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).

Lemma conv_sym : forall (e : env) (x y : term), conv e x y -> conv e y x.