lean_workbook_plus_4052

Proved

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

For all $a,b,c,$ positive real number. Show that $\frac{a}{b}+\frac{b}{c}+\frac{c}{a} \geqslant 3 + \frac{(c-a)^2}{b^2+ab+bc+ca}.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_4052 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a / b + b / c + c / a >= 3 + (c - a) ^ 2 / (b ^ 2 + a * b + b * c + c * a)   :=  by sorry

Source

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

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