Lemma alexander_succ from the Aether Catalog (Bridges/AlexanderKnotNumberBridge)

Proved

Bridges.AlexanderTorus.alexander_succ

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

aether-catalogbridges

Helper lemma from Bridges.AlexanderTorus.

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

Preamble

import Mathlib
import Definitions.Def_Bridges_AlexanderKnotNumberBridge

open Bridges.AlexanderTorus Polynomial Finset

Formal statement

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