case refine'_1
p n k : ℕ
n_big : 2 < n
p_le_n : p ≤ n
big : 2 * n < 3 * p
⊢ p ≠ 2

case refine'_2
p n k : ℕ
n_big : 2 < n
p_le_n : p ≤ n
big : 2 * n < 3 * p
⊢ n ≤ 2 * n - n
p n k : ℕ
n_big : 2 < n
p_le_n : p ≤ n
big : 2 * n < 3 * p
⊢ ↑(factorization (centralBinom n)) p = 0
refine' factorization_choose_of_lt_three_mul _ p_le_n (p_le_n.trans _) big
case refine'_1
n k : ℕ
n_big : 2 < n
p_le_n : 2 ≤ n
big : 2 * n < 3 * 2
⊢ False
case refine'_1
p n k : ℕ
n_big : 2 < n
p_le_n : p ≤ n
big : 2 * n < 3 * p
⊢ p ≠ 2
rintro rfl
no goals
case refine'_1
n k : ℕ
n_big : 2 < n
p_le_n : 2 ≤ n
big : 2 * n < 3 * 2
⊢ False
linarith
no goals
case refine'_2
p n k : ℕ
n_big : 2 < n
p_le_n : p ≤ n
big : 2 * n < 3 * p
⊢ n ≤ 2 * n - n
rw [two_mul, add_tsub_cancel_left]