Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsAffineOpen.biInf
∀ {X : AlgebraicGeometry.Scheme}
[AlgebraicGeometry.IsAffineHom (CategoryTheory.Limits.pullback.diagonal (CategoryTheory.Limits.terminal.from X))]
{ι : Type u_1} (s : Set ι),
s.Finite →
s.Nonempty →
∀ {U : ι → X.Opens},
(∀ i ∈ s, AlgebraicGeometry.IsAffineOpen (U i)) → AlgebraicGeometry.IsAffineOpen (⨅ i ∈ s, U i)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Set.ofPredproof · cited by 6,101
- TopCat.carrierstatement · cited by 3,184
- Set.Nonemptystatement and proof · cited by 2,627
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
- Set.Finitestatement and proof · cited by 1,814
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement · cited by 1,734
- iInfstatement · cited by 1,690
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