(* 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 mem2_splice1 p1 p3 x y z :
mem2 (p1 ++ p3) x y -> mem2 (p1 ++ z :: p3) x y.