A sum-cubic bound on a nonnegative sphere

Proved

WorkbookSource.plus_48969

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

lean-workbooksource-checked

For $a, b, c\geq 0,a^2+b^2+c^2=3$ prove that: $6abc+11(a+b+c)\geq (a+b+c)^3+12$

Source: InternLM Lean-Workbook, record lean_workbook_plus_48969 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_48969 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (hab : a^2 + b^2 + c^2 = 3) : 6 * a * b * c + 11 * (a + b + c) ≥ (a + b + c)^3 + 12   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_48969; Apache-2.0

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