A weighted reciprocal square bounds an asymmetric quadratic reciprocal

Proved

WorkbookSource.plus_30454

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

For $x,y,z \in \mathbb{R}^{+}$ $\frac{y+z}{x+y+z}(\frac{1}{x}+\frac{1}{y}+\frac{1}{z})^2 \geq \frac{12}{x^2+yz}$ It is stronger than yours

Source: InternLM Lean-Workbook, record lean_workbook_plus_30454 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_30454 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (y + z) / (x + y + z) * (1 / x + 1 / y + 1 / z) ^ 2 ≥ 12 / (x ^ 2 + y * z)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_30454; Apache-2.0

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