Notation "cnt '$' m '@'  'S'" := (getStepType cnt m Suspend) (at level 80).

(* Specifications: *)
Lemma updThreadC_compatible: forall (tp : t) m i c (ctn : containsThread tp i) (Hcomp: mem_compatible tp m), mem_compatible (updThreadC ctn c) m.
Lemma suspend_step_det: forall m tp tp' tp'' i (cnt: containsThread tp i) (Hstep: suspend_thread m cnt tp') (Hstep': suspend_thread m cnt tp''), tp' = tp''.
Lemma suspend_containsThread: forall m tp tp' i j (cnti: containsThread tp i) (Hsuspend: suspend_thread m cnti tp'), containsThread tp j <-> containsThread tp' j.