proposition: Theorem div2_bound : forall k n, 2 * k <= n -> k <= div2 n.
proof: Proof. intros ? n H; case_eq (mod2 n); intro Heq. rewrite (div2_odd _ Heq) in H. lia. rewrite (div2_even _ Heq) in H. lia. Qed.
imports: Coq.Classes.Morphisms Coq.Classes.Morphisms_Prop Coq.Bool.Bool Coq.Arith.Arith Coq.micromega.Lia Coq.NArith.NArith Coq.ZArith.ZArith bbv.N_Z_nat_conversions bbv.Nomega