Some definitions of interest.
compose	Def (f o g)(x) == f(g(x))
	Thm* A,B,C:Type, f:(BC), g:(AB). f o g  AC
increasing	Def increasing(f;k) == i:(k-1). f(i)<f(i+1)
	Thm* k:, f:(k). increasing(f;k)  Prop
int_seg	Def {i..j} == {k:| i  k < j }
	Thm* m,n:. {m..n}  Type
nat	Def  == {i:| 0i }
	Thm*   Type

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