Definition pl_tl_length_rec_def_0 (n : nat) :=
  forall (d : preDTA) (pl : prec_list) (tl : term_list),
  pl_tl_length pl n -> liste_reconnait d pl tl -> n = lst_length tl.Definition pl_tl_length_rec_def_1 (d : preDTA) (pl : prec_list)
  (tl : term_list) :=
  forall n : nat,
  pl_tl_length_rec_def_0 n ->
  pl_tl_length pl (S n) -> liste_reconnait d pl tl -> S n = lst_length tl.

Lemma pl_tl_length_rec_0 : pl_tl_length_rec_def_0 0.