A strict arithmetic-geometric mean comparison

Proved

WorkbookSource.problem_19781

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

lean-workbooksource-checked

From A.M. G.M. inequality, $\sqrt{(a^2)(a^2 + 1)} < \frac{a^2 + a^2 + 1}{2}$

Source: InternLM Lean-Workbook, record lean_workbook_19781 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_19781 : ∀ a : ℝ, Real.sqrt (a^2 * (a^2 + 1)) < (a^2 + a^2 + 1) / 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_19781; Apache-2.0

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