| | Some definitions of interest. |
|
| assert | Def  b == if b True else False fi |
| | | Thm*  b: . b  Prop |
|
| iff | Def P   Q == (P  Q) & (P Q) |
| | | Thm* A,B:Prop. (A B) Prop |
|
| int_seg | Def {i..j } == {k: | i  k < j } |
| | | Thm* m,n:. {m..n} Type |
|
| member-paren | Def member-paren(x,y.E(x;y);i;s) == ( xs.InjCase(x; a. E(a;i), E(a;i))) |
|
| l_bexists | Def (xL.P(x)) == reduce( x,b. P(x)   b;false;L) |
| | | Thm* T:Type, L:T List, P:(T  ). (xL.P(x)) |
|
| 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|| |
| | | 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 |
