Theorems · Theorem · real analysis
Polynomial.eventually_cofinite_not_isRoot
∀ {R : Type u_2} [inst : CommRing R] [IsDomain R] {P : Polynomial R}, P ≠ 0 → ∀ᶠ (x : R) in Filter.cofinite, ¬P.IsRoot x- Defined in
- Mathlib.Analysis.Polynomial.Basic
- Cited by
- 1 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.
Cites8
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
- Polynomialstatement and proof · cited by 5,681
- Filter.Eventuallystatement · cited by 3,134
- IsDomainstatement and proof · cited by 2,196
- Filter.cofinitestatement · cited by 251
- Polynomial.IsRootstatement · cited by 152
- Set.Finite.compl_mem_cofiniteproof · cited by 14
- Polynomial.finite_setOfPred_isRootproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.finite_abs_eval_le_of_degree_ltproof · cited by 1