Proof using.
red. unfold prefix_within_term_inductive in *.
intuition;
red; intros; simpl in *; intuition.
unfold prefix_within_term. intros. simpl in *.
intuition.
Qed.

Lemma prefix_within_term_inductive_state_same_packet_subset :
refined_raft_net_invariant_state_same_packet_subset prefix_within_term_inductive.