(18steps total) PrintForm Definitions Lemmas graph 1 3 Sections Graphs Doc

At: dfs-dfl-traversal 1 2 1
1. the_graph: Graph
2. the_obj: GraphObject(the_graph)
3. L: Vertices(the_graph) List
4. s: traversal(the_graph)
5. x: Vertices(the_graph)
6. dfl-traversal(the_graph;L;s)
7. j:Vertices(the_graph). (inr(j) s) (inl(j) s) j-the_graph- > *x
8. s1: traversal(the_graph)
9. s2: traversal(the_graph)
10. s3: traversal(the_graph)
11. i: Vertices(the_graph)
12. j: Vertices(the_graph)
13. i-the_graph- > j
14. paren(Vertices(the_graph);s2)
15. k:Vertices(the_graph). (inr(k) s2) j-the_graph- > *k
16. paren(Vertices(the_graph);s3)
17. x-the_graph- > *i
18. j:Vertices(the_graph). (inr(j) s1) (inl(j) s1) j-the_graph- > *i
19. dfl-traversal(the_graph;L @ [x];s1)
20. x-the_graph- > *j
21. (j:Vertices(the_graph). (inr(j) s2 @ s1) (inl(j) s2 @ s1) j-the_graph- > *i) dfl-traversal(the_graph;L @ [x];s2 @ s1) dfl-traversal(the_graph;L @ [x];s3 @ s2 @ s1)
22. dfl-traversal(the_graph;L @ [x];s1) dfl-traversal(the_graph;L @ [x];s2 @ s1)
j:Vertices(the_graph). (inr(j) s2 @ s1) (inl(j) s2 @ s1) j-the_graph- > *i
By:
Auto
THEN
RWO Thm* x:T, l1,l2:T List. (x l1 @ l2) (x l1) (x l2) -2
THEN
SplitOrHyps
Generated subgoals:

123. j1: Vertices(the_graph)
24. (inr(j1) s2)
25. (inl(j1) s2 @ s1)
j1-the_graph- > *i		1 step
 
223. j1: Vertices(the_graph)
24. (inr(j1) s1)
25. (inl(j1) s2 @ s1)
j1-the_graph- > *i		1 step

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listconsnilunioninlinruniverseimpliesorall

(18steps total) PrintForm Definitions Lemmas graph 1 3 Sections Graphs Doc