lean_workbook_plus_79051

Proved

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

Let $a,b,c > 0$ such that $ab + bc + ca + abc \ge 4$ . Prove that \n $a + b + c \ge 3 + \frac{{{{\left( {b - c} \right)}^2}}}{{b + c + 4}}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_79051 (a b c : ℝ) (hab : 0 < a) (hbc : 0 < b) (hca : 0 < c) (habc : 0 < a * b * c) (h : a * b + b * c + c * a + a * b * c >= 4) : a + b + c >= 3 + (b - c) ^ 2 / (b + c + 4)   :=  by sorry

Source

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

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