Theorems · Theorem · field theory
IntermediateField.mem_fixedField_iff
∀ {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))
(x : E), x ∈ IntermediateField.fixedField H ↔ ∀ f ∈ H, f x = x- Defined in
- Mathlib.FieldTheory.Galois.Basic
- Cited by
- 4 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Subgroupstatement and proof · cited by 3,593
- AlgEquivstatement and proof · cited by 1,681
- IntermediateFieldstatement · cited by 988
- IntermediateField.fixedFieldstatement · cited by 25
Cited by4
Results whose statement or proof uses this declaration.
- InfiniteGalois.fixedField_fixingSubgroupproof · cited by 3
- IsGalois.mem_bot_iff_fixedproof · cited by 2
- NumberField.IsCMField.complexConj_eq_self_iffproof · cited by 1
- IntermediateField.restrictRestrictAlgEquivMapHom_surjectiveproof · cited by 0