proposition: Lemma mod2_S_eq : forall n k, mod2 n = mod2 k -> mod2 (S n) = mod2 (S k).
proof: Proof. intros. do 2 rewrite mod2_S_not. rewrite H. 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