Theorems · Theorem · real analysis
hasStrictFDerivAt_iff_hasStrictDerivAt
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : AddCommGroup F] [inst_2 : Module 𝕜 F]
[inst_3 : TopologicalSpace F] {f : 𝕜 → F} {x : 𝕜} [inst_4 : ContinuousSMul 𝕜 F] {f' : 𝕜 →L[𝕜] F},
HasStrictFDerivAt f f' x ↔ HasStrictDerivAt f (f' 1) x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousLinearMapstatement and proof · cited by 5,352
- ContinuousSMulstatement and proof · cited by 1,016
- HasStrictFDerivAtstatement · cited by 261
- HasStrictDerivAtstatement · cited by 163
- hasFDerivAtFilter_iff_hasDerivAtFilterproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- HasStrictFDerivAt.hasStrictDerivAtproof · cited by 18