Theorems · Theorem · field theory
Polynomial.finiteMultiplicity_X_sub_C
∀ {R : Type u} [inst : Ring R] {p : Polynomial R} (a : R), p ≠ 0 → FiniteMultiplicity (Polynomial.X - Polynomial.C a) p- Defined in
- Mathlib.Algebra.Polynomial.Div
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- Nontrivialproof · cited by 2,416
- Polynomial.Xstatement · cited by 1,639
- Polynomial.Cstatement · cited by 1,598
- WithBotproof · cited by 1,498
- FiniteMultiplicitystatement · cited by 73
- Polynomial.monic_X_sub_Cproof · cited by 41
- Polynomial.degree_X_sub_Cproof · cited by 10
- Polynomial.Nontrivial.of_polynomial_neproof · cited by 10
Cited by8
Results whose statement or proof uses this declaration.
- Polynomial.rootMultiplicityproof · cited by 79
- Polynomial.le_rootMultiplicity_iffproof · cited by 10
- Polynomial.rootMultiplicity_eq_multiplicityproof · cited by 8
- Polynomial.exists_eq_pow_rootMultiplicity_mul_and_not_dvdproof · cited by 7
- Polynomial.rootMultiplicity_mulproof · cited by 3
- Polynomial.rootMultiplicity_eq_natFind_of_ne_zerostatement and proof · cited by 1
- Polynomial.rootMultiplicity_le_one_of_separableproof · cited by 1
- Polynomial.rootMultiplicity_eq_nat_find_of_nonzerostatement · cited by 0