reserve S for non empty non void ManySortedSign,
  A for MSAlgebra over S;
reserve A for non-empty MSAlgebra over S;

theorem Th16:
  for s being SortSymbol of S holds id ((the Sorts of A).s) is
  Translation of A,s,s
proof
  let s be SortSymbol of S;
  thus TranslationRel S reduces s,s by REWRITE1:12;
A1: <*s*> is RedSequence of TranslationRel S by REWRITE1:6;
A2: len <*s*> = 0+1 by FINSEQ_1:40;
A3: len {} = 0;
A4: for i being (Element of NAT), f being Function, s1,s2 being SortSymbol
  of S st i in dom {} & f = {}.i & s1 = <*s*>.i & s2 = <*s*>.(i+1) holds f
  is_e.translation_of A,s1,s2;
A5: <*s*>.1 = s;
  id ((the Sorts of A).s) = compose({}, (the Sorts of A).s) by FUNCT_7:39;
  hence thesis by A1,A2,A3,A5,A4;
end;
