
theorem Th16:
  for X being non empty set, i, f being object
  holds f in product({i} --> X) iff ex x being Element of X st f = {i} --> x
proof
  let X be non empty set, i,f be object;
  hereby
    assume f in product({i} --> X);
    then f in {{i} --> x where x is Element of X : not contradiction} by Th15;
    hence ex x being Element of X st f = {i} --> x;
  end;
  assume ex x being Element of X st f = {i} --> x;
  then f in {{i} --> x where x is Element of X : not contradiction};
  hence thesis by Th15;
end;
