Theorems · Theorem · field theory
Polynomial.rootMultiplicity_sub_one_le_derivative_rootMultiplicity
∀ {R : Type u} [inst : CommRing R] [NoZeroDivisors R] [CharZero R] (p : Polynomial R) (t : R),
Polynomial.rootMultiplicity t p - 1 ≤ Polynomial.rootMultiplicity t (Polynomial.derivative p)- Defined in
- Mathlib.Algebra.Polynomial.FieldDivision
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 128 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.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- Polynomialstatement and proof · cited by 5,681
- CharZerostatement and proof · cited by 932
- Eq.leproof · cited by 605
- NoZeroDivisorsstatement and proof · cited by 545
- Polynomial.derivativestatement and proof · cited by 331
- Polynomial.IsRootproof · cited by 152
- zero_tsubproof · cited by 100
- Polynomial.rootMultiplicitystatement and proof · cited by 79
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.card_roots_le_derivativeproof · cited by 0