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_two: forall U1 c m c' m' U2 c'' m'', effstep Sem U1 c m c' m' -> effstep Sem U2 c' m' c'' m'' -> effstep_plus (fun b z => U1 b z || (U2 b z && valid_block_dec m b)) c m c'' m''.