disjoint_iUnion₂_left — Mathlib

English

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

Русский

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

LaTeX

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

Lean4

theorem disjoint_iUnion₂_left {s : ∀ i, κ i → Set α} {t : Set α} :
    Disjoint (⋃ (i) (j), s i j) t ↔ ∀ i j, Disjoint (s i j) t :=
  iSup₂_disjoint_iff

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