Theorems · Theorem · complex analysis
Complex.differentiableOn_dslope
∀ {E : Type u} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] [CompleteSpace E] {f : ℂ → E} {s : Set ℂ}
{c : ℂ}, s ∈ nhds c → (DifferentiableOn ℂ (dslope f c) s ↔ DifferentiableOn ℂ f s)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 285 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Filterstatement · cited by 8,121
- Complexstatement and proof · cited by 5,565
- nhdsstatement and proof · cited by 5,554
- CompleteSpacestatement and proof · cited by 2,532
- DifferentiableOnstatement and proof · cited by 419
- Set.sdiff_subsetproof · cited by 156
- dslopestatement and proof · cited by 40
- DifferentiableOn.monoproof · cited by 39
- DifferentiableOn.differentiableAtproof · cited by 26
Cited by3
Results whose statement or proof uses this declaration.
- Complex.differentiableOn_update_limUnder_of_isLittleOproof · cited by 4
- Complex.affine_of_mapsTo_ball_of_norm_dslope_eq_divproof · cited by 2