Theorems · Theorem · global analysis
HasFPowerSeriesWithinOnBall.differentiableOn
∀ {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} {r : ENNReal} {f : E → F} {x : E} {s : Set E} [CompleteSpace F],
HasFPowerSeriesWithinOnBall f p s x r → DifferentiableOn 𝕜 f (insert x s ∩ Metric.eball x r)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- ENNRealstatement and proof · cited by 9,879
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Filterproof · cited by 8,121
- CompleteSpacestatement and proof · cited by 2,532
- nhdsWithinproof · cited by 1,912
- eq_or_neproof · cited by 1,117
- FormalMultilinearSeriesstatement and proof · cited by 615
- DifferentiableWithinAtproof · cited by 453
- DifferentiableOnstatement · cited by 419
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