
theorem Th20:
  for V being RealUnitarySpace, W being strict Subspace of V holds
  (Omega).V /\ W = W & W /\ (Omega).V = W
proof
  let V be RealUnitarySpace;
  let W be strict Subspace of V;
  (Omega).V = the UNITSTR of V by RUSUB_1:def 3;
  then
A1: the carrier of (Omega).V /\ W = (the carrier of V) /\ (the carrier of W
  ) by Def2;
  the carrier of W c= the carrier of V by RUSUB_1:def 1;
  hence (Omega).V /\ W = W by A1,RUSUB_1:24,XBOOLE_1:28;
  hence thesis by Th14;
end;
