Theorems · Theorem · field theory
IsGalois.intermediateFieldEquivSubgroup_apply
∀ {F : Type u_1} [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E]
[inst_3 : FiniteDimensional F E] [inst_4 : IsGalois F E] (a : IntermediateField F E),
IsGalois.intermediateFieldEquivSubgroup a = OrderDual.toDual a.fixingSubgroup- Defined in
- Mathlib.FieldTheory.Galois.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- Equivstatement · cited by 8,337
- Fieldstatement and proof · cited by 7,404
- Subgroupstatement · cited by 3,593
- FiniteDimensionalstatement and proof · cited by 1,854
- AlgEquivstatement · cited by 1,681
- IntermediateFieldstatement and proof · cited by 988
- OrderDualstatement · cited by 927
- OrderDual.toDualstatement · cited by 481
- RelIsostatement · cited by 456
- IsGaloisstatement and proof · cited by 149
Cited by3
Results whose statement or proof uses this declaration.
- IsGalois.fixedField_eq_iff_fixingSubgroup_eqproof · cited by 0
- IsCyclotomicExtension.Rat.card_intermediateFieldEquivSubgroupCharproof · cited by 0
- IsCyclotomicExtension.Rat.mem_intermediateFieldEquivSubgroupChar_iffproof · cited by 0