Theorems · Theorem · complex analysis
DifferentiableOn.deriv
∀ {E : Type u} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] [CompleteSpace E] {s : Set ℂ} {f : ℂ → E},
DifferentiableOn ℂ f s → IsOpen s → DifferentiableOn ℂ (deriv f) s- 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.
- Setstatement and proof · cited by 53,352
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Complexstatement and proof · cited by 5,565
- CompleteSpacestatement and proof · cited by 2,532
- IsOpenstatement and proof · cited by 2,400
- derivstatement · cited by 676
- DifferentiableOnstatement and proof · cited by 419
- DifferentiableOn.analyticOnNhdproof · cited by 21
- AnalyticOnNhd.derivproof · cited by 3
- AnalyticOnNhd.differentiableOnproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Derivative.normalizedDerivOfComplex_mdifferentiableproof · cited by 1
- Complex.IsExactOn.differentiableOnproof · cited by 1
- E2_mdifferentiableproof · cited by 1