(** *** Asymmetry and transitivity. *)

(* Specifications: *)
Theorem lt_asymm : forall n m, n < m -> ~ m < n.
Notation lt_ngt := lt_asymm (only parsing).
Theorem lt_trans : forall n m p, n < m -> m < p -> n < p.
Theorem le_trans : forall n m p, n <= m -> m <= p -> n <= p.
#[global]
Instance lt_strorder : StrictOrder lt.