(** *** Least-upper bound properties of [max] *)

(* Specifications: *)
Lemma le_max_l n m : n <= max n m.
Lemma max_le_iff n m p : p <= max n m <-> p <= n \/ p <= m.
Lemma max_lt_iff n m p : p < max n m <-> p < n \/ p < m.
Lemma max_lub_l n m p : max n m <= p -> n <= p.
(** Properties of [min] *)
Lemma min_spec n m :
(n < m /\ min n m == n) \/ (m <= n /\ min n m == m).
Lemma min_spec_le n m :
(n <= m /\ min n m == n) \/ (m <= n /\ min n m == m).