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

At: dfs-df-traversal 1 2
1. the_graph: Graph
2. the_obj: GraphObject(the_graph)
3. s: traversal(the_graph)
4. i: Vertices(the_graph)
5. df-traversal(the_graph;s)
6. j:Vertices(the_graph). (inr(j) s) (inl(j) s) j-the_graph- > *i
7. s1: traversal(the_graph)
8. s2: traversal(the_graph)
9. s3: traversal(the_graph)
10. i1: Vertices(the_graph)
11. j: Vertices(the_graph)
12. i1-the_graph- > j
13. paren(Vertices(the_graph);s2)
14. k:Vertices(the_graph). (inr(k) s2) j-the_graph- > *k
15. paren(Vertices(the_graph);s3)
16. df-traversal(the_graph;s2 @ s1) (j:Vertices(the_graph). (inr(j) s2 @ s1) (inl(j) s2 @ s1) j-the_graph- > *i1) df-traversal(the_graph;s3 @ s2 @ s1)
17. df-traversal(the_graph;s1)
18. j:Vertices(the_graph). (inr(j) s1) (inl(j) s1) j-the_graph- > *i1
19. df-traversal(the_graph;s2 @ s1)
df-traversal(the_graph;s3 @ s2 @ s1)
By: BackThruSomeHyp
Generated subgoal:

120. j1: Vertices(the_graph)
21. (inr(j1) s2 @ s1)
22. (inl(j1) s2 @ s1)
j1-the_graph- > *i1		5 steps

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unioninlinrimpliesall

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