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
  W1 is Submodule of W2 implies W2 /\ (W1 + W3) = (W1 /\ W2) + (W2 /\ W3
  ) by Lm11,RMOD_2:29;
