English
The infimum of two elements in a preorder forms a binary product in the corresponding category.
Русский
Голова наименьшего (inf) двух элементов в порядке образует бинарный произведение в соответствующей категории.
LaTeX
$$$ \\text{isLimitBinaryFan}(X,Y) : IsLimit( BinaryFan.mk(P:= X \\inf Y, \\mathrm{homOfLE}\\,\\inf\\_\\_ , \\mathrm{homOfLE}\\,\\inf\\_\\_ )) $$$
Lean4
/-- The infimum of two elements in a preordered type is a binary product in
the category associated to this preorder. -/
def isLimitBinaryFan (X Y : C) : IsLimit (BinaryFan.mk (P := X ⊓ Y) (homOfLE inf_le_left) (homOfLE inf_le_right)) :=
BinaryFan.isLimitMk (fun s ↦ homOfLE (le_inf (leOfHom s.fst) (leOfHom s.snd))) (by intros; rfl) (by intros; rfl)
(by intros; rfl)
