Prove2Me

A cyclic rational difference sum at fixed sum three

Proved
WorkbookSource.base_5494

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

lean-workbooksource-checked

a,b,c >0; \ \ \ a+b+c=3 . Prove that a−bcb(1+c)+b−cac(1+a)+c−aba(1+b)≥0\frac{a-bc}{b(1+c)}+\frac{b-ca}{c(1+a)}+\frac{c-ab}{a(1+b)} \ge 0

Source: InternLM Lean-Workbook, record lean_workbook_5494 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_5494 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b + c = 3) : (a - b * c) / (b * (1 + c)) + (b - c * a) / (c * (1 + a)) + (c - a * b) / (a * (1 + b)) ≥ 0  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_5494; Apache-2.0

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