Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.zeroLocus_biInf_of_nonempty
∀ {X : AlgebraicGeometry.Scheme} {U : X.Opens} {ι : Type u_1} (I : ι → Ideal ↑(X.presheaf.obj (Opposite.op U)))
{t : Set ι}, t.Finite → t.Nonempty → X.zeroLocus ↑(⨅ i ∈ t, I i) = ⋃ i ∈ t, X.zeroLocus ↑(I i)- Defined in
- Mathlib.AlgebraicGeometry.AffineScheme
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- SetLike.coestatement and proof · cited by 8,199
- Oppositestatement · cited by 8,081
- Idealstatement and proof · cited by 4,748
- TopCat.carrierstatement and proof · cited by 3,184
- Compl.complproof · cited by 2,925
- Set.Nonemptystatement and proof · cited by 2,627
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- Set.iUnionstatement and proof · cited by 2,483
- CommRingCatstatement · cited by 2,333
- TopologicalSpace.Opensstatement · cited by 2,040
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.zeroLocus_iInf_of_nonemptyproof · cited by 1