lean_workbook_plus_25240

Proved

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

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

ab+bc+ca \ge 3

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_25240 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) (habc : a * b * c = 1) (h : 1 / (1 + a ^ 2) + 1 / (1 + b ^ 2) + 1 / (1 + c ^ 2) = 3 / 2) : a * b + b * c + c * a ≥ 3   :=  by sorry

Source

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

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