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 Th36:
  (0).W = (0).V
proof
  the carrier of (0).W = {0.W} & the carrier of (0).V = {0.V} by Def3;
  then
A1: the carrier of (0).W = the carrier of (0).V by Def2;
  (0).W is Submodule of V by Th26;
  hence thesis by A1,Th29;
end;
