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;
reserve A1,A2,B for Element of Submodules(V);

theorem
  for V being RightMod of R holds LattStr (# Submodules(V), SubJoin(V),
    SubMeet(V) #) is 01_Lattice
proof
  let V be RightMod of R;
  LattStr (# Submodules(V), SubJoin(V), SubMeet(V) #) is lower-bounded
  upper-bounded Lattice by Th48,Th49;
  hence thesis;
end;
