Theorems · Theorem · number theory

NumberField.hermiteTheorem.natDegree_le_rankOfDiscrBdd

∀ {K : Type u_1} [inst : Field K] [inst_1 : NumberField K] {N : ℕ},
  |NumberField.discr K| ≤ ↑N →
    ∀ (a : NumberField.RingOfIntegers K),
      ℚ⟮↑a⟯ = ⊤ → (minpoly ℤ ↑a).natDegree ≤ NumberField.hermiteTheorem.rankOfDiscrBdd N

Defined in: Mathlib.NumberTheory.NumberField.Discriminant.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 317 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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

Setstatement · cited by 53,352
Top.topstatement and proof · cited by 9,680
Fieldstatement and proof · cited by 7,404
Polynomialproof · cited by 5,681
Algebra.algebraMapproof · cited by 4,706
absstatement and proof · cited by 1,814
Module.finrankproof · cited by 1,770
Polynomial.natDegreestatement and proof · cited by 1,105
IntermediateFieldstatement · cited by 988
NumberFieldstatement and proof · cited by 653
minpolystatement · cited by 439
NumberField.RingOfIntegersstatement and proof · cited by 413

Cited by2

Results whose statement or proof uses this declaration.

NumberField.hermiteTheorem.finite_of_discr_bdd_of_isRealproof · cited by 1
NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplexproof · cited by 1