Fixpoint effstepN (n:nat) : (block -> Z -> bool) -> C -> mem -> C -> mem -> Prop :=
    match n with
      | O => fun U c m c' m' => (c,m) = (c',m') /\ U = (fun b z => false)
      | S k => fun U c1 m1 c3 m3 => exists c2, exists m2, exists U1, exists U2,
        effstep Sem U1 c1 m1 c2 m2 /\
        effstepN k U2 c2 m2 c3 m3 /\
        U = (fun b z => U1 b z || (U2 b z && valid_block_dec m1 b))
    end.

Lemma effstepN_valid n U c1 m1 c2 m2 (Step:effstepN n U c1 m1 c2 m2) b z (EFF:U b z = true): Mem.valid_block m1 b.