reserve V for RealLinearSpace;
reserve W,W1,W2,W3 for Subspace of V;
reserve u,u1,u2,v,v1,v2 for VECTOR of V;
reserve a,a1,a2 for Real;
reserve X,Y,x,y,y1,y2 for set;

theorem Th9:
  for W being strict Subspace of V holds (0).V + W = W & W + (0).V = W
proof
  let W be strict Subspace of V;
  (0).V is Subspace of W by RLSUB_1:39;
  then the carrier of (0).V c= the carrier of W by RLSUB_1:def 2;
  hence (0).V + W = W by Lm3;
  hence thesis by Lm1;
end;
