English
For a,b : ∀ i, α(i), the size of the combined interval Ico(a,b) equals the product of the coordinatewise interval sizes minus 1: #(Ico a b) = ∏ i #(Icc(a(i), b(i))) − 1.
Русский
Для функций a,b: ∀ i, α(i) выполняется: |Ico(a,b)| = (∏ᵢ |Icc(a(i), b(i))|) − 1.
LaTeX
$$$$ \\#(Ico(a,b)) = \\prod_{i} \\#(Icc(a(i), b(i))) - 1 $$$$
Lean4
theorem card_Icc : #(Icc a b) = ∏ i, #(Icc (a i) (b i)) :=
card_piFinset _