Theorems · Theorem · number theory

NumberField.coe_discr

∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K],
  ↑(NumberField.discr K) = Algebra.discr ℚ ⇑(NumberField.integralBasis K)

Defined in: Mathlib.NumberTheory.NumberField.Discriminant.Defs
Cited by: 4 results in Mathlib
Foundations: Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cites12

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
Module.Basisstatement · cited by 1,477
nonZeroDivisorsproof · cited by 895
NumberFieldstatement and proof · cited by 653
NumberField.RingOfIntegersstatement · cited by 413
Module.Free.ChooseBasisIndexstatement · cited by 133
NumberField.discrstatement · cited by 53
Algebra.discrstatement · cited by 38
NumberField.integralBasisstatement · cited by 25
NumberField.RingOfIntegers.basisproof · cited by 12
Algebra.discr_localizationLocalizationproof · cited by 3

Cited by4

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasisproof · cited by 4
NumberField.discr_ne_zeroproof · cited by 2
NumberField.discr_eq_basisMatrix_det_sqproof · cited by 1
NumberField.discr_eq_discr_of_algEquivproof · cited by 1