Theorems · Theorem · real analysis
AnalyticOnNhd.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∞}, AnalyticOnNhd 𝕜 f Set.univ → ContDiff 𝕜 n f- Defined in
- Mathlib.Analysis.Calculus.ContDiff.Defs
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 197 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.
- 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
- AnalyticOnNhdstatement and proof · cited by 206
- AnalyticOnNhd.analyticOnproof · cited by 23
- AnalyticOn.contDiffproof · cited by 2
Cited by7
Results whose statement or proof uses this declaration.
- contDiff_constproof · cited by 36
- IsBoundedBilinearMap.contDiffproof · cited by 19
- Complex.contDiff_expproof · cited by 11
- IsBoundedLinearMap.contDiffproof · cited by 6
- contDiff_circleMapproof · cited by 0
- contDiff_zero_funproof · cited by 0
- contDiff_omega_iff_analyticOnNhdproof · cited by 0