Prove2Me

A quadratic-factor product bound above one

Proved
WorkbookSource.base_8123

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

lean-workbooksource-checked

Let a,b,c≥1a,b,c \ge 1 , Prove that : (2a2+1)(2b2+1)(2c2+1)≥3(a+b+c)2(2a^2+1)(2b^2+1)(2c^2+1) \ge 3\left (a+b+c\right )^2

Source: InternLM Lean-Workbook, record lean_workbook_8123 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_8123 (a b c : ℝ) (ha : 1 ≤ a) (hb : 1 ≤ b) (hc : 1 ≤ c) : (2 * a ^ 2 + 1) * (2 * b ^ 2 + 1) * (2 * c ^ 2 + 1) ≥ 3 * (a + b + c) ^ 2  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_8123; Apache-2.0

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