Prove2Me

A cyclic product inequality at fixed pairwise sum

Proved
WorkbookSource.base_3622

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let's a,b,c>0: ab+bc+ca=3. Prove: (a+b)(a+bc)+(b+c)(b+ca)+(c+a)(c+ab)≥12(a+b)(a+bc)+(b+c)(b+ca)+(c+a)(c+ab)\geq 12

Source: InternLM Lean-Workbook, record lean_workbook_3622 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_3622 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a * b + b * c + c * a = 3) : (a + b) * (a + b * c) + (b + c) * (b + c * a) + (c + a) * (c + a * b) ≥ 12  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_3622; Apache-2.0

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