Theorems · Theorem · field theory
Polynomial.map_roots_le_of_injective
∀ {A : Type u_1} {B : Type u_2} [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : IsDomain A] [inst_3 : IsDomain B]
(p : Polynomial A) {f : A →+* B}, Function.Injective ⇑f → Multiset.map (⇑f) p.roots ≤ (Polynomial.map f p).roots- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 136 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Multisetstatement · cited by 2,627
- IsDomainstatement and proof · cited by 2,196
- Multiset.mapstatement · cited by 876
- Polynomial.mapstatement and proof · cited by 806
- Polynomial.rootsstatement · cited by 264
- Multiset.map_congrproof · cited by 232
- Polynomial.map_zeroproof · cited by 33
- Polynomial.roots.congr_simpproof · cited by 31
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.roots_map_of_injective_of_card_eq_natDegreeproof · cited by 1