Lean-Workbook Plus 64837: A floor inequality for a positive number and its reciprocal

Proved

WorkbookRestored.plus_64837

by wamlart · Sep 12, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

lean-workbookrestored-importssource-checked

For every real $x>0$ , $\lfloor x\rfloor+\lfloor 1/x\rfloor\ge1$ , with integer-valued floors.

Source: Lean-Workbook row lean_workbook_plus_64837 (Apache-2.0). The unchanged proposition comes from the original record; its missing mathematical imports and namespaces are restored here.

Preamble

import Mathlib.Data.Real.Archimedean
open Int

Formal statement

theorem WorkbookRestored.plus_64837 (x : ℝ) (hx : 0 < x) : 1 ≤ floor x + floor (1 / x)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_64837; immutable original Prove2Me node 93342ceb-12cf-449e-9d6f-6e4ef691beed

View graph