A strict product bound for integers above two

Proved

WorkbookSource.problem_39173

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

lean-workbooksource-checked

Prove that if $a, b$ are integers and $a, b>2$ , then $ab>a+b$

Source: InternLM Lean-Workbook, record lean_workbook_39173 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved. This is a strict integer bound; the related record plus_53847 gives a non-strict real inequality under a different premise.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_39173 (a b : ℤ) (h₁ : 2 < a) (h₂ : 2 < b) : a * b > a + b  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_39173; Apache-2.0

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