Proof using.
intros. unfold handleTimeout, tryToBecomeLeader in *.
break_match; find_inversion; subst; auto.
Qed.

Lemma handleInput_applied_entries :
forall net h inp os st' ms,
raft_intermediate_reachable net ->
handleInput h inp (nwState net h) = (os, st', ms) ->
applied_entries (nwState net) = applied_entries (update name_eq_dec (nwState net) h st').