(********************************************************************)
(*                      Framing result                              *)
(********************************************************************)

Lemma inject_frame U W K this s1 s2 s:
s1 \+ s \In Coh (U \+ W \+ (Unit, K)) ->
network_step U this s1 s2 ->
hook_complete U -> hook_complete W ->
hooks_consistent (U \+ W).1 K ->
world_not_hooked U K ->
network_step (U \+ W \+ (Unit, K)) this (s1 \+ s) (s2 \+ s).