(** * Emptyness *)

Definition empty (i: interv) : Prop := fst i >= snd i.

(* Specifications: *)
Lemma empty_dec: forall i, {empty i} + {~empty i}.
Lemma is_notempty: forall i, fst i < snd i -> ~empty i.
Lemma empty_notin: forall x i, empty i -> ~In x i.
Lemma in_notempty: forall x i, In x i -> ~empty i.