Definition pl_path_incl_length_def (plp : pl_path) 
  (pl : prec_list) : Prop :=
  forall n : nat,
  pl_path_incl plp pl -> pl_tl_length pl n -> pl_path_length plp = n.

Lemma forall_incl_length : forall (pl : prec_list) (n : nat), (forall p : pl_path, pl_path_incl p pl -> pl_path_length p = n) -> pl_tl_length pl n.