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').
Lemma rewt_left R x y z : rewt R x y -> rew R y z -> rewt R x z.
Lemma sym_app P R : sym (P ++ R) = sym P ++ sym R.
Lemma fresh_spec' l a : a el l -> a < fresh l.
Lemma fresh_spec (a : symbol) (l : string) : a el l -> fresh l <> a.