Section AppendEntriesRequestReplyCorrespondence.
Context {orig_base_params : BaseParams}.
Context {one_node_params : OneNodeParams orig_base_params}.
Context {raft_params : RaftParams orig_base_params}.
Proof using.
red. unfold append_entries_request_reply_correspondence. intros.
simpl in *. intuition.
Qed.
Proof using.
red. unfold append_entries_request_reply_correspondence. intros.
simpl in *.
find_apply_hyp_hyp. intuition.
- copy_eapply_prop_hyp pBody pBody; auto.
unfold exists_equivalent_network_with_aer in *.
break_exists_name net'.
break_exists_name pli.
break_exists_name plt.
break_exists_name ci.
break_exists_name n.
intuition.
remember mkNetwork as mkN.
remember mkPacket as mkP.
unfold Net.name in *. simpl in *.
exists (mkN (ps' ++ [mkP (pDst p) (pSrc p) (AppendEntries t n pli plt es ci)]) st').
subst.
exists pli,plt,ci,n. simpl in *; intuition.
eapply @RIR_handleInput with (net := net') (inp := Timeout); eauto;
simpl; repeat find_rewrite; eauto.
intros.
do_in_app. intuition.
find_apply_hyp_hyp.
intuition.
- exfalso.
do_in_map. subst. simpl in *.
unfold handleTimeout, tryToBecomeLeader in *.
repeat break_match; find_inversion; intuition; do_in_map; subst; simpl in *; congruence.
Qed.
Proof using.
red. unfold append_entries_request_reply_correspondence. intros.
simpl in *.
find_apply_hyp_hyp. intuition.
- copy_eapply_prop_hyp pBody pBody; auto.
unfold exists_equivalent_network_with_aer in *.
break_exists_name net'.
break_exists_name pli.
break_exists_name plt.
break_exists_name ci.
break_exists_name n.
intuition.
remember mkNetwork as mkN.
remember mkPacket as mkP.
unfold Net.name in *. simpl in *.
exists (mkN (ps' ++ [mkP (pDst p) (pSrc p) (AppendEntries t n pli plt es ci)]) st').
subst.
exists pli,plt,ci,n. simpl in *; intuition.
eapply @RIR_handleInput with (net := net') (inp := ClientRequest client id c); eauto;
simpl; repeat find_rewrite; eauto.
intros.
do_in_app. intuition.
find_apply_hyp_hyp.
intuition.
- exfalso.
do_in_map. subst. simpl in *.
unfold handleClientRequest in *.
repeat break_match; find_inversion; intuition; do_in_map; subst; simpl in *; congruence.
Qed.
Proof using.
red. unfold append_entries_request_reply_correspondence. intros.
simpl in *.
find_apply_hyp_hyp. intuition.
- copy_eapply_prop_hyp pBody pBody; auto.
unfold exists_equivalent_network_with_aer in *.
break_exists_name net'.
break_exists_name pli.
break_exists_name plt.
break_exists_name ci.
break_exists_name n.
intuition.
remember mkNetwork as mkN.
remember mkPacket as mkP.
unfold Net.name in *. simpl in *.
exists (mkN (ps' ++ [mkP (pDst p) (pSrc p) (AppendEntries t n pli plt es ci)]) st').
subst.
exists pli,plt,ci,n. simpl in *; intuition.
eapply @RIR_doLeader with (net := net'); eauto;
simpl; repeat find_rewrite; eauto.
intros.
do_in_app. intuition.
find_apply_hyp_hyp.
intuition.
- exfalso.
do_in_map. subst. simpl in *.
unfold doLeader in *.
repeat break_match; find_inversion; intuition; do_in_map; subst; simpl in *; congruence.
Qed.
Proof using.
red. unfold append_entries_request_reply_correspondence. intros.
simpl in *.
find_apply_hyp_hyp. intuition.
- copy_eapply_prop_hyp pBody pBody; auto.
unfold exists_equivalent_network_with_aer in *.
break_exists_name net'.
break_exists_name pli.
break_exists_name plt.
break_exists_name ci.
break_exists_name n.
intuition.
remember mkNetwork as mkN.
remember mkPacket as mkP.
unfold Net.name in *. simpl in *.
exists (mkN (ps' ++ [mkP (pDst p) (pSrc p) (AppendEntries t n pli plt es ci)]) st').
subst.
exists pli,plt,ci,n. simpl in *; intuition.
eapply @RIR_doGenericServer with (net := net'); eauto;
simpl; repeat find_rewrite; eauto.
intros.
do_in_app. intuition.
find_apply_hyp_hyp.
intuition.
- exfalso.
do_in_map. subst. simpl in *.
unfold doGenericServer in *.
repeat break_match; find_inversion; intuition; do_in_map; subst; simpl in *; congruence.
Qed.
Proof using.
red. unfold append_entries_request_reply_correspondence. intros.
simpl in *.
find_reverse_rewrite.
find_apply_hyp_hyp.
unfold exists_equivalent_network_with_aer in *.
break_exists_name net''.
break_exists_name pli.
break_exists_name plt.
break_exists_name ci.
break_exists_name n.
intuition. subst.
remember mkNetwork as mkN.
remember mkPacket as mkP.
unfold Net.name in *. simpl in *.
exists (mkN ((nwPackets net) ++ [mkP (pDst p) (pSrc p) (AppendEntries t n pli plt es ci)]) (nwState net')).
subst.
exists pli,plt,ci,n. simpl in *; repeat find_rewrite; intuition.
eapply @RIR_step_failure with (net := net''); [|eapply @StepFailure_reboot with (h := h) (failed := [h])]; eauto;
simpl; repeat find_rewrite; eauto.
f_equal.
apply functional_extensionality.
intros. repeat find_higher_order_rewrite.
unfold update. repeat break_if; subst; eauto; congruence.
Qed.
Proof using.
intros.
pose proof dup_drop_reorder _ packet_eq_dec _ _ ltac:(eauto).
match goal with
| [ H : dup_drop_step_star _ _ _ |- _ ] =>
eapply step_failure_dup_drop_step with (f := []) (Sigma := nwState net) in H
end.
eapply step_failure_star_raft_intermediate_reachable_extend with (f := []) (f' := []) (tr := []); [|eauto].
destruct net, net'. simpl in *. subst.
auto.
Qed.
Proof using.
red. unfold append_entries_request_reply_correspondence. intros.
simpl in *.
find_apply_hyp_hyp.
find_apply_hyp_hyp.
unfold exists_equivalent_network_with_aer in *.
break_exists_name net''.
break_exists_name pli.
break_exists_name plt.
break_exists_name ci.
break_exists_name n.
intuition.
(exists (mkNetwork (nwPackets net' ++ [{|
pSrc := pDst p;
pDst := pSrc p;
pBody := AppendEntries t n pli plt es ci |}]) (nwState net'))).
repeat eexists; intuition; eauto.
repeat find_rewrite.
break_exists_exists; intuition; repeat find_rewrite; eauto.
eapply subset_reachable with (net := net''); eauto.
- simpl in *. repeat find_rewrite.
apply functional_extensionality. eauto.
- simpl.
intros. repeat find_rewrite. do_in_app. intuition.
Qed.
Proof using.
intros.
unfold handleAppendEntries in *.
repeat break_match; find_inversion; auto; congruence.
Qed.
Proof using.
red. unfold append_entries_request_reply_correspondence. intros.
simpl in *.
find_apply_hyp_hyp. intuition.
- copy_eapply_prop_hyp pBody pBody; auto; [|repeat find_rewrite; in_crush].
unfold exists_equivalent_network_with_aer in *.
break_exists_name net'.
break_exists_name pli'.
break_exists_name plt'.
break_exists_name ci'.
break_exists_name n'.
intuition.
remember mkNetwork as mkN.
remember mkPacket as mkP.
unfold Net.name in *. simpl in *.
exists (mkN (ps' ++ [mkP (pDst p0) (pSrc p0) (AppendEntries t0 n' pli' plt' es0 ci')]) st').
subst.
exists pli',plt',ci',n'. simpl in *; intuition.
repeat find_rewrite.
match goal with
| H : nwPackets net' = (?xs ++ ?p :: ?ys) ++ ?l |- _ =>
assert (nwPackets net' = xs ++ p :: (ys ++ l))
by (find_rewrite_lem app_ass; rewrite app_comm_cons; auto);
clear H
end.
eapply @RIR_handleMessage with (net := net') (p := p);
simpl; repeat find_rewrite; eauto;
simpl; repeat break_let; eauto; try find_inversion; eauto.
intros. do_in_app. simpl in *.
intuition; try find_apply_hyp_hyp; intuition; in_crush.
- subst. simpl in *. subst. unfold exists_equivalent_network_with_aer.
find_eapply_lem_hyp RIR_step_failure; [|eapply StepFailure_dup with (failed := [])]; eauto.
remember mkNetwork as mkN.
remember mkPacket as mkP.
unfold Net.name in *. simpl in *.
match goal with
| _ : raft_intermediate_reachable (mkN (?p :: _) _ ) |- _ =>
(exists (mkN (ps' ++ [p]) st'))
end.
subst.
(exists pli, plt, ci, n).
simpl in *. intuition.
+ match goal with
| _ : raft_intermediate_reachable (mkNetwork ?ps ?st) |- _ =>
eapply @RIR_handleMessage with (net := (mkNetwork ps st)) (p := p)
(xs := (p :: xs))
end; eauto;
simpl in *; repeat find_rewrite; simpl in *; repeat break_let; eauto;
repeat find_inversion; eauto.
intros.
do_in_app. simpl in *. intuition.
find_apply_hyp_hyp. intuition; subst; auto.
+ f_equal. f_equal.
destruct p; simpl in *; f_equal; intuition.
subst.
find_apply_lem_hyp handleAppendEntries_reply_spec; auto.
intuition. subst. auto.
Qed.
Proof using.
red. unfold append_entries_request_reply_correspondence. intros.
simpl in *.
find_apply_hyp_hyp. intuition.
- copy_eapply_prop_hyp pBody pBody; auto; [|repeat find_rewrite; in_crush].
unfold exists_equivalent_network_with_aer in *.
break_exists_name net'.
break_exists_name pli'.
break_exists_name plt'.
break_exists_name ci'.
break_exists_name n'.
intuition.
remember mkNetwork as mkN.
remember mkPacket as mkP.
unfold Net.name in *. simpl in *.
exists (mkN (ps' ++ [mkP (pDst p0) (pSrc p0) (AppendEntries t0 n' pli' plt' es0 ci')]) st').
subst.
exists pli',plt',ci',n'. simpl in *; intuition.
repeat find_rewrite.
match goal with
| H : nwPackets net' = (?xs ++ ?p :: ?ys) ++ ?l |- _ =>
assert (nwPackets net' = xs ++ p :: (ys ++ l))
by (find_rewrite_lem app_ass; rewrite app_comm_cons; auto);
clear H
end.
eapply @RIR_handleMessage with (net := net') (p := p);
simpl; repeat find_rewrite; eauto;
simpl; repeat break_let; eauto; try find_inversion; eauto.
intros. do_in_app. simpl in *.
intuition; try find_apply_hyp_hyp; intuition; in_crush.
- do_in_map.
subst. simpl in *.
find_apply_lem_hyp handleAppendEntriesReply_packets.
subst. simpl in *. intuition.
Qed.

Lemma append_entries_request_reply_correspondence_request_vote :
raft_net_invariant_request_vote append_entries_request_reply_correspondence.