Lemma X_add_one_mul_alexander from the Aether Catalog (Bridges/AlexanderKnotNumberBridge)

Proved

Bridges.AlexanderTorus.X_add_one_mul_alexander

by raver1975 · Sep 18, 2026 · Mathlib c5ea003 (Lean v4.30.0)

aether-catalogbridges

Helper lemma from Bridges.AlexanderTorus.

theorem Bridges.AlexanderTorus.X_add_one_mul_alexander (N : ℕ) :
    (X + 1) * alexander N = 1 - (-1) ^ N * X ^ N
 := by sorry

Preamble

import Mathlib
import Definitions.Def_Bridges_AlexanderKnotNumberBridge

open Bridges.AlexanderTorus Polynomial Finset

Formal statement

theorem Bridges.AlexanderTorus.X_add_one_mul_alexander (N : ℕ) :
    (X + 1) * alexander N = 1 - (-1) ^ N * X ^ N
 := by sorry