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

At: dfs-dfl-traversal 1 2
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)
dfl-traversal(the_graph;L @ [x];(s3 @ s2) @ s1)
By:
RWO Thm* as,bs,cs:T List. ((as @ bs) @ cs) = (as @ (bs @ cs)) 0
THEN
BackThruSomeHyp
Generated subgoals:

1 j:Vertices(the_graph). (inr(j) s2 @ s1) (inl(j) s2 @ s1) j-the_graph- > *i3 steps
 
2 dfl-traversal(the_graph;L @ [x];s2 @ s1)1 step

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listconsnilunioninlinruniverseequalimpliesall

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