Theorems · Theorem · field theory
Polynomial.HasSeparableContraction.natSepDegree_eq
∀ {F : Type u} [inst : Field F] {f : Polynomial F} {q : ℕ} [ExpChar F q] (hf : Polynomial.HasSeparableContraction q f),
f.natSepDegree = hf.degreeIf a polynomial has separable contraction, then its separable degree is equal to the degree of the given separable contraction.
- Defined in
- Mathlib.FieldTheory.SeparableDegree
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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 and proof · cited by 5,681
- ExpCharstatement and proof · cited by 276
- Polynomial.natSepDegreestatement · cited by 53
- Polynomial.HasSeparableContractionstatement and proof · cited by 8
- Polynomial.HasSeparableContraction.degreestatement · cited by 5
- Polynomial.HasSeparableContraction.isSeparableContractionproof · cited by 1
- Polynomial.IsSeparableContraction.natSepDegree_eqproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Irreducible.natSepDegree_dvd_natDegreeproof · cited by 0