Theorems · Theorem · field theory
IntermediateField.fixingSubgroup_le
∀ {F : Type u_1} [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E]
{K1 K2 : IntermediateField F E}, K1 ≤ K2 → K2.fixingSubgroup ≤ K1.fixingSubgroupThe map K ↦ Gal(E/K) is inclusion-reversing.
- Defined in
- Mathlib.FieldTheory.Galois.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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 · cited by 3,593
- AlgEquivstatement and proof · cited by 1,681
- IntermediateFieldstatement and proof · cited by 988
- IntermediateField.fixingSubgroupstatement and proof · cited by 41
Cited by3
Results whose statement or proof uses this declaration.
- IntermediateField.fixingSubgroup_antitoneproof · cited by 2
- IntermediateField.finrank_eq_fixingSubgroup_indexproof · cited by 1
- InfiniteGalois.fixingSubgroup_fixedFieldproof · cited by 0