(** ** Consequences of the minimalist interface: facts about [max] and [min]. *)
Module MinMaxLogicalProperties (Import O:TotalOrder')(Import M:HasMinMax O).
Module Import Private_Tac := !MakeOrderTac O O.
(** An alternative characterisation of [max], equivalent to [max_l /\ max_r] *)

Lemma max_spec n m :
(n < m /\ max n m == m) \/ (m <= n /\ max n m == n).