Theorems · Theorem · complex analysis
HasFPowerSeriesAt.has_fpower_series_dslope_fslope
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {p : FormalMultilinearSeries 𝕜 𝕜 E} {f : 𝕜 → E} {z₀ : 𝕜},
HasFPowerSeriesAt f p z₀ → HasFPowerSeriesAt (dslope f z₀) p.fslope z₀- Defined in
- Mathlib.Analysis.Analytic.IsolatedZeros
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites40
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpaceproof · cited by 24,529
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- AddCommMonoidproof · cited by 12,281
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- nhdsproof · cited by 5,554
- Filter.Eventuallyproof · cited by 3,134
- one_mulproof · cited by 2,841
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- SummationFilter.unconditionalproof · cited by 2,068
- one_smulproof · cited by 1,374
Cited by1
Results whose statement or proof uses this declaration.
- HasFPowerSeriesAt.has_fpower_series_iterate_dslope_fslopeproof · cited by 4