disjoint_iUnion₂_right — Mathlib

English

Disjoint s (⋃ i j, t i j) iff ∀ i j, Disjoint s (t i j).

Русский

Дисjoint s с ⋃ i j, t i j эквивалентен ∀ i j, Disjoint s (t i j).

LaTeX

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

Lean4

theorem disjoint_iUnion₂_right {s : Set α} {t : ∀ i, κ i → Set α} :
    Disjoint s (⋃ (i) (j), t i j) ↔ ∀ i j, Disjoint s (t i j) :=
  disjoint_iSup₂_iff

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