Some definitions of interest.
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
int_seg	Def  {i..j} == {k:| i  k < j }
	Thm*  m,n:. {m..n}  Type
is_discrete	Def  A Discrete == x,y:A. Dec(x = y)
	Thm*  A:Type. (A Discrete)  Prop
nat	Def   == {i:| 0i }
	Thm*    Type
surject	Def  Surj(A; B; f) == b:B. a:A. f(a) = b
	Thm*  A,B:Type, f:(AB). Surj(A; B; f)  Prop

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