Some definitions of interest.
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
split_factor2	Def  split_factor2(g; x; y)(u) Def  == if u=x g(x)+g(xy) ; u=y g(y)+g(xy) ; u=xy 0 else g(u) fi
	Thm*  k:{2...}, g:({2..k}), x,y:{2..k}. Thm*  xy<k  split_factor2(g; x; y)  {2..k}

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