Proof using.
unfold committed, directly_committed.
simpl. intros.
break_exists_exists.
find_higher_order_rewrite.
intuition.
break_exists_exists.  intuition.
find_higher_order_rewrite. auto.
Qed.

Lemma lifted_committed_ext' :
forall ps ps' st st' t e,
(forall h, st' h = st h) ->
lifted_committed (mkNetwork ps st) e t ->
lifted_committed (mkNetwork ps' st') e t.