proposition: Lemma mod_0_r: forall (m: nat), m mod 0 = match (1 mod 0) with | 0 => 0 | _ => m end.
proof: Proof. intros. 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