Definition at_least_left (o:option elt)(o':option elt') :=
  match o with
   | None => None
   | _  => Some (o,o')
  end.Definition at_least_right (o:option elt)(o':option elt') :=
  match o' with
   | None => None
   | _  => Some (o,o')
  end.

(* Specifications: *)
Lemma combine_l_1 : forall m (Hm:NoDupA (@eqk elt) m) m' (Hm':NoDupA (@eqk elt') m')(x:key), find x (combine_l m m') = at_least_left (find x m) (find x m').
Lemma combine_r_1 : forall m (Hm:NoDupA (@eqk elt) m) m' (Hm':NoDupA (@eqk elt') m')(x:key), find x (combine_r m m') = at_least_right (find x m) (find x m').