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 U c1 c2 c3 m1 m2 m3,
effstep_star U c1 m1 c2 m2 -> effstep_plus U c2 m2 c3 m3 ->
effstep_plus U c1 m1 c3 m3.