Inductive delta : env -> term -> term -> Prop :=
      delta_intro :
        forall (e : env) (n : nat) (d T : term),
        item (Def d T) e n -> delta e (Ref n) (lift (S n) d).Inductive delta : env -> term -> term -> Prop :=
      delta_intro :
        forall (e : env) (n : nat) (d T : term),
        item (Def d T) e n -> delta e (Ref n) (lift (S n) d).

(* Specifications: *)
Lemma delta_rule : Basic_rule.
Lemma delta_reduce : forall (n : nat) (e : env), {def : term | delta e (Ref n) def} + {(forall x : term, ~ delta e (Ref n) x)}.
Lemma sort_delta_norm : forall (e : env) (s : sort), normal delta e (Srt s).
Lemma prod_delta_norm : forall (e : env) (A B : term), normal delta e (Prod A B).