
theorem Th29:
  for V being RealUnitarySpace, W1,W2,W3 being Subspace of V st W1
  is strict Subspace of W3 holds W1 + (W2 /\ W3) = (W1 + W2) /\ W3
proof
  let V be RealUnitarySpace;
  let W1,W2,W3 be Subspace of V;
  assume
A1: W1 is strict Subspace of W3;
  thus (W1 + W2) /\ W3 = W3 /\ (W1 + W2) by Th14
    .= (W1 /\ W3) + (W3 /\ W2) by A1,Lm9,RUSUB_1:24
    .= W1 + (W3 /\ W2) by A1,Th17
    .= W1 + (W2 /\ W3) by Th14;
end;
