Section AllEntriesLog.
Context {orig_base_params : BaseParams}.
Context {one_node_params : OneNodeParams orig_base_params}.
Context {raft_params : RaftParams orig_base_params}.
Context {llli : logs_leaderLogs_interface}.
Context {aerlli : append_entries_leaderLogs_interface}.
Context {rlmli : refined_log_matching_lemmas_interface}.
Context {aellti : allEntries_leaderLogs_term_interface}.
Context {llci : leaderLogs_contiguous_interface}.
Context {ollpti : one_leaderLog_per_term_interface}.
Context {llsi : leaderLogs_sorted_interface}.
Context {tsi : term_sanity_interface}.
Context {rri : raft_refinement_interface}.
Context {aetsi : allEntries_term_sanity_interface}.
(* strategy : prove allEntries_log as inductive invariant, then prove allEntries_leaderLogs inductive from that *)
Definition no_entries_past_current_term_host_lifted net :=
forall (h : name) e,
In e (log (snd (nwState net h))) ->
eTerm e <= currentTerm (snd (nwState net h)).
Proof using rri tsi.
unfold no_entries_past_current_term_host_lifted.
pose proof deghost_spec.
do 4 intro.
repeat find_reverse_higher_order_rewrite.
eapply lift_prop; eauto.
intros.
find_apply_lem_hyp no_entries_past_current_term_invariant; eauto.
Qed.
(** Succeed iff [x] is in the list [ls], represented with left-associated nested tuples. *)
Ltac inList x ls :=
match ls with
| x => idtac
| (_, x) => idtac
| (?LS, _) => inList x LS
end.
(** Try calling tactic function [f] on every element of tupled list [ls], keeping the first call not to fail. *)
Ltac app f ls :=
match ls with
| (?LS, ?X) => f X || app f LS || fail 1
| _ => f ls
end.
(** Run [f] on every element of [ls], not just the first that doesn't fail. *)
Ltac all f ls :=
match ls with
| (?LS, ?X) => f X; all f LS
| (_, _) => fail 1
| _ => f ls
end.
Proof using rlmli.
intros.
unfold haveNewEntries in *. do_bool. intuition;
[unfold not_empty in *; break_match; subst; simpl in *; intuition; congruence|].
break_match; try congruence.
do_bool. find_apply_lem_hyp findAtIndex_elim. intuition.
assert (es <> nil) by (destruct es; subst; simpl in *; intuition; congruence).
find_eapply_lem_hyp maxIndex_non_empty.
break_exists. intuition.
find_copy_eapply_lem_hyp entries_sorted_nw_invariant; eauto.
match goal with
| H : In e es |- _ => copy_eapply maxIndex_is_max H; eauto
end.
repeat find_rewrite.
find_eapply_lem_hyp entries_match_nw_host_invariant; eauto.
Qed.
Proof using.
intros. destruct l2; intuition.
simpl in *. right.
destruct l1; intuition.
find_copy_eapply_lem_hyp findAtIndex_None; simpl in *; eauto.
unfold contiguous_range_exact_lo in *.
simpl in *. intuition.
destruct (lt_eq_lt_dec 0 (eIndex e)); intuition; eauto.
destruct (lt_eq_lt_dec (eIndex e0) (eIndex e)); intuition.
exfalso. repeat break_if; do_bool; intuition.
match goal with
| H : forall _, _ < _ <= _ -> _ |- _ =>
specialize (H (eIndex e))
end; conclude_using lia.
simpl in *. break_exists. intuition; subst; intuition.
eapply findAtIndex_None; eauto.
Qed.
Proof using.
intros. find_eapply_lem_hyp maxIndex_le; intuition; eauto.
break_exists. intuition.
unfold contiguous_range_exact_lo in *.
intuition.
find_insterU. conclude_using eauto. lia.
Qed.
Proof using.
induction l1; intros; simpl in *; intuition; eauto.
subst. find_insterU. conclude_using ltac:(apply in_app_iff; intuition eauto).
intuition.
Qed.
Proof using.
intros. do_in_app. intuition.
match goal with
| H : sorted (?l ++ ?l'), _ : In _ ?l, _ : In _ ?l' |- _ =>
eapply sorted_app_in_in in H
end; eauto.  lia.
Qed.
Proof using.
intros. do_in_app. intuition.
find_eapply_lem_hyp Prefix_In; [|eauto].
match goal with
| H : sorted (?l ++ ?l'), _ : In _ ?l, _ : In _ ?l' |- _ =>
eapply sorted_app_in_in in H
end; eauto. lia.
Qed.
Proof using.
intros. do_in_app. intuition.
match goal with
| H : sorted (?l ++ ?l'), _ : In _ ?l, _ : In _ ?l' |- _ =>
eapply sorted_app_in_in in H
end; eauto.  lia.
Qed.
Proof using.
induction l; intros; simpl in *; intuition; subst_max; intuition.
- find_apply_hyp_hyp. intuition.
- find_apply_hyp_hyp. intuition.
Qed.
Proof using.
intros.
assert (eIndex e' <= eIndex e) by
(eapply sorted_term_index_le; eauto;
find_apply_hyp_hyp;
destruct (lt_eq_lt_dec (eTerm e') (eTerm e)); intuition).
find_eapply_lem_hyp removeAfterIndex_le_In; eauto.
repeat find_rewrite.
do_in_app. intuition.
find_apply_hyp_hyp. intuition.
Qed.
Proof using.
intros.
induction l; simpl in *; intuition.
break_match; intuition. subst. simpl. auto.
Qed.
Proof using.
intros; induction l1; simpl in *; intuition.
- destruct l2; simpl in *; intuition.
match goal with
| H : forall _, ?e = _ \/ _ -> _ |- _ =>
specialize (H e)
end; intuition.
Qed.
Proof using aetsi rri tsi llsi ollpti llci aellti rlmli aerlli llli.
red. unfold allEntries_log in *. simpl in *. intros.
repeat find_higher_order_rewrite.
destruct_update; simpl in *;
[|find_apply_hyp_hyp; intuition;
right; break_exists_exists; intuition;
repeat find_higher_order_rewrite;
destruct_update; simpl in *;
eauto; rewrite update_elections_data_appendEntries_leaderLogs; eauto].
find_eapply_lem_hyp update_elections_data_appendEntries_allEntries_detailed; eauto.
intuition;
[|repeat find_rewrite;
find_eapply_lem_hyp appendEntries_haveNewEntries_false; eauto].
find_copy_apply_hyp_hyp. intuition;
[|right; break_exists_exists; intuition;
repeat find_higher_order_rewrite; destruct_update; simpl in *; eauto;
try rewrite update_elections_data_appendEntries_leaderLogs; eauto; subst;
find_apply_lem_hyp handleAppendEntries_currentTerm_leaderId; intuition;
repeat find_rewrite; auto].
destruct (in_dec entry_eq_dec e (log d)); intuition.
right.
find_copy_apply_lem_hyp handleAppendEntries_log_detailed.
intuition; repeat find_rewrite; intuition.
- subst.
find_copy_eapply_lem_hyp allEntries_term_sanity_invariant; eauto.
destruct (lt_eq_lt_dec t0 (currentTerm d)); intuition; unfold ghost_data in *; simpl in *; try lia.
+ eapply append_entries_leaderLogs_invariant in H1; eauto.
break_exists. break_and.
match goal with
| H : In (?t, ?ll) (leaderLogs (fst (nwState _ ?leader))) |- _ =>
(exists t, leader, ll)
end.
split;
[repeat find_higher_order_rewrite;
destruct_update; simpl in *;
eauto; rewrite update_elections_data_appendEntries_leaderLogs; eauto|];
split; auto; intuition;
[break_exists; intuition;
find_eapply_lem_hyp leaderLogs_contiguous_invariant; eauto; lia|].
subst. repeat find_rewrite. intuition.
+ subst.
find_eapply_lem_hyp allEntries_leaderLogs_term_invariant; eauto. intuition.
* subst. exfalso.
find_copy_eapply_lem_hyp logs_leaderLogs_invariant; eauto.
pose proof H1 as H1'.
eapply append_entries_leaderLogs_invariant in H1; eauto.
break_exists; intuition;
[break_exists; intuition;
find_eapply_lem_hyp leaderLogs_contiguous_invariant; eauto; lia|].
subst. clean.
repeat find_rewrite.
find_eapply_lem_hyp one_leaderLog_per_term_log_invariant; eauto;
conclude_using eauto. subst.
match goal with
| H : In _ _ -> False |- _ =>
apply H
end.
find_copy_eapply_lem_hyp entries_sorted_invariant; eauto.
unfold entries_sorted in *.
repeat find_rewrite.
match goal with
| _ : removeAfterIndex ?l (eIndex ?e) = _ |- _ =>
assert (In e (removeAfterIndex l (eIndex e))) by
(eapply removeAfterIndex_le_In; eauto)
end.
repeat find_rewrite.
do_in_app; intuition.
assert (exists e', eIndex e' = eIndex e /\ In e' (x1 ++ x4)) by
(eapply entries_contiguous_nw_invariant; eauto;
intuition; [eapply entries_contiguous_invariant; eauto|];
eapply le_trans; [eapply maxIndex_is_max; eauto|];
eapply maxIndex_le'; eauto;
[eapply entries_contiguous_invariant; eauto|
eapply entries_contiguous_nw_invariant; eauto]).
break_exists. intuition.
find_copy_eapply_lem_hyp sorted_app_sorted_app_in1_in2. 5: { eauto. } 4: { eauto. }
all:(try solve [eapply entries_sorted_nw_invariant; eauto]).
all:(try solve [repeat find_reverse_rewrite; eauto using removeAfterIndex_sorted]).
find_apply_hyp_hyp.
find_eapply_lem_hyp entries_match_nw_host_invariant; eauto; repeat conclude_using eauto.
match goal with
| H : eIndex _ = eIndex _ |- _ =>
eapply uniqueIndices_elim_eq in H
end; eauto using sorted_uniqueIndices.
subst. auto.
* exfalso.
pose proof H1 as H1'.
eapply append_entries_leaderLogs_invariant in H1; eauto.
break_exists; intuition;
[break_exists; intuition;
find_eapply_lem_hyp leaderLogs_contiguous_invariant; eauto; lia|].
subst. clean.
find_eapply_lem_hyp one_leaderLog_per_term_log_invariant; eauto;
conclude_using eauto. subst.
match goal with
| H : In _ _ -> False |- _ =>
apply H
end.
repeat find_rewrite. apply in_app_iff; intuition.
- subst.
find_copy_eapply_lem_hyp allEntries_term_sanity_invariant; eauto.
destruct (lt_eq_lt_dec t0 (currentTerm d)); intuition; unfold ghost_data in *; simpl in *; try lia.
+ eapply append_entries_leaderLogs_invariant in H1; eauto.
break_exists. break_and.
match goal with
| H : In (?t, ?ll) (leaderLogs (fst (nwState _ ?leader))) |- _ =>
(exists t, leader, ll)
end. find_higher_order_rewrite.
split;
[subst; find_higher_order_rewrite;
destruct_update; simpl in *;
eauto; rewrite update_elections_data_appendEntries_leaderLogs; eauto|];
split; auto.
intuition;
[break_exists; intuition;
find_eapply_lem_hyp leaderLogs_contiguous_invariant; eauto; lia|].
subst. repeat find_rewrite. intuition.
+ subst.
find_eapply_lem_hyp allEntries_leaderLogs_term_invariant; eauto. intuition.
* { subst. exfalso.
find_copy_eapply_lem_hyp logs_leaderLogs_invariant; eauto.
pose proof H1 as H1'.
eapply append_entries_leaderLogs_invariant in H1; eauto.
break_exists; intuition;
[break_exists; intuition;
find_eapply_lem_hyp leaderLogs_contiguous_invariant; eauto; lia|].
subst. clean.
repeat find_rewrite.
find_eapply_lem_hyp one_leaderLog_per_term_log_invariant; eauto;
conclude_using eauto. subst.
match goal with
| H : In _ _ -> False |- _ =>
apply H
end.
find_copy_eapply_lem_hyp entries_sorted_invariant; eauto.
unfold entries_sorted in *.
repeat find_rewrite.
match goal with
| _ : removeAfterIndex ?l (eIndex ?e) = _ |- _ =>
assert (In e (removeAfterIndex l (eIndex e))) by
(eapply removeAfterIndex_le_In; eauto)
end.
repeat find_rewrite.
do_in_app; intuition.
find_apply_lem_hyp findAtIndex_elim. intuition.
find_copy_apply_lem_hyp maxIndex_non_empty.
break_exists.
intuition.
match goal with
| _ : In ?e' (log _), _ : maxIndex ?l = eIndex ?e' |- _ =>
destruct (le_lt_dec (eIndex e) (maxIndex l))
end.
- assert (exists e', eIndex e' = eIndex e /\ In e' (x1 ++ x4)) by
(eapply entries_contiguous_nw_invariant; eauto; intuition;
eapply entries_gt_0_invariant; eauto).
break_exists. intuition.
find_copy_eapply_lem_hyp sorted_app_sorted_app_in1_in2. 5: { eauto. } 4: { eauto. }
all:(try solve [eapply entries_sorted_nw_invariant; eauto]).
all:(try solve [repeat find_reverse_rewrite; eauto using removeAfterIndex_sorted]).
find_apply_hyp_hyp.
find_eapply_lem_hyp entries_match_nw_host_invariant; eauto; repeat conclude_using eauto.
match goal with
| H : eIndex _ = eIndex _ |- _ =>
eapply uniqueIndices_elim_eq in H
end; eauto using sorted_uniqueIndices.
subst. auto.
- exfalso.
repeat find_rewrite.
match goal with
| _ : eIndex ?e' = eIndex ?x,
_ : eIndex ?x < ?i,
_ : context [removeAfterIndex ?l ?i] |- _ =>
assert (In e' (removeAfterIndex l i)) by
(eapply removeAfterIndex_le_In; auto; lia)
end.
repeat find_rewrite.
do_in_app. intuition.
+ find_copy_eapply_lem_hyp sorted_app_sorted_app_in1_in2. 4: { eauto. }
all:eauto.
all:(try solve [eapply entries_sorted_nw_invariant; eauto]).
all:(try solve [repeat find_reverse_rewrite; eauto using removeAfterIndex_sorted]).
repeat find_apply_hyp_hyp. repeat find_rewrite. intuition.
+ find_eapply_lem_hyp leaderLogs_sorted_invariant; eauto.
find_copy_eapply_lem_hyp sorted_app_in2_in2. 3: { eauto. }
all:eauto.
all:(try solve [eapply entries_sorted_nw_invariant; eauto]).
match goal with
| H : eIndex ?e1 = eIndex ?e2, _ : In ?e1 ?ll, _ : In ?e2 ?ll |- _ =>
eapply @uniqueIndices_elim_eq with (xs := ll) in H
end; eauto using sorted_uniqueIndices.
subst. intuition.
}
* exfalso.
pose proof H1 as H1'.
eapply append_entries_leaderLogs_invariant in H1; eauto.
break_exists; intuition;
[break_exists; intuition;
find_eapply_lem_hyp leaderLogs_contiguous_invariant; eauto; lia|].
subst. clean.
find_eapply_lem_hyp one_leaderLog_per_term_log_invariant; eauto;
conclude_using eauto. subst.
match goal with
| H : In _ _ -> False |- _ =>
apply H
end.
repeat find_rewrite. apply in_app_iff; intuition.
- find_copy_eapply_lem_hyp allEntries_term_sanity_invariant; eauto.
destruct (lt_eq_lt_dec t0 t); intuition; unfold ghost_data in *; simpl in *; try lia.
+ match goal with
| H : context [pBody] |- _ =>
copy_eapply append_entries_leaderLogs_invariant H
end; eauto.
break_exists. break_and. subst.
match goal with
| H : In (?t, ?ll) (leaderLogs (fst (nwState _ ?leader))) |- _ =>
(exists t, leader, ll)
end.
split;
[find_higher_order_rewrite;
destruct_update; simpl in *;
eauto; rewrite update_elections_data_appendEntries_leaderLogs; eauto|];
split; auto. intuition; subst.
* contradict n0.
apply in_app_iff. right. eapply removeAfterIndex_le_In; eauto.
find_eapply_lem_hyp leaderLogs_sorted_invariant; eauto.
eapply le_trans; [eapply maxIndex_is_max; eauto|]. lia.
* {
break_exists. intuition. unfold Prefix_sane in *. intuition.
- destruct (le_lt_dec (eIndex e) (eIndex x3)).
+ match goal with
| H : In e _ -> False |- _ => apply H
end.
apply in_app_iff. right. apply removeAfterIndex_le_In; auto.
+ match goal with
| H : In e _ -> False |- _ => apply H
end.
apply in_app_iff. left.
apply in_app_iff. right.
find_eapply_lem_hyp leaderLogs_sorted_invariant; eauto.
eapply prefix_contiguous; eauto.
find_copy_eapply_lem_hyp entries_sorted_nw_invariant; eauto.
eapply contiguous_app; eauto.
eapply entries_contiguous_nw_invariant; eauto.
- contradict n0.
repeat find_rewrite.
apply in_app_iff. right.
find_eapply_lem_hyp leaderLogs_sorted_invariant; eauto.
apply removeAfterIndex_le_In; auto.
eapply maxIndex_is_max; eauto.
}
* contradict n0. intuition.
+ subst.
find_eapply_lem_hyp allEntries_leaderLogs_term_invariant; eauto. intuition.
* { subst. exfalso.
find_copy_eapply_lem_hyp logs_leaderLogs_invariant; eauto.
pose proof H1 as H1'.
eapply append_entries_leaderLogs_invariant in H1; eauto.
break_exists. break_and.
repeat find_rewrite.
find_eapply_lem_hyp one_leaderLog_per_term_log_invariant; eauto.
conclude_using eauto. subst. intuition.
- repeat find_rewrite.
destruct (le_lt_dec (eIndex e) (eIndex x6)).
+ match goal with
| H : In e _ -> False |- _ => apply H
end.
apply in_app_iff. right. apply removeAfterIndex_le_In; auto.
+ match goal with
| H : In e _ -> False |- _ => apply H
end.
apply in_app_iff. left.
find_copy_eapply_lem_hyp entries_sorted_invariant.
find_eapply_lem_hyp maxIndex_le'; eauto;
[|eapply entries_contiguous_invariant; eauto|eapply entries_contiguous_nw_invariant; eauto].
find_copy_eapply_lem_hyp entries_contiguous_nw_invariant; eauto.
unfold contiguous_range_exact_lo in *.
break_and.
find_copy_eapply_lem_hyp entries_sorted_invariant.
match goal with
| H : forall _, _ < _ <= _ -> _ |- _ =>
specialize (H (eIndex e));
conclude_using ltac:(intuition; eapply le_trans; [eapply maxIndex_is_max; eauto|]; eauto)
end.
break_exists. break_and.
match goal with
| H : eIndex ?x = eIndex e |- _ =>
copy_eapply entries_match_nw_host_invariant H
end; eauto.
find_copy_eapply_lem_hyp leaderLogs_sorted_invariant; eauto.
conclude_using
ltac:(match goal with
| H : _ |- _ => apply H
end; do_in_app; intuition;
match goal with
| H : In ?x _ |- In ?x _ =>
copy_eapply Prefix_maxIndex H
end; [|idtac|eauto]; eauto; lia).
conclude_using eauto. conclude_using auto.
match goal with
| H : _ = _ |- _ =>
eapply uniqueIndices_elim_eq in H
end; eauto; eauto using sorted_uniqueIndices.
subst. auto.
- break_exists. break_and.
destruct (le_lt_dec (eIndex e) (eIndex x6)).
+ match goal with
| H : In e _ -> False |- _ => apply H
end.
apply in_app_iff. right. apply removeAfterIndex_le_In; auto.
+ match goal with
| _ : removeAfterIndex _ (eIndex ?e) = ?l |- _ =>
assert (In e l) by (repeat find_reverse_rewrite;
eapply removeAfterIndex_le_In; auto)
end.
find_copy_eapply_lem_hyp entries_sorted_invariant.
assert (exists e', eIndex e' = eIndex e /\ In e' (x1 ++ x2)) by
(eapply entries_contiguous_nw_invariant; eauto;
intuition;
eapply le_trans; [eapply maxIndex_is_max; eauto|];
eapply maxIndex_le'; eauto;
[eapply entries_contiguous_invariant; eauto|
eapply entries_contiguous_nw_invariant; eauto]).
do_in_app. intuition.
* break_exists. break_and.
match goal with
| H : eIndex _ = eIndex _ |- _ =>
copy_eapply sorted_app_sorted_app_in1_in2_prefix H
end; eauto.
all:try solve [repeat find_reverse_rewrite; eauto using removeAfterIndex_sorted].
all:try solve [eapply entries_sorted_nw_invariant; eauto].
find_apply_hyp_hyp.
match goal with
| H : In e _ -> False |- _ => apply H
end.
apply in_app_iff. left.
match goal with
| H : eIndex _ = eIndex _ |- _ =>
copy_eapply entries_match_nw_host_invariant H
end; eauto. concludes. repeat conclude_using eauto.
match goal with
| H : eIndex _ = eIndex _ |- _ =>
copy_eapply uniqueIndices_elim_eq H
end; eauto using sorted_uniqueIndices. subst. auto.
* find_copy_eapply_lem_hyp leaderLogs_sorted_invariant; eauto.
unfold Prefix_sane in *.
intuition; [|find_eapply_lem_hyp maxIndex_is_max; eauto; lia].
find_eapply_lem_hyp prefix_contiguous. 2: { eauto. }
all:eauto.
all:try solve [eapply contiguous_app; [|eapply entries_contiguous_nw_invariant; eauto];
eapply entries_sorted_nw_invariant; eauto].
match goal with
| H : In e _ -> False |- _ => apply H
end. intuition.
- subst.
destruct (le_lt_dec (eIndex e) (eIndex x6)).
+ match goal with
| H : In e _ -> False |- _ => apply H
end.
apply in_app_iff. right. apply removeAfterIndex_le_In; auto.
+ match goal with
| _ : removeAfterIndex _ (eIndex ?e) = ?l |- _ =>
assert (In e l) by (repeat find_reverse_rewrite;
eapply removeAfterIndex_le_In; auto)
end.
find_copy_eapply_lem_hyp entries_sorted_invariant.
assert (exists e', eIndex e' = eIndex e /\ In e' (x1 ++ x4)) by
(eapply entries_contiguous_nw_invariant; eauto;
intuition;
eapply le_trans; [eapply maxIndex_is_max; eauto|];
eapply maxIndex_le'; eauto;
[eapply entries_contiguous_invariant; eauto|
eapply entries_contiguous_nw_invariant; eauto]).
do_in_app. intuition.
* break_exists. break_and.
match goal with
| H : eIndex _ = eIndex _ |- _ =>
copy_eapply sorted_app_sorted_app_in1_in2 H
end; eauto.
all:try solve [repeat find_reverse_rewrite; eauto using removeAfterIndex_sorted].
all:try solve [eapply entries_sorted_nw_invariant; eauto].
find_apply_hyp_hyp.
match goal with
| H : In e _ -> False |- _ => apply H
end.
apply in_app_iff. left.
match goal with
| H : eIndex _ = eIndex _ |- _ =>
copy_eapply entries_match_nw_host_invariant H
end; eauto. concludes. repeat conclude_using eauto.
match goal with
| H : eIndex _ = eIndex _ |- _ =>
copy_eapply uniqueIndices_elim_eq H
end; eauto using sorted_uniqueIndices. subst. auto.
* match goal with
| H : In e _ -> False |- _ => apply H
end. intuition.
}
* { exfalso.
find_copy_apply_lem_hyp append_entries_leaderLogs_invariant; eauto.
break_exists; intuition.
copy_eapply_prop_hyp append_entries_leaderLogs pBody; eauto.
break_exists; break_and.
subst.
find_eapply_lem_hyp one_leaderLog_per_term_log_invariant; eauto;
conclude_using eauto. subst.
match goal with
| H : In _ _ -> False |- _ =>
apply H
end.
find_copy_apply_lem_hyp leaderLogs_sorted_invariant; auto.
find_copy_apply_lem_hyp maxIndex_is_max; auto.
destruct (le_lt_dec (eIndex e) (eIndex x1));
[apply in_app_iff; right; eapply removeAfterIndex_le_In; eauto|].
repeat find_rewrite. apply in_app_iff; intuition.
- lia.
- break_exists; break_and.
unfold Prefix_sane in *. break_or_hyp; try lia.
left; apply in_app_iff; right.
eapply prefix_contiguous; eauto.
eapply contiguous_app; [|eapply entries_contiguous_nw_invariant; eauto];
eapply entries_sorted_nw_invariant; eauto.
- subst. intuition.
}
- find_copy_eapply_lem_hyp allEntries_term_sanity_invariant; eauto.
destruct (lt_eq_lt_dec t0 t); intuition; unfold ghost_data in *; simpl in *; try lia.
+ match goal with
| H : context [pBody] |- _ =>
copy_eapply append_entries_leaderLogs_invariant H
end; eauto.
break_exists. break_and. subst.
match goal with
| H : In (?t, ?ll) (leaderLogs (fst (nwState _ ?leader))) |- _ =>
(exists t, leader, ll)
end.
split;
[find_higher_order_rewrite;
destruct_update; simpl in *;
eauto; rewrite update_elections_data_appendEntries_leaderLogs; eauto|];
split; auto. intuition; subst.
* contradict n0.
apply in_app_iff. right. eapply removeAfterIndex_le_In; eauto.
find_eapply_lem_hyp leaderLogs_sorted_invariant; eauto.
eapply le_trans; [eapply maxIndex_is_max; eauto|]. lia.
* {
break_exists. intuition. unfold Prefix_sane in *. intuition.
- destruct (le_lt_dec (eIndex e) (eIndex x4)).
+ match goal with
| H : In e _ -> False |- _ => apply H
end.
apply in_app_iff. right. apply removeAfterIndex_le_In; auto.
+ match goal with
| H : In e _ -> False |- _ => apply H
end.
apply in_app_iff. left.
apply in_app_iff. right.
find_eapply_lem_hyp leaderLogs_sorted_invariant; eauto.
eapply prefix_contiguous; eauto.
find_copy_eapply_lem_hyp entries_sorted_nw_invariant; eauto.
eapply contiguous_app; eauto.
eapply entries_contiguous_nw_invariant; eauto.
- contradict n0.
repeat find_rewrite.
apply in_app_iff. right.
find_eapply_lem_hyp leaderLogs_sorted_invariant; eauto.
apply removeAfterIndex_le_In; auto.
eapply maxIndex_is_max; eauto.
}
* contradict n0. intuition.
+ subst.
find_eapply_lem_hyp allEntries_leaderLogs_term_invariant; eauto. intuition.
* { subst. exfalso.
find_copy_eapply_lem_hyp logs_leaderLogs_invariant; eauto.
pose proof H1 as H1'.
eapply append_entries_leaderLogs_invariant in H1; eauto.
break_exists. break_and.
find_eapply_lem_hyp one_leaderLog_per_term_log_invariant; eauto.
repeat find_rewrite.
conclude_using eauto. subst.
find_eapply_lem_hyp le_antisym; eauto.
destruct x1.
- simpl in *. destruct x2; simpl in *; auto.
break_match; auto.
match goal with
| H : _ \/ (exists _, _) \/ _ |- _ =>
clear H
end.
break_and. subst.
cut (e1 = x6); intros; subst; auto.
find_apply_lem_hyp findAtIndex_elim.
break_and.
find_copy_apply_lem_hyp entries_sorted_invariant.
eapply uniqueIndices_elim_eq; eauto using sorted_uniqueIndices.
eapply removeAfterIndex_in with (i := (eIndex e)).
unfold raft_data, ghost_data in *; simpl in *.
unfold raft_data, ghost_data in *; simpl in *.
repeat find_rewrite. intuition.
- simpl in *.
match goal with
| H : forall _, ?e = _ \/ _ -> _ |- _ =>
specialize (H e)
end. conclude_using auto.
repeat find_rewrite.
find_apply_lem_hyp findAtIndex_elim. break_and.
find_eapply_lem_hyp term_ne_in_l2. 7: { eauto. } all:eauto.
all:try solve [eapply entries_sorted_invariant; eauto].
all:try solve [intros; find_eapply_lem_hyp no_entries_past_current_term_host_lifted_invariant; unfold ghost_data, raft_data in *; simpl in *;
unfold ghost_data, raft_data in *; simpl in *;
repeat find_rewrite; eauto].
assert (eIndex e0 <= maxIndex x4) by
(repeat find_rewrite;
eapply maxIndex_is_max; eauto;
eapply leaderLogs_sorted_invariant; eauto).
assert (eIndex x7 < eIndex e0) by
(eapply entries_contiguous_nw_invariant; eauto; intuition).
intuition.
+ break_exists. break_and.
unfold Prefix_sane in *. intuition.
find_copy_eapply_lem_hyp Prefix_maxIndex_eq; eauto.
find_eapply_lem_hyp entries_sorted_nw_invariant; eauto.
find_eapply_lem_hyp sorted_gt_maxIndex; eauto; lia.
+ subst.
find_eapply_lem_hyp entries_sorted_nw_invariant; eauto.
find_eapply_lem_hyp sorted_gt_maxIndex; eauto; try lia.
destruct x4; simpl in *; congruence.
}
* { exfalso.
find_copy_apply_lem_hyp append_entries_leaderLogs_invariant; eauto.
break_exists; intuition. subst.
copy_eapply_prop_hyp append_entries_leaderLogs pBody; eauto.
break_exists; break_and.
subst.
find_eapply_lem_hyp one_leaderLog_per_term_log_invariant; eauto;
conclude_using eauto. subst.
match goal with
| H : In _ _ -> False |- _ =>
apply H
end.
find_copy_apply_lem_hyp leaderLogs_sorted_invariant; auto.
find_copy_apply_lem_hyp maxIndex_is_max; auto.
destruct (le_lt_dec (eIndex e) (eIndex x2));
[apply in_app_iff; right; eapply removeAfterIndex_le_In; eauto|].
repeat find_rewrite. apply in_app_iff; intuition.
- lia.
- break_exists; break_and.
unfold Prefix_sane in *. break_or_hyp; try lia.
left; apply in_app_iff; right.
eapply prefix_contiguous; eauto.
eapply contiguous_app; [|eapply entries_contiguous_nw_invariant; eauto];
eapply entries_sorted_nw_invariant; eauto.
- subst. intuition.
}
Qed.
Proof using.
intros. unfold handleAppendEntriesReply, advanceCurrentTerm in *.
repeat (break_match; try find_inversion; simpl in *; do_bool; auto).
Qed.

Lemma allEntries_log_append_entries_reply :
refined_raft_net_invariant_append_entries_reply allEntries_log.