simp at hx
case mk
α' : Type u_1
α : Type u_2
inst✝ : DecidableEq α'
s : Finset α
f : α ↪ α'
y : α
x : α'
hx : x ∈ map f s
⊢ filter (fun x_1 => f x_1 = x) s = {y} ↔ x = f y
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