Prove2Me

A squared pair-sum reciprocal inequality at fixed sum three

Proved
WorkbookSource.plus_79177

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

lean-workbooksource-checked

Let a,b,ca,b,c be positive real numbers such that a+b+c=3a+b+c=3 . Prove that a(b+c)2+b(c+a)2+c(a+b)2≥129+7abc\frac{a}{(b+c)^2}+\frac{b}{(c+a)^2}+\frac{c}{(a+b)^2}\ge\frac{12}{9+7abc}

Source: InternLM Lean-Workbook, record lean_workbook_plus_79177 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.plus_79177 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b + c = 3) : (a / (b + c) ^ 2 + b / (c + a) ^ 2 + c / (a + b) ^ 2) ≥ 12 / (9 + 7 * a * b * c)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_79177; Apache-2.0

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