lean_workbook_plus_46786

Disproved

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

Strengthening: Given $a, b, c \geq 0$ and $ab + bc + ca = 1$ , prove that $\frac{a^{2}}{b} + \frac{b^{2}}{c} + \frac{c^{2}}{a} - 2(a^{2} + b^{2} + c^{2}) \geq a + b + c - 2$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_46786 :  ∀ a b c : ℝ, a ≥ 0 ∧ b ≥ 0 ∧ c ≥ 0 ∧ a * b + b * c + c * a = 1 → a ^ 2 / b + b ^ 2 / c + c ^ 2 / a - 2 * (a ^ 2 + b ^ 2 + c ^ 2) ≥ a + b + c - 2   :=  by sorry

Source

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

View graph