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
  for X being set, f,g being Relation st dom g c= X & g c= f holds g c= f|X
proof
  let X be set, f,g be Relation;
  assume dom g c= X & g c= f;
  then g|dom g c= f|X by Th71;
  hence thesis;
end;
