English
A definitional equality for finprod: finprod f equals 1 if the finite support is empty, otherwise it is the product over the finite support of f, with a downward-PLift index.
Русский
Определение finprod: если пространство опоры пусто, то finprod f = 1, иначе — произведение по опоре; индексы используют поведение вниз по PLift.
LaTeX
$$$\\mathrm{finprod}(f) = \\begin{cases} \\prod_{i\\in s} f(i\\downarrow), & (\\text{support of } f \\text{ finite and contained}) \\\\ 1, & \\text{otherwise} \\end{cases}$$$
Lean4
theorem finprod_def' : eta_helper Eq✝ @finprod.{} @(delta% @definition✝) :=
by
intros
delta finprod
rw [show wrapped✝ = ⟨@definition✝.{}, rfl✝⟩ from Subtype.ext✝ wrapped✝.2.symm✝]
rfl
