Theorems · Theorem · algebraic geometry
PrimeSpectrum.zeroLocus_bUnion
∀ {R : Type u} [inst : CommSemiring R] (s : Set (Set R)),
PrimeSpectrum.zeroLocus (⋃ s' ∈ s, s') = ⋂ s' ∈ s, PrimeSpectrum.zeroLocus s'- Defined in
- Mathlib.RingTheory.Spectrum.Prime.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
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Cites7
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
- CommSemiringstatement and proof · cited by 10,911
- Set.iUnionstatement and proof · cited by 2,483
- Set.iInterstatement and proof · cited by 1,084
- PrimeSpectrumstatement · cited by 625
- PrimeSpectrum.zeroLocusstatement and proof · cited by 164
- PrimeSpectrum.zeroLocus_iUnionproof · cited by 4
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