Some definitions of interest.
complete_intseg_mset	Def  complete_intseg_mset(a; b; f)(x) == if a  x < b f(x) else 0 fi
	Thm*  a,b:, f:({a..b}). complete_intseg_mset(a; b; f)
prime_factorization_of	Def  f is a factorization of k Def  == (x:Prime. k<x  f(x) = 0) & k = {2..k+1}(prime_mset_complete(f))
	Thm*  f:(Prime), k:. f is a factorization of k  Prop
eval_factorization	Def  {a..b}(f) ==  i:{a..b}. if(i)
	Thm*  a,b:, f:({a..b}). {a..b}(f)
is_prime_factorization	Def  is_prime_factorization(a; b; f) == i:{a..b}. 0<f(i)  prime(i)
	Thm*  a,b:, f:({a..b}). is_prime_factorization(a; b; f)  Prop
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
prime_nats	Def  Prime == {x:| prime(x) }
nat	Def   == {i:| 0i }
	Thm*    Type
prime_mset_complete	Def  prime_mset_complete(f)(x) == if is_prime(x) f(x) else 0 fi
	Thm*  f:(Prime). prime_mset_complete(f)

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