(** 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_S (n m : nat) (H : le n m) :
le_Tle (le_S _ _ H) = Tle_S _ _ (le_Tle H).