Theorems · Theorem · global analysis

fderivWithin_const_sub

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {f : E → F}
  {x : E} {s : Set E},
  UniqueDiffWithinAt 𝕜 s x → ∀ (c : F), fderivWithin 𝕜 (fun y => c - f y) s x = -fderivWithin 𝕜 f s x

Defined in

Mathlib.Analysis.Calculus.FDeriv.Add

Cited by

1 results in Mathlib

Foundations

Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace