A rational bound on the positive quadrant of a circle

Proved

WorkbookSource.base_1320

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

lean-workbooksource-checked

If $a^2+b^2=4$ , and $a,b$ are positive real numbers, Prove that $ab/(a+b+2)$ is less than or equal to $\sqrt2-1$

Source: InternLM Lean-Workbook, record lean_workbook_1320 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_1320 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) (hab : a * b > 0) (hab2 : a + b + 2 > 0) (hab3 : a ^ 2 + b ^ 2 = 4) : a * b / (a + b + 2) ≤ Real.sqrt 2 - 1  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_1320; Apache-2.0

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