fib_isSol_fibRec — Mathlib

English

For any commutative ring β, fibRec has the same characteristic polynomial X^2 - (X + 1).

Русский

Для любого кольца β последовательность fibRec имеет характеристический многочлен X^2 - (X + 1).

LaTeX

$$$\forall \beta\ [\mathrm{CommRing}\ \beta],\ \ fibRec.charPoly = X^2 - (X + 1)$$$

Lean4

/-- As expected, the Fibonacci sequence is a solution of `fibRec`. -/
theorem fib_isSol_fibRec : fibRec.IsSolution (fun x => x.fib : ℕ → α) :=
  by
  rw [fibRec]
  intro n
  simp only
  rw [Nat.fib_add_two, add_comm]
  simp [Finset.sum_fin_eq_sum_range, Finset.sum_range_succ']

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