SET007 Axioms: SET007+99.ax
%------------------------------------------------------------------------------
% File : SET007+99 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Semigroup Operations on Finite Subsets
% 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 : setwop_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 59 ( 11 unt; 0 def)
% Number of atoms : 680 ( 89 equ)
% Maximal formula atoms : 27 ( 11 avg)
% Number of connectives : 705 ( 84 ~; 14 |; 306 &)
% ( 0 <=>; 301 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 13 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 1 prp; 0-3 aty)
% Number of functors : 46 ( 46 usr; 4 con; 0-6 aty)
% Number of variables : 264 ( 264 !; 0 ?)
% 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(t1_setwop_2,axiom,
$true ).
fof(t2_setwop_2,axiom,
$true ).
fof(t3_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(B,B),B)
& m2_relset_1(E,k2_zfmisc_1(B,B),B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,A,B)
& m2_relset_1(F,A,B) )
=> ( ( v1_binop_1(E,B)
& v2_binop_1(E,B) )
=> ( C = D
| k7_setwiseo(A,B,E,k3_setwiseo(A,C,D),F) = k2_binop_1(B,B,B,E,k8_funct_2(A,B,F,C),k8_funct_2(A,B,F,D)) ) ) ) ) ) ) ) ) ).
fof(t4_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,k5_finsub_1(A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(B,B),B)
& m2_relset_1(E,k2_zfmisc_1(B,B),B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,A,B)
& m2_relset_1(F,A,B) )
=> ( ( v1_binop_1(E,B)
& v2_binop_1(E,B) )
=> ( ( D = k1_xboole_0
& ~ v1_setwiseo(E,B) )
| r2_hidden(C,D)
| k7_setwiseo(A,B,E,k5_setwiseo(A,D,k2_setwiseo(A,C)),F) = k2_binop_1(B,B,B,E,k7_setwiseo(A,B,E,D,F),k8_funct_2(A,B,F,C)) ) ) ) ) ) ) ) ) ).
fof(t5_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(B,B),B)
& m2_relset_1(F,k2_zfmisc_1(B,B),B) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,A,B)
& m2_relset_1(G,A,B) )
=> ( ( v1_binop_1(F,B)
& v2_binop_1(F,B) )
=> ( C = D
| C = E
| D = E
| k7_setwiseo(A,B,F,k4_setwiseo(A,C,D,E),G) = k2_binop_1(B,B,B,F,k2_binop_1(B,B,B,F,k8_funct_2(A,B,G,C),k8_funct_2(A,B,G,D)),k8_funct_2(A,B,G,E)) ) ) ) ) ) ) ) ) ) ).
fof(t6_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,k5_finsub_1(A))
=> ! [D] :
( m1_subset_1(D,k5_finsub_1(A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(B,B),B)
& m2_relset_1(E,k2_zfmisc_1(B,B),B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,A,B)
& m2_relset_1(F,A,B) )
=> ( ( v1_binop_1(E,B)
& v2_binop_1(E,B)
& r1_xboole_0(C,D) )
=> ( ( ~ ( C != k1_xboole_0
& D != k1_xboole_0 )
& ~ v1_setwiseo(E,B) )
| k7_setwiseo(A,B,E,k5_setwiseo(A,C,D),F) = k2_binop_1(B,B,B,E,k7_setwiseo(A,B,E,C,F),k7_setwiseo(A,B,E,D,F)) ) ) ) ) ) ) ) ) ).
fof(t7_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,k5_finsub_1(A))
=> ! [E] :
( m1_subset_1(E,k5_finsub_1(B))
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(C,C),C)
& m2_relset_1(F,k2_zfmisc_1(C,C),C) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,A,C)
& m2_relset_1(G,A,C) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,B,C)
& m2_relset_1(H,B,C) )
=> ( ( v1_binop_1(F,C)
& v2_binop_1(F,C) )
=> ( ( E = k1_xboole_0
& ~ v1_setwiseo(F,C) )
| ! [I] :
( ( v1_relat_1(I)
& v1_funct_1(I) )
=> ~ ( k1_relat_1(I) = E
& k2_relat_1(I) = D
& v2_funct_1(I)
& k2_partfun1(B,C,H,E) = k5_relat_1(I,G) ) )
| k7_setwiseo(B,C,F,E,H) = k7_setwiseo(A,C,F,D,G) ) ) ) ) ) ) ) ) ) ) ).
fof(t8_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,k5_finsub_1(A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& m2_relset_1(E,A,B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(C,C),C)
& m2_relset_1(F,k2_zfmisc_1(C,C),C) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,B,C)
& m2_relset_1(G,B,C) )
=> ( ( v1_binop_1(F,C)
& v2_binop_1(F,C)
& v2_funct_1(E) )
=> ( ( D = k1_xboole_0
& ~ v1_setwiseo(F,C) )
| k7_setwiseo(B,C,F,k8_setwiseo(A,B,E,D),G) = k7_setwiseo(A,C,F,D,k7_funct_2(A,B,C,E,G)) ) ) ) ) ) ) ) ) ) ).
fof(t9_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,k5_finsub_1(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(B,B),B)
& m2_relset_1(D,k2_zfmisc_1(B,B),B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& m2_relset_1(E,A,B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,A,B)
& m2_relset_1(F,A,B) )
=> ( ( v1_binop_1(D,B)
& v2_binop_1(D,B)
& k2_partfun1(A,B,E,C) = k2_partfun1(A,B,F,C) )
=> ( ( C = k1_xboole_0
& ~ v1_setwiseo(D,B) )
| k7_setwiseo(A,B,D,C,E) = k7_setwiseo(A,B,D,C,F) ) ) ) ) ) ) ) ) ).
fof(t10_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,k5_finsub_1(A))
=> ! [D] :
( m1_subset_1(D,B)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(B,B),B)
& m2_relset_1(E,k2_zfmisc_1(B,B),B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,A,B)
& m2_relset_1(F,A,B) )
=> ( ( v1_binop_1(E,B)
& v2_binop_1(E,B)
& v1_setwiseo(E,B)
& D = k3_binop_1(B,E)
& k8_setwiseo(A,B,F,C) = k2_setwiseo(B,D) )
=> k7_setwiseo(A,B,E,C,F) = D ) ) ) ) ) ) ) ).
fof(t11_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,k5_finsub_1(A))
=> ! [D] :
( m1_subset_1(D,B)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(B,B),B)
& m2_relset_1(E,k2_zfmisc_1(B,B),B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(B,B),B)
& m2_relset_1(F,k2_zfmisc_1(B,B),B) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,A,B)
& m2_relset_1(G,A,B) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,A,B)
& m2_relset_1(H,A,B) )
=> ( ( v1_binop_1(E,B)
& v2_binop_1(E,B)
& v1_setwiseo(E,B)
& D = k3_binop_1(B,E)
& k2_binop_1(B,B,B,F,D,D) = D
& ! [I] :
( m1_subset_1(I,B)
=> ! [J] :
( m1_subset_1(J,B)
=> ! [K] :
( m1_subset_1(K,B)
=> ! [L] :
( m1_subset_1(L,B)
=> k2_binop_1(B,B,B,E,k2_binop_1(B,B,B,F,I,J),k2_binop_1(B,B,B,F,K,L)) = k2_binop_1(B,B,B,F,k2_binop_1(B,B,B,E,I,K),k2_binop_1(B,B,B,E,J,L)) ) ) ) ) )
=> k2_binop_1(B,B,B,F,k7_setwiseo(A,B,E,C,G),k7_setwiseo(A,B,E,C,H)) = k7_setwiseo(A,B,E,C,k6_funcop_1(B,A,F,G,H)) ) ) ) ) ) ) ) ) ) ).
fof(t12_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,k5_finsub_1(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(B,B),B)
& m2_relset_1(D,k2_zfmisc_1(B,B),B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& m2_relset_1(E,A,B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,A,B)
& m2_relset_1(F,A,B) )
=> ( ( v1_binop_1(D,B)
& v2_binop_1(D,B)
& v1_setwiseo(D,B) )
=> k2_binop_1(B,B,B,D,k7_setwiseo(A,B,D,C,E),k7_setwiseo(A,B,D,C,F)) = k7_setwiseo(A,B,D,C,k6_funcop_1(B,A,D,E,F)) ) ) ) ) ) ) ) ).
fof(t13_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,k5_finsub_1(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(B,B),B)
& m2_relset_1(D,k2_zfmisc_1(B,B),B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(B,B),B)
& m2_relset_1(E,k2_zfmisc_1(B,B),B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,A,B)
& m2_relset_1(F,A,B) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,A,B)
& m2_relset_1(G,A,B) )
=> ( ( v1_binop_1(D,B)
& v2_binop_1(D,B)
& v1_setwiseo(D,B)
& v1_finseqop(D,B)
& E = k8_finseqop(B,D,k6_partfun1(B),k6_finseqop(B,D)) )
=> k2_binop_1(B,B,B,E,k7_setwiseo(A,B,D,C,F),k7_setwiseo(A,B,D,C,G)) = k7_setwiseo(A,B,D,C,k6_funcop_1(B,A,E,F,G)) ) ) ) ) ) ) ) ) ).
fof(t14_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,k5_finsub_1(A))
=> ! [D] :
( m1_subset_1(D,B)
=> ! [E] :
( m1_subset_1(E,B)
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(B,B),B)
& m2_relset_1(F,k2_zfmisc_1(B,B),B) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k2_zfmisc_1(B,B),B)
& m2_relset_1(G,k2_zfmisc_1(B,B),B) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,A,B)
& m2_relset_1(H,A,B) )
=> ( ( v1_binop_1(F,B)
& v2_binop_1(F,B)
& v1_setwiseo(F,B)
& D = k3_binop_1(B,F)
& r6_binop_1(B,G,F)
& k2_binop_1(B,B,B,G,E,D) = D )
=> k2_binop_1(B,B,B,G,E,k7_setwiseo(A,B,F,C,H)) = k7_setwiseo(A,B,F,C,k8_funcop_1(B,A,G,E,H)) ) ) ) ) ) ) ) ) ) ).
fof(t15_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,k5_finsub_1(A))
=> ! [D] :
( m1_subset_1(D,B)
=> ! [E] :
( m1_subset_1(E,B)
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(B,B),B)
& m2_relset_1(F,k2_zfmisc_1(B,B),B) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k2_zfmisc_1(B,B),B)
& m2_relset_1(G,k2_zfmisc_1(B,B),B) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,A,B)
& m2_relset_1(H,A,B) )
=> ( ( v1_binop_1(F,B)
& v2_binop_1(F,B)
& v1_setwiseo(F,B)
& D = k3_binop_1(B,F)
& r6_binop_1(B,G,F)
& k2_binop_1(B,B,B,G,D,E) = D )
=> k2_binop_1(B,B,B,G,k7_setwiseo(A,B,F,C,H),E) = k7_setwiseo(A,B,F,C,k7_funcop_1(B,A,G,H,E)) ) ) ) ) ) ) ) ) ) ).
fof(t16_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,k5_finsub_1(A))
=> ! [D] :
( m1_subset_1(D,B)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(B,B),B)
& m2_relset_1(E,k2_zfmisc_1(B,B),B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(B,B),B)
& m2_relset_1(F,k2_zfmisc_1(B,B),B) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,A,B)
& m2_relset_1(G,A,B) )
=> ( ( v1_binop_1(E,B)
& v2_binop_1(E,B)
& v1_setwiseo(E,B)
& v1_finseqop(E,B)
& r6_binop_1(B,F,E) )
=> k2_binop_1(B,B,B,F,D,k7_setwiseo(A,B,E,C,G)) = k7_setwiseo(A,B,E,C,k8_funcop_1(B,A,F,D,G)) ) ) ) ) ) ) ) ) ).
fof(t17_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,k5_finsub_1(A))
=> ! [D] :
( m1_subset_1(D,B)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(B,B),B)
& m2_relset_1(E,k2_zfmisc_1(B,B),B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(B,B),B)
& m2_relset_1(F,k2_zfmisc_1(B,B),B) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,A,B)
& m2_relset_1(G,A,B) )
=> ( ( v1_binop_1(E,B)
& v2_binop_1(E,B)
& v1_setwiseo(E,B)
& v1_finseqop(E,B)
& r6_binop_1(B,F,E) )
=> k2_binop_1(B,B,B,F,k7_setwiseo(A,B,E,C,G),D) = k7_setwiseo(A,B,E,C,k7_funcop_1(B,A,F,G,D)) ) ) ) ) ) ) ) ) ).
fof(t18_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,k5_finsub_1(A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(C,C),C)
& m2_relset_1(E,k2_zfmisc_1(C,C),C) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,A,C)
& m2_relset_1(F,A,C) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k2_zfmisc_1(B,B),B)
& m2_relset_1(G,k2_zfmisc_1(B,B),B) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,C,B)
& m2_relset_1(H,C,B) )
=> ( ( v1_binop_1(E,C)
& v2_binop_1(E,C)
& v1_setwiseo(E,C)
& v1_binop_1(G,B)
& v2_binop_1(G,B)
& v1_setwiseo(G,B)
& k8_funct_2(C,B,H,k3_binop_1(C,E)) = k3_binop_1(B,G)
& ! [I] :
( m1_subset_1(I,C)
=> ! [J] :
( m1_subset_1(J,C)
=> k8_funct_2(C,B,H,k2_binop_1(C,C,C,E,I,J)) = k2_binop_1(B,B,B,G,k8_funct_2(C,B,H,I),k8_funct_2(C,B,H,J)) ) ) )
=> k8_funct_2(C,B,H,k7_setwiseo(A,C,E,D,F)) = k7_setwiseo(A,B,G,D,k7_funct_2(A,C,B,F,H)) ) ) ) ) ) ) ) ) ) ).
fof(t19_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,k5_finsub_1(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(B,B),B)
& m2_relset_1(D,k2_zfmisc_1(B,B),B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,B,B)
& m2_relset_1(E,B,B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,A,B)
& m2_relset_1(F,A,B) )
=> ( ( v1_binop_1(D,B)
& v2_binop_1(D,B)
& v1_setwiseo(D,B)
& k8_funct_2(B,B,E,k3_binop_1(B,D)) = k3_binop_1(B,D)
& r7_binop_1(B,E,D) )
=> k8_funct_2(B,B,E,k7_setwiseo(A,B,D,C,F)) = k7_setwiseo(A,B,D,C,k7_funct_2(A,B,B,F,E)) ) ) ) ) ) ) ) ).
fof(t20_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,k5_finsub_1(A))
=> ! [D] :
( m1_subset_1(D,B)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(B,B),B)
& m2_relset_1(E,k2_zfmisc_1(B,B),B) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(B,B),B)
& m2_relset_1(F,k2_zfmisc_1(B,B),B) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,A,B)
& m2_relset_1(G,A,B) )
=> ( ( v1_binop_1(E,B)
& v2_binop_1(E,B)
& v1_setwiseo(E,B)
& v1_finseqop(E,B)
& r6_binop_1(B,F,E) )
=> k8_funct_2(B,B,k8_funcop_1(B,B,F,D,k6_partfun1(B)),k7_setwiseo(A,B,E,C,G)) = k7_setwiseo(A,B,E,C,k7_funct_2(A,B,B,G,k8_funcop_1(B,B,F,D,k6_partfun1(B)))) ) ) ) ) ) ) ) ) ).
fof(t21_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,k5_finsub_1(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(B,B),B)
& m2_relset_1(D,k2_zfmisc_1(B,B),B) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& m2_relset_1(E,A,B) )
=> ( ( v1_binop_1(D,B)
& v2_binop_1(D,B)
& v1_setwiseo(D,B)
& v1_finseqop(D,B) )
=> k8_funct_2(B,B,k6_finseqop(B,D),k7_setwiseo(A,B,D,C,E)) = k7_setwiseo(A,B,D,C,k7_funct_2(A,B,B,E,k6_finseqop(B,D))) ) ) ) ) ) ) ).
fof(d1_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> k1_setwop_2(A,B,C) = k4_finsop_1(A,k3_finsop_1(A,k5_numbers,C),B) ) ) ) ).
fof(t22_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_finseq_1(D,A)
=> ( ( r2_hidden(C,k5_finsop_1(D))
=> k8_funct_2(k5_numbers,A,k1_setwop_2(A,D,B),C) = k1_funct_1(D,C) )
& ( ~ r2_hidden(C,k5_finsop_1(D))
=> k8_funct_2(k5_numbers,A,k1_setwop_2(A,D,B),C) = B ) ) ) ) ) ) ).
fof(t23_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m2_finseq_1(C,A)
=> k2_partfun1(k5_numbers,A,k1_setwop_2(A,C,B),k5_finsop_1(C)) = C ) ) ) ).
fof(t24_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m2_finseq_1(C,A)
=> ! [D] :
( m2_finseq_1(D,A)
=> k2_partfun1(k5_numbers,A,k1_setwop_2(A,k8_finseq_1(A,C,D),B),k5_finsop_1(C)) = C ) ) ) ) ).
fof(t25_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m2_finseq_1(C,A)
=> k2_relat_1(k1_setwop_2(A,C,B)) = k2_xboole_0(k2_relat_1(C),k2_setwiseo(A,B)) ) ) ) ).
fof(t26_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,B)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,A)
& m2_relset_1(D,B,A) )
=> ! [E] :
( m2_finseq_1(E,B)
=> k7_funct_2(k5_numbers,B,A,k1_setwop_2(B,E,C),D) = k1_setwop_2(A,k5_finseqop(B,A,E,D),k8_funct_2(B,A,D,C)) ) ) ) ) ) ).
fof(d2_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ( ( v2_binop_1(C,A)
& v1_binop_1(C,A) )
=> ( ( ~ v1_setwiseo(C,A)
& ~ r1_xreal_0(np__1,k3_finseq_1(B)) )
| k2_finsop_1(A,B,C) = k7_setwiseo(k5_numbers,A,C,k3_setwop_2(B),k1_setwop_2(A,B,k3_binop_1(A,C))) ) ) ) ) ) ).
fof(t27_setwop_2,axiom,
$true ).
fof(t28_setwop_2,axiom,
$true ).
fof(t29_setwop_2,axiom,
$true ).
fof(t30_setwop_2,axiom,
$true ).
fof(t31_setwop_2,axiom,
$true ).
fof(t32_setwop_2,axiom,
$true ).
fof(t33_setwop_2,axiom,
$true ).
fof(t34_setwop_2,axiom,
$true ).
fof(t35_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m2_relset_1(B,k2_zfmisc_1(A,A),A) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( v1_setwiseo(B,A)
=> k2_finsop_1(A,k1_finsop_1(A,C,k3_binop_1(A,B)),B) = k3_binop_1(A,B) ) ) ) ) ).
fof(t36_setwop_2,axiom,
$true ).
fof(t37_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( v2_binop_1(C,A)
=> ( ( ~ ( r1_xreal_0(np__1,D)
& r1_xreal_0(np__1,E) )
& ~ v1_setwiseo(C,A) )
| k2_finsop_1(A,k1_finsop_1(A,k1_nat_1(D,E),B),C) = k2_binop_1(A,A,A,C,k2_finsop_1(A,k1_finsop_1(A,D,B),C),k2_finsop_1(A,k1_finsop_1(A,E,B),C)) ) ) ) ) ) ) ) ).
fof(t38_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( v1_binop_1(C,A)
& v2_binop_1(C,A) )
=> ( ( ~ ( r1_xreal_0(np__1,D)
& r1_xreal_0(np__1,E) )
& ~ v1_setwiseo(C,A) )
| k2_finsop_1(A,k1_finsop_1(A,k2_nat_1(D,E),B),C) = k2_finsop_1(A,k1_finsop_1(A,E,k2_finsop_1(A,k1_finsop_1(A,D,B),C)),C) ) ) ) ) ) ) ) ).
fof(t39_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& m2_relset_1(C,k2_zfmisc_1(B,B),B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,B,A)
& m2_relset_1(E,B,A) )
=> ! [F] :
( m2_finseq_1(F,B)
=> ( ( v1_setwiseo(C,B)
& v1_setwiseo(D,A)
& k8_funct_2(B,A,E,k3_binop_1(B,C)) = k3_binop_1(A,D)
& ! [G] :
( m1_subset_1(G,B)
=> ! [H] :
( m1_subset_1(H,B)
=> k8_funct_2(B,A,E,k2_binop_1(B,B,B,C,G,H)) = k2_binop_1(A,A,A,D,k8_funct_2(B,A,E,G),k8_funct_2(B,A,E,H)) ) ) )
=> k8_funct_2(B,A,E,k2_finsop_1(B,F,C)) = k2_finsop_1(A,k5_finseqop(B,A,F,E),D) ) ) ) ) ) ) ) ).
fof(t40_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m2_relset_1(B,k2_zfmisc_1(A,A),A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,A)
& m2_relset_1(C,A,A) )
=> ! [D] :
( m2_finseq_1(D,A)
=> ( ( v1_setwiseo(B,A)
& k8_funct_2(A,A,C,k3_binop_1(A,B)) = k3_binop_1(A,B)
& r7_binop_1(A,C,B) )
=> k8_funct_2(A,A,C,k2_finsop_1(A,D,B)) = k2_finsop_1(A,k5_finseqop(A,A,D,C),B) ) ) ) ) ) ).
fof(t41_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ! [E] :
( m2_finseq_1(E,A)
=> ( ( v2_binop_1(C,A)
& v1_setwiseo(C,A)
& v1_finseqop(C,A)
& r6_binop_1(A,D,C) )
=> k8_funct_2(A,A,k8_funcop_1(A,A,D,B,k6_partfun1(A)),k2_finsop_1(A,E,C)) = k2_finsop_1(A,k5_finseqop(A,A,E,k8_funcop_1(A,A,D,B,k6_partfun1(A))),C) ) ) ) ) ) ) ).
fof(t42_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m2_relset_1(B,k2_zfmisc_1(A,A),A) )
=> ! [C] :
( m2_finseq_1(C,A)
=> ( ( v1_binop_1(B,A)
& v2_binop_1(B,A)
& v1_setwiseo(B,A)
& v1_finseqop(B,A) )
=> k8_funct_2(A,A,k6_finseqop(A,B),k2_finsop_1(A,C,B)) = k2_finsop_1(A,k5_finseqop(A,A,C,k6_finseqop(A,B)),B) ) ) ) ) ).
fof(t43_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ! [E] :
( m2_finseq_1(E,A)
=> ! [F] :
( m2_finseq_1(F,A)
=> ( ( v1_binop_1(C,A)
& v2_binop_1(C,A)
& v1_setwiseo(C,A)
& B = k3_binop_1(A,C)
& k2_binop_1(A,A,A,D,B,B) = B
& ! [G] :
( m1_subset_1(G,A)
=> ! [H] :
( m1_subset_1(H,A)
=> ! [I] :
( m1_subset_1(I,A)
=> ! [J] :
( m1_subset_1(J,A)
=> k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,D,G,H),k2_binop_1(A,A,A,D,I,J)) = k2_binop_1(A,A,A,D,k2_binop_1(A,A,A,C,G,I),k2_binop_1(A,A,A,C,H,J)) ) ) ) )
& k3_finseq_1(E) = k3_finseq_1(F) )
=> k2_binop_1(A,A,A,D,k2_finsop_1(A,E,C),k2_finsop_1(A,F,C)) = k2_finsop_1(A,k1_finseqop(A,A,A,D,E,F),C) ) ) ) ) ) ) ) ).
fof(t44_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_finseq_2(F,A,k4_finseq_2(E,A))
=> ! [G] :
( m2_finseq_2(G,A,k4_finseq_2(E,A))
=> ( ( v1_binop_1(C,A)
& v2_binop_1(C,A)
& v1_setwiseo(C,A)
& B = k3_binop_1(A,C)
& k2_binop_1(A,A,A,D,B,B) = B
& ! [H] :
( m1_subset_1(H,A)
=> ! [I] :
( m1_subset_1(I,A)
=> ! [J] :
( m1_subset_1(J,A)
=> ! [K] :
( m1_subset_1(K,A)
=> k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,D,H,I),k2_binop_1(A,A,A,D,J,K)) = k2_binop_1(A,A,A,D,k2_binop_1(A,A,A,C,H,J),k2_binop_1(A,A,A,C,I,K)) ) ) ) ) )
=> k2_binop_1(A,A,A,D,k2_finsop_1(A,F,C),k2_finsop_1(A,G,C)) = k2_finsop_1(A,k1_finseqop(A,A,A,D,F,G),C) ) ) ) ) ) ) ) ) ).
fof(t45_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m2_relset_1(B,k2_zfmisc_1(A,A),A) )
=> ! [C] :
( m2_finseq_1(C,A)
=> ! [D] :
( m2_finseq_1(D,A)
=> ( ( v1_binop_1(B,A)
& v2_binop_1(B,A)
& v1_setwiseo(B,A)
& k3_finseq_1(C) = k3_finseq_1(D) )
=> k2_binop_1(A,A,A,B,k2_finsop_1(A,C,B),k2_finsop_1(A,D,B)) = k2_finsop_1(A,k1_finseqop(A,A,A,B,C,D),B) ) ) ) ) ) ).
fof(t46_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m2_relset_1(B,k2_zfmisc_1(A,A),A) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_finseq_2(D,A,k4_finseq_2(C,A))
=> ! [E] :
( m2_finseq_2(E,A,k4_finseq_2(C,A))
=> ( ( v1_binop_1(B,A)
& v2_binop_1(B,A)
& v1_setwiseo(B,A) )
=> k2_binop_1(A,A,A,B,k2_finsop_1(A,D,B),k2_finsop_1(A,E,B)) = k2_finsop_1(A,k1_finseqop(A,A,A,B,D,E),B) ) ) ) ) ) ) ).
fof(t47_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( v1_binop_1(D,A)
& v2_binop_1(D,A)
& v1_setwiseo(D,A) )
=> k2_finsop_1(A,k1_finsop_1(A,E,k2_binop_1(A,A,A,D,B,C)),D) = k2_binop_1(A,A,A,D,k2_finsop_1(A,k1_finsop_1(A,E,B),D),k2_finsop_1(A,k1_finsop_1(A,E,C),D)) ) ) ) ) ) ) ).
fof(t48_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m2_relset_1(B,k2_zfmisc_1(A,A),A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_finseq_2(E,A,k4_finseq_2(D,A))
=> ! [F] :
( m2_finseq_2(F,A,k4_finseq_2(D,A))
=> ( ( v1_binop_1(B,A)
& v2_binop_1(B,A)
& v1_setwiseo(B,A)
& v1_finseqop(B,A)
& C = k8_finseqop(A,B,k6_partfun1(A),k6_finseqop(A,B)) )
=> k2_binop_1(A,A,A,C,k2_finsop_1(A,E,B),k2_finsop_1(A,F,B)) = k2_finsop_1(A,k1_finseqop(A,A,A,C,E,F),B) ) ) ) ) ) ) ) ).
fof(t49_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(A,A),A)
& m2_relset_1(E,k2_zfmisc_1(A,A),A) )
=> ! [F] :
( m2_finseq_1(F,A)
=> ( ( v1_binop_1(D,A)
& v2_binop_1(D,A)
& v1_setwiseo(D,A)
& B = k3_binop_1(A,D)
& r6_binop_1(A,E,D)
& k2_binop_1(A,A,A,E,C,B) = B )
=> k2_binop_1(A,A,A,E,C,k2_finsop_1(A,F,D)) = k2_finsop_1(A,k3_finseqop(A,A,A,E,C,F),D) ) ) ) ) ) ) ) ).
fof(t50_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(A,A),A)
& m2_relset_1(E,k2_zfmisc_1(A,A),A) )
=> ! [F] :
( m2_finseq_1(F,A)
=> ( ( v1_binop_1(D,A)
& v2_binop_1(D,A)
& v1_setwiseo(D,A)
& B = k3_binop_1(A,D)
& r6_binop_1(A,E,D)
& k2_binop_1(A,A,A,E,B,C) = B )
=> k2_binop_1(A,A,A,E,k2_finsop_1(A,F,D),C) = k2_finsop_1(A,k2_finseqop(A,A,A,E,F,C),D) ) ) ) ) ) ) ) ).
fof(t51_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ! [E] :
( m2_finseq_1(E,A)
=> ( ( v1_binop_1(C,A)
& v2_binop_1(C,A)
& v1_setwiseo(C,A)
& v1_finseqop(C,A)
& r6_binop_1(A,D,C) )
=> k2_binop_1(A,A,A,D,B,k2_finsop_1(A,E,C)) = k2_finsop_1(A,k3_finseqop(A,A,A,D,B,E),C) ) ) ) ) ) ) ).
fof(t52_setwop_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m2_relset_1(C,k2_zfmisc_1(A,A),A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,A),A)
& m2_relset_1(D,k2_zfmisc_1(A,A),A) )
=> ! [E] :
( m2_finseq_1(E,A)
=> ( ( v1_binop_1(C,A)
& v2_binop_1(C,A)
& v1_setwiseo(C,A)
& v1_finseqop(C,A)
& r6_binop_1(A,D,C) )
=> k2_binop_1(A,A,A,D,k2_finsop_1(A,E,C),B) = k2_finsop_1(A,k2_finseqop(A,A,A,D,E,B),C) ) ) ) ) ) ) ).
fof(dt_k1_setwop_2,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(B,A)
& m1_subset_1(C,A) )
=> ( v1_funct_1(k1_setwop_2(A,B,C))
& v1_funct_2(k1_setwop_2(A,B,C),k5_numbers,A)
& m2_relset_1(k1_setwop_2(A,B,C),k5_numbers,A) ) ) ).
fof(dt_k2_setwop_2,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> m1_subset_1(k2_setwop_2(A),k5_finsub_1(k5_numbers)) ) ).
fof(redefinition_k2_setwop_2,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> k2_setwop_2(A) = k1_finseq_1(A) ) ).
fof(dt_k3_setwop_2,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> m1_subset_1(k3_setwop_2(A),k5_finsub_1(k5_numbers)) ) ).
fof(redefinition_k3_setwop_2,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> k3_setwop_2(A) = k1_relat_1(A) ) ).
%------------------------------------------------------------------------------