| | Some definitions of interest. |
|
| increasing | Def increasing(f;k) ==  i: (k-1). f(i) < f(i+1) |
| | | Thm* k:, f:(k   ). increasing(f;k)  Prop |
|
| int_seg | Def {i..j } == {k:| i  k < j } |
| | | Thm* m,n:. {m..n} Type |
|
| nat | Def == {i:| 0i } |
| | | Thm* Type |
|
| le | Def AB ==  B < A |
| | | Thm* i,j:. (ij) Prop |
|
| length | Def ||as|| == Case of as; nil  0 ; a.as' ||as'||+1 (recursive) |
| | | Thm* A:Type, l:A List. ||l|| |
| | | Thm* ||nil|| |
|
| map | Def map(f;as) == Case of as; nil nil ; a.as' [(f(a)) / map(f;as')] (recursive) |
| | | Thm* A,B:Type, f:(AB), l:A List. map(f;l) B List |
| | | Thm* A,B:Type, f:(AB), l:A List . map(f;l) B List |
|
| nat_plus | Def == {i:| 0 < i } |
| | | Thm* Type |
|
| select | Def l[i] == hd(nth_tl(i;l)) |
| | | Thm* A:Type, l:A List, n:. 0n   n < ||l|| l[n] A |
