eapply permutation_insertion;eauto.
apply is_permutation_refl.
Qed.

(* Specifications: *)
Lemma length_recursion : forall (A:Set),forall (P:list A->Prop),(forall (x:list A),(forall (y:list A),(length y)<(length x)->(P y))->(P x))->(forall (a:list A),(P a)).
intros.