reserve S for non empty non void ManySortedSign;
reserve X for non-empty ManySortedSet of S;
reserve x,y,z for set, i,j for Nat;

theorem
  for A1,A2 being MSAlgebra over S st A2 is empty
  for h being ManySortedFunction of A1,A2
  holds h is_homomorphism A1,A2
  proof
    let A1,A2 be MSAlgebra over S such that
A1: the Sorts of A2 is empty-yielding;
    let h be ManySortedFunction of A1,A2;
    let o be OperSymbol of S;
    assume Args(o,A1) <> {};
    let x be Element of Args(o,A1);
    (the Sorts of A2).the_result_sort_of o = {} by A1; then
A2: Result(o,A2) = {} by PRALG_2:3;
    thus (h.(the_result_sort_of o)).(Den(o,A1).x) = {} by A1
    .= Den(o,A2).(h#x) by A2;
  end;
