| Some definitions of interest. |
|
eq_int | Def i= j == if i=j true ; false fi |
| | Thm* i,j: . (i= j) ![](FONT/bool.png) |
|
sublist | Def L1 L2
Def == f:( ||L1||![](FONT/dash.png) ![](FONT/then_med.png) ||L2||).
Def == increasing(f;||L1||) & ( j: ||L1||. L1[j] = L2[(f(j))] T) |
| | Thm* T:Type, L1,L2:T List. L1 L2 Prop |
|
increasing | Def increasing(f;k) == i: (k-1). f(i)<f(i+1) |
| | Thm* k: , f:( k![](FONT/dash.png) ![](FONT/then_med.png) ). increasing(f;k) Prop |
|
int_seg | Def {i..j } == {k: | i k < j } |
| | Thm* m,n: . {m..n } Type |
|
label | Def t ...$L == t |
|
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) |
|
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 |