English
If α is finite, then Sym2 α is finite, given by elems := univ.sym2 with a complete map.
Русский
Если α конечна, то Sym2 α конечна, задана через элементы univ.sym2 и полноту отображения.
LaTeX
$$If $Fintype(\alpha)$ then $Fintype(Sym2(\alpha))$ with $elems := Finset.univ.sym2$ and $complete$ as in the definition.$$
Lean4
instance _root_.Sym2.instFintype [Fintype α] : Fintype (Sym2 α)
where
elems := Finset.univ.sym2
complete := fun x ↦ by rw [mem_sym2_iff];
exact
(fun a _ ↦ mem_univ a)
-- Note(kmill): Using a default argument to make this simp lemma more general.