(* File: My_Nth.v  (last edited on 25/10/2000) (c) Klaus Weich  *)
Require Export List.
Require Export Plus.
Section My_Nth.
Variable B : Set.
Inductive my_nth : nat -> list B -> B -> Prop :=
| My_NthO : forall (l : list B) (a : B), my_nth 0 (a :: l) a
| My_NthS :
forall (n : nat) (l : list B) (b : B),
my_nth n l b -> forall a : B, my_nth (S n) (a :: l) b.

(* Specifications: *)
Lemma inv_nth_nil : forall (n : nat) (a : B), my_nth n nil a -> False.
intros.