#[local]
Hint Resolve ltk_trans ltk_not_eqk ltk_not_eqke : ordered_type.
#[local]
Hint Immediate eqk_sym eqke_sym : ordered_type.
Global Instance eqk_equiv : Equivalence eqk.
Global Instance ltk_compat' : Proper (eqke==>eqke==>iff) ltk.
(* Additional facts *)

Lemma eqk_not_ltk : forall x x', eqk x x' -> ~ltk x x'.