| | Some definitions of interest. |
|
| append | Def as @ bs == Case of as; nil  bs ; a.as' [a / (as' @ bs)] (recursive) |
| | | Thm*  T:Type, as,bs:T List. (as @ bs)  T List |
|
| iff | Def P   Q == (P  Q) & (P Q) |
| | | Thm* A,B:Prop. (A B) Prop |
|
| l_disjoint | Def l_disjoint(T;l1;l2) == x:T.  ((x l1) & (x l2)) |
| | | Thm* T:Type, l,l':T List. l_disjoint(T;l;l') Prop |
|
| l_member | Def (x l) ==  i: . i < ||l|| & x = l[i] T |
| | | Thm* T:Type, x:T, l:T List. (x l) Prop |
|
| no_repeats | Def no_repeats(T;l) == i,j:. i < ||l|| j < ||l|| i = j l[i] = l[j] T |
| | | Thm* T:Type, l:T List. no_repeats(T;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:| 0 i } |
| | | Thm* Type |
|
| not | Def A == A False |
| | | Thm* A:Prop. (A) Prop |
|
| select | Def l[i] == hd(nth_tl(i;l)) |
| | | Thm* A:Type, l:A List, n:. 0n n < ||l|| l[n] A |
