induction l;
intuition; simpl in *.
destruct n; simpl in *; trivial.
destruct n; simpl in *.
eapply H0.
intuition.
destruct n; try omega; simpl in *.
eapply IHl; intuition.
eapply IHl; intuition.
Qed.

(* Specifications: *)
Lemma list_skipn_strong_ind : forall (A : Type) l (P : list A -> Prop) ,
P nil ->
(forall x, (forall n, n > 0 -> P (skipn n x)) -> P x) ->
P l.