A shifted quadratic ratio upper bound at fixed sum three

Proved

WorkbookSource.base_12676

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

lean-workbooksource-checked

Prove that $\sum \frac{x}{x^2+y+z} \leq 1$ for positive reals $x, y, z$ such that $x + y + z = 3$ .

Source: InternLM Lean-Workbook, record lean_workbook_12676 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_12676 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) (h : x + y + z = 3) : x / (x ^ 2 + y + z) + y / (y ^ 2 + z + x) + z / (z ^ 2 + x + y) ≤ 1  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_12676; Apache-2.0

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