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Theorems · Theorem · real analysis

iteratedFDeriv_neg_apply

∀ {𝕜 : Type u_1} [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] {x : E} {i : ℕ}
  {f : E → F}, iteratedFDeriv 𝕜 i (-f) x = -iteratedFDeriv 𝕜 i f x
Defined in
Mathlib.Analysis.Calculus.ContDiff.Operations
Cited by
2 results in Mathlib
Foundations
Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace
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Around this declaration

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

Function.HasTemperateGrowth.neg · cited by 3HasTemperateGrowth.negiteratedFDeriv_neg · cited by 1iteratedFDeriv_negNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldContinuousMultilinearMap · cited by 1016ContinuousMultilinearMapSet.mem_univ · cited by 416Set.mem_univiteratedFDeriv · cited by 211iteratedFDerivuniqueDiffOn_univ · cited by 66uniqueDiffOn_univiteratedFDerivWithin_neg_apply · cited by 3iteratedFDerivWithin_neg_…iteratedFDeriv_neg_applyCITED BYCITES

Cites8

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Cited by2

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