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

At: dfs-df-traversal 2 2 1
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. i1: Vertices(the_graph)
10. (inr(i1) s1)
11. (inl(i1) s1)
12. paren(Vertices(the_graph);s2)
13. l_disjoint(Vertices(the_graph)+Vertices(the_graph);s2;s1)
14. no_repeats(Vertices(the_graph)+Vertices(the_graph);s2)
15. j:Vertices(the_graph). (inr(j) s2) i1-the_graph- > *j
16. j:Vertices(the_graph). i1-the_graph- > j j = i1 (inl(j) s2) (inl(j) s1) (inr(j) s1)
17. df-traversal(the_graph;s1)
18. j:Vertices(the_graph). (inr(j) s1) (inl(j) s1) j-the_graph- > *i1
19. j: Vertices(the_graph)
20. (inr(j) [inr(i1) / s1])
21. (inl(j) [inr(i1) / s1])
j-the_graph- > *i1
By:
RWO Thm* l:T List, a,x:T. (x [a / l]) x = a (x l) -2
THEN
SplitOrHyps
Generated subgoals:

120. inr(j) = inr(i1) Vertices(the_graph)+Vertices(the_graph)
21. (inl(j) [inr(i1) / s1])
j-the_graph- > *i1		1 step
 
220. (inr(j) s1)
21. (inl(j) [inr(i1) / s1])
j-the_graph- > *i1		2 steps

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listconsunioninlinruniverseequalimpliesorall

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