rcases hx with ⟨y',h1,rfl⟩
case mk
α' : Type u_1
α : Type u_2
inst✝ : DecidableEq α'
s : Finset α
f : α ↪ α'
y : α
x : α'
hx : ∃ a ∈ s, f a = x
⊢ filter (fun x_1 => f x_1 = x) s = {y} ↔ x = f y
case mk.intro.intro
α' : Type u_1
α : Type u_2
inst✝ : DecidableEq α'
s : Finset α
f : α ↪ α'
y y' : α
h1 : y' ∈ s
⊢ filter (fun x => f x = f y') s = {y} ↔ f y' = f y