A product of shifted variables under a quadratic norm constraint

Proved

WorkbookCorrected.base_8243

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

corrected-formalizationlean-workbooksource-checked

Let $a,b,c$ positive real numbers such that $a^2+b^2+c^2=3$ . Prove that: $(a+2)(b+2)(c+2) \geq (a+b+c)^3$

Source: InternLM Lean-Workbook, record lean_workbook_8243 (Apache-2.0). Natural-language proposition preserved; missing source domain assumptions restored. Proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookCorrected.base_8243 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (h : a^2 + b^2 + c^2 = 3) :
  (a + 2) * (b + 2) * (c + 2) ≥ (a + b + c)^3  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_8243; Apache-2.0

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