proposition: Lemma pring_aux_lemma : forall p r r', r [=] r' -> pring_aux p r [=] pring_aux p r'.
proof: Proof. simple induction p; 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)