A product of shifted squares at positive sum three

Proved

WorkbookSource.base_27454

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

lean-workbooksource-checked

prove $(a^2+3)(b^2+3)(c^2+3)\geq 4(a+b+c+1)^2$ given $a,b,c>0$ and $a+b+c=3$

Source: InternLM Lean-Workbook, record lean_workbook_27454 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_27454 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 3) : (a^2 + 3) * (b^2 + 3) * (c^2 + 3) ≥ 4 * (a + b + c + 1)^2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_27454; Apache-2.0

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