A strict product bound on the unit circle

Proved

WorkbookSource.problem_20060

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

lean-workbooksource-checked

Let $a,b$ be reals such that $a^2+ b^ 2= 1.$ Prove that $(a+1)(b +2)<5$

Source: InternLM Lean-Workbook, record lean_workbook_20060 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble

import Mathlib
open Real

Formal statement

theorem WorkbookSource.problem_20060 (a b: ℝ) (hab : a^2 + b^2 = 1): (a + 1) * (b + 2) < 5  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_20060; Apache-2.0

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