(* insertion d'un état *)
Definition insert_state (d : preDTA) (a : ad) (s : state) : preDTA :=
MapPut state d a s.
Definition insert_main_state_0 (d : preDTA) (a : ad)
(s : state) : DTA := dta (insert_state d a s) a.
Definition insert_main_state (d : preDTA) (s : state) : DTA :=
insert_main_state_0 d (new_preDTA_ad d) s.
Definition insert_ostate (d : preDTA) (a : ad) (o : option state) : preDTA :=
match o with
| None => d
| Some s => MapPut state d a s
end.
Definition insert_main_ostate_0 (d : preDTA) (a : ad)
(o : option state) : DTA := dta (insert_ostate d a o) a.

Lemma insert_ostate_2 :
forall (d0 d1 : preDTA) (a0 a1 a : ad) (s s0 s1 s0' s1' : state) (t : term),
MapGet state d0 a0 = Some s0 ->
MapGet state d1 a1 = Some s1 ->
MapGet state (u_merge d0 d1) (uad_conv_0 a0) = Some s0' ->
MapGet state (u_merge d0 d1) (uad_conv_1 a1) = Some s1' ->
preDTA_ref_ok (u_merge d0 d1) ->
MapGet state (u_merge d0 d1) a = None ->
a <> uad_conv_1 a1 ->
(reconnaissance d1 a1 t <->
reconnaissance (insert_ostate (u_merge d0 d1) a (Some s))
(uad_conv_1 a1) t).