End MinMaxLogicalProperties.
(** ** Properties requiring a decidable order *)
Module MinMaxDecProperties (Import O:OrderedTypeFull')(Import M:HasMinMax O).
(** Induction principles for [max]. *)

Lemma max_case_strong n m (P:t -> Type) :
(forall x y, x==y -> P x -> P y) ->
(m<=n -> P n) -> (n<=m -> P m) -> P (max n m).