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

theorem Th74:
  for f being PartFunc of X,Y for g being Function of X,Y st Y =
  {} implies X = {} holds f tolerates g iff
   for x being object st x in dom f holds f.x = g.x
proof
  let f be PartFunc of X,Y;
  let g be Function of X,Y;
  assume Y = {} implies X = {};
  then dom g = X by Def1;
  hence thesis by PARTFUN1:53;
end;
