,D,E,I,J) )
=> k1_tmap_1(A,B,F,E,K,J) = k1_tmap_1(A,B,C,G,H,L) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t10_tmap_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(A)) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,C,B)
& m2_relset_1(E,C,B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,D,B)
& m2_relset_1(F,D,B) )
=> ( k2_partfun1(C,B,E,k5_subset_1(A,C,D)) = k2_partfun1(D,B,F,k5_subset_1(A,C,D))
=> ( ( m1_subset_1(C,k1_zfmisc_1(D))
=> k1_tmap_1(A,B,C,D,E,F) = F )
& ( k1_tmap_1(A,B,C,D,E,F) = F
=> m1_subset_1(C,k1_zfmisc_1(D)) )
& ( m1_subset_1(D,k1_zfmisc_1(C))
=> k1_tmap_1(A,B,C,D,E,F) = E )
& ( k1_tmap_1(A,B,C,D,E,F) = E
=> m1_subset_1(D,k1_zfmisc_1(C)) ) ) ) ) ) ) ) ) ) ).
fof(t11_tmap_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_pre_topc(B,A)
=> ( v1_pre_topc(g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)))
& m1_pre_topc(g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)),A) ) ) ) ).
fof(t12_tmap_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v2_pre_topc(C)
& l1_pre_topc(C) )
=> ( B = g1_pre_topc(u1_struct_0(C),u1_pre_topc(C))
=> ( m1_pre_topc(B,A)
<=> m1_pre_topc(C,A) ) ) ) ) ) ).
fof(t13_tmap_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v2_pre_topc(C)
& l1_pre_topc(C) )
=> ( C = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
=> ( ( v1_borsuk_1(B,A)
& m1_pre_topc(B,A) )
<=> ( v1_borsuk_1(C,A)
& m1_pre_topc(C,A) ) ) ) ) ) ) ).
fof(t14_tmap_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( v2_pre_topc(C)
& l1_pre_topc(C) )
=> ( C = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
=> ( ( v1_tsep_1(B,A)
& m1_pre_topc(B,A) )
<=> ( v1_tsep_1(C,A)
& m1_pre_topc(C,A) ) ) ) ) ) ) ).
fof(t15_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ( m1_pre_topc(B,C)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ? [E] :
( m1_subset_1(E,u1_struct_0(C))
& E = D ) ) ) ) ) ) ).
fof(t16_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k1_tsep_1(A,B,C)))
=> ~ ( ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> E != D )
& ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> E != D ) ) ) ) ) ) ).
fof(t17_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ( ~ r1_tsep_1(A,B,C)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k2_tsep_1(A,B,C)))
=> ( ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& E = D )
& ? [E] :
( m1_subset_1(E,u1_struct_0(C))
& E = D ) ) ) ) ) ) ) ).
fof(t18_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k1_tsep_1(A,B,C)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(C)))
=> ~ ( v4_pre_topc(E,B)
& r2_hidden(D,E)
& v4_pre_topc(F,C)
& r2_hidden(D,F)
& ! [G] :
( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k1_tsep_1(A,B,C))))
=> ~ ( v4_pre_topc(G,k1_tsep_1(A,B,C))
& r2_hidden(D,G)
& r1_tarski(G,k2_xboole_0(E,F)) ) ) ) ) ) ) ) ) ) ).
fof(t19_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k1_tsep_1(A,B,C)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(C)))
=> ~ ( v3_pre_topc(E,B)
& r2_hidden(D,E)
& v3_pre_topc(F,C)
& r2_hidden(D,F)
& ! [G] :
( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k1_tsep_1(A,B,C))))
=> ~ ( v3_pre_topc(G,k1_tsep_1(A,B,C))
& r2_hidden(D,G)
& r1_tarski(G,k2_xboole_0(E,F)) ) ) ) ) ) ) ) ) ) ).
fof(t20_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k1_tsep_1(A,B,C)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> ( ( E = D
& F = D )
=> ! [G] :
( m1_connsp_2(G,B,E)
=> ! [H] :
( m1_connsp_2(H,C,F)
=> ? [I] :
( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k1_tsep_1(A,B,C))))
& v3_pre_topc(I,k1_tsep_1(A,B,C))
& r2_hidden(D,I)
& r1_tarski(I,k2_xboole_0(G,H)) ) ) ) ) ) ) ) ) ) ) ).
fof(t21_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k1_tsep_1(A,B,C)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> ( ( E = D
& F = D )
=> ! [G] :
( m1_connsp_2(G,B,E)
=> ! [H] :
( m1_connsp_2(H,C,F)
=> ? [I] :
( m1_connsp_2(I,k1_tsep_1(A,B,C),D)
& r1_tarski(I,k2_xboole_0(G,H)) ) ) ) ) ) ) ) ) ) ) ).
fof(t22_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ( m1_pre_topc(B,C)
=> ( ~ r1_tsep_1(A,B,C)
& ~ r1_tsep_1(A,C,B) ) ) ) ) ) ).
fof(t23_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ( m1_pre_topc(B,C)
=> ( ( r1_tsep_1(A,B,D)
& r1_tsep_1(A,D,B) )
| ( ~ r1_tsep_1(A,C,D)
& ~ r1_tsep_1(A,D,C) ) ) ) ) ) ) ) ).
fof(t24_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ( m1_pre_topc(B,C)
=> ( ( ~ r1_tsep_1(A,C,D)
& ~ r1_tsep_1(A,D,C) )
| ( r1_tsep_1(A,B,D)
& r1_tsep_1(A,D,B) ) ) ) ) ) ) ) ).
fof(t25_tmap_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> k1_tsep_1(A,B,B) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) ) ) ).
fof(t26_tmap_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> k2_tsep_1(A,B,B) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) ) ) ).
fof(t27_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& m1_pre_topc(E,A) )
=> ( ( m1_pre_topc(B,C)
& m1_pre_topc(D,E) )
=> m1_pre_topc(k1_tsep_1(A,B,D),k1_tsep_1(A,C,E)) ) ) ) ) ) ) ).
fof(t28_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& m1_pre_topc(E,A) )
=> ( ( m1_pre_topc(B,D)
& m1_pre_topc(C,E) )
=> ( r1_tsep_1(A,B,C)
| m1_pre_topc(k2_tsep_1(A,B,C),k2_tsep_1(A,D,E)) ) ) ) ) ) ) ) ).
fof(t29_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ( ( m1_pre_topc(B,C)
& m1_pre_topc(D,C) )
=> m1_pre_topc(k1_tsep_1(A,B,D),C) ) ) ) ) ) ).
fof(t30_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ( ( m1_pre_topc(B,D)
& m1_pre_topc(C,D) )
=> ( r1_tsep_1(A,B,C)
| m1_pre_topc(k2_tsep_1(A,B,C),D) ) ) ) ) ) ) ).
fof(t31_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ( ~ ( ( r1_tsep_1(A,B,C)
| r1_tsep_1(A,C,B) )
& ~ ( r1_tsep_1(A,D,C)
& r1_tsep_1(A,C,D) )
& ~ ( k2_tsep_1(A,k1_tsep_1(A,B,D),C) = k2_tsep_1(A,D,C)
& k2_tsep_1(A,C,k1_tsep_1(A,B,D)) = k2_tsep_1(A,C,D) ) )
& ~ ( ~ ( r1_tsep_1(A,B,C)
& r1_tsep_1(A,C,B) )
& ( r1_tsep_1(A,D,C)
| r1_tsep_1(A,C,D) )
& ~ ( k2_tsep_1(A,k1_tsep_1(A,B,D),C) = k2_tsep_1(A,B,C)
& k2_tsep_1(A,C,k1_tsep_1(A,B,D)) = k2_tsep_1(A,C,B) ) ) ) ) ) ) ) ).
fof(t32_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ( ~ r1_tsep_1(A,B,C)
=> ( ( m1_pre_topc(B,D)
=> m1_pre_topc(k2_tsep_1(A,B,C),k2_tsep_1(A,D,C)) )
& ( m1_pre_topc(C,D)
=> m1_pre_topc(k2_tsep_1(A,B,C),k2_tsep_1(A,B,D)) ) ) ) ) ) ) ) ).
fof(t33_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ( m1_pre_topc(B,C)
=> ( ( ~ r1_tsep_1(A,C,D)
& ~ r1_tsep_1(A,D,C) )
| ( k2_tsep_1(A,C,k1_tsep_1(A,B,D)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
& k2_tsep_1(A,C,k1_tsep_1(A,D,B)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) ) ) ) ) ) ) ) ).
fof(t34_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ( ~ r1_tsep_1(A,B,C)
=> ( ( m1_pre_topc(B,D)
=> ( ~ r1_tsep_1(A,k2_tsep_1(A,D,C),B)
& ~ r1_tsep_1(A,k2_tsep_1(A,C,D),B) ) )
& ( m1_pre_topc(C,D)
=> ( ~ r1_tsep_1(A,k2_tsep_1(A,B,D),C)
& ~ r1_tsep_1(A,k2_tsep_1(A,D,B),C) ) ) ) ) ) ) ) ) ).
fof(t35_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& m1_pre_topc(E,A) )
=> ( ( m1_pre_topc(B,C)
& m1_pre_topc(D,E) )
=> ( ( ~ r1_tsep_1(A,C,E)
& ~ r1_tsep_1(A,k2_tsep_1(A,C,E),k1_tsep_1(A,B,D)) )
| ( r1_tsep_1(A,C,D)
& r1_tsep_1(A,E,B) ) ) ) ) ) ) ) ) ).
fof(t36_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& m1_pre_topc(E,A) )
=> ( ( m1_pre_topc(k1_tsep_1(A,B,C),k1_tsep_1(A,D,E))
& m1_pre_topc(k2_tsep_1(A,D,k1_tsep_1(A,B,C)),B)
& m1_pre_topc(k2_tsep_1(A,E,k1_tsep_1(A,B,C)),C) )
=> ( m1_pre_topc(B,C)
| m1_pre_topc(C,B)
| ( ~ r1_tsep_1(A,D,k1_tsep_1(A,B,C))
& ~ r1_tsep_1(A,E,k1_tsep_1(A,B,C)) ) ) ) ) ) ) ) ) ).
fof(t37_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& m1_pre_topc(E,A) )
=> ! [F] :
( ( ~ v3_struct_0(F)
& m1_pre_topc(F,A) )
=> ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = k1_tsep_1(A,k1_tsep_1(A,D,E),F)
& m1_pre_topc(k2_tsep_1(A,D,k1_tsep_1(A,B,C)),B)
& m1_pre_topc(k2_tsep_1(A,E,k1_tsep_1(A,B,C)),C)
& m1_pre_topc(k2_tsep_1(A,F,k1_tsep_1(A,B,C)),k2_tsep_1(A,B,C)) )
=> ( r1_tsep_1(A,B,C)
| m1_pre_topc(B,C)
| m1_pre_topc(C,B)
| ( ~ r1_tsep_1(A,D,k1_tsep_1(A,B,C))
& ~ r1_tsep_1(A,E,k1_tsep_1(A,B,C)) ) ) ) ) ) ) ) ) ) ).
fof(t38_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& m1_pre_topc(E,A) )
=> ! [F] :
( ( ~ v3_struct_0(F)
& m1_pre_topc(F,A) )
=> ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = k1_tsep_1(A,k1_tsep_1(A,D,E),F)
& m1_pre_topc(k2_tsep_1(A,D,k1_tsep_1(A,B,C)),B)
& m1_pre_topc(k2_tsep_1(A,E,k1_tsep_1(A,B,C)),C)
& m1_pre_topc(k2_tsep_1(A,F,k1_tsep_1(A,B,C)),k2_tsep_1(A,B,C)) )
=> ( r1_tsep_1(A,B,C)
| m1_pre_topc(B,C)
| m1_pre_topc(C,B)
| m1_pre_topc(k1_tsep_1(A,B,C),k1_tsep_1(A,D,E))
| ( ~ r1_tsep_1(A,k1_tsep_1(A,D,E),k1_tsep_1(A,B,C))
& ~ r1_tsep_1(A,F,k1_tsep_1(A,B,C)) ) ) ) ) ) ) ) ) ) ).
fof(t39_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ( ~ ( ~ r1_tsep_1(A,k1_tsep_1(A,B,C),D)
& r1_tsep_1(A,B,D)
& r1_tsep_1(A,C,D) )
& ~ ( ~ ( r1_tsep_1(A,B,D)
& r1_tsep_1(A,C,D) )
& r1_tsep_1(A,k1_tsep_1(A,B,C),D) )
& ~ ( ~ r1_tsep_1(A,D,k1_tsep_1(A,B,C))
& r1_tsep_1(A,D,B)
& r1_tsep_1(A,D,C) )
& ~ ( ~ ( r1_tsep_1(A,D,B)
& r1_tsep_1(A,D,C) )
& r1_tsep_1(A,D,k1_tsep_1(A,B,C)) ) ) ) ) ) ) ).
fof(t40_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ( ( r1_tsep_1(A,k1_tsep_1(A,B,C),D)
=> ( r1_tsep_1(A,B,D)
& r1_tsep_1(A,C,D) ) )
& ( ( r1_tsep_1(A,B,D)
& r1_tsep_1(A,C,D) )
=> r1_tsep_1(A,k1_tsep_1(A,B,C),D) )
& ( r1_tsep_1(A,D,k1_tsep_1(A,B,C))
=> ( r1_tsep_1(A,D,B)
& r1_tsep_1(A,D,C) ) )
& ( ( r1_tsep_1(A,D,B)
& r1_tsep_1(A,D,C) )
=> r1_tsep_1(A,D,k1_tsep_1(A,B,C)) ) ) ) ) ) ) ).
fof(t41_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ( ~ r1_tsep_1(A,B,C)
=> ( ( ~ r1_tsep_1(A,k2_tsep_1(A,B,C),D)
=> ( ~ r1_tsep_1(A,B,D)
& ~ r1_tsep_1(A,C,D) ) )
& ( ~ r1_tsep_1(A,D,k2_tsep_1(A,B,C))
=> ( ~ r1_tsep_1(A,D,B)
& ~ r1_tsep_1(A,D,C) ) ) ) ) ) ) ) ) ).
fof(t42_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ( ~ r1_tsep_1(A,B,C)
=> ( ( ( r1_tsep_1(A,B,D)
| r1_tsep_1(A,C,D) )
=> r1_tsep_1(A,k2_tsep_1(A,B,C),D) )
& ( ( r1_tsep_1(A,D,B)
| r1_tsep_1(A,D,C) )
=> r1_tsep_1(A,D,k2_tsep_1(A,B,C)) ) ) ) ) ) ) ) ).
fof(t43_tmap_1,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] :
( ( ~ v3_struct_0(C)
& v1_borsuk_1(C,A)
& m1_pre_topc(C,A) )
=> ( ~ r1_tsep_1(A,C,B)
=> ( v1_borsuk_1(k2_tsep_1(A,C,B),B)
& m1_pre_topc(k2_tsep_1(A,C,B),B) ) ) ) ) ) ).
fof(t44_tmap_1,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] :
( ( ~ v3_struct_0(C)
& v1_tsep_1(C,A)
& m1_pre_topc(C,A) )
=> ( ~ r1_tsep_1(A,C,B)
=> ( v1_tsep_1(k2_tsep_1(A,C,B),B)
& m1_pre_topc(k2_tsep_1(A,C,B),B) ) ) ) ) ) ).
fof(t45_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v1_borsuk_1(D,A)
& m1_pre_topc(D,A) )
=> ( ( m1_pre_topc(B,D)
& r1_tsep_1(A,D,C) )
=> ( v1_borsuk_1(B,k1_tsep_1(A,B,C))
& m1_pre_topc(B,k1_tsep_1(A,B,C))
& v1_borsuk_1(B,k1_tsep_1(A,C,B))
& m1_pre_topc(B,k1_tsep_1(A,C,B)) ) ) ) ) ) ) ).
fof(t46_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v1_tsep_1(D,A)
& m1_pre_topc(D,A) )
=> ( ( m1_pre_topc(B,D)
& r1_tsep_1(A,D,C) )
=> ( v1_tsep_1(B,k1_tsep_1(A,B,C))
& m1_pre_topc(B,k1_tsep_1(A,B,C))
& v1_tsep_1(B,k1_tsep_1(A,C,B))
& m1_pre_topc(B,k1_tsep_1(A,C,B)) ) ) ) ) ) ) ).
fof(d2_tmap_1,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)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_tmap_1(A,B,C,D)
<=> ! [E] :
( m1_connsp_2(E,B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D))
=> ? [F] :
( m1_connsp_2(F,A,D)
& r1_tarski(k4_pre_topc(A,B,C,F),E) ) ) ) ) ) ) ) ).
fof(t47_tmap_1,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(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( r1_tmap_1(B,A,C,D)
<=> ! [E] :
( m1_connsp_2(E,A,k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,D))
=> m1_connsp_2(k5_pre_topc(B,A,C,E),B,D) ) ) ) ) ) ) ).
fof(t48_tmap_1,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)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_tmap_1(A,B,C,D)
<=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
=> ~ ( v3_pre_topc(E,B)
& r2_hidden(k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),E)
& ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( v3_pre_topc(F,A)
& r2_hidden(D,F)
& r1_tarski(k4_pre_topc(A,B,C,F),E) ) ) ) ) ) ) ) ) ) ).
fof(t49_tmap_1,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(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( v5_pre_topc(C,B,A)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> r1_tmap_1(B,A,C,D) ) ) ) ) ) ).
fof(t50_tmap_1,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) )
=> ( ( u1_struct_0(B) = u1_struct_0(C)
& r1_tarski(u1_pre_topc(C),u1_pre_topc(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
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( r1_tmap_1(A,B,D,F)
=> r1_tmap_1(A,C,E,F) ) ) ) ) ) ) ) ) ) ).
fof(t51_tmap_1,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) )
=> ( ( u1_struct_0(A) = u1_struct_0(B)
& r1_tarski(u1_pre_topc(B),u1_pre_topc(A)) )
=> ! [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)) )
=> ! [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)) )
=> ( D = E
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ( ( F = G
& r1_tmap_1(B,C,E,G) )
=> r1_tmap_1(A,C,D,F) ) ) ) ) ) ) ) ) ) ) ).
fof(t52_tmap_1,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(B),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(A)) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(C))
=> ( ( G = k8_funct_2(u1_struct_0(B),u1_struct_0(C),D,F)
& r1_tmap_1(B,C,D,F)
& r1_tmap_1(C,A,E,G) )
=> r1_tmap_1(B,A,k7_funct_2(u1_struct_0(B),u1_struct_0(C),u1_struct_0(A),D,E),F) ) ) ) ) ) ) ) ) ).
fof(t53_tmap_1,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(C),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(C),u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( v5_pre_topc(D,C,B)
& r1_tmap_1(B,A,E,F) )
=> ! [G] :
( m1_subset_1(G,u1_struct_0(C))
=> ( r2_hidden(G,k5_pre_topc(C,B,D,k1_struct_0(B,F)))
=> r1_tmap_1(C,A,k7_funct_2(u1_struct_0(C),u1_struct_0(B),u1_struct_0(A),D,E),G) ) ) ) ) ) ) ) ) ) ).
fof(t54_tmap_1,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(C),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(C),u1_struct_0(A)) )
=> ! [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] :
( m1_subset_1(F,u1_struct_0(C))
=> ( ( r1_tmap_1(C,A,D,F)
& v5_pre_topc(E,A,B) )
=> r1_tmap_1(C,B,k7_funct_2(u1_struct_0(C),u1_struct_0(A),u1_struct_0(B),D,E),F) ) ) ) ) ) ) ) ).
fof(t55_tmap_1,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)) )
=> ( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r1_tmap_1(A,B,C,D) ) ) ) ) ) ).
fof(t56_tmap_1,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) )
=> ( ( u1_struct_0(B) = u1_struct_0(C)
& r1_tarski(u1_pre_topc(C),u1_pre_topc(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(D,A,B)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(C))
& v5_pre_topc(D,A,C)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)) ) ) ) ) ) ) ).
fof(t57_tmap_1,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) )
=> ( ( u1_struct_0(A) = u1_struct_0(B)
& r1_tarski(u1_pre_topc(B),u1_pre_topc(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& v5_pre_topc(D,B,C)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
=> ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(C))
& v5_pre_topc(D,A,C)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)) ) ) ) ) ) ) ).
fof(d3_tmap_1,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_pre_topc(C,A)
=> ! [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)) )
=> k2_tmap_1(A,B,C,D) = k2_partfun1(u1_struct_0(A),u1_struct_0(B),D,u1_struct_0(C)) ) ) ) ) ).
fof(t58_tmap_1,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(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( r2_hidden(E,u1_struct_0(C))
=> k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,E) = k1_funct_1(k2_tmap_1(B,A,C,D),E) ) ) ) ) ) ) ).
fof(t59_tmap_1,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(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(A)) )
=> ( ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( r2_hidden(F,u1_struct_0(C))
=> k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,F) = k1_funct_1(E,F) ) )
=> k2_tmap_1(B,A,C,D) = E ) ) ) ) ) ) ).
fof(t60_tmap_1,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(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
=> D = k2_tmap_1(B,A,C,D) ) ) ) ) ) ).
fof(t61_tmap_1,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(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
=> ( r1_tarski(E,u1_struct_0(C))
=> k4_pre_topc(B,A,D,E) = k4_pre_topc(C,A,k2_tmap_1(B,A,C,D),E) ) ) ) ) ) ) ).
fof(t62_tmap_1,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,A) )
=> ! [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] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
=> ( r1_tarski(k5_pre_topc(A,B,D,E),u1_struct_0(C))
=> k5_pre_topc(A,B,D,E) = k5_pre_topc(C,B,k2_tmap_1(A,B,C,D),E) ) ) ) ) ) ) ).
fof(t63_tmap_1,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(C),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(C),u1_struct_0(A)) )
=> ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(A))
& k2_tmap_1(B,A,C,E) = D ) ) ) ) ) ).
fof(t64_tmap_1,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(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,B) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(D))
=> ( ( E = F
& r1_tmap_1(B,A,C,E) )
=> r1_tmap_1(D,A,k2_tmap_1(B,A,D,C),F) ) ) ) ) ) ) ) ).
fof(t65_tmap_1,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(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,B) )
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(D))
=> ( ( r1_tarski(E,u1_struct_0(D))
& m1_connsp_2(E,B,F)
& F = G )
=> ( r1_tmap_1(B,A,C,F)
<=> r1_tmap_1(D,A,k2_tmap_1(B,A,D,C),G) ) ) ) ) ) ) ) ) ) ).
fof(t66_tmap_1,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(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,B) )
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(D))
=> ( ( v3_pre_topc(E,B)
& r2_hidden(F,E)
& r1_tarski(E,u1_struct_0(D))
& F = G )
=> ( r1_tmap_1(B,A,C,F)
<=> r1_tmap_1(D,A,k2_tmap_1(B,A,D,C),G) ) ) ) ) ) ) ) ) ) ).
fof(t67_tmap_1,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(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v1_tsep_1(D,B)
& m1_pre_topc(D,B) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(D))
=> ( E = F
=> ( r1_tmap_1(B,A,C,E)
<=> r1_tmap_1(D,A,k2_tmap_1(B,A,D,C),F) ) ) ) ) ) ) ) ) ).
fof(t68_tmap_1,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))
& v5_pre_topc(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ( v1_funct_1(k2_tmap_1(A,B,D,C))
& v1_funct_2(k2_tmap_1(A,B,D,C),u1_struct_0(D),u1_struct_0(B))
& v5_pre_topc(k2_tmap_1(A,B,D,C),D,B)
& m2_relset_1(k2_tmap_1(A,B,D,C),u1_struct_0(D),u1_struct_0(B)) ) ) ) ) ) ).
fof(t69_tmap_1,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] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [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(B),u1_struct_0(C))
& m2_relset_1(F,u1_struct_0(B),u1_struct_0(C)) )
=> k2_tmap_1(A,C,D,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),E,F)) = k7_funct_2(u1_struct_0(D),u1_struct_0(B),u1_struct_0(C),k2_tmap_1(A,B,D,E),F) ) ) ) ) ) ) ).
fof(t70_tmap_1,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] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [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)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(F,u1_struct_0(A),u1_struct_0(B)) )
=> ( ( v5_pre_topc(E,B,C)
& v5_pre_topc(k2_tmap_1(A,B,D,F),D,B) )
=> v5_pre_topc(k2_tmap_1(A,C,D,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),F,E)),D,C) ) ) ) ) ) ) ) ).
fof(t71_tmap_1,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] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& v5_pre_topc(E,B,C)
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(F,u1_struct_0(A),u1_struct_0(B)) )
=> ( ( v1_funct_1(k2_tmap_1(A,B,D,F))
& v1_funct_2(k2_tmap_1(A,B,D,F),u1_struct_0(D),u1_struct_0(B))
& v5_pre_topc(k2_tmap_1(A,B,D,F),D,B)
& m2_relset_1(k2_tmap_1(A,B,D,F),u1_struct_0(D),u1_struct_0(B)) )
=> ( v1_funct_1(k2_tmap_1(A,C,D,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),F,E)))
& v1_funct_2(k2_tmap_1(A,C,D,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),F,E)),u1_struct_0(D),u1_struct_0(C))
& v5_pre_topc(k2_tmap_1(A,C,D,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),F,E)),D,C)
& m2_relset_1(k2_tmap_1(A,C,D,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),F,E)),u1_struct_0(D),u1_struct_0(C)) ) ) ) ) ) ) ) ) ).
fof(d4_tmap_1,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_pre_topc(C,A)
=> ! [D] :
( m1_pre_topc(D,A)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(B)) )
=> ( m1_pre_topc(D,C)
=> k3_tmap_1(A,B,C,D,E) = k2_partfun1(u1_struct_0(C),u1_struct_0(B),E,u1_struct_0(D)) ) ) ) ) ) ) ).
fof(t72_tmap_1,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,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(D),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(D),u1_struct_0(B)) )
=> ( m1_pre_topc(C,D)
=> ! [F] :
( m1_subset_1(F,u1_struct_0(D))
=> ( r2_hidden(F,u1_struct_0(C))
=> k8_funct_2(u1_struct_0(D),u1_struct_0(B),E,F) = k1_funct_1(k3_tmap_1(A,B,D,C,E),F) ) ) ) ) ) ) ) ) ).
fof(t73_tmap_1,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,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(D),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(D),u1_struct_0(B)) )
=> ( m1_pre_topc(C,D)
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(C),u1_struct_0(B))
& m2_relset_1(F,u1_struct_0(C),u1_struct_0(B)) )
=> ( ! [G] :
( m1_subset_1(G,u1_struct_0(D))
=> ( r2_hidden(G,u1_struct_0(C))
=> k8_funct_2(u1_struct_0(D),u1_struct_0(B),E,G) = k1_funct_1(F,G) ) )
=> k3_tmap_1(A,B,D,C,E) = F ) ) ) ) ) ) ) ) ).
fof(t74_tmap_1,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,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(C),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(C),u1_struct_0(B)) )
=> D = k3_tmap_1(A,B,C,C,D) ) ) ) ) ).
fof(t75_tmap_1,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,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(D),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(D),u1_struct_0(B)) )
=> ( m1_pre_topc(C,D)
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(D)))
=> ( r1_tarski(F,u1_struct_0(C))
=> k4_pre_topc(D,B,E,F) = k4_pre_topc(C,B,k3_tmap_1(A,B,D,C,E),F) ) ) ) ) ) ) ) ) ).
fof(t76_tmap_1,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,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(D),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(D),u1_struct_0(B)) )
=> ( m1_pre_topc(C,D)
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B)))
=> ( r1_tarski(k5_pre_topc(D,B,E,F),u1_struct_0(C))
=> k5_pre_topc(D,B,E,F) = k5_pre_topc(C,B,k3_tmap_1(A,B,D,C,E),F) ) ) ) ) ) ) ) ) ).
fof(t77_tmap_1,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,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [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(C),u1_struct_0(B))
& m2_relset_1(F,u1_struct_0(C),u1_struct_0(B)) )
=> ( ( F = k2_tmap_1(A,B,C,E)
& m1_pre_topc(D,C) )
=> k3_tmap_1(A,B,C,D,F) = k2_tmap_1(A,B,D,E) ) ) ) ) ) ) ) ).
fof(t78_tmap_1,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,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [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)) )
=> ( m1_pre_topc(C,D)
=> k3_tmap_1(A,B,D,C,k2_tmap_1(A,B,D,E)) = k2_tmap_1(A,B,C,E) ) ) ) ) ) ) ).
fof(t79_tmap_1,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,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& m1_pre_topc(E,A) )
=> ( ( m1_pre_topc(D,C)
& m1_pre_topc(E,D) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(C),u1_struct_0(B))
& m2_relset_1(F,u1_struct_0(C),u1_struct_0(B)) )
=> k3_tmap_1(A,B,D,E,k3_tmap_1(A,B,C,D,F)) = k3_tmap_1(A,B,C,E,F) ) ) ) ) ) ) ) ).
fof(t80_tmap_1,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,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [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(C),u1_struct_0(B))
& m2_relset_1(F,u1_struct_0(C),u1_struct_0(B)) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(D),u1_struct_0(B))
& m2_relset_1(G,u1_struct_0(D),u1_struct_0(B)) )
=> ( ( D = A
& E = G )
=> ( k3_tmap_1(A,B,D,C,G) = F
<=> k2_tmap_1(A,B,C,E) = F ) ) ) ) ) ) ) ) ) ).
fof(t81_tmap_1,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,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(B)) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(D))
=> ( ( F = G
& m1_pre_topc(D,C)
& r1_tmap_1(C,B,E,F) )
=> r1_tmap_1(D,B,k3_tmap_1(A,B,C,D,E),G) ) ) ) ) ) ) ) ) ).
fof(t82_tmap_1,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,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [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)) )
=> ( m1_pre_topc(C,D)
=> ! [F] :
( m1_subset_1(F,u1_struct_0(D))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(C))
=> ( ( F = G
& r1_tmap_1(D,B,k2_tmap_1(A,B,D,E),F) )
=> r1_tmap_1(C,B,k2_tmap_1(A,B,C,E),G) ) ) ) ) ) ) ) ) ) ).
fof(t83_tmap_1,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,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(D),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(D),u1_struct_0(B)) )
=> ( m1_pre_topc(C,D)
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(D)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(D))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(C))
=> ( ( r1_tarski(F,u1_struct_0(C))
& m1_connsp_2(F,D,G)
& G = H )
=> ( r1_tmap_1(D,B,E,G)
<=> r1_tmap_1(C,B,k3_tmap_1(A,B,D,C,E),H) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t84_tmap_1,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,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(D),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(D),u1_struct_0(B)) )
=> ( m1_pre_topc(C,D)
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(D)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(D))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(C))
=> ( ( v3_pre_topc(F,D)
& r2_hidden(G,F)
& r1_tarski(F,u1_struct_0(C))
& G = H )
=> ( r1_tmap_1(D,B,E,G)
<=> r1_tmap_1(C,B,k3_tmap_1(A,B,D,C,E),H) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t85_tmap_1,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] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(D),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(D),u1_struct_0(A)) )
=> ( m1_pre_topc(C,D)
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(D))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(C))
=> ( ( v3_pre_topc(F,B)
& r2_hidden(G,F)
& r1_tarski(F,u1_struct_0(C))
& G = H )
=> ( r1_tmap_1(D,A,E,G)
<=> r1_tmap_1(C,A,k3_tmap_1(B,A,D,C,E),H) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t86_tmap_1,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,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(D),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(D),u1_struct_0(B)) )
=> ( ( v1_tsep_1(C,D)
& m1_pre_topc(C,D) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(D))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(C))
=> ( F = G
=> ( r1_tmap_1(D,B,E,F)
<=> r1_tmap_1(C,B,k3_tmap_1(A,B,D,C,E),G) ) ) ) ) ) ) ) ) ) ) ).
fof(t87_tmap_1,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] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(D),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(D),u1_struct_0(A)) )
=> ( ( v1_tsep_1(C,B)
& m1_pre_topc(C,B)
& m1_pre_topc(C,D) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(D))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(C))
=> ( F = G
=> ( r1_tmap_1(D,A,E,F)
<=> r1_tmap_1(C,A,k3_tmap_1(B,A,D,C,E),G) ) ) ) ) ) ) ) ) ) ) ).
fof(t88_tmap_1,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,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(D),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(D),u1_struct_0(B)) )
=> ( g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) = D
=> ! [F] :
( m1_subset_1(F,u1_struct_0(D))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(C))
=> ( ( F = G
& r1_tmap_1(C,B,k3_tmap_1(A,B,D,C,E),G) )
=> r1_tmap_1(D,B,E,F) ) ) ) ) ) ) ) ) ) ).
fof(t89_tmap_1,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,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(B))
& v5_pre_topc(E,C,B)
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(B)) )
=> ( m1_pre_topc(D,C)
=> ( v1_funct_1(k3_tmap_1(A,B,C,D,E))
& v1_funct_2(k3_tmap_1(A,B,C,D,E),u1_struct_0(D),u1_struct_0(B))
& v5_pre_topc(k3_tmap_1(A,B,C,D,E),D,B)
& m2_relset_1(k3_tmap_1(A,B,C,D,E),u1_struct_0(D),u1_struct_0(B)) ) ) ) ) ) ) ) ).
fof(t90_tmap_1,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,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& m1_pre_topc(E,A) )
=> ( ( m1_pre_topc(C,D)
& m1_pre_topc(E,C) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(D),u1_struct_0(B))
& m2_relset_1(F,u1_struct_0(D),u1_struct_0(B)) )
=> ( ( v1_funct_1(k3_tmap_1(A,B,D,C,F))
& v1_funct_2(k3_tmap_1(A,B,D,C,F),u1_struct_0(C),u1_struct_0(B))
& v5_pre_topc(k3_tmap_1(A,B,D,C,F),C,B)
& m2_relset_1(k3_tmap_1(A,B,D,C,F),u1_struct_0(C),u1_struct_0(B)) )
=> ( v1_funct_1(k3_tmap_1(A,B,D,E,F))
& v1_funct_2(k3_tmap_1(A,B,D,E,F),u1_struct_0(E),u1_struct_0(B))
& v5_pre_topc(k3_tmap_1(A,B,D,E,F),E,B)
& m2_relset_1(k3_tmap_1(A,B,D,E,F),u1_struct_0(E),u1_struct_0(B)) ) ) ) ) ) ) ) ) ) ).
fof(t91_tmap_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(A),k7_grcat_1(A),B) = B ) ) ).
fof(t92_tmap_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C) = C )
=> B = k7_grcat_1(A) ) ) ) ).
fof(t93_tmap_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_struct_0(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)) )
=> ( k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),k7_grcat_1(A),C) = C
& k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),C,k7_grcat_1(B)) = C ) ) ) ) ).
fof(t94_tmap_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v1_funct_1(k7_grcat_1(A))
& v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A))
& v5_pre_topc(k7_grcat_1(A),A,A)
& m2_relset_1(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) ) ) ).
fof(d5_tmap_1,axiom,
$true ).
fof(d6_tmap_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> k4_tmap_1(A,B) = k2_tmap_1(A,A,B,k7_grcat_1(A)) ) ) ).
fof(t95_tmap_1,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))
=> ( r2_hidden(C,u1_struct_0(B))
=> k1_funct_1(k4_tmap_1(A,B),C) = C ) ) ) ) ).
fof(t96_tmap_1,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,u1_struct_0(B))
=> D = k1_funct_1(C,D) ) )
=> k4_tmap_1(A,B) = C ) ) ) ) ).
fof(t97_tmap_1,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,A) )
=> ! [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)) )
=> k2_tmap_1(A,B,C,D) = k7_funct_2(u1_struct_0(C),u1_struct_0(A),u1_struct_0(B),k4_tmap_1(A,C),D) ) ) ) ) ).
fof(t98_tmap_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ( v1_funct_1(k4_tmap_1(A,B))
& v1_funct_2(k4_tmap_1(A,B),u1_struct_0(B),u1_struct_0(A))
& v5_pre_topc(k4_tmap_1(A,B),B,A)
& m2_relset_1(k4_tmap_1(A,B),u1_struct_0(B),u1_struct_0(A)) ) ) ) ).
fof(t99_tmap_1,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)))
=> r1_tarski(u1_pre_topc(A),k5_tmap_1(A,B)) ) ) ).
fof(t102_tmap_1,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)))
=> r2_hidden(B,k5_tmap_1(A,B)) ) ) ).
fof(t103_tmap_1,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)))
=> ( r2_hidden(B,u1_pre_topc(A))
<=> u1_pre_topc(A) = k5_tmap_1(A,B) ) ) ) ).
fof(d8_tmap_1,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)))
=> k6_tmap_1(A,B) = g1_pre_topc(u1_struct_0(A),k5_tmap_1(A,B)) ) ) ).
fof(t104_tmap_1,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)))
=> ( u1_struct_0(k6_tmap_1(A,B)) = u1_struct_0(A)
& u1_pre_topc(k6_tmap_1(A,B)) = k5_tmap_1(A,B) ) ) ) ).
fof(t105_tmap_1,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(k6_tmap_1(A,B))))
=> ( C = B
=> v3_pre_topc(C,k6_tmap_1(A,B)) ) ) ) ) ).
fof(t106_tmap_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(B,A)
<=> g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = k6_tmap_1(A,B) ) ) ) ).
fof(d9_tmap_1,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)))
=> k7_tmap_1(A,B) = k6_partfun1(u1_struct_0(A)) ) ) ).
fof(t107_tmap_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(B,A)
=> k7_tmap_1(A,B) = k7_grcat_1(A) ) ) ) ).
fof(t108_tmap_1,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,u1_struct_0(A))
=> ( ~ r2_hidden(C,B)
=> r1_tmap_1(A,k6_tmap_1(A,B),k7_tmap_1(A,B),C) ) ) ) ) ).
fof(t109_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ( r1_xboole_0(u1_struct_0(C),B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> r1_tmap_1(C,k6_tmap_1(A,B),k2_tmap_1(A,k6_tmap_1(A,B),C,k7_tmap_1(A,B)),D) ) ) ) ) ) ).
fof(t110_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ( u1_struct_0(C) = B
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> r1_tmap_1(C,k6_tmap_1(A,B),k2_tmap_1(A,k6_tmap_1(A,B),C,k7_tmap_1(A,B)),D) ) ) ) ) ) ).
fof(t111_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ( r1_xboole_0(u1_struct_0(C),B)
=> ( v1_funct_1(k2_tmap_1(A,k6_tmap_1(A,B),C,k7_tmap_1(A,B)))
& v1_funct_2(k2_tmap_1(A,k6_tmap_1(A,B),C,k7_tmap_1(A,B)),u1_struct_0(C),u1_struct_0(k6_tmap_1(A,B)))
& v5_pre_topc(k2_tmap_1(A,k6_tmap_1(A,B),C,k7_tmap_1(A,B)),C,k6_tmap_1(A,B))
& m2_relset_1(k2_tmap_1(A,k6_tmap_1(A,B),C,k7_tmap_1(A,B)),u1_struct_0(C),u1_struct_0(k6_tmap_1(A,B))) ) ) ) ) ) ).
fof(t112_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ( u1_struct_0(C) = B
=> ( v1_funct_1(k2_tmap_1(A,k6_tmap_1(A,B),C,k7_tmap_1(A,B)))
& v1_funct_2(k2_tmap_1(A,k6_tmap_1(A,B),C,k7_tmap_1(A,B)),u1_struct_0(C),u1_struct_0(k6_tmap_1(A,B)))
& v5_pre_topc(k2_tmap_1(A,k6_tmap_1(A,B),C,k7_tmap_1(A,B)),C,k6_tmap_1(A,B))
& m2_relset_1(k2_tmap_1(A,k6_tmap_1(A,B),C,k7_tmap_1(A,B)),u1_struct_0(C),u1_struct_0(k6_tmap_1(A,B))) ) ) ) ) ) ).
fof(t113_tmap_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(B,A)
<=> ( v1_funct_1(k7_tmap_1(A,B))
& v1_funct_2(k7_tmap_1(A,B),u1_struct_0(A),u1_struct_0(k6_tmap_1(A,B)))
& v5_pre_topc(k7_tmap_1(A,B),A,k6_tmap_1(A,B))
& m2_relset_1(k7_tmap_1(A,B),u1_struct_0(A),u1_struct_0(k6_tmap_1(A,B))) ) ) ) ) ).
fof(d10_tmap_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ! [C] :
( ( v1_pre_topc(C)
& v2_pre_topc(C)
& l1_pre_topc(C) )
=> ( C = k8_tmap_1(A,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( D = u1_struct_0(B)
=> C = k6_tmap_1(A,D) ) ) ) ) ) ) ).
fof(t114_tmap_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ( u1_struct_0(k8_tmap_1(A,B)) = u1_struct_0(A)
& ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( C = u1_struct_0(B)
=> u1_pre_topc(k8_tmap_1(A,B)) = k5_tmap_1(A,C) ) ) ) ) ) ).
fof(t115_tmap_1,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_pre_topc(C,k8_tmap_1(A,B))
=> ( u1_struct_0(C) = u1_struct_0(B)
=> ( v1_tsep_1(C,k8_tmap_1(A,B))
& m1_pre_topc(C,k8_tmap_1(A,B)) ) ) ) ) ) ).
fof(t116_tmap_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ( ( v1_tsep_1(B,A)
& m1_pre_topc(B,A) )
<=> g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = k8_tmap_1(A,B) ) ) ) ).
fof(d11_tmap_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(k8_tmap_1(A,B)))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(k8_tmap_1(A,B))) )
=> ( C = k9_tmap_1(A,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( D = u1_struct_0(B)
=> C = k7_tmap_1(A,D) ) ) ) ) ) ) ).
fof(t117_tmap_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ( ( v1_tsep_1(B,A)
& m1_pre_topc(B,A) )
=> k9_tmap_1(A,B) = k7_grcat_1(A) ) ) ) ).
fof(t118_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ( r1_tsep_1(A,B,C)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> r1_tmap_1(C,k8_tmap_1(A,B),k2_tmap_1(A,k8_tmap_1(A,B),C,k9_tmap_1(A,B)),D) ) ) ) ) ) ).
fof(t119_tmap_1,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(B))
=> r1_tmap_1(B,k8_tmap_1(A,B),k2_tmap_1(A,k8_tmap_1(A,B),B,k9_tmap_1(A,B)),C) ) ) ) ).
fof(t120_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ( r1_tsep_1(A,B,C)
=> ( v1_funct_1(k2_tmap_1(A,k8_tmap_1(A,B),C,k9_tmap_1(A,B)))
& v1_funct_2(k2_tmap_1(A,k8_tmap_1(A,B),C,k9_tmap_1(A,B)),u1_struct_0(C),u1_struct_0(k8_tmap_1(A,B)))
& v5_pre_topc(k2_tmap_1(A,k8_tmap_1(A,B),C,k9_tmap_1(A,B)),C,k8_tmap_1(A,B))
& m2_relset_1(k2_tmap_1(A,k8_tmap_1(A,B),C,k9_tmap_1(A,B)),u1_struct_0(C),u1_struct_0(k8_tmap_1(A,B))) ) ) ) ) ) ).
fof(t121_tmap_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ( v1_funct_1(k2_tmap_1(A,k8_tmap_1(A,B),B,k9_tmap_1(A,B)))
& v1_funct_2(k2_tmap_1(A,k8_tmap_1(A,B),B,k9_tmap_1(A,B)),u1_struct_0(B),u1_struct_0(k8_tmap_1(A,B)))
& v5_pre_topc(k2_tmap_1(A,k8_tmap_1(A,B),B,k9_tmap_1(A,B)),B,k8_tmap_1(A,B))
& m2_relset_1(k2_tmap_1(A,k8_tmap_1(A,B),B,k9_tmap_1(A,B)),u1_struct_0(B),u1_struct_0(k8_tmap_1(A,B))) ) ) ) ).
fof(t122_tmap_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ( v1_tsep_1(B,A)
& m1_pre_topc(B,A) )
<=> ( v1_funct_1(k9_tmap_1(A,B))
& v1_funct_2(k9_tmap_1(A,B),u1_struct_0(A),u1_struct_0(k8_tmap_1(A,B)))
& v5_pre_topc(k9_tmap_1(A,B),A,k8_tmap_1(A,B))
& m2_relset_1(k9_tmap_1(A,B),u1_struct_0(A),u1_struct_0(k8_tmap_1(A,B))) ) ) ) ) ).
fof(t123_tmap_1,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,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B)) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(D))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k1_tsep_1(A,C,D)))
=> ( ( H = F
& H = G )
=> ( r1_tmap_1(k1_tsep_1(A,C,D),B,E,H)
<=> ( r1_tmap_1(C,B,k3_tmap_1(A,B,k1_tsep_1(A,C,D),C,E),F)
& r1_tmap_1(D,B,k3_tmap_1(A,B,k1_tsep_1(A,C,D),D,E),G) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t124_tmap_1,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)) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& m1_pre_topc(E,A) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k1_tsep_1(A,D,E)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(D))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(E))
=> ( ( F = G
& F = H )
=> ( r1_tmap_1(k1_tsep_1(A,D,E),B,k2_tmap_1(A,B,k1_tsep_1(A,D,E),C),F)
<=> ( r1_tmap_1(D,B,k2_tmap_1(A,B,D,C),G)
& r1_tmap_1(E,B,k2_tmap_1(A,B,E,C),H) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t125_tmap_1,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)) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& m1_pre_topc(E,A) )
=> ( A = k1_tsep_1(A,D,E)
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(D))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(E))
=> ( ( F = G
& F = H )
=> ( r1_tmap_1(A,B,C,F)
<=> ( r1_tmap_1(D,B,k2_tmap_1(A,B,D,C),G)
& r1_tmap_1(E,B,k2_tmap_1(A,B,E,C),H) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t126_tmap_1,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,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ( r4_tsep_1(A,C,D)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B)) )
=> ( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B))
& v5_pre_topc(E,k1_tsep_1(A,C,D),B)
& m2_relset_1(E,u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B)) )
<=> ( v1_funct_1(k3_tmap_1(A,B,k1_tsep_1(A,C,D),C,E))
& v1_funct_2(k3_tmap_1(A,B,k1_tsep_1(A,C,D),C,E),u1_struct_0(C),u1_struct_0(B))
& v5_pre_topc(k3_tmap_1(A,B,k1_tsep_1(A,C,D),C,E),C,B)
& m2_relset_1(k3_tmap_1(A,B,k1_tsep_1(A,C,D),C,E),u1_struct_0(C),u1_struct_0(B))
& v1_funct_1(k3_tmap_1(A,B,k1_tsep_1(A,C,D),D,E))
& v1_funct_2(k3_tmap_1(A,B,k1_tsep_1(A,C,D),D,E),u1_struct_0(D),u1_struct_0(B))
& v5_pre_topc(k3_tmap_1(A,B,k1_tsep_1(A,C,D),D,E),D,B)
& m2_relset_1(k3_tmap_1(A,B,k1_tsep_1(A,C,D),D,E),u1_struct_0(D),u1_struct_0(B)) ) ) ) ) ) ) ) ) ).
fof(t127_tmap_1,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)
& v1_borsuk_1(C,A)
& m1_pre_topc(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v1_borsuk_1(D,A)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B)) )
=> ( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B))
& v5_pre_topc(E,k1_tsep_1(A,C,D),B)
& m2_relset_1(E,u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B)) )
<=> ( v1_funct_1(k3_tmap_1(A,B,k1_tsep_1(A,C,D),C,E))
& v1_funct_2(k3_tmap_1(A,B,k1_tsep_1(A,C,D),C,E),u1_struct_0(C),u1_struct_0(B))
& v5_pre_topc(k3_tmap_1(A,B,k1_tsep_1(A,C,D),C,E),C,B)
& m2_relset_1(k3_tmap_1(A,B,k1_tsep_1(A,C,D),C,E),u1_struct_0(C),u1_struct_0(B))
& v1_funct_1(k3_tmap_1(A,B,k1_tsep_1(A,C,D),D,E))
& v1_funct_2(k3_tmap_1(A,B,k1_tsep_1(A,C,D),D,E),u1_struct_0(D),u1_struct_0(B))
& v5_pre_topc(k3_tmap_1(A,B,k1_tsep_1(A,C,D),D,E),D,B)
& m2_relset_1(k3_tmap_1(A,B,k1_tsep_1(A,C,D),D,E),u1_struct_0(D),u1_struct_0(B)) ) ) ) ) ) ) ) ).
fof(t128_tmap_1,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)
& v1_tsep_1(C,A)
& m1_pre_topc(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v1_tsep_1(D,A)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B)) )
=> ( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B))
& v5_pre_topc(E,k1_tsep_1(A,C,D),B)
& m2_relset_1(E,u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B)) )
<=> ( v1_funct_1(k3_tmap_1(A,B,k1_tsep_1(A,C,D),C,E))
& v1_funct_2(k3_tmap_1(A,B,k1_tsep_1(A,C,D),C,E),u1_struct_0(C),u1_struct_0(B))
& v5_pre_topc(k3_tmap_1(A,B,k1_tsep_1(A,C,D),C,E),C,B)
& m2_relset_1(k3_tmap_1(A,B,k1_tsep_1(A,C,D),C,E),u1_struct_0(C),u1_struct_0(B))
& v1_funct_1(k3_tmap_1(A,B,k1_tsep_1(A,C,D),D,E))
& v1_funct_2(k3_tmap_1(A,B,k1_tsep_1(A,C,D),D,E),u1_struct_0(D),u1_struct_0(B))
& v5_pre_topc(k3_tmap_1(A,B,k1_tsep_1(A,C,D),D,E),D,B)
& m2_relset_1(k3_tmap_1(A,B,k1_tsep_1(A,C,D),D,E),u1_struct_0(D),u1_struct_0(B)) ) ) ) ) ) ) ) ).
fof(t129_tmap_1,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,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ( r4_tsep_1(A,C,D)
=> ! [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)) )
=> ( ( v1_funct_1(k2_tmap_1(A,B,k1_tsep_1(A,C,D),E))
& v1_funct_2(k2_tmap_1(A,B,k1_tsep_1(A,C,D),E),u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B))
& v5_pre_topc(k2_tmap_1(A,B,k1_tsep_1(A,C,D),E),k1_tsep_1(A,C,D),B)
& m2_relset_1(k2_tmap_1(A,B,k1_tsep_1(A,C,D),E),u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B)) )
<=> ( v1_funct_1(k2_tmap_1(A,B,C,E))
& v1_funct_2(k2_tmap_1(A,B,C,E),u1_struct_0(C),u1_struct_0(B))
& v5_pre_topc(k2_tmap_1(A,B,C,E),C,B)
& m2_relset_1(k2_tmap_1(A,B,C,E),u1_struct_0(C),u1_struct_0(B))
& v1_funct_1(k2_tmap_1(A,B,D,E))
& v1_funct_2(k2_tmap_1(A,B,D,E),u1_struct_0(D),u1_struct_0(B))
& v5_pre_topc(k2_tmap_1(A,B,D,E),D,B)
& m2_relset_1(k2_tmap_1(A,B,D,E),u1_struct_0(D),u1_struct_0(B)) ) ) ) ) ) ) ) ) ).
fof(t130_tmap_1,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)) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v1_borsuk_1(D,A)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& v1_borsuk_1(E,A)
& m1_pre_topc(E,A) )
=> ( ( v1_funct_1(k2_tmap_1(A,B,k1_tsep_1(A,D,E),C))
& v1_funct_2(k2_tmap_1(A,B,k1_tsep_1(A,D,E),C),u1_struct_0(k1_tsep_1(A,D,E)),u1_struct_0(B))
& v5_pre_topc(k2_tmap_1(A,B,k1_tsep_1(A,D,E),C),k1_tsep_1(A,D,E),B)
& m2_relset_1(k2_tmap_1(A,B,k1_tsep_1(A,D,E),C),u1_struct_0(k1_tsep_1(A,D,E)),u1_struct_0(B)) )
<=> ( v1_funct_1(k2_tmap_1(A,B,D,C))
& v1_funct_2(k2_tmap_1(A,B,D,C),u1_struct_0(D),u1_struct_0(B))
& v5_pre_topc(k2_tmap_1(A,B,D,C),D,B)
& m2_relset_1(k2_tmap_1(A,B,D,C),u1_struct_0(D),u1_struct_0(B))
& v1_funct_1(k2_tmap_1(A,B,E,C))
& v1_funct_2(k2_tmap_1(A,B,E,C),u1_struct_0(E),u1_struct_0(B))
& v5_pre_topc(k2_tmap_1(A,B,E,C),E,B)
& m2_relset_1(k2_tmap_1(A,B,E,C),u1_struct_0(E),u1_struct_0(B)) ) ) ) ) ) ) ) ).
fof(t131_tmap_1,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)) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v1_tsep_1(D,A)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& v1_tsep_1(E,A)
& m1_pre_topc(E,A) )
=> ( ( v1_funct_1(k2_tmap_1(A,B,k1_tsep_1(A,D,E),C))
& v1_funct_2(k2_tmap_1(A,B,k1_tsep_1(A,D,E),C),u1_struct_0(k1_tsep_1(A,D,E)),u1_struct_0(B))
& v5_pre_topc(k2_tmap_1(A,B,k1_tsep_1(A,D,E),C),k1_tsep_1(A,D,E),B)
& m2_relset_1(k2_tmap_1(A,B,k1_tsep_1(A,D,E),C),u1_struct_0(k1_tsep_1(A,D,E)),u1_struct_0(B)) )
<=> ( v1_funct_1(k2_tmap_1(A,B,D,C))
& v1_funct_2(k2_tmap_1(A,B,D,C),u1_struct_0(D),u1_struct_0(B))
& v5_pre_topc(k2_tmap_1(A,B,D,C),D,B)
& m2_relset_1(k2_tmap_1(A,B,D,C),u1_struct_0(D),u1_struct_0(B))
& v1_funct_1(k2_tmap_1(A,B,E,C))
& v1_funct_2(k2_tmap_1(A,B,E,C),u1_struct_0(E),u1_struct_0(B))
& v5_pre_topc(k2_tmap_1(A,B,E,C),E,B)
& m2_relset_1(k2_tmap_1(A,B,E,C),u1_struct_0(E),u1_struct_0(B)) ) ) ) ) ) ) ) ).
fof(t132_tmap_1,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)) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& m1_pre_topc(E,A) )
=> ( ( A = k1_tsep_1(A,D,E)
& r4_tsep_1(A,D,E) )
=> ( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
<=> ( v1_funct_1(k2_tmap_1(A,B,D,C))
& v1_funct_2(k2_tmap_1(A,B,D,C),u1_struct_0(D),u1_struct_0(B))
& v5_pre_topc(k2_tmap_1(A,B,D,C),D,B)
& m2_relset_1(k2_tmap_1(A,B,D,C),u1_struct_0(D),u1_struct_0(B))
& v1_funct_1(k2_tmap_1(A,B,E,C))
& v1_funct_2(k2_tmap_1(A,B,E,C),u1_struct_0(E),u1_struct_0(B))
& v5_pre_topc(k2_tmap_1(A,B,E,C),E,B)
& m2_relset_1(k2_tmap_1(A,B,E,C),u1_struct_0(E),u1_struct_0(B)) ) ) ) ) ) ) ) ) ).
fof(t133_tmap_1,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)) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v1_borsuk_1(D,A)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& v1_borsuk_1(E,A)
& m1_pre_topc(E,A) )
=> ( A = k1_tsep_1(A,D,E)
=> ( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
<=> ( v1_funct_1(k2_tmap_1(A,B,D,C))
& v1_funct_2(k2_tmap_1(A,B,D,C),u1_struct_0(D),u1_struct_0(B))
& v5_pre_topc(k2_tmap_1(A,B,D,C),D,B)
& m2_relset_1(k2_tmap_1(A,B,D,C),u1_struct_0(D),u1_struct_0(B))
& v1_funct_1(k2_tmap_1(A,B,E,C))
& v1_funct_2(k2_tmap_1(A,B,E,C),u1_struct_0(E),u1_struct_0(B))
& v5_pre_topc(k2_tmap_1(A,B,E,C),E,B)
& m2_relset_1(k2_tmap_1(A,B,E,C),u1_struct_0(E),u1_struct_0(B)) ) ) ) ) ) ) ) ) ).
fof(t134_tmap_1,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)) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v1_tsep_1(D,A)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& v1_tsep_1(E,A)
& m1_pre_topc(E,A) )
=> ( A = k1_tsep_1(A,D,E)
=> ( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
<=> ( v1_funct_1(k2_tmap_1(A,B,D,C))
& v1_funct_2(k2_tmap_1(A,B,D,C),u1_struct_0(D),u1_struct_0(B))
& v5_pre_topc(k2_tmap_1(A,B,D,C),D,B)
& m2_relset_1(k2_tmap_1(A,B,D,C),u1_struct_0(D),u1_struct_0(B))
& v1_funct_1(k2_tmap_1(A,B,E,C))
& v1_funct_2(k2_tmap_1(A,B,E,C),u1_struct_0(E),u1_struct_0(B))
& v5_pre_topc(k2_tmap_1(A,B,E,C),E,B)
& m2_relset_1(k2_tmap_1(A,B,E,C),u1_struct_0(E),u1_struct_0(B)) ) ) ) ) ) ) ) ) ).
fof(t135_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ( r3_tsep_1(A,B,C)
<=> ( r1_tsep_1(A,B,C)
& ! [D] :
( ( ~ v3_struct_0(D)
& v2_pre_topc(D)
& l1_pre_topc(D) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k1_tsep_1(A,B,C)),u1_struct_0(D))
& m2_relset_1(E,u1_struct_0(k1_tsep_1(A,B,C)),u1_struct_0(D)) )
=> ( ( v1_funct_1(k3_tmap_1(A,D,k1_tsep_1(A,B,C),B,E))
& v1_funct_2(k3_tmap_1(A,D,k1_tsep_1(A,B,C),B,E),u1_struct_0(B),u1_struct_0(D))
& v5_pre_topc(k3_tmap_1(A,D,k1_tsep_1(A,B,C),B,E),B,D)
& m2_relset_1(k3_tmap_1(A,D,k1_tsep_1(A,B,C),B,E),u1_struct_0(B),u1_struct_0(D))
& v1_funct_1(k3_tmap_1(A,D,k1_tsep_1(A,B,C),C,E))
& v1_funct_2(k3_tmap_1(A,D,k1_tsep_1(A,B,C),C,E),u1_struct_0(C),u1_struct_0(D))
& v5_pre_topc(k3_tmap_1(A,D,k1_tsep_1(A,B,C),C,E),C,D)
& m2_relset_1(k3_tmap_1(A,D,k1_tsep_1(A,B,C),C,E),u1_struct_0(C),u1_struct_0(D)) )
=> ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k1_tsep_1(A,B,C)),u1_struct_0(D))
& v5_pre_topc(E,k1_tsep_1(A,B,C),D)
& m2_relset_1(E,u1_struct_0(k1_tsep_1(A,B,C)),u1_struct_0(D)) ) ) ) ) ) ) ) ) ) ).
fof(t136_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ( r3_tsep_1(A,B,C)
<=> ( r1_tsep_1(A,B,C)
& ! [D] :
( ( ~ v3_struct_0(D)
& v2_pre_topc(D)
& l1_pre_topc(D) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(D))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(D)) )
=> ( ( v1_funct_1(k2_tmap_1(A,D,B,E))
& v1_funct_2(k2_tmap_1(A,D,B,E),u1_struct_0(B),u1_struct_0(D))
& v5_pre_topc(k2_tmap_1(A,D,B,E),B,D)
& m2_relset_1(k2_tmap_1(A,D,B,E),u1_struct_0(B),u1_struct_0(D))
& v1_funct_1(k2_tmap_1(A,D,C,E))
& v1_funct_2(k2_tmap_1(A,D,C,E),u1_struct_0(C),u1_struct_0(D))
& v5_pre_topc(k2_tmap_1(A,D,C,E),C,D)
& m2_relset_1(k2_tmap_1(A,D,C,E),u1_struct_0(C),u1_struct_0(D)) )
=> ( v1_funct_1(k2_tmap_1(A,D,k1_tsep_1(A,B,C),E))
& v1_funct_2(k2_tmap_1(A,D,k1_tsep_1(A,B,C),E),u1_struct_0(k1_tsep_1(A,B,C)),u1_struct_0(D))
& v5_pre_topc(k2_tmap_1(A,D,k1_tsep_1(A,B,C),E),k1_tsep_1(A,B,C),D)
& m2_relset_1(k2_tmap_1(A,D,k1_tsep_1(A,B,C),E),u1_struct_0(k1_tsep_1(A,B,C)),u1_struct_0(D)) ) ) ) ) ) ) ) ) ) ).
fof(t137_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ( A = k1_tsep_1(A,B,C)
=> ( r3_tsep_1(A,B,C)
<=> ( r1_tsep_1(A,B,C)
& ! [D] :
( ( ~ v3_struct_0(D)
& v2_pre_topc(D)
& l1_pre_topc(D) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(D))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(D)) )
=> ( ( v1_funct_1(k2_tmap_1(A,D,B,E))
& v1_funct_2(k2_tmap_1(A,D,B,E),u1_struct_0(B),u1_struct_0(D))
& v5_pre_topc(k2_tmap_1(A,D,B,E),B,D)
& m2_relset_1(k2_tmap_1(A,D,B,E),u1_struct_0(B),u1_struct_0(D))
& v1_funct_1(k2_tmap_1(A,D,C,E))
& v1_funct_2(k2_tmap_1(A,D,C,E),u1_struct_0(C),u1_struct_0(D))
& v5_pre_topc(k2_tmap_1(A,D,C,E),C,D)
& m2_relset_1(k2_tmap_1(A,D,C,E),u1_struct_0(C),u1_struct_0(D)) )
=> ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(D))
& v5_pre_topc(E,A,D)
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(D)) ) ) ) ) ) ) ) ) ) ) ).
fof(d12_tmap_1,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,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(B)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(D),u1_struct_0(B))
& m2_relset_1(F,u1_struct_0(D),u1_struct_0(B)) )
=> ( ( r1_tsep_1(A,C,D)
| k3_tmap_1(A,B,C,k2_tsep_1(A,C,D),E) = k3_tmap_1(A,B,D,k2_tsep_1(A,C,D),F) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B))
& m2_relset_1(G,u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B)) )
=> ( G = k10_tmap_1(A,B,C,D,E,F)
<=> ( k3_tmap_1(A,B,k1_tsep_1(A,C,D),C,G) = E
& k3_tmap_1(A,B,k1_tsep_1(A,C,D),D,G) = F ) ) ) ) ) ) ) ) ) ) ).
fof(t138_tmap_1,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,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B)) )
=> E = k10_tmap_1(A,B,C,D,k3_tmap_1(A,B,k1_tsep_1(A,C,D),C,E),k3_tmap_1(A,B,k1_tsep_1(A,C,D),D,E)) ) ) ) ) ) ).
fof(t139_tmap_1,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,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ( A = k1_tsep_1(A,C,D)
=> ! [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)) )
=> E = k10_tmap_1(A,B,C,D,k2_tmap_1(A,B,C,E),k2_tmap_1(A,B,D,E)) ) ) ) ) ) ) ).
fof(t140_tmap_1,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,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ( ~ r1_tsep_1(A,C,D)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(B)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(D),u1_struct_0(B))
& m2_relset_1(F,u1_struct_0(D),u1_struct_0(B)) )
=> ( ( k3_tmap_1(A,B,k1_tsep_1(A,C,D),C,k10_tmap_1(A,B,C,D,E,F)) = E
& k3_tmap_1(A,B,k1_tsep_1(A,C,D),D,k10_tmap_1(A,B,C,D,E,F)) = F )
<=> k3_tmap_1(A,B,C,k2_tsep_1(A,C,D),E) = k3_tmap_1(A,B,D,k2_tsep_1(A,C,D),F) ) ) ) ) ) ) ) ) ).
fof(t141_tmap_1,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,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(B)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(D),u1_struct_0(B))
& m2_relset_1(F,u1_struct_0(D),u1_struct_0(B)) )
=> ( k3_tmap_1(A,B,C,k2_tsep_1(A,C,D),E) = k3_tmap_1(A,B,D,k2_tsep_1(A,C,D),F)
=> ( ( m1_pre_topc(C,D)
=> k10_tmap_1(A,B,C,D,E,F) = F )
& ( k10_tmap_1(A,B,C,D,E,F) = F
=> m1_pre_topc(C,D) )
& ( m1_pre_topc(D,C)
=> k10_tmap_1(A,B,C,D,E,F) = E )
& ( k10_tmap_1(A,B,C,D,E,F) = E
=> m1_pre_topc(D,C) ) ) ) ) ) ) ) ) ) ).
fof(t142_tmap_1,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,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(B)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(D),u1_struct_0(B))
& m2_relset_1(F,u1_struct_0(D),u1_struct_0(B)) )
=> ( ( r1_tsep_1(A,C,D)
| k3_tmap_1(A,B,C,k2_tsep_1(A,C,D),E) = k3_tmap_1(A,B,D,k2_tsep_1(A,C,D),F) )
=> k10_tmap_1(A,B,C,D,E,F) = k10_tmap_1(A,B,D,C,F,E) ) ) ) ) ) ) ) ).
fof(t143_tmap_1,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,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& m1_pre_topc(E,A) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(C),u1_struct_0(B))
& m2_relset_1(F,u1_struct_0(C),u1_struct_0(B)) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(D),u1_struct_0(B))
& m2_relset_1(G,u1_struct_0(D),u1_struct_0(B)) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,u1_struct_0(E),u1_struct_0(B))
& m2_relset_1(H,u1_struct_0(E),u1_struct_0(B)) )
=> ~ ( ( r1_tsep_1(A,C,D)
| k3_tmap_1(A,B,C,k2_tsep_1(A,C,D),F) = k3_tmap_1(A,B,D,k2_tsep_1(A,C,D),G) )
& ( r1_tsep_1(A,C,E)
| k3_tmap_1(A,B,C,k2_tsep_1(A,C,E),F) = k3_tmap_1(A,B,E,k2_tsep_1(A,C,E),H) )
& ( r1_tsep_1(A,D,E)
| k3_tmap_1(A,B,D,k2_tsep_1(A,D,E),G) = k3_tmap_1(A,B,E,k2_tsep_1(A,D,E),H) )
& k10_tmap_1(A,B,k1_tsep_1(A,C,D),E,k10_tmap_1(A,B,C,D,F,G),H) != k10_tmap_1(A,B,C,k1_tsep_1(A,D,E),F,k10_tmap_1(A,B,D,E,G,H)) ) ) ) ) ) ) ) ) ) ).
fof(t144_tmap_1,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,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ( ~ r1_tsep_1(A,C,D)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(B))
& v5_pre_topc(E,C,B)
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(B)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(D),u1_struct_0(B))
& v5_pre_topc(F,D,B)
& m2_relset_1(F,u1_struct_0(D),u1_struct_0(B)) )
=> ( ( k3_tmap_1(A,B,C,k2_tsep_1(A,C,D),E) = k3_tmap_1(A,B,D,k2_tsep_1(A,C,D),F)
& r4_tsep_1(A,C,D) )
=> ( v1_funct_1(k10_tmap_1(A,B,C,D,E,F))
& v1_funct_2(k10_tmap_1(A,B,C,D,E,F),u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B))
& v5_pre_topc(k10_tmap_1(A,B,C,D,E,F),k1_tsep_1(A,C,D),B)
& m2_relset_1(k10_tmap_1(A,B,C,D,E,F),u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B)) ) ) ) ) ) ) ) ) ) ).
fof(t145_tmap_1,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,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ( r1_tsep_1(A,C,D)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(B))
& v5_pre_topc(E,C,B)
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(B)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(D),u1_struct_0(B))
& v5_pre_topc(F,D,B)
& m2_relset_1(F,u1_struct_0(D),u1_struct_0(B)) )
=> ( r4_tsep_1(A,C,D)
=> ( v1_funct_1(k10_tmap_1(A,B,C,D,E,F))
& v1_funct_2(k10_tmap_1(A,B,C,D,E,F),u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B))
& v5_pre_topc(k10_tmap_1(A,B,C,D,E,F),k1_tsep_1(A,C,D),B)
& m2_relset_1(k10_tmap_1(A,B,C,D,E,F),u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B)) ) ) ) ) ) ) ) ) ) ).
fof(t146_tmap_1,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)
& v1_borsuk_1(C,A)
& m1_pre_topc(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v1_borsuk_1(D,A)
& m1_pre_topc(D,A) )
=> ( ~ r1_tsep_1(A,C,D)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(B))
& v5_pre_topc(E,C,B)
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(B)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(D),u1_struct_0(B))
& v5_pre_topc(F,D,B)
& m2_relset_1(F,u1_struct_0(D),u1_struct_0(B)) )
=> ( k3_tmap_1(A,B,C,k2_tsep_1(A,C,D),E) = k3_tmap_1(A,B,D,k2_tsep_1(A,C,D),F)
=> ( v1_funct_1(k10_tmap_1(A,B,C,D,E,F))
& v1_funct_2(k10_tmap_1(A,B,C,D,E,F),u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B))
& v5_pre_topc(k10_tmap_1(A,B,C,D,E,F),k1_tsep_1(A,C,D),B)
& m2_relset_1(k10_tmap_1(A,B,C,D,E,F),u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B)) ) ) ) ) ) ) ) ) ) ).
fof(t147_tmap_1,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)
& v1_tsep_1(C,A)
& m1_pre_topc(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v1_tsep_1(D,A)
& m1_pre_topc(D,A) )
=> ( ~ r1_tsep_1(A,C,D)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(B))
& v5_pre_topc(E,C,B)
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(B)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(D),u1_struct_0(B))
& v5_pre_topc(F,D,B)
& m2_relset_1(F,u1_struct_0(D),u1_struct_0(B)) )
=> ( k3_tmap_1(A,B,C,k2_tsep_1(A,C,D),E) = k3_tmap_1(A,B,D,k2_tsep_1(A,C,D),F)
=> ( v1_funct_1(k10_tmap_1(A,B,C,D,E,F))
& v1_funct_2(k10_tmap_1(A,B,C,D,E,F),u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B))
& v5_pre_topc(k10_tmap_1(A,B,C,D,E,F),k1_tsep_1(A,C,D),B)
& m2_relset_1(k10_tmap_1(A,B,C,D,E,F),u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B)) ) ) ) ) ) ) ) ) ) ).
fof(t148_tmap_1,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)
& v1_borsuk_1(C,A)
& m1_pre_topc(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v1_borsuk_1(D,A)
& m1_pre_topc(D,A) )
=> ( r1_tsep_1(A,C,D)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(B))
& v5_pre_topc(E,C,B)
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(B)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(D),u1_struct_0(B))
& v5_pre_topc(F,D,B)
& m2_relset_1(F,u1_struct_0(D),u1_struct_0(B)) )
=> ( v1_funct_1(k10_tmap_1(A,B,C,D,E,F))
& v1_funct_2(k10_tmap_1(A,B,C,D,E,F),u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B))
& v5_pre_topc(k10_tmap_1(A,B,C,D,E,F),k1_tsep_1(A,C,D),B)
& m2_relset_1(k10_tmap_1(A,B,C,D,E,F),u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B)) ) ) ) ) ) ) ) ) ).
fof(t149_tmap_1,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)
& v1_tsep_1(C,A)
& m1_pre_topc(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v1_tsep_1(D,A)
& m1_pre_topc(D,A) )
=> ( r1_tsep_1(A,C,D)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(B))
& v5_pre_topc(E,C,B)
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(B)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(D),u1_struct_0(B))
& v5_pre_topc(F,D,B)
& m2_relset_1(F,u1_struct_0(D),u1_struct_0(B)) )
=> ( v1_funct_1(k10_tmap_1(A,B,C,D,E,F))
& v1_funct_2(k10_tmap_1(A,B,C,D,E,F),u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B))
& v5_pre_topc(k10_tmap_1(A,B,C,D,E,F),k1_tsep_1(A,C,D),B)
& m2_relset_1(k10_tmap_1(A,B,C,D,E,F),u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B)) ) ) ) ) ) ) ) ) ).
fof(t150_tmap_1,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] :
( ( ~ v3_struct_0(C)
& m1_pre_topc(C,A) )
=> ( r3_tsep_1(A,B,C)
<=> ( r1_tsep_1(A,B,C)
& ! [D] :
( ( ~ v3_struct_0(D)
& v2_pre_topc(D)
& l1_pre_topc(D) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(D))
& v5_pre_topc(E,B,D)
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(D)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(C),u1_struct_0(D))
& v5_pre_topc(F,C,D)
& m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) )
=> ( v1_funct_1(k10_tmap_1(A,D,B,C,E,F))
& v1_funct_2(k10_tmap_1(A,D,B,C,E,F),u1_struct_0(k1_tsep_1(A,B,C)),u1_struct_0(D))
& v5_pre_topc(k10_tmap_1(A,D,B,C,E,F),k1_tsep_1(A,B,C),D)
& m2_relset_1(k10_tmap_1(A,D,B,C,E,F),u1_struct_0(k1_tsep_1(A,B,C)),u1_struct_0(D)) ) ) ) ) ) ) ) ) ) ).
fof(t151_tmap_1,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,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& m1_pre_topc(D,A) )
=> ( A = k1_tsep_1(A,C,D)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(B))
& v5_pre_topc(E,C,B)
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(B)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(D),u1_struct_0(B))
& v5_pre_topc(F,D,B)
& m2_relset_1(F,u1_struct_0(D),u1_struct_0(B)) )
=> ( ( k3_tmap_1(A,B,k1_tsep_1(A,C,D),C,k10_tmap_1(A,B,C,D,E,F)) = E
& k3_tmap_1(A,B,k1_tsep_1(A,C,D),D,k10_tmap_1(A,B,C,D,E,F)) = F
& r4_tsep_1(A,C,D) )
=> ( v1_funct_1(k10_tmap_1(A,B,C,D,E,F))
& v1_funct_2(k10_tmap_1(A,B,C,D,E,F),u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(k10_tmap_1(A,B,C,D,E,F),A,B)
& m2_relset_1(k10_tmap_1(A,B,C,D,E,F),u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ) ) ) ) ) ).
fof(t152_tmap_1,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)
& v1_borsuk_1(C,A)
& m1_pre_topc(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v1_borsuk_1(D,A)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(B))
& v5_pre_topc(E,C,B)
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(B)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(D),u1_struct_0(B))
& v5_pre_topc(F,D,B)
& m2_relset_1(F,u1_struct_0(D),u1_struct_0(B)) )
=> ( ( A = k1_tsep_1(A,C,D)
& k3_tmap_1(A,B,k1_tsep_1(A,C,D),C,k10_tmap_1(A,B,C,D,E,F)) = E
& k3_tmap_1(A,B,k1_tsep_1(A,C,D),D,k10_tmap_1(A,B,C,D,E,F)) = F )
=> ( v1_funct_1(k10_tmap_1(A,B,C,D,E,F))
& v1_funct_2(k10_tmap_1(A,B,C,D,E,F),u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(k10_tmap_1(A,B,C,D,E,F),A,B)
& m2_relset_1(k10_tmap_1(A,B,C,D,E,F),u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ) ) ) ) ).
fof(t153_tmap_1,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)
& v1_tsep_1(C,A)
& m1_pre_topc(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v1_tsep_1(D,A)
& m1_pre_topc(D,A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(B))
& v5_pre_topc(E,C,B)
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(B)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(D),u1_struct_0(B))
& v5_pre_topc(F,D,B)
& m2_relset_1(F,u1_struct_0(D),u1_struct_0(B)) )
=> ( ( A = k1_tsep_1(A,C,D)
& k3_tmap_1(A,B,k1_tsep_1(A,C,D),C,k10_tmap_1(A,B,C,D,E,F)) = E
& k3_tmap_1(A,B,k1_tsep_1(A,C,D),D,k10_tmap_1(A,B,C,D,E,F)) = F )
=> ( v1_funct_1(k10_tmap_1(A,B,C,D,E,F))
& v1_funct_2(k10_tmap_1(A,B,C,D,E,F),u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(k10_tmap_1(A,B,C,D,E,F),A,B)
& m2_relset_1(k10_tmap_1(A,B,C,D,E,F),u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ) ) ) ) ).
fof(dt_k1_tmap_1,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(A))
& ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(A))
& v1_funct_1(E)
& v1_funct_2(E,C,B)
& m1_relset_1(E,C,B)
& v1_funct_1(F)
& v1_funct_2(F,D,B)
& m1_relset_1(F,D,B) )
=> ( v1_funct_1(k1_tmap_1(A,B,C,D,E,F))
& v1_funct_2(k1_tmap_1(A,B,C,D,E,F),k4_subset_1(A,C,D),B)
& m2_relset_1(k1_tmap_1(A,B,C,D,E,F),k4_subset_1(A,C,D),B) ) ) ).
fof(dt_k2_tmap_1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& m1_pre_topc(C,A)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_funct_1(k2_tmap_1(A,B,C,D))
& v1_funct_2(k2_tmap_1(A,B,C,D),u1_struct_0(C),u1_struct_0(B))
& m2_relset_1(k2_tmap_1(A,B,C,D),u1_struct_0(C),u1_struct_0(B)) ) ) ).
fof(dt_k3_tmap_1,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& m1_pre_topc(C,A)
& m1_pre_topc(D,A)
& v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(B))
& m1_relset_1(E,u1_struct_0(C),u1_struct_0(B)) )
=> ( v1_funct_1(k3_tmap_1(A,B,C,D,E))
& v1_funct_2(k3_tmap_1(A,B,C,D,E),u1_struct_0(D),u1_struct_0(B))
& m2_relset_1(k3_tmap_1(A,B,C,D,E),u1_struct_0(D),u1_struct_0(B)) ) ) ).
fof(dt_k4_tmap_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_pre_topc(B,A) )
=> ( v1_funct_1(k4_tmap_1(A,B))
& v1_funct_2(k4_tmap_1(A,B),u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(k4_tmap_1(A,B),u1_struct_0(B),u1_struct_0(A)) ) ) ).
fof(dt_k5_tmap_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k5_tmap_1(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k6_tmap_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_pre_topc(k6_tmap_1(A,B))
& v2_pre_topc(k6_tmap_1(A,B))
& l1_pre_topc(k6_tmap_1(A,B)) ) ) ).
fof(dt_k7_tmap_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_funct_1(k7_tmap_1(A,B))
& v1_funct_2(k7_tmap_1(A,B),u1_struct_0(A),u1_struct_0(k6_tmap_1(A,B)))
& m2_relset_1(k7_tmap_1(A,B),u1_struct_0(A),u1_struct_0(k6_tmap_1(A,B))) ) ) ).
fof(dt_k8_tmap_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_pre_topc(B,A) )
=> ( v1_pre_topc(k8_tmap_1(A,B))
& v2_pre_topc(k8_tmap_1(A,B))
& l1_pre_topc(k8_tmap_1(A,B)) ) ) ).
fof(dt_k9_tmap_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& m1_pre_topc(B,A) )
=> ( v1_funct_1(k9_tmap_1(A,B))
& v1_funct_2(k9_tmap_1(A,B),u1_struct_0(A),u1_struct_0(k8_tmap_1(A,B)))
& m2_relset_1(k9_tmap_1(A,B),u1_struct_0(A),u1_struct_0(k8_tmap_1(A,B))) ) ) ).
fof(dt_k10_tmap_1,axiom,
! [A,B,C,D,E,F] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& ~ v3_struct_0(C)
& m1_pre_topc(C,A)
& ~ v3_struct_0(D)
& m1_pre_topc(D,A)
& v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(B))
& m1_relset_1(E,u1_struct_0(C),u1_struct_0(B))
& v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(D),u1_struct_0(B))
& m1_relset_1(F,u1_struct_0(D),u1_struct_0(B)) )
=> ( v1_funct_1(k10_tmap_1(A,B,C,D,E,F))
& v1_funct_2(k10_tmap_1(A,B,C,D,E,F),u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B))
& m2_relset_1(k10_tmap_1(A,B,C,D,E,F),u1_struct_0(k1_tsep_1(A,C,D)),u1_struct_0(B)) ) ) ).
fof(d7_tmap_1,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)))
=> k5_tmap_1(A,B) = a_2_0_tmap_1(A,B) ) ) ).
fof(t100_tmap_1,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)))
=> r1_tarski(a_2_1_tmap_1(A,B),k5_tmap_1(A,B)) ) ) ).
fof(t101_tmap_1,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)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r2_hidden(C,u1_pre_topc(A))
& r2_hidden(D,a_2_1_tmap_1(A,B)) )
=> ( r2_hidden(k4_subset_1(u1_struct_0(A),C,D),k5_tmap_1(A,B))
& r2_hidden(k5_subset_1(u1_struct_0(A),C,D),k5_tmap_1(A,B)) ) ) ) ) ) ) ).
fof(fraenkel_a_2_0_tmap_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_2_0_tmap_1(B,C))
<=> ? [D,E] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
& A = k4_subset_1(u1_struct_0(B),D,k5_subset_1(u1_struct_0(B),E,C))
& r2_hidden(D,u1_pre_topc(B))
& r2_hidden(E,u1_pre_topc(B)) ) ) ) ).
fof(fraenkel_a_2_1_tmap_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_2_1_tmap_1(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
& A = k5_subset_1(u1_struct_0(B),D,C)
& r2_hidden(D,u1_pre_topc(B)) ) ) ) ).
%------------------------------------------------------------------------------