Theorems · Theorem · number theory

NumberField.Units.regOfFamily_of_isMaxRank

∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K]
  {u : Fin (NumberField.Units.rank K) → (NumberField.RingOfIntegers K)ˣ} (hu : NumberField.Units.IsMaxRank u),
  NumberField.Units.regOfFamily u =
    ZLattice.covolume (Submodule.span ℤ (Set.range ⇑(NumberField.Units.basisOfIsMaxRank hu))) MeasureTheory.volume

Defined in: Mathlib.NumberTheory.NumberField.Units.Regulator
Cited by: 4 results in Mathlib
Foundations: Depth 306 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cites18

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

DFunLike.coestatement and proof · cited by 62,936
Realstatement and proof · cited by 25,697
Fieldstatement and proof · cited by 7,404
Set.rangestatement and proof · cited by 4,705
Unitsstatement and proof · cited by 2,804
Submodule.spanstatement and proof · cited by 1,504
Module.Basisstatement · cited by 1,477
MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
NumberFieldstatement and proof · cited by 653
NumberField.InfinitePlacestatement · cited by 604
NumberField.RingOfIntegersstatement and proof · cited by 413
NumberField.Units.dirichletUnitTheorem.w₀statement · cited by 72

Cited by4

Results whose statement or proof uses this declaration.

NumberField.Units.regulator_eq_regOfFamily_fundSystemproof · cited by 7
NumberField.Units.regOfFamily_eq_det'proof · cited by 3
NumberField.Units.regOfFamily_posproof · cited by 2
NumberField.Units.regOfFamily_div_regOfFamilyproof · cited by 1