A cyclic ratio sum with a pair-product correction at fixed sum two

Proved

WorkbookSource.base_53756

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

lean-workbooksource-checked

Let $a,b,c>0$ such that: $a+b+c=2$ . Prove that: $\frac{a}{b}+\frac{b}{c}+\frac{c}{a} +3(ab+bc+ac) \geq 7$

Source: InternLM Lean-Workbook, record lean_workbook_53756 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_53756 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b + c = 2) : a / b + b / c + c / a + 3 * (a * b + b * c + a * c) ≥ 7  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_53756; Apache-2.0

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