Theorems · Theorem · field theory
Polynomial.le_rootMultiplicity_mul
∀ {R : Type u} [inst : CommRing R] {p q : Polynomial R} (x : R),
p * q ≠ 0 → Polynomial.rootMultiplicity x p + Polynomial.rootMultiplicity x q ≤ Polynomial.rootMultiplicity x (p * q)- Defined in
- Mathlib.Algebra.Polynomial.Div
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
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.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- pow_addproof · cited by 315
- Polynomial.rootMultiplicitystatement and proof · cited by 79
- mul_dvd_mulproof · cited by 24
- Polynomial.le_rootMultiplicity_iffproof · cited by 10
- Polynomial.pow_rootMultiplicity_dvdproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.rootMultiplicity_le_rootMultiplicity_of_dvdproof · cited by 0