theorem Th22:
  for W being strict Submodule of V holds (Omega).V /\ W = W & W
  /\ (Omega).V = W
proof
  let W be strict Submodule of V;
  the carrier of (Omega).V /\ W = (the carrier of V) /\ (the carrier of W)
  & the carrier of W c= the carrier of V by Def2,RMOD_2:def 2;
  hence (Omega).V /\ W = W by RMOD_2:29,XBOOLE_1:28;
  hence thesis by Th14;
end;
