Theorems · Theorem · real analysis

ContDiff.analyticOnNhd

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {E : Type uE} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type uF} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {s : Set E}
  {f : E → F}, ContDiff 𝕜 ⊤ f → AnalyticOnNhd 𝕜 f s

Defined in: Mathlib.Analysis.Calculus.ContDiff.Defs
Cited by: 1 results in Mathlib
Foundations: Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NontriviallyNormedField NormedAddCommGroup NormedSpace NormedAddCommGroup NormedSpace

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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
Top.topstatement and proof · cited by 9,680
NontriviallyNormedFieldstatement and proof · cited by 8,742
ENatstatement · cited by 4,985
Set.univproof · cited by 3,945
WithTopstatement · cited by 3,754
ContDiffstatement and proof · cited by 352
Set.subset_univproof · cited by 228
AnalyticOnNhdstatement · cited by 206
AnalyticOnproof · cited by 161

Cited by1

Results whose statement or proof uses this declaration.

contDiff_omega_iff_analyticOnNhdproof · cited by 0