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
  for W1,W2 being strict Submodule of V holds W1 + W2 = W2 iff W1 /\ W2 = W1
proof
  let W1,W2 be strict Submodule of V;
  W1 + W2 = W2 iff W1 is Submodule of W2 by Th8;
  hence thesis by Th17;
end;
