Hint Resolve sym_word_l sym_word_R.

(* Specifications: *)
Lemma sym_mono A P :
A <<= P -> sym A <<= sym P.
Lemma tau1_sym A : tau1 A <<= sym A.
Lemma tau2_sym A : tau2 A <<= sym A.
Lemma rewt_sym R x y Sigma:
sym R <<= Sigma -> x <<= Sigma -> rewt R x y -> y <<= Sigma.