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Theorems · Theorem · number theory

IsCyclotomicExtension.Rat.ramificationIdx_eq_of_not_dvd

∀ {m : ℕ} (p : ℕ) [hp : Fact (Nat.Prime p)] (K : Type u_1) [inst : Field K] [inst_1 : NumberField K]
  (P : Ideal (NumberField.RingOfIntegers K)) [hP₁ : P.IsPrime] [hP₂ : P.LiesOver (Ideal.span {↑p})] [NeZero m]
  [hK : IsCyclotomicExtension {m} ℚ K], ¬p ∣ m → P.ramificationIdx ℤ = 1
Defined in
Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal
Cited by
1 results in Mathlib
Foundations
Depth 322 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FactFieldNumberFieldIdeal.IsPrimeIdeal.LiesOverNeZeroIsCyclotomicExtension

Around this declaration

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Cites50

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

  • DFunLike.coeproof · cited by 62,936
  • Setstatement · cited by 53,352
  • Fieldstatement and proof · cited by 7,404
  • ENatproof · cited by 4,985
  • Idealstatement and proof · cited by 4,748
  • Equiv.symmproof · cited by 3,681
  • Factstatement and proof · cited by 2,726
  • le_antisymmproof · cited by 2,068
  • Nat.Primestatement and proof · cited by 2,059
  • LT.lt.ne'proof · cited by 1,417
  • ZModproof · cited by 1,024
  • Ideal.spanstatement and proof · cited by 948

Cited by1

Results whose statement or proof uses this declaration.