refine' exists_congr fun i ↦ and_congr_right fun hi ↦ _
case a
α : Type u_1
β : Type u_2
inst✝¹ : DecidableEq α
inst✝ : DecidableEq β
s d : ℕ
hd : d ≠ 0
h : d ≤ s
x : Finset ℕ
⊢ (∃ a < d, filter (fun j => j % d = a) (range s) = x) ↔
    ∃ a < d, image (fun x => a + d * x) (range ((s - a - 1) / d + 1)) = x
case a
α : Type u_1
β : Type u_2
inst✝¹ : DecidableEq α
inst✝ : DecidableEq β
s d : ℕ
hd : d ≠ 0
h : d ≤ s
x : Finset ℕ
i : ℕ
hi : i < d
⊢ filter (fun j => j % d = i) (range s) = x ↔ image (fun x => i + d * x) (range ((s - i - 1) / d + 1)) = x