Theorems · Theorem · number theory

NumberField.discr_mem_differentIdeal

∀ (K : Type u_1) (𝒪 : Type u_2) [inst : Field K] [inst_1 : NumberField K] [inst_2 : CommRing 𝒪] [inst_3 : Algebra 𝒪 K]
  [IsFractionRing 𝒪 K] [inst_5 : IsDedekindDomain 𝒪] [inst_6 : CharZero 𝒪] [Module.Finite ℤ 𝒪],
  ↑(NumberField.discr K) ∈ differentIdeal ℤ 𝒪

Defined in: Mathlib.NumberTheory.NumberField.Discriminant.Different
Cited by: 1 results in Mathlib
Foundations: Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField CommRing Algebra IsFractionRing IsDedekindDomain CharZero Module.Finite

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites18

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

DFunLike.coeproof · cited by 62,936
CommRingstatement and proof · cited by 17,173
Algebrastatement and proof · cited by 11,388
Fieldstatement and proof · cited by 7,404
Idealstatement · cited by 4,748
Module.Finitestatement and proof · cited by 1,032
CharZerostatement and proof · cited by 932
IsFractionRingstatement and proof · cited by 738
IsDedekindDomainstatement and proof · cited by 668
NumberFieldstatement and proof · cited by 653
Int.cast_natCastproof · cited by 393
Int.cast_negproof · cited by 224

Cited by1

Results whose statement or proof uses this declaration.

NumberField.isCoprime_differentIdeal_of_isCoprime_discrproof · cited by 1