English
left k is an embedding Fin2 n → Fin2 (k + n) defined by mapping fz to fz and iterating fs on successors.
Русский
left k задаёт вложение Fin2 n в Fin2 (k+n) через отображение fz к fz и обход по successors.
LaTeX
$$$\text{left}(k) : \forall \{n\},\ \mathrm{Fin2}\,n \to \mathrm{Fin2}(k+n)$, с definicией: \mathrm{left}(k)(\mathrm{fz}) = \mathrm{fz},\ \mathrm{left}(k)(\mathrm{fs}\ i) = \mathrm{fs}(\mathrm{left}(k)(i)).$$$
Lean4
/-- `left k` is the embedding `Fin2 n → Fin2 (k + n)` -/
def left (k) : ∀ {n}, Fin2 n → Fin2 (k + n)
| _, @fz _ => fz
| _, @fs _ i => fs (left k i)
