gaugeSeminorm_ball_one — Mathlib

English

The gaugeSeminorm ball equals the unit ball for p in the open-ball sense.

Русский

Мяч gaugeSeminorm равен единичному шару p в смысле открытых шаров.

LaTeX

$$$$ gaugeSeminorm (p.balanced_ball_zero 1) (p.convex_ball 0 1) (p.absorbent_ball_zero zero_lt_one) = p. $$$$

Lean4

theorem gaugeSeminorm_ball_one (hs : IsOpen s) : (gaugeSeminorm hs₀ hs₁ hs₂).ball 0 1 = s :=
  by
  rw [Seminorm.ball_zero_eq]
  exact gauge_lt_one_eq_self_of_isOpen hs₁ hs₂.zero_mem hs

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