Proof using.
intros.
simpl in *; break_if; do_bool; auto; omega.
Qed.

Lemma handleClientRequest_preserves_lastApplied_entries:
forall h (net : network) (d : raft_data)
client id c out l,
raft_intermediate_reachable net ->
handleClientRequest h (nwState net h) client id c = (out, d, l) ->
removeAfterIndex (log d) (lastApplied d) = removeAfterIndex (log (nwState net h))
(lastApplied (nwState net h)).