(* In fact, this may be used as an alternative definition for InfA: *)

(* Specifications: *)
Lemma InfA_alt :
forall l x, SortA l -> (InfA x l <-> (forall y, InA y l -> ltA x y)).
Lemma InfA_app : forall l1 l2 a, InfA a l1 -> InfA a l2 -> InfA a (l1++l2).
Lemma SortA_app :
forall l1 l2, SortA l1 -> SortA l2 ->
(forall x y, InA x l1 -> InA y l2 -> ltA x y) ->
SortA (l1 ++ l2).
Lemma SortA_NoDupA : forall l, SortA l -> NoDupA l.
Section EqlistA.