(** ** Cardinal and (non-)emptiness *)

(* Specifications: *)
Lemma cardinal_Empty : forall s, Empty s <-> cardinal s = 0.
Lemma cardinal_inv_1 : forall s, cardinal s = 0 -> Empty s.
#[global]
Hint Resolve cardinal_inv_1 : fset.
Lemma cardinal_inv_2 :
forall s n, cardinal s = S n -> { x : elt | In x s }.
Lemma cardinal_inv_2b :
forall s, cardinal s <> 0 -> { x : elt | In x s }.
Lemma cardinal_Empty : forall s, Empty s <-> cardinal s = 0.
Lemma cardinal_inv_1 : forall s, cardinal s = 0 -> Empty s.
#[global]
Hint Resolve cardinal_inv_1 : core.
Lemma cardinal_inv_2 :
forall s n, cardinal s = S n -> { x : elt | In x s }.
Lemma cardinal_inv_2b :
forall s, cardinal s <> 0 -> { x : elt | In x s }.