Some definitions of interest.
bijection_type	Def  A bij B == {f:(AB)| Bij(A; B; f) }
	Thm*  A,B:Type. A bij B  Type
biject	Def  Bij(A; B; f) == Inj(A; B; f) & Surj(A; B; f)
	Thm*  A,B:Type, f:(AB). Bij(A; B; f)  Prop
injection_type	Def  A inj B == {f:(AB)| Inj(A; B; f) }
	Thm*  A,B:Type. A inj B  Type
subtype	Def  S  T == x:S. x  T

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