
theorem
  for S being feasible ManySortedSign, S9 being Subsignature of S for T
being ManySortedSign, f,g being Function st f,g form_morphism_between S,T holds
  f|the carrier of S9, g|the carrier' of S9 form_morphism_between S9,T
proof
  let S be feasible ManySortedSign, S9 be Subsignature of S;
  let T be ManySortedSign, f,g be Function;
A1: g|the carrier' of S9 = g*id the carrier' of S9 by RELAT_1:65;
  id the carrier of S9, id the carrier' of S9 form_morphism_between S9,S &
  f| the carrier of S9 = f*id the carrier of S9 by Def2,RELAT_1:65;
  hence thesis by A1,PUA2MSS1:29;
end;
