reserve V,W for Z_Module;
reserve T for linear-transformation of V,W;

theorem
  for X being Subset of V st V is Submodule of W holds X is Subset of W
  proof
    let X be Subset of V;
    assume V is Submodule of W; then
    A1: [#]V c= [#]W by VECTSP_4:def 2;
    X c= [#]W by A1;
    hence thesis;
  end;
