Proof using.
intros; induction l; simpl in *; intuition.
- subst. break_if; congruence.
- break_match. subst. break_if; try congruence.
auto.
Qed.

Lemma getLastId_None :
forall st c i o,
getLastId st c = None ->
In (c, (i, o)) (clientCache st) ->
False.