Theorems · Theorem · several complex variables

AnalyticWithinAt.comp_of_eq

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} {G : Type u_4} [inst : NontriviallyNormedField 𝕜]
  [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F]
  [inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace 𝕜 G] {g : F → G} {f : E → F} {y : F} {x : E} {t : Set F}
  {s : Set E},
  AnalyticWithinAt 𝕜 g t y → AnalyticWithinAt 𝕜 f s x → Set.MapsTo f s t → f x = y → AnalyticWithinAt 𝕜 (g ∘ f) s x

Version of AnalyticWithinAt.comp where point equality is a separate hypothesis.

Defined in

Mathlib.Analysis.Analytic.Composition

Cited by

0 results in Mathlib

Foundations

Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace