End AssortedListProperties.
(* ********************************************************************* *)
(** ** Properties of [map] and [dom] *)
(** The following lemmas are used mainly to simplify applications of [map] and [dom] to association lists.  See also the [simpl_alist] and [rewrite_alist] tactics below. *)
Section Properties.
Variables A B : Set.
Variables f1 : A -> A.
Variables f2 : B -> B.
Variables x : atom.
Variables b : A.
Variables a : B.
Variables E F G : list (asn A B).

Lemma uniq_map :
uniq (map f1 f2 E) <-> uniq E.