Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.affineBasisCover_map_range
∀ (X : AlgebraicGeometry.Scheme) (x : ↥X) (r : ↑⋯.choose), Set.range ⇑(X.affineBasisCover.f ⟨x, r⟩) = ⇑(X.affineCover.f x) '' (PrimeSpectrum.basicOpen r).carrier
- Defined in
- Mathlib.AlgebraicGeometry.Cover.Open
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites48
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- CategoryTheory.Functor.objstatement · cited by 19,642
- Oppositestatement · cited by 8,081
- Set.imagestatement and proof · cited by 5,609
- Set.rangestatement and proof · cited by 4,705
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- CategoryTheory.Isostatement · cited by 3,963
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- ContinuousMapstatement · cited by 2,491
- CommRingCatstatement · cited by 2,333
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.affineBasisCover_is_basisproof · cited by 2