Theorems · Theorem · real analysis
Polynomial.isBigO_atTop_of_degree_le
∀ {𝕜 : Type u_1} [inst : NormedField 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜] (P Q : Polynomial 𝕜)
[OrderTopology 𝕜], P.degree ≤ Q.degree → (fun x => Polynomial.eval x P) =O[Filter.atTop] fun x => Polynomial.eval x Q- Defined in
- Mathlib.Analysis.Polynomial.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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.Eventuallyproof · cited by 3,134
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Filter.atTopstatement and proof · cited by 2,405
- WithBotstatement · cited by 1,498
- OrderTopologystatement and proof · cited by 1,355
- NormedFieldstatement and proof · cited by 1,084
- Polynomial.evalstatement and proof · cited by 796
- Polynomial.degreestatement and proof · cited by 643
- Asymptotics.IsBigOstatement and proof · cited by 506
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.isBigO_atBot_of_degree_leproof · cited by 0
- Polynomial.isBigO_of_degree_leproof · cited by 0