Theorems · Theorem · algebraic geometry
PrimeSpectrum.exist_mem_one_of_mem_two
∀ {R : Type u_1} [inst : CommRing R] [IsNoetherianRing R] {p₁ p₀ p₂ : PrimeSpectrum R},
p₀ < p₁ → p₁ < p₂ → ∀ {x : R}, x ∈ p₂.asIdeal → ∃ q, x ∈ q.asIdeal ∧ p₀ < q ∧ q < p₂- Cited by
- 1 results in Mathlib
- Foundations
- Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsNoetherianRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Set.Elemproof · cited by 7,166
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- LT.lt.leproof · cited by 2,189
- le_reflproof · cited by 2,061
- Set.Iicproof · cited by 1,111
- OrderIsoproof · cited by 874
- PrimeSpectrumstatement and proof · cited by 625
- Eq.leproof · cited by 605
- OrderIso.symmproof · cited by 475
Cited by1
Results whose statement or proof uses this declaration.
- PrimeSpectrum.exist_ltSeries_mem_one_of_mem_lastproof · cited by 1