English
An initial segment embedding between the < relations of two partial orders is an order embedding.
Русский
Начальное отрезковое отображение между отношениями ‹‰› двух частичных порядков является вложением порядка.
LaTeX
$$$\\\\text{toOrderEmbedding} \\\\bigl[f: r \\\\preccurlyeq_i s\\\\bigr] \\\\colon \\\\alpha \hookrightarrow \\\\beta$ is an order embedding.$$
Lean4
/-- An initial segment embedding between the `<` relations of two partial orders is an order
embedding. -/
def toOrderEmbedding [PartialOrder α] [PartialOrder β] (f : α ≤i β) : α ↪o β :=
f.orderEmbeddingOfLTEmbedding