simple induction t. simpl in |- *; trivial.
intros. rewrite al2_t. elim (IsNull (cx2 n di0 cx0 al0 mem0 ad0 da0)). apply H.
apply H.
Qed.

Lemma mem2_t :
forall (t : nat) (di0 cx0 al0 : BV) (mem0 : Memo) (ad0 da0 : BV),
mem2 (S t) di0 cx0 al0 mem0 ad0 da0 =
match IsNull (cx2 t di0 cx0 al0 mem0 ad0 da0) return Memo with
| true => mem2 t di0 cx0 al0 mem0 ad0 da0
| false =>
MemoWrite (mem2 t di0 cx0 al0 mem0 ad0 da0)
(BV_to_nat (ad2 t di0 cx0 al0 mem0 ad0 da0))
(da2 t di0 cx0 al0 mem0 ad0 da0)
end.