(* ucycleb is the boolean predicate, but ucycle is defined as a Prop *)
(* so that it can be used as a coercion target. *)
Definition ucycle p : Prop := cycle e p && uniq p.

Lemma mem2l_cat {p1 p2 x} : x \notin p1 -> mem2 (p1 ++ p2) x =1 mem2 p2 x.