Theorems · Theorem · complex analysis
Complex.norm_cderiv_le
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {z : ℂ} {M r : ℝ} {f : ℂ → E},
0 < r → (∀ w ∈ Metric.sphere z r, ‖f w‖ ≤ M) → ‖Complex.cderiv r f z‖ ≤ M / r- Cited by
- 1 results in Mathlib
- Foundations
- Depth 263 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites42
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- mul_oneproof · cited by 3,885
- LE.le.transproof · cited by 3,151
- one_mulproof · cited by 2,841
- LT.lt.leproof · cited by 2,189
- Nat.cast_zeroproof · cited by 1,870
- Real.piproof · cited by 1,774
Cited by1
Results whose statement or proof uses this declaration.
- Complex.norm_cderiv_ltproof · cited by 1