proposition: Lemma double_div2 : forall n, S (2 * Nat.div2 n) >= n.
proof: Proof. intro n. destruct (Nat.Even_or_Odd n). rewrite NatCompat.Even_double; [| exact H]; unfold Nat.double; lia. rewrite NatCompat.Odd_double; auto; unfold Nat.double; lia. Qed.
imports: Coq(Lia PeanoNat) CoLoR(LogicUtil NatCompat)