| | 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)  |
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| eval_factorization | Def   {a..b}(f) == i:{a..b}. if(i) |
| | | Thm* a,b:, f:({a..b}). {a..b}(f) |
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| 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 |
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| int_seg | Def {i..j} == {k:| i k < j } |
| | | Thm* m,n:. {m..n} Type |
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| int_upper | Def {i...} == {j:| ij } |
| | | Thm* n:. {n...} Type |
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| prime_nats | Def Prime == {x:| prime(x) } |
|
| nat | Def == {i:| 0i } |
| | | Thm* Type |
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| prime | Def prime(a) ==  a = 0 & (a ~ 1) & (b,c:. a | b c a | b  a | c) |
| | | Thm* a:. prime(a) Prop |
|
| not | Def A == A False |
| | | Thm* A:Prop. (A) Prop |
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| 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) |
