proposition: Theorem div2_minus_2 : forall n k, 2 * k <= n -> div2 (n - 2 * k) = div2 n - k.
proof: Proof. induction n as [n] using strong; intros. do 2 (destruct n; simpl in *; intuition; repeat rewrite untimes2 in *). destruct k; simpl in *; intuition. destruct k; simpl in *; intuition. rewrite <- plus_n_Sm. apply 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