ext x
α : Type u_1
β : Type u_2
inst✝¹ : DecidableEq α
inst✝ : DecidableEq β
s d : ℕ
hd : d ≠ 0
h : d ≤ s
⊢ { parts := image (fun i => filter (fun j => j % d = i) (range s)) (range d), supIndep := ⋯, sup_parts := ⋯,
        not_bot_mem := ⋯ }.parts =
    image (fun i => image (fun x => i + d * x) (range ((s - i - 1) / d + 1))) (range d)
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
⊢ x ∈
      { parts := image (fun i => filter (fun j => j % d = i) (range s)) (range d), supIndep := ⋯, sup_parts := ⋯,
          not_bot_mem := ⋯ }.parts ↔
    x ∈ image (fun i => image (fun x => i + d * x) (range ((s - i - 1) / d + 1))) (range d)