Proof using.
intros n; elim n; simpl in |- *; auto.
intros n0 H l1; case l1; simpl in |- *; auto with arith.
intros l2 H1; Contradict H1; auto with arith.
Qed.

Theorem skip_n_length :
forall (n : nat) (l1 : list A), length (skip_n l1 n) = length l1 - n.