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_trans: forall n1 n2 U1 st1 m1 st2 m2 U2 st3 m3, effstepN n1 U1 st1 m1 st2 m2 -> effstepN n2 U2 st2 m2 st3 m3 -> effstepN (n1+n2) (fun b z => U1 b z || (U2 b z && valid_block_dec m1 b)) st1 m1 st3 m3.