Theorems · Theorem · algebraic geometry
PrimeSpectrum.subset_vanishingIdeal_zeroLocus
∀ {R : Type u} [inst : CommSemiring R] (s : Set R), s ⊆ ↑(PrimeSpectrum.vanishingIdeal (PrimeSpectrum.zeroLocus s))- Defined in
- Mathlib.RingTheory.Spectrum.Prime.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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Cites8
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
- SetLike.coestatement · cited by 8,199
- Idealstatement · cited by 4,748
- PrimeSpectrum.zeroLocusstatement · cited by 164
- GaloisConnection.le_u_lproof · cited by 52
- PrimeSpectrum.vanishingIdealstatement · cited by 36
- PrimeSpectrum.gc_setproof · cited by 7
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