intros P H w.
elim P.
intros.
unfold pred_compatible in Pred_compatible_prf.
apply Pred_compatible_prf with (w (Build_finiteT H);; Seqtl w);
auto with algebra.
Qed.

(* Specifications: *)
Lemma Seqtl_cons_inv : forall v : seq n A, Seqtl (a;; v) =' v in _.
intros.