| Some definitions of interest. |
|
iff | Def P ![](FONT/if_big.png) Q == (P ![](FONT/eq.png) Q) & (P ![](FONT/if_big.png) Q) |
| | Thm* A,B:Prop. (A ![](FONT/if_big.png) B) Prop |
|
l_member | Def (x l) == i: . i<||l|| & x = l[i] T |
| | Thm* T:Type, x:T, l:T List. (x l) Prop |
|
length | Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) |
| | Thm* A:Type, l:A List. ||l|| ![](FONT/int.png) |
| | Thm* ||nil|| ![](FONT/int.png) |
|
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![](FONT/dash.png) B), l:A List. map(f;l) B List |
| | Thm* A,B:Type, f:(A![](FONT/dash.png) B), l:A List . map(f;l) B List![](FONT/plus.png) |
|
nat | Def == {i: | 0 i } |
| | Thm* Type |
|
select | Def l[i] == hd(nth_tl(i;l)) |
| | Thm* A:Type, l:A List, n: . 0 n ![](FONT/eq.png) n<||l|| ![](FONT/eq.png) l[n] A |