Prove2Me

A squared pairwise sum bounds a cubic elementary symmetric sum

Proved
WorkbookSource.base_35325

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

lean-workbooksource-checked

Let a,b,c,d∈Ra,b,c,d \in R ,prove that: (ab+bc+cd+ad+ca+db)2≥94(a+b+c+d)(abc+bcd+cda+dab).(ab+bc+cd+ad+ca+db)^2\geq \frac{9}{4}(a+b+c+d)(abc+bcd+cda+dab).

Source: InternLM Lean-Workbook, record lean_workbook_35325 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_35325 (a b c d : ℝ) : (a * b + b * c + c * d + d * a + a * c + b * d) ^ 2 ≥ (9 / 4) * (a + b + c + d) * (a * b * c + b * c * d + c * d * a + d * a * b)  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_35325; Apache-2.0

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