Theorems · Theorem · several complex variables

HasFPowerSeriesWithinOnBall.comp_sub

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F}
  {p : FormalMultilinearSeries 𝕜 E F} {s : Set E} {x : E} {r : ENNReal},
  HasFPowerSeriesWithinOnBall f p s x r →
    ∀ (y : E), HasFPowerSeriesWithinOnBall (fun z => f (z - y)) p (s + {y}) (x + y) r

Defined in

Mathlib.Analysis.Analytic.Basic

Cited by

1 results in Mathlib

Foundations

Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace