Proof using.
red. unfold lastApplied_le_commitIndex. intros.
subst.
simpl in *. repeat find_higher_order_rewrite.
destruct_update; simpl in *; eauto.
Qed.

Lemma lastApplied_le_commitIndex_state_same_packet_subset :
raft_net_invariant_state_same_packet_subset lastApplied_le_commitIndex.