English
Equality of filtered Finsets by a predicate is equivalent to the pointwise equality of membership for elements satisfying the predicate.
Русский
Равенство фильтрованных по p множеств эквивалентно покомпонентному равенству принадлежности элементов, удовлетворяющих p.
LaTeX
$$$\text{Finset.filter } p s = \text{Finset.filter } p t \iff \forall a.\; p(a) \Rightarrow (a \in s) \iff (a \in t)$$$
Lean4
/-- The initial segment of the colexicographic order on sets with `#s` elements and ending at
`s`. -/
def initSeg (s : Finset α) : Finset (Finset α) :=
{t | #s = #t ∧ toColex t ≤ toColex s}