Theorems · Theorem · field theory
Polynomial.rootMultiplicity_le_one_of_separable
∀ {R : Type u} [inst : CommRing R] [Nontrivial R] {p : Polynomial R},
p.Separable → ∀ (x : R), Polynomial.rootMultiplicity x p ≤ 1- Defined in
- Mathlib.FieldTheory.Separable
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- ENatproof · cited by 4,985
- Nat.cast_oneproof · cited by 2,501
- Nontrivialstatement and proof · cited by 2,416
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- Nat.cast_leproof · cited by 159
- Polynomial.Separablestatement and proof · cited by 117
- multiplicityproof · cited by 117
- Polynomial.rootMultiplicitystatement and proof · cited by 79
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.count_roots_le_oneproof · cited by 1