theorem Th15:
  W1 /\ W2 is Subspace of W1 & W1 /\ W2 is Subspace of W2
proof
  the carrier of W1 /\ W2 c= the carrier of W1 by Lm7;
  hence W1 /\ W2 is Subspace of W1 by VECTSP_4:27;
  the carrier of W2 /\ W1 c= the carrier of W2 by Lm7;
  hence thesis by VECTSP_4:27;
end;
