(* State something about hook direction *)

(* Specifications: *)
Lemma injectL (U W : world) K :
valid (U \+ W \+ (Unit, K)) ->
hook_complete U -> hook_complete W ->
hooks_consistent (getc (U \+ W)) K ->
world_not_hooked U K ->
injects U (U \+ W \+ (Unit, K)) K.
Lemma injectR (U W : world) K :
valid (W \+ U \+ (Unit, K)) ->
hook_complete U -> hook_complete W ->
hooks_consistent (getc (U \+ W)) K ->
world_not_hooked U K ->
injects U (W \+ U \+ (Unit, K)) K.
Lemma locProjR (W1 W2 : world) l s1 s2:
(s1 \+ s2) \In Coh (W1 \+ W2) -> l \in dom W2.1 ->
s2 \In Coh W2 -> getStatelet (s1 \+ s2) l = getStatelet s2 l.