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 omega.
+ 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; omega|].
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; omega|].
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. Focus 5. eauto. Focus 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; omega|].
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 omega.
+ 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; omega|].
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; omega|].
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. Focus 5. eauto. Focus 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; omega)
end.
repeat find_rewrite.
do_in_app. intuition.
+ find_copy_eapply_lem_hyp sorted_app_sorted_app_in1_in2. Focus 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. Focus 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 (xs0 := 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; omega|].
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 omega.
+ 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|]. omega.
* {
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; omega).
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; omega].
find_eapply_lem_hyp prefix_contiguous. Focus 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.
- omega.
- break_exists; break_and.
unfold Prefix_sane in *. break_or_hyp; try omega.
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 omega.
+ 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|]. omega.
* {
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. Focus 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; omega.
+ subst.
find_eapply_lem_hyp entries_sorted_nw_invariant; eauto.
find_eapply_lem_hyp sorted_gt_maxIndex; eauto; try omega.
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.
- omega.
- break_exists; break_and.
unfold Prefix_sane in *. break_or_hyp; try omega.
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.

Lemma handleAppendEntriesReply_currentTerm_leaderId :
forall h st h' t es res st' m,
handleAppendEntriesReply h st h' t es res = (st', m) ->
currentTerm st < currentTerm st' \/
(currentTerm st = currentTerm st' /\ leaderId st' = leaderId st).