Theorems · Theorem · global analysis

ContDiffWithinAt.lineMap

∀ {𝕜 : Type u_1} {V : Type u_2} {E : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup V]
  [inst_2 : NormedSpace 𝕜 V] [inst_3 : NormedAddCommGroup E] [inst_4 : NormedSpace 𝕜 E] {f₁ f₂ : E → V} {g : E → 𝕜}
  {s : Set E} {x : E} {n : WithTop ℕ∞},
  ContDiffWithinAt 𝕜 n f₁ s x →
    ContDiffWithinAt 𝕜 n f₂ s x →
      ContDiffWithinAt 𝕜 n g s x → ContDiffWithinAt 𝕜 n (fun x => (AffineMap.lineMap (f₁ x) (f₂ x)) (g x)) s x

Defined in

Mathlib.Analysis.Calculus.AddTorsor.AffineMap

Cited by

0 results in Mathlib

Foundations

Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace