Some definitions of interest.
eval_factorization	Def  {a..b}(f) ==  i:{a..b}. if(i)
	Thm*  a,b:, f:({a..b}). {a..b}(f)
int_seg	Def  {i..j} == {k:| i  k < j }
	Thm*  m,n:. {m..n}  Type
int_upper	Def  {i...} == {j:| ij }
	Thm*  n:. {n...}  Type
nat	Def   == {i:| 0i }
	Thm*    Type
le	Def  AB == B<A
	Thm*  i,j:. (ij)  Prop
nat_plus	Def   == {i:| 0<i }
	Thm*    Type
reduce_factorization	Def  reduce_factorization(f; j)(i) == if i=j f(i)-1 else f(i) fi
	Thm*  a,b:, f:({a..b}), j:{a..b}. Thm*  0<f(j)  reduce_factorization(f; j)  {a..b}

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