Proof using.
intros.
match goal with
| [ H : context [step_failure _ _ _ ] |- _ ] => invcs H
end.
- unfold RaftNetHandler in *. repeat break_let. subst. find_inversion.
find_apply_lem_hyp applied_implies_input_update_split.
break_exists. intuition; break_exists.
+ find_erewrite_lem doGenericServer_log.
find_erewrite_lem doLeader_same_log.
exfalso. eauto using aiis_intro_state, handleMessage_aais.
+ exfalso. eauto using aiis_intro_state.
+ intuition. do_in_app. intuition.
* do_in_map. subst. simpl in *.
{ repeat (do_in_app; intuition).
- exfalso. eauto using aiis_intro_state, handleMessage_sends_log.
- find_eapply_lem_hyp doLeader_messages; eauto.
exfalso. eauto using aiis_intro_state, handleMessage_aais.
- exfalso. eauto using doGenericServer_packets.
}
* exfalso. eauto using aiis_intro_packet.
- unfold RaftInputHandler in *. repeat break_let. subst. find_inversion.
find_apply_lem_hyp applied_implies_input_update_split.
break_exists. intuition; break_exists.
+ find_erewrite_lem doGenericServer_log.
find_erewrite_lem doLeader_same_log.
eauto using handleInputs_aais.
+ exfalso. eauto using aiis_intro_state.
+ intuition. do_in_app. intuition.
* do_in_map. subst. simpl in *.
{ repeat (do_in_app; intuition).
- destruct inp; simpl in *.
+ exfalso. eapply handleTimeout_not_is_append_entries; eauto.
eauto using mEntries_some_is_applied_entries.
+ exfalso. eauto using handleClientRequest_no_messages.
- find_eapply_lem_hyp doLeader_messages; eauto.
eauto using handleInputs_aais.
- exfalso. eauto using doGenericServer_packets.
}
* exfalso. eauto using aiis_intro_packet.
- unfold applied_implies_input_state in H2.
break_exists. intuition; break_exists; simpl in *.
+ exfalso; eauto  using aiis_intro_state.
+ break_and. simpl in *.
exfalso. eauto using aiis_intro_packet.
- unfold applied_implies_input_state in H2.
break_exists. intuition; break_exists; simpl in *.
+ exfalso; eauto  using aiis_intro_state.
+ intuition.
* subst. exfalso. eauto using aiis_intro_packet.
* exfalso. apply H1. eapply aiis_intro_packet; eauto.
congruence.
- congruence.
- unfold applied_implies_input_state in H2.
break_exists. intuition; break_exists; simpl in *.
+ update_destruct_max_simplify; exfalso; eauto using aiis_intro_state.
+ intuition.
exfalso. eauto using aiis_intro_packet.
Qed.
Definition aiis_host (net : network) : Prop :=
exists h e,
correct_entry client id i e /\
In e (log (nwState net h)).

Lemma name_dec :
forall (P : name -> Prop)
(P_dec : forall x, {P x} + {~P x}),
{exists x, P x} + {~ exists x, P x}.