Prove2Me

A pair-product ratio sum is at least four

Proved
WorkbookSource.base_18791

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

lean-workbooksource-checked

Let a,b,c are positive Prove

(c+a)(c+b)a2+b2+ab+(a+c)(a+b)b2+c2+bc+(b+a)(b+c)c2+a2+ac≥4\frac{(c+a)(c+b)}{a^2+b^2+ab}+\frac{(a+c)(a+b)}{b^2+c^2+bc}+\frac{(b+a)(b+c)}{c^2+a^2+ac}\geq4

Source: InternLM Lean-Workbook, record lean_workbook_18791 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_18791 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (c + a) * (c + b) / (a ^ 2 + b ^ 2 + a * b) + (a + c) * (a + b) / (b ^ 2 + c ^ 2 + b * c) + (b + a) * (b + c) / (c ^ 2 + a ^ 2 + a * c) ≥ 4  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_18791; Apache-2.0

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