disjoint_iUnion_right — Mathlib

English

Disjoint t with ⋃ i s i is equivalent to ∀ i, Disjoint t (s i).

Русский

Дисjoint t с ⋃ i s i равносилен тому, что для каждого i тождественно t дисjoint с s i.

LaTeX

$$$$\\mathrm{Disjoint}\\,t\\left(\\bigcup_{i} s(i)\\right) \\iff \\forall i, \\mathrm{Disjoint}\\,t\\,(s(i)).$$$$

Lean4

@[simp]
theorem disjoint_iUnion_right {ι : Sort*} {s : ι → Set α} : Disjoint t (⋃ i, s i) ↔ ∀ i, Disjoint t (s i) :=
  disjoint_iSup_iff

Похожие утверждения