import num

!!! ∀ x : ℕ. (x > 0) ==> reduce(~*~, 1, factor x) == x
dummy : Unit
dummy = unit

||| The size (cardinality) of a set.
!!! setSize2 {} == 0
!!! setSize2 {1} == 1
!!! setSize2 {1..10} == 10
!!! setSize2 {1,1,1,2,3} == 3
!!! ∀ s : Set(N). setSize2 s == setSize2 (s ∪ s)
setSize2 : Set(N) -> N
setSize2 s = reduce(~+~, 0, each (\x.1, bag s))