reserve x,y,y1,y2 for object;
reserve R for Ring;
reserve a for Scalar of R;
reserve V,X,Y for RightMod of R;
reserve u,u1,u2,v,v1,v2 for Vector of V;
reserve V1,V2,V3 for Subset of V;
reserve W,W1,W2 for Submodule of V;
reserve w,w1,w2 for Vector of W;

theorem
  x in W1 & W1 is Submodule of W2 implies x in W2
proof
  assume x in W1 & W1 is Submodule of W2;
  then x in the carrier of W1 & the carrier of W1 c= the carrier of W2 by Def2;
  hence thesis;
end;
