Theorems · Theorem · field theory
Polynomial.natSepDegree_le_of_dvd
∀ {F : Type u} [inst : Field F] (f g : Polynomial F), f ∣ g → g ≠ 0 → f.natSepDegree ≤ g.natSepDegree- Defined in
- Mathlib.FieldTheory.SeparableDegree
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 180 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebraproof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- IsAlgClosedproof · cited by 150
- Finset.card_le_cardproof · cited by 118
- AlgebraicClosureproof · cited by 53
- Polynomial.natSepDegreestatement · cited by 53
- Polynomial.map_ne_zeroproof · cited by 22
- Polynomial.map_dvdproof · cited by 10
- Polynomial.natSepDegree_eq_of_isAlgClosedproof · cited by 9
- Multiset.toFinset_subsetproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- minpoly.natSepDegree_eq_one_iff_pow_memproof · cited by 4
- Polynomial.Monic.eq_X_pow_char_pow_sub_C_pow_of_natSepDegree_eq_oneproof · cited by 1
- perfectField_iff_splits_of_natSepDegree_eq_oneproof · cited by 1