Theorems · Theorem · complex analysis
HasDerivAt.ofReal_comp
∀ {z : ℝ} {f : ℝ → ℝ} {u : ℝ}, HasDerivAt f u z → HasDerivAt (fun y => ↑(f y)) (↑u) zIf a function f : ℝ → ℝ is differentiable at a (real) point x, then it is also
differentiable as a function ℝ → ℂ.
- Defined in
- Mathlib.Analysis.Complex.RealDeriv
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Complexstatement · cited by 5,565
- mul_oneproof · cited by 3,885
- Complex.ofRealstatement and proof · cited by 1,654
- HasDerivAtstatement and proof · cited by 493
- HasDerivAt.congr_simpproof · cited by 82
- Complex.ofRealCLMproof · cited by 39
- HasDerivAt.scompproof · cited by 11
- ContinuousLinearMap.hasDerivAtproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- bernoulliFourierCoeff_recurrenceproof · cited by 2
- Complex.partialGamma_add_oneproof · cited by 1
- EulerSine.integral_cos_mul_cos_pow_auxproof · cited by 1