Prove2Me

An asymmetric squared-reciprocal lower bound

Proved
WorkbookSource.base_9008

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

lean-workbooksource-checked

Let a,b,c>0a, b, c > 0 . Prove that:

1(a+b)2+1(a+c)2+8(b+c)2≥4ab+bc+ca\frac{1}{(a+b)^2}+\frac{1}{(a+c)^2}+\frac{8}{(b+c)^2} \ge \frac{4}{ab+bc+ca}

Source: InternLM Lean-Workbook, record lean_workbook_9008 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_9008 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (1 / (a + b) ^ 2 + 1 / (a + c) ^ 2 + 8 / (b + c) ^ 2) ≥ 4 / (a * b + b * c + c * a)  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_9008; Apache-2.0

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