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.

(* Specifications: *)
Lemma eqk_not_ltk : forall x x', eqk x x' -> ~ltk x x'.
Lemma ltk_eqk : forall e e' e'', ltk e e' -> eqk e' e'' -> ltk e e''.
Lemma eqk_ltk : forall e e' e'', eqk e e' -> ltk e' e'' -> ltk e e''.
Lemma InA_eqke_eqk : forall x m, InA eqke x m -> InA eqk x m.