English
A definitional equality for finprod: finprod f equals the delta-form decomposition stated earlier.
Русский
Определительная равенство для finprod: итог равен разложению в форму delta как выше.
LaTeX
$$$\\mathrm{finprod}(f) = \\big(\\text{if }\\cdots\\text{ then }\\cdots \\text{ else } 1\\big)$$$
Lean4
@[to_additive]
theorem finprod_eq_dif {p : Prop} [Decidable p] (f : p → M) : ∏ᶠ i, f i = if h : p then f h else 1 :=
by
split_ifs with h
· haveI : Unique p := ⟨⟨h⟩, fun _ => rfl⟩
exact finprod_unique f
· haveI : IsEmpty p := ⟨h⟩
exact finprod_of_isEmpty f