Proof using.
intros. unfold handleClientRequest in *.
break_match; find_inversion; subst; auto.
Qed.

(* Specifications: *)
Lemma tryToBecomeLeader_clientCache :
forall n st out st' ms,
tryToBecomeLeader n st = (out, st', ms) ->
clientCache st' = clientCache st.
Lemma tryToBecomeLeader_stateMachine :
forall n st out st' ms,
tryToBecomeLeader n st = (out, st', ms) ->
stateMachine st' = stateMachine st.
Lemma tryToBecomeLeader_same_lastApplied :
forall n st out st' ms,
tryToBecomeLeader n st = (out, st', ms) ->
lastApplied st' = lastApplied st.