Proof using.
eauto using clientCache_to_ks_assoc_none.
Qed.

Lemma cacheApplyEntry_stateMachine_apply :
forall st e os st' id o o' d,
cacheApplyEntry st e = (os, st') ->
getLastId st (eClient e) = Some (id, o) ->
id < eId e ->
handler (eInput e) (stateMachine st) = (o', d) ->
stateMachine st' = d.