Definition thread_safety {Z} (Jspec : juicy_ext_spec Z) m ge (tp : jstate ge) PHI (mcompat : mem_compatible_with tp m PHI) n
  i (cnti : containsThread tp i) := forall (ora : Z),
    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 Jspec 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 Jspec 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 Jspec ge n ora q_new (getThreadR cnti)
    end.

Lemma state_inv_upd1 : forall {Z} (Jspec : juicy_ext_spec Z) Gamma (n : nat) (m : mem) (ge : genv) (tr : event_trace) (sch : schedule) (tp : ThreadPool.t) (PHI : rmap) (lev : level PHI = n) (envcoh : env_coherence Jspec ge Gamma PHI) (mcompat : mem_compatible_with tp m PHI) (extcompat : joins (ghost_of PHI) (Some (ext_ref tt, NoneP) :: nil)) (lock_sparse : lock_sparsity (lset tp)) (lock_coh : lock_coherence' tp PHI m mcompat) (safety : exists i (cnti : containsThread tp i), let phi := getThreadR cnti in (exists k, getThreadC cnti = Krun k /\ forall c, join_sub (Some (ext_ref tt, NoneP) :: nil) c -> joins (ghost_of phi) (ghost_fmap (approx (level phi)) (approx (level phi)) c) -> exists b, joins b (ghost_fmap (approx (level phi)) (approx (level phi)) c) /\ exists phi' (Hr : resource_at phi' = resource_at phi), level phi' = level phi /\ ghost_of phi' = b /\ forall ora, jsafeN Jspec ge n ora k (personal_mem (mem_cohere'_res _ _ _ (compatible_threadRes_cohere cnti (mem_compatible_forget mcompat)) Hr))) /\ forall j (cntj : containsThread tp j), j <> i -> thread_safety Jspec m ge tp PHI mcompat n j cntj) (wellformed : threads_wellformed tp) (uniqkrun : unique_Krun tp sch), state_bupd (state_invariant Jspec Gamma n) (m, (tr, sch, tp)).