Theorems · Theorem · field theory
IsGalois.IntermediateField.AdjoinSimple.card_aut_eq_finrank
∀ (F : Type u_1) [inst : Field F] (E : Type u_2) [inst_1 : Field E] [inst_2 : Algebra F E] [FiniteDimensional F E]
{α : E},
IsIntegral F α →
IsSeparable F α →
(Polynomial.map (algebraMap F ↥F⟮α⟯) (minpoly F α)).Splits → Nat.card Gal(↥F⟮α⟯/F) = Module.finrank F ↥F⟮α⟯- Defined in
- Mathlib.FieldTheory.Galois.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapstatement and proof · cited by 4,706
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankstatement · cited by 1,770
- AlgEquivstatement and proof · cited by 1,681
- IntermediateFieldstatement · cited by 988
- Nat.cardstatement and proof · cited by 844
- Polynomial.mapstatement and proof · cited by 806
- minpolystatement and proof · cited by 439
- IsIntegralstatement and proof · cited by 427
Cited by1
Results whose statement or proof uses this declaration.
- IsGalois.card_aut_eq_finrankproof · cited by 16