Theorems · Theorem · number theory

NumberField.Units.regOfFamily_ne_zero

∀ {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 → NumberField.Units.regOfFamily u ≠ 0

Defined in: Mathlib.NumberTheory.NumberField.Units.Regulator
Cited by: 1 results in Mathlib
Foundations: Depth 308 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cites10

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

Realstatement · cited by 25,697
Fieldstatement and proof · cited by 7,404
Unitsstatement and proof · cited by 2,804
LT.lt.ne'proof · cited by 1,417
NumberFieldstatement and proof · cited by 653
NumberField.RingOfIntegersstatement and proof · cited by 413
NumberField.Units.rankstatement and proof · cited by 46
NumberField.Units.regOfFamilystatement · cited by 12
NumberField.Units.IsMaxRankstatement and proof · cited by 12
NumberField.Units.regOfFamily_posproof · cited by 2

Cited by1

Results whose statement or proof uses this declaration.

NumberField.Units.regOfFamily_ne_zero_iffproof · cited by 0