Theorems · Theorem · real analysis
ContDiffOn.analyticOn
∀ {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}, ContDiffOn 𝕜 ⊤ f s → AnalyticOn 𝕜 f s- Defined in
- Mathlib.Analysis.Calculus.ContDiff.Defs
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- WithTopstatement · cited by 3,754
- ContDiffOnstatement and proof · cited by 294
- AnalyticOnstatement · cited by 161
- ContDiffWithinAt.analyticWithinAtproof · cited by 13
Cited by15
Results whose statement or proof uses this declaration.
- contDiffOn_univproof · cited by 25
- contDiffOn_succ_iff_fderivWithinproof · cited by 8
- ContDiffWithinAt.iteratedFDerivWithin_comp_permproof · cited by 2
- ContDiff.analyticOnNhdproof · cited by 1
- Complex.analyticOn_cosproof · cited by 0
- contDiffOn_omega_iff_analyticOnproof · cited by 0
- Complex.analyticOn_coshproof · cited by 0
- Complex.analyticOn_sinproof · cited by 0
- Complex.analyticOn_sinhproof · cited by 0
- Real.analyticOn_arcoshproof · cited by 0
- Real.analyticOn_arsinhproof · cited by 0
- Real.analyticOn_cosproof · cited by 0