Theorems · Theorem · field theory
Polynomial.card_le_degree_of_subset_roots
∀ {R : Type u} [inst : CommRing R] [inst_1 : IsDomain R] {p : Polynomial R} {Z : Finset R},
Z.val ⊆ p.roots → Z.card ≤ p.natDegree- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- CommRingstatement and proof · cited by 17,173
- Finsetstatement and proof · cited by 13,712
- Polynomialstatement and proof · cited by 5,681
- LE.le.transproof · cited by 3,151
- Multisetstatement · cited by 2,627
- Finset.cardstatement · cited by 2,327
- IsDomainstatement and proof · cited by 2,196
- Polynomial.natDegreestatement · cited by 1,105
- Finset.valstatement and proof · cited by 438
- Polynomial.rootsstatement and proof · cited by 264
- Multiset.card_le_cardproof · cited by 11
- Polynomial.card_roots'proof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- FiniteField.orderOf_frobeniusAlgHomproof · cited by 3