Theorems · Theorem · field theory
IsSepClosed.splits_of_separable
∀ {k : Type u} {inst : Field k} [self : IsSepClosed k] (p : Polynomial k), p.Separable → p.Splits- Defined in
- Mathlib.FieldTheory.IsSepClosed
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- IsSepClosed
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement · cited by 5,681
- Polynomial.Splitsstatement · cited by 290
- Polynomial.Separablestatement · cited by 117
- IsSepClosedstatement and proof · cited by 41
Cited by4
Results whose statement or proof uses this declaration.
- IsSepClosed.exists_rootproof · cited by 4
- IsSepClosed.degree_eq_one_of_irreducibleproof · cited by 1
- IsSepClosed.splits_codomainproof · cited by 1
- IsSepClosed.splits_domainproof · cited by 0