lipschitzWith_sub — Mathlib

English

NormOneClass is inherited to the SeparationQuotient from the parent structure.

Русский

NormOneClass наследуется для SeparationQuotient от исходной структуры.

LaTeX

$$$ \\text{NormOneClass}(\\mathrm{SeparationQuotient}(\\alpha)).$$$

Lean4

theorem lipschitzWith_sub : LipschitzWith 2 (fun (p : ℝ≥0 × ℝ≥0) ↦ p.1 - p.2) :=
  by
  rw [← isometry_subtype_coe.lipschitzWith_iff]
  have : Isometry (Prod.map ((↑) : ℝ≥0 → ℝ) ((↑) : ℝ≥0 → ℝ)) := isometry_subtype_coe.prodMap isometry_subtype_coe
  convert (((LipschitzWith.prod_fst.comp this.lipschitz).sub (LipschitzWith.prod_snd.comp this.lipschitz)).max_const 0)
  norm_num

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