induction ls; intuition; simpl in *.
case_eq (eqb d' d); intuition.
rewrite eqb_leibniz in H0.
subst.
intuition.
case_eq (eqb d' a0); intuition.
Qed.

(* Specifications: *)
Lemma arrayLookup_app_some : forall ls d d' v v',
arrayLookup ls d = Some v ->
arrayLookup (ls ++ (d, v') :: nil) d' = arrayLookup ls d'.