Theorems · Theorem · global analysis

DifferentiableAt.const_add

∀ {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} (c : F), DifferentiableAt 𝕜 f x → DifferentiableAt 𝕜 (fun y => c + f y) x

Alias of the reverse direction of differentiableAt_const_add_iff.

Defined in

Mathlib.Analysis.Calculus.FDeriv.Add

Cited by

6 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace