Module Type CompareFacts (Import O:DecStrOrder').
Local Infix "?=" := compare (at level 70, no associativity).
Hint Rewrite compare_eq_iff compare_lt_iff compare_gt_iff : order.
Instance compare_compat : Proper (eq==>eq==>Logic.eq) compare.

Lemma compare_refl x : (x ?= x) = Eq.