SET007 Axioms: SET007+767.ax
%------------------------------------------------------------------------------
% File : SET007+767 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On Some Properties of Real Hilbert Space. Part I
% 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 : bhsp_6 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 20 ( 0 unt; 0 def)
% Number of atoms : 396 ( 13 equ)
% Maximal formula atoms : 31 ( 19 avg)
% Number of connectives : 435 ( 59 ~; 0 |; 269 &)
% ( 8 <=>; 99 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 17 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 33 ( 32 usr; 0 prp; 1-3 aty)
% Number of functors : 27 ( 27 usr; 6 con; 0-5 aty)
% Number of variables : 86 ( 79 !; 7 ?)
% 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(d1_bhsp_6,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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ( ( v1_binop_1(u1_rlvect_1(A),u1_struct_0(A))
& v2_binop_1(u1_rlvect_1(A),u1_struct_0(A))
& v1_setwiseo(u1_rlvect_1(A),u1_struct_0(A)) )
=> ! [B] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( C = k1_bhsp_6(A,B)
<=> ? [D] :
( m2_finseq_1(D,u1_struct_0(A))
& v2_funct_1(D)
& k5_relset_1(k5_numbers,u1_struct_0(A),D) = B
& C = k2_finsop_1(u1_struct_0(A),D,u1_rlvect_1(A)) ) ) ) ) ) ) ).
fof(t1_bhsp_6,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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ( ( v1_binop_1(u1_rlvect_1(A),u1_struct_0(A))
& v2_binop_1(u1_rlvect_1(A),u1_struct_0(A))
& v1_setwiseo(u1_rlvect_1(A),u1_struct_0(A)) )
=> ! [B] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( ( r1_tarski(B,k4_relset_1(u1_struct_0(A),u1_struct_0(A),C))
& ! [D] :
( r2_hidden(D,k4_relset_1(u1_struct_0(A),u1_struct_0(A),C))
=> k1_funct_1(C,D) = D ) )
=> k1_bhsp_6(A,B) = k5_bhsp_5(u1_struct_0(A),u1_struct_0(A),u1_rlvect_1(A),B,C) ) ) ) ) ) ).
fof(t2_bhsp_6,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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ( ( v1_binop_1(u1_rlvect_1(A),u1_struct_0(A))
& v2_binop_1(u1_rlvect_1(A),u1_struct_0(A))
& v1_setwiseo(u1_rlvect_1(A),u1_struct_0(A)) )
=> ! [B] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r1_xboole_0(B,C)
=> ! [D] :
( ( v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> ( D = k4_subset_1(u1_struct_0(A),B,C)
=> k1_bhsp_6(A,D) = k4_rlvect_1(A,k1_bhsp_6(A,B),k1_bhsp_6(A,C)) ) ) ) ) ) ) ) ).
fof(d2_bhsp_6,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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_bhsp_6(B,A)
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( ( v1_finset_1(E)
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( ~ v1_xboole_0(E)
& r1_tarski(E,B)
& ! [F] :
( ( v1_finset_1(F)
& m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( r1_tarski(E,F)
& r1_tarski(F,B)
& r1_xreal_0(D,k3_bhsp_1(A,k6_rlvect_1(A,C,k1_bhsp_6(A,F)))) ) ) ) ) ) ) ) ) ) ) ).
fof(d3_bhsp_6,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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_bhsp_6(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( C = k2_bhsp_6(A,B)
<=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( ( v1_finset_1(E)
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( ~ v1_xboole_0(E)
& r1_tarski(E,B)
& ! [F] :
( ( v1_finset_1(F)
& m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( r1_tarski(E,F)
& r1_tarski(F,B)
& r1_xreal_0(D,k3_bhsp_1(A,k6_rlvect_1(A,C,k1_bhsp_6(A,F)))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d4_bhsp_6,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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k6_supinf_1)
& v2_hahnban(B,A)
& v3_hahnban(B,A)
& m2_relset_1(B,u1_struct_0(A),k6_supinf_1) )
=> ( v2_bhsp_6(B,A)
<=> ? [C] :
( m1_subset_1(C,k1_numbers)
& ~ r1_xreal_0(C,np__0)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r1_xreal_0(k18_complex1(k8_funct_2(u1_struct_0(A),k6_supinf_1,B,D)),k11_binop_2(C,k3_bhsp_1(A,D))) ) ) ) ) ) ).
fof(d5_bhsp_6,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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_bhsp_6(B,A)
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),k6_supinf_1)
& v2_hahnban(D,A)
& v3_hahnban(D,A)
& m2_relset_1(D,u1_struct_0(A),k6_supinf_1) )
=> ( v2_bhsp_6(D,A)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(E,np__0)
& ! [F] :
( ( v1_finset_1(F)
& m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( ~ v1_xboole_0(F)
& r1_tarski(F,B)
& ! [G] :
( ( v1_finset_1(G)
& m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( r1_tarski(F,G)
& r1_tarski(G,B)
& r1_xreal_0(E,k18_complex1(k8_funct_2(u1_struct_0(A),k6_supinf_1,D,k6_rlvect_1(A,C,k1_bhsp_6(A,G))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d6_bhsp_6,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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),k6_supinf_1)
& m2_relset_1(C,u1_struct_0(A),k6_supinf_1) )
=> ( r1_bhsp_6(A,B,C)
<=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(E,np__0)
& ! [F] :
( ( v1_finset_1(F)
& m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( ~ v1_xboole_0(F)
& r1_tarski(F,B)
& ! [G] :
( ( v1_finset_1(G)
& m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( r1_tarski(F,G)
& r1_tarski(G,B)
& r1_xreal_0(E,k18_complex1(k10_binop_2(D,k5_bhsp_5(k1_numbers,u1_struct_0(A),k33_binop_2,G,C)))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d7_bhsp_6,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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),k6_supinf_1)
& m2_relset_1(C,u1_struct_0(A),k6_supinf_1) )
=> ( r1_bhsp_6(A,B,C)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( D = k3_bhsp_6(A,B,C)
<=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(E,np__0)
& ! [F] :
( ( v1_finset_1(F)
& m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( ~ v1_xboole_0(F)
& r1_tarski(F,B)
& ! [G] :
( ( v1_finset_1(G)
& m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( r1_tarski(F,G)
& r1_tarski(G,B)
& r1_xreal_0(E,k18_complex1(k10_binop_2(D,k5_bhsp_5(k1_numbers,u1_struct_0(A),k33_binop_2,G,C)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t3_bhsp_6,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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_bhsp_6(B,A)
=> v3_bhsp_6(B,A) ) ) ) ).
fof(t4_bhsp_6,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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k6_supinf_1)
& v2_hahnban(B,A)
& v3_hahnban(B,A)
& m2_relset_1(B,u1_struct_0(A),k6_supinf_1) )
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(A))
=> ( r1_xreal_0(np__1,k3_finseq_1(C))
=> ! [D] :
( m2_finseq_1(D,k1_numbers)
=> ( ( k5_finsop_1(C) = k5_finsop_1(D)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k5_finsop_1(D))
=> k1_funct_1(D,E) = k1_funct_1(B,k1_funct_1(C,E)) ) ) )
=> k8_funct_2(u1_struct_0(A),k6_supinf_1,B,k2_finsop_1(u1_struct_0(A),C,u1_rlvect_1(A))) = k2_finsop_1(k1_numbers,D,k33_binop_2) ) ) ) ) ) ) ).
fof(t5_bhsp_6,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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ( ( v1_binop_1(u1_rlvect_1(A),u1_struct_0(A))
& v2_binop_1(u1_rlvect_1(A),u1_struct_0(A))
& v1_setwiseo(u1_rlvect_1(A),u1_struct_0(A)) )
=> ! [B] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),k6_supinf_1)
& v2_hahnban(C,A)
& v3_hahnban(C,A)
& m2_relset_1(C,u1_struct_0(A),k6_supinf_1) )
=> k8_funct_2(u1_struct_0(A),k6_supinf_1,C,k1_bhsp_6(A,B)) = k5_bhsp_5(k1_numbers,u1_struct_0(A),k33_binop_2,B,C) ) ) ) ) ) ).
fof(t6_bhsp_6,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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ( ( v1_binop_1(u1_rlvect_1(A),u1_struct_0(A))
& v2_binop_1(u1_rlvect_1(A),u1_struct_0(A))
& v1_setwiseo(u1_rlvect_1(A),u1_struct_0(A)) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( v3_bhsp_6(B,A)
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),k6_supinf_1)
& v2_hahnban(D,A)
& v3_hahnban(D,A)
& m2_relset_1(D,u1_struct_0(A),k6_supinf_1)
& v2_bhsp_6(D,A)
& ? [E] :
( m1_subset_1(E,k1_numbers)
& ~ r1_xreal_0(E,np__0)
& ! [F] :
( ( v1_finset_1(F)
& m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( ~ v1_xboole_0(F)
& r1_tarski(F,B)
& ! [G] :
( ( v1_finset_1(G)
& m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( r1_tarski(F,G)
& r1_tarski(G,B)
& r1_xreal_0(E,k18_complex1(k10_binop_2(k8_funct_2(u1_struct_0(A),k6_supinf_1,D,C),k5_bhsp_5(k1_numbers,u1_struct_0(A),k33_binop_2,G,D)))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t7_bhsp_6,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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ( ( v1_binop_1(u1_rlvect_1(A),u1_struct_0(A))
& v2_binop_1(u1_rlvect_1(A),u1_struct_0(A))
& v1_setwiseo(u1_rlvect_1(A),u1_struct_0(A)) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_bhsp_6(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),k6_supinf_1)
& v2_hahnban(C,A)
& v3_hahnban(C,A)
& m2_relset_1(C,u1_struct_0(A),k6_supinf_1) )
=> ( v2_bhsp_6(C,A)
=> r1_bhsp_6(A,B,C) ) ) ) ) ) ) ).
fof(t8_bhsp_6,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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ( ( v1_binop_1(u1_rlvect_1(A),u1_struct_0(A))
& v2_binop_1(u1_rlvect_1(A),u1_struct_0(A))
& v1_setwiseo(u1_rlvect_1(A),u1_struct_0(A)) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_bhsp_6(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),k6_supinf_1)
& v2_hahnban(C,A)
& v3_hahnban(C,A)
& m2_relset_1(C,u1_struct_0(A),k6_supinf_1) )
=> ( v2_bhsp_6(C,A)
=> r1_bhsp_6(A,B,C) ) ) ) ) ) ) ).
fof(t9_bhsp_6,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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v1_xboole_0(B)
=> v1_bhsp_6(B,A) ) ) ) ).
fof(t10_bhsp_6,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)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ( ( v1_binop_1(u1_rlvect_1(A),u1_struct_0(A))
& v2_binop_1(u1_rlvect_1(A),u1_struct_0(A))
& v1_setwiseo(u1_rlvect_1(A),u1_struct_0(A))
& v4_bhsp_3(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_bhsp_6(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ~ ( ~ r1_xreal_0(C,np__0)
& ! [D] :
( ( v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( ~ v1_xboole_0(D)
& r1_tarski(D,B)
& ! [E] :
( ( v1_finset_1(E)
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( ~ v1_xboole_0(E)
& r1_tarski(E,B)
& r1_xboole_0(D,E)
& r1_xreal_0(C,k3_bhsp_1(A,k1_bhsp_6(A,E))) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_k1_bhsp_6,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)
& v2_bhsp_1(A)
& l1_bhsp_1(A)
& v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k1_bhsp_6(A,B),u1_struct_0(A)) ) ).
fof(dt_k2_bhsp_6,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)
& v2_bhsp_1(A)
& l1_bhsp_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m1_subset_1(k2_bhsp_6(A,B),u1_struct_0(A)) ) ).
fof(dt_k3_bhsp_6,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),k6_supinf_1)
& m1_relset_1(C,u1_struct_0(A),k6_supinf_1) )
=> m1_subset_1(k3_bhsp_6(A,B,C),k1_numbers) ) ).
%------------------------------------------------------------------------------