Theorems · Theorem · field theory
Polynomial.rootMultiplicity_mul
∀ {R : Type u} [inst : CommRing R] [IsDomain R] {p q : Polynomial R} {x : R},
p * q ≠ 0 → Polynomial.rootMultiplicity x (p * q) = Polynomial.rootMultiplicity x p + Polynomial.rootMultiplicity x q- Defined in
- Mathlib.Algebra.Polynomial.RingDivision
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
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.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement and proof · cited by 5,681
- IsDomainstatement and proof · cited by 2,196
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- multiplicityproof · cited by 117
- Polynomial.rootMultiplicitystatement and proof · cited by 79
- right_ne_zero_of_mulproof · cited by 38
- left_ne_zero_of_mulproof · cited by 27
- Polynomial.rootMultiplicity_eq_multiplicityproof · cited by 8
- Polynomial.finiteMultiplicity_X_sub_Cproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.roots_mulproof · cited by 12
- Polynomial.isRoot_of_isRoot_of_dvd_derivative_mulproof · cited by 1
- Polynomial.isRoot_of_isRoot_iff_dvd_derivative_mulproof · cited by 0