Proof using.
induction l; intros; simpl in *; intuition.
break_if; simpl in *; intuition.
Qed.

Lemma findGtIndex_app_in_2 :
forall l1 l2 e,
sorted (l1 ++ l2) ->
In e l2 ->
exists l',
findGtIndex (l1 ++ l2) (eIndex e) = l1 ++ l' /\
Prefix l' l2.