English
A set s has cardinality 3 iff there exist distinct x, y, z with s = {x, y, z}.
Русский
Множество s имеет кардиналитет 3 тогда и только тогда, когда существуют x,y,z попарно различны такие, что s = {x,y,z}.
LaTeX
$$$s.ncard = 3 \iff \exists x \exists y \exists z\ (x \neq y \land x \neq z \land y \neq z \land s = \{x,y,z\})$$$
Lean4
/-- A set `s` is countable if the corresponding subtype is countable,
i.e., there exists an injective map `f : s → ℕ`.
Note that this is an abbreviation, so `hs : Set.Countable s` in the proof context
is the same as an instance `Countable s`.
For a constructive version, see `Encodable`.
-/
protected def Countable (s : Set α) : Prop :=
Countable s
