A cubed difference ratio sum bounds the total

Proved

WorkbookSource.base_19366

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

lean-workbooksource-checked

Let $a,b,c$ be positive real numbers . Prove that $\frac{(b+c-a)^3}{a^2}+\frac{(c+a-b)^3}{b^2}+\frac{(a+b-c)^3}{c^2}\ge a+b+c.$

Source: InternLM Lean-Workbook, record lean_workbook_19366 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_19366 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (b + c - a) ^ 3 / a ^ 2 + (c + a - b) ^ 3 / b ^ 2 + (a + b - c) ^ 3 / c ^ 2 ≥ a + b + c  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_19366; Apache-2.0

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