English
Another formulation of the product factorization for the closed interval in a product: card(Icc(x,y)) = card(Icc(x1,y1)) × card(Icc(x2,y2)).
Русский
Другая формулировка разложения кардиналитета для замкнутого интервала в произведении: card(Icc(x,y)) = card(Icc(x1,y1)) × card(Icc(x2,y2)).
LaTeX
$$$ \#(Icc\,x,y) = \#(Icc\,x.1,y.1) \cdot \#(Icc\,x.2,y.2) $$$
Lean4
/-- Given a finset on `α`, lift it to being a finset on `WithTop α`
using `WithTop.some` and then insert `⊤`. -/
def insertTop : Finset α ↪o Finset (WithTop α) :=
OrderEmbedding.ofMapLEIff (fun s => cons ⊤ (s.map Embedding.coeWithTop) <| by simp)
(fun s t => by rw [le_iff_subset, cons_subset_cons, map_subset_map, le_iff_subset])
