withSeminorms — Mathlib

English

The seminorm family induces a standard seminorms-based structure, i.e., WithSeminorms (seminormFamily 𝕜 E F).

Русский

Семинормальная структура порождается семинормной семейством: WithSeminorms (seminormFamily 𝕜 E F).

LaTeX

$$withSeminorms : WithSeminorms (seminormFamily 𝕜 E F)$$

Lean4

theorem withSeminorms : WithSeminorms (seminormFamily 𝕜 E F) :=
  let e : E × F⋆ ≃ (Σ _ : E × F⋆, Fin 1) := .symm <| .sigmaUnique _ _
  isInducing_inducingFn.withSeminorms <| withSeminorms_pi (fun _ ↦ norm_withSeminorms 𝕜 𝕜) |>.congr_equiv e

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