Prove2Me

Adding one decreases a cyclic ratio sum

Proved
WorkbookSource.base_3162

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

lean-workbooksource-checked

Prove that if a,b,c>0a,b,c > 0 then a+1b+1+b+1c+1+c+1a+1≤ab+bc+ca\frac{a+1}{b+1}+\frac{b+1}{c+1}+\frac{c+1}{a+1} \leq \frac{a}{b}+\frac{b}{c}+\frac{c}{a}

Source: InternLM Lean-Workbook, record lean_workbook_3162 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_3162 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a + 1) / (b + 1) + (b + 1) / (c + 1) + (c + 1) / (a + 1) ≤ a / b + b / c + c / a  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_3162; Apache-2.0

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