
theorem Th3:
  for V being RealUnitarySpace, W1,W2 being Subspace of V, x being
  object holds x in W1 /\ W2 iff x in W1 & x in W2
proof
  let V be RealUnitarySpace;
  let W1,W2 be Subspace of V;
  let x be object;
  x in W1 /\ W2 iff x in the carrier of W1 /\ W2 by STRUCT_0:def 5;
  then x in W1 /\ W2 iff x in (the carrier of W1) /\ (the carrier of W2) by
Def2;
  then x in W1 /\ W2 iff x in the carrier of W1 & x in the carrier of W2 by
XBOOLE_0:def 4;
  hence thesis by STRUCT_0:def 5;
end;
