reserve P for non empty Poset,
  i, j, k for Element of P;
reserve S for non void non empty ManySortedSign;
reserve OAF for OrderedAlgFam of P, S;
reserve B for Binding of OAF;
reserve x for set,
  A for non empty set;

theorem
  for S be void ManySortedSign holds id the carrier of S, id the
  carrier' of S form_morphism_between S,S
proof
  let S be void ManySortedSign;
  per cases;
  suppose
    S is empty;
    hence thesis by Lm1;
  end;
  suppose
    S is non empty;
    hence thesis by Lm2;
  end;
end;
