
theorem
  for S being ManySortedSign, T being feasible ManySortedSign for T9
  being Subsignature of T, f,g being Function st f,g form_morphism_between S,T9
  holds f,g form_morphism_between S,T
proof
  let S be ManySortedSign, T be feasible ManySortedSign;
  let T9 be Subsignature of T, f,g be Function such that
A1: f,g form_morphism_between S,T9;
  rng f c= the carrier of T9 by A1;
  then
A2: (id the carrier of T9)*f = f by RELAT_1:53;
  rng g c= the carrier' of T9 by A1;
  then
A3: (id the carrier' of T9)*g = g by RELAT_1:53;
  id the carrier of T9, id the carrier' of T9 form_morphism_between T9,T
  by Def2;
  hence thesis by A1,A2,A3,PUA2MSS1:29;
end;
