English
The antisymmetrization of a product preorder α × β is order-isomorphic to the product of antisymmetrizations: Antisymmetrization (α × β) ≃o Antisymmetrization α × Antisymmetrization β.
Русский
Антисимметризация произведения preorder α × β изоморфна порядку продукции антисимметризаций: Antisymmetrization (α × β) ≃o Antisymmetrization α × Antisymmetrization β.
LaTeX
$$$\\text{Antisymmetrization.prodEquiv}: \\text{Antisymmetrization}(α \\times β) \\cong_o (\\text{Antisymmetrization}(α) \\times \\text{Antisymmetrization}(β))$$$
Lean4
/-- `ofAntisymmetrization` as an order embedding. -/
@[simps]
noncomputable def ofAntisymmetrization : Antisymmetrization α (· ≤ ·) ↪o α :=
{ Quotient.outRelEmbedding _ with toFun := _root_.ofAntisymmetrization _ }
