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'.