simple induction 1; auto with arith pts; intros.
elim H0; intros; auto with arith pts.
elim H1; auto with arith pts.
elim H1; intros.
apply par_delta with d T; auto with arith pts.
Qed.

Lemma bd_par_red1_red :
forall (e : env) (M N : term), bd_par_red1 e M N -> red beta_delta e M N.