| | 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 |
|
| list-connect | Def L-G- > *x == ( yL.y-G- > *x) |
|
| non-trivial-loop | Def non-trivial-loop(G;i) == j:Vertices(G).  j = i & i-G- > *j & j-G- > *i |
|
| connect | Def x-the_graph- > *y == p:Vertices(the_graph) List. path(the_graph;p) & p[0] = x & last(p) = y |
| | | Thm* For any graph
x,y:V. x-the_graph- > *y Prop |
|
| traversal | Def traversal(G) == (Vertices(G)+Vertices(G)) List |
| | | Thm* For any graph
Traversal Type |
|
| gr_v | Def Vertices(t) == 1of(t) |
| | | Thm* t:Graph. Vertices(t) Type |
|
| graph | Def Graph == v:Type e:Type(e  vv)Top |
| | | Thm* Graph Type{i'} |
|
| iff | Def P   Q == (P  Q) & (P Q) |
| | | Thm* A,B:Prop. (A B) Prop |
|
| l_member | Def (x l) == i: . i < ||l|| & x = l[i] T |
| | | Thm* T:Type, x:T, l:T List. (x l) Prop |
|
| not | Def A == A False |
| | | Thm* A:Prop. (A) Prop |
