unfold di' in |- *. unfold compo' in |- *.
unfold di3 in |- *. unfold ad_2_1, compo_2_1 in |- *. unfold di1, cx1, al1, mem1, ad1, da1 in |- *.
simple induction t. auto.
intros. rewrite di_t. rewrite ad2_t. rewrite H.
replace (cx n di_init cx_init al_init mem_init) with
(cx' n di_init cx_init al_init mem_init DC_a DC_d).
unfold cx', compo' in |- *. unfold cx3 in |- *. unfold cx_2_1, compo_2_1 in |- *.
unfold di1, cx1, al1, mem1, ad1, da1 in |- *.
trivial. rewrite cx_cx'. trivial.
Qed.

(* Specifications: *)
Lemma al_al' :
forall t : nat,
al t di_init cx_init al_init mem_init =
al' t di_init cx_init al_init mem_init DC_a DC_d.