(* Decompose the initial protocol *)
Notation l := (plab p).Notation coh := (coh p).Definition W := mkWorld p.

(* Specifications: *)
Lemma cohIVd d : cohI d -> valid (dstate d).
Lemma cohIVs d : cohI d -> valid (dsoup d).
Lemma cohIDom d : cohI d -> dom (dstate d) =i nodes p d.