Theorems · Theorem · real analysis
Asymptotics.IsTheta.inv
∀ {α : Type u_1} {𝕜 : Type u_14} {𝕜' : Type u_15} [inst : NormedField 𝕜] [inst_1 : NormedField 𝕜'] {l : Filter α}
{f : α → 𝕜} {g : α → 𝕜'}, f =Θ[l] g → (fun x => (f x)⁻¹) =Θ[l] fun x => (g x)⁻¹- Defined in
- Mathlib.Analysis.Asymptotics.Theta
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedFieldNormedField
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement and proof · cited by 8,121
- NormedFieldstatement and proof · cited by 1,084
- Asymptotics.IsThetastatement and proof · cited by 115
- Asymptotics.IsBigO.eq_zero_impproof · cited by 4
- Asymptotics.IsBigO.inv_revproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- EisensteinSeries.linear_inv_isBigO_leftproof · cited by 2
- Asymptotics.IsTheta.divproof · cited by 2
- Asymptotics.isTheta_invproof · cited by 1
- EisensteinSeries.linear_inv_isBigO_right_addproof · cited by 1
- Asymptotics.IsTheta.zpowproof · cited by 0