A mixed cubic-quartic inequality at fixed sum

Proved

WorkbookSource.base_25519

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

lean-workbooksource-checked

(Inequality rearrangement) Let $a,b,c$ be positive real numbers such that $a+b+c=3$ . Prove that $3(a^3+b^3+c^3)\geq 3abc+2(a^3c+b^3c+abc^2)$

Source: InternLM Lean-Workbook, record lean_workbook_25519 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_25519 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 3) : 3 * (a^3 + b^3 + c^3) ≥ 3 * a * b * c + 2 * (a^3 * c + b^3 * c + a * b * c^2)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_25519; Apache-2.0

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