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 W1 is Submodule of W2 + W3
proof
  assume
A1: W1 is Submodule of W2;
  W2 is Submodule of W2 + W3 by Th7;
  hence thesis by A1,RMOD_2:26;
end;
