Theorems · Theorem · field theory
InfiniteGalois.isOpen_iff_finite
∀ {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], IsOpen L.fixingSubgroup.carrier ↔ FiniteDimensional k ↥L- Defined in
- Mathlib.FieldTheory.Galois.Infinite
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites38
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Filterproof · cited by 8,121
- Fieldstatement and proof · cited by 7,404
- nhdsproof · cited by 5,554
- Subgroupproof · cited by 3,593
- IsOpenstatement and proof · cited by 2,400
- FiniteDimensionalstatement and proof · cited by 1,854
- AlgEquivstatement and proof · cited by 1,681
- IntermediateFieldstatement and proof · cited by 988
- le_transproof · cited by 985
- RingHomClass.toRingHomproof · cited by 746
Cited by1
Results whose statement or proof uses this declaration.
- InfiniteGalois.isOpen_and_normal_iff_finite_and_isGaloisproof · cited by 0