balanced_ball_zero — Mathlib

English

Balls centered at the origin are balanced with respect to scalar multiplication.

Русский

Шары, centered at origin, сбалансированы по отношению к умножению на скаляры.

LaTeX

$$$\forall r>0:\; \text{Balanced } 𝕜 (\mathrm{Metric.ball}(0,E,r)).$$$

Lean4

/-- Balls at the origin are balanced. -/
theorem balanced_ball_zero : Balanced 𝕜 (Metric.ball (0 : E) r) :=
  by
  rw [← ball_normSeminorm 𝕜]
  exact (normSeminorm _ _).balanced_ball_zero r

Похожие утверждения