{a..b
}(f) == i:{a..b}. if(i)
a,b:
, f:({a..b}
). {a..b}(f) 
} == {k:| i 
k < j }m,n:. {m..n} Type
== {i:| 0i } Type
j
f(i)-1 else f(i) fia,b:, f:({a..b}), j:{a..b}.
Thm* 0<f(j)
reduce_factorization(f; j) {a..b}| Some definitions of interest. | |
| eval_factorization | {a..b}(f) == i:{a..b}. if(i) |
| a,b:, f:({a..b}). {a..b}(f) | |
| int_seg | } == {k:| i k < j } |
| m,n:. {m..n} Type | |
| nat | == {i:| 0i } |
| Type | |
| reduce_factorization | j f(i)-1 else f(i) fi |
| a,b:, f:({a..b}), j:{a..b}.
Thm* 0<f(j) reduce_factorization(f; j) {a..b} |
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