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 Th29:
  for W1,W2 being strict Submodule of V holds the carrier of W1 =
  the carrier of W2 implies W1 = W2
proof
  let W1,W2 be strict Submodule of V;
  assume the carrier of W1 = the carrier of W2;
  then W1 is Submodule of W2 & W2 is Submodule of W1 by Th27;
  hence thesis by Th25;
end;
