A four-variable quadratic bound under a weighted sum constraint

Proved

WorkbookSource.plus_33897

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

lean-workbooksource-checked

Let $a,b,c,d$ be real numbers such that $a+2b+3c+4d=10$ , prove that: $a^2+b^2+c^2+d^2+ab+ac+ad+bc+bd+cd\ge5$ .

Source: InternLM Lean-Workbook, record lean_workbook_plus_33897 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_33897 (a b c d : ℝ) (h : a + 2 * b + 3 * c + 4 * d = 10) :
  a^2 + b^2 + c^2 + d^2 + a * b + a * c + a * d + b * c + b * d + c * d ≥ 5   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_33897; Apache-2.0

View graph