Proof using misi.
intros.
erewrite handleClientRequest_lastApplied; eauto.
find_apply_lem_hyp handleClientRequest_log.
intuition; repeat find_rewrite; eauto.
break_exists; intuition; repeat find_rewrite.
erewrite removeAfterIndex_cons; eauto.
get_invariant_pre max_index_sanity_invariant.
unfold maxIndex_sanity, maxIndex_lastApplied in *. intuition.
match goal with
| H : forall _, lastApplied _ <= maxIndex _ |- _ =>
specialize (H h)
end. omega.
Qed.

(* Specifications: *)
Lemma client_cache_keys_correct_clientCache_complete :
forall net,
client_cache_keys_correct net ->
client_cache_complete net.