Theorems · Theorem · field theory
Polynomial.natSepDegree_ne_zero
∀ {F : Type u} [inst : Field F] (f : Polynomial F), f.natDegree ≠ 0 → f.natSepDegree ≠ 0A non-constant polynomial has non-zero separable degree.
- Defined in
- Mathlib.FieldTheory.SeparableDegree
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- Algebra.algebraMapproof · cited by 4,706
- Finset.cardproof · cited by 2,327
- Polynomial.natDegreestatement and proof · cited by 1,105
- Multiset.toFinsetproof · cited by 230
- Polynomial.arootsproof · cited by 89
- Polynomial.natSepDegreestatement · cited by 53
- Polynomial.SplittingFieldproof · cited by 42
- Multiset.mem_toFinsetproof · cited by 39
- Finset.nonempty_iff_ne_emptyproof · cited by 34
- Finset.card_eq_zeroproof · cited by 34
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.natSepDegree_eq_zero_iffproof · cited by 3