Proof using.
intros.
replace net with (snd (failed, net)); [|simpl; auto].
eapply step_failure_star_raft_intermediate_reachable'; eauto.
Qed.

Lemma step_failure_star_raft_intermediate_reachable_extend :
forall f net f' net' tr,
step_failure_star (f, net) (f', net') tr ->
raft_intermediate_reachable net ->
raft_intermediate_reachable net'.