| | Some definitions of interest. |
|
| reverse | Def rev(as) == Case of as; nil  nil ; a.as' rev(as') @ [a] (recursive) |
| | | Thm*  T:Type, as:T List. rev(as)  T List |
|
| 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 |
|
| not | Def A == A False |
| | | Thm* A:Prop. (A) Prop |
