A strict pair-product bound above one

Proved

WorkbookSource.problem_11882

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

lean-workbooksource-checked

For $a,b,c>1$ then $ab+bc+ca>3$

Source: InternLM Lean-Workbook, record lean_workbook_11882 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_11882 (a b c : ℝ) (hab : 1 < a) (hbc : 1 < b) (hca : 1 < c) : a * b + b * c + c * a > 3  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_11882; Apache-2.0

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