
theorem Th5:
  for F being Field for V,W being VectSp of F holds (Omega).W is
  Subspace of V implies W is Subspace of V
proof
  let F be Field;
  let V,W be VectSp of F;
  assume
A1: (Omega).W is Subspace of V;
  hence the carrier of W c= the carrier of V by VECTSP_4:def 2;
  thus 0.W = 0.(Omega).W .= 0.V by A1,VECTSP_4:def 2;
  thus thesis by A1,VECTSP_4:def 2;
end;
