lean_workbook_plus_27351

Proved

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

Let $a,b,c>0$ such that $\sum_{cyc}a^2b^2\sum_{cyc}\frac{1}{a^3}=4$ . Prove that:\n\n $\frac{ab}{b+c^2}+\frac{bc}{c+a^2}+\frac{ca}{a+b^2}\geq a+b+c-1$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_27351 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b + c = 1) (h : a^2 * b^2 * (1 / a^3 + 1 / b^3 + 1 / c^3) = 4) : a * b / (b + c^2) + b * c / (c + a^2) + c * a / (a + b^2) ≥ a + b + c - 1   :=  by sorry

Source

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

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