. apply Nat.choose_pos; linarith
case h
m : ℕ
⊢ 0 < Nat.choose (2 * m + 1) m

case a
m : ℕ
⊢ ∏ p in Finset.filter Nat.Prime (Finset.Ioc (m + 1) (2 * m + 1)), p ∣ Nat.choose (2 * m + 1) m
case a
m : ℕ
⊢ ∏ p in Finset.filter Nat.Prime (Finset.Ioc (m + 1) (2 * m + 1)), p ∣ Nat.choose (2 * m + 1) m