traversal(the_graph)traversal(the_graph)Prop
s:traversal(the_graph), i:Vertices(the_graph). (inl(i) 
s) 
(inr(i) s) 
P(i,s,nil)
s1,s2,s3:traversal(the_graph), i,j:Vertices(the_graph).
i-the_graph- > j
paren(Vertices(the_graph);s2)
(k:Vertices(the_graph). (inr(k) s2) j-the_graph- > *k)
paren(Vertices(the_graph);s3) P(j,s1,s2) P(i,s2 @ s1,s3) P(i,s1,s3 @ s2)
s1,s2:traversal(the_graph), i:Vertices(the_graph).
(inr(i) s1)
(inl(i) s1)
paren(Vertices(the_graph);s2)
l_disjoint(Vertices(the_graph)+Vertices(the_graph);s2;s1)
no_repeats(Vertices(the_graph)+Vertices(the_graph);s2)
(j:Vertices(the_graph). (inr(j) s2) i-the_graph- > *j)
(j:Vertices(the_graph). i-the_graph- > j j = i (inl(j) s2) (inl(j) s1) (inr(j) s1))
P(i,[inr(i) / s1],s2) P(i,s1,[inl(i) / (s2 @ [inr(i)])])
j:Vertices(the_graph).
i1-the_graph- > j j = i1 (inl(j) s2) member-paren(x,y.the_obj.eq(x,y);j;s1)
j:Vertices(the_graph). (inr(j) s2) i1-the_graph- > *j
x,y:Vertices(the_graph). the_obj.eq(x,y) 
x = y
T:Type, s:T, x:Vertices(the_graph), f:(TVertices(the_graph)T).
L:Vertices(the_graph) List.
(y:Vertices(the_graph). x-the_graph- > y (y L))
& the_obj.eacc(f,s,x) = list_accum(s',x'.f(s',x');s;L)
T:Type, s:T, f:(TVertices(the_graph)T).
L:Vertices(the_graph) List.
no_repeats(Vertices(the_graph);L)
& (y:Vertices(the_graph). (y L))
& the_obj.vacc(f,s) = list_accum(s',x'.f(s',x');s;L)
s1)
(inl(i1) s1) (inr(i1) s1)
None
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