An asymmetric cubic-product bound at unit sum

Proved

WorkbookSource.base_31826

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

lean-workbooksource-checked

Let a,b,c>0 and a+b+c=1, prove that

$\frac {2 + c + c^3}{4} \ge abc + ab + 2bc + 2ca$

Source: InternLM Lean-Workbook, record lean_workbook_31826 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_31826 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b + c = 1) : (2 + c + c^3) / 4 ≥ a * b * c + a * b + 2 * b * c + 2 * c * a  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_31826; Apache-2.0

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