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

theorem Th46:
  for S1 being Signature, S2 being Extension of S1, S3 being
  Extension of S2 holds S3 is Extension of S1
proof
  let S1 be Signature, S2 be Extension of S1, S3 be Extension of S2;
A1: S2 is Subsignature of S3 by Def5;
  S1 is Subsignature of S2 by Def5;
  then S1 is Subsignature of S3 by A1,INSTALG1:16;
  hence thesis by Def5;
end;
