apply Finset.card_image_of_injOn
C : Type u_1
J : Type u_2
r : C → J → Prop
inst✝¹ : Fintype J
inst✝ : Fintype C
c : C
⊢ (Finset.image Prod.snd (Finset.filter (fun a => a.contestant = c) (A r))).card =
    (Finset.filter (fun a => a.contestant = c) (A r)).card
case H
C : Type u_1
J : Type u_2
r : C → J → Prop
inst✝¹ : Fintype J
inst✝ : Fintype C
c : C
⊢ Set.InjOn Prod.snd ↑(Finset.filter (fun a => a.contestant = c) (A r))