SET007 Axioms: SET007+810.ax
%------------------------------------------------------------------------------
% File : SET007+810 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Complex Linear Space of 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 : csspace [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 146 ( 8 unt; 0 def)
% Number of atoms : 1428 ( 121 equ)
% Maximal formula atoms : 21 ( 9 avg)
% Number of connectives : 1400 ( 118 ~; 4 |; 920 &)
% ( 18 <=>; 340 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 29 ( 28 usr; 0 prp; 1-3 aty)
% Number of functors : 76 ( 76 usr; 15 con; 0-6 aty)
% Number of variables : 381 ( 373 !; 8 ?)
% 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_csspace,axiom,
( ~ v3_struct_0(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace))
& v3_rlvect_1(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace))
& v1_clvect_1(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace)) ) ).
fof(rc1_csspace,axiom,
? [A] :
( l1_csspace(A)
& v1_csspace(A) ) ).
fof(rc2_csspace,axiom,
? [A] :
( l1_csspace(A)
& ~ v3_struct_0(A)
& v1_csspace(A) ) ).
fof(fc2_csspace,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(k2_numbers,A),A)
& m1_relset_1(D,k2_zfmisc_1(k2_numbers,A),A)
& v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(A,A),k2_numbers)
& m1_relset_1(E,k2_zfmisc_1(A,A),k2_numbers) )
=> ( ~ v3_struct_0(g1_csspace(A,B,C,D,E))
& v1_csspace(g1_csspace(A,B,C,D,E)) ) ) ).
fof(rc3_csspace,axiom,
? [A] :
( l1_csspace(A)
& ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v1_csspace(A)
& v2_csspace(A) ) ).
fof(fc3_csspace,axiom,
( ~ v3_struct_0(g1_csspace(k11_csspace,k10_csspace(k7_csspace,k11_csspace),k8_csspace(k7_csspace,k11_csspace),k9_csspace(k7_csspace,k11_csspace),k19_csspace))
& v1_csspace(g1_csspace(k11_csspace,k10_csspace(k7_csspace,k11_csspace),k8_csspace(k7_csspace,k11_csspace),k9_csspace(k7_csspace,k11_csspace),k19_csspace)) ) ).
fof(fc4_csspace,axiom,
( ~ v3_struct_0(k20_csspace)
& v3_rlvect_1(k20_csspace)
& v4_rlvect_1(k20_csspace)
& v5_rlvect_1(k20_csspace)
& v6_rlvect_1(k20_csspace)
& v2_clvect_1(k20_csspace) ) ).
fof(d1_csspace,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( A = k1_csspace
<=> ! [B] :
( r2_hidden(B,A)
<=> ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k2_numbers)
& m2_relset_1(B,k5_numbers,k2_numbers) ) ) ) ) ).
fof(d2_csspace,axiom,
! [A] :
( r2_hidden(A,k1_csspace)
=> k2_csspace(A) = A ) ).
fof(d3_csspace,axiom,
! [A] :
( r2_hidden(A,k2_numbers)
=> k3_csspace(A) = A ) ).
fof(t1_csspace,axiom,
? [A] :
( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k1_csspace,k1_csspace),k1_csspace)
& m2_relset_1(A,k2_zfmisc_1(k1_csspace,k1_csspace),k1_csspace)
& ! [B] :
( m1_subset_1(B,k1_csspace)
=> ! [C] :
( m1_subset_1(C,k1_csspace)
=> k2_binop_1(k1_csspace,k1_csspace,k1_csspace,A,B,C) = k2_comseq_1(k5_numbers,k2_csspace(B),k2_csspace(C)) ) )
& v1_binop_1(A,k1_csspace)
& v2_binop_1(A,k1_csspace) ) ).
fof(t2_csspace,axiom,
? [A] :
( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k2_numbers,k1_csspace),k1_csspace)
& m2_relset_1(A,k2_zfmisc_1(k2_numbers,k1_csspace),k1_csspace)
& ! [B,C] :
( ( r2_hidden(B,k2_numbers)
& r2_hidden(C,k1_csspace) )
=> k1_funct_1(A,k4_tarski(B,C)) = k4_comseq_1(k5_numbers,k2_csspace(C),k3_csspace(B)) ) ) ).
fof(d4_csspace,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k1_csspace,k1_csspace),k1_csspace)
& m2_relset_1(A,k2_zfmisc_1(k1_csspace,k1_csspace),k1_csspace) )
=> ( A = k4_csspace
<=> ! [B] :
( m1_subset_1(B,k1_csspace)
=> ! [C] :
( m1_subset_1(C,k1_csspace)
=> k2_binop_1(k1_csspace,k1_csspace,k1_csspace,A,B,C) = k2_comseq_1(k5_numbers,k2_csspace(B),k2_csspace(C)) ) ) ) ) ).
fof(d5_csspace,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k2_numbers,k1_csspace),k1_csspace)
& m2_relset_1(A,k2_zfmisc_1(k2_numbers,k1_csspace),k1_csspace) )
=> ( A = k5_csspace
<=> ! [B,C] :
( ( r2_hidden(B,k2_numbers)
& r2_hidden(C,k1_csspace) )
=> k1_funct_1(A,k4_tarski(B,C)) = k4_comseq_1(k5_numbers,k2_csspace(C),k3_csspace(B)) ) ) ) ).
fof(d6_csspace,axiom,
! [A] :
( m1_subset_1(A,k1_csspace)
=> ( A = k6_csspace
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_comseq_1(k2_csspace(A),B) = k5_complex1 ) ) ) ).
fof(t3_csspace,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> k2_csspace(A) = A ) ).
fof(t4_csspace,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace)))
=> k2_rlvect_1(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace),A,B) = k2_comseq_1(k5_numbers,k2_csspace(A),k2_csspace(B)) ) ) ).
fof(t5_csspace,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace)))
=> k1_clvect_1(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace),B,A) = k4_comseq_1(k5_numbers,k2_csspace(B),A) ) ) ).
fof(t6_csspace,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace)))
=> k4_rlvect_1(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace),k4_rlvect_1(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace),A,B),C) = k4_rlvect_1(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace),A,k4_rlvect_1(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace),B,C)) ) ) ) ).
fof(t7_csspace,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace)))
=> k4_rlvect_1(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace),A,k1_rlvect_1(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace))) = A ) ).
fof(t8_csspace,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace)))
=> ? [B] :
( m1_subset_1(B,u1_struct_0(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace)))
& k4_rlvect_1(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace),A,B) = k1_rlvect_1(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace)) ) ) ).
fof(t9_csspace,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace)))
=> k1_clvect_1(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace),k4_rlvect_1(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace),B,C),A) = k4_rlvect_1(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace),k1_clvect_1(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace),B,A),k1_clvect_1(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace),C,A)) ) ) ) ).
fof(t10_csspace,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace)))
=> k1_clvect_1(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace),C,k8_complex1(A,B)) = k4_rlvect_1(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace),k1_clvect_1(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace),C,A),k1_clvect_1(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace),C,B)) ) ) ) ).
fof(t11_csspace,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace)))
=> k1_clvect_1(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace),C,k9_complex1(A,B)) = k1_clvect_1(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace),k1_clvect_1(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace),C,B),A) ) ) ) ).
fof(t12_csspace,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace)))
=> k1_clvect_1(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace),A,k6_complex1) = A ) ).
fof(d7_csspace,axiom,
k7_csspace = g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace) ).
fof(d8_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_clvect_1(B,A)
=> ( v1_xboole_0(B)
| k8_csspace(A,B) = k1_realset1(u1_rlvect_1(A),B) ) ) ) ) ).
fof(d9_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_clvect_1(B,A)
=> ( v1_xboole_0(B)
| k9_csspace(A,B) = k7_relat_1(u1_clvect_1(A),k2_zfmisc_1(k2_numbers,B)) ) ) ) ) ).
fof(d10_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_clvect_1(B,A)
=> ( v1_xboole_0(B)
| k10_csspace(A,B) = k1_rlvect_1(A) ) ) ) ) ).
fof(t13_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_clvect_1(B,A)
=> ( v1_xboole_0(B)
| m1_clvect_1(g1_clvect_1(B,k10_csspace(A,B),k8_csspace(A,B),k9_csspace(A,B)),A) ) ) ) ) ).
fof(d11_csspace,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k7_csspace)))
=> ( A = k11_csspace
<=> ( ~ v1_xboole_0(A)
& ! [B] :
( r2_hidden(B,A)
<=> ( r2_hidden(B,k1_csspace)
& v1_series_1(k11_seq_1(k9_comseq_1(k5_numbers,k2_csspace(B)),k9_comseq_1(k5_numbers,k2_csspace(B)))) ) ) ) ) ) ).
fof(t14_csspace,axiom,
( v3_clvect_1(k11_csspace,k7_csspace)
& ~ v1_xboole_0(k11_csspace) ) ).
fof(t15_csspace,axiom,
m1_clvect_1(g1_clvect_1(k11_csspace,k10_csspace(k7_csspace,k11_csspace),k8_csspace(k7_csspace,k11_csspace),k9_csspace(k7_csspace,k11_csspace)),k7_csspace) ).
fof(t16_csspace,axiom,
( ~ v3_struct_0(g1_clvect_1(k11_csspace,k10_csspace(k7_csspace,k11_csspace),k8_csspace(k7_csspace,k11_csspace),k9_csspace(k7_csspace,k11_csspace)))
& v3_rlvect_1(g1_clvect_1(k11_csspace,k10_csspace(k7_csspace,k11_csspace),k8_csspace(k7_csspace,k11_csspace),k9_csspace(k7_csspace,k11_csspace)))
& v4_rlvect_1(g1_clvect_1(k11_csspace,k10_csspace(k7_csspace,k11_csspace),k8_csspace(k7_csspace,k11_csspace),k9_csspace(k7_csspace,k11_csspace)))
& v5_rlvect_1(g1_clvect_1(k11_csspace,k10_csspace(k7_csspace,k11_csspace),k8_csspace(k7_csspace,k11_csspace),k9_csspace(k7_csspace,k11_csspace)))
& v6_rlvect_1(g1_clvect_1(k11_csspace,k10_csspace(k7_csspace,k11_csspace),k8_csspace(k7_csspace,k11_csspace),k9_csspace(k7_csspace,k11_csspace)))
& v2_clvect_1(g1_clvect_1(k11_csspace,k10_csspace(k7_csspace,k11_csspace),k8_csspace(k7_csspace,k11_csspace),k9_csspace(k7_csspace,k11_csspace)))
& l1_clvect_1(g1_clvect_1(k11_csspace,k10_csspace(k7_csspace,k11_csspace),k8_csspace(k7_csspace,k11_csspace),k9_csspace(k7_csspace,k11_csspace))) ) ).
fof(t17_csspace,axiom,
( u1_struct_0(k7_csspace) = k1_csspace
& ! [A] :
( m1_subset_1(A,u1_struct_0(k7_csspace))
<=> ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(k7_csspace))
<=> ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(k7_csspace))
=> A = k2_csspace(A) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(k7_csspace))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k7_csspace))
=> k4_rlvect_1(k7_csspace,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(k7_csspace))
=> k1_clvect_1(k7_csspace,B,A) = k4_comseq_1(k5_numbers,k2_csspace(B),A) ) ) ) ).
fof(d12_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k12_csspace(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_numbers,u1_csspace(A),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C)) ) ) ) ).
fof(d13_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_csspace(A) )
=> ( v2_csspace(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k2_numbers)
=> ( ( k12_csspace(A,B,B) = np__0
=> B = k1_rlvect_1(A) )
& ( B = k1_rlvect_1(A)
=> k12_csspace(A,B,B) = np__0 )
& r1_xreal_0(np__0,k3_complex1(k12_csspace(A,B,B)))
& np__0 = k4_complex1(k12_csspace(A,B,B))
& k12_csspace(A,B,C) = k15_complex1(k12_csspace(A,C,B))
& k12_csspace(A,k2_rlvect_1(A,B,C),D) = k8_complex1(k12_csspace(A,B,D),k12_csspace(A,C,D))
& k12_csspace(A,k1_clvect_1(A,B,E),C) = k9_complex1(E,k12_csspace(A,B,C)) ) ) ) ) ) ) ) ).
fof(t18_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> k12_csspace(A,k1_rlvect_1(A),k1_rlvect_1(A)) = np__0 ) ).
fof(t19_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k12_csspace(A,B,k4_rlvect_1(A,C,D)) = k8_complex1(k12_csspace(A,B,C),k12_csspace(A,B,D)) ) ) ) ) ).
fof(t20_csspace,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [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)
& v2_csspace(B)
& l1_csspace(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> k12_csspace(B,C,k1_clvect_1(B,D,A)) = k9_complex1(k15_complex1(A),k12_csspace(B,C,D)) ) ) ) ) ).
fof(t21_csspace,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [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)
& v2_csspace(B)
& l1_csspace(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> k12_csspace(B,k1_clvect_1(B,C,A),D) = k12_csspace(B,C,k1_clvect_1(B,D,k15_complex1(A))) ) ) ) ) ).
fof(t22_csspace,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v2_clvect_1(C)
& v2_csspace(C)
& l1_csspace(C) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> k12_csspace(C,k4_rlvect_1(C,k1_clvect_1(C,D,A),k1_clvect_1(C,E,B)),F) = k8_complex1(k9_complex1(A,k12_csspace(C,D,F)),k9_complex1(B,k12_csspace(C,E,F))) ) ) ) ) ) ) ).
fof(t23_csspace,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v2_clvect_1(C)
& v2_csspace(C)
& l1_csspace(C) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> k12_csspace(C,D,k4_rlvect_1(C,k1_clvect_1(C,E,A),k1_clvect_1(C,F,B))) = k8_complex1(k9_complex1(k15_complex1(A),k12_csspace(C,D,E)),k9_complex1(k15_complex1(B),k12_csspace(C,D,F))) ) ) ) ) ) ) ).
fof(t24_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k12_csspace(A,k5_rlvect_1(A,B),C) = k12_csspace(A,B,k5_rlvect_1(A,C)) ) ) ) ).
fof(t25_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k12_csspace(A,k5_rlvect_1(A,B),C) = k10_complex1(k12_csspace(A,B,C)) ) ) ) ).
fof(t26_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k12_csspace(A,B,k5_rlvect_1(A,C)) = k10_complex1(k12_csspace(A,B,C)) ) ) ) ).
fof(t27_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k12_csspace(A,k5_rlvect_1(A,B),k5_rlvect_1(A,C)) = k12_csspace(A,B,C) ) ) ) ).
fof(t28_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k12_csspace(A,k6_rlvect_1(A,B,C),D) = k11_complex1(k12_csspace(A,B,D),k12_csspace(A,C,D)) ) ) ) ) ).
fof(t29_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k12_csspace(A,B,k6_rlvect_1(A,C,D)) = k11_complex1(k12_csspace(A,B,C),k12_csspace(A,B,D)) ) ) ) ) ).
fof(t30_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k12_csspace(A,k6_rlvect_1(A,B,C),k6_rlvect_1(A,D,E)) = k8_complex1(k11_complex1(k11_complex1(k12_csspace(A,B,D),k12_csspace(A,B,E)),k12_csspace(A,C,D)),k12_csspace(A,C,E)) ) ) ) ) ) ).
fof(t31_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k12_csspace(A,k1_rlvect_1(A),B) = np__0 ) ) ).
fof(t32_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k12_csspace(A,B,k1_rlvect_1(A)) = np__0 ) ) ).
fof(t33_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k12_csspace(A,k4_rlvect_1(A,B,C),k4_rlvect_1(A,B,C)) = k8_complex1(k8_complex1(k8_complex1(k12_csspace(A,B,B),k12_csspace(A,B,C)),k12_csspace(A,C,B)),k12_csspace(A,C,C)) ) ) ) ).
fof(t34_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k12_csspace(A,k4_rlvect_1(A,B,C),k6_rlvect_1(A,B,C)) = k11_complex1(k8_complex1(k11_complex1(k12_csspace(A,B,B),k12_csspace(A,B,C)),k12_csspace(A,C,B)),k12_csspace(A,C,C)) ) ) ) ).
fof(t35_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k12_csspace(A,k6_rlvect_1(A,B,C),k6_rlvect_1(A,B,C)) = k8_complex1(k11_complex1(k11_complex1(k12_csspace(A,B,B),k12_csspace(A,B,C)),k12_csspace(A,C,B)),k12_csspace(A,C,C)) ) ) ) ).
fof(t36_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k17_complex1(k12_csspace(A,B,B)) = k3_complex1(k12_csspace(A,B,B)) ) ) ).
fof(t37_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_xreal_0(k17_complex1(k12_csspace(A,B,C)),k4_real_1(k9_square_1(k17_complex1(k12_csspace(A,B,B))),k9_square_1(k17_complex1(k12_csspace(A,C,C))))) ) ) ) ).
fof(d14_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_csspace(A,B,C)
<=> k12_csspace(A,B,C) = np__0 ) ) ) ) ).
fof(t38_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_csspace(A,B,C)
=> r1_csspace(A,B,k5_rlvect_1(A,C)) ) ) ) ) ).
fof(t39_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_csspace(A,B,C)
=> r1_csspace(A,k5_rlvect_1(A,B),C) ) ) ) ) ).
fof(t40_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_csspace(A,B,C)
=> r1_csspace(A,k5_rlvect_1(A,B),k5_rlvect_1(A,C)) ) ) ) ) ).
fof(t41_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r1_csspace(A,B,k1_rlvect_1(A)) ) ) ).
fof(t42_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_csspace(A,B,C)
=> k12_csspace(A,k4_rlvect_1(A,B,C),k4_rlvect_1(A,B,C)) = k8_complex1(k12_csspace(A,B,B),k12_csspace(A,C,C)) ) ) ) ) ).
fof(t43_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_csspace(A,B,C)
=> k12_csspace(A,k6_rlvect_1(A,B,C),k6_rlvect_1(A,B,C)) = k8_complex1(k12_csspace(A,B,B),k12_csspace(A,C,C)) ) ) ) ) ).
fof(d15_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k13_csspace(A,B) = k9_square_1(k17_complex1(k12_csspace(A,B,B))) ) ) ).
fof(t44_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( k13_csspace(A,B) = np__0
<=> B = k1_rlvect_1(A) ) ) ) ).
fof(t45_csspace,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [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)
& v2_csspace(B)
& l1_csspace(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> k13_csspace(B,k1_clvect_1(B,C,A)) = k4_real_1(k17_complex1(A),k13_csspace(B,C)) ) ) ) ).
fof(t46_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r1_xreal_0(np__0,k13_csspace(A,B)) ) ) ).
fof(t47_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_xreal_0(k17_complex1(k12_csspace(A,B,C)),k4_real_1(k13_csspace(A,B),k13_csspace(A,C))) ) ) ) ).
fof(t48_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_xreal_0(k13_csspace(A,k4_rlvect_1(A,B,C)),k3_real_1(k13_csspace(A,B),k13_csspace(A,C))) ) ) ) ).
fof(t49_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k13_csspace(A,k5_rlvect_1(A,B)) = k13_csspace(A,B) ) ) ).
fof(t50_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_xreal_0(k5_real_1(k13_csspace(A,B),k13_csspace(A,C)),k13_csspace(A,k6_rlvect_1(A,B,C))) ) ) ) ).
fof(t51_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_xreal_0(k18_complex1(k5_real_1(k13_csspace(A,B),k13_csspace(A,C))),k13_csspace(A,k6_rlvect_1(A,B,C))) ) ) ) ).
fof(d16_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k14_csspace(A,B,C) = k13_csspace(A,k6_rlvect_1(A,B,C)) ) ) ) ).
fof(t52_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k14_csspace(A,B,C) = k14_csspace(A,C,B) ) ) ) ).
fof(t53_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k15_csspace(A,B,B) = np__0 ) ) ).
fof(t54_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r1_xreal_0(k15_csspace(A,B,C),k3_real_1(k15_csspace(A,B,D),k15_csspace(A,D,C))) ) ) ) ) ).
fof(t55_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ~ ( B != C
& k15_csspace(A,B,C) = np__0 )
& ~ ( k15_csspace(A,B,C) != np__0
& B = C ) ) ) ) ) ).
fof(t56_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_xreal_0(np__0,k15_csspace(A,B,C)) ) ) ) ).
fof(t57_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ~ ( B != C
& r1_xreal_0(k15_csspace(A,B,C),np__0) )
& ~ ( ~ r1_xreal_0(k15_csspace(A,B,C),np__0)
& B = C ) ) ) ) ) ).
fof(t58_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k15_csspace(A,B,C) = k9_square_1(k17_complex1(k12_csspace(A,k6_rlvect_1(A,B,C),k6_rlvect_1(A,B,C)))) ) ) ) ).
fof(t59_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> r1_xreal_0(k15_csspace(A,k4_rlvect_1(A,B,C),k4_rlvect_1(A,D,E)),k3_real_1(k15_csspace(A,B,D),k15_csspace(A,C,E))) ) ) ) ) ) ).
fof(t60_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> r1_xreal_0(k15_csspace(A,k6_rlvect_1(A,B,C),k6_rlvect_1(A,D,E)),k3_real_1(k15_csspace(A,B,D),k15_csspace(A,C,E))) ) ) ) ) ) ).
fof(t61_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k15_csspace(A,k6_rlvect_1(A,B,C),k6_rlvect_1(A,D,C)) = k15_csspace(A,B,D) ) ) ) ) ).
fof(t62_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r1_xreal_0(k15_csspace(A,k6_rlvect_1(A,B,C),k6_rlvect_1(A,D,C)),k3_real_1(k15_csspace(A,C,B),k15_csspace(A,C,D))) ) ) ) ) ).
fof(d17_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( C = k16_csspace(A,B)
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_normsp_1(A,C,D) = k5_rlvect_1(A,k2_normsp_1(A,B,D)) ) ) ) ) ) ).
fof(d18_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ( D = k17_csspace(A,B,C)
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k2_normsp_1(A,D,E) = k4_rlvect_1(A,k2_normsp_1(A,B,E),C) ) ) ) ) ) ) ).
fof(t63_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> k6_clvect_1(A,B,C) = k6_clvect_1(A,C,B) ) ) ) ).
fof(t64_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> k18_csspace(A,B,k18_csspace(A,C,D)) = k18_csspace(A,k18_csspace(A,B,C),D) ) ) ) ) ).
fof(t65_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ( ( v5_seqm_3(B)
& v5_seqm_3(C)
& D = k18_csspace(A,B,C) )
=> v5_seqm_3(D) ) ) ) ) ) ).
fof(t66_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ( ( v5_seqm_3(B)
& v5_seqm_3(C)
& D = k7_clvect_1(A,B,C) )
=> v5_seqm_3(D) ) ) ) ) ) ).
fof(t67_csspace,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [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)
& v2_csspace(B)
& l1_csspace(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(B))
& m2_relset_1(C,k5_numbers,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(B))
& m2_relset_1(D,k5_numbers,u1_struct_0(B)) )
=> ( ( v5_seqm_3(C)
& D = k9_clvect_1(B,C,A) )
=> v5_seqm_3(D) ) ) ) ) ) ).
fof(t68_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v5_seqm_3(B)
<=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k2_normsp_1(A,B,C) = k2_normsp_1(A,B,k1_nat_1(C,np__1)) ) ) ) ) ).
fof(t69_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v5_seqm_3(B)
<=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_normsp_1(A,B,C) = k2_normsp_1(A,B,k1_nat_1(C,D)) ) ) ) ) ) ).
fof(t70_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v5_seqm_3(B)
<=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_normsp_1(A,B,C) = k2_normsp_1(A,B,D) ) ) ) ) ) ).
fof(t71_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> k7_clvect_1(A,B,C) = k18_csspace(A,B,k16_csspace(A,C)) ) ) ) ).
fof(t72_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> B = k17_csspace(A,B,k1_rlvect_1(A)) ) ) ).
fof(t73_csspace,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [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)
& v2_csspace(B)
& l1_csspace(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(B))
& m2_relset_1(C,k5_numbers,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(B))
& m2_relset_1(D,k5_numbers,u1_struct_0(B)) )
=> k9_clvect_1(B,k18_csspace(B,C,D),A) = k18_csspace(B,k9_clvect_1(B,C,A),k9_clvect_1(B,D,A)) ) ) ) ) ).
fof(t74_csspace,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v2_clvect_1(C)
& v2_csspace(C)
& l1_csspace(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(C))
& m2_relset_1(D,k5_numbers,u1_struct_0(C)) )
=> k9_clvect_1(C,D,k8_complex1(A,B)) = k18_csspace(C,k9_clvect_1(C,D,A),k9_clvect_1(C,D,B)) ) ) ) ) ).
fof(t75_csspace,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v2_clvect_1(C)
& v2_csspace(C)
& l1_csspace(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(C))
& m2_relset_1(D,k5_numbers,u1_struct_0(C)) )
=> k9_clvect_1(C,D,k9_complex1(A,B)) = k9_clvect_1(C,k9_clvect_1(C,D,B),A) ) ) ) ) ).
fof(t76_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> k9_clvect_1(A,B,k6_complex1) = B ) ) ).
fof(t77_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> k9_clvect_1(A,B,k10_complex1(k6_complex1)) = k16_csspace(A,B) ) ) ).
fof(t78_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> k8_clvect_1(A,C,B) = k17_csspace(A,C,k5_rlvect_1(A,B)) ) ) ) ).
fof(t79_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> k7_clvect_1(A,B,C) = k16_csspace(A,k7_clvect_1(A,C,B)) ) ) ) ).
fof(t80_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> B = k8_clvect_1(A,B,k1_rlvect_1(A)) ) ) ).
fof(t81_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> B = k16_csspace(A,k16_csspace(A,B)) ) ) ).
fof(t82_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> k7_clvect_1(A,B,k18_csspace(A,C,D)) = k7_clvect_1(A,k7_clvect_1(A,B,C),D) ) ) ) ) ).
fof(t83_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> k7_clvect_1(A,k18_csspace(A,B,C),D) = k18_csspace(A,B,k7_clvect_1(A,C,D)) ) ) ) ) ).
fof(t84_csspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> k7_clvect_1(A,B,k7_clvect_1(A,C,D)) = k18_csspace(A,k7_clvect_1(A,B,C),D) ) ) ) ) ).
fof(t85_csspace,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [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)
& v2_csspace(B)
& l1_csspace(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(B))
& m2_relset_1(C,k5_numbers,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(B))
& m2_relset_1(D,k5_numbers,u1_struct_0(B)) )
=> k9_clvect_1(B,k7_clvect_1(B,C,D),A) = k7_clvect_1(B,k9_clvect_1(B,C,A),k9_clvect_1(B,D,A)) ) ) ) ) ).
fof(t86_csspace,axiom,
? [A] :
( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k11_csspace,k11_csspace),k2_numbers)
& m2_relset_1(A,k2_zfmisc_1(k11_csspace,k11_csspace),k2_numbers)
& ! [B,C] :
( ( r2_hidden(B,k11_csspace)
& r2_hidden(C,k11_csspace) )
=> k1_funct_1(A,k4_tarski(B,C)) = k8_comseq_3(k3_comseq_1(k5_numbers,k2_csspace(B),k1_comseq_2(k5_numbers,k2_csspace(C)))) ) ) ).
fof(d19_csspace,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k11_csspace,k11_csspace),k2_numbers)
& m2_relset_1(A,k2_zfmisc_1(k11_csspace,k11_csspace),k2_numbers) )
=> ( A = k19_csspace
<=> ! [B,C] :
( ( r2_hidden(B,k11_csspace)
& r2_hidden(C,k11_csspace) )
=> k1_funct_1(A,k4_tarski(B,C)) = k8_comseq_3(k3_comseq_1(k5_numbers,k2_csspace(B),k1_comseq_2(k5_numbers,k2_csspace(C)))) ) ) ) ).
fof(d20_csspace,axiom,
k20_csspace = g1_csspace(k11_csspace,k10_csspace(k7_csspace,k11_csspace),k8_csspace(k7_csspace,k11_csspace),k9_csspace(k7_csspace,k11_csspace),k19_csspace) ).
fof(t87_csspace,axiom,
! [A] :
( l1_csspace(A)
=> ( ( ~ v3_struct_0(g1_clvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u1_clvect_1(A)))
& v3_rlvect_1(g1_clvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u1_clvect_1(A)))
& v4_rlvect_1(g1_clvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u1_clvect_1(A)))
& v5_rlvect_1(g1_clvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u1_clvect_1(A)))
& v6_rlvect_1(g1_clvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u1_clvect_1(A)))
& v2_clvect_1(g1_clvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u1_clvect_1(A)))
& l1_clvect_1(g1_clvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u1_clvect_1(A))) )
=> ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A) ) ) ) ).
fof(t88_csspace,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k2_numbers)
& m2_relset_1(A,k5_numbers,k2_numbers) )
=> ( ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_comseq_1(A,B) = k5_complex1 )
=> ( v1_comseq_3(A)
& k8_comseq_3(A) = k5_complex1 ) ) ) ).
fof(dt_l1_csspace,axiom,
! [A] :
( l1_csspace(A)
=> l1_clvect_1(A) ) ).
fof(existence_l1_csspace,axiom,
? [A] : l1_csspace(A) ).
fof(abstractness_v1_csspace,axiom,
! [A] :
( l1_csspace(A)
=> ( v1_csspace(A)
=> A = g1_csspace(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u1_clvect_1(A),u1_csspace(A)) ) ) ).
fof(symmetry_r1_csspace,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( r1_csspace(A,B,C)
=> r1_csspace(A,C,B) ) ) ).
fof(dt_k1_csspace,axiom,
~ v1_xboole_0(k1_csspace) ).
fof(dt_k2_csspace,axiom,
! [A] :
( v1_funct_1(k2_csspace(A))
& v1_funct_2(k2_csspace(A),k5_numbers,k2_numbers)
& m2_relset_1(k2_csspace(A),k5_numbers,k2_numbers) ) ).
fof(dt_k3_csspace,axiom,
! [A] : m1_subset_1(k3_csspace(A),k2_numbers) ).
fof(dt_k4_csspace,axiom,
( v1_funct_1(k4_csspace)
& v1_funct_2(k4_csspace,k2_zfmisc_1(k1_csspace,k1_csspace),k1_csspace)
& m2_relset_1(k4_csspace,k2_zfmisc_1(k1_csspace,k1_csspace),k1_csspace) ) ).
fof(dt_k5_csspace,axiom,
( v1_funct_1(k5_csspace)
& v1_funct_2(k5_csspace,k2_zfmisc_1(k2_numbers,k1_csspace),k1_csspace)
& m2_relset_1(k5_csspace,k2_zfmisc_1(k2_numbers,k1_csspace),k1_csspace) ) ).
fof(dt_k6_csspace,axiom,
m1_subset_1(k6_csspace,k1_csspace) ).
fof(dt_k7_csspace,axiom,
( ~ v3_struct_0(k7_csspace)
& v3_rlvect_1(k7_csspace)
& v4_rlvect_1(k7_csspace)
& v5_rlvect_1(k7_csspace)
& v6_rlvect_1(k7_csspace)
& v2_clvect_1(k7_csspace)
& l1_clvect_1(k7_csspace) ) ).
fof(dt_k8_csspace,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_funct_1(k8_csspace(A,B))
& v1_funct_2(k8_csspace(A,B),k2_zfmisc_1(B,B),B)
& m2_relset_1(k8_csspace(A,B),k2_zfmisc_1(B,B),B) ) ) ).
fof(dt_k9_csspace,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_funct_1(k9_csspace(A,B))
& v1_funct_2(k9_csspace(A,B),k2_zfmisc_1(k2_numbers,B),B)
& m2_relset_1(k9_csspace(A,B),k2_zfmisc_1(k2_numbers,B),B) ) ) ).
fof(dt_k10_csspace,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& l1_clvect_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k10_csspace(A,B),B) ) ).
fof(dt_k11_csspace,axiom,
m1_subset_1(k11_csspace,k1_zfmisc_1(u1_struct_0(k7_csspace))) ).
fof(dt_k12_csspace,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_csspace(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k12_csspace(A,B,C),k2_numbers) ) ).
fof(dt_k13_csspace,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k13_csspace(A,B),k1_numbers) ) ).
fof(dt_k14_csspace,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k14_csspace(A,B,C),k1_numbers) ) ).
fof(dt_k15_csspace,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k15_csspace(A,B,C),k1_numbers) ) ).
fof(commutativity_k15_csspace,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> k15_csspace(A,B,C) = k15_csspace(A,C,B) ) ).
fof(redefinition_k15_csspace,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> k15_csspace(A,B,C) = k14_csspace(A,B,C) ) ).
fof(dt_k16_csspace,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m1_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v1_funct_1(k16_csspace(A,B))
& v1_funct_2(k16_csspace(A,B),k5_numbers,u1_struct_0(A))
& m2_relset_1(k16_csspace(A,B),k5_numbers,u1_struct_0(A)) ) ) ).
fof(dt_k17_csspace,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m1_relset_1(B,k5_numbers,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( v1_funct_1(k17_csspace(A,B,C))
& v1_funct_2(k17_csspace(A,B,C),k5_numbers,u1_struct_0(A))
& m2_relset_1(k17_csspace(A,B,C),k5_numbers,u1_struct_0(A)) ) ) ).
fof(dt_k18_csspace,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m1_relset_1(B,k5_numbers,u1_struct_0(A))
& v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m1_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v1_funct_1(k18_csspace(A,B,C))
& v1_funct_2(k18_csspace(A,B,C),k5_numbers,u1_struct_0(A))
& m2_relset_1(k18_csspace(A,B,C),k5_numbers,u1_struct_0(A)) ) ) ).
fof(commutativity_k18_csspace,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m1_relset_1(B,k5_numbers,u1_struct_0(A))
& v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m1_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> k18_csspace(A,B,C) = k18_csspace(A,C,B) ) ).
fof(redefinition_k18_csspace,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m1_relset_1(B,k5_numbers,u1_struct_0(A))
& v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m1_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> k18_csspace(A,B,C) = k6_clvect_1(A,B,C) ) ).
fof(dt_k19_csspace,axiom,
( v1_funct_1(k19_csspace)
& v1_funct_2(k19_csspace,k2_zfmisc_1(k11_csspace,k11_csspace),k2_numbers)
& m2_relset_1(k19_csspace,k2_zfmisc_1(k11_csspace,k11_csspace),k2_numbers) ) ).
fof(dt_k20_csspace,axiom,
( ~ v3_struct_0(k20_csspace)
& l1_csspace(k20_csspace) ) ).
fof(dt_u1_csspace,axiom,
! [A] :
( l1_csspace(A)
=> ( v1_funct_1(u1_csspace(A))
& v1_funct_2(u1_csspace(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_numbers)
& m2_relset_1(u1_csspace(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_numbers) ) ) ).
fof(dt_g1_csspace,axiom,
! [A,B,C,D,E] :
( ( m1_subset_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(k2_numbers,A),A)
& m1_relset_1(D,k2_zfmisc_1(k2_numbers,A),A)
& v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(A,A),k2_numbers)
& m1_relset_1(E,k2_zfmisc_1(A,A),k2_numbers) )
=> ( v1_csspace(g1_csspace(A,B,C,D,E))
& l1_csspace(g1_csspace(A,B,C,D,E)) ) ) ).
fof(free_g1_csspace,axiom,
! [A,B,C,D,E] :
( ( m1_subset_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(k2_numbers,A),A)
& m1_relset_1(D,k2_zfmisc_1(k2_numbers,A),A)
& v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(A,A),k2_numbers)
& m1_relset_1(E,k2_zfmisc_1(A,A),k2_numbers) )
=> ! [F,G,H,I,J] :
( g1_csspace(A,B,C,D,E) = g1_csspace(F,G,H,I,J)
=> ( A = F
& B = G
& C = H
& D = I
& E = J ) ) ) ).
%------------------------------------------------------------------------------