proposition: Lemma nring_apart : forall m n : nat, m <> n -> (nring m:R) [#] nring n.
proof: Proof. intros m n H. elim (lt_eq_lt_dec m n); intro H0. elim H0; intro H1. apply less_imp_ap. apply nring_less. assumption. elim (H H1). apply Greater_imp_ap. apply nring_less. assumption. Qed.
imports: CoRN.tactics.FieldReflection CoRN.tactics.Rational CoRN.algebra.CSetoids Coq(Lia)