Definition thread_step_plus U c m c' m' :=
    exists n, thread_stepN (S n) U c m c' m'.Definition thread_step_star U c m c' m' :=
    exists n, thread_stepN n U c m c' m'.

Lemma thread_step_plus_two: forall U c m c' m' c'' m'', thread_step Sem ge U c m c' m' -> thread_step Sem ge U c' m' c'' m'' -> thread_step_plus U c m c'' m''.