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Lemma alexander_semiprime_degree_sum from the Aether Catalog (Bridges/AlexanderKnotNumberBridge)

Proved
Bridges.AlexanderTorus.alexander_semiprime_degree_sum

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

aether-catalogbridges

Helper lemma from Bridges.AlexanderTorus.

theorem Bridges.AlexanderTorus.alexander_semiprime_degree_sum {p q : ℕ} (hp : p.Prime) (hq : q.Prime) :
    (p - 1) + (q - 1) + (p - 1) * (q - 1) = p * q - 1
 := by sorry
Preamble
import Mathlib
import Definitions.Def_Bridges_AlexanderKnotNumberBridge

open Bridges.AlexanderTorus Polynomial Finset
Formal statement
theorem Bridges.AlexanderTorus.alexander_semiprime_degree_sum {p q : ℕ} (hp : p.Prime) (hq : q.Prime) :
    (p - 1) + (q - 1) + (p - 1) * (q - 1) = p * q - 1
 := by sorry

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