prod_subset_compl_diagonal_iff_disjoint

English

The product set s × t is contained in the complement of the diagonal Δ(α) if and only if s and t are disjoint.

Русский

Произведение множеств s × t вложено в комплемент диагонали тогда и только тогда, когда s и t дизjoint.

LaTeX

$$$s \\times t \\subseteq \\Delta(\\alpha)^c \\iff \\operatorname{Disjoint}(s,t).$$$

Lean4

@[simp]
theorem prod_subset_compl_diagonal_iff_disjoint : s ×ˢ t ⊆ (diagonal α)ᶜ ↔ Disjoint s t :=
  prod_subset_iff.trans disjoint_iff_forall_ne.symm

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