ext p
C : Type u_1
J : Type u_2
r : C → J → Prop
inst✝¹ : Fintype J
inst✝ : Fintype C
c : C
⊢ Finset.filter (fun p => JudgePair.Agree r p c ∧ p.Distinct) Finset.univ =
    Finset.image Prod.snd (Finset.filter (fun a => a.contestant = c) (A r))
case a
C : Type u_1
J : Type u_2
r : C → J → Prop
inst✝¹ : Fintype J
inst✝ : Fintype C
c : C
p : JudgePair J
⊢ p ∈ Finset.filter (fun p => JudgePair.Agree r p c ∧ p.Distinct) Finset.univ ↔
    p ∈ Finset.image Prod.snd (Finset.filter (fun a => a.contestant = c) (A r))