(** A list of [n] elements, all equal to [x]. *)
Fixpoint list_repeat {A: Type} (n: nat) (x: A) {struct n} :=
match n with
| O => nil
| S m => x :: list_repeat m x
end.

Lemma length_list_repeat:
forall (A: Type) n (x: A), length (list_repeat n x) = n.