Prove2Me

A product inequality for nonnegative variables of sum three

Proved
WorkbookSource.base_460

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

lean-workbooksource-checked

Let a,b,c≥0a,b,c\geq 0 and a+b+c=3.a+b+c =3 . Prove that

(4−ab)(4−bc)(4−ca)+abc≥28(4-ab)(4-bc)(4-ca)+ abc \geq 28

Source: InternLM Lean-Workbook, record lean_workbook_460 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_460 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) (habc : a + b + c = 3) : (4 - a * b) * (4 - b * c) * (4 - c * a) + a * b * c ≥ 28  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_460; Apache-2.0

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