induction n; intuition; simpl in *.
inversion H. trivial.
inversion H; clear H; subst.
f_equal.
eapply IHn; eauto.
congruence.
Qed.

(* Specifications: *)
Lemma pred_count_listRepeat_ne_inv : forall n (A : Type)(a1 a2 : A) count,
a1 <> a2 ->
pred_count (eq a1) (listRepeat a2 n) count ->
count = O.