Some definitions of interest.
is_finite_type	Def  Finite(A) == n:. A ~ n
	Thm*  A:Type. Finite(A)  Prop
unboundedly_infinite	Def  Unbounded(A) == k:. (k inj A)
	Thm*  A:Type. Unbounded(A)  Prop
nat	Def   == {i:| 0i }
	Thm*    Type
not	Def  A == A  False
	Thm*  A:Prop. (A)  Prop

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