reserve A,X,X1,X2,Y,Y1,Y2 for set, a,b,c,d,x,y,z for object;
reserve P,P1,P2,Q,R,S for Relation;

theorem
  Y c= X implies (R|X)|Y = R|Y
proof
  Y c= X implies X /\ Y = Y by XBOOLE_1:28;
  hence thesis by Th65;
end;
