Proof using.
induction c; intros; simpl in *; try congruence.
break_if; eauto.
- subst. find_inversion.
break_let. subst. simpl in *. break_if; try congruence.
destruct p. simpl in *. eauto.
- break_let; subst; simpl in *. break_if; try congruence. eauto.
Qed.

(* Specifications: *)
Lemma clientCache_to_ks_assoc_getLastId :
forall st client id,
assoc clientId_eq_dec (clientCache_to_ks (clientCache st)) client = Some id ->
exists o,
getLastId st client = Some (id, o).