 reserve x,y,z,t for object,X,Y,Z,W for set;
 reserve R,S,T for Relation;

theorem
  (S * R = S & R * (R \ id dom R) = {} & R * S = R &
    S * (S \ id dom S) = {} implies CL S = CL R) &
  (R * S = S & (R \ id dom R) * R = {} & S * R = R &
    (S \ id dom S) * S = {} implies CL S = CL R)
by Th39;
