Section InjectLemmas.
Variable this : nid.
Variables (W V : world) (K : hooks) (A : Type) (w : injects V W K).
Notation W2 := (inj_ext w).
Variable (e1 : DT this V A).

Lemma inject_rule i j (r : cont A) :
i \In Coh V ->
verify i e1 (fun x i' => forall j',
i' \+ j' \In Coh W -> network_rely W2 this j j' -> r x (i' \+ j')) ->
verify (i \+ j) (inject w e1) r.