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)])])
member-paren(x,y.the_obj.eq(x,y);i1;s1)
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
((inl(i1) s2) inl(i1) = inr(i1) Vertices(the_graph)+Vertices(the_graph))
a,b:T List, t:T. l_disjoint(T;b;[t / a]) 
(t b) & l_disjoint(T;b;a)
-4
| 1 | 15. l_disjoint(Vertices(the_graph)+Vertices(the_graph);s2;s1) 16. no_repeats(Vertices(the_graph)+Vertices(the_graph);s2) 17. paren(Vertices(the_graph);s2) 18. j:Vertices(the_graph). (inr(j) s2) i1-the_graph- > *j19. (inl(i1) s2) (inr(i1) s2) | 1 step |
| 2 | 15. l_disjoint(Vertices(the_graph)+Vertices(the_graph);s2;s1) 16. no_repeats(Vertices(the_graph)+Vertices(the_graph);s2) 17. paren(Vertices(the_graph);s2) 18. j:Vertices(the_graph). (inr(j) s2) i1-the_graph- > *j19. inl(i1) = inr(i1) Vertices(the_graph)+Vertices(the_graph) (inr(i1) s2) | 1 step |
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