Section Prop_R_stable_env.
Hypothesis R_stable : R_stable_env R.
Hypothesis R_stable' : R_stable_env R'.
red in |- *.
simple induction 1; intros; auto with pts.
apply ctx_rule.
apply R_stable with R'0 e0; auto with pts.
Qed.
red in |- *; red in |- *.
simple induction 1; intros; auto with pts.
apply rt_step.
apply R_stable with R'0 e; auto with pts.
apply rt_trans with y0; auto with pts.
Qed.

Lemma R_rst_stable : R_stable_env (R_rst R).