Definition rec_co_def_3 (t : term) : Prop :=
  forall (d : preDTA) (a : ad),
  preDTA_ref_ok d -> reconnaissance d a t -> reconnaissance_co d a a t.Definition rec_co_def_4 (d : preDTA) (l : prec_list) 
  (tl : term_list) : Prop :=
  forall a : ad,
  preDTA_ref_ok d ->
  liste_reconnait d l tl ->
  (forall u : term,
   term_list_occur u tl ->
   forall (d : preDTA) (a : ad),
   preDTA_ref_ok d -> reconnaissance d a u -> reconnaissance_co d a a u) ->
  (forall b : ad, prec_occur l b -> coacc d a b) ->
  liste_reconnait_co d l a tl.

Lemma rec_co_10 : forall (a : ad) (tl : term_list), (forall u : term, term_list_occur u tl -> rec_co_def_3 u) -> rec_co_def_3 (app a tl).