lean_workbook_plus_36474

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Let $a,b,c>0$ and $\dfrac{1}{a^2+1}+\dfrac{2}{ b^2+1}+\dfrac{2}{ c^2+1}=1.$ Prove that

a+2b+ 2c\ge 10

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_36474 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c)(habc : a * b * c = 1) : 1 / (a^2 + 1) + 2 / (b^2 + 1) + 2 / (c^2 + 1) = 1 → a + 2 * b + 2 * c ≥ 10   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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