lean_workbook_plus_27233

Proved

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

If $a,b,c$ are positive numbers such that $ab+bc+ca=1$ , then \n $(a^{2}+1)(b^{2}+1)(c^{2}+1) \geq \frac 4{3}$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_27233 (a b c : ℝ) (hab : 0 < a) (hbc : 0 < b) (hca : 0 < c) (habc : a * b + b * c + c * a = 1) : (a^2 + 1) * (b^2 + 1) * (c^2 + 1) ≥ 4 / 3   :=  by sorry

Source

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

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