Proof using.
intros.
induction H10.
- intuition.
-  match goal with [H : step_failure _ _ _ |- _ ] => invcs H end.
+ match goal with
| [ H : refined_raft_intermediate_reachable _ |- _ ?x ] =>
assert (refined_raft_intermediate_reachable x) as Hpost
by (eapply RRIR_step_failure; eauto; eapply StepFailure_deliver; eauto)
end.
unfold refined_net_handlers in *. simpl in *.
unfold RaftNetHandler, update_elections_data_net in *.
repeat break_let.
repeat find_inversion.
match goal with
| [ H : refined_raft_intermediate_reachable ?net, H' : context [net]  |- _ ] =>
match type of H' with
| refined_raft_intermediate_reachable _ => move H after H'
end
end.
assert
(refined_raft_intermediate_reachable
{|
nwPackets := (xs ++ ys) ++ send_packets (pDst p) l2;
nwState := update name_eq_dec (nwState net) (pDst p)
(update_elections_data_net (pDst p)
(pSrc p)
(pBody p)
(nwState net (pDst p)), r0) |})
by (eapply RRIR_handleMessage; eauto; in_crush).
assert
(refined_raft_intermediate_reachable
{|
nwPackets := ((xs ++ ys)
++ send_packets (pDst p) l2)
++ send_packets (pDst p) l3 ;
nwState := update name_eq_dec
(nwState
{|
nwPackets := (xs ++ ys) ++ send_packets (pDst p) l2;
nwState := update name_eq_dec (nwState net)
(pDst p)
(update_elections_data_net
(pDst p) (pSrc p)
(pBody p) (nwState net (pDst p)), r0) |})
(pDst p)
(update_elections_data_net (pDst p)
(pSrc p) (pBody p) (nwState net (pDst p)), r1) |})
by
(eapply RRIR_doLeader; eauto;
[simpl in *; break_if; try congruence; eauto| in_crush]).
eapply_prop refined_raft_net_invariant_do_generic_server'. eauto.
eapply_prop refined_raft_net_invariant_do_leader'. eauto.
eapply refined_raft_invariant_handle_message' with (P := P); auto.
eauto. eauto.   auto. eauto.  eauto. eauto using in_app_or. auto.
eauto.
simpl. break_if; intuition eauto.
eauto.
simpl. eapply in_app_or. auto. auto.
simpl. break_if; eauto; congruence.
simpl. intros.
break_if; subst;
repeat rewrite update_same by auto;
repeat rewrite update_neq by auto; auto.
simpl. in_crush.
+ match goal with
| [ H : refined_raft_intermediate_reachable _ |- _ ?x ] =>
assert (refined_raft_intermediate_reachable x) as Hpost
by (eapply RRIR_step_failure; eauto; eapply StepFailure_input; eauto)
end.
unfold refined_input_handlers in *. simpl in *.
unfold RaftInputHandler, update_elections_data_input in *. repeat break_let.
repeat find_inversion.
match goal with
| [ H : refined_raft_intermediate_reachable ?net, H' : context [net]  |- _ ] =>
match type of H' with
| refined_raft_intermediate_reachable _ => move H after H'
end
end.
assert
(refined_raft_intermediate_reachable
{|
nwPackets := nwPackets net ++ send_packets h l2;
nwState := update name_eq_dec (nwState net) h
(update_elections_data_input h
inp
(nwState net h), r0) |})
by (eapply RRIR_handleInput; eauto; in_crush).
assert
(refined_raft_intermediate_reachable
{|
nwPackets := (nwPackets net
++ send_packets h l2)
++ send_packets h l4 ;
nwState := update name_eq_dec
(nwState
{|
nwPackets := nwPackets net ++ send_packets h l2;
nwState := update name_eq_dec
(nwState net)
h
(update_elections_data_input h inp
(nwState net h), r0) |})
h
(update_elections_data_input h inp (nwState net h), r1) |})
by
(eapply RRIR_doLeader; eauto;
[simpl in *; break_if; try congruence; eauto| in_crush]).
eapply_prop refined_raft_net_invariant_do_generic_server'. eauto.
eapply_prop refined_raft_net_invariant_do_leader'. eauto.
eapply refined_raft_invariant_handle_input' with (P := P); auto.
eauto. all:auto. all: eauto. eauto using in_app_or.
simpl. break_if; intuition eauto.
eauto.
simpl. eapply in_app_or.
auto.
simpl. break_if; eauto; congruence.
simpl. intros.
break_if; subst;
repeat rewrite update_same by auto;
repeat rewrite update_neq by auto; auto.
simpl. unfold send_packets.  intros. in_crush.
+ match goal with
| [ H : nwPackets ?net = _ |- _ {| nwPackets := ?ps ; nwState := ?st |} ] =>
assert (forall p, In p (nwPackets {| nwPackets := ps ; nwState := st |}) ->
In p (nwPackets net)) by (intros; simpl in *; find_rewrite; in_crush)
end.
eapply_prop refined_raft_net_invariant_state_same_packet_subset; [|eauto|idtac|];
eauto.
+ match goal with
| [ H : nwPackets ?net = _ |- _ {| nwPackets := ?ps ; nwState := ?st |} ] =>
assert (forall p, In p (nwPackets {| nwPackets := ps ; nwState := st |}) ->
In p (nwPackets net)) by (intros; simpl in *; find_rewrite; in_crush)
end.
eapply_prop refined_raft_net_invariant_state_same_packet_subset; [|eauto|idtac|];
eauto.
+ auto.
+ eapply_prop refined_raft_net_invariant_reboot'; eauto;
intros; simpl in *; repeat break_if; intuition; subst; intuition eauto.
* econstructor. eauto. eapply StepFailure_reboot; eauto.
* destruct (nwState net h); auto.
- eapply refined_raft_invariant_handle_input'; eauto.
eapply RRIR_handleInput; eauto.
- eapply refined_raft_invariant_handle_message'; eauto.
eapply RRIR_handleMessage; eauto.
- eapply_prop refined_raft_net_invariant_do_leader'; eauto.
eapply RRIR_doLeader; eauto.
- eapply_prop refined_raft_net_invariant_do_generic_server'; eauto.
eapply RRIR_doGenericServer; eauto.
Qed.
Ltac workhorse :=
try match goal with
| [ |- mkNetwork _ _ = mkNetwork _ _ ] => f_equal
end;
try match goal with
| [ |- (fun _ => _) = (fun _ => _) ] => apply functional_extensionality; intros
end;
repeat break_match;
repeat match goal with
| [ H : (_, _) = (_, _) |- _ ] => invc H
end;
repeat (simpl in *; subst);
repeat rewrite map_app;
repeat rewrite map_map.

(* Specifications: *)
Theorem simulation_1 :
forall net,
refined_raft_intermediate_reachable net ->
raft_intermediate_reachable (deghost net).