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 effstepN_sub_val: forall n c m c' m' (U V : block -> Z -> bool),
effstepN n U c m c' m' ->
(forall b z, Mem.valid_block m b -> U b z = true -> V b z = true) ->
effstepN n V c m c' m'.