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

Lemma clientCache_to_ks_assoc_getLastId_none :
forall st client,
assoc clientId_eq_dec (clientCache_to_ks (clientCache st)) client = None ->
getLastId st client = None.