Theorems · Definition · algebraic geometry
PrimeSpectrum.BasicConstructibleSetData.toSet
{R : Type u_1} → [inst : CommSemiring R] → PrimeSpectrum.BasicConstructibleSetData R → Set (PrimeSpectrum R)Given the data of a basic constructible set s, namely a tuple (f, g₁, ..., gₙ) such that
s = V(g₁, ..., gₙ) \ V(f), return s.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses no axioms
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommSemiringstatement and proof · cited by 10,911
- Set.rangeproof · cited by 4,705
- PrimeSpectrumstatement · cited by 625
- PrimeSpectrum.zeroLocusproof · cited by 164
- PrimeSpectrum.BasicConstructibleSetDatastatement and proof · cited by 22
- PrimeSpectrum.BasicConstructibleSetData.gproof · cited by 13
- PrimeSpectrum.BasicConstructibleSetData.fproof · cited by 12
Cited by5
Results whose statement or proof uses this declaration.
- PrimeSpectrum.ConstructibleSetData.toSetproof · cited by 8
- PrimeSpectrum.exists_constructibleSetData_iffproof · cited by 2
- PrimeSpectrum.BasicConstructibleSetData.toSet_mapstatement · cited by 1
- PrimeSpectrum.exists_range_eq_of_isConstructibleproof · cited by 1
- PrimeSpectrum.ConstructibleSetData.toSet_mapproof · cited by 1