Theorems · Theorem · commutative algebra
ValuationSubring.eq_self_or_eq_top_of_le
∀ {K : Type u} [inst : Field K] {A : ValuationSubring K} [Ring.KrullDimLE 1 ↥A] {B : ValuationSubring K},
A ≤ B → A = B ∨ B = ⊤- Cited by
- 3 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldRing.KrullDimLE
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Top.topstatement and proof · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- Bot.botproof · cited by 4,720
- Equiv.symmproof · cited by 3,681
- Equiv.apply_symm_applyproof · cited by 346
- PrimeSpectrum.asIdealproof · cited by 333
- ValuationSubringstatement and proof · cited by 187
- Ring.KrullDimLEstatement and proof · cited by 79
- ValuationSubring.ofPrimeproof · cited by 10
- ValuationSubring.primeSpectrumEquivproof · cited by 2
- IsLocalRing.Ring.KrullDimLE.eq_bot_or_eq_topproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- ValuationSubring.eq_of_le_of_ne_topproof · cited by 1
- ValuationSubring.eq_of_le_of_ne_selfproof · cited by 0
- ValuationSubring.eq_of_ltproof · cited by 0