(* Quicker than autorewrite with Esimpl :-) *)
 Ltac Esimpl := try rewrite_db Esimpl; rsimpl; simpl.

Lemma PsubX_ok P' P k l : (forall P l, (P--P')@l == P@l - P'@l) -> (PsubX Psub P' k P) @ l == P@l - P'@l * (hd l)^k.