simple induction t. auto.
intros. rewrite al_t. elim (IsNull (cx n di0 cx0 al0 mem0)). apply H. apply H.
Qed.

Lemma mem_t :
forall (t : nat) (di0 cx0 al0 : BV) (mem0 : Memo),
mem (S t) di0 cx0 al0 mem0 =
match IsNull (cx t di0 cx0 al0 mem0) return Memo with
| true => mem t di0 cx0 al0 mem0
| false =>
MemoWrite (mem t di0 cx0 al0 mem0) (BV_to_nat (di t di0 cx0 al0 mem0))
(al t di0 cx0 al0 mem0)
end.