lean_workbook_plus_27630

Proved

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

Let $a,b,c$ be positive real numbers .Prove that $( a+b+\dfrac{1}{2})(b+c+\dfrac{1}{2})(c+a+\dfrac{1}{2})\geq (2a+\dfrac{1}{2})(2b+\dfrac{1}{2})(2c+\dfrac{1}{2}) .$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_27630 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a + b + 1 / 2) * (b + c + 1 / 2) * (c + a + 1 / 2) ≥ (2 * a + 1 / 2) * (2 * b + 1 / 2) * (2 * c + 1 / 2)   :=  by sorry

Source

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

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