(* 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_9 : forall (d0 d1 : preDTA) (a0 a1 a : ad) (s0' s1' : state) (t : term), preDTA_ref_ok d0 -> preDTA_ref_ok d1 -> dta_compat d0 d1 -> MapGet state (u_merge d0 d1) (uad_conv_0 a0) = Some s0' -> MapGet state (u_merge d0 d1) (uad_conv_1 a1) = Some s1' -> a = new_preDTA_ad (u_merge d0 d1) -> (reconnaissance d0 a0 t \/ reconnaissance d1 a1 t <-> reconnaissance (insert_ostate (u_merge d0 d1) a (Some (union_mpl s0' s1'))) a t).