theorem
 for f being Function, x,y being object st x <> y
 holds f+~(x,y)+~(x,z) = f+~(x,y)
proof let f be Function,x,y be object;
 assume x <> y;
  then not x in rng(f+~(x,y)) by Th100;
 hence f+~(x,y)+~(x,z) = f+~(x,y) by Th103;
end;
