disjoint_withBotCoe — Mathlib

English

Disjointness of boxes corresponds to disjointness of their underlying sets and vice versa.

Русский

Дисjoint коробок эквивалентен дисjointности их базовых множеств и наоборот.

LaTeX

$$$\Disjoint (I : Set(\iota \to \mathbb{R})) J \iff \Disjoint I J$$$

Lean4

@[simp, norm_cast]
theorem disjoint_withBotCoe {I J : WithBot (Box ι)} : Disjoint (I : Set (ι → ℝ)) J ↔ Disjoint I J :=
  by
  simp only [disjoint_iff_inf_le, ← withBotCoe_subset_iff, coe_inf]
  rfl

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