Prove2Me

A refined squared reciprocal sum inequality

Proved
WorkbookSource.base_18254

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

lean-workbooksource-checked

Let a,b,c>0.Prove: 1a2+1b2+1c2+1(a+b+c)2≥725(1a+1b+1c+1a+b+c)2\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}+\frac{1}{(a+b+c)^2}\geq \frac{7}{25}(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{a+b+c})^2

Source: InternLM Lean-Workbook, record lean_workbook_18254 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_18254 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) : (1 / a ^ 2 + 1 / b ^ 2 + 1 / c ^ 2 + 1 / (a + b + c) ^ 2) ≥ (7 / 25) * (1 / a + 1 / b + 1 / c + 1 / (a + b + c)) ^ 2  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_18254; Apache-2.0

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