lean_workbook_plus_35537

Proved

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

Given that $a,b,c$ are positive real numbers, prove $(a+b+1)(b+c+1)(c+a+1)+2 \geq 7(ab+bc+ca)+2(a+b+c+abc)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_35537 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a + b + 1) * (b + c + 1) * (c + a + 1) + 2 ≥ 7 * (a * b + b * c + a * c) + 2 * (a + b + c + a * b * c)   :=  by sorry

Source

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

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