proposition: Theorem Zdiv_small: forall a b, 0 <= a < b -> a/b = 0.
proof: Proof. Proof Z.div_small. Theorem Zmod_small: forall a n, 0 <= a < n -> a mod n = a. Proof Z.mod_small. Lemma Z_div_ge : forall a b c:Z, c > 0 -> a >= b -> a/c >= b/c. Proof. intros. apply Z.le_ge. apply Z.div_le_mono; auto using Z.gt_lt, Z.ge_le. Qed.
imports: ZArith_base Zbool ZArithRing Zcomplements Setoid Morphisms