Prove2Me

A shifted-square product bound at sum three

Proved
WorkbookSource.plus_63738

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

lean-workbooksource-checked

If a,b,ca,b,c are real numbers such that a+b+c=3a+b+c=3 , then

(a2+1)(b2+1)(c2+1)≥(a+1)(b+1)(c+1)+(abc−1)2+29(3−ab−bc−ca)27(a^2+1)(b^2+1)(c^2+1)\ge (a+1)(b+1)(c+1)+(abc-1)^2+\dfrac{29(3-ab-bc-ca)}{27}

Source: InternLM Lean-Workbook, record lean_workbook_plus_63738 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.plus_63738 (a b c : ℝ) (hab : a + b + c = 3) : (a^2 + 1) * (b^2 + 1) * (c^2 + 1) ≥ (a + 1) * (b + 1) * (c + 1) + (a * b * c - 1)^2 + (29 * (3 - a * b - b * c - a * c)) / 27   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_63738; Apache-2.0

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