no goals
R : Type u_2
A : Type u_1
inst✝³ : CommSemiring R
inst✝² : CommRing A
inst✝¹ : Algebra R A
𝒜 : ℕ → Submodule R A
inst✝ : GradedAlgebra 𝒜
I : HomogeneousIdeal 𝒜
t : (Set (ProjectiveSpectrum 𝒜))ᵒᵈ
⊢ (fun I => zeroLocus 𝒜 ↑I) I ≤ t ↔ I ≤ (fun t => vanishingIdeal t) t
simpa [show I.toIdeal ≤ (vanishingIdeal t).toIdeal ↔ I ≤ vanishingIdeal t from Iff.rfl] using
  subset_zeroLocus_iff_le_vanishingIdeal t I.toIdeal