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;
reserve C1 for Coset of W1;
reserve C2 for Coset of W2;

theorem
  for V being strict RightMod of R, W1,W2 being Submodule of V holds W1
  + W2 = V iff for v being Vector of V ex v1,v2 being Vector of V st v1 in W1 &
  v2 in W2 & v = v1 + v2 by Lm14;
