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

At: dfsl-properties 2 1 3 2
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. j:Vertices(the_graph). (inr(j) s') i-the_graph- > *j
12. dfs(the_obj;s;i) = (s' @ s)
13. df-traversal(the_graph;s' @ s)
14. (inl(i) s)
15. s2: traversal(the_graph)
16. s' = ([inl(i)] @ s2 @ [inr(i)]) traversal(the_graph)
17. l_disjoint(Vertices(the_graph)+Vertices(the_graph);s2;s)
18. paren(Vertices(the_graph);s2)
19. no_repeats(Vertices(the_graph)+Vertices(the_graph);s2) & (inr(i) s2)
20. j:Vertices(the_graph). (inr(j) s2) i-the_graph- > *j
dfsl-traversal(the_graph;L1 @ [i];([inl(i)] @ s2 @ [inr(i)]) @ s)
By: let h 11 in (Thin h) THEN (Thin h) THEN (MoveToHyp 0 h) THEN (SubstFor s' -1) THEN (Thin h+2) THEN (Thin h-1)
Generated subgoal:

110. (inl(i) s)
11. s2: traversal(the_graph)
12. l_disjoint(Vertices(the_graph)+Vertices(the_graph);s2;s)
13. paren(Vertices(the_graph);s2)
14. no_repeats(Vertices(the_graph)+Vertices(the_graph);s2) & (inr(i) s2)
15. j:Vertices(the_graph). (inr(j) s2) i-the_graph- > *j
16. df-traversal(the_graph;([inl(i)] @ s2 @ [inr(i)]) @ s)
dfsl-traversal(the_graph;L1 @ [i];([inl(i)] @ s2 @ [inr(i)]) @ s)		147 steps

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