theorem Th11:
  (Omega).M + W = the ModuleStr of M & W + (Omega).M = the ModuleStr of M
proof
  consider W9 being strict Subspace of M such that
A1: the carrier of W9 = the carrier of (Omega).M;
A2: the carrier of W c= the carrier of W9 by A1,VECTSP_4:def 2;
A3: W9 is Subspace of (Omega).M by Lm6;
  W + (Omega).M = W + W9 by A1,Lm5
    .= W9 by A2,Lm3
    .= the ModuleStr of M by A1,A3,VECTSP_4:31;
  hence thesis by Lm1;
end;
