simple induction 1; intros; auto with arith pts.
apply red_trans with (App (Abs T M') N'); auto 10 with arith pts.
red in |- *; red in |- *.
apply rt_step.
apply ctx_rule.
left; auto with arith pts.
apply red_trans with (lift (S n) d); auto with arith pts.
red in |- *; red in |- *.
apply rt_step.
apply ctx_rule.
right.
apply delta_intro with T; auto with arith pts.
Qed.

(* Specifications: *)
Lemma bd_par_red1_stable_env : R_stable_env bd_par_red1.
red in |- *.