A cubic symmetric lower bound at total one

Proved

WorkbookSource.base_43233

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

lean-workbooksource-checked

Let $a,b,c,d$ non-negative reals such that $a + b + c + d = 1$ . Prove that

$5(a^3 + b^3 + c^3 + d^3) + 12(abc + bcd + cda + dab)\geq1$

Source: InternLM Lean-Workbook, record lean_workbook_43233 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_43233 (a b c d : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) (hd : d ≥ 0) (hab : a + b + c + d = 1) : 5 * (a ^ 3 + b ^ 3 + c ^ 3 + d ^ 3) + 12 * (a * b * c + b * c * d + c * d * a + d * a * b) ≥ 1  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_43233; Apache-2.0

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