Theorems · Theorem · field theory
Polynomial.map_mem_nthRootsFinset
∀ {R : Type u} {n : ℕ} [inst : CommRing R] [inst_1 : IsDomain R] {S : Type u_1} {F : Type u_2} [inst_2 : CommRing S]
[inst_3 : IsDomain S] [inst_4 : FunLike F R S] [MonoidHomClass F R S] {a x : R},
x ∈ Polynomial.nthRootsFinset n a → ∀ (f : F), f x ∈ Polynomial.nthRootsFinset n (f a)- 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.
Cites11
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
- Finsetstatement · cited by 13,712
- FunLikestatement and proof · cited by 2,560
- IsDomainstatement and proof · cited by 2,196
- map_powproof · cited by 503
- MonoidHomClassstatement and proof · cited by 244
- Polynomial.nthRootsFinsetstatement and proof · cited by 23
- Polynomial.mem_nthRootsFinsetproof · cited by 6
- Polynomial.nthRootsFinset_zeroproof · cited by 4
- Polynomial.nthRootsFinset.congr_simpproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.map_mem_nthRootsFinset_oneproof · cited by 1