Theorems · Theorem · global analysis
HasFPowerSeriesAt.hasFDerivAt
∀ {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 → HasFDerivAt f ((continuousMultilinearCurryFin1 𝕜 E F) (p 1)) x- Cited by
- 4 results in Mathlib
- Foundations
- Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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
- ContinuousMultilinearMapstatement · cited by 1,016
- LinearIsometryEquivstatement · cited by 748
- FormalMultilinearSeriesstatement and proof · cited by 615
- HasFDerivAtstatement · cited by 350
- HasFPowerSeriesAtstatement and proof · cited by 94
- continuousMultilinearCurryFin1statement · cited by 58
Cited by4
Results whose statement or proof uses this declaration.
- hasStrictFDerivAt_exp_of_mem_ballproof · cited by 2
- HasFPowerSeriesAt.fderiv_eqproof · cited by 2
- HasFPowerSeriesAt.differentiableAtproof · cited by 1
- HasFPowerSeriesOnBall.hasFDerivAtproof · cited by 1