lean_workbook_plus_11995

Proved

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

Let $a, b, c>0$ and $(a+b) (b+c) =4$ . Prove that $(2a+b) (a+b) +(b+2c) (b+c) \geq 8+ \frac{1}{2}(a+2b+c) (c+a)$ Determine when equality holds.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_11995 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 1) (h : (a + b) * (b + c) = 4) :
  (2 * a + b) * (a + b) + (b + 2 * c) * (b + c) ≥ 8 + 1 / 2 * (a + 2 * b + c) * (c + a)   :=  by sorry

Source

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

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