Theorems · Theorem · real analysis

ContDiff.clm_comp

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} {G : Type u_4} [inst : NontriviallyNormedField 𝕜]
  [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F]
  [inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace 𝕜 G] {X : Type u_5} [inst_7 : NormedAddCommGroup X]
  [inst_8 : NormedSpace 𝕜 X] {n : WithTop ℕ∞} {g : X → F →L[𝕜] G} {f : X → E →L[𝕜] F},
  ContDiff 𝕜 n g → ContDiff 𝕜 n f → ContDiff 𝕜 n fun x => g x ∘SL f x

Defined in

Mathlib.Analysis.Calculus.ContDiff.Comp

Cited by

2 results in Mathlib

Foundations

Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace