Theorems · Theorem · several complex variables

AnalyticWithinAt.mono

∀ {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} {s t : Set E}
  {x : E}, AnalyticWithinAt 𝕜 f s x → t ⊆ s → AnalyticWithinAt 𝕜 f t x

Defined in

Mathlib.Analysis.Analytic.Basic

Cited by

3 results in Mathlib

Foundations

Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace