Theorems · Theorem · field theory
FiniteGaloisIntermediateField.adjoin_simple_le_iff
∀ {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]
{x : K} {L : FiniteGaloisIntermediateField k K},
FiniteGaloisIntermediateField.adjoin k {x} ≤ L ↔ x ∈ L.toIntermediateField- Defined in
- Mathlib.FieldTheory.Galois.GaloisClosure
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Set.Elemstatement · cited by 7,166
- IntermediateFieldstatement · cited by 988
- IsGaloisstatement and proof · cited by 149
- FiniteGaloisIntermediateFieldstatement and proof · cited by 32
- FiniteGaloisIntermediateField.toIntermediateFieldstatement and proof · cited by 25
- FiniteGaloisIntermediateField.adjoinstatement and proof · cited by 11
Cited by3
Results whose statement or proof uses this declaration.
- InfiniteGalois.normal_iff_isGaloisproof · cited by 2
- InfiniteGalois.proj_adjoin_singleton_valstatement and proof · cited by 1
- InfiniteGalois.fixingSubgroup_isClosedproof · cited by 0