Two sharp bounds under a circle constraint

Proved

WorkbookSource.plus_44787

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

lean-workbooksource-checked

Let $a ,b$ be real numbers such that $a^2+b^2=8$ . Prove that $-12\leq 2(a+b)-ab\leq 6$ .

Source: InternLM Lean-Workbook, record lean_workbook_plus_44787 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble

import Mathlib
open Real

Formal statement

theorem WorkbookSource.plus_44787 (a b : ℝ) (h : a ^ 2 + b ^ 2 = 8) : -12 ≤ 2 * (a + b) - a * b ∧ 2 * (a + b) - a * b ≤ 6   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_44787; Apache-2.0

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