intro n
P : ℤ[X]
t : ℤ
ht : t ∈ periodicPts fun x => Polynomial.eval x P
C : Cycle ℤ := Cycle.map (fun x => Polynomial.eval x P - x) (periodicOrbit (fun x => Polynomial.eval x P) t)
HC : ∀ {n : ℕ}, (fun x => Polynomial.eval x P)^[n + 1] t - (fun x => Polynomial.eval x P)^[n] t ∈ C
⊢ ∀ (n : ℕ),
    Polynomial.eval ((fun x => Polynomial.eval x P)^[n] t) P - (fun x => Polynomial.eval x P)^[n] t ∣
      Polynomial.eval ((fun x => Polynomial.eval x P)^[n + 1] t) P - (fun x => Polynomial.eval x P)^[n + 1] t
P : ℤ[X]
t : ℤ
ht : t ∈ periodicPts fun x => Polynomial.eval x P
C : Cycle ℤ := Cycle.map (fun x => Polynomial.eval x P - x) (periodicOrbit (fun x => Polynomial.eval x P) t)
HC : ∀ {n : ℕ}, (fun x => Polynomial.eval x P)^[n + 1] t - (fun x => Polynomial.eval x P)^[n] t ∈ C
n : ℕ
⊢ Polynomial.eval ((fun x => Polynomial.eval x P)^[n] t) P - (fun x => Polynomial.eval x P)^[n] t ∣
    Polynomial.eval ((fun x => Polynomial.eval x P)^[n + 1] t) P - (fun x => Polynomial.eval x P)^[n + 1] t