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
  for V being strict RealLinearSpace holds V in Subspaces(V)
proof
  let V be strict RealLinearSpace;
  (Omega).V in Subspaces(V) by Def3;
  hence thesis;
end;
