Theorems · Theorem · field theory
IsGalois.intermediateFieldEquivSubgroup_symm_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] (H : (Subgroup Gal(E/F))ᵒᵈ),
IsGalois.intermediateFieldEquivSubgroup.symm H = IntermediateField.fixedField (OrderDual.ofDual H)- Defined in
- Mathlib.FieldTheory.Galois.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- Equivstatement · cited by 8,337
- 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 · cited by 988
- OrderDualstatement and proof · cited by 927
- OrderIsostatement · cited by 874
- OrderIso.symmstatement · cited by 475
- OrderDual.ofDualstatement · cited by 400
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