not_disjoint_coe_iff_nonempty_inter

English

Not disjointness of I and J is equivalent to the nonemptiness of their intersection.

Русский

Не располагаться коробки I и J эквивалентно не пустому пересечению I и J.

LaTeX

$$$\neg\text{Disjoint } (I : WithBot(Box ι)) J \iff (I \cap J : Set(ι \to \mathbb{R})).Nonempty$$$

Lean4

theorem not_disjoint_coe_iff_nonempty_inter : ¬Disjoint (I : WithBot (Box ι)) J ↔ (I ∩ J : Set (ι → ℝ)).Nonempty := by
  rw [disjoint_coe, Set.not_disjoint_iff_nonempty_inter]

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