Proof using.
induction l; intros; simpl in *; intuition.
- subst. break_if; eauto.
do_bool; omega.
- break_if; eauto. do_bool.
specialize (H1 e); intuition. omega.
Qed.

Lemma prefix_within_term_inductive_append_entries :
refined_raft_net_invariant_append_entries prefix_within_term_inductive.