i:
(||p||-1). p[i]-the_graph- > p[(i+1)])p:V List. path(the_graph;p) 
Propt:Graph. Vertices(t) Type
e:Type(e
vv)Top Type{i'}
0 ; a.as' ||as'||+1 (recursive)A:Type, l:A List. ||l|| 
nil ; h.t tA:Type, l:A List. tl(l) A List| Some definitions of interest. | |
| 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 | |
| gr_v | Def Vertices(t) == 1of(t) |
| Thm* t:Graph. Vertices(t) Type | |
| graph | Def Graph == v:Typee:Type(evv)Top |
| Thm* Graph Type{i'} | |
| length | Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) |
| Thm* A:Type, l:A List. ||l|| | |
| Thm* ||nil|| | |
| tl | Def tl(l) == Case of l; nil nil ; h.t t |
| Thm* A:Type, l:A List. tl(l) A List |
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