Theorems · Theorem · commutative algebra
Valued.isClopen_valuationSubring
∀ {Γ₀ : Type v} [inst : LinearOrderedCommGroupWithZero Γ₀] (K : Type u) [inst_1 : Field K] [hv : Valued K Γ₀],
IsClopen ↑Valued.v.valuationSubringThe valuation subring of a valued field is clopen.
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- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coestatement · cited by 8,199
- Fieldstatement and proof · cited by 7,404
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- IsClopenstatement · cited by 189
- ValuationSubringstatement · cited by 187
- Valued.vstatement · cited by 163
- Valuedstatement and proof · cited by 70
- Valuation.valuationSubringstatement · cited by 56
- Valued.isClopen_integerproof · cited by 1
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