Proof using lmi lacimi si smci.
intros.
find_copy_apply_lem_hyp logs_sorted_invariant.
pose proof entries_contiguous.
match goal with
| H : context [contiguous_range_exact_lo] |- _ =>
specialize (H ({| nwPackets := ps; nwState := sigma |}))
end.
concludes. simpl in *.
find_copy_apply_lem_hyp state_machine_correct_invariant.
unfold state_machine_correct in *. intuition.
unfold logs_sorted in *. intuition.
unfold doGenericServer in *.
break_let. find_inversion.
find_copy_apply_lem_hyp applyEntries_spec. intuition. repeat find_rewrite.
eapply applyEntries_output_correct
with (es := rev (removeAfterIndex (log (sigma h)) (lastApplied (sigma h)))) in Heqp; eauto.
- rewrite <- rev_app_distr in *.
eapply output_correct_prefix; eauto.
break_if.
+ do_bool.
erewrite findGtIndex_removeAfterIndex_i_lt_i' in *; eauto.
match goal with
| |- context [applied_entries (update _ ?sigma ?h ?st)] =>
pose proof applied_entries_update sigma h st
end. conclude_using intuition.
intuition; simpl in *;
unfold raft_data in *; simpl in *; find_rewrite; auto using Prefix_refl.
unfold applied_entries in *.
break_exists. intuition. repeat find_rewrite.
eapply contiguous_sorted_subset_prefix; eauto using removeAfterIndex_contiguous, removeAfterIndex_sorted.
intros.
find_copy_apply_lem_hyp removeAfterIndex_In_le; eauto.
find_apply_lem_hyp removeAfterIndex_in.
apply removeAfterIndex_le_In; eauto; try omega.
find_copy_apply_lem_hyp commitIndex_lastApplied_match_invariant.
unfold commitIndex_lastApplied_match in *. simpl in *.
match goal with
| _ : ?x >= ?y |- _ =>
assert (y <= x) by omega
end.
eapply_prop_hyp le le; eauto. intuition.
+ do_bool.
erewrite findGtIndex_removeAfterIndex_i'_le_i in *; eauto.
match goal with
| |- context [applied_entries (update _ ?sigma ?h ?st)] =>
pose proof applied_entries_update sigma h st
end. conclude_using intuition.
intuition; simpl in *;
unfold raft_data in *; simpl in *; find_rewrite; auto using Prefix_refl.
unfold applied_entries in *.
break_exists. intuition. repeat find_rewrite.
eapply contiguous_sorted_subset_prefix; eauto using removeAfterIndex_contiguous, removeAfterIndex_sorted.
intros.
find_copy_apply_lem_hyp removeAfterIndex_In_le; eauto.
find_apply_lem_hyp removeAfterIndex_in.
apply removeAfterIndex_le_In; eauto; try omega.
find_copy_apply_lem_hyp lastApplied_lastApplied_match_invariant.
unfold lastApplied_lastApplied_match in *. simpl in *.
match goal with
| _ : ?x >= ?y |- _ =>
assert (y <= x) by omega
end.
eapply_prop_hyp le le; eauto. intuition.
- unfold client_cache_complete in *.
simpl in *.
intros. subst.
find_apply_lem_hyp In_rev. find_apply_hyp_hyp.
break_exists. intuition. repeat find_rewrite.
match goal with
| H : Some _ = Some _ |- _ =>
invcs H
end. auto.
- intros. find_apply_lem_hyp In_rev. eauto.
Qed.
Ltac intermediate_networks :=
match goal with
| Hdgs : doGenericServer ?h ?st' = _,
Hdl : doLeader ?st ?h = _ |- context [update _ (nwState ?net) ?h ?st''] =>
replace st with (update name_eq_dec (nwState net) h st h) in Hdl by eauto using update_eq;
replace st' with (update name_eq_dec (update name_eq_dec (nwState net) h st) h st' h) in Hdgs by eauto using update_eq;
let H := fresh "H" in
assert (update name_eq_dec (nwState net) h st'' =
update name_eq_dec (update name_eq_dec (update name_eq_dec (nwState net) h st) h st') h st'') by (repeat rewrite update_overwrite; auto); unfold data in *; simpl in *; rewrite H; clear H
end.

(* Specifications: *)
Lemma in_output_trace_step_output_correct :
forall failed failed' (net net' : network (params := @multi_params _ _ raft_params)) os,
in_output_trace client id out os ->
@raft_intermediate_reachable _ _ raft_params net ->
step_failure (failed, net) (failed', net') os ->
output_correct client id out (applied_entries (nwState net')).