lean_workbook_plus_30378

Proved

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

Prove that in a right-angled triangle $ABC$ , $\sqrt{b^{2}+c^{2}}\geq\frac{\sqrt{2}}{2}(b+c)$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_30378 (b c : ℝ) (h : b > 0 ∧ c > 0) (hab : b * b + c * c = 1) : Real.sqrt (b * b + c * c) ≥ Real.sqrt 2 / 2 * (b + c)   :=  by sorry

Source

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

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