Theorems · Theorem · algebraic geometry
ProjectiveSpectrum.zeroLocus_anti_mono
∀ {A : Type u_1} {σ : Type u_2} [inst : CommRing A] [inst_1 : SetLike σ A] [inst_2 : AddSubmonoidClass σ A] (𝒜 : ℕ → σ)
[inst_3 : GradedRing 𝒜] {s t : Set A}, s ⊆ t → ProjectiveSpectrum.zeroLocus 𝒜 t ⊆ ProjectiveSpectrum.zeroLocus 𝒜 s- Cited by
- 1 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- CommRingstatement and proof · cited by 17,173
- SetLikestatement and proof · cited by 1,084
- GradedRingstatement and proof · cited by 424
- AddSubmonoidClassstatement and proof · cited by 346
- ProjectiveSpectrumstatement · cited by 86
- GaloisConnection.monotone_lproof · cited by 76
- ProjectiveSpectrum.zeroLocusstatement · cited by 42
- ProjectiveSpectrum.gc_setproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- ProjectiveSpectrum.isTopologicalBasis_basic_opensproof · cited by 1