Theorems · Theorem · functional analysis

PiTensorProduct.mapL_comp

∀ {ι : Type u_1} [inst : Fintype ι] {𝕜 : Type u_2} {E : ι → Type u_3} [inst_1 : (i : ι) → SeminormedAddCommGroup (E i)]
  [inst_2 : NontriviallyNormedField 𝕜] [inst_3 : (i : ι) → NormedSpace 𝕜 (E i)] {E' : ι → Type u_5} {E'' : ι → Type u_6}
  [inst_4 : (i : ι) → SeminormedAddCommGroup (E' i)] [inst_5 : (i : ι) → NormedSpace 𝕜 (E' i)]
  [inst_6 : (i : ι) → SeminormedAddCommGroup (E'' i)] [inst_7 : (i : ι) → NormedSpace 𝕜 (E'' i)]
  (g : (i : ι) → E' i →L[𝕜] E'' i) (f : (i : ι) → E i →L[𝕜] E' i),
  (PiTensorProduct.mapL fun i => g i ∘SL f i) = PiTensorProduct.mapL g ∘SL PiTensorProduct.mapL f

Defined in

Mathlib.Analysis.Normed.Module.PiTensorProduct.ProjectiveSeminorm

Cited by

1 results in Mathlib

Foundations

Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeSeminormedAddCommGroupNontriviallyNormedFieldNormedSpaceSeminormedAddCommGroupNormedSpaceSeminormedAddCommGroupNormedSpace