| | Some definitions of interest. |
|
| upto | Def upto(n) == if n= 0 nil else upto(n-1) @ [(n-1)] fi (recursive) |
| | | Thm* n: . upto(n) n List |
|
| append | Def as @ bs == Case of as; nil bs ; a.as' [a / (as' @ bs)] (recursive) |
| | | Thm* T:Type, as,bs:T List. (as @ bs) T List |
|
| firstn | Def firstn(n;as)
Def == Case of as
Def == Canil nil
Def == Caa.as' if 0< n [a / firstn(n-1;as')] else nil fi
Def (recursive) |
| | | Thm* A:Type, as:A List, n: . firstn(n;as) A List |
|
| nat | Def == {i: | 0 i } |
| | | Thm* Type |
|
| le | Def A B == B<A |
| | | Thm* i,j: . (i j) Prop |
|
| map | Def map(f;as) == Case of as; nil nil ; a.as' [(f(a)) / map(f;as')]
Def (recursive) |
| | | Thm* A,B:Type, f:(A B), l:A List. map(f;l) B List |
| | | Thm* A,B:Type, f:(A B), l:A List . map(f;l) B List |