Lemma states_kill_ref_ok_invar : forall (d : preDTA) (s s' : state) (sigma : signature), state_ref_ok s d -> predta_correct_wrt_sign d sigma -> states_kill (dta_non_empty_states d) s = Some s' -> state_ref_ok s' (preDTA_kill (dta_non_empty_states d) d).