Theorems · Theorem · complex analysis
HasFPowerSeriesAt.eq_zero
∀ {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} {x : 𝕜}, HasFPowerSeriesAt 0 p x → p = 0A one-dimensional formal multilinear series representing the zero function is zero.
- Defined in
- Mathlib.Analysis.Analytic.Uniqueness
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousMultilinearMapproof · cited by 1,016
- smul_zeroproof · cited by 665
- FormalMultilinearSeriesstatement and proof · cited by 615
- zero_applyproof · cited by 251
- Finset.prod_const_oneproof · cited by 100
- HasFPowerSeriesAtstatement and proof · cited by 94
- FormalMultilinearSeries.extproof · cited by 39
- ContinuousMultilinearMap.ext_ringproof · cited by 20
Cited by2
Results whose statement or proof uses this declaration.
- HasFPowerSeriesAt.eq_formalMultilinearSeriesproof · cited by 6
- HasFPowerSeriesAt.eq_zero_of_eventuallyproof · cited by 1