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_star_plus_trans : forall U1 c1 c2 c3 U2 m1 m2 m3, effstep_star U1 c1 m1 c2 m2 -> effstep_plus U2 c2 m2 c3 m3 -> effstep_plus (fun b z => U1 b z || (U2 b z && valid_block_dec m1 b)) c1 m1 c3 m3.