#[local]
Hint Resolve cardinal_inv_1 : map.

(* Specifications: *)
Lemma cardinal_inv_2 :
forall m n, cardinal m = S n -> { p : key*elt | MapsTo (fst p) (snd p) m }.
Lemma cardinal_inv_2b :
forall m, cardinal m <> 0 -> { p : key*elt | MapsTo (fst p) (snd p) m }.