Definition threads_safety m (tp : jstate ge) PHI (mcompat : mem_compatible_with tp m PHI) n :=
  forall i (cnti : containsThread tp i) (ora : ZT),
    match getThreadC cnti with
    | Krun c => semax.jsafeN Jspec ge n ora c (jm_ cnti mcompat)
    | Kblocked c =>
      (* The dry memory will change, so when we prove safety after an
      external we must only inspect the rmap m_phi part of the juicy
      memory.  This means more proof for each of the synchronisation
      primitives. *)
      jsafe_phi ge n ora c (getThreadR cnti)
    | Kresume c v =>
      forall c',
        (* [v] is not used here. The problem is probably coming from
           the definition of JuicyMachine.resume_thread'. *)
        cl_after_external None c = Some c' ->
        (* same quantification as in Kblocked *)
        jsafe_phi_bupd ge n ora c' (getThreadR cnti)
    | Kinit v1 v2 =>
      val_inject (Mem.flat_inj (Mem.nextblock m)) v2 v2 /\
      exists q_new,
      cl_initial_core ge v1 (v2 :: nil) q_new /\
      jsafe_phi ge n ora q_new (getThreadR cnti)
    end.Definition threads_wellformed (tp : jstate ge) :=
  forall i (cnti : containsThread tp i),
    match getThreadC cnti with
    | Krun q => Logic.True
    | Kblocked q => cl_at_external q <> None
    | Kresume q v => cl_at_external q <> None /\ v = Vundef
    | Kinit _ _ => Logic.True
    end.(* Havent' move this, but it's already defined in the concurrent_machien...
 * Probably in the wrong part...
 * SC: I had to change unique_Krun to include ~ Halted. Because halted
 * threads are still in Krun. (Although, ass you know right now there are no Hatled
 * threads...)  *)
Definition unique_Krun (tp : jstate ge) sch :=
  (lt 1 tp.(num_threads).(pos.n) -> forall i cnti q,
      @getThreadC _ _ _ i tp cnti = Krun q ->
      exists sch', sch = i :: sch').Definition no_Krun (tp : jstate ge) :=
  forall i cnti q, @getThreadC _ _ _ i tp cnti <> Krun q.

Lemma unique_Krun_no_Krun_updThread tp i sch cnti c' phi' : (forall q, c' <> Krun q) -> unique_Krun tp (i :: sch) -> no_Krun (@updThread _ _ _ i tp cnti c' phi').