A mixed-power cyclic ratio lower bound

Proved

WorkbookSource.base_18130

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

lean-workbooksource-checked

Prove the inequality:

$\frac {a^2}{b} + \frac {b^3}{c^2} + \frac {c^4}{a^3} \ge - a + 2b + 2c.$

where $a,b,c$ are positive real numbers.

Source: InternLM Lean-Workbook, record lean_workbook_18130 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_18130 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^2 / b + b^3 / c^2 + c^4 / a^3 ≥ -a + 2 * b + 2 * c  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_18130; Apache-2.0

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