coe_disjoint — Mathlib

English

Disjointness of clopen sets corresponds to disjointness of their underlying sets: for s,t ∈ Clopens α, Disjoint (s : Set α) t ↔ Disjoint s t.

Русский

Потоковая разобщённость клопных множеств соответствует разобщённости их подмножеств: Disjoint (s : Set α) t ⇔ Disjoint s t.

LaTeX

$$$\text{Disjoint}((s : \mathrm{Set}(\alpha)), t) \;\iff\; \text{Disjoint}(s,t)\quad (s,t \in \mathrm{Clopens}(\alpha)).$$$

Lean4

@[simp, norm_cast]
theorem coe_disjoint {s t : Clopens α} : Disjoint (s : Set α) t ↔ Disjoint s t := by
  simp [disjoint_iff, ← SetLike.coe_set_eq]

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