A weighted squared reciprocal sum lower bound

Proved

WorkbookSource.plus_42193

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

lean-workbooksource-checked

Prove that $\sum\frac1{(2a+2b+c)^2}\ge\frac{27}{25(a+b+c)^2}$ , where $a, b, c>0$ .

Source: InternLM Lean-Workbook, record lean_workbook_plus_42193 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_42193 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (1 / (2 * a + 2 * b + c) ^ 2 + 1 / (2 * b + 2 * c + a) ^ 2 + 1 / (2 * c + 2 * a + b) ^ 2) ≥ 27 / (25 * (a + b + c) ^ 2)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_42193; Apache-2.0

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