Theorems · Theorem · field theory
IntermediateField.finrank_fixedField_eq_card
∀ {F : Type u_1} [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] (H : Subgroup Gal(E/F))
[FiniteDimensional F E], Module.finrank (↥(IntermediateField.fixedField H)) E = Nat.card ↥H- Defined in
- Mathlib.FieldTheory.Galois.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- Fintypeproof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- Subgroupstatement and proof · cited by 3,593
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankstatement and proof · cited by 1,770
- AlgEquivstatement and proof · cited by 1,681
- IntermediateFieldstatement · cited by 988
- Nat.cardstatement · cited by 844
- Fintype.ofFiniteproof · cited by 255
- Nat.card_eq_fintype_cardproof · cited by 200
- IntermediateField.fixedFieldstatement and proof · cited by 25
Cited by3
Results whose statement or proof uses this declaration.
- IsGalois.fixedField_fixingSubgroupproof · cited by 2
- IsGalois.card_fixingSubgroup_eq_finrankproof · cited by 1
- IsGalois.of_card_aut_eq_finrankproof · cited by 1