(** Natural numbers form a preorder with le (less than or equal relation). *)
(** The pre-order category ω. *)
Definition OmegaCat : Category := PreOrder_Cat OmegaPreOrder.
Notation "'ω'" := (OmegaCat) : omegacat_scope.

Lemma le_Tle_n (n : nat) : le_Tle (le_n n) = Tle_n n.