simple induction 1; intros; auto with arith pts.
red in |- *; red in |- *.
apply rt_trans with (App (Abs T M') N'); auto with arith pts.
change (red beta e0 (App (Abs T M0) N0) (App (Abs T M') N')) in |- *.
auto with arith pts.
Qed.

(* Specifications: *)
Lemma beta_par_red1_stable_env : R_stable_env beta_par_red1.
red in |- *.