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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
Defined in
Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries
Cited by
19 results in Mathlib
Foundations
Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

iteratedDerivWithin_univ · cited by 16iteratedDerivWithin_univFunction.HasTemperateGrowth.comp · cited by 12HasTemperateGrowth.compcontDiff_iff_continuous_differentiable · cited by 6contDiff_iff_continuous_d…iteratedFDeriv_succ_apply_right · cited by 4iteratedFDeriv_succ_apply…ContDiffAt.iteratedFDeriv_right · cited by 4ContDiffAt.iteratedFDeriv…ContDiffAt.differentiableAt_iteratedFDeriv · cited by 4ContDiffAt.differentiable…HasFTaylorSeriesUpTo.eq_iteratedFDeriv · cited by 2HasFTaylorSeriesUpTo.eq_i…iteratedFDerivWithin_eq_iteratedFDeriv · cited by 2iteratedFDerivWithin_eq_i…iteratedFDerivWithin_of_isOpen · cited by 2iteratedFDerivWithin_of_i…ContDiffAt.restrictScalars_iteratedFDeriv_eventuallyEq · cited by 2ContDiffAt.restrictScalar…ftaylorSeriesWithin_univ · cited by 1ftaylorSeriesWithin_univnorm_iteratedFDeriv_one · cited by 0norm_iteratedFDeriv_onenorm_iteratedFDeriv_prod_le · cited by 0norm_iteratedFDeriv_prod_…LinearIsometryEquiv.norm_iteratedFDeriv_comp_left · cited by 0LinearIsometryEquiv.norm_…iteratedFDeriv_sum · cited by 0iteratedFDeriv_sumNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldSet.univ · cited by 3945Set.univContinuousMultilinearMap · cited by 1016ContinuousMultilinearMapfderiv · cited by 398fderiviteratedFDeriv · cited by 211iteratedFDeriviteratedFDerivWithin · cited by 147iteratedFDerivWithinfderivWithin_univ · cited by 29fderivWithin_univContinuousMultilinearMap.uncurry0 · cited by 28ContinuousMultilinearMap.…ContinuousLinearMap.uncurryLeft · cited by 7ContinuousLinearMap.uncur…iteratedFDerivWithin_univCITED BYCITES

Cites11

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Cited by19

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