Prove2Me

A weighted squared reciprocal sum bounds four divided by the total

Proved
WorkbookSource.plus_71510

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

lean-workbooksource-checked

For positive real numbers a,b,c.a, b, c. Prove that a+b+2c(c+2a)2+b+c+2a(a+2b)2+c+a+2b(b+2c)2≥4a+b+c\frac{a+b+2c}{(c+2a)^2}+\frac{b+c+2a}{(a+2b)^2}+\frac{c+a+2b}{(b+2c)^2}\geq \frac{4}{a+b+c}

Source: InternLM Lean-Workbook, record lean_workbook_plus_71510 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.plus_71510 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a + b + 2 * c) / (c + 2 * a) ^ 2 + (b + c + 2 * a) / (a + 2 * b) ^ 2 + (c + a + 2 * b) / (b + 2 * c) ^ 2 ≥ 4 / (a + b + c)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_71510; Apache-2.0

View graph