reserve S,S9 for non void Signature,
  f,g for Function;

theorem Th36:
  f,g form_a_replacement_in S implies (the carrier of S)-indexing
  f is Function of the carrier of S, the carrier of S with-replacement (f,g)
proof
  assume f,g form_a_replacement_in S;
  then (the carrier of S)-indexing f, (the carrier' of S)-indexing g
  form_morphism_between S, S with-replacement (f,g) by Def4;
  hence thesis by INSTALG1:9;
end;
