iUnion₂_comm — Mathlib

English

For s : ∀ x : β, x = b → Set α, the union over x with h: x = b equals the set at b with h = rfl: ⋃ (x) (h : x = b), s x h = s b rfl.

Русский

Для s: ∀ x : β, x = b → Set α, объединение по x с h: x = b даёт s b rfl.

LaTeX

$$$$\\bigcup_{x} \\; s(x,h) = s(b,\\mathrm{rfl})$$$$

Lean4

theorem iUnion₂_comm (s : ∀ i, κ i → ∀ i', κ' i' → Set α) :
    ⋃ (i) (j) (i') (j'), s i j i' j' = ⋃ (i') (j') (i) (j), s i j i' j' :=
  iSup₂_comm _

Похожие утверждения