Proof using.
intros. unfold getLastId in *. induction (clientCache st).
- simpl in *. congruence.
- simpl in *. break_let. subst. simpl in *.
break_if; repeat find_inversion; auto.
Qed.

(* Specifications: *)
(* FIXME: move to StructTact *)
Lemma i_lt_assoc_default_0 :
forall K K_eq_dec ks (k : K) i,
i < assoc_default K_eq_dec ks k 0 ->
exists i',
assoc K_eq_dec ks k = Some i' /\
i < i'.