| | Some definitions of interest. |
|
| sum | Def sum(f(x) | x < k) == primrec(k;0; x,n. n+f(x)) |
| | | Thm*  n: , f:(n   ). sum(f(x) | x < n)  |
|
| eq_int | Def i= j == if i=j true ; false fi |
| | | Thm* i,j:. (i=j)  |
|
| gt | Def i > j == j < i |
| | | Thm* i,j:. (i > j) Prop |
|
| int_seg | Def {i..j } == {k:| i  k < j } |
| | | Thm* m,n:. {m..n} Type |
|
| length | Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) |
| | | Thm* A:Type, l:A List. ||l|| |
| | | Thm* ||nil|| |
|
| nat | Def == {i:| 0i } |
| | | Thm* Type |
|
| select | Def l[i] == hd(nth_tl(i;l)) |
| | | Thm* A:Type, l:A List, n:. 0n   n < ||l|| l[n] A |
