Nuprl - Proof: dfsl-properties 2 1 2

(158steps 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. L1: Vertices(the_graph) List
5. s: traversal(the_graph)
6. i: Vertices(the_graph)
7. paren(Vertices(the_graph);s)
8. no_repeats(Vertices(the_graph)+Vertices(the_graph);s)
9. dfsl-traversal(the_graph;L1;s)
10. s': traversal(the_graph)
11. (inr(i) s) & (inl(i) s) (s2:traversal(the_graph). s' = ([inl(i)] @ s2 @ [inr(i)]) traversal(the_graph))
12. l_disjoint(Vertices(the_graph)+Vertices(the_graph);s';s)
13. no_repeats(Vertices(the_graph)+Vertices(the_graph);s')
14. paren(Vertices(the_graph);s')
15. j:Vertices(the_graph). (inr(j) s') i-the_graph- > *j
16. dfs(the_obj;s;i) = (s' @ s)
17. df-traversal(the_graph;s' @ s)
18. (inl(i) s)
19. s' = nil

dfsl-traversal(the_graph;L1 @ [i];nil @ s)

By: AssertBY df-traversal(the_graph;s) ((HypSubst -1 -3) THEN (Reduce -3)) THEN Thin -2 THEN RepeatFor 8 (Thin -3) THEN Reduce 0

Generated subgoal:

1 10. (inl(i) s)
11. df-traversal(the_graph;s)
dfsl-traversal(the_graph;L1 @ [i];s) 1 step

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(158steps total) PrintForm Definitions Lemmas graph 1 3 Sections Graphs Doc