Proof using rmri miaei.
intros.
find_apply_lem_hyp msg_simulation_1.
match goal with
| [ H : refined_raft_intermediate_reachable _ |- _ ] =>
eapply advanceCommitIndex_committed in H
end;
repeat rewrite msg_deghost_spec' in *;
eauto using committed_lifted_committed, lifted_committed_committed.
Qed.

Lemma and_imp_2 :
forall P Q : Prop,
P /\ (P -> Q) -> P /\ Q.