Prove2Me

A cyclic ratio sum with signed pairwise corrections

Proved
WorkbookSource.base_2835

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

lean-workbooksource-checked

Given that a,b,ca,b,c are positive real numbers. Prove that

ab+bc+ca+a−ba+b+b−cb+c+c−ac+a≥3\frac{a}{b}+\frac{b}{c}+\frac{c}{a}+\frac{a-b}{a+b}+\frac{b-c}{b+c}+\frac{c-a}{c+a}\geq 3

Source: InternLM Lean-Workbook, record lean_workbook_2835 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_2835 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a / b + b / c + c / a + (a - b) / (a + b) + (b - c) / (b + c) + (c - a) / (c + a)) ≥ 3  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_2835; Apache-2.0

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