apply Finset.mul_card_image_le_card_of_maps_to h
C : Type u_1
J : Type u_2
r : C → J → Prop
inst✝¹ : Fintype J
inst✝ : Fintype C
z : ℕ
hJ : Fintype.card J = 2 * z + 1
h : ∀ a ∈ A r, a.1 ∈ Finset.univ
⊢ 2 * z * z * Fintype.card C ≤ (A r).card
case hn
C : Type u_1
J : Type u_2
r : C → J → Prop
inst✝¹ : Fintype J
inst✝ : Fintype C
z : ℕ
hJ : Fintype.card J = 2 * z + 1
h : ∀ a ∈ A r, a.1 ∈ Finset.univ
⊢ ∀ a ∈ Finset.univ, 2 * z * z ≤ (Finset.filter (fun x => x.1 = a) (A r)).card