Section Context_Closure.
Variable R : red_rule.
Definition red := R_rt (ctxt R).
Definition conv := R_rst (ctxt R).
Hint Unfold red conv: pts.
Proof fun e : env => rt_trans term (ctxt R e).
Proof fun e : env => rst_trans term (ctxt R e).
Proof fun e : env => rst_sym term (ctxt R e).
Proof fun e : env => clos_rt_clos_rst term (ctxt R e).
intros.
apply conv_sym; apply red_conv; auto with pts.
Qed.

Lemma red_red_abs :
forall (e : env) (A A' M M' : term),
red e A A' -> red (Ax A' :: e) M M' -> red e (Abs A M) (Abs A' M').