
theorem
  for S,S9 being non empty non void ManySortedSign for f being Function
  of the carrier of S9, the carrier of S for g being Function st f,g
  form_morphism_between S9,S for s1,s2 being SortSymbol of S9 st TranslationRel
  S9 reduces s1,s2 holds TranslationRel S reduces f.s1, f.s2
proof
  let S,S9 be non empty non void ManySortedSign;
  set A = the non-empty MSAlgebra over S;
  let f be Function of the carrier of S9, the carrier of S;
  let g be Function;
  assume
A1: f,g form_morphism_between S9,S;
  then A|(S9,f,g) is non-empty MSAlgebra over S9 by Th22;
  hence thesis by A1,Lm1;
end;
