Prove2Me

A squared-product bound in three real variables

Proved
WorkbookSource.base_5822

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

My solution :

((1+ab)(1+ac)−2)2≥0⇔(1+ab)(1+ac)≥2ab+ac+a2bc \left((1+\frac{a}{b})(1+\frac{a}{c})-2\right)^2\ge 0 \Leftrightarrow (1+\frac{a}{b})(1+\frac{a}{c})\ge 2\sqrt{\frac{a}{b}+\frac{a}{c}+\frac{a^2}{bc}}

which is equivalent with : (a+b)2(a+c)2≥4abc(a+b+c) (a+b)^2(a+c)^2\ge 4abc(a+b+c)

Source: InternLM Lean-Workbook, record lean_workbook_5822 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_5822  (a b c : ℝ) :
  (a + b)^2 * (a + c)^2 ≥ 4 * a * b * c * (a + b + c)  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_5822; Apache-2.0

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