Theorems · Theorem · real analysis
Polynomial.eventually_atBot_not_isRoot
∀ {𝕜 : Type u_1} [inst : NormedField 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜] (P : Polynomial 𝕜),
P ≠ 0 → ∀ᶠ (x : 𝕜) in Filter.atBot, ¬P.IsRoot x- Defined in
- Mathlib.Analysis.Polynomial.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Set.ofPredproof · cited by 6,101
- Polynomialstatement and proof · cited by 5,681
- Filter.Eventuallystatement · cited by 3,134
- IsStrictOrderedRingstatement and proof · cited by 2,490
- NormedFieldstatement and proof · cited by 1,084
- Filter.atBotstatement · cited by 512
- Polynomial.IsRootstatement and proof · cited by 152
- Set.Finite.compl_mem_cofiniteproof · cited by 14
- Polynomial.finite_setOfPred_isRootproof · cited by 7
- Filter.atBot_le_cofiniteproof · cited by 1
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