proposition: Theorem drop_mod2_add : forall n k, mod2 (n + 2 * k) = mod2 n.
proof: Proof. intros. induction n. simpl. rewrite Nat.add_0_r. replace (k + k) with (2 * k) by lia. apply mod2_double. replace (S n + 2 * k) with (S (n + 2 * k)) by lia. apply mod2_S_eq; 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