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

theorem
  g is one-to-one & rng g misses the carrier' of S implies f,g
  form_a_replacement_in S
proof
  assume
A1: g is one-to-one;
  assume rng g misses the carrier' of S;
  then (the carrier' of S) /\ rng g = {};
  then (the carrier' of S) /\ rng g c= dom g;
  hence thesis by A1,Th33;
end;
