| | Some definitions of interest. |
|
| assert | Def  b == if b True else False fi |
| | | Thm*  b: . b  Prop |
|
| 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 |
|
| path | Def path(the_graph;p) == 0 < ||p|| & (i: (||p||-1). p[i]-the_graph- > p[(i+1)]) |
| | | Thm* For any graph
p:V List. path(the_graph;p) Prop |
|
| edge | Def x-the_graph- > y == e:Edges(the_graph). Incidence(the_graph)(e) = < x,y > |
| | | Thm* For any graph
x,y:V. x-the_graph- > y Prop |
|
| 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'} |
|
| int_seg | Def {i..j } == {k: | i  k < j } |
| | | Thm* m,n:. {m..n} Type |
|
| last | Def last(L) == L[(||L||-1)] |
| | | Thm* T:Type, L:T List.  null(L)   last(L) T |
|
| 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 |
|
| null | Def null(as) == Case of as; nil true ; a.as' false |
| | | Thm* T:Type, as:T List. null(as) |
| | | Thm* null(nil) |
|
| select | Def l[i] == hd(nth_tl(i;l)) |
| | | Thm* A:Type, l:A List, n:. 0n n < ||l|| l[n] A |
