Theorems · Definition · algebraic geometry
PrimeSpectrum.ConstructibleSetData.toSet
{R : Type u_1} → [inst : CommSemiring R] → PrimeSpectrum.ConstructibleSetData R → Set (PrimeSpectrum R)Given the data of a constructible set s, namely finitely many tuples (f, g₁, ..., gₙ) such
that s = ⋃ (f, g₁, ..., gₙ), V(g₁, ..., gₙ) \ V(f), return s.
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.iUnionproof · cited by 2,483
- PrimeSpectrumstatement · cited by 625
- PrimeSpectrum.BasicConstructibleSetDataproof · cited by 22
- PrimeSpectrum.ConstructibleSetDatastatement and proof · cited by 10
- PrimeSpectrum.BasicConstructibleSetData.toSetproof · cited by 4
Cited by8
Results whose statement or proof uses this declaration.
- PrimeSpectrum.ConstructibleSetData.isConstructible_toSetstatement · cited by 2
- ChevalleyThm.chevalley_polynomialCstatement and proof · cited by 2
- PrimeSpectrum.exists_constructibleSetData_iffstatement and proof · cited by 2
- ChevalleyThm.chevalley_mvPolynomialCstatement and proof · cited by 1
- PrimeSpectrum.ConstructibleSetData.toSet_mapstatement · cited by 1
- PrimeSpectrum.isConstructible_comap_Cproof · cited by 1
- PrimeSpectrum.exists_range_eq_of_isConstructibleproof · cited by 1
- chevalley_mvPolynomial_mvPolynomialstatement and proof · cited by 0