SET007 Axioms: SET007+900.ax
%------------------------------------------------------------------------------
% File : SET007+900 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Supercondensed Sets, Subcondensed Sets and Condensed Sets
% 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 : isomichi [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 104 ( 1 unt; 0 def)
% Number of atoms : 597 ( 40 equ)
% Maximal formula atoms : 19 ( 5 avg)
% Number of connectives : 546 ( 53 ~; 5 |; 243 &)
% ( 25 <=>; 220 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 43 ( 41 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 3 con; 0-3 aty)
% Number of variables : 210 ( 196 !; 14 ?)
% 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_isomichi,axiom,
! [A] :
( ~ v1_realset1(A)
=> ( ~ v3_struct_0(k2_tex_1(A))
& v1_pre_topc(k2_tex_1(A))
& v2_pre_topc(k2_tex_1(A))
& v2_tdlat_3(k2_tex_1(A))
& v3_tdlat_3(k2_tex_1(A))
& v4_tdlat_3(k2_tex_1(A))
& v5_tdlat_3(k2_tex_1(A))
& ~ v3_realset2(k2_tex_1(A)) ) ) ).
fof(rc1_isomichi,axiom,
? [A] :
( l1_pre_topc(A)
& ~ v3_struct_0(A)
& v1_pre_topc(A)
& v2_pre_topc(A)
& v2_tdlat_3(A)
& ~ v3_realset2(A) ) ).
fof(cc1_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_tops_1(B,A)
=> ( v1_isomichi(B,A)
& v2_isomichi(B,A) ) ) ) ) ).
fof(cc2_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v1_isomichi(B,A)
& v2_isomichi(B,A) )
=> v4_tops_1(B,A) ) ) ) ).
fof(rc2_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v4_tops_1(B,A)
& v1_isomichi(B,A)
& v2_isomichi(B,A) ) ) ).
fof(cc3_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v2_isomichi(B,A)
=> v1_decomp_1(B,A) ) ) ) ).
fof(cc4_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_decomp_1(B,A)
=> v2_isomichi(B,A) ) ) ) ).
fof(fc2_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v3_pre_topc(k2_pre_topc(A),A)
& v4_pre_topc(k2_pre_topc(A),A)
& v1_tops_1(k2_pre_topc(A),A)
& v5_tops_1(k2_pre_topc(A),A)
& v6_tops_1(k2_pre_topc(A),A) ) ) ).
fof(fc3_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v1_xboole_0(k1_pre_topc(A))
& v3_pre_topc(k1_pre_topc(A),A)
& v4_pre_topc(k1_pre_topc(A),A)
& v2_tops_1(k1_pre_topc(A),A)
& v3_tops_1(k1_pre_topc(A),A)
& v5_tops_1(k1_pre_topc(A),A)
& v6_tops_1(k1_pre_topc(A),A)
& v1_membered(k1_pre_topc(A))
& v2_membered(k1_pre_topc(A))
& v3_membered(k1_pre_topc(A))
& v4_membered(k1_pre_topc(A))
& v5_membered(k1_pre_topc(A)) ) ) ).
fof(rc3_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v5_tops_1(B,A)
& v6_tops_1(B,A) ) ) ).
fof(fc4_isomichi,axiom,
! [A,B] :
( ( v2_pre_topc(A)
& l1_pre_topc(A)
& v6_tops_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v5_tops_1(k3_subset_1(u1_struct_0(A),B),A) ) ).
fof(fc5_isomichi,axiom,
! [A,B] :
( ( v2_pre_topc(A)
& l1_pre_topc(A)
& v5_tops_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v6_tops_1(k3_subset_1(u1_struct_0(A),B),A) ) ).
fof(cc5_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v6_tops_1(B,A)
=> v3_pre_topc(B,A) ) ) ) ).
fof(cc6_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v5_tops_1(B,A)
=> v4_pre_topc(B,A) ) ) ) ).
fof(fc6_isomichi,axiom,
! [A,B] :
( ( v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v3_pre_topc(k1_tops_1(A,k6_pre_topc(A,B)),A)
& v6_tops_1(k1_tops_1(A,k6_pre_topc(A,B)),A) ) ) ).
fof(fc7_isomichi,axiom,
! [A,B] :
( ( v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v4_pre_topc(k6_pre_topc(A,k1_tops_1(A,B)),A)
& v5_tops_1(k6_pre_topc(A,k1_tops_1(A,B)),A) ) ) ).
fof(cc7_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v6_tops_1(B,A)
=> ( v3_pre_topc(B,A)
& v4_tops_1(B,A)
& v1_decomp_1(B,A)
& v1_isomichi(B,A)
& v2_isomichi(B,A) ) ) ) ) ).
fof(cc8_isomichi,axiom,
! [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)
& v4_tops_1(B,A) )
=> ( v3_pre_topc(B,A)
& v6_tops_1(B,A) ) ) ) ) ).
fof(cc9_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v5_tops_1(B,A)
=> ( v4_pre_topc(B,A)
& v4_tops_1(B,A)
& v1_decomp_1(B,A)
& v1_isomichi(B,A)
& v2_isomichi(B,A) ) ) ) ) ).
fof(cc10_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v4_pre_topc(B,A)
& v4_tops_1(B,A) )
=> ( v4_pre_topc(B,A)
& v5_tops_1(B,A) ) ) ) ) ).
fof(fc8_isomichi,axiom,
! [A,B] :
( ( v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> v4_pre_topc(k2_tops_1(A,B),A) ) ).
fof(fc9_isomichi,axiom,
! [A,B] :
( ( v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v3_pre_topc(k1_isomichi(A,B),A)
& v4_tops_1(k1_isomichi(A,B),A)
& v6_tops_1(k1_isomichi(A,B),A)
& v1_decomp_1(k1_isomichi(A,B),A)
& v1_isomichi(k1_isomichi(A,B),A)
& v2_isomichi(k1_isomichi(A,B),A) ) ) ).
fof(fc10_isomichi,axiom,
! [A,B] :
( ( v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_xboole_0(k1_isomichi(A,k1_isomichi(A,B)))
& v3_pre_topc(k1_isomichi(A,k1_isomichi(A,B)),A)
& v4_pre_topc(k1_isomichi(A,k1_isomichi(A,B)),A)
& v2_tops_1(k1_isomichi(A,k1_isomichi(A,B)),A)
& v3_tops_1(k1_isomichi(A,k1_isomichi(A,B)),A)
& v4_tops_1(k1_isomichi(A,k1_isomichi(A,B)),A)
& v5_tops_1(k1_isomichi(A,k1_isomichi(A,B)),A)
& v6_tops_1(k1_isomichi(A,k1_isomichi(A,B)),A)
& v1_membered(k1_isomichi(A,k1_isomichi(A,B)))
& v2_membered(k1_isomichi(A,k1_isomichi(A,B)))
& v3_membered(k1_isomichi(A,k1_isomichi(A,B)))
& v4_membered(k1_isomichi(A,k1_isomichi(A,B)))
& v5_membered(k1_isomichi(A,k1_isomichi(A,B)))
& v1_decomp_1(k1_isomichi(A,k1_isomichi(A,B)),A)
& v1_isomichi(k1_isomichi(A,k1_isomichi(A,B)),A)
& v2_isomichi(k1_isomichi(A,k1_isomichi(A,B)),A) ) ) ).
fof(cc11_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_isomichi(B,A)
=> ( ~ v4_isomichi(B,A)
& ~ v5_isomichi(B,A) ) ) ) ) ).
fof(cc12_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_isomichi(B,A)
=> ( ~ v3_isomichi(B,A)
& ~ v5_isomichi(B,A) ) ) ) ) ).
fof(cc13_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v5_isomichi(B,A)
=> ( ~ v3_isomichi(B,A)
& ~ v4_isomichi(B,A) ) ) ) ) ).
fof(cc14_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_isomichi(B,A)
=> ( v3_isomichi(B,A)
& ~ v4_isomichi(B,A)
& ~ v5_isomichi(B,A) ) ) ) ) ).
fof(cc15_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v2_isomichi(B,A)
=> ( v3_isomichi(B,A)
& ~ v4_isomichi(B,A)
& ~ v5_isomichi(B,A) ) ) ) ) ).
fof(cc16_isomichi,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v2_tdlat_3(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( ~ v1_xboole_0(B)
& v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v3_isomichi(B,A)
& v4_isomichi(B,A)
& ~ v5_isomichi(B,A) ) ) ) ) ).
fof(rc4_isomichi,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_pre_topc(A)
& v2_pre_topc(A)
& v2_tdlat_3(A)
& ~ v3_realset2(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v3_isomichi(B,A)
& v4_isomichi(B,A)
& ~ v5_isomichi(B,A) ) ) ).
fof(rc5_isomichi,axiom,
? [A] :
( l1_pre_topc(A)
& ~ v3_struct_0(A)
& v1_pre_topc(A)
& v2_pre_topc(A)
& ~ v3_realset2(A)
& v6_isomichi(A)
& v7_isomichi(A) ) ).
fof(rc6_isomichi,axiom,
? [A] :
( l1_pre_topc(A)
& ~ v3_struct_0(A)
& v1_pre_topc(A)
& v2_pre_topc(A)
& v8_isomichi(A) ) ).
fof(rc7_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v3_isomichi(B,A)
& ~ v4_isomichi(B,A)
& ~ v5_isomichi(B,A) ) ) ).
fof(rc8_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& v7_isomichi(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v3_isomichi(B,A)
& v4_isomichi(B,A)
& ~ v5_isomichi(B,A) ) ) ).
fof(rc9_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& v8_isomichi(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v3_isomichi(B,A)
& ~ v4_isomichi(B,A)
& v5_isomichi(B,A) ) ) ).
fof(fc11_isomichi,axiom,
! [A,B] :
( ( v2_pre_topc(A)
& l1_pre_topc(A)
& v3_isomichi(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v3_isomichi(k3_subset_1(u1_struct_0(A),B),A)
& ~ v4_isomichi(k3_subset_1(u1_struct_0(A),B),A)
& ~ v5_isomichi(k3_subset_1(u1_struct_0(A),B),A) ) ) ).
fof(fc12_isomichi,axiom,
! [A,B] :
( ( v2_pre_topc(A)
& v7_isomichi(A)
& l1_pre_topc(A)
& v4_isomichi(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v3_isomichi(k3_subset_1(u1_struct_0(A),B),A)
& v4_isomichi(k3_subset_1(u1_struct_0(A),B),A)
& ~ v5_isomichi(k3_subset_1(u1_struct_0(A),B),A) ) ) ).
fof(fc13_isomichi,axiom,
! [A,B] :
( ( v2_pre_topc(A)
& v8_isomichi(A)
& l1_pre_topc(A)
& v5_isomichi(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v3_isomichi(k3_subset_1(u1_struct_0(A),B),A)
& ~ v4_isomichi(k3_subset_1(u1_struct_0(A),B),A)
& v5_isomichi(k3_subset_1(u1_struct_0(A),B),A) ) ) ).
fof(t1_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> k5_subset_1(u1_struct_0(A),k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,B))),k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,C)))) = k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,k5_subset_1(u1_struct_0(A),B,C)))) ) ) ) ).
fof(t2_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,k4_subset_1(u1_struct_0(A),B,C)))) = k4_subset_1(u1_struct_0(A),k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,B))),k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,C)))) ) ) ) ).
fof(d1_isomichi,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_isomichi(B,A)
<=> k1_tops_1(A,k6_pre_topc(A,B)) = k1_tops_1(A,B) ) ) ) ).
fof(d2_isomichi,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v2_isomichi(B,A)
<=> k6_pre_topc(A,k1_tops_1(A,B)) = k6_pre_topc(A,B) ) ) ) ).
fof(t3_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_pre_topc(B,A)
=> v1_isomichi(B,A) ) ) ) ).
fof(t4_isomichi,axiom,
! [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)
=> v2_isomichi(B,A) ) ) ) ).
fof(d3_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_tops_1(B,A)
<=> ( k6_pre_topc(A,k1_tops_1(A,B)) = k6_pre_topc(A,B)
& k1_tops_1(A,k6_pre_topc(A,B)) = k1_tops_1(A,B) ) ) ) ) ).
fof(t5_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_tops_1(B,A)
<=> ( v2_isomichi(B,A)
& v1_isomichi(B,A) ) ) ) ) ).
fof(t6_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_isomichi(B,A)
=> v2_isomichi(k3_subset_1(u1_struct_0(A),B),A) ) ) ) ).
fof(t7_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v2_isomichi(B,A)
=> v1_isomichi(k3_subset_1(u1_struct_0(A),B),A) ) ) ) ).
fof(t8_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_isomichi(B,A)
<=> r1_tarski(k1_tops_1(A,k6_pre_topc(A,B)),B) ) ) ) ).
fof(t9_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v2_isomichi(B,A)
<=> r1_tarski(B,k6_pre_topc(A,k1_tops_1(A,B))) ) ) ) ).
fof(t10_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_tops_1(B,A)
<=> ( r1_tarski(k1_tops_1(A,k6_pre_topc(A,B)),B)
& r1_tarski(B,k6_pre_topc(A,k1_tops_1(A,B))) ) ) ) ) ).
fof(t11_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v6_tops_1(k2_pre_topc(A),A)
& v5_tops_1(k2_pre_topc(A),A) ) ) ).
fof(t12_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v6_tops_1(k1_pre_topc(A),A)
& v5_tops_1(k1_pre_topc(A),A) ) ) ).
fof(t13_isomichi,axiom,
$true ).
fof(t14_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> k1_tops_1(A,k6_pre_topc(A,k1_pre_topc(A))) = k1_pre_topc(A) ) ).
fof(t15_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v6_tops_1(B,A)
=> v5_tops_1(k3_subset_1(u1_struct_0(A),B),A) ) ) ) ).
fof(t16_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v5_tops_1(B,A)
=> v6_tops_1(k3_subset_1(u1_struct_0(A),B),A) ) ) ) ).
fof(t17_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v6_tops_1(k1_tops_1(A,k6_pre_topc(A,B)),A)
& v5_tops_1(k6_pre_topc(A,k1_tops_1(A,B)),A) ) ) ) ).
fof(t18_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v6_tops_1(B,A)
<=> ( v1_isomichi(B,A)
& v3_pre_topc(B,A) ) ) ) ) ).
fof(t19_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v5_tops_1(B,A)
<=> ( v2_isomichi(B,A)
& v4_pre_topc(B,A) ) ) ) ) ).
fof(t20_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_tops_1(B,A)
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& v6_tops_1(C,A)
& r1_tarski(C,B)
& r1_tarski(B,k6_pre_topc(A,C)) ) ) ) ) ).
fof(t21_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_tops_1(B,A)
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& v5_tops_1(C,A)
& r1_tarski(k1_tops_1(A,C),B)
& r1_tarski(B,C) ) ) ) ) ).
fof(d4_isomichi,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k2_tops_1(A,B) = k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k1_tops_1(A,B)) ) ) ).
fof(t22_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> v4_pre_topc(k2_tops_1(A,B),A) ) ) ).
fof(t23_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_tops_1(B,A)
<=> ( k2_tops_1(A,B) = k6_subset_1(u1_struct_0(A),k6_pre_topc(A,k1_tops_1(A,B)),k1_tops_1(A,k6_pre_topc(A,B)))
& k2_tops_1(A,B) = k5_subset_1(u1_struct_0(A),k6_pre_topc(A,k1_tops_1(A,B)),k6_pre_topc(A,k1_tops_1(A,k3_subset_1(u1_struct_0(A),B)))) ) ) ) ) ).
fof(d5_isomichi,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> k1_isomichi(A,B) = k1_tops_1(A,k2_tops_1(A,B)) ) ) ).
fof(t24_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v6_tops_1(k1_isomichi(A,B),A)
& k1_isomichi(A,B) = k6_subset_1(u1_struct_0(A),k1_tops_1(A,k6_pre_topc(A,B)),k6_pre_topc(A,k1_tops_1(A,B)))
& k1_isomichi(A,B) = k5_subset_1(u1_struct_0(A),k1_tops_1(A,k6_pre_topc(A,B)),k1_tops_1(A,k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)))) ) ) ) ).
fof(t25_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_isomichi(B,A)
<=> ( v6_tops_1(k1_tops_1(A,B),A)
& v1_xboole_0(k1_isomichi(A,B)) ) ) ) ) ).
fof(t26_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v2_isomichi(B,A)
<=> ( v5_tops_1(k6_pre_topc(A,B),A)
& v1_xboole_0(k1_isomichi(A,B)) ) ) ) ) ).
fof(t27_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_tops_1(B,A)
<=> ( v6_tops_1(k1_tops_1(A,B),A)
& v5_tops_1(k6_pre_topc(A,B),A)
& v1_xboole_0(k1_isomichi(A,B)) ) ) ) ) ).
fof(t28_isomichi,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ( A = k2_limfunc1(B)
=> k1_tops_1(k3_topmetr,A) = k12_prob_1(B) ) ) ) ).
fof(t29_isomichi,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ( A = k3_limfunc1(B)
=> k1_tops_1(k3_topmetr,A) = k4_limfunc1(B) ) ) ) ).
fof(t30_isomichi,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( A = k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k2_limfunc1(B),k3_borsuk_5(B,C)),k3_limfunc1(C))
=> k6_pre_topc(k3_topmetr,A) = u1_struct_0(k3_topmetr) ) ) ) ) ).
fof(t31_isomichi,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( A = k2_borsuk_5(B,C)
=> k1_tops_1(k3_topmetr,A) = k1_xboole_0 ) ) ) ) ).
fof(t32_isomichi,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ( A = k3_borsuk_5(B,C)
=> k1_tops_1(k3_topmetr,A) = k1_xboole_0 ) ) ) ) ).
fof(t33_isomichi,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> k6_subset_1(k1_numbers,k2_limfunc1(A),k12_prob_1(B)) = k1_rcomp_1(B,A) ) ) ).
fof(t34_isomichi,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ~ r1_xreal_0(B,A)
=> r1_xboole_0(k3_limfunc1(B),k12_prob_1(A)) ) ) ) ).
fof(t35_isomichi,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(B,A)
=> k3_borsuk_5(A,B) = k1_xboole_0 ) ) ) ).
fof(t36_isomichi,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> r1_tarski(k3_borsuk_5(A,B),k3_limfunc1(A)) ) ) ).
fof(t37_isomichi,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( A = k4_subset_1(k1_numbers,k12_prob_1(B),k2_borsuk_5(C,D))
=> ( r1_xreal_0(C,B)
| r1_xreal_0(D,C)
| k1_tops_1(k3_topmetr,A) = k12_prob_1(B) ) ) ) ) ) ) ).
fof(t38_isomichi,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> r1_xboole_0(k1_rcomp_1(A,B),k4_limfunc1(B)) ) ) ).
fof(t39_isomichi,axiom,
! [A] :
( v1_xreal_0(A)
=> k6_subset_1(k1_numbers,k3_limfunc1(A),k4_limfunc1(A)) = k1_seq_4(A) ) ).
fof(t40_isomichi,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ~ r1_xreal_0(B,A)
=> k1_rcomp_1(A,B) = k6_subset_1(k1_numbers,k3_limfunc1(A),k4_limfunc1(B)) ) ) ) ).
fof(t41_isomichi,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ~ r1_xreal_0(B,A)
=> k1_numbers = k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k12_prob_1(A),k1_rcomp_1(A,B)),k4_limfunc1(B)) ) ) ) ).
fof(t42_isomichi,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> k2_rcomp_1(A,B) = k6_subset_1(k1_numbers,k4_limfunc1(A),k3_limfunc1(B)) ) ) ).
fof(t43_isomichi,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ~ ( ~ r1_xreal_0(C,B)
& ~ r1_xreal_0(A,C)
& k6_subset_1(k1_numbers,k12_prob_1(A),k1_rcomp_1(B,C)) != k4_subset_1(k1_numbers,k12_prob_1(B),k2_rcomp_1(C,A)) ) ) ) ) ).
fof(t44_isomichi,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( A = k4_subset_1(k1_numbers,k2_limfunc1(B),k1_rcomp_1(C,D))
=> ( r1_xreal_0(C,B)
| r1_xreal_0(D,C)
| k1_tops_1(k3_topmetr,A) = k4_subset_1(k1_numbers,k12_prob_1(B),k2_rcomp_1(C,D)) ) ) ) ) ) ) ).
fof(t45_isomichi,axiom,
! [A,B] :
~ ( r3_xboole_0(A,B)
& ~ r1_tarski(A,B)
& ~ r2_xboole_0(B,A) ) ).
fof(d6_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_isomichi(B,A)
<=> r1_tarski(k1_tops_1(A,k6_pre_topc(A,B)),k6_pre_topc(A,k1_tops_1(A,B))) ) ) ) ).
fof(d7_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_isomichi(B,A)
<=> r2_xboole_0(k6_pre_topc(A,k1_tops_1(A,B)),k1_tops_1(A,k6_pre_topc(A,B))) ) ) ) ).
fof(d8_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v5_isomichi(B,A)
<=> ~ r3_xboole_0(k6_pre_topc(A,k1_tops_1(A,B)),k1_tops_1(A,k6_pre_topc(A,B))) ) ) ) ).
fof(t46_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( ~ v3_isomichi(B,A)
& ~ v4_isomichi(B,A)
& ~ v5_isomichi(B,A) ) ) ) ).
fof(t47_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_isomichi(B,A)
<=> v1_xboole_0(k1_isomichi(A,B)) ) ) ) ).
fof(d9_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v6_isomichi(A)
<=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v3_isomichi(B,A) ) ) ) ).
fof(d10_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v7_isomichi(A)
<=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v4_isomichi(B,A) ) ) ) ).
fof(d11_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v8_isomichi(A)
<=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v5_isomichi(B,A) ) ) ) ).
fof(t48_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_isomichi(B,A)
<=> v3_isomichi(k3_subset_1(u1_struct_0(A),B),A) ) ) ) ).
fof(t49_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v4_isomichi(B,A)
<=> v4_isomichi(k3_subset_1(u1_struct_0(A),B),A) ) ) ) ).
fof(t50_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v5_isomichi(B,A)
<=> v5_isomichi(k3_subset_1(u1_struct_0(A),B),A) ) ) ) ).
fof(t51_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_isomichi(B,A)
=> ( k1_tops_1(A,k6_pre_topc(A,B)) = k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,B)))
& k6_pre_topc(A,k1_tops_1(A,B)) = k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,B))) ) ) ) ) ).
fof(t52_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( k1_tops_1(A,k6_pre_topc(A,B)) = k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,B)))
| k6_pre_topc(A,k1_tops_1(A,B)) = k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,B))) )
=> v3_isomichi(B,A) ) ) ) ).
fof(t53_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v3_isomichi(B,A)
& v3_isomichi(C,A) )
=> ( k5_subset_1(u1_struct_0(A),k1_tops_1(A,k6_pre_topc(A,B)),k1_tops_1(A,k6_pre_topc(A,C))) = k1_tops_1(A,k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C)))
& k4_subset_1(u1_struct_0(A),k6_pre_topc(A,k1_tops_1(A,B)),k6_pre_topc(A,k1_tops_1(A,C))) = k6_pre_topc(A,k1_tops_1(A,k4_subset_1(u1_struct_0(A),B,C))) ) ) ) ) ) ).
fof(t54_isomichi,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v3_isomichi(B,A)
& v3_isomichi(C,A) )
=> ( v3_isomichi(k4_subset_1(u1_struct_0(A),B,C),A)
& v3_isomichi(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ) ).
fof(dt_k1_isomichi,axiom,
! [A,B] :
( ( l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k1_isomichi(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
%------------------------------------------------------------------------------