Instance mkPX_ext : Proper (Pequiv ==> eq ==> Pequiv ==> Pequiv) mkPX.(* Quicker than autorewrite with Esimpl :-) *)
 Ltac Esimpl := try rewrite_db Esimpl; rsimpl; simpl.

Lemma PmulC_aux_ok c P l : (PmulC_aux P c)@l == P@l * [c].