Theorems · Theorem · real analysis
iteratedFDeriv_zero_eq_comp
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {E : Type uE} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {F : Type uF} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F},
iteratedFDeriv 𝕜 0 f = ⇑(continuousMultilinearCurryFin0 𝕜 E F).symm ∘ f- Cited by
- 4 results in Mathlib
- Foundations
- Depth 175 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.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousMultilinearMapstatement · cited by 1,016
- LinearIsometryEquivstatement · cited by 748
- LinearIsometryEquiv.symmstatement · cited by 287
- iteratedFDerivstatement · cited by 211
- continuousMultilinearCurryFin0statement · cited by 34
Cited by4
Results whose statement or proof uses this declaration.
- norm_iteratedFDeriv_zeroproof · cited by 14
- AnalyticOnNhd.iteratedFDerivproof · cited by 2
- tsupport_iteratedFDeriv_subsetproof · cited by 2
- CPolynomialOn.iteratedFDerivproof · cited by 0