Theorems · Theorem · field theory
IsGalois.is_separable_splitting_field
∀ (F : Type u_1) [inst : Field F] (E : Type u_2) [inst_1 : Field E] [inst_2 : Algebra F E] [FiniteDimensional F E] [IsGalois F E], ∃ p, p.Separable ∧ Polynomial.IsSplittingField F E p
- Defined in
- Mathlib.FieldTheory.Galois.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
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
- Top.topproof · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement · cited by 5,681
- FiniteDimensionalstatement and proof · cited by 1,854
- Subalgebraproof · cited by 1,353
- IntermediateFieldproof · cited by 988
- Algebra.adjoinproof · cited by 535
- minpolyproof · cited by 439
- IntermediateField.adjoinproof · cited by 382
- eq_top_iffproof · cited by 236
- Set.singleton_subset_iffproof · cited by 206
Cited by2
Results whose statement or proof uses this declaration.
- IsGalois.tfaeproof · cited by 2
- IsGalois.sup_rightproof · cited by 0