Theorems · Theorem · field theory
FiniteGaloisIntermediateField.adjoin_val
∀ {k : Type u_1} {K : Type u_2} [inst : Field k] [inst_1 : Field K] [inst_2 : Algebra k K] [inst_3 : IsGalois k K]
(s : Set K) [inst_4 : Finite ↑s],
(FiniteGaloisIntermediateField.adjoin k s).toIntermediateField =
IntermediateField.normalClosure k (↥(IntermediateField.adjoin k s)) K- Defined in
- Mathlib.FieldTheory.Galois.GaloisClosure
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Set.Elemstatement and proof · cited by 7,166
- Finitestatement and proof · cited by 3,029
- IntermediateFieldstatement · cited by 988
- IntermediateField.adjoinstatement · cited by 382
- IsGaloisstatement and proof · cited by 149
- IntermediateField.normalClosurestatement · cited by 38
- FiniteGaloisIntermediateField.toIntermediateFieldstatement · cited by 25
- FiniteGaloisIntermediateField.adjoinstatement · cited by 11
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