Theorems · Theorem · real analysis
HasStrictDerivAt.hasStrictFDerivAt
∀ {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} {f' : F} {x : 𝕜} [inst_4 : ContinuousSMul 𝕜 F],
HasStrictDerivAt f f' x → HasStrictFDerivAt f (ContinuousLinearMap.toSpanSingleton 𝕜 f') xAlias of the forward direction of hasStrictDerivAt_iff_hasStrictFDerivAt.
- Defined in
- Mathlib.Analysis.Calculus.Deriv.Basic
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousSMulstatement and proof · cited by 1,016
- HasStrictFDerivAtstatement · cited by 261
- HasStrictDerivAtstatement · cited by 163
- ContinuousLinearMap.toSpanSingletonstatement · cited by 133
- hasStrictDerivAt_iff_hasStrictFDerivAtproof · cited by 1
Cited by21
Results whose statement or proof uses this declaration.
- HasStrictDerivAt.hasDerivAtproof · cited by 52
- HasStrictDerivAt.real_of_complexproof · cited by 6
- HasStrictFDerivAt.comp_hasStrictDerivAtproof · cited by 5
- Real.differentiableAt_rpow_const_of_neproof · cited by 3
- HasStrictDerivAt.scompproof · cited by 3
- HasStrictDerivAt.fun_finsetProdproof · cited by 2
- Function.Periodic.differentiableAt_cuspFunctionproof · cited by 2
- HasStrictDerivAt.complexToReal_fderivproof · cited by 2
- HasStrictDerivAt.fun_powproof · cited by 1
- HasStrictDerivAt.fun_pow'proof · cited by 1
- HasStrictDerivAt.congr_derivproof · cited by 1
- HasStrictDerivAt.cpowproof · cited by 1