proposition: Lemma even_or_odd_plus : forall k : nat, {j : nat & {k = j + j} + {k = S (j + j)}}.
proof: Proof. induction k as [| k IH]. - exists 0; left; reflexivity. - destruct IH as [j [H | H]]. + now exists j; right; rewrite H. + now exists (S j); left; rewrite H, Nat.add_succ_r. Qed.
imports: Coq.Arith.Compare_dec CoRN.logic.CornBasics Coq.ZArith.ZArith Coq.setoid_ring.ZArithRing Coq.Arith.Wf_nat Coq(Lia)