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).

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