Proof using.
intros.
induction H10.
- intuition.
-  match goal with [H : step_failure _ _ _ |- _ ] => invcs H end.
+ unfold mgv_refined_net_handlers in *. simpl in *.
unfold refined_net_handlers in *. simpl in *.
unfold RaftNetHandler in *.
repeat break_let.
repeat find_inversion.
remember (update_elections_data_net (pDst p) (pSrc p) (snd (pBody p))
(nwState net (pDst p))) as post_ghost_state.
assert
(msg_refined_raft_intermediate_reachable
{|
nwPackets := (xs ++ ys) ++ send_packets (pDst p)
(@add_ghost_msg _ _ ghost_log_params (pDst p)
(post_ghost_state, r0) l4);
nwState := update name_eq_dec (nwState net) (pDst p)
(post_ghost_state, r0) |})
by (subst; eapply MRRIR_handleMessage; eauto; in_crush).
assert
(msg_refined_raft_intermediate_reachable
{|
nwPackets := (xs ++ ys) ++
send_packets (pDst p)
(@add_ghost_msg _ _ ghost_log_params (pDst p)
(post_ghost_state, r0) l4)
++
send_packets (pDst p)
(@add_ghost_msg _ _ ghost_log_params (pDst p)
(post_ghost_state, r1) l5);
nwState := update name_eq_dec (nwState net) (pDst p)
(post_ghost_state, r1) |}) by
(eapply MRRIR_doLeader; eauto;
try solve [in_crush];
simpl in *; intros; repeat break_if; try congruence; auto).
subst.
eapply_prop msg_refined_raft_net_invariant_do_generic_server. eauto.
eapply_prop msg_refined_raft_net_invariant_do_leader. eauto.
eapply msg_refined_raft_invariant_handle_message with (P := P); eauto using in_app_or.
auto.
simpl. break_if; intuition eauto.
eauto.
simpl. eapply in_app_or.
simpl.
{ clear H11.
match goal with
| H : msg_refined_raft_intermediate_reachable ?net |-
msg_refined_raft_intermediate_reachable ?net' =>
assert (net = net')
end.
simpl.
f_equal; auto.
- repeat rewrite app_ass. auto.
- apply functional_extensionality.
intros. repeat break_if; simpl; auto.
- repeat find_rewrite; auto.
}
simpl in *. break_if; eauto; congruence.
simpl in *.
intros. repeat break_if; auto.
intros. simpl in *.
in_crush.
unfold add_ghost_msg in *. do_in_map.
subst. do_in_app. intuition; try do_in_app; intuition.
* left. apply in_app_iff. left. apply in_app_iff. right.
simpl in *.
rewrite map_map.
apply in_map_iff.
eexists; intuition; eauto.
simpl in *. f_equal. f_equal.
unfold write_ghost_log. simpl.
find_apply_lem_hyp doGenericServer_log.
find_apply_lem_hyp doLeader_log.
repeat find_rewrite. auto.
* left. apply in_app_iff. right.
simpl in *.
rewrite map_map.
apply in_map_iff.
eexists; intuition; eauto.
simpl in *. f_equal. f_equal.
unfold write_ghost_log. simpl.
find_apply_lem_hyp doGenericServer_log.
find_apply_lem_hyp doLeader_log.
repeat find_rewrite. auto.
* right.
simpl in *.
rewrite map_map.
apply in_map_iff.
eexists; intuition; eauto.
+ unfold mgv_refined_input_handlers in *. simpl in *.
unfold refined_input_handlers in *. simpl in *.
unfold RaftInputHandler in *.
repeat break_let.
repeat find_inversion.
remember (update_elections_data_input h inp
(nwState net h))
as post_ghost_state.
assert
(msg_refined_raft_intermediate_reachable
{|
nwPackets := (nwPackets net) ++ send_packets h
(@add_ghost_msg _ _ ghost_log_params h
(post_ghost_state, r0) l4);
nwState := update name_eq_dec (nwState net) h
(post_ghost_state, r0) |})
by (subst; eapply MRRIR_handleInput; eauto; in_crush).
assert
(msg_refined_raft_intermediate_reachable
{|
nwPackets := (nwPackets net) ++
send_packets h
(@add_ghost_msg _ _ ghost_log_params h
(post_ghost_state, r0) l4)
++
send_packets h
(@add_ghost_msg _ _ ghost_log_params h
(post_ghost_state, r1) l6);
nwState := update name_eq_dec (nwState net) h
(post_ghost_state, r1) |}) by
(eapply MRRIR_doLeader; eauto;
try solve [in_crush];
simpl in *; intros; repeat break_if; try congruence; auto).
subst.
eapply_prop msg_refined_raft_net_invariant_do_generic_server. eauto.
eapply_prop msg_refined_raft_net_invariant_do_leader. eauto.
eapply msg_refined_raft_invariant_handle_input with (P := P); eauto using in_app_or.
auto.
simpl. break_if; intuition eauto.
eauto.
simpl. eapply in_app_or.
simpl.
{ clear H11.
match goal with
| H : msg_refined_raft_intermediate_reachable ?net |-
msg_refined_raft_intermediate_reachable ?net' =>
assert (net = net')
end.
simpl.
f_equal; auto.
- repeat rewrite app_ass. auto.
- apply functional_extensionality.
intros. repeat break_if; simpl; auto.
- repeat find_rewrite; auto.
}
simpl in *. break_if; eauto; congruence.
simpl in *.
intros. repeat break_if; auto.
intros. simpl in *.
in_crush.
unfold add_ghost_msg in *. do_in_map.
subst. do_in_app. intuition; try do_in_app; intuition.
* left. apply in_app_iff. left. apply in_app_iff. right.
simpl in *.
rewrite map_map.
apply in_map_iff.
eexists; intuition; eauto.
simpl in *. f_equal. f_equal.
unfold write_ghost_log. simpl.
find_apply_lem_hyp doGenericServer_log.
find_apply_lem_hyp doLeader_log.
repeat find_rewrite. auto.
* left. apply in_app_iff. right.
simpl in *.
rewrite map_map.
apply in_map_iff.
eexists; intuition; eauto.
simpl in *. f_equal. f_equal.
unfold write_ghost_log. simpl.
find_apply_lem_hyp doGenericServer_log.
find_apply_lem_hyp doLeader_log.
repeat find_rewrite. auto.
* right.
simpl in *.
rewrite map_map.
apply in_map_iff.
eexists; intuition; eauto.
+ match goal with
| [ H : nwPackets ?net = _ |- _ {| nwPackets := ?ps ; nwState := ?st |} ] =>
assert (forall p, In p (nwPackets {| nwPackets := ps ; nwState := st |}) ->
In p (nwPackets net)) by (intros; simpl in *; find_rewrite; in_crush)
end.
eapply_prop msg_refined_raft_net_invariant_state_same_packet_subset; [|eauto|idtac|];
eauto.
+ match goal with
| [ H : nwPackets ?net = _ |- _ {| nwPackets := ?ps ; nwState := ?st |} ] =>
assert (forall p, In p (nwPackets {| nwPackets := ps ; nwState := st |}) ->
In p (nwPackets net)) by (intros; simpl in *; find_rewrite; in_crush)
end.
eapply_prop msg_refined_raft_net_invariant_state_same_packet_subset; [|eauto|idtac|];
eauto.
+ auto.
+ eapply_prop msg_refined_raft_net_invariant_reboot; eauto;
intros; simpl in *; repeat break_if; intuition; subst; intuition eauto.
destruct (nwState net h); auto.
- eapply msg_refined_raft_invariant_handle_input; eauto.
- eapply msg_refined_raft_invariant_handle_message; eauto.
- eapply_prop msg_refined_raft_net_invariant_do_leader; eauto.
- eapply_prop msg_refined_raft_net_invariant_do_generic_server; eauto.
Qed.

(* Specifications: *)
Lemma msg_refined_raft_invariant_handle_message' P :
forall xs p ys net st' ps' gd d l,
msg_refined_raft_net_invariant_append_entries' P ->
msg_refined_raft_net_invariant_append_entries_reply' P ->
msg_refined_raft_net_invariant_request_vote' P ->
msg_refined_raft_net_invariant_request_vote_reply' P ->
handleMessage (pSrc p) (pDst p) (snd (pBody p)) (snd (nwState net (pDst p))) = (d, l) ->
update_elections_data_net (pDst p) (pSrc p) (snd (pBody p)) (nwState net (pDst p)) = gd ->
P net ->
msg_refined_raft_intermediate_reachable net ->
msg_refined_raft_intermediate_reachable (mkNetwork ps' st') ->
nwPackets net = xs ++ p :: ys ->
(forall h, st' h = update name_eq_dec (nwState net) (pDst p) (gd, d) h) ->
(forall p', In p' ps' -> In p' (xs ++ ys) \/
In p' (send_packets (pDst p) (@add_ghost_msg _ _ ghost_log_params (pDst p) (gd, d) l))) ->
P (mkNetwork ps' st').