SET007 Axioms: SET007+850.ax
%------------------------------------------------------------------------------
% File : SET007+850 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Differentiable Functions on Normed Linear Spaces. Part II
% 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 : ndiff_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 20 ( 0 unt; 0 def)
% Number of atoms : 783 ( 37 equ)
% Maximal formula atoms : 110 ( 39 avg)
% Number of connectives : 903 ( 140 ~; 0 |; 596 &)
% ( 5 <=>; 162 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 23 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 29 ( 28 usr; 0 prp; 1-5 aty)
% Number of functors : 37 ( 37 usr; 4 con; 0-6 aty)
% Number of variables : 158 ( 152 !; 6 ?)
% 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_ndiff_2,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_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( m1_struct_0(D,k8_lopban_1(A,B),k10_lopban_1(A,B))
=> ! [E] :
( m1_struct_0(E,k8_lopban_1(B,C),k10_lopban_1(B,C))
=> k1_ndiff_2(A,B,C,D,E) = k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),k13_lopban_1(A,B,D),k13_lopban_1(B,C,E)) ) ) ) ) ) ).
fof(d2_ndiff_2,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_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k16_lopban_1(A,B)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k16_lopban_1(B,C)))
=> k2_ndiff_2(A,B,C,D,E) = k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),k13_lopban_1(A,B,D),k13_lopban_1(B,C,E)) ) ) ) ) ) ).
fof(t1_ndiff_2,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_normsp_1(A)
& ~ v3_realset2(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& ~ v3_realset2(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ~ ( r1_ndiff_1(B,A,C,D)
& ! [E] :
( m1_nfcont_1(E,B,D)
=> ~ ( r1_tarski(E,k4_relset_1(u1_struct_0(B),u1_struct_0(A),C))
& ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k5_numbers,k1_numbers)
& v1_fdiff_1(G)
& m2_relset_1(G,k5_numbers,k1_numbers) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,k5_numbers,u1_struct_0(B))
& v5_seqm_3(H)
& m2_relset_1(H,k5_numbers,u1_struct_0(B)) )
=> ( ( k5_relset_1(k5_numbers,u1_struct_0(B),H) = k1_struct_0(B,D)
& r1_tarski(k5_relset_1(k5_numbers,u1_struct_0(B),k3_normsp_1(B,k2_ndiff_1(B,F,G),H)),E) )
=> ( v4_normsp_1(k1_ndiff_1(A,k4_normsp_1(A,k3_nfcont_1(B,A,C,k3_normsp_1(B,k2_ndiff_1(B,F,G),H)),k3_nfcont_1(B,A,C,H)),k18_seq_1(G)),A)
& k17_lopban_1(B,A,k3_ndiff_1(B,A,C,D),F) = k8_normsp_1(A,k1_ndiff_1(A,k4_normsp_1(A,k3_nfcont_1(B,A,C,k3_normsp_1(B,k2_ndiff_1(B,F,G),H)),k3_nfcont_1(B,A,C,H)),k18_seq_1(G))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t2_ndiff_2,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_normsp_1(A)
& ~ v3_realset2(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& ~ v3_realset2(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( r1_ndiff_1(B,A,C,D)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k5_numbers,k1_numbers)
& v1_fdiff_1(F)
& m2_relset_1(F,k5_numbers,k1_numbers) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k5_numbers,u1_struct_0(B))
& v5_seqm_3(G)
& m2_relset_1(G,k5_numbers,u1_struct_0(B)) )
=> ( ( k5_relset_1(k5_numbers,u1_struct_0(B),G) = k1_struct_0(B,D)
& r1_tarski(k5_relset_1(k5_numbers,u1_struct_0(B),k3_normsp_1(B,k2_ndiff_1(B,E,F),G)),k4_relset_1(u1_struct_0(B),u1_struct_0(A),C)) )
=> ( v4_normsp_1(k1_ndiff_1(A,k4_normsp_1(A,k3_nfcont_1(B,A,C,k3_normsp_1(B,k2_ndiff_1(B,E,F),G)),k3_nfcont_1(B,A,C,G)),k18_seq_1(F)),A)
& k17_lopban_1(B,A,k3_ndiff_1(B,A,C,D),E) = k8_normsp_1(A,k1_ndiff_1(A,k4_normsp_1(A,k3_nfcont_1(B,A,C,k3_normsp_1(B,k2_ndiff_1(B,E,F),G)),k3_nfcont_1(B,A,C,G)),k18_seq_1(F))) ) ) ) ) ) ) ) ) ) ) ).
fof(t3_ndiff_2,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_normsp_1(A)
& ~ v3_realset2(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& ~ v3_realset2(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_nfcont_1(E,A,D)
=> ( r1_tarski(E,k4_relset_1(u1_struct_0(A),u1_struct_0(B),C))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ( ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,k5_numbers,k1_numbers)
& v1_fdiff_1(H)
& m2_relset_1(H,k5_numbers,k1_numbers) )
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,k5_numbers,u1_struct_0(A))
& v5_seqm_3(I)
& m2_relset_1(I,k5_numbers,u1_struct_0(A)) )
=> ( ( k5_relset_1(k5_numbers,u1_struct_0(A),I) = k1_struct_0(A,D)
& r1_tarski(k5_relset_1(k5_numbers,u1_struct_0(A),k3_normsp_1(A,k2_ndiff_1(A,F,H),I)),E) )
=> ( v4_normsp_1(k1_ndiff_1(B,k4_normsp_1(B,k3_nfcont_1(A,B,C,k3_normsp_1(A,k2_ndiff_1(A,F,H),I)),k3_nfcont_1(A,B,C,I)),k18_seq_1(H)),B)
& G = k8_normsp_1(B,k1_ndiff_1(B,k4_normsp_1(B,k3_nfcont_1(A,B,C,k3_normsp_1(A,k2_ndiff_1(A,F,H),I)),k3_nfcont_1(A,B,C,I)),k18_seq_1(H))) ) ) ) )
<=> ! [H] :
( m1_subset_1(H,k1_numbers)
=> ~ ( ~ r1_xreal_0(H,np__0)
& ! [I] :
( m1_subset_1(I,k1_numbers)
=> ~ ( ~ r1_xreal_0(I,np__0)
& ! [J] :
( m1_subset_1(J,k1_numbers)
=> ~ ( ~ r1_xreal_0(I,k18_complex1(J))
& J != np__0
& r2_hidden(k4_rlvect_1(A,k3_rlvect_1(A,F,J),D),E)
& r1_xreal_0(H,k1_normsp_1(B,k6_rlvect_1(B,k3_rlvect_1(B,k6_rlvect_1(B,k4_finseq_4(u1_struct_0(A),u1_struct_0(B),C,k4_rlvect_1(A,k3_rlvect_1(A,F,J),D)),k4_finseq_4(u1_struct_0(A),u1_struct_0(B),C,D)),k2_real_1(J)),G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d3_ndiff_2,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_normsp_1(A)
& ~ v3_realset2(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& ~ v3_realset2(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r1_ndiff_2(A,B,C,D,E)
<=> ? [F] :
( m1_nfcont_1(F,A,D)
& r1_tarski(F,k4_relset_1(u1_struct_0(A),u1_struct_0(B),C))
& ? [G] :
( m1_subset_1(G,u1_struct_0(B))
& ! [H] :
( m1_subset_1(H,k1_numbers)
=> ~ ( ~ r1_xreal_0(H,np__0)
& ! [I] :
( m1_subset_1(I,k1_numbers)
=> ~ ( ~ r1_xreal_0(I,np__0)
& ! [J] :
( m1_subset_1(J,k1_numbers)
=> ~ ( ~ r1_xreal_0(I,k18_complex1(J))
& J != np__0
& r2_hidden(k4_rlvect_1(A,k3_rlvect_1(A,E,J),D),F)
& r1_xreal_0(H,k1_normsp_1(B,k6_rlvect_1(B,k3_rlvect_1(B,k6_rlvect_1(B,k4_finseq_4(u1_struct_0(A),u1_struct_0(B),C,k4_rlvect_1(A,k3_rlvect_1(A,E,J),D)),k4_finseq_4(u1_struct_0(A),u1_struct_0(B),C,D)),k2_real_1(J)),G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t4_ndiff_2,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_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ~ ( ~ r1_xreal_0(k1_normsp_1(A,k6_rlvect_1(A,B,C)),np__0)
& B = C )
& ~ ( B != C
& r1_xreal_0(k1_normsp_1(A,k6_rlvect_1(A,B,C)),np__0) ) ) ) ) )
& ! [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_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k1_normsp_1(A,k6_rlvect_1(A,B,C)) = k1_normsp_1(A,k6_rlvect_1(A,C,B)) ) ) )
& ! [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_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k1_normsp_1(A,k6_rlvect_1(A,B,C)) = np__0
<=> B = C ) ) ) )
& ! [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_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ~ ( k1_normsp_1(A,k6_rlvect_1(A,B,C)) != np__0
& B = C )
& ~ ( B != C
& k1_normsp_1(A,k6_rlvect_1(A,B,C)) = np__0 ) ) ) ) )
& ! [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_normsp_1(A)
& l1_normsp_1(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,k1_numbers)
=> ~ ( ~ r1_xreal_0(E,np__0)
& ~ r1_xreal_0(k6_real_1(E,np__2),k1_normsp_1(A,k6_rlvect_1(A,B,D)))
& ~ r1_xreal_0(k6_real_1(E,np__2),k1_normsp_1(A,k6_rlvect_1(A,D,C)))
& r1_xreal_0(E,k1_normsp_1(A,k6_rlvect_1(A,B,C))) ) ) ) ) ) )
& ! [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_normsp_1(A)
& l1_normsp_1(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,k1_numbers)
=> ~ ( ~ r1_xreal_0(E,np__0)
& ~ r1_xreal_0(k6_real_1(E,np__2),k1_normsp_1(A,k6_rlvect_1(A,B,D)))
& ~ r1_xreal_0(k6_real_1(E,np__2),k1_normsp_1(A,k6_rlvect_1(A,C,D)))
& r1_xreal_0(E,k1_normsp_1(A,k6_rlvect_1(A,B,C))) ) ) ) ) ) )
& ! [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_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( ! [C] :
( m1_subset_1(C,k1_numbers)
=> ~ ( ~ r1_xreal_0(C,np__0)
& r1_xreal_0(C,k1_normsp_1(A,B)) ) )
=> B = k1_rlvect_1(A) ) ) )
& ! [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_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& r1_xreal_0(D,k1_normsp_1(A,k6_rlvect_1(A,B,C))) ) )
=> B = C ) ) ) ) ) ).
fof(d4_ndiff_2,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_normsp_1(A)
& ~ v3_realset2(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& ~ v3_realset2(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r1_ndiff_2(A,B,C,D,E)
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( F = k3_ndiff_2(A,B,C,D,E)
<=> ? [G] :
( m1_nfcont_1(G,A,D)
& r1_tarski(G,k4_relset_1(u1_struct_0(A),u1_struct_0(B),C))
& ! [H] :
( m1_subset_1(H,k1_numbers)
=> ~ ( ~ r1_xreal_0(H,np__0)
& ! [I] :
( m1_subset_1(I,k1_numbers)
=> ~ ( ~ r1_xreal_0(I,np__0)
& ! [J] :
( m1_subset_1(J,k1_numbers)
=> ~ ( ~ r1_xreal_0(I,k18_complex1(J))
& J != np__0
& r2_hidden(k4_rlvect_1(A,k3_rlvect_1(A,E,J),D),G)
& r1_xreal_0(H,k1_normsp_1(B,k6_rlvect_1(B,k3_rlvect_1(B,k6_rlvect_1(B,k4_finseq_4(u1_struct_0(A),u1_struct_0(B),C,k4_rlvect_1(A,k3_rlvect_1(A,E,J),D)),k4_finseq_4(u1_struct_0(A),u1_struct_0(B),C,D)),k2_real_1(J)),F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t5_ndiff_2,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_normsp_1(A)
& ~ v3_realset2(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& ~ v3_realset2(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r1_ndiff_2(A,B,C,D,E)
<=> ? [F] :
( m1_nfcont_1(F,A,D)
& r1_tarski(F,k4_relset_1(u1_struct_0(A),u1_struct_0(B),C))
& ? [G] :
( m1_subset_1(G,u1_struct_0(B))
& ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,k5_numbers,k1_numbers)
& v1_fdiff_1(H)
& m2_relset_1(H,k5_numbers,k1_numbers) )
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,k5_numbers,u1_struct_0(A))
& v5_seqm_3(I)
& m2_relset_1(I,k5_numbers,u1_struct_0(A)) )
=> ( ( k5_relset_1(k5_numbers,u1_struct_0(A),I) = k1_struct_0(A,D)
& r1_tarski(k5_relset_1(k5_numbers,u1_struct_0(A),k3_normsp_1(A,k2_ndiff_1(A,E,H),I)),F) )
=> ( v4_normsp_1(k1_ndiff_1(B,k4_normsp_1(B,k3_nfcont_1(A,B,C,k3_normsp_1(A,k2_ndiff_1(A,E,H),I)),k3_nfcont_1(A,B,C,I)),k18_seq_1(H)),B)
& G = k8_normsp_1(B,k1_ndiff_1(B,k4_normsp_1(B,k3_nfcont_1(A,B,C,k3_normsp_1(A,k2_ndiff_1(A,E,H),I)),k3_nfcont_1(A,B,C,I)),k18_seq_1(H))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t6_ndiff_2,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_normsp_1(A)
& ~ v3_realset2(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& ~ v3_realset2(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( r1_ndiff_1(B,A,C,D)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( r1_ndiff_2(B,A,C,D,E)
& k3_ndiff_2(B,A,C,D,E) = k17_lopban_1(B,A,k3_ndiff_1(B,A,C,D),E)
& ? [F] :
( m1_nfcont_1(F,B,D)
& r1_tarski(F,k4_relset_1(u1_struct_0(B),u1_struct_0(A),C))
& ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k5_numbers,k1_numbers)
& v1_fdiff_1(G)
& m2_relset_1(G,k5_numbers,k1_numbers) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,k5_numbers,u1_struct_0(B))
& v5_seqm_3(H)
& m2_relset_1(H,k5_numbers,u1_struct_0(B)) )
=> ( ( k5_relset_1(k5_numbers,u1_struct_0(B),H) = k1_struct_0(B,D)
& r1_tarski(k5_relset_1(k5_numbers,u1_struct_0(B),k3_normsp_1(B,k2_ndiff_1(B,E,G),H)),F) )
=> ( v4_normsp_1(k1_ndiff_1(A,k4_normsp_1(A,k3_nfcont_1(B,A,C,k3_normsp_1(B,k2_ndiff_1(B,E,G),H)),k3_nfcont_1(B,A,C,H)),k18_seq_1(G)),A)
& k3_ndiff_2(B,A,C,D,E) = k8_normsp_1(A,k1_ndiff_1(A,k4_normsp_1(A,k3_nfcont_1(B,A,C,k3_normsp_1(B,k2_ndiff_1(B,E,G),H)),k3_nfcont_1(B,A,C,H)),k18_seq_1(G))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t7_ndiff_2,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_normsp_1(A)
& ~ v3_realset2(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& ~ v3_realset2(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v3_ndiff_1(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( k4_finseq_4(u1_struct_0(A),u1_struct_0(B),C,k1_rlvect_1(A)) = k1_rlvect_1(B)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( ~ r1_xreal_0(E,np__0)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( ~ r1_xreal_0(E,k1_normsp_1(A,F))
=> r1_xreal_0(k1_normsp_1(B,k4_finseq_4(u1_struct_0(A),u1_struct_0(B),C,F)),k4_real_1(D,k1_normsp_1(A,F))) ) ) ) ) ) ) ) ) ) ) ).
fof(t8_ndiff_2,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_normsp_1(A)
& ~ v3_realset2(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& ~ v3_realset2(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& ~ v3_realset2(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v3_ndiff_1(D,A,C)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)) )
=> ( k4_finseq_4(u1_struct_0(A),u1_struct_0(C),D,k1_rlvect_1(A)) = k1_rlvect_1(C)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(A))
& v1_lopban_1(E,B,A)
& v2_lopban_1(E,B,A)
& v3_lopban_1(E,B,A)
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) )
=> ( v1_funct_1(k1_partfun1(u1_struct_0(B),u1_struct_0(A),u1_struct_0(A),u1_struct_0(C),E,D))
& v3_ndiff_1(k1_partfun1(u1_struct_0(B),u1_struct_0(A),u1_struct_0(A),u1_struct_0(C),E,D),B,C)
& m2_relset_1(k1_partfun1(u1_struct_0(B),u1_struct_0(A),u1_struct_0(A),u1_struct_0(C),E,D),u1_struct_0(B),u1_struct_0(C)) ) ) ) ) ) ) ) ).
fof(t9_ndiff_2,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_normsp_1(A)
& ~ v3_realset2(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& ~ v3_realset2(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& ~ v3_realset2(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v3_ndiff_1(D,A,B)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& v1_lopban_1(E,B,C)
& v2_lopban_1(E,B,C)
& v3_lopban_1(E,B,C)
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( v1_funct_1(k1_partfun1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_struct_0(C),D,E))
& v3_ndiff_1(k1_partfun1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_struct_0(C),D,E),A,C)
& m2_relset_1(k1_partfun1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_struct_0(C),D,E),u1_struct_0(A),u1_struct_0(C)) ) ) ) ) ) ) ).
fof(t10_ndiff_2,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_normsp_1(A)
& ~ v3_realset2(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& ~ v3_realset2(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& ~ v3_realset2(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v3_ndiff_1(D,A,B)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ( k4_finseq_4(u1_struct_0(A),u1_struct_0(B),D,k1_rlvect_1(A)) = k1_rlvect_1(B)
=> ! [E] :
( ( v1_funct_1(E)
& v3_ndiff_1(E,B,C)
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( k4_finseq_4(u1_struct_0(B),u1_struct_0(C),E,k1_rlvect_1(B)) = k1_rlvect_1(C)
=> ( v1_funct_1(k1_partfun1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_struct_0(C),D,E))
& v3_ndiff_1(k1_partfun1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_struct_0(C),D,E),A,C)
& m2_relset_1(k1_partfun1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_struct_0(C),D,E),u1_struct_0(A),u1_struct_0(C)) ) ) ) ) ) ) ) ) ).
fof(t11_ndiff_2,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_normsp_1(A)
& ~ v3_realset2(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& ~ v3_realset2(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& ~ v3_realset2(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v3_ndiff_1(D,A,B)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ( k4_finseq_4(u1_struct_0(A),u1_struct_0(B),D,k1_rlvect_1(A)) = k1_rlvect_1(B)
=> ! [E] :
( ( v1_funct_1(E)
& v3_ndiff_1(E,B,C)
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( k4_finseq_4(u1_struct_0(B),u1_struct_0(C),E,k1_rlvect_1(B)) = k1_rlvect_1(C)
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(A),u1_struct_0(B))
& v1_lopban_1(F,A,B)
& v2_lopban_1(F,A,B)
& v3_lopban_1(F,A,B)
& m2_relset_1(F,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_funct_1(k1_partfun1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_struct_0(C),k1_vfunct_1(u1_struct_0(A),B,F,D),E))
& v3_ndiff_1(k1_partfun1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_struct_0(C),k1_vfunct_1(u1_struct_0(A),B,F,D),E),A,C)
& m2_relset_1(k1_partfun1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_struct_0(C),k1_vfunct_1(u1_struct_0(A),B,F,D),E),u1_struct_0(A),u1_struct_0(C)) ) ) ) ) ) ) ) ) ) ).
fof(t12_ndiff_2,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_normsp_1(A)
& ~ v3_realset2(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& ~ v3_realset2(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& ~ v3_realset2(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v3_ndiff_1(D,A,B)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ( k4_finseq_4(u1_struct_0(A),u1_struct_0(B),D,k1_rlvect_1(A)) = k1_rlvect_1(B)
=> ! [E] :
( ( v1_funct_1(E)
& v3_ndiff_1(E,B,C)
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( k4_finseq_4(u1_struct_0(B),u1_struct_0(C),E,k1_rlvect_1(B)) = k1_rlvect_1(C)
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(A),u1_struct_0(B))
& v1_lopban_1(F,A,B)
& v2_lopban_1(F,A,B)
& v3_lopban_1(F,A,B)
& m2_relset_1(F,u1_struct_0(A),u1_struct_0(B)) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(B),u1_struct_0(C))
& v1_lopban_1(G,B,C)
& v2_lopban_1(G,B,C)
& v3_lopban_1(G,B,C)
& m2_relset_1(G,u1_struct_0(B),u1_struct_0(C)) )
=> ( v1_funct_1(k1_vfunct_1(u1_struct_0(A),C,k1_partfun1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_struct_0(C),D,G),k1_partfun1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_struct_0(C),k1_vfunct_1(u1_struct_0(A),B,F,D),E)))
& v3_ndiff_1(k1_vfunct_1(u1_struct_0(A),C,k1_partfun1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_struct_0(C),D,G),k1_partfun1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_struct_0(C),k1_vfunct_1(u1_struct_0(A),B,F,D),E)),A,C)
& m2_relset_1(k1_vfunct_1(u1_struct_0(A),C,k1_partfun1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_struct_0(C),D,G),k1_partfun1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_struct_0(C),k1_vfunct_1(u1_struct_0(A),B,F,D),E)),u1_struct_0(A),u1_struct_0(C)) ) ) ) ) ) ) ) ) ) ) ).
fof(t13_ndiff_2,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_normsp_1(A)
& ~ v3_realset2(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& ~ v3_realset2(B)
& l1_normsp_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_rlvect_1(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& v7_rlvect_1(D)
& v2_normsp_1(D)
& ~ v3_realset2(D)
& l1_normsp_1(D) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
=> ( r1_ndiff_1(A,B,E,C)
=> ! [F] :
( ( v1_funct_1(F)
& m2_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
=> ( r1_ndiff_1(B,D,F,k4_finseq_4(u1_struct_0(A),u1_struct_0(B),E,C))
=> ( r1_ndiff_1(A,D,k1_partfun1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_struct_0(D),E,F),C)
& k3_ndiff_1(A,D,k1_partfun1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_struct_0(D),E,F),C) = k2_ndiff_2(A,B,D,k3_ndiff_1(A,B,E,C),k3_ndiff_1(B,D,F,k4_finseq_4(u1_struct_0(A),u1_struct_0(B),E,C))) ) ) ) ) ) ) ) ) ) ).
fof(dt_k1_ndiff_2,axiom,
! [A,B,C,D,E] :
( ( ~ 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_normsp_1(A)
& l1_normsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B)
& ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C)
& m1_subset_1(D,k10_lopban_1(A,B))
& m1_subset_1(E,k10_lopban_1(B,C)) )
=> m1_struct_0(k1_ndiff_2(A,B,C,D,E),k8_lopban_1(A,C),k10_lopban_1(A,C)) ) ).
fof(dt_k2_ndiff_2,axiom,
! [A,B,C,D,E] :
( ( ~ 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_normsp_1(A)
& l1_normsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& l1_normsp_1(B)
& ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C)
& m1_subset_1(D,u1_struct_0(k16_lopban_1(A,B)))
& m1_subset_1(E,u1_struct_0(k16_lopban_1(B,C))) )
=> m1_subset_1(k2_ndiff_2(A,B,C,D,E),u1_struct_0(k16_lopban_1(A,C))) ) ).
fof(dt_k3_ndiff_2,axiom,
! [A,B,C,D,E] :
( ( ~ 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_normsp_1(A)
& ~ v3_realset2(A)
& l1_normsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_normsp_1(B)
& ~ v3_realset2(B)
& l1_normsp_1(B)
& v1_funct_1(C)
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& m1_subset_1(D,u1_struct_0(A))
& m1_subset_1(E,u1_struct_0(A)) )
=> m1_subset_1(k3_ndiff_2(A,B,C,D,E),u1_struct_0(B)) ) ).
%------------------------------------------------------------------------------