proposition: Lemma mod_add_r: forall a b, b <> 0 -> (a + b) mod b = a mod b.
proof: Proof. intros. rewrite <- Nat.add_mod_idemp_r by lia. rewrite Nat.mod_same by lia. rewrite Nat.add_0_r. reflexivity. 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