Theorems · Theorem · real analysis
iteratedFDerivWithin_univ
∀ {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}
{n : ℕ}, iteratedFDerivWithin 𝕜 n f Set.univ = iteratedFDeriv 𝕜 n f- Cited by
- 19 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Set.univstatement · cited by 3,945
- ContinuousMultilinearMapstatement and proof · cited by 1,016
- fderivproof · cited by 398
- iteratedFDerivstatement · cited by 211
- iteratedFDerivWithinstatement · cited by 147
- fderivWithin_univproof · cited by 29
- ContinuousMultilinearMap.uncurry0proof · cited by 28
- ContinuousLinearMap.uncurryLeftproof · cited by 7
Cited by19
Results whose statement or proof uses this declaration.
- iteratedDerivWithin_univproof · cited by 16
- Function.HasTemperateGrowth.compproof · cited by 12
- contDiff_iff_continuous_differentiableproof · cited by 6
- iteratedFDeriv_succ_apply_rightproof · cited by 4
- ContDiffAt.iteratedFDeriv_rightproof · cited by 4
- ContDiffAt.differentiableAt_iteratedFDerivproof · cited by 4
- HasFTaylorSeriesUpTo.eq_iteratedFDerivproof · cited by 2
- iteratedFDerivWithin_eq_iteratedFDerivproof · cited by 2
- iteratedFDerivWithin_of_isOpenproof · cited by 2
- ContDiffAt.restrictScalars_iteratedFDeriv_eventuallyEqproof · cited by 2
- ftaylorSeriesWithin_univproof · cited by 1
- norm_iteratedFDeriv_oneproof · cited by 0