Proof using lmi.
intros. find_apply_lem_hyp log_matching_invariant.
unfold log_matching, log_matching_hosts in *.
intuition.
unfold contiguous_range_exact_lo. intuition; eauto.
find_apply_hyp_hyp. omega.
Qed.

Lemma doGenericServer_output_correct :
forall h ps sigma os st' ms,
raft_intermediate_reachable (mkNetwork ps sigma) ->
doGenericServer h (sigma h) = (os, st', ms) ->
in_output_list client id out os ->
output_correct client id out (applied_entries (update name_eq_dec sigma h st')).