proposition: Lemma to_Codd_even : forall n : nat, (Nat.Odd n -> Codd n) and (Nat.Even n -> Ceven n).
proof: Proof. induction n as [| n IH]; split. - intros H%Nat.odd_spec; discriminate H. - intros _; exact Ceven_O. - now intros H%Nat.Odd_succ; apply IH in H; apply Codd_S. - now intros H%Nat.Even_succ; apply IH in H; apply Ceven_S. Qed.
imports: Coq.Arith.Compare_dec CoRN.logic.CornBasics Coq.ZArith.ZArith Coq.setoid_ring.ZArithRing Coq.Arith.Wf_nat Coq(Lia)