lean_workbook_plus_67334

Proved

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

Let $x$ belong to a group. If $x^{2}\neq e$ and $x^{6}= e$ , prove that $x^{4}\neq e$ and $x^{5}\neq e$ . What can we say about the order of $x$ ?

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_67334 {G : Type*} [Group G] (x : G) (hx : x ^ 2 ≠ 1) (hx1 : x ^ 6 = 1) : x ^ 4 ≠ 1 ∧ x ^ 5 ≠ 1   :=  by sorry

Source