proposition: Lemma pring_convert : forall p, pring p [=] nring (nat_of_P p).
proof: Proof. intros; unfold pring, nat_of_P in |- *; simpl in |- *. astepr (pring_aux p (nring 1)). simpl in |- *; algebra. Qed.
imports: CoRN.tactics.CornTac CoRN.algebra.CSums CoRN.algebra.CAbMonoids Coq.Sorting.Permutation CoRN.util.SetoidPermutation Coq.Setoids.Setoid Coq.Classes.Morphisms Coq(Lia)