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Theorems · Theorem · number theory

NumberField.Units.regOfFamily_pos

∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K]
  {u : Fin (NumberField.Units.rank K) → (NumberField.RingOfIntegers K)ˣ},
  NumberField.Units.IsMaxRank u → 0 < NumberField.Units.regOfFamily u
Defined in
Mathlib.NumberTheory.NumberField.Units.Regulator
Cited by
2 results in Mathlib
Foundations
Depth 307 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldNumberField
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

NumberField.Units.regulator_pos · cited by 3Units.regulator_posNumberField.Units.regOfFamily_ne_zero · cited by 1Units.regOfFamily_ne_zeroDFunLike.coe · cited by 62936DFunLike.coeReal · cited by 25697RealField · cited by 7404FieldSet.range · cited by 4705Set.rangeUnits · cited by 2804UnitsSubmodule.span · cited by 1504Submodule.spanMeasureTheory.MeasureSpace.volume · cited by 1323MeasureSpace.volumeNumberField · cited by 653NumberFieldNumberField.RingOfIntegers · cited by 413NumberField.RingOfIntegersNumberField.Units.rank · cited by 46Units.rankNumberField.Units.regOfFamily · cited by 12Units.regOfFamilyNumberField.Units.IsMaxRank · cited by 12Units.IsMaxRankNumberField.Units.basisOfIsMaxRank · cited by 9Units.basisOfIsMaxRankZLattice.covolume_pos · cited by 5ZLattice.covolume_posNumberField.Units.regOfFamily_of_isMaxRank · cited by 4Units.regOfFamily_of_isMa…Units.regOfFamily_posCITED BYCITES

Cites15

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Cited by2

Results whose statement or proof uses this declaration.