case a
n p b : ℕ
pp : Prime p
hn : n ≠ 0
hb : n ≤ p ^ b
x : ℕ
⊢ x ∈ Finset.filter (fun i => p ^ i ∣ n) (Ico 1 n) ↔ x ∈ Finset.filter (fun i => p ^ i ∣ n) (Icc 1 b)
n p b : ℕ
pp : Prime p
hn : n ≠ 0
hb : n ≤ p ^ b
⊢ Finset.filter (fun i => p ^ i ∣ n) (Ico 1 n) = Finset.filter (fun i => p ^ i ∣ n) (Icc 1 b)
ext x
case a
n p b : ℕ
pp : Prime p
hn : n ≠ 0
hb : n ≤ p ^ b
x : ℕ
⊢ p ^ x ∣ n → 1 ≤ x → (x < n ↔ x ≤ b)
case a
n p b : ℕ
pp : Prime p
hn : n ≠ 0
hb : n ≤ p ^ b
x : ℕ
⊢ x ∈ Finset.filter (fun i => p ^ i ∣ n) (Ico 1 n) ↔ x ∈ Finset.filter (fun i => p ^ i ∣ n) (Icc 1 b)
simp only [Finset.mem_filter, mem_Ico, mem_Icc, and_congr_left_iff, and_congr_right_iff]
case a
n p b : ℕ
pp : Prime p
hn : n ≠ 0
hb : n ≤ p ^ b
x : ℕ
h1 : p ^ x ∣ n
⊢ x < n ↔ x ≤ b
case a
n p b : ℕ
pp : Prime p
hn : n ≠ 0
hb : n ≤ p ^ b
x : ℕ
⊢ p ^ x ∣ n → 1 ≤ x → (x < n ↔ x ≤ b)
rintro h1 -
no goals
case a
n p b : ℕ
pp : Prime p
hn : n ≠ 0
hb : n ≤ p ^ b
x : ℕ
h1 : p ^ x ∣ n
⊢ x < n ↔ x ≤ b
simp [lt_of_pow_dvd_right hn pp.two_le h1,
  (pow_le_iff_le_right pp.two_le).1 ((le_of_dvd hn.bot_lt h1).trans hb)]