A shifted pairwise product bound at fixed sum three

Proved

WorkbookSource.base_20030

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

lean-workbooksource-checked

For non-negative reals $a,b,c$ such that $a+b+c=3$ , show that $(a+b+1)(b+c+1)(c+a+1) \le 27$

Source: InternLM Lean-Workbook, record lean_workbook_20030 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_20030 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (habc : a + b + c = 3) : (a + b + 1) * (b + c + 1) * (c + a + 1) ≤ 27  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_20030; Apache-2.0

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