Theorems · Theorem · real analysis
AnalyticOn.contDiff
∀ {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] {f : E → F}
{n : WithTop ℕ∞}, AnalyticOn 𝕜 f Set.univ → ContDiff 𝕜 n f- Defined in
- Mathlib.Analysis.Calculus.ContDiff.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ENatstatement and proof · cited by 4,985
- Set.univstatement and proof · cited by 3,945
- WithTopstatement and proof · cited by 3,754
- ContDiffstatement · cited by 352
- AnalyticOnstatement and proof · cited by 161
- uniqueDiffOn_univproof · cited by 66
- contDiffOn_univproof · cited by 25
- AnalyticOn.contDiffOnproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- AnalyticOnNhd.contDiffproof · cited by 7
- contDiff_sigmoidproof · cited by 2