Theorems · Theorem · field theory
Polynomial.mem_nthRootsFinset
∀ {R : Type u} [inst : CommRing R] [inst_1 : IsDomain R] {n : ℕ},
0 < n → ∀ (a : R) {x : R}, x ∈ Polynomial.nthRootsFinset n a ↔ x ^ n = a- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- IsDomainstatement and proof · cited by 2,196
- Multiset.mem_toFinsetproof · cited by 39
- Polynomial.nthRootsFinsetstatement · cited by 23
- Polynomial.mem_nthRootsproof · cited by 9
- Polynomial.nthRootsFinset_defproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.nthRootsFinset_pairwise_associated_sub_one_sub_of_primeproof · cited by 2
- Polynomial.map_mem_nthRootsFinsetproof · cited by 1
- IsPrimitiveRoot.mem_nthRootsFinsetproof · cited by 0
- Polynomial.one_mem_nthRootsFinsetproof · cited by 0
- Polynomial.ne_zero_of_mem_nthRootsFinsetproof · cited by 0
- Polynomial.mul_mem_nthRootsFinsetproof · cited by 0