theorem Th30:
  for W1 being strict Subspace of M holds W1 is Subspace of W3
  implies W1 + (W2 /\ W3) = (W1 + W2) /\ W3
proof
  let W1 be strict Subspace of M;
  assume
A1: W1 is Subspace of W3;
  hence (W1 + W2) /\ W3 = (W1 /\ W3) + (W3 /\ W2) by Lm13,VECTSP_4:29
    .= W1 + (W2 /\ W3) by A1,Th16;
end;
