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

Lemma coh_split W1 W2 s :
s \In Coh (W1 \+ W2) ->
hook_complete W1 -> hook_complete W2 ->
exists s1 s2 : state,
[/\ s1 \In Coh W1, s2 \In Coh W2 & s = s1 \+ s2].