theorem Th18:
  for a being FinSequence of INT.Ring
  st len a = len b2 & g is additive homogeneous holds
  g.Sum(lmlt(a,b2)) = Sum(lmlt(a,g*b2))
  proof
    let a be FinSequence of INT.Ring such that
    A1: len a = len b2 and
    A2: g is additive homogeneous;
    thus g.Sum(lmlt(a,b2)) = Sum(g*lmlt(a,b2)) by A2,Th16
    .= Sum(lmlt(a,g*b2)) by A1,A2,Th17;
  end;
