theorem Th21:
  for W being strict Subspace of M holds (Omega).M /\ W = W & W /\
  (Omega).M = W
proof
  let W be strict Subspace of M;
A1: the carrier of (Omega).M /\ W = (the carrier of the ModuleStr of M) /\ (
the carrier of W) & the carrier of W c= the carrier of M by Def2,VECTSP_4:def 2
  ;
  hence (Omega).M /\ W = W by VECTSP_4:29,XBOOLE_1:28;
  thus thesis by A1,VECTSP_4:29,XBOOLE_1:28;
end;
