(* === is a morphism *)
Instance PEadd_ext : Proper (NPEequiv ==> NPEequiv ==> NPEequiv) (@PEadd C).

Lemma PEpow_nz l e n : ~ e @ l == 0 -> ~ (e^n) @ l == 0.
Local Notation "a &&& b" := (if a then b else false)
(at level 40, left associativity).