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Theorems · Theorem · global analysis

differentiable_neg_iff

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F},
  Differentiable 𝕜 (-f) ↔ Differentiable 𝕜 f
Defined in
Mathlib.Analysis.Calculus.FDeriv.Add
Cited by
0 results in Mathlib
Foundations
Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace
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NormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldneg_neg · cited by 960neg_negDifferentiable · cited by 298DifferentiableDifferentiable.neg · cited by 6Differentiable.negdifferentiable_neg_iffCITED BYCITES

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