#[global]
Instance eqb_compat : Proper (eq==>eq==>Logic.eq) eqb.
End OrderedTypeFacts.
(** * Tests of the order tactic  Is it at least capable of proving some basic properties ? *)
Module OrderedTypeTest (Import O:OrderedType').
Module Import MO := OrderedTypeFacts O.
Local Open Scope order.

Lemma neq_eq x y z : ~x==y -> y==z -> ~x==z. Proof. order. Qed.