A square-root comparison for two variables

Proved

WorkbookSource.problem_51562

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

lean-workbooksource-checked

by Minkowski,we have: $\sqrt{(8+x^{2})(8+y^{2})}\geq 8+xy$

Source: InternLM Lean-Workbook, record lean_workbook_51562 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_51562 (x y : ℝ) : 8 + x * y ≤ Real.sqrt ((8 + x ^ 2) * (8 + y ^ 2))  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_51562; Apache-2.0

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