Theorems · Theorem · functional analysis

PiTensorProduct.mapL_add

∀ {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}
  [inst_4 : (i : ι) → SeminormedAddCommGroup (E' i)] [inst_5 : (i : ι) → NormedSpace 𝕜 (E' i)]
  (f : (i : ι) → E i →L[𝕜] E' i) [inst_6 : DecidableEq ι] (i : ι) (u v : E i →L[𝕜] E' i),
  PiTensorProduct.mapL (Function.update f i (u + v)) =
    PiTensorProduct.mapL (Function.update f i u) + PiTensorProduct.mapL (Function.update f i v)

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

FintypeSeminormedAddCommGroupNontriviallyNormedFieldNormedSpaceSeminormedAddCommGroupNormedSpaceDecidableEq