Lemma preDTA_produit_l_correct_wrt_sign_invar : forall (d : preDTA) (a : ad) (s : state) (sigma : signature), predta_correct_wrt_sign d sigma -> predta_correct_wrt_sign (M1 state a s) sigma -> predta_correct_wrt_sign (preDTA_produit_l a s d) sigma.