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

theorem Th18:
  for f,g being XFinSequence of NAT, i being Integer st dom f = dom g &
  for n being object st n in dom f holds f.n=i*g.n holds Sum f = i * Sum g
  proof
    let f,g be XFinSequence of NAT, i be Integer;
    assume dom f = dom g &
    for n being object st n in dom f holds f.n=i*g.n;
    then f=i(#)g by VALUED_1:def 5;
    hence Sum f = i * Sum g by AFINSQ_2:64;
  end;
