A cubic reciprocal product sum bounds the reciprocal sum

Proved

WorkbookSource.plus_56288

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

lean-workbooksource-checked

Prove that $\dfrac{ab}{c^3} + \dfrac{bc}{a^3} + \dfrac{ca}{b^3} \ge \dfrac 1 a + \dfrac 1 b + \dfrac 1 c$ where a,b,c are positive real numbers.

Source: InternLM Lean-Workbook, record lean_workbook_plus_56288 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_56288 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a * b / c ^ 3 + b * c / a ^ 3 + c * a / b ^ 3 ≥ 1 / a + 1 / b + 1 / c   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_56288; Apache-2.0

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