lean_workbook_plus_15094

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

$\frac{1}{x^{2}+4}\geq\frac{4-x}{16}\iff x(x-2)^{2}\geq\ 0$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_15094 : ∀ x : ℝ, (x ^ 2 + 4 ≠ 0 ∧ 16 ≠ 0) →
  (1 / (x ^ 2 + 4) ≥ (4 - x) / 16 ↔ x * (x - 2) ^ 2 ≥ 0)   :=  by sorry

Source