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Theorems · Theorem · real analysis

IsSymmSndFDerivAt.eq

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} {F : Type u_3} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F} {x : E},
  IsSymmSndFDerivAt 𝕜 f x → ∀ (v w : E), ((fderiv 𝕜 (fderiv 𝕜 f) x) v) w = ((fderiv 𝕜 (fderiv 𝕜 f) x) w) v
Defined in
Mathlib.Analysis.Calculus.FDeriv.Symmetric
Cited by
0 results in Mathlib
Foundations
Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace
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DFunLike.coe · cited by 62936DFunLike.coeRingHom.id · cited by 18349RingHom.idNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldContinuousLinearMap · cited by 5352ContinuousLinearMapfderiv · cited by 398fderivIsSymmSndFDerivAt · cited by 10IsSymmSndFDerivAtIsSymmSndFDerivAt.eqCITED BYCITES

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