Prove2Me

A cubic-factor upper bound under a sum constraint

Proved
WorkbookSource.base_2098

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

lean-workbooksource-checked

Let a,b,c≥0a,b,c\ge0 and a+b+c=3.a+b+c=3. Prove that

(3a−bc)(3b−ca)(3c−ab)≤8abc.(3a-bc)(3b-ca)(3c-ab)\leq 8 abc .

Source: InternLM Lean-Workbook, record lean_workbook_2098 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_2098 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (hab : a + b + c = 3) : (3 * a - b * c) * (3 * b - c * a) * (3 * c - a * b) ≤ 8 * a * b * c  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_2098; Apache-2.0

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