disjoint_toFinset — Mathlib

English

Disjointness is preserved under converting multisets to finite sets: Disjoint m1.toFinset m2.toFinset ⇔ Disjoint m1 m2.

Русский

Не пересечение сохраняется при переходе из много множеств в конечные множества: Disjoint m1.toFinset m2.toFinset ⇔ Disjoint m1 m2.

LaTeX

$$$\\operatorname{Disjoint}(m_1^{\\!toFinset}, m_2^{\\!toFinset}) \\iff \\operatorname{Disjoint}(m_1, m_2)$$$

Lean4

@[simp]
theorem disjoint_toFinset {m1 m2 : Multiset α} : _root_.Disjoint m1.toFinset m2.toFinset ↔ Disjoint m1 m2 := by
  simp [disjoint_left, Finset.disjoint_left]

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