(* invariant de reconnaissance pour conv_0 au travers de u_merge *)

Definition u_merge_inv_0_dta (p0 : preDTA) (a : ad) 
  (t : term) (pr : reconnaissance p0 a t) :=
  forall p1 : preDTA, reconnaissance (u_merge p0 p1) (uad_conv_0 a) t.Definition u_merge_inv_0_st (p0 : preDTA) (s : state) 
  (t : term) (pr : state_reconnait p0 s t) :=
  forall p1 : preDTA, state_reconnait (u_merge p0 p1) (umpl_conv_0 s) t.Definition u_merge_inv_0_lst (p0 : preDTA) (pl : prec_list) 
  (lt : term_list) (pr : liste_reconnait p0 pl lt) :=
  forall p1 : preDTA, liste_reconnait (u_merge p0 p1) (upl_conv_0 pl) lt.

Lemma u_merge_2 : forall (p0 p1 : preDTA) (a : ad) (t : term), reconnaissance p0 a t -> reconnaissance (u_merge p0 p1) (uad_conv_0 a) t.