edist_eq_pi_restrict — Mathlib

English

For finite 𝔖, edist f g equals the edistance between pi-restricted UniformFun representations over 𝔖.

Русский

Для конечного 𝔖 евдист между f и g равен евдисту между зип-restricted UniformFun-представлениями над 𝔖.

LaTeX

$$edist f g = edist (UniformFun.ofFun ( (⋃₀ 𝔖).restrict (toFun 𝔖 f) )) (UniformFun.ofFun ( (⋃₀ 𝔖).restrict (toFun 𝔖 g) ))$$

Lean4

theorem edist_eq_pi_restrict [Fintype 𝔖] {f g : α →ᵤ[𝔖] β} :
    edist f g =
      edist (fun s : 𝔖 ↦ UniformFun.ofFun ((s : Set α).restrict (toFun 𝔖 f)))
        (fun s : 𝔖 ↦ UniformFun.ofFun ((s : Set α).restrict (toFun 𝔖 g))) :=
  by
  simp_rw [edist_def', iSup_subtype', edist_pi_def, Finset.sup_univ_eq_iSup]
  rfl

Похожие утверждения