(* === is a morphism *)

Instance PEadd_ext : Proper (NPEequiv ==> NPEequiv ==> NPEequiv) (@PEadd C).Instance PEsub_ext : Proper (NPEequiv ==> NPEequiv ==> NPEequiv) (@PEsub C).Instance PEmul_ext : Proper (NPEequiv ==> NPEequiv ==> NPEequiv) (@PEmul C).Instance PEopp_ext : Proper (NPEequiv ==> NPEequiv) (@PEopp C).Instance PEpow_ext : Proper (NPEequiv ==> eq ==> NPEequiv) (@PEpow C).

Lemma PE_1_r (e : PExpr C) : (e * 1 === e)%poly.