Prove2Me

A squared-norm-squared bound at fixed positive sum

Proved
WorkbookSource.base_21853

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

lean-workbooksource-checked

Let a,b,ca,b,c be positive reals such that a+b+c=3;a+b+c=3; prove that

(a2+b2+c2)2≥4(a2+b2+c2)−abc(a+b+c)(a^2+b^2+c^2)^2\geq 4(a^2+b^2+c^2)-abc(a+b+c)

Source: InternLM Lean-Workbook, record lean_workbook_21853 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_21853 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 3) : (a^2 + b^2 + c^2)^2 ≥ 4 * (a^2 + b^2 + c^2) - a * b * c * (a + b + c)  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_21853; Apache-2.0

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