Proof using.
intros t; elim t; simpl in |- *; auto.
intros a a0 l [H1| H1]; try (case H1; fail).
injection H1; intros H2 H3; rewrite H3; auto.
intros h H h0 H0 a l H1.
case in_app_or with (1 := H1); auto; intros H2.
case in_map_inv with (1 := H2).
intros (a1, l1) (Ha1, Hl1); auto.
apply innodeL; apply (H a l1).
injection Hl1; intros Hl2 Hl3; rewrite Hl3; auto.
case in_map_inv with (1 := H2).
intros (a1, l1) (Ha1, Hl1); auto.
apply innodeR; apply (H0 a l1).
injection Hl1; intros Hl2 Hl3; rewrite Hl3; auto.
Qed.

(* For every leaf in the tree there is an associated key in the code *)
Theorem inb_compute_ex :
forall a p, inb (leaf a) p -> exists l : _, In (a, l) (compute_code p).