Proof using.
unfold update_elections_data_appendEntries.
intros. break_let. break_match; auto.
break_if; auto.
simpl. intuition.
Qed.

Lemma lifted_transitive_commit_invariant :
forall net h e e' t,
msg_refined_raft_intermediate_reachable net ->
In e (log (snd (nwState net h))) ->
In e' (log (snd (nwState net h))) ->
eIndex e <= eIndex e' ->
lifted_committed net e' t ->
lifted_committed net e t.