Proof using.
intros.
unfold doLeader in *.
repeat break_match; tuple_inversion; auto; eauto using advanceCommitIndex_commitIndex.
eapply le_trans; [eapply advanceCommitIndex_commitIndex with (h := h0)|]; eauto.
Qed.

Lemma lastApplied_le_commitIndex_doLeader :
raft_net_invariant_do_leader lastApplied_le_commitIndex.