proposition: Lemma ring_rw_correct : forall n lH l, interp_PElist l lH -> forall lmp, mk_monpol_list lH = lmp -> forall pe npe, norm_subst n lmp pe = npe -> PEeval l pe == Pphi_dev l npe.
proof: Proof. intros n lH l H1 lmp Heq1 pe npe Heq2. rewrite Pphi_dev_ok. rewrite <- Heq2;rewrite <- Heq1. apply norm_subst_ok. trivial. Qed.
imports: Setoid Morphisms BinList BinPos BinNat BinInt Ring_theory