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Theorems · Theorem · real analysis

iteratedFDeriv_neg

∀ {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] {i : ℕ}
  {f : E → F}, iteratedFDeriv 𝕜 i (-f) = -iteratedFDeriv 𝕜 i f
Defined in
Mathlib.Analysis.Calculus.ContDiff.Operations
Cited by
1 results in Mathlib
Foundations
Depth 178 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.

InnerProductSpace.laplacian_neg · cited by 1InnerProductSpace.laplaci…NormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldContinuousMultilinearMap · cited by 1016ContinuousMultilinearMapiteratedFDeriv · cited by 211iteratedFDeriviteratedFDeriv_neg_apply · cited by 2iteratedFDeriv_neg_applyiteratedFDeriv_negCITED BYCITES

Cites6

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Cited by1

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