proposition: Lemma mod_0_r: forall (m: Z), m mod 0 = match (1 mod 0) with | 0 => 0 | _ => m end.
proof: Proof. intros. destruct m; reflexivity. Qed.
imports: Coq.Classes.Morphisms Coq.ZArith.BinInt Coq.micromega.Lia Coq.ZArith.ZArith