Proof using.
intros. induction l; simpl in *; auto.
repeat (break_if; simpl; intuition); do_bool;
try congruence.
symmetry. apply findGtIndex_nil.
intros. find_apply_lem_hyp removeAfterIndex_in.
find_apply_hyp_hyp. intuition.
Qed.

(* Specifications: *)
Lemma findGtIndex_app_1 :
forall l l' i,
maxIndex l' <= i ->
findGtIndex (l ++ l') i = findGtIndex l i.