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_split: forall U c m c' m', thread_step_plus U c m c' m' -> exists c'', exists m'', thread_step Sem ge U c m c'' m'' /\ thread_step_star U c'' m'' c' m'.