Theorems · Theorem · field theory
IsGalois.fixedField_eq_iff_fixingSubgroup_eq
∀ {F : Type u_1} [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] [FiniteDimensional F E]
[IsGalois F E] {K : IntermediateField F E} {H : Subgroup Gal(E/F)},
IntermediateField.fixedField H = K ↔ K.fixingSubgroup = H- Defined in
- Mathlib.FieldTheory.Galois.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Subgroupstatement and proof · cited by 3,593
- FiniteDimensionalstatement and proof · cited by 1,854
- AlgEquivstatement and proof · cited by 1,681
- IntermediateFieldstatement and proof · cited by 988
- OrderDual.toDualproof · cited by 481
- IsGaloisstatement and proof · cited by 149
- IntermediateField.fixingSubgroupstatement and proof · cited by 41
- IntermediateField.fixedFieldstatement and proof · cited by 25
- IsGalois.intermediateFieldEquivSubgroupproof · cited by 10
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