Prove2Me

A cyclic quadratic reciprocal upper bound

Proved
WorkbookSource.base_38183

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

lean-workbooksource-checked

Given a,b,c>0. a, b, c > 0. Prove that: 3(a+b+c)2(ab+bc+ca)≥ aa2+b2+bb2+c2+cc2+a2 \frac {3(a + b + c)}{2(ab + bc + ca)} \geq\ \frac {a}{a^2 + b^2} + \frac {b}{b^2 + c^2} + \frac {c}{c^2 + a^2}

Source: InternLM Lean-Workbook, record lean_workbook_38183 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_38183 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (3 * (a + b + c)) / (2 * (a * b + b * c + c * a)) ≥ a / (a ^ 2 + b ^ 2) + b / (b ^ 2 + c ^ 2) + c / (c ^ 2 + a ^ 2)  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_38183; Apache-2.0

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