proposition: Theorem div2_S_double : forall n, div2 (S (2 * n)) = n.
proof: Proof. induction n; simpl; intuition; f_equal; rethink. 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