 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 Th13:
  for X, Y being complex-membered set
  holds X c= Y implies addRel(X,z) c= addRel(Y,z)
proof
  let X, Y be complex-membered set;
  assume A1: X c= Y;
  now
    let x,y be object;
    reconsider a=x,b=y as set by TARSKI:1;
    assume A2: [x,y] in addRel(X,z);
    then [a,b] in addRel(X,z);
    then a in X & b in X by MMLQUER2:4;
    then reconsider a,b as Complex;
    [a,b] in addRel(X,z) by A2;
    then a in X & b in X & b = z + a by Th11;
    hence [x,y] in addRel(Y,z) by A1, Th11;
  end;
  hence thesis by RELAT_1:def 3;
end;
