Scheme rewt_ind' := Induction for rewt Sort Prop.
Instance PreOrder_rewt R : PreOrder (rewt R).

(* Specifications: *)
Lemma rewt_app_L R x x' y : rewt R x x' -> rewt R (y ++ x) (y ++ x').
Instance Proper_rewt R : Proper (rewt R ==> rewt R ==> rewt R) (@app symbol).
Lemma rewt_subset R P x y :
rewt R x y -> R <<= P -> rewt P x y.
Lemma rewt_left R x y z :
rewt R x y -> rew R y z -> rewt R x z.