End ListProperties.
(* *********************************************************************** *)
(** * 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_env] and [rewrite_env] tactics below. *)
Section Properties.
Variables A B key : Type.
Variable  f       : A -> B.
Variable  x       : atom.
Variable  b       : A.
Variables E F G   : list (atom*A).

Axiom dom_map :
dom (map f E) [=] dom E.