Theorems · Theorem · real analysis

ContinuousLinearMap.dslope_comp

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] (f : E →L[𝕜] F)
  (g : 𝕜 → E) (a b : 𝕜), (a = b → DifferentiableAt 𝕜 g a) → dslope (⇑f ∘ g) a b = f (dslope g a b)

Defined in

Mathlib.Analysis.Calculus.DSlope

Cited by

1 results in Mathlib

Foundations

Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace