 reserve X, Y for set, A for Ordinal;
 reserve z,z1,z2 for Complex;
 reserve r,r1,r2 for Real;
 reserve q,q1,q2 for Rational;
 reserve i,i1,i2 for Integer;
 reserve n,n1,n2 for Nat;

theorem
  multRel(NAT,n1) * multRel(NAT,n2) = multRel(NAT,n1*n2)
proof
  A1: multRel(NAT,n1) * multRel(NAT,n2) c= multRel(NAT,n1*n2) by Th51;
  now
    let x,y be object;
    reconsider a=x,b=y as set by TARSKI:1;
    assume A2: [x,y] in multRel(NAT,n1*n2);
    then [a,b] in multRel(NAT,n1*n2);
    then A3: a in NAT & b in NAT by MMLQUER2:4;
    then reconsider a,b as Nat;
    A4: b = n1 * n2 * a by A2, Th42;
    set c = n1 * a;
    c in NAT & b = n2 * c by A4, ORDINAL1:def 12;
    then [a,c] in multRel(NAT,n1) & [c,b] in multRel(NAT,n2) by A3, Th42;
    hence [x,y] in multRel(NAT,n1) * multRel(NAT,n2) by RELAT_1:def 8;
  end;
  then multRel(NAT,n1*n2) c= multRel(NAT,n1) * multRel(NAT,n2)
    by RELAT_1:def 3;
  hence thesis by A1, XBOOLE_0:def 10;
end;
