Notation typ2 := (typ the_PTS) (only parsing).Notation wf_type2 := (wf_type the_PTS) (only parsing).Definition rule_sound :=
    forall (e : env) (x y : term),
    R e x y -> forall T : term, typ the_PTS e x T -> typ the_PTS e y T.

Theorem clos_trans_sound : forall P : red_rule, rule_sound P -> rule_sound (fun e : env => clos_trans term (P e)).