(* TO BE A DOUBLE-LINK: *)
Definition double_link(m:fmap)(x x':dart):Prop:=
x <> x' /\ expe m x x'.

(* Specifications: *)
Lemma double_link_comm: forall (m:fmap)(x x':dart),
inv_hmap m -> double_link m x x' -> double_link m x' x.
Lemma double_link_succ :forall (m:fmap)(x x':dart),
inv_hmap m -> double_link m x x' ->
(succ m zero x \/ succ m zero x').
Lemma double_link_exd:forall(m:fmap)(x x':dart),
inv_hmap m -> double_link m x x' -> exd m x /\ exd m x'.