Theorems · Theorem · global analysis

HasLineDerivWithinAt.mono_of_mem_nhdsWithin

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type u_2} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {E : Type u_3} [inst_3 : NormedAddCommGroup E] [inst_4 : NormedSpace 𝕜 E] {f : E → F}
  {f' : F} {s t : Set E} {x v : E},
  HasLineDerivWithinAt 𝕜 f f' t x v → t ∈ nhdsWithin x s → HasLineDerivWithinAt 𝕜 f f' s x v

Defined in

Mathlib.Analysis.Calculus.LineDeriv.Basic

Cited by

1 results in Mathlib

Foundations

Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace