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(* modify it under the terms of the GNU Lesser General Public License *)
(* as published by the Free Software Foundation; either version 2.1   *)
(* of the License, or (at your option) any later version.             *)
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(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the      *)
(* GNU General Public License for more details.                       *)
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(* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA *)
(* 02110-1301 USA                                                     *)
(* invariant pour le kill_empty states de correction par rapport a une signature *)

(* Specifications: *)
Lemma prec_list_kill_correct_wrt_sign_invar :
forall (m : Map bool) (p p' : prec_list) (n : nat),
pl_tl_length p n ->
prec_list_kill m p = Some p' -> pl_tl_length p' n.
Lemma states_kill_aux_correct_wrt_sign_invar :
forall (s : state) (m : Map bool) (sigma : signature),
state_correct_wrt_sign s sigma ->
state_correct_wrt_sign (states_kill_aux m s) sigma.
Lemma states_kill_correct_wrt_sign_invar :
forall (s s' : state) (m : Map bool) (sigma : signature),
state_correct_wrt_sign s sigma ->
states_kill m s = Some s' -> state_correct_wrt_sign s' sigma.
Lemma preDTA_kill_correct_wrt_sign_invar :
forall (d : preDTA) (m : Map bool) (sigma : signature),
predta_correct_wrt_sign d sigma ->
predta_correct_wrt_sign (preDTA_kill m d) sigma.
Lemma DTA_kill_correct_wrt_sign_invar :
forall (d : DTA) (m : Map bool) (sigma : signature),
dta_correct_wrt_sign d sigma -> dta_correct_wrt_sign (DTA_kill m d) sigma.
Lemma DTA_kill_empty_states_lazy_correct_wrt_sign_invar :
forall (d : DTA) (sigma : signature),
dta_correct_wrt_sign d sigma ->
dta_correct_wrt_sign (DTA_kill_empty_states_lazy d) sigma.
Lemma kill_empty_correct_wrt_sign_invar :
forall (d : DTA) (sigma : signature),
dta_correct_wrt_sign d sigma ->
dta_correct_wrt_sign (DTA_kill_empty_states d) sigma.
Lemma kill_empty_lazy_correct_wrt_sign_invar :
forall (d : DTA) (sigma : signature),
dta_correct_wrt_sign d sigma ->
dta_correct_wrt_sign (DTA_kill_empty_states_lazy d) sigma.