reserve X,Y for set, x,y,z for object, i,j,n for natural number;

theorem Th2:
  for I,J being set for f being ManySortedSet of I
  for g being ManySortedSet of J holds g is f-tolerating iff
  for x st x in I & x in J holds f.x = g.x
  proof
    let I,J be set; let f be ManySortedSet of I;
    let g be ManySortedSet of J;
    dom f = I & dom g = J by PARTFUN1:def 2;
    hence thesis by Th1;
  end;
