Section AppendEntriesRequestsCameFromLeaders.
Context {orig_base_params : BaseParams}.
Context {one_node_params : OneNodeParams orig_base_params}.
Context {raft_params : RaftParams orig_base_params}.
Context {lhlli : leaders_have_leaderLogs_interface}.
Context {rri : raft_refinement_interface}.
Ltac start :=
red; unfold append_entries_came_from_leaders; intros;
subst; simpl in *; find_higher_order_rewrite;
update_destruct_hyp; subst; rewrite_update; eauto; simpl in *.
Ltac prove_in :=
match goal with
| [ _ : nwPackets ?net = _,
_ : In (?p : packet) _ |- _] =>
assert (In p (nwPackets net)) by (repeat find_rewrite; do_in_app; intuition)
| [ _ : nwPackets ?net = _,
_ : pBody ?p = _ |- _] =>
assert (In p (nwPackets net)) by (repeat find_rewrite; intuition)
end.
Ltac contra :=  (exfalso; intuition; find_false;
repeat eexists; eauto).
Proof using.
red. unfold append_entries_came_from_leaders. intros.
subst. simpl in *.
find_apply_hyp_hyp. intuition eauto.
- prove_in. find_apply_hyp_hyp.
break_exists.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto; subst; auto.
rewrite update_elections_data_appendEntries_leaderLogs. repeat find_rewrite.
eauto.
- subst. simpl in *. subst.
find_apply_lem_hyp handleAppendEntries_not_append_entries.
exfalso. intuition. find_false.
repeat eexists; eauto.
Qed.
Proof using.
red. unfold append_entries_came_from_leaders. intros.
subst. simpl in *.
find_apply_hyp_hyp. intuition eauto.
- prove_in. find_apply_hyp_hyp.
break_exists.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto; subst; auto.
repeat find_rewrite. eauto.
- subst. simpl in *. subst.
find_apply_lem_hyp handleAppendEntriesReply_packets.
subst. simpl in *. intuition.
Qed.
Proof using.
red. unfold append_entries_came_from_leaders. intros.
subst. simpl in *.
find_apply_hyp_hyp. intuition eauto.
- prove_in. find_apply_hyp_hyp.
break_exists.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto; subst; auto.
rewrite leaderLogs_update_elections_data_requestVote. repeat find_rewrite.
eauto.
- subst. simpl in *. subst.
find_apply_lem_hyp handleRequestVote_no_append_entries.
contra.
Qed.
Proof using.
red. unfold append_entries_came_from_leaders. intros.
subst. simpl in *.
find_apply_hyp_hyp. intuition eauto.
prove_in. find_apply_hyp_hyp.
break_exists.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto; subst; auto.
eexists.
eapply update_elections_data_requestVoteReply_old. repeat find_rewrite. eauto.
Qed.
Proof using.
red. unfold append_entries_came_from_leaders. intros.
subst. simpl in *.
find_apply_hyp_hyp. intuition eauto.
- find_apply_hyp_hyp.
break_exists.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto; subst; auto.
rewrite update_elections_data_client_request_leaderLogs. repeat find_rewrite.
eauto.
- do_in_map. subst. simpl in *.
find_eapply_lem_hyp handleClientRequest_no_append_entries; eauto.
contra.
Qed.
Proof using.
red. unfold append_entries_came_from_leaders. intros.
subst. simpl in *.
find_apply_hyp_hyp. intuition eauto.
- find_apply_hyp_hyp.
break_exists.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto; subst; auto.
rewrite update_elections_data_timeout_leaderLogs. repeat find_rewrite.
eauto.
- do_in_map. subst. simpl in *.
find_eapply_lem_hyp handleTimeout_packets; eauto.
contra.
Qed.
Proof using lhlli.
red. unfold append_entries_came_from_leaders. intros.
match goal with
| H : nwState ?net ?h = (?gd, ?d) |- _ =>
replace gd with (fst (nwState net h)) in * by (rewrite H; reflexivity);
replace d with (snd (nwState net h)) in * by (rewrite H; reflexivity);
clear H
end.
subst. simpl in *.
find_apply_hyp_hyp. intuition eauto.
- find_apply_hyp_hyp.
break_exists.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto; subst; auto.
- do_in_map. subst. simpl in *.
find_eapply_lem_hyp doLeader_messages; eauto.
repeat break_and.
subst.
find_eapply_lem_hyp leaders_have_leaderLogs_invariant; eauto.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto; subst; auto.
Qed.
Proof using.
red. unfold append_entries_came_from_leaders. intros.
match goal with
| H : nwState ?net ?h = (?gd, ?d) |- _ =>
replace gd with (fst (nwState net h)) in * by (rewrite H; reflexivity);
replace d with (snd (nwState net h)) in * by (rewrite H; reflexivity);
clear H
end.
subst. simpl in *.
find_apply_hyp_hyp. intuition eauto.
- find_apply_hyp_hyp.
break_exists.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto; subst; auto.
- do_in_map. subst. simpl in *.
find_eapply_lem_hyp doGenericServer_packets. subst. simpl in *. intuition.
Qed.
Proof using.
red. unfold append_entries_came_from_leaders. intros.
match goal with
| H : nwState ?net ?h = (?gd, ?d) |- _ =>
replace gd with (fst (nwState net h)) in * by (rewrite H; reflexivity);
replace d with (snd (nwState net h)) in * by (rewrite H; reflexivity);
clear H
end.
subst. simpl in *. find_reverse_rewrite.
find_apply_hyp_hyp.
repeat find_higher_order_rewrite.
update_destruct; subst_max; rewrite_update; simpl in *; eauto; subst; auto.
Qed.

Lemma append_entries_came_from_leaders_state_same_packet_subset :
refined_raft_net_invariant_state_same_packet_subset append_entries_came_from_leaders.