A weighted cyclic quadratic reciprocal lower bound

Proved

WorkbookSource.base_22250

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

lean-workbooksource-checked

Prove that: $\dfrac{a}{b^2+3c^2+5bc} + \dfrac{b}{c^2+3a^2+5ca} + \dfrac{c}{a^2+3b^2+5ab} \geq \dfrac{1}{a+b+c}$ given $a,b,c \in R$ and $a,b,c >0$

Source: InternLM Lean-Workbook, record lean_workbook_22250 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_22250 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a / (b ^ 2 + 3 * c ^ 2 + 5 * b * c) + b / (c ^ 2 + 3 * a ^ 2 + 5 * c * a) + c / (a ^ 2 + 3 * b ^ 2 + 5 * a * b)) ≥ 1 / (a + b + c)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_22250; Apache-2.0

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