(** * Addendum to the standard library of Coq *)
Require Export Omega.
Global Obligation Tactic := idtac.
Notation "[ x ; .. ; y ]" := (cons x .. (cons y nil) .. ).

Lemma map_nth2
(A B : Type) (f : A -> B) (l : list A) b d n :
(f d) = b ->
nth n (map f l) b = f (nth n l d).