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Theorems · Theorem · real analysis

HasStrictDerivAt.neg

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {f' : F} {x : 𝕜}, HasStrictDerivAt f f' x → HasStrictDerivAt (-f) (-f') x
Defined in
Mathlib.Analysis.Calculus.Deriv.Add
Cited by
2 results in Mathlib
Foundations
Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpace
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Around this declaration

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

HasStrictDerivAt.fun_neg · cited by 6HasStrictDerivAt.fun_neghasStrictDerivAt_neg · cited by 2hasStrictDerivAt_negNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldHasStrictDerivAt · cited by 163HasStrictDerivAtHasDerivAtFilter.neg · cited by 7HasDerivAtFilter.negHasStrictDerivAt.negCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.