Lemma preDTA_kill_ref_ok_distinct_invar : forall (d : preDTA) (sigma : signature), preDTA_ref_ok_distinct d d -> predta_correct_wrt_sign d sigma -> preDTA_ref_ok_distinct (preDTA_kill (dta_non_empty_states d) d) (preDTA_kill (dta_non_empty_states d) d).