proposition: Lemma mod2_S_not : forall n, mod2 (S n) = if (mod2 n) then false else true.
proof: Proof. intros. induction n; auto. rewrite mod2_S_S. destruct (mod2 n); replace (mod2 (S n)); 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