Theorems · Theorem · complex analysis
Complex.IsExactOn.differentiableOn
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {f : ℂ → E} [CompleteSpace E] {U : Set ℂ},
IsOpen U → Complex.IsExactOn f U → DifferentiableOn ℂ f U- Defined in
- Mathlib.Analysis.Complex.HasPrimitives
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 288 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- HasDerivAtproof · cited by 493
- DifferentiableOnstatement and proof · cited by 419
- HasDerivAt.derivproof · cited by 147
- DifferentiableAt.differentiableWithinAtproof · cited by 96
- HasDerivAt.differentiableAtproof · cited by 73
- Complex.IsExactOnstatement and proof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Complex.isConservativeOn_and_continuousOn_iff_isDifferentiableOnproof · cited by 1