proposition: Lemma div2_add_double n m : Nat.div2 (2 * n + m) = n + Nat.div2 m.
proof: Proof. induction n; ins. rewrite Nat.add_0_r in *. rewrite (Nat.add_comm n); ins; f_equal; ins. Qed.
imports: NPeano Arith micromega.Lia Setoid HahnBase