(44steps total) PrintForm Definitions Lemmas graph 1 3 Sections Graphs Doc

At: dfs-df-traversal 2 2 2 1 2
1. the_graph: Graph
2. the_obj: GraphObject(the_graph)
3. s1: traversal(the_graph)
4. s2: traversal(the_graph)
5. i1: Vertices(the_graph)
6. (inr(i1) s1)
7. (inl(i1) s1)
8. paren(Vertices(the_graph);s2)
9. l_disjoint(Vertices(the_graph)+Vertices(the_graph);s2;s1)
10. no_repeats(Vertices(the_graph)+Vertices(the_graph);s2)
11. j:Vertices(the_graph). (inr(j) s2) i1-the_graph- > *j
12. j:Vertices(the_graph). i1-the_graph- > j j = i1 (inl(j) s2) (inl(j) s1) (inr(j) s1)
13. df-traversal(the_graph;s1)
14. j:Vertices(the_graph). (inr(j) s1) (inl(j) s1) j-the_graph- > *i1
15. df-traversal(the_graph;s2 @ [inr(i1) / s1])
16. i: Vertices(the_graph)
17. s1@0: traversal(the_graph)
18. s2@0: traversal(the_graph)
19. j:Vertices(the_graph). i-the_graph- > *j non-trivial-loop(the_graph;j)
20. [inl(i1) / (s2 @ [inr(i1)] @ s1)] = (s1@0 @ [inl(i)] @ s2@0) traversal(the_graph)
21. j: Vertices(the_graph)
22. i-the_graph- > *j
(inr(j) s2@0)
By:
Analyze -6
THEN
All Reduce
THEN
SplitCons -3
Generated subgoals:

117. s2@0: traversal(the_graph)
18. j:Vertices(the_graph). i-the_graph- > *j non-trivial-loop(the_graph;j)
19. j: Vertices(the_graph)
20. i-the_graph- > *j
21. inl(i1) = inl(i) Vertices(the_graph)+Vertices(the_graph)
22. (s2 @ [inr(i1) / s1]) = s2@0 traversal(the_graph)
(inr(j) s2@0)		21 steps
 
217. u: Vertices(the_graph)+Vertices(the_graph)
18. v: (Vertices(the_graph)+Vertices(the_graph)) List
19. s2@0: traversal(the_graph)
20. j:Vertices(the_graph). i-the_graph- > *j non-trivial-loop(the_graph;j)
21. j: Vertices(the_graph)
22. i-the_graph- > *j
23. inl(i1) = u
24. (s2 @ [inr(i1) / s1]) = (v @ [inl(i) / s2@0]) traversal(the_graph)
(inr(j) s2@0)		1 step

About:
consconsnilunioninlinrequalimpliesorall

(44steps total) PrintForm Definitions Lemmas graph 1 3 Sections Graphs Doc