Proof using uii si.
unfold raft_net_invariant_do_leader, log_matching. intuition.
- find_apply_lem_hyp doLeader_doesn't_touch_log.
unfold log_matching_hosts in *; simpl in *.
match goal with
H : nwState _ _ = _ |- _ => symmetry in H
end.
intuition;
repeat find_higher_order_rewrite;
repeat break_if; repeat find_rewrite; simpl in *; eauto.
- find_reverse_rewrite.
eapply doLeader_log_matching_nw; eauto.
+ eauto using logs_sorted_invariant.
+ unfold log_matching. auto.
+ apply UniqueIndices_invariant; auto.
Qed.
Ltac do_state_same_packet_subset :=
repeat find_inversion;
eapply log_matching_state_same_packet_subset; eauto; intros; simpl in *;
try (try find_higher_order_rewrite; break_if; subst; auto);
try (try find_apply_hyp_hyp; intuition).
Ltac assert_do_leader :=
match goal with
| [ _ : nwPackets ?net = _,
H : doLeader ?s ?h = (?out ?s' ?ms) |- _ ] =>
match goal with
| [ |-
log_matching {|
nwPackets := map ?f (ms) ++ ?xs ++ ?ys;
nwState := _ |}
] =>
assert (log_matching {| nwPackets :=
xs ++ ys;
nwState := fun nm =>
if name_eq_dec nm h then s
else nwState net nm |})
| [ |-
log_matching {|
nwPackets := ?p :: map ?f (ms) ++ ?xs ++ ?ys;
nwState := _ |}
] =>
assert (log_matching {| nwPackets :=
p :: xs ++ ys;
nwState := fun nm =>
if name_eq_dec nm h then s
else nwState net nm |})
| [ |-
log_matching {|
nwPackets := map ?f (?l1 ++ ms) ++ ?xs ++ ?ys;
nwState := _ |}
] =>
assert (log_matching {| nwPackets :=
map f l1 ++ xs ++ ys;
nwState := fun nm =>
if name_eq_dec nm h then s
else nwState net nm |})
| [ |-
log_matching {|
nwPackets := ?p ::map ?f (?l1 ++ ms) ++ ?xs ++ ?ys;
nwState := _ |}
] =>
assert (log_matching {| nwPackets :=
p :: map f l1 ++ xs ++ ys;
nwState := fun nm =>
if name_eq_dec nm h then s
else nwState net nm |})
| [ |-
log_matching {|
nwPackets := map ?f (ms ++ ?l1) ++ ?xs ++ ?ys;
nwState := _ |}
] =>
assert (log_matching {| nwPackets :=
map f l1 ++ xs ++ ys;
nwState := fun nm =>
if name_eq_dec nm h then s
else nwState net nm |})
| [ |-
log_matching {|
nwPackets := map ?f (?l1 ++ ?l2 ++ ms) ++ ?xs ++ ?ys;
nwState := _ |}
] =>
assert (log_matching {| nwPackets :=
map f (l1 ++ l2) ++ xs ++ ys;
nwState := fun nm =>
if name_eq_dec nm h then s
else nwState net nm |})
| [ |-
log_matching {|
nwPackets := map ?f (?l1 ++ ms ++ ?l2) ++ ?xs ++ ?ys;
nwState := _ |}
] =>
assert (log_matching {| nwPackets :=
map f (l1 ++ l2) ++ xs ++ ys;
nwState := fun nm =>
if name_eq_dec nm h then s
else nwState net nm |})
| [ |-
log_matching {|
nwPackets := map ?f (ms ++ ?l1 ++ ?l2) ++ ?xs ++ ?ys;
nwState := _ |}
] =>
assert (log_matching {| nwPackets :=
map f (l1 ++ l2) ++ xs ++ ys;
nwState := fun nm =>
if name_eq_dec nm h then s
else nwState net nm |})
end
end.
Ltac contradict_leader_sublog :=
match goal with
| H : eIndex _ = S _ |- _ =>
exfalso; apply S_maxIndex_not_in in H; intuition; apply H; eauto
| H : S _ = eIndex _ |- _ =>
symmetry in H; exfalso; apply S_maxIndex_not_in in H; intuition; apply H; eauto
end.
Definition host_independent_log_matching_nw net :=
(forall p t leaderId prevLogIndex prevLogTerm entries leaderCommit,
In p (nwPackets net) ->
pBody p = AppendEntries t leaderId prevLogIndex prevLogTerm entries leaderCommit ->
(forall i,
prevLogIndex < i <= maxIndex entries ->
exists e,
eIndex e = i /\
In e entries) /\
(forall e,
In e entries ->
prevLogIndex < eIndex e) /\
(forall p' t' leaderId' prevLogIndex' prevLogTerm' entries' leaderCommit',
In p' (nwPackets net) ->
pBody p' = AppendEntries t' leaderId' prevLogIndex' prevLogTerm' entries' leaderCommit' ->
(forall e1 e2,
In e1 entries ->
In e2 entries' ->
eIndex e1 = eIndex e2 ->
eTerm e1 = eTerm e2 ->
(forall e3,
prevLogIndex' < eIndex e3 <= eIndex e1 ->
In e3 entries ->
In e3 entries') /\
(forall e3,
In e3 entries ->
eIndex e3 = prevLogIndex' ->
eTerm e3 = prevLogTerm') /\
(prevLogIndex <> 0 -> prevLogIndex = prevLogIndex' -> prevLogTerm = prevLogTerm')))).

(* Specifications: *)
Lemma host_independent_log_matching_nw_invariant :
forall net net',
host_independent_log_matching_nw net ->
(forall p,
is_append_entries (pBody p) ->
In p (nwPackets net') ->
In p (nwPackets net)) ->
host_independent_log_matching_nw net'.