A quadratic bound for four weakly ordered numbers

Proved

WorkbookSource.problem_9704

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Prove that if $a\le b\le c\le d$ , then $(a + b + c + d)^2\ge\(8(ac + bd)$ .

Source: InternLM Lean-Workbook, record lean_workbook_9704 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_9704 (a b c d : ℝ) (hab : a ≤ b) (hbc : b ≤ c) (hcd : c ≤ d) : (a + b + c + d) ^ 2 ≥ 8 * (a * c + b * d)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_9704; Apache-2.0

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