lean_workbook_plus_77752

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

$\left\lfloor\sqrt[k]n\right\rfloor=m$ $\iff$ $m+1>n^{\frac 1k}\ge m$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_77752 (n m : ℕ) (k : ℕ) (hn : 0 < n) (hk : 0 < k) : (⌊(n:ℝ)^(1/k)⌋ = m) ↔ (m + 1 > (n:ℝ)^(1/k) ∧ (n:ℝ)^(1/k) ≥ m)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

View graph