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

theorem
  (R c= R * R & R * (R \ id rng R) = {} implies R /\ (id rng R) = id rng R) &
  (R c= R * R & (R \ id dom R) * R = {} implies
    R /\ (id dom R) = id dom R) by Th22,XBOOLE_1:28;
