English
There is an order-embedding of Antisymmetrization α (≤) into α, given by the out-relational embedding, i.e., the quotient out-rel embedding is injective and preserves order.
Русский
Существует вложение порядка антисимметризации α (≤) в α, задаваемое вложением Quotient.outRelEmbedding, сохраняющее и инъективное по отношению к порядку.
LaTeX
$$$\\text{ofAntisymmetrization} : Anti(α) \\hookrightarrow α$ preserves ≤ and is injective$$
Lean4
@[simp]
theorem antisymmetrization_apply_mk (f : α →o β) (a : α) :
f.antisymmetrization (toAntisymmetrization _ a) = toAntisymmetrization _ (f a) :=
@Quotient.map_mk _ _ (_root_.id _) (_root_.id _) f (liftFun_antisymmRel f) _