p:Vertices(the_graph) List. path(the_graph;p) & p[0] = x & last(p) = y
x,y:V. x-the_graph- > *y 
Propt:Graph. Vertices(t) Type
e:Type(e
vv)Top Type{i'} l) == i:
. i < ||l|| & x = l[i] TT:Type, x:T, l:T List. (x l) Prop| Some definitions of interest. | |
| 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 | |
| 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'} | |
| l_member | Def (x l) == i:. i < ||l|| & x = l[i] T |
| Thm* T:Type, x:T, l:T List. (x l) Prop |
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