ball_div — Mathlib

English

In a seminormed commutative group, for all x, δ and s, the quotient of Ball(x, δ) by s equals the left translate by x of the δ-thickening of s⁻¹; Ball(x, δ) / s = x · Thickening(δ, s⁻¹).

Русский

В семиномерной коммутативной группе для любых x, δ и s 회 Ball(x, δ) / s = x · Thickening(δ, s⁻¹).

LaTeX

$$$\mathbb{B}(x, \delta) / s = x \cdot \operatorname{thickening}(\delta, s^{-1})$$$

Lean4

@[to_additive (attr := simp)]
theorem ball_div : ball x δ / s = x • thickening δ s⁻¹ := by simp [div_eq_mul_inv]

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