(** [Z.ge] is compatible with a positive division. *)

(* Specifications: *)
Lemma Z_div_ge : forall a b c:Z, c > 0 -> a >= b -> a/c >= b/c.
(** * Relations between usual operations and Z.modulo and Z.div *)
Lemma Z_mod_plus_full : forall a b c:Z, (a + b * c) mod c = a mod c.
Lemma Z_div_plus_full : forall a b c:Z, c <> 0 -> (a + b * c) / c = a / c + b.
Proof Z.div_add.
Theorem Z_div_plus_full_l: forall a b c : Z, b <> 0 -> (a * b + c) / b = a + c / b.
Proof Z.div_add_l.