Theorems · Theorem · field theory

Valued.integer.totallyBounded_iff_finite_residueField

∀ {K : Type u_1} {Γ₀ : Type u_2} [inst : Field K] [inst_1 : LinearOrderedCommGroupWithZero Γ₀] [inst_2 : Valued K Γ₀]
  [Valued.v.RankOne] [IsDiscreteValuationRing ↥(Valued.integer K)],
  TotallyBounded Set.univ ↔ Finite (Valued.ResidueField K)

Defined in: Mathlib.Topology.Algebra.Valued.LocallyCompact
Cited by: 1 results in Mathlib
Foundations: Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field LinearOrderedCommGroupWithZero Valued Valuation.RankOne IsDiscreteValuationRing

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Cites80

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
Setproof · cited by 53,352
Realproof · cited by 25,697
Semiringproof · cited by 13,802
RingHomproof · cited by 10,189
Fieldstatement and proof · cited by 7,404
Set.ofPredproof · cited by 6,101
Set.imageproof · cited by 5,609
Norm.normproof · cited by 5,413
Idealproof · cited by 4,748
Algebra.algebraMapproof · cited by 4,706
Set.univstatement and proof · cited by 3,945

Cited by1

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Valued.integer.compactSpace_iff_completeSpace_and_isDiscreteValuationRing_and_finite_residueFieldproof · cited by 0