import Mathlib

set_option maxHeartbeats 0

open BigOperators Real Nat Topology Rat

theorem amc12_2001_p5 :
  Finset.prod (Finset.filter (λ x => ¬ Even x) (Finset.range 10000)) (id : ℕ → ℕ) = (10000!) / ((2^5000) * (5000!)) := by sorry