induction arr; intuition; simpl in *.
discriminate.
case_eq (eqb a a0); intuition;
rewrite H0 in *.
inversion H; clear H; subst.
rewrite eqb_leibniz in H0.
subst.
intuition.
right.
eapply IHarr.
eauto.
Qed.

Lemma notInArrayLookupNone :
forall (A B : Set)(eqd : EqDec A)(arr : Array A B) a,
(~ In a (fst (unzip arr))) ->
(arr # a) = None.