Section Prop_R_lift_subst.
Variable R : red_rule.
Hypothesis R_lifts : R_lift R.
Hypothesis R_substs : R_subst R.
Proof R_rt_lift (ctxt R) (ctxt_lift R R_lifts).
Proof R_rst_lift (ctxt R) (ctxt_lift R R_lifts).
Proof R_rt_subst (ctxt R) (ctxt_subst R R_substs).

Lemma conv_subst : R_subst (conv R).