Some definitions of interest.
int_seg	Def  {i..j} == {k:| i  k < j }
	Thm*  m,n:. {m..n}  Type
iter_via_intseg	Def  Iter(f;u) i:{a..b}. e(i) Def  == if a<b f((Iter(f;u) i:{a..b-1}. e(i)),e(b-1)) else u fi Def  (recursive)
	Thm*  f:(AAA), u:A, a,b:, e:({a..b}A). (Iter(f;u) i:{a..b}. e(i))  A
nat	Def   == {i:| 0i }
	Thm*    Type
trivial_factorization	Def  trivial_factorization(z)(i) == if i=z 1 else 0 fi
	Thm*  a,b:, z:{a..b}. trivial_factorization(z)  {a..b}

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