Theorems · Theorem · field theory
Valued.integer.properSpace_iff_completeSpace_and_isDiscreteValuationRing_integer_and_finite_residueField
∀ {K : Type u_1} {Γ₀ : Type u_2} [inst : Field K] [inst_1 : LinearOrderedCommGroupWithZero Γ₀] [inst_2 : Valued K Γ₀]
[inst_3 : Valued.v.RankOne],
ProperSpace K ↔ CompleteSpace K ∧ IsDiscreteValuationRing ↥(Valued.integer K) ∧ Finite (Valued.ResidueField K)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Finitestatement and proof · cited by 3,029
- CompleteSpacestatement · cited by 2,532
- Metric.closedBallproof · cited by 704
- Subringstatement · cited by 602
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- Set.image_univproof · cited by 322
- ProperSpacestatement · cited by 190
- Subtype.range_coe_subtypeproof · cited by 170
- Valued.vstatement and proof · cited by 163
- IsDiscreteValuationRingstatement and proof · cited by 117
- Valuedstatement and proof · cited by 70
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