induction ls; destruct i; intuition; simpl in *.
econstructor.
econstructor.
eauto.
Qed.

(* Specifications: *)
Lemma listReplace_twice_nil :
forall (A : Set)(n : nat) (a1 a2 def : A),
listReplace (listReplace nil n a1 def) n a2 def =
listReplace nil n a2 def.