Theorems · Theorem · field theory
Polynomial.card_roots_map_le_natDegree
∀ {A : Type u_3} {B : Type u_4} [inst : Semiring A] [inst_1 : CommRing B] [inst_2 : IsDomain B] {f : A →+* B}
(p : Polynomial A), (Polynomial.map f p).roots.card ≤ p.natDegree- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 3 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.
Cites12
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
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- LE.le.transproof · cited by 3,151
- IsDomainstatement and proof · cited by 2,196
- Polynomial.natDegreestatement · cited by 1,105
- Polynomial.mapstatement and proof · cited by 806
- Multiset.cardstatement · cited by 375
- Polynomial.rootsstatement · cited by 264
- Polynomial.natDegree_map_leproof · cited by 13
- Polynomial.card_roots'proof · cited by 9
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.roots_map_of_injective_of_card_eq_natDegreeproof · cited by 1
- Polynomial.roots_map_of_map_ne_zero_of_card_eq_natDegreeproof · cited by 1
- Polynomial.ncard_rootSet_leproof · cited by 0