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

theorem Th11:
  for S being non empty non void ManySortedSign, s1,s2 being
  SortSymbol of S for A being feasible MSAlgebra over S, f being Function st f
  is_e.translation_of A,s1,s2 holds f is Function of (the Sorts of A).s1, (the
  Sorts of A).s2 & (the Sorts of A).s1 <> {} & (the Sorts of A).s2 <> {}
proof
  let S be non empty non void ManySortedSign, s1,s2 be SortSymbol of S;
  let A be feasible MSAlgebra over S;
  let f be Function;
  assume f is_e.translation_of A,s1,s2;
  then consider o being OperSymbol of S such that
A1: the_result_sort_of o = s2 and
A2: ex i being Element of NAT st i in dom the_arity_of o & ((
the_arity_of o)/.i) = s1 & ex a being Function st a in Args(o,A) & f = transl(o
  ,i,a,A);
  Result(o,A) = (the Sorts of A).the_result_sort_of o by PRALG_2:3;
  hence thesis by A1,A2,Def1,Th3,Th10;
end;
