Theorems · Theorem · commutative algebra
ValuationSubring.eq_of_le_of_ne_self
∀ {K : Type u} [inst : Field K] (A : ValuationSubring K) [Ring.KrullDimLE 1 ↥A] {B : ValuationSubring K},
A ≤ B → A ≠ B → B = ⊤- Cited by
- 0 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldRing.KrullDimLE
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Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- ValuationSubringstatement and proof · cited by 187
- Ring.KrullDimLEstatement and proof · cited by 79
- ValuationSubring.eq_self_or_eq_top_of_leproof · cited by 3
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