∀ {ι : Type u_1} {A : Type u_2} {σ : Type u_3} [inst : CommRing A] [inst_1 : SetLike σ A] (𝒜 : ι → σ) (x : Submonoid A)
  (p : HomogeneousLocalization.NumDenSameDeg 𝒜 x),
  HomogeneousLocalization.NumDenSameDeg.embedding 𝒜 x p = Localization.mk ↑p.num ⟨↑p.den, ⋯⟩