case h
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
t t' : Set (ProjectiveSpectrum 𝒜)
⊢ HomogeneousIdeal.toIdeal (vanishingIdeal (t ∪ t')) = HomogeneousIdeal.toIdeal (vanishingIdeal t ⊓ vanishingIdeal t')
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
t t' : Set (ProjectiveSpectrum 𝒜)
⊢ vanishingIdeal (t ∪ t') = vanishingIdeal t ⊓ vanishingIdeal t'
ext1
no goals
case h
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
t t' : Set (ProjectiveSpectrum 𝒜)
⊢ HomogeneousIdeal.toIdeal (vanishingIdeal (t ∪ t')) = HomogeneousIdeal.toIdeal (vanishingIdeal t ⊓ vanishingIdeal t')
exact (gc_ideal 𝒜).u_inf