A cyclic shifted ratio with a pairwise-product correction

Proved

WorkbookSource.base_17288

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

lean-workbooksource-checked

Let $a,b,c$ is positive real number satisfy $a+b+c=3$ prove that $\frac{a}{b+c^2}+\frac{b}{c+a^2}+\frac{c}{a+b^2}+\frac{ab+bc+ca}{72} \ge \frac{37}{24}$

Source: InternLM Lean-Workbook, record lean_workbook_17288 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_17288 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 3) : (a / (b + c ^ 2) + b / (c + a ^ 2) + c / (a + b ^ 2) + (a * b + b * c + c * a) / 72) ≥ 37 / 24  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_17288; Apache-2.0

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