Section AlwaysInject.
Variables (V W : world) (K : hooks) (A : Type) (w : injects V W K) (this: nid).
Notation W2 := (inj_ext w).

Lemma rely_split s1 s1' s2 s2' :
s1 \In Coh V -> s2 \In Coh V ->
network_rely W this (s1 \+ s1') (s2 \+ s2') ->
network_rely V this s1 s2 /\ network_rely (inj_ext w) this s1' s2'.