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 pl_path_incl_length_3 : forall (p : pl_path) (p0 : prec_list), pl_path_incl p p0 -> pl_path_incl_length_def p p0.