English
If de : IsDenseEmbedding e, then IsDenseEmbedding.subtypeEmb p e is an IsDenseEmbedding.
Русский
Если de : IsDenseEmbedding e, то IsDenseEmbedding.subtypeEmb p e — плотное вложение.
LaTeX
$$$IsDenseEmbedding.subtype\\ e \\Rightarrow IsDenseEmbedding (IsDenseEmbedding.subtypeEmb p e)$$$
Lean4
/-- The dense embedding of a subtype inside its closure. -/
@[simps]
def subtypeEmb {α : Type*} (p : α → Prop) (e : α → β) (x : { x // p x }) : { x // x ∈ closure (e '' {x | p x}) } :=
⟨e x, subset_closure <| mem_image_of_mem e x.prop⟩