proposition: Theorem div2_odd : forall n, mod2 n = true -> n = S (2 * div2 n).
proof: Proof. induction n as [n] using strong; simpl; intuition. destruct n as [|n]; simpl in *. discriminate. destruct n as [|n]; simpl in *; intuition. do 2 f_equal. replace (div2 n + S (div2 n + 0)) with (S (div2 n + (div2 n + 0))); auto. 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