A cyclic ratio sum with a triple-product correction

Proved

WorkbookSource.base_17986

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

lean-workbooksource-checked

Let $a,b,c>0$ such that $a+b+c=3$ . Prove that: $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}+abc \geq 4$

Source: InternLM Lean-Workbook, record lean_workbook_17986 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_17986 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) (hab : a + b + c = 3) : a / b + b / c + c / a + a * b * c ≥ 4  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_17986; Apache-2.0

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