Proof using.
induction l; intros; simpl in *; intuition.
subst. destruct l'; simpl in *; intuition.
- exfalso. specialize (H0 e). intuition.
- exfalso. specialize (H3 e0). conclude_using intuition.
intuition.
Qed.

Lemma findGtIndex_non_empty :
forall l i,
i < maxIndex l ->
findGtIndex l i <> [].