English
A recursion principle for FinEnum that either ends at Empty or continues with Option α, transporting P along an equivalence when sizes match.
Русский
Принцип рекурсии по FinEnum: FinEnum либо пуст, либо продолжает через Option α, переносит P через эквивариантность при совпадении размерностей.
LaTeX
$$$\\text{recEmptyOption}(finChoice,congr,empty,option)(α) : P α$; defined by cases on card α.$$
Lean4
/-- This is an arbitrary choice of insertion rank for a default instance.
It keeps the mapping of the existing `α`-inhabitants intact, modulo `Fin.castSucc`. -/
instance instFinEnumOptionLast (α : Type u) [FinEnum α] : FinEnum (Option α) :=
insertNone α (Fin.last _)