A reciprocal pair-product sum correction bounds eight divided by the total

Proved

WorkbookSource.base_54805

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

lean-workbooksource-checked

Let $a, b, c, d$ be positive real numbers. Prove that $1+\frac{6}{ab+ac+ad+bc+bd+cd}\geq\frac{8}{a+b+c+d},$

Source: InternLM Lean-Workbook, record lean_workbook_54805 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_54805 (a b c d : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) : 1 + 6 / (a * b + a * c + a * d + b * c + b * d + c * d) ≥ 8 / (a + b + c + d)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_54805; Apache-2.0

View graph