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

Lemma nth_map_cst :
forall {A B} (l:list A) n (d:B), nth n (map (fun _ => d) l) d = d.