Theorems · Theorem · field theory
InfiniteGalois.normal_iff_isGalois
∀ {k : Type u_1} {K : Type u_2} [inst : Field k] [inst_1 : Field K] [inst_2 : Algebra k K] (L : IntermediateField k K)
[IsGalois k K], L.fixingSubgroup.Normal ↔ IsGalois k ↥L- Defined in
- Mathlib.FieldTheory.Galois.Infinite
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
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
- Fieldstatement and proof · cited by 7,404
- Subgroupproof · cited by 3,593
- iSupproof · cited by 2,415
- le_antisymmproof · cited by 2,068
- AlgEquivstatement and proof · cited by 1,681
- le_rflproof · cited by 1,558
- IntermediateFieldstatement and proof · cited by 988
- Subgroup.Normalstatement and proof · cited by 334
- Subgroup.mapproof · cited by 301
- inf_le_leftproof · cited by 286
- le_iSupproof · cited by 207
Cited by2
Results whose statement or proof uses this declaration.
- IsAbelianGalois.tower_botproof · cited by 1
- InfiniteGalois.isOpen_and_normal_iff_finite_and_isGaloisproof · cited by 0