Theorems · Theorem · number theory

NumberField.basisOfFractionalIdeal_apply

∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K]
  (I : (FractionalIdeal (nonZeroDivisors (NumberField.RingOfIntegers K)) K)ˣ) (i : Module.Free.ChooseBasisIndex ℤ ↥↑↑I),
  (NumberField.basisOfFractionalIdeal K I) i = ↑((NumberField.fractionalIdealBasis K ↑I) i)

Defined in: Mathlib.NumberTheory.NumberField.FractionalIdeal
Cited by: 1 results in Mathlib
Foundations: Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cites17

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

DFunLike.coestatement · cited by 62,936
Fieldstatement and proof · cited by 7,404
Submodulestatement · cited by 7,192
Unitsstatement and proof · cited by 2,804
Units.valstatement and proof · cited by 1,966
Module.Basisstatement · cited by 1,477
nonZeroDivisorsstatement and proof · cited by 895
NumberFieldstatement and proof · cited by 653
Submodule.subtypeproof · cited by 480
FractionalIdealstatement and proof · cited by 423
NumberField.RingOfIntegersstatement and proof · cited by 413
LinearMap.restrictScalarsproof · cited by 215

Cited by1

Results whose statement or proof uses this declaration.

NumberField.det_basisOfFractionalIdeal_eq_absNormproof · cited by 1