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_0 : pl_path_incl_length_def pl_path_nil prec_empty.