Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.OpenCover.iSup_opensRange
∀ {X : AlgebraicGeometry.Scheme} (𝒰 : X.OpenCover), ⨆ i, AlgebraicGeometry.Scheme.Hom.opensRange (𝒰.f i) = ⊤- Defined in
- Mathlib.AlgebraicGeometry.Cover.Open
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Top.topstatement and proof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- iSupstatement · cited by 2,415
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
- AlgebraicGeometry.Scheme.Opensstatement · cited by 1,149
Cited by9
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.OpenCover.isOpenCover_opensRangeproof · cited by 4
- AlgebraicGeometry.HasAffineProperty.of_openCoverproof · cited by 3
- AlgebraicGeometry.IsZariskiLocalAtTarget.mk'proof · cited by 3
- AlgebraicGeometry.IsZariskiLocalAtTarget.of_openCoverproof · cited by 2
- AlgebraicGeometry.isLocallyNoetherian_iff_of_affine_openCoverproof · cited by 2
- AlgebraicGeometry.IsZariskiLocalAtSource.mk'proof · cited by 2
- AlgebraicGeometry.IsZariskiLocalAtSource.of_openCoverproof · cited by 2
- AlgebraicGeometry.HasRingHomProperty.of_source_openCoverproof · cited by 2
- AlgebraicGeometry.HasAffineProperty.iff_of_openCoverproof · cited by 1