reserve R for Ring,
  V for RightMod of R,
  W,W1,W2,W3 for Submodule of V,
  u,u1, u2,v,v1,v2 for Vector of V,
  x,y,y1,y2 for object;

theorem Th9:
  for W being strict Submodule of V holds (0).V + W = W & W + (0). V = W
proof
  let W be strict Submodule of V;
  (0).V is Submodule of W by RMOD_2:39;
  then the carrier of (0).V c= the carrier of W by RMOD_2:def 2;
  hence (0).V + W = W by Lm3;
  hence thesis by Lm1;
end;
