lean_workbook_plus_11812

Proved

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

Given reals $a,b,c>0$ with $a^2+b^2+c^2=1$ prove that \n

\frac{1-c^2}{ab+c^2}+\frac{1-b^2}{ac+b^2}+\frac{1-a^2}{bc+a^2}\ge 3

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_11812 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) (h : a^2 + b^2 + c^2 = 1) : (1 - c^2) / (a * b + c^2) + (1 - b^2) / (a * c + b^2) + (1 - a^2) / (b * c + a^2) ≥ 3   :=  by sorry

Source

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

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