Theorems · Theorem · real analysis

ContDiffPointwiseHolderAt.clm_apply

∀ {E : Type u_1} {F : Type u_2} {G : Type u_3} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
  [inst_2 : NormedAddCommGroup F] [inst_3 : NormedSpace ℝ F] [inst_4 : NormedAddCommGroup G] [inst_5 : NormedSpace ℝ G]
  {k : ℕ} {α : ↑unitInterval} {a : E} {f : E → F →L[ℝ] G} {g : E → F},
  ContDiffPointwiseHolderAt k α f a →
    ContDiffPointwiseHolderAt k α g a → ContDiffPointwiseHolderAt k α (fun x => (f x) (g x)) a

Defined in

Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise

Cited by

0 results in Mathlib

Foundations

Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace