Definition effstep_plus U c m c' m' :=
    exists n, effstepN (S n) U c m c' m'.Definition effstep_star U c m c' m' :=
    exists n, effstepN n U c m c' m'.

Lemma effstep_plus_split: forall U c m c' m', effstep_plus U c m c' m' -> exists c'', exists m'', exists U1, exists U2, effstep Sem U1 c m c'' m'' /\ effstep_star U2 c'' m'' c' m' /\ U = (fun b z => U1 b z || (U2 b z && valid_block_dec m b)).