Theorems · Theorem · field theory
Polynomial.natSepDegree_C_mul
∀ {F : Type u} [inst : Field F] (f : Polynomial F) {x : F}, x ≠ 0 → (Polynomial.C x * f).natSepDegree = f.natSepDegree- Defined in
- Mathlib.FieldTheory.SeparableDegree
- Cited by
- 1 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.
Cites17
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
- CommRingproof · cited by 17,173
- Algebraproof · cited by 11,388
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Finset.cardproof · cited by 2,327
- IsDomainproof · cited by 2,196
- Polynomial.Cstatement and proof · cited by 1,598
- Module.IsTorsionFreeproof · cited by 600
- Multiset.toFinsetproof · cited by 230
- IsAlgClosedproof · cited by 150
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.natSepDegree_C_mul_X_sub_C_powproof · cited by 0