Theorems · Theorem · real analysis
HasDerivAt.isBigO_sub
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {f' : F} {x : 𝕜},
HasDerivAt f f' x → (fun x_1 => f x_1 - f x) =O[nhds x] fun x_1 => x_1 - x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 168 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.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- nhdsstatement · cited by 5,554
- Asymptotics.IsBigOstatement · cited by 506
- HasDerivAtstatement and proof · cited by 493
- HasDerivAt.hasFDerivAtproof · cited by 27
- HasFDerivAt.isBigO_subproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- circleIntegrable_sub_zpow_iffproof · cited by 0