Nuprl - Proof: dfs-dfl-traversal 1

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

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- > *j (j@0:Vertices(the_graph). (inr(j@0) s1) (inl(j@0) s1) j@0-the_graph- > *j) dfl-traversal(the_graph;L @ [x];s1) dfl-traversal(the_graph;L @ [x];s2 @ s1)
18. x-the_graph- > *i (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)
19. x-the_graph- > *i
20. j:Vertices(the_graph). (inr(j) s1) (inl(j) s1) j-the_graph- > *i
21. dfl-traversal(the_graph;L @ [x];s1)

dfl-traversal(the_graph;L @ [x];(s3 @ s2) @ s1)

By: AssertBY x-the_graph- > *j Connect THEN Repeat ThinTrivial THEN Analyze -1

Generated subgoals:

1 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)
j@0:Vertices(the_graph). (inr(j@0) s1) (inl(j@0) s1) j@0-the_graph- > *j 1 step

2 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) 5 steps

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

1	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)` `j@0:Vertices(the_graph). (inr(j@0) s1) (inl(j@0) s1) j@0-the_graph- > *j`	1 step

2	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)`	5 steps