(* Wrapping up the coherence predicate *)
Definition GreeterCoh := CohPred (CohPredMixin l1 l2 l3).Notation coh := GreeterCoh.

(* Specifications: *)
Lemma greet_safe_coh this to d m : greet_safe this to d m -> coh d.
Lemma greet_safe_def this to d msg : greet_safe this to d msg <-> exists b pf, @greet_step this to d msg pf = Some b.