SET007 Axioms: SET007+770.ax
%------------------------------------------------------------------------------
% File : SET007+770 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Real Linear Space of Real 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 : rsspace [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 51 ( 8 unt; 0 def)
% Number of atoms : 261 ( 38 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 228 ( 18 ~; 4 |; 131 &)
% ( 9 <=>; 66 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 1 prp; 0-3 aty)
% Number of functors : 41 ( 41 usr; 12 con; 0-6 aty)
% Number of variables : 75 ( 71 !; 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_rsspace,axiom,
( ~ v3_struct_0(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace))
& v2_rlvect_1(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace))
& v3_rlvect_1(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace)) ) ).
fof(fc2_rsspace,axiom,
( ~ v1_xboole_0(k11_rsspace)
& v1_rlsub_1(k11_rsspace,k7_rsspace) ) ).
fof(fc3_rsspace,axiom,
( ~ v3_struct_0(g1_bhsp_1(k11_rsspace,k10_rsspace(k7_rsspace,k11_rsspace),k8_rsspace(k7_rsspace,k11_rsspace),k9_rsspace(k7_rsspace,k11_rsspace),k12_rsspace))
& v1_bhsp_1(g1_bhsp_1(k11_rsspace,k10_rsspace(k7_rsspace,k11_rsspace),k8_rsspace(k7_rsspace,k11_rsspace),k9_rsspace(k7_rsspace,k11_rsspace),k12_rsspace)) ) ).
fof(fc4_rsspace,axiom,
( ~ v3_struct_0(k13_rsspace)
& v3_rlvect_1(k13_rsspace)
& v4_rlvect_1(k13_rsspace)
& v5_rlvect_1(k13_rsspace)
& v6_rlvect_1(k13_rsspace)
& v7_rlvect_1(k13_rsspace) ) ).
fof(d1_rsspace,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( A = k1_rsspace
<=> ! [B] :
( r2_hidden(B,A)
<=> ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& m2_relset_1(B,k5_numbers,k1_numbers) ) ) ) ) ).
fof(d2_rsspace,axiom,
! [A] :
( r2_hidden(A,k1_rsspace)
=> k2_rsspace(A) = A ) ).
fof(d3_rsspace,axiom,
! [A] :
( r2_hidden(A,k1_numbers)
=> k3_rsspace(A) = A ) ).
fof(t1_rsspace,axiom,
? [A] :
( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k1_rsspace,k1_rsspace),k1_rsspace)
& m2_relset_1(A,k2_zfmisc_1(k1_rsspace,k1_rsspace),k1_rsspace)
& ! [B] :
( m1_subset_1(B,k1_rsspace)
=> ! [C] :
( m1_subset_1(C,k1_rsspace)
=> k2_binop_1(k1_rsspace,k1_rsspace,k1_rsspace,A,B,C) = k9_seq_1(k2_rsspace(B),k2_rsspace(C)) ) )
& v1_binop_1(A,k1_rsspace)
& v2_binop_1(A,k1_rsspace) ) ).
fof(t2_rsspace,axiom,
? [A] :
( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_rsspace),k1_rsspace)
& m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_rsspace),k1_rsspace)
& ! [B,C] :
( ( r2_hidden(B,k1_numbers)
& r2_hidden(C,k1_rsspace) )
=> k1_funct_1(A,k4_tarski(B,C)) = k14_seq_1(k2_rsspace(C),k3_rsspace(B)) ) ) ).
fof(d4_rsspace,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k1_rsspace,k1_rsspace),k1_rsspace)
& m2_relset_1(A,k2_zfmisc_1(k1_rsspace,k1_rsspace),k1_rsspace) )
=> ( A = k4_rsspace
<=> ! [B] :
( m1_subset_1(B,k1_rsspace)
=> ! [C] :
( m1_subset_1(C,k1_rsspace)
=> k2_binop_1(k1_rsspace,k1_rsspace,k1_rsspace,A,B,C) = k9_seq_1(k2_rsspace(B),k2_rsspace(C)) ) ) ) ) ).
fof(d5_rsspace,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_rsspace),k1_rsspace)
& m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_rsspace),k1_rsspace) )
=> ( A = k5_rsspace
<=> ! [B,C] :
( ( r2_hidden(B,k1_numbers)
& r2_hidden(C,k1_rsspace) )
=> k1_funct_1(A,k4_tarski(B,C)) = k14_seq_1(k2_rsspace(C),k3_rsspace(B)) ) ) ) ).
fof(d6_rsspace,axiom,
! [A] :
( m1_subset_1(A,k1_rsspace)
=> ( A = k6_rsspace
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,k2_rsspace(A),B) = np__0 ) ) ) ).
fof(t3_rsspace,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> k2_rsspace(A) = A ) ).
fof(t4_rsspace,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace)))
=> k2_rlvect_1(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace),A,B) = k9_seq_1(k2_rsspace(A),k2_rsspace(B)) ) ) ).
fof(t5_rsspace,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace)))
=> k3_rlvect_1(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace),B,A) = k14_seq_1(k2_rsspace(B),A) ) ) ).
fof(t6_rsspace,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace)))
=> k4_rlvect_1(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace),k4_rlvect_1(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace),A,B),C) = k4_rlvect_1(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace),A,k4_rlvect_1(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace),B,C)) ) ) ) ).
fof(t7_rsspace,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace)))
=> k4_rlvect_1(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace),A,k1_rlvect_1(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace))) = A ) ).
fof(t8_rsspace,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace)))
=> ? [B] :
( m1_subset_1(B,u1_struct_0(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace)))
& k4_rlvect_1(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace),A,B) = k1_rlvect_1(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace)) ) ) ).
fof(t9_rsspace,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace)))
=> k3_rlvect_1(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace),k4_rlvect_1(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace),B,C),A) = k4_rlvect_1(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace),k3_rlvect_1(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace),B,A),k3_rlvect_1(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace),C,A)) ) ) ) ).
fof(t10_rsspace,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace)))
=> k3_rlvect_1(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace),C,k3_real_1(A,B)) = k4_rlvect_1(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace),k3_rlvect_1(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace),C,A),k3_rlvect_1(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace),C,B)) ) ) ) ).
fof(t11_rsspace,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace)))
=> k3_rlvect_1(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace),C,k4_real_1(A,B)) = k3_rlvect_1(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace),k3_rlvect_1(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace),C,B),A) ) ) ) ).
fof(t12_rsspace,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace)))
=> k3_rlvect_1(g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace),A,np__1) = A ) ).
fof(d7_rsspace,axiom,
k7_rsspace = g2_rlvect_1(k1_rsspace,k6_rsspace,k4_rsspace,k5_rsspace) ).
fof(d8_rsspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_rlsub_1(B,A)
=> ( v1_xboole_0(B)
| k8_rsspace(A,B) = k1_realset1(u1_rlvect_1(A),B) ) ) ) ) ).
fof(d9_rsspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_rlsub_1(B,A)
=> ( v1_xboole_0(B)
| k9_rsspace(A,B) = k2_partfun1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A),u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,B)) ) ) ) ) ).
fof(d10_rsspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_rlsub_1(B,A)
=> ( v1_xboole_0(B)
| k10_rsspace(A,B) = k1_rlvect_1(A) ) ) ) ) ).
fof(t13_rsspace,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_rlsub_1(B,A)
=> ( v1_xboole_0(B)
| m1_rlsub_1(g2_rlvect_1(B,k10_rsspace(A,B),k8_rsspace(A,B),k9_rsspace(A,B)),A) ) ) ) ) ).
fof(d11_rsspace,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k7_rsspace)))
=> ( A = k11_rsspace
<=> ! [B] :
( r2_hidden(B,A)
<=> ( r2_hidden(B,k1_rsspace)
& v1_series_1(k11_seq_1(k2_rsspace(B),k2_rsspace(B))) ) ) ) ) ).
fof(t14_rsspace,axiom,
$true ).
fof(t15_rsspace,axiom,
m1_rlsub_1(g2_rlvect_1(k11_rsspace,k10_rsspace(k7_rsspace,k11_rsspace),k8_rsspace(k7_rsspace,k11_rsspace),k9_rsspace(k7_rsspace,k11_rsspace)),k7_rsspace) ).
fof(t16_rsspace,axiom,
( ~ v3_struct_0(g2_rlvect_1(k11_rsspace,k10_rsspace(k7_rsspace,k11_rsspace),k8_rsspace(k7_rsspace,k11_rsspace),k9_rsspace(k7_rsspace,k11_rsspace)))
& v3_rlvect_1(g2_rlvect_1(k11_rsspace,k10_rsspace(k7_rsspace,k11_rsspace),k8_rsspace(k7_rsspace,k11_rsspace),k9_rsspace(k7_rsspace,k11_rsspace)))
& v4_rlvect_1(g2_rlvect_1(k11_rsspace,k10_rsspace(k7_rsspace,k11_rsspace),k8_rsspace(k7_rsspace,k11_rsspace),k9_rsspace(k7_rsspace,k11_rsspace)))
& v5_rlvect_1(g2_rlvect_1(k11_rsspace,k10_rsspace(k7_rsspace,k11_rsspace),k8_rsspace(k7_rsspace,k11_rsspace),k9_rsspace(k7_rsspace,k11_rsspace)))
& v6_rlvect_1(g2_rlvect_1(k11_rsspace,k10_rsspace(k7_rsspace,k11_rsspace),k8_rsspace(k7_rsspace,k11_rsspace),k9_rsspace(k7_rsspace,k11_rsspace)))
& v7_rlvect_1(g2_rlvect_1(k11_rsspace,k10_rsspace(k7_rsspace,k11_rsspace),k8_rsspace(k7_rsspace,k11_rsspace),k9_rsspace(k7_rsspace,k11_rsspace)))
& l2_rlvect_1(g2_rlvect_1(k11_rsspace,k10_rsspace(k7_rsspace,k11_rsspace),k8_rsspace(k7_rsspace,k11_rsspace),k9_rsspace(k7_rsspace,k11_rsspace))) ) ).
fof(t17_rsspace,axiom,
( u1_struct_0(k7_rsspace) = k1_rsspace
& ! [A] :
( m1_subset_1(A,u1_struct_0(k7_rsspace))
<=> ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(k7_rsspace))
=> A = k2_rsspace(A) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(k7_rsspace))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k7_rsspace))
=> k4_rlvect_1(k7_rsspace,A,B) = k9_seq_1(k2_rsspace(A),k2_rsspace(B)) ) )
& ! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k7_rsspace))
=> k3_rlvect_1(k7_rsspace,B,A) = k14_seq_1(k2_rsspace(B),A) ) ) ) ).
fof(t18_rsspace,axiom,
? [A] :
( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k11_rsspace,k11_rsspace),k1_numbers)
& m2_relset_1(A,k2_zfmisc_1(k11_rsspace,k11_rsspace),k1_numbers)
& ! [B,C] :
( ( r2_hidden(B,k11_rsspace)
& r2_hidden(C,k11_rsspace) )
=> k2_seq_1(k2_zfmisc_1(k11_rsspace,k11_rsspace),k1_numbers,A,k4_tarski(B,C)) = k2_series_1(k11_seq_1(k2_rsspace(B),k2_rsspace(C))) ) ) ).
fof(d12_rsspace,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k11_rsspace,k11_rsspace),k1_numbers)
& m2_relset_1(A,k2_zfmisc_1(k11_rsspace,k11_rsspace),k1_numbers) )
=> ( A = k12_rsspace
<=> ! [B,C] :
( ( r2_hidden(B,k11_rsspace)
& r2_hidden(C,k11_rsspace) )
=> k2_seq_1(k2_zfmisc_1(k11_rsspace,k11_rsspace),k1_numbers,A,k4_tarski(B,C)) = k2_series_1(k11_seq_1(k2_rsspace(B),k2_rsspace(C))) ) ) ) ).
fof(d13_rsspace,axiom,
k13_rsspace = g1_bhsp_1(k11_rsspace,k10_rsspace(k7_rsspace,k11_rsspace),k8_rsspace(k7_rsspace,k11_rsspace),k9_rsspace(k7_rsspace,k11_rsspace),k12_rsspace) ).
fof(t19_rsspace,axiom,
! [A] :
( l1_bhsp_1(A)
=> ( ( ~ v3_struct_0(g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A)))
& v3_rlvect_1(g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A)))
& v4_rlvect_1(g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A)))
& v5_rlvect_1(g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A)))
& v6_rlvect_1(g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A)))
& v7_rlvect_1(g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A)))
& l2_rlvect_1(g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A))) )
=> ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) ) ) ) ).
fof(t20_rsspace,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,A,B) = np__0 )
=> ( v1_series_1(A)
& k2_series_1(A) = np__0 ) ) ) ).
fof(t21_rsspace,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k1_numbers)
& m2_relset_1(A,k5_numbers,k1_numbers) )
=> ( ( ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r1_xreal_0(np__0,k2_seq_1(k5_numbers,k1_numbers,A,B)) )
& v1_series_1(A)
& k2_series_1(A) = np__0 )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,A,B) = np__0 ) ) ) ).
fof(dt_k1_rsspace,axiom,
~ v1_xboole_0(k1_rsspace) ).
fof(dt_k2_rsspace,axiom,
! [A] :
( v1_funct_1(k2_rsspace(A))
& v1_funct_2(k2_rsspace(A),k5_numbers,k1_numbers)
& m2_relset_1(k2_rsspace(A),k5_numbers,k1_numbers) ) ).
fof(dt_k3_rsspace,axiom,
! [A] : m1_subset_1(k3_rsspace(A),k1_numbers) ).
fof(dt_k4_rsspace,axiom,
( v1_funct_1(k4_rsspace)
& v1_funct_2(k4_rsspace,k2_zfmisc_1(k1_rsspace,k1_rsspace),k1_rsspace)
& m2_relset_1(k4_rsspace,k2_zfmisc_1(k1_rsspace,k1_rsspace),k1_rsspace) ) ).
fof(dt_k5_rsspace,axiom,
( v1_funct_1(k5_rsspace)
& v1_funct_2(k5_rsspace,k2_zfmisc_1(k1_numbers,k1_rsspace),k1_rsspace)
& m2_relset_1(k5_rsspace,k2_zfmisc_1(k1_numbers,k1_rsspace),k1_rsspace) ) ).
fof(dt_k6_rsspace,axiom,
m1_subset_1(k6_rsspace,k1_rsspace) ).
fof(dt_k7_rsspace,axiom,
( ~ v3_struct_0(k7_rsspace)
& v3_rlvect_1(k7_rsspace)
& v4_rlvect_1(k7_rsspace)
& v5_rlvect_1(k7_rsspace)
& v6_rlvect_1(k7_rsspace)
& v7_rlvect_1(k7_rsspace)
& l2_rlvect_1(k7_rsspace) ) ).
fof(dt_k8_rsspace,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_funct_1(k8_rsspace(A,B))
& v1_funct_2(k8_rsspace(A,B),k2_zfmisc_1(B,B),B)
& m2_relset_1(k8_rsspace(A,B),k2_zfmisc_1(B,B),B) ) ) ).
fof(dt_k9_rsspace,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_funct_1(k9_rsspace(A,B))
& v1_funct_2(k9_rsspace(A,B),k2_zfmisc_1(k1_numbers,B),B)
& m2_relset_1(k9_rsspace(A,B),k2_zfmisc_1(k1_numbers,B),B) ) ) ).
fof(dt_k10_rsspace,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k10_rsspace(A,B),B) ) ).
fof(dt_k11_rsspace,axiom,
m1_subset_1(k11_rsspace,k1_zfmisc_1(u1_struct_0(k7_rsspace))) ).
fof(dt_k12_rsspace,axiom,
( v1_funct_1(k12_rsspace)
& v1_funct_2(k12_rsspace,k2_zfmisc_1(k11_rsspace,k11_rsspace),k1_numbers)
& m2_relset_1(k12_rsspace,k2_zfmisc_1(k11_rsspace,k11_rsspace),k1_numbers) ) ).
fof(dt_k13_rsspace,axiom,
( ~ v3_struct_0(k13_rsspace)
& l1_bhsp_1(k13_rsspace) ) ).
%------------------------------------------------------------------------------