intros.
apply conv_trans with (Prod A' B).
elim H; simpl in |- *; intros; auto with pts.
apply conv_trans with (Prod y B); auto with pts.
elim H0; intros; auto with pts.
apply conv_trans with (Prod A' y); auto with pts.
Qed.
End Context_Closure.
Hint Unfold red conv: pts.
Hint Resolve red_conv red_sym_conv red_red_abs red_red_app red_red_prod
conv_conv_abs conv_conv_app conv_conv_prod: pts.
Hint Immediate conv_sym: pts.
Section Properties.
Variable R R' : red_rule.
Section Prop_R_lift.
Hypothesis R_lifts : R_lift R.
Hypothesis R_lifts' : R_lift R'.

Lemma ctxt_lift : R_lift (ctxt R).
red in |- *.