Corollary gsoThreadC_suspend:
    forall m tp tp' i j (cnt: containsThread tp i) (cntj: containsThread tp j)
      (cntj': containsThread tp' j) (Hneq: i <> j)
      (Hsuspend: suspend_thread m cnt tp'),
      getThreadC cntj = getThreadC cntj'.

Lemma step_containsThread : forall tp tp' m m' i j U tr tr' (cntj: containsThread tp j) (Hstep: MachStep (i :: U, tr, tp) m (U, tr', tp') m'), containsThread tp' j.