Proof using rri.
unfold msg_refined_raft_net_invariant_state_same_packet_subset, commit_recorded_committed,
commit_recorded, committed, directly_committed.
intros.
specialize (H1 h e).
repeat find_rewrite_lem deghost_spec.
repeat find_rewrite_lem msg_deghost_spec'.
repeat find_higher_order_rewrite.
find_apply_hyp_hyp.
break_exists_exists.
repeat find_rewrite_lem msg_deghost_spec'.
repeat rewrite msg_deghost_spec'.
repeat find_higher_order_rewrite.
intuition.
break_exists_exists.
intuition.
find_apply_hyp_hyp.
repeat find_rewrite_lem msg_deghost_spec'.
repeat rewrite msg_deghost_spec'.
repeat find_higher_order_rewrite.
auto.
Qed.

Lemma everything_state_same_packet_subset :
msg_refined_raft_net_invariant_state_same_packet_subset' everything.