Some definitions of interest.
compose_iter	Def  f{i}(x) == if i=0 x else f(f{i-1}(x)) fi  (recursive)
	Thm*  f:(AA), i:. f{i}  AA
identity	Def  Id(x) == x
	Thm*  A:Type. Id  AA
inject	Def  Inj(A; B; f) == a1,a2:A. f(a1) = f(a2)  B  a1 = a2
	Thm*  A,B:Type, f:(AB). Inj(A; B; f)  Prop
int_seg	Def  {i..j} == {k:| i  k < j }
	Thm*  m,n:. {m..n}  Type
nat	Def   == {i:| 0i }
	Thm*    Type
nat_plus	Def   == {i:| 0<i }
	Thm*    Type

About: IF YOU CAN SEE THIS go to /sfa/Nuprl/Shared/Xindentation_hack_doc.html