Prove2Me

A fixed-sum cyclic ratio and reciprocal-product lower bound

Proved
WorkbookSource.base_834

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

lean-workbooksource-checked

If a,b,c>0,a+b+c=3a,b,c>0,a+b+c=3 prove that: aa+b+bb+c+cc+a+1abc≥52\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+a}+\frac{1}{abc}\ge\frac{5}{2}

Source: InternLM Lean-Workbook, record lean_workbook_834 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_834 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b + c = 3) : a / (a + b) + b / (b + c) + c / (c + a) + 1 / (a * b * c) ≥ 5 / 2  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_834; Apache-2.0

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