Proof using.
unfold directly_committed.
intuition.
break_exists_exists.
intuition.
find_higher_order_rewrite. auto.
Qed.

Lemma lifted_committed_state_same :
forall (net net' : ghost_log_network) e t,
(forall h, nwState net' h = nwState net h) ->
lifted_committed net e t ->
lifted_committed net' e t.