(* Specialization of results about lists modulo. *)
Notation In:=(InA eq).
Notation Inf:=(lelistA lt).
Notation Sort:=(sort lt).
Notation NoDup:=(NoDupA eq).

(* Specifications: *)
Lemma In_eq : forall l x y, eq x y -> In x l -> In y l.
(* ltk ignore the second components *)
Lemma ltk_right_r : forall x k e e', ltk x (k,e) -> ltk x (k,e').
Lemma ltk_trans : forall e e' e'', ltk e e' -> ltk e' e'' -> ltk e e''.
#[local]
Hint Resolve eqk_trans eqke_trans eqk_refl eqke_refl : ordered_type.