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_schedule: forall tpc tpc' mc mc' i U1 U2 U1' tr tr' (Hstep: MachStep (i :: U1, tr, tpc) mc (U2, tr ++ tr', tpc') mc'), exists U2', MachStep (i :: U1', tr, tpc) mc (U2', tr ++ tr', tpc') mc'.