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Theorems · Theorem · real analysis

HasStrictDerivAt.add

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {f g : 𝕜 → F} {f' g' : F} {x : 𝕜},
  HasStrictDerivAt f f' x → HasStrictDerivAt g g' x → HasStrictDerivAt (f + g) (f' + g') x
Defined in
Mathlib.Analysis.Calculus.Deriv.Add
Cited by
4 results in Mathlib
Foundations
Depth 167 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.

Complex.hasStrictDerivAt_cos · cited by 5Complex.hasStrictDerivAt_…Complex.hasStrictDerivAt_cosh · cited by 4Complex.hasStrictDerivAt_…Polynomial.hasStrictDerivAt · cited by 3Polynomial.hasStrictDeriv…HasStrictDerivAt.fun_add · cited by 0HasStrictDerivAt.fun_addNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldHasStrictDerivAt · cited by 163HasStrictDerivAtHasDerivAtFilter.add · cited by 5HasDerivAtFilter.addHasStrictDerivAt.addCITED BYCITES

Cites5

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Cited by4

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