Theorems · Theorem · complex analysis
Differentiable.contDiff
∀ {E : Type u} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] [CompleteSpace E] {f : ℂ → E},
Differentiable ℂ f → ∀ {n : WithTop ℕ∞}, ContDiff ℂ n fA complex differentiable function f : ℂ → E is continuously differentiable at every point.
- Defined in
- Mathlib.Analysis.Complex.CauchyIntegral
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 287 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
- Complexstatement and proof · cited by 5,565
- ENatstatement and proof · cited by 4,985
- WithTopstatement and proof · cited by 3,754
- CompleteSpacestatement and proof · cited by 2,532
- ContDiffstatement · cited by 352
- Differentiablestatement and proof · cited by 298
- contDiff_iff_contDiffAtproof · cited by 28
- AnalyticAt.contDiffAtproof · cited by 8
- Differentiable.analyticAtproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Differentiable.derivproof · cited by 2
- DirichletCharacter.continuousOn_neg_logDeriv_LFunction_of_nontrivproof · cited by 1
- DirichletCharacter.continuousOn_neg_logDeriv_LFunctionTrivChar₁proof · cited by 1