| | 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 |
|
| l_ball | Def (xL.P(x)) == reduce( x,b. P(x)  b;true;L) |
| | | Thm* T:Type, L:T List, P:(T  ). (xL.P(x)) |
|
| 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|| |
|
| not | Def A == A False |
| | | Thm* A:Prop. (A) Prop |
|
| rev_implies | Def P Q == Q P |
| | | Thm* A,B:Prop. (A B) Prop |
|
| select | Def l[i] == hd(nth_tl(i;l)) |
| | | Thm* A:Type, l:A List, n:. 0n n < ||l|| l[n] A |
