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

theorem
  (R * R = R & R * (R \ id dom R) = {} & [x,y] in R & x <> y implies
    x in ((dom R) \ dom CL R) & y in dom CL R) &
  (R * R = R & (R \ id dom R) * R = {} & [x,y] in R & x <> y implies
    y in ((rng R) \ dom CL R) & x in dom CL R)
proof
  R \ CL R = R \ id dom R by XBOOLE_1:47;
  hence thesis by Th29;
end;
