reserve n,k,b for Nat, i for Integer;

theorem Th5:
  for X,Y being finite natural-membered set
  holds rng (Sgm0(X)^Sgm0(Y)) = rng Sgm0(X\/Y)
  proof
    let X,Y be finite natural-membered set;
    thus rng (Sgm0(X)^Sgm0(Y)) = rng Sgm0(X) \/ rng Sgm0(Y) by AFINSQ_1:26
    .= X \/ rng Sgm0(Y) by AFINSQ_2:def 4
    .= X \/ Y by AFINSQ_2:def 4
    .= rng Sgm0(X\/Y) by AFINSQ_2:def 4;
  end;
