Module Import MX := OrderedTypeFacts X.Module Import PX := KeyOrderedType X.Definition key := X.t.Definition t (elt:Type) := list (X.t * elt).Notation eqk := (eqk (elt:=elt)).Notation eqke := (eqke (elt:=elt)).Notation ltk := (ltk (elt:=elt)).Notation MapsTo := (MapsTo (elt:=elt)).Notation In := (In (elt:=elt)).Notation Sort := (sort ltk).Notation Inf := (lelistA (ltk)).(** * [empty] *)

Definition empty : t elt := nil.Definition Empty m := forall (a : key)(e:elt) , ~ MapsTo a e m.

(* Specifications: *)
Lemma empty_1 : Empty empty.
Lemma empty_sorted : Sort empty.