Some definitions of interest.
one_one_corr_2	Def  A ~ B == f:(AB), g:(BA). InvFuns(A;B;f;g)
	Thm*  A,B:Type. (A ~ B)  Prop
unboundedly_infinite	Def  Unbounded(A) == k:. (k inj A)
	Thm*  A:Type. Unbounded(A)  Prop

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