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 incl_sound : forall P Q : red_rule, (forall (e : env) (x y : term), P e x y -> Q e x y) -> rule_sound Q -> rule_sound P.