Theorems · Theorem · field theory
Polynomial.card_nthRoots
∀ {R : Type u} [inst : CommRing R] [inst_1 : IsDomain R] (n : ℕ) (a : R), (Polynomial.nthRoots n a).card ≤ n- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Polynomialproof · cited by 5,681
- IsDomainstatement and proof · cited by 2,196
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- WithBotproof · cited by 1,498
- pow_zeroproof · cited by 1,094
- le_transproof · cited by 985
- Polynomial.degreeproof · cited by 643
- map_subproof · cited by 565
- WithBot.someproof · cited by 541
Cited by3
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.nthRoots_eqproof · cited by 3
- card_rootsOfUnityproof · cited by 2
- isCyclic_of_injective_ringHomproof · cited by 1