(* MachStep that doesn't change the schedule,
    Reduces the set of valid schedules... 
   *)
  Inductive has_unique_running tp:Prop :=
  | HasUniqueRun i (cnti : ThreadPool.containsThread tp i) q:
      ThreadPool.getThreadC cnti = Krun q ->
      has_unique_running tp.(* MachStep that doesn't change the schedule,
    Reduces the set of valid schedules... 
   *)
  Inductive has_unique_running tp:Prop :=
  | HasUniqueRun i (cnti : ThreadPool.containsThread tp i) q:
      ThreadPool.getThreadC cnti = Krun q ->
      has_unique_running tp.

Lemma MachStep_preserve_unique: forall U tr st tr' st' m m', valid (tr, st, m) U -> MachStep (U,tr,st) m (U,tr',st') m' -> has_unique_running st'.