A mixed reciprocal sum is at least one

Proved

WorkbookSource.plus_23444

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

lean-workbooksource-checked

Let $a,b,c>0$ and $a+b+c=3$ . Prove that $\frac{2}{ab+bc+ca}+\frac{1}{a^2b+b^2c+c^2 a}\ge 1.$

Source: InternLM Lean-Workbook, record lean_workbook_plus_23444 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_23444 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b + c = 3) : 2 / (a * b + b * c + c * a) + 1 / (a^2 * b + b^2 * c + c^2 * a) ≥ 1   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_23444; Apache-2.0

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