A cyclic rational comparison involving a triple product

Proved

WorkbookSource.base_4667

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

lean-workbooksource-checked

If $a,b,c>0$ than prove that: $\frac{a+b+c}{1+abc}\geq\frac{a}{1+a^2b}+\frac{b}{1+b^2c}+\frac{c}{1+c^2a}$

Source: InternLM Lean-Workbook, record lean_workbook_4667 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_4667 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a + b + c) / (1 + a * b * c) ≥ a / (1 + a ^ 2 * b) + b / (1 + b ^ 2 * c) + c / (1 + c ^ 2 * a)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_4667; Apache-2.0

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