reserve P,Q,X,Y,Z for set, p,x,x9,x1,x2,y,z for object;
reserve D for non empty set;

theorem
  for f,g being PartFunc of X,Y st (Y = {} implies X = {}) & f tolerates
  g ex h being Function of X,Y st f tolerates h & g tolerates h
proof
  let f,g be PartFunc of X,Y;
  assume ( Y = {} implies X = {})& f tolerates g;
  then
  ex h being PartFunc of X,Y st h is total & f tolerates h & g tolerates h
  by PARTFUN1:68;
  hence thesis;
end;
