lean_workbook_plus_44976

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove that $a\sqrt{bc}\le \sqrt{abc}$ given $a\le 1$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_44976 (a b c : ℝ) (ha : 0 < a ∧ a ≤ 1) (hb : 0 < b) (hc : 0 < c) : a * Real.sqrt (b * c) ≤ Real.sqrt (a * b * c)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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