Theorems · Theorem · field theory
IntermediateField.le_iff_le
∀ {F : Type u_1} [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] (H : Subgroup Gal(E/F))
(K : IntermediateField F E), K ≤ IntermediateField.fixedField H ↔ H ≤ K.fixingSubgroup- Defined in
- Mathlib.FieldTheory.Galois.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- SetLike.coeproof · cited by 8,199
- Fieldstatement and proof · cited by 7,404
- Set.Elemproof · cited by 7,166
- Subgroupstatement and proof · cited by 3,593
- AlgEquivstatement and proof · cited by 1,681
- IntermediateFieldstatement and proof · cited by 988
- IntermediateField.fixingSubgroupstatement and proof · cited by 41
- Subtype.memproof · cited by 26
- IntermediateField.fixedFieldstatement and proof · cited by 25
Cited by5
Results whose statement or proof uses this declaration.
- IntermediateField.fixingSubgroup_fixedFieldproof · cited by 3
- InfiniteGalois.fixedField_fixingSubgroupproof · cited by 3
- IsGalois.fixedField_fixingSubgroupproof · cited by 2
- InfiniteGalois.isOpen_iff_finiteproof · cited by 1
- InfiniteGalois.fixingSubgroup_fixedFieldproof · cited by 0