(*========================================================== exd, A, A_1 on D for hmap ==========================================================*)
(* Action of D on exd: *)

(* Specifications: *)
Lemma not_exd_D : forall (m:fmap)(x:dart),
inv_hmap m -> ~exd (D m x) x.
Lemma exd_D : forall (m:fmap)(x z:dart),
inv_hmap m ->
x <> z -> (exd m z <-> exd (D m x) z).