A shifted product upper bound under a cubic relation

Proved

WorkbookSource.base_316

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

lean-workbooksource-checked

Let $a,b,c>0$ and $a+b+c+2=abc$ . Prove that $(a-1)(b-1)(c-1)(ab+bc+ca-1) \leq 11$

Source: InternLM Lean-Workbook, record lean_workbook_316 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_316 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c)(habc : a + b + c + 2 = a * b * c) :  (a - 1) * (b - 1) * (c - 1) * (a * b + b * c + c * a - 1) ≤ 11  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_316; Apache-2.0

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