A quadratic sum times two reciprocals bounds a pairwise sum

Proved

WorkbookSource.base_4359

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

lean-workbooksource-checked

Let $a,b,c$ be positive real numbers . Prove that $(a^2+b^2+c^2 )\left(\frac{1}{a+2c}+\frac{1}{b+2c} \right) \geq a+b.$

Source: InternLM Lean-Workbook, record lean_workbook_4359 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_4359 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) : (a^2 + b^2 + c^2) * (1/(a + 2 * c) + 1/(b + 2 * c)) ≥ a + b  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_4359; Apache-2.0

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