
theorem Th16:
  for V being RealUnitarySpace, W1,W2 being Subspace of V holds W1
  /\ W2 is Subspace of W1 & W1 /\ W2 is Subspace of W2
proof
  let V be RealUnitarySpace;
  let W1,W2 be Subspace of V;
  the carrier of W1 /\ W2 c= the carrier of W1 by Lm4;
  hence W1 /\ W2 is Subspace of W1 by RUSUB_1:22;
  the carrier of W2 /\ W1 c= the carrier of W2 by Lm4;
  then the carrier of W1 /\ W2 c= the carrier of W2 by Th14;
  hence thesis by RUSUB_1:22;
end;
