lean_workbook_plus_79734

Proved

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

Let $a, b, c>0$ such that $(a+b)(b+c)(c+a)=1.$ Prove that the following inequality holds: $ab+bc+ca\leq\frac{3}{4}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_79734 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 1) (h : (a + b) * (b + c) * (c + a) = 1) :
  a * b + b * c + c * a ≤ 3 / 4   :=  by sorry

Source

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

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