A cyclic product bound for shifted cubes

Proved

WorkbookSource.base_2823

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

lean-workbooksource-checked

Prove the ineq for $a,b,c>0$ $(1+a^3)(1+b^3)(1+c^3)$ ≥ $(1+ab^2)(1+bc^2)(1+ca^2)$

Source: InternLM Lean-Workbook, record lean_workbook_2823 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_2823 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (1 + a ^ 3) * (1 + b ^ 3) * (1 + c ^ 3) ≥ (1 + a * b ^ 2) * (1 + b * c ^ 2) * (1 + c * a ^ 2)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_2823; Apache-2.0

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