apply distinct_judge_pairs_card_lower_bound r hJ
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
c : C
a✝ : c ∈ Finset.univ
⊢ 2 * z * z ≤ (Finset.filter (fun p => JudgePair.Agree r p c ∧ p.Distinct) Finset.univ).card
no goals