Theorems · Theorem · real analysis

HasFTaylorSeriesUpToOn.add

∀ {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] {s : Set E}
  {f : E → F} {p : E → FormalMultilinearSeries 𝕜 E F} {n : WithTop ℕ∞} {q : E → FormalMultilinearSeries 𝕜 E F}
  {g : E → F},
  HasFTaylorSeriesUpToOn n f p s → HasFTaylorSeriesUpToOn n g q s → HasFTaylorSeriesUpToOn n (f + g) (p + q) s

Defined in

Mathlib.Analysis.Calculus.ContDiff.Operations

Cited by

2 results in Mathlib

Foundations

Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace