Theorems · Theorem · field theory
Polynomial.emultiplicity_le_one_of_separable
∀ {R : Type u} [inst : CommSemiring R] {p q : Polynomial R}, ¬IsUnit q → p.Separable → emultiplicity q p ≤ 1- Defined in
- Mathlib.FieldTheory.Separable
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement and proof · cited by 5,681
- ENatstatement · cited by 4,985
- IsUnitstatement and proof · cited by 1,602
- sqproof · cited by 280
- emultiplicitystatement and proof · cited by 156
- Polynomial.Separablestatement and proof · cited by 117
- Order.add_one_le_of_ltproof · cited by 13
- pow_dvd_of_le_emultiplicityproof · cited by 8
- Polynomial.isUnit_of_self_mul_dvd_separableproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.Separable.squarefreeproof · cited by 6
- Polynomial.rootMultiplicity_le_one_of_separableproof · cited by 1
- IsCyclotomicExtension.Rat.ramificationIdx_eq_of_not_dvdproof · cited by 1