Proof using.
intros. induction l; simpl in *; auto.
Qed.

(* Specifications: *)
Lemma findGtIndex_app_in_1 :
forall l1 l2 e,
sorted (l1 ++ l2) ->
In e l1 ->
exists l',
findGtIndex (l1 ++ l2) (eIndex e) = l' /\
forall x,
In x l' -> In x l1.
Lemma filter_and :
forall A (l : list A) f g,
(forall x, In x l -> f x = true) ->
filter (fun x => f x && g x) l = filter (fun x => g x) l.