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

Lemma inject_step U W K this s1 s2 s1' s2' :
valid (U \+ W) ->
s1 \In Coh U -> s2 \In Coh U ->
hook_complete U -> hook_complete W ->
network_step (U \+ W \+ (Unit, K)) this (s1 \+ s1') (s2 \+ s2') ->
network_step U this s1 s2 /\ s1' = s2' \/
network_step W this s1' s2' /\ s1 = s2.