Section Exports.
Definition inj_ext := E.
Definition injects := injects.
Definition Inject := Inject.

Lemma sem_split (U V : world) (K : hooks) (w : injects U V K) s1 s1' s2 s2' this:
s1 \In Coh U -> s2 \In Coh U ->
network_step V this (s1 \+ s1') (s2 \+ s2') ->
(network_step U this s1 s2   /\ s1' = s2') \/
(network_step (inj_ext w) this s1' s2' /\ s1 = s2).