lean_workbook_plus_8086

Proved

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

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

abc\leq 1

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_8086 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) (h : (a + b - 1) ^ 2 / c + (b + c - 1) ^ 2 / a + (c + a - 1) ^ 2 / b = a + b + c) : a * b * c ≤ 1   :=  by sorry

Source

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

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