SET007 Axioms: SET007+825.ax
%------------------------------------------------------------------------------
% File : SET007+825 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Complex Banach Space of Bounded Complex Sequences
% 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 : csspace4 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 65 ( 6 unt; 0 def)
% Number of atoms : 791 ( 67 equ)
% Maximal formula atoms : 30 ( 12 avg)
% Number of connectives : 830 ( 104 ~; 0 |; 534 &)
% ( 18 <=>; 174 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 11 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 33 ( 31 usr; 1 prp; 0-3 aty)
% Number of functors : 49 ( 49 usr; 11 con; 0-5 aty)
% Number of variables : 181 ( 177 !; 4 ?)
% 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_csspace4,axiom,
~ v1_xboole_0(k1_csspace4) ).
fof(fc2_csspace4,axiom,
v3_clvect_1(k1_csspace4,k7_csspace) ).
fof(fc3_csspace4,axiom,
( ~ v3_struct_0(g1_clvect_1(k1_csspace4,k10_csspace(k7_csspace,k1_csspace4),k8_csspace(k7_csspace,k1_csspace4),k9_csspace(k7_csspace,k1_csspace4)))
& v3_rlvect_1(g1_clvect_1(k1_csspace4,k10_csspace(k7_csspace,k1_csspace4),k8_csspace(k7_csspace,k1_csspace4),k9_csspace(k7_csspace,k1_csspace4)))
& v4_rlvect_1(g1_clvect_1(k1_csspace4,k10_csspace(k7_csspace,k1_csspace4),k8_csspace(k7_csspace,k1_csspace4),k9_csspace(k7_csspace,k1_csspace4)))
& v5_rlvect_1(g1_clvect_1(k1_csspace4,k10_csspace(k7_csspace,k1_csspace4),k8_csspace(k7_csspace,k1_csspace4),k9_csspace(k7_csspace,k1_csspace4)))
& v6_rlvect_1(g1_clvect_1(k1_csspace4,k10_csspace(k7_csspace,k1_csspace4),k8_csspace(k7_csspace,k1_csspace4),k9_csspace(k7_csspace,k1_csspace4)))
& v1_clvect_1(g1_clvect_1(k1_csspace4,k10_csspace(k7_csspace,k1_csspace4),k8_csspace(k7_csspace,k1_csspace4),k9_csspace(k7_csspace,k1_csspace4)))
& v2_clvect_1(g1_clvect_1(k1_csspace4,k10_csspace(k7_csspace,k1_csspace4),k8_csspace(k7_csspace,k1_csspace4),k9_csspace(k7_csspace,k1_csspace4))) ) ).
fof(fc4_csspace4,axiom,
( ~ v3_struct_0(g2_clvect_1(k1_csspace4,k10_csspace(k7_csspace,k1_csspace4),k8_csspace(k7_csspace,k1_csspace4),k9_csspace(k7_csspace,k1_csspace4),k2_csspace4))
& v3_rlvect_1(g2_clvect_1(k1_csspace4,k10_csspace(k7_csspace,k1_csspace4),k8_csspace(k7_csspace,k1_csspace4),k9_csspace(k7_csspace,k1_csspace4),k2_csspace4))
& v4_rlvect_1(g2_clvect_1(k1_csspace4,k10_csspace(k7_csspace,k1_csspace4),k8_csspace(k7_csspace,k1_csspace4),k9_csspace(k7_csspace,k1_csspace4),k2_csspace4))
& v5_rlvect_1(g2_clvect_1(k1_csspace4,k10_csspace(k7_csspace,k1_csspace4),k8_csspace(k7_csspace,k1_csspace4),k9_csspace(k7_csspace,k1_csspace4),k2_csspace4))
& v6_rlvect_1(g2_clvect_1(k1_csspace4,k10_csspace(k7_csspace,k1_csspace4),k8_csspace(k7_csspace,k1_csspace4),k9_csspace(k7_csspace,k1_csspace4),k2_csspace4))
& v2_clvect_1(g2_clvect_1(k1_csspace4,k10_csspace(k7_csspace,k1_csspace4),k8_csspace(k7_csspace,k1_csspace4),k9_csspace(k7_csspace,k1_csspace4),k2_csspace4))
& v4_clvect_1(g2_clvect_1(k1_csspace4,k10_csspace(k7_csspace,k1_csspace4),k8_csspace(k7_csspace,k1_csspace4),k9_csspace(k7_csspace,k1_csspace4),k2_csspace4)) ) ).
fof(fc5_csspace4,axiom,
( ~ v3_struct_0(k3_csspace4)
& v3_rlvect_1(k3_csspace4)
& v4_rlvect_1(k3_csspace4)
& v5_rlvect_1(k3_csspace4)
& v6_rlvect_1(k3_csspace4)
& v2_clvect_1(k3_csspace4)
& v5_clvect_1(k3_csspace4) ) ).
fof(rc1_csspace4,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ? [C] :
( m1_relset_1(C,A,u1_struct_0(B))
& ~ v1_xboole_0(C)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_funct_2(C,A,u1_struct_0(B))
& v1_partfun1(C,A,u1_struct_0(B))
& v1_csspace4(C,A,B) ) ) ).
fof(fc6_csspace4,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ~ v1_xboole_0(k4_csspace4(A,B)) ) ).
fof(fc7_csspace4,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ( ~ v3_struct_0(g1_clvect_1(k4_csspace4(A,B),k10_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k8_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k9_csspace(k3_clopban1(A,B),k4_csspace4(A,B))))
& v3_rlvect_1(g1_clvect_1(k4_csspace4(A,B),k10_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k8_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k9_csspace(k3_clopban1(A,B),k4_csspace4(A,B))))
& v4_rlvect_1(g1_clvect_1(k4_csspace4(A,B),k10_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k8_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k9_csspace(k3_clopban1(A,B),k4_csspace4(A,B))))
& v5_rlvect_1(g1_clvect_1(k4_csspace4(A,B),k10_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k8_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k9_csspace(k3_clopban1(A,B),k4_csspace4(A,B))))
& v6_rlvect_1(g1_clvect_1(k4_csspace4(A,B),k10_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k8_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k9_csspace(k3_clopban1(A,B),k4_csspace4(A,B))))
& v1_clvect_1(g1_clvect_1(k4_csspace4(A,B),k10_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k8_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k9_csspace(k3_clopban1(A,B),k4_csspace4(A,B))))
& v2_clvect_1(g1_clvect_1(k4_csspace4(A,B),k10_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k8_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k9_csspace(k3_clopban1(A,B),k4_csspace4(A,B)))) ) ) ).
fof(fc8_csspace4,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ( ~ v3_struct_0(k5_csspace4(A,B))
& v3_rlvect_1(k5_csspace4(A,B))
& v4_rlvect_1(k5_csspace4(A,B))
& v5_rlvect_1(k5_csspace4(A,B))
& v6_rlvect_1(k5_csspace4(A,B))
& v1_clvect_1(k5_csspace4(A,B))
& v2_clvect_1(k5_csspace4(A,B)) ) ) ).
fof(fc9_csspace4,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ( ~ v3_struct_0(k9_csspace4(A,B))
& v3_rlvect_1(k9_csspace4(A,B))
& v4_rlvect_1(k9_csspace4(A,B))
& v5_rlvect_1(k9_csspace4(A,B))
& v6_rlvect_1(k9_csspace4(A,B))
& v2_clvect_1(k9_csspace4(A,B))
& v5_clvect_1(k9_csspace4(A,B)) ) ) ).
fof(fc10_csspace4,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& v4_clopban1(B)
& l2_clvect_1(B) )
=> ( ~ v3_struct_0(k9_csspace4(A,B))
& v3_rlvect_1(k9_csspace4(A,B))
& v4_rlvect_1(k9_csspace4(A,B))
& v5_rlvect_1(k9_csspace4(A,B))
& v6_rlvect_1(k9_csspace4(A,B))
& v2_clvect_1(k9_csspace4(A,B))
& v5_clvect_1(k9_csspace4(A,B))
& v4_clopban1(k9_csspace4(A,B)) ) ) ).
fof(d1_csspace4,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k7_csspace)))
=> ( A = k1_csspace4
<=> ! [B] :
( r2_hidden(B,A)
<=> ( r2_hidden(B,k1_csspace)
& v1_comseq_2(k2_csspace(B)) ) ) ) ) ).
fof(d2_csspace4,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k1_csspace4,k1_numbers)
& m2_relset_1(A,k1_csspace4,k1_numbers) )
=> ( A = k2_csspace4
<=> ! [B] :
( r2_hidden(B,k1_csspace4)
=> k2_seq_1(k1_csspace4,k1_numbers,A,B) = k3_pscomp_1(k1_pscomp_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,k2_csspace(B)))) ) ) ) ).
fof(t1_csspace4,axiom,
$true ).
fof(t2_csspace4,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( ( v1_comseq_2(A)
& k3_pscomp_1(k1_pscomp_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,A))) = np__0 )
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_comseq_1(A,B) = k5_complex1 ) ) ) ).
fof(d3_csspace4,axiom,
k3_csspace4 = g2_clvect_1(k1_csspace4,k10_csspace(k7_csspace,k1_csspace4),k8_csspace(k7_csspace,k1_csspace4),k9_csspace(k7_csspace,k1_csspace4),k2_csspace4) ).
fof(t3_csspace4,axiom,
( u1_struct_0(k3_csspace4) = k1_csspace4
& ! [A] :
( m1_subset_1(A,u1_struct_0(k3_csspace4))
<=> ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers)
& v1_comseq_2(k2_csspace(A)) ) )
& k1_rlvect_1(k3_csspace4) = k6_csspace
& ! [A] :
( m1_subset_1(A,u1_struct_0(k3_csspace4))
=> A = k2_csspace(A) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(k3_csspace4))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k3_csspace4))
=> k2_rlvect_1(k3_csspace4,A,B) = k2_comseq_1(k5_numbers,k2_csspace(A),k2_csspace(B)) ) )
& ! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k3_csspace4))
=> k1_clvect_1(k3_csspace4,B,A) = k4_comseq_1(k5_numbers,k2_csspace(B),A) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(k3_csspace4))
=> ( k5_rlvect_1(k3_csspace4,A) = k5_comseq_1(k5_numbers,k2_csspace(A))
& k2_csspace(k5_rlvect_1(k3_csspace4,A)) = k5_comseq_1(k5_numbers,k2_csspace(A)) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(k3_csspace4))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k3_csspace4))
=> k6_rlvect_1(k3_csspace4,A,B) = k6_comseq_1(k5_numbers,k2_csspace(A),k2_csspace(B)) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(k3_csspace4))
=> v1_comseq_2(k2_csspace(A)) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(k3_csspace4))
=> k5_clvect_1(k3_csspace4,A) = k3_pscomp_1(k1_pscomp_1(k5_numbers,k1_numbers,k9_comseq_1(k5_numbers,k2_csspace(A)))) ) ) ).
fof(t4_csspace4,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k3_csspace4))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k3_csspace4))
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ( ( k5_clvect_1(k3_csspace4,A) = np__0
=> A = k1_rlvect_1(k3_csspace4) )
& ( A = k1_rlvect_1(k3_csspace4)
=> k5_clvect_1(k3_csspace4,A) = np__0 )
& r1_xreal_0(np__0,k5_clvect_1(k3_csspace4,A))
& r1_xreal_0(k5_clvect_1(k3_csspace4,k2_rlvect_1(k3_csspace4,A,B)),k3_real_1(k5_clvect_1(k3_csspace4,A),k5_clvect_1(k3_csspace4,B)))
& k5_clvect_1(k3_csspace4,k1_clvect_1(k3_csspace4,A,C)) = k4_real_1(k17_complex1(C),k5_clvect_1(k3_csspace4,A)) ) ) ) ) ).
fof(t5_csspace4,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,u1_struct_0(k3_csspace4))
& m2_relset_1(A,k5_numbers,u1_struct_0(k3_csspace4)) )
=> ( v1_csspace3(A,k3_csspace4)
=> v6_clvect_1(A,k3_csspace4) ) ) ).
fof(t6_csspace4,axiom,
( ~ v3_struct_0(k3_csspace4)
& v3_rlvect_1(k3_csspace4)
& v4_rlvect_1(k3_csspace4)
& v5_rlvect_1(k3_csspace4)
& v6_rlvect_1(k3_csspace4)
& v2_clvect_1(k3_csspace4)
& v5_clvect_1(k3_csspace4)
& v4_clopban1(k3_csspace4)
& l2_clvect_1(k3_csspace4) ) ).
fof(d4_csspace4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,u1_struct_0(B))
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ( v1_csspace4(C,A,B)
<=> ? [D] :
( m1_subset_1(D,k1_numbers)
& r1_xreal_0(np__0,D)
& ! [E] :
( m1_subset_1(E,A)
=> r1_xreal_0(k5_clvect_1(B,k8_funct_2(A,u1_struct_0(B),C,E)),D) ) ) ) ) ) ) ).
fof(t7_csspace4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,u1_struct_0(B))
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ( ! [D] :
( m1_subset_1(D,A)
=> k8_funct_2(A,u1_struct_0(B),C,D) = k1_rlvect_1(B) )
=> v1_csspace4(C,A,B) ) ) ) ) ).
fof(d5_csspace4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_clopban1(A,B))))
=> ( C = k4_csspace4(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ( v1_funct_1(D)
& v1_funct_2(D,A,u1_struct_0(B))
& v1_csspace4(D,A,B)
& m2_relset_1(D,A,u1_struct_0(B)) ) ) ) ) ) ) ).
fof(t8_csspace4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> v3_clvect_1(k4_csspace4(A,B),k3_clopban1(A,B)) ) ) ).
fof(t9_csspace4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> m1_clvect_1(g1_clvect_1(k4_csspace4(A,B),k10_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k8_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k9_csspace(k3_clopban1(A,B),k4_csspace4(A,B))),k3_clopban1(A,B)) ) ) ).
fof(d6_csspace4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> k5_csspace4(A,B) = g1_clvect_1(k4_csspace4(A,B),k10_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k8_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k9_csspace(k3_clopban1(A,B),k4_csspace4(A,B))) ) ) ).
fof(t10_csspace4,axiom,
$true ).
fof(t11_csspace4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k5_csspace4(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k5_csspace4(A,B)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k5_csspace4(A,B)))
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,A,u1_struct_0(B))
& v1_csspace4(F,A,B)
& m2_relset_1(F,A,u1_struct_0(B)) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,A,u1_struct_0(B))
& v1_csspace4(G,A,B)
& m2_relset_1(G,A,u1_struct_0(B)) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,A,u1_struct_0(B))
& v1_csspace4(H,A,B)
& m2_relset_1(H,A,u1_struct_0(B)) )
=> ( ( F = C
& G = D
& H = E )
=> ( E = k4_rlvect_1(k5_csspace4(A,B),C,D)
<=> ! [I] :
( m1_subset_1(I,A)
=> k8_funct_2(A,u1_struct_0(B),H,I) = k4_rlvect_1(B,k8_funct_2(A,u1_struct_0(B),F,I),k8_funct_2(A,u1_struct_0(B),G,I)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t12_csspace4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k5_csspace4(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k5_csspace4(A,B)))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,u1_struct_0(B))
& v1_csspace4(E,A,B)
& m2_relset_1(E,A,u1_struct_0(B)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,A,u1_struct_0(B))
& v1_csspace4(F,A,B)
& m2_relset_1(F,A,u1_struct_0(B)) )
=> ( ( E = C
& F = D )
=> ! [G] :
( m1_subset_1(G,k2_numbers)
=> ( D = k1_clvect_1(k5_csspace4(A,B),C,G)
<=> ! [H] :
( m1_subset_1(H,A)
=> k8_funct_2(A,u1_struct_0(B),F,H) = k1_clvect_1(B,k8_funct_2(A,u1_struct_0(B),E,H),G) ) ) ) ) ) ) ) ) ) ) ).
fof(t13_csspace4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> k1_rlvect_1(k5_csspace4(A,B)) = k2_funcop_1(A,k1_rlvect_1(B)) ) ) ).
fof(d7_csspace4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ! [C] :
( r2_hidden(C,k4_csspace4(A,B))
=> k6_csspace4(A,B,C) = C ) ) ) ).
fof(t14_csspace4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,u1_struct_0(B))
& v1_csspace4(C,A,B)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ( ~ v1_xboole_0(k7_csspace4(A,B,C))
& v1_seq_4(k7_csspace4(A,B,C)) ) ) ) ) ).
fof(t15_csspace4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,u1_struct_0(B))
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ( v1_csspace4(C,A,B)
<=> v1_seq_4(k7_csspace4(A,B,C)) ) ) ) ) ).
fof(t16_csspace4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,k4_csspace4(A,B),k1_numbers)
& m2_relset_1(C,k4_csspace4(A,B),k1_numbers)
& ! [D] :
( r2_hidden(D,k4_csspace4(A,B))
=> k2_seq_1(k4_csspace4(A,B),k1_numbers,C,D) = k3_pscomp_1(k7_csspace4(A,B,k6_csspace4(A,B,D))) ) ) ) ) ).
fof(d9_csspace4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k4_csspace4(A,B),k1_numbers)
& m2_relset_1(C,k4_csspace4(A,B),k1_numbers) )
=> ( C = k8_csspace4(A,B)
<=> ! [D] :
( r2_hidden(D,k4_csspace4(A,B))
=> k2_seq_1(k4_csspace4(A,B),k1_numbers,C,D) = k3_pscomp_1(k7_csspace4(A,B,k6_csspace4(A,B,D))) ) ) ) ) ) ).
fof(t17_csspace4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,u1_struct_0(B))
& v1_csspace4(C,A,B)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> k6_csspace4(A,B,C) = C ) ) ) ).
fof(t18_csspace4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,u1_struct_0(B))
& v1_csspace4(C,A,B)
& m2_relset_1(C,A,u1_struct_0(B)) )
=> k2_seq_1(k4_csspace4(A,B),k1_numbers,k8_csspace4(A,B),C) = k3_pscomp_1(k7_csspace4(A,B,C)) ) ) ) ).
fof(d10_csspace4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> k9_csspace4(A,B) = g2_clvect_1(k4_csspace4(A,B),k10_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k8_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k9_csspace(k3_clopban1(A,B),k4_csspace4(A,B)),k8_csspace4(A,B)) ) ) ).
fof(t19_csspace4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> k2_funcop_1(A,k1_rlvect_1(B)) = k1_rlvect_1(k9_csspace4(A,B)) ) ) ).
fof(t20_csspace4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k9_csspace4(A,B)))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,u1_struct_0(B))
& v1_csspace4(D,A,B)
& m2_relset_1(D,A,u1_struct_0(B)) )
=> ( D = C
=> ! [E] :
( m1_subset_1(E,A)
=> r1_xreal_0(k5_clvect_1(B,k8_funct_2(A,u1_struct_0(B),D,E)),k5_clvect_1(k9_csspace4(A,B),C)) ) ) ) ) ) ) ).
fof(t21_csspace4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k9_csspace4(A,B)))
=> r1_xreal_0(np__0,k5_clvect_1(k9_csspace4(A,B),C)) ) ) ) ).
fof(t22_csspace4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k9_csspace4(A,B)))
=> ( C = k1_rlvect_1(k9_csspace4(A,B))
=> np__0 = k5_clvect_1(k9_csspace4(A,B),C) ) ) ) ) ).
fof(t23_csspace4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k9_csspace4(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k9_csspace4(A,B)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k9_csspace4(A,B)))
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,A,u1_struct_0(B))
& v1_csspace4(F,A,B)
& m2_relset_1(F,A,u1_struct_0(B)) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,A,u1_struct_0(B))
& v1_csspace4(G,A,B)
& m2_relset_1(G,A,u1_struct_0(B)) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,A,u1_struct_0(B))
& v1_csspace4(H,A,B)
& m2_relset_1(H,A,u1_struct_0(B)) )
=> ( ( F = C
& G = D
& H = E )
=> ( E = k2_rlvect_1(k9_csspace4(A,B),C,D)
<=> ! [I] :
( m1_subset_1(I,A)
=> k8_funct_2(A,u1_struct_0(B),H,I) = k4_rlvect_1(B,k8_funct_2(A,u1_struct_0(B),F,I),k8_funct_2(A,u1_struct_0(B),G,I)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t24_csspace4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k9_csspace4(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k9_csspace4(A,B)))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,u1_struct_0(B))
& v1_csspace4(E,A,B)
& m2_relset_1(E,A,u1_struct_0(B)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,A,u1_struct_0(B))
& v1_csspace4(F,A,B)
& m2_relset_1(F,A,u1_struct_0(B)) )
=> ( ( E = C
& F = D )
=> ! [G] :
( m1_subset_1(G,k2_numbers)
=> ( D = k1_clvect_1(k9_csspace4(A,B),C,G)
<=> ! [H] :
( m1_subset_1(H,A)
=> k8_funct_2(A,u1_struct_0(B),F,H) = k1_clvect_1(B,k8_funct_2(A,u1_struct_0(B),E,H),G) ) ) ) ) ) ) ) ) ) ) ).
fof(t25_csspace4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k9_csspace4(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k9_csspace4(A,B)))
=> ! [E] :
( m1_subset_1(E,k2_numbers)
=> ( ( k5_clvect_1(k9_csspace4(A,B),C) = np__0
=> C = k1_rlvect_1(k9_csspace4(A,B)) )
& ( C = k1_rlvect_1(k9_csspace4(A,B))
=> k5_clvect_1(k9_csspace4(A,B),C) = np__0 )
& k5_clvect_1(k9_csspace4(A,B),k1_clvect_1(k9_csspace4(A,B),C,E)) = k4_real_1(k17_complex1(E),k5_clvect_1(k9_csspace4(A,B),C))
& r1_xreal_0(k5_clvect_1(k9_csspace4(A,B),k2_rlvect_1(k9_csspace4(A,B),C,D)),k3_real_1(k5_clvect_1(k9_csspace4(A,B),C),k5_clvect_1(k9_csspace4(A,B),D))) ) ) ) ) ) ) ).
fof(t26_csspace4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> v5_clvect_1(k9_csspace4(A,B)) ) ) ).
fof(t27_csspace4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ( ~ v3_struct_0(k9_csspace4(A,B))
& v3_rlvect_1(k9_csspace4(A,B))
& v4_rlvect_1(k9_csspace4(A,B))
& v5_rlvect_1(k9_csspace4(A,B))
& v6_rlvect_1(k9_csspace4(A,B))
& v2_clvect_1(k9_csspace4(A,B))
& v5_clvect_1(k9_csspace4(A,B))
& l2_clvect_1(k9_csspace4(A,B)) ) ) ) ).
fof(t28_csspace4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k9_csspace4(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k9_csspace4(A,B)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k9_csspace4(A,B)))
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,A,u1_struct_0(B))
& v1_csspace4(F,A,B)
& m2_relset_1(F,A,u1_struct_0(B)) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,A,u1_struct_0(B))
& v1_csspace4(G,A,B)
& m2_relset_1(G,A,u1_struct_0(B)) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,A,u1_struct_0(B))
& v1_csspace4(H,A,B)
& m2_relset_1(H,A,u1_struct_0(B)) )
=> ( ( F = C
& G = D
& H = E )
=> ( E = k6_rlvect_1(k9_csspace4(A,B),C,D)
<=> ! [I] :
( m1_subset_1(I,A)
=> k8_funct_2(A,u1_struct_0(B),H,I) = k6_rlvect_1(B,k8_funct_2(A,u1_struct_0(B),F,I),k8_funct_2(A,u1_struct_0(B),G,I)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t29_csspace4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ( v4_clopban1(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(k9_csspace4(A,B)))
& m2_relset_1(C,k5_numbers,u1_struct_0(k9_csspace4(A,B))) )
=> ( v1_csspace3(C,k9_csspace4(A,B))
=> v6_clvect_1(C,k9_csspace4(A,B)) ) ) ) ) ) ).
fof(t30_csspace4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& v4_clopban1(B)
& l2_clvect_1(B) )
=> ( ~ v3_struct_0(k9_csspace4(A,B))
& v3_rlvect_1(k9_csspace4(A,B))
& v4_rlvect_1(k9_csspace4(A,B))
& v5_rlvect_1(k9_csspace4(A,B))
& v6_rlvect_1(k9_csspace4(A,B))
& v2_clvect_1(k9_csspace4(A,B))
& v5_clvect_1(k9_csspace4(A,B))
& v4_clopban1(k9_csspace4(A,B))
& l2_clvect_1(k9_csspace4(A,B)) ) ) ) ).
fof(t31_csspace4,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> ( ( v1_comseq_2(A)
& v1_comseq_2(B) )
=> v1_comseq_2(k2_comseq_1(k5_numbers,A,B)) ) ) ) ).
fof(t32_csspace4,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> ( v1_comseq_2(B)
=> v1_comseq_2(k4_comseq_1(k5_numbers,B,A)) ) ) ) ).
fof(t33_csspace4,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( v1_comseq_2(A)
<=> v3_seq_2(k9_comseq_1(k5_numbers,A)) ) ) ).
fof(t34_csspace4,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k2_numbers)
& m2_relset_1(C,k5_numbers,k2_numbers) )
=> ( A = k6_comseq_1(k5_numbers,B,C)
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k1_comseq_1(A,D) = k11_complex1(k1_comseq_1(B,D),k1_comseq_1(C,D)) ) ) ) ) ) ).
fof(dt_k1_csspace4,axiom,
m1_subset_1(k1_csspace4,k1_zfmisc_1(u1_struct_0(k7_csspace))) ).
fof(dt_k2_csspace4,axiom,
( v1_funct_1(k2_csspace4)
& v1_funct_2(k2_csspace4,k1_csspace4,k1_numbers)
& m2_relset_1(k2_csspace4,k1_csspace4,k1_numbers) ) ).
fof(dt_k3_csspace4,axiom,
( ~ v3_struct_0(k3_csspace4)
& l2_clvect_1(k3_csspace4) ) ).
fof(dt_k4_csspace4,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> m1_subset_1(k4_csspace4(A,B),k1_zfmisc_1(u1_struct_0(k3_clopban1(A,B)))) ) ).
fof(dt_k5_csspace4,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ( ~ v3_struct_0(k5_csspace4(A,B))
& v3_rlvect_1(k5_csspace4(A,B))
& v4_rlvect_1(k5_csspace4(A,B))
& v5_rlvect_1(k5_csspace4(A,B))
& v6_rlvect_1(k5_csspace4(A,B))
& v2_clvect_1(k5_csspace4(A,B))
& l1_clvect_1(k5_csspace4(A,B)) ) ) ).
fof(dt_k6_csspace4,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ( v1_funct_1(k6_csspace4(A,B,C))
& v1_funct_2(k6_csspace4(A,B,C),A,u1_struct_0(B))
& v1_csspace4(k6_csspace4(A,B,C),A,B)
& m2_relset_1(k6_csspace4(A,B,C),A,u1_struct_0(B)) ) ) ).
fof(dt_k7_csspace4,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B)
& v1_funct_1(C)
& v1_funct_2(C,A,u1_struct_0(B))
& m1_relset_1(C,A,u1_struct_0(B)) )
=> ( ~ v1_xboole_0(k7_csspace4(A,B,C))
& m1_subset_1(k7_csspace4(A,B,C),k1_zfmisc_1(k1_numbers)) ) ) ).
fof(dt_k8_csspace4,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ( v1_funct_1(k8_csspace4(A,B))
& v1_funct_2(k8_csspace4(A,B),k4_csspace4(A,B),k1_numbers)
& m2_relset_1(k8_csspace4(A,B),k4_csspace4(A,B),k1_numbers) ) ) ).
fof(dt_k9_csspace4,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ( ~ v3_struct_0(k9_csspace4(A,B))
& l2_clvect_1(k9_csspace4(A,B)) ) ) ).
fof(d8_csspace4,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v5_clvect_1(B)
& l2_clvect_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,u1_struct_0(B))
& m2_relset_1(C,A,u1_struct_0(B)) )
=> k7_csspace4(A,B,C) = a_3_0_csspace4(A,B,C) ) ) ) ).
fof(fraenkel_a_3_0_csspace4,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v2_clvect_1(C)
& v5_clvect_1(C)
& l2_clvect_1(C)
& v1_funct_1(D)
& v1_funct_2(D,B,u1_struct_0(C))
& m2_relset_1(D,B,u1_struct_0(C)) )
=> ( r2_hidden(A,a_3_0_csspace4(B,C,D))
<=> ? [E] :
( m1_subset_1(E,B)
& A = k5_clvect_1(C,k8_funct_2(B,u1_struct_0(C),D,E)) ) ) ) ).
%------------------------------------------------------------------------------