import Mathlib

set_option maxHeartbeats 0

open BigOperators Real Nat Topology Rat

theorem amc12a_2020_p4
  (S : Finset ℕ)
  (h₀ : ∀ (n : ℕ), n ∈ S ↔ 1000 ≤ n ∧ n ≤ 9999 ∧ (∀ (d : ℕ), d ∈ Nat.digits 10 n → Even d) ∧ 5 ∣ n) :
  S.card = 100 := by sorry