Theorems · Theorem · global analysis
HasFPowerSeriesAt.hasStrictFDerivAt
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {F : Type v} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F]
{p : FormalMultilinearSeries 𝕜 E F} {f : E → F} {x : E},
HasFPowerSeriesAt f p x → HasStrictFDerivAt f ((continuousMultilinearCurryFin1 𝕜 E F) (p 1)) x- Cited by
- 7 results in Mathlib
- Foundations
- Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- 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
- ContinuousLinearMapstatement · cited by 5,352
- nhdsWithinproof · cited by 1,912
- SProd.sprodproof · cited by 1,750
- ContinuousMultilinearMapstatement · cited by 1,016
- LinearIsometryEquivstatement · cited by 748
- FormalMultilinearSeriesstatement and proof · cited by 615
- Asymptotics.IsLittleOproof · cited by 375
Cited by7
Results whose statement or proof uses this declaration.
- HasFPowerSeriesAt.hasFDerivAtproof · cited by 4
- hasStrictFDerivAt_exp_smul_const_of_mem_ballproof · cited by 3
- hasStrictFDerivAt_exp_zero_of_radius_posproof · cited by 3
- AnalyticAt.hasStrictFDerivAtproof · cited by 2
- hasStrictFDerivAt_exp_of_mem_ballproof · cited by 2
- HasFiniteFPowerSeriesOnBall.hasStrictFDerivAtproof · cited by 2
- HasFPowerSeriesAt.hasStrictDerivAtproof · cited by 1