Global Instance eqk_equiv : Equivalence eqk.Global Instance eqke_equiv : Equivalence eqke.Global Instance ltk_strorder : StrictOrder ltk.Global Instance ltk_compat : Proper (eqk==>eqk==>iff) ltk.Global Instance ltk_compat' : Proper (eqke==>eqke==>iff) ltk.

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