intuition.
unfold arrayUpdate.
destruct arr.
simpl.
rewrite eqb_refl.
trivial.
simpl.
rewrite eqb_refl.
trivial.
Qed.

Theorem arrayLookup_arrayUpdate_ne :
forall arr p1 p2 v,
p1 <> p2 ->
arrayLookup (arrayUpdate (Some arr) p1 (Some v)) p2 = arrayLookup arr p2.