Inductive R_exp : value -> value -> Prop :=
      Rex_intro :
        forall (e : env) (x y : term), ctxt R e x y -> R_exp (e, y) (e, x).Inductive R_exp : value -> value -> Prop :=
      Rex_intro :
        forall (e : env) (x y : term), ctxt R e x y -> R_exp (e, y) (e, x).

(* Specifications: *)
Lemma commut_subterm_R_exp : commut value subterm R_exp.
Lemma subterm_sn : forall (e : env) (t : term), sn (ctxt R) e t -> forall (f : env) (u : term), subterm (f, u) (e, t) -> sn (ctxt R) f u.