Theorems · Theorem · field theory
Polynomial.natSepDegree_X_sub_C
∀ {F : Type u} [inst : Field F] (x : F), (Polynomial.X - Polynomial.C x).natSepDegree = 1- Defined in
- Mathlib.FieldTheory.SeparableDegree
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 154 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.
- DFunLike.coestatement and proof · cited by 62,936
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- Finset.cardproof · cited by 2,327
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- Multiset.toFinsetproof · cited by 230
- Finset.card_singletonproof · cited by 144
- Polynomial.natSepDegreestatement · cited by 53
- Polynomial.SplittingFieldproof · cited by 42
Cited by4
Results whose statement or proof uses this declaration.
- Irreducible.natSepDegree_eq_one_iff_of_monic'proof · cited by 3
- Polynomial.natSepDegree_X_pow_char_pow_sub_Cproof · cited by 3
- minpoly.natSepDegree_eq_one_iff_eq_expand_X_sub_Cproof · cited by 1
- Polynomial.natSepDegree_X_sub_C_powproof · cited by 1