import Mathlib

set_option maxHeartbeats 0

open BigOperators Real Nat Topology Rat

theorem amc12_2000_p15 (f : ℂ → ℂ) (h₀ : ∀ x, f (x / 3) = x ^ 2 + x + 1)
  (h₁ : Fintype (f ⁻¹' {7})) : (∑ y ∈ (f ⁻¹' {7}).toFinset, y / 3) = -1 / 9 := by sorry