A strict quadratic bound from two comparisons

Proved

WorkbookSource.problem_53369

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

lean-workbooksource-checked

if $a> c\ ,\ b> d$ prove: $( a+b+c+d )^{2}> 8 ( ad+bc )$

Source: InternLM Lean-Workbook, record lean_workbook_53369 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_53369 (a b c d : ℝ) (h1 : a > c) (h2 : b > d) : (a + b + c + d)^2 > 8 * (a * d + b * c)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_53369; Apache-2.0

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