Theorems · Theorem · real analysis
norm_deriv_eq_norm_fderiv
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {x : 𝕜}, ‖deriv f x‖ = ‖fderiv 𝕜 f x‖- Defined in
- Mathlib.Analysis.Calculus.Deriv.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Norm.normstatement and proof · cited by 5,413
- ContinuousLinearMapstatement · cited by 5,352
- derivstatement and proof · cited by 676
- fderivstatement · cited by 398
- ContinuousLinearMap.norm_toSpanSingletonproof · cited by 11
Cited by4
Results whose statement or proof uses this declaration.
- Complex.norm_deriv_le_div_of_mapsTo_ballproof · cited by 2
- norm_deriv_le_of_lip'proof · cited by 1
- norm_deriv_le_of_lipschitzproof · cited by 0
- norm_deriv_le_of_lipschitzOnproof · cited by 0