Nuprl - Proof: dfs-dfl-traversal 3

(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. s':traversal(the_graph). (x-the_graph- > *x (j:Vertices(the_graph). (inr(j) s) (inl(j) s) j-the_graph- > *x) dfl-traversal(the_graph;L @ [x];s) dfl-traversal(the_graph;L @ [x];s' @ s)) & l_disjoint(Vertices(the_graph)+Vertices(the_graph);s';s) & no_repeats(Vertices(the_graph)+Vertices(the_graph);s') & paren(Vertices(the_graph);s') & (j:Vertices(the_graph). (inr(j) s') x-the_graph- > *j) & dfs(the_obj;s;x) = (s' @ s)

dfl-traversal(the_graph;L @ [x];dfs(the_obj;s;x))

By: ExRepD THEN AssertBY x-the_graph- > *x Connect THEN Repeat ThinTrivial THEN SubstFor dfs(the_obj;s;x) 0 THEN BackThruSomeHyp

Generated subgoal:

1 8. s': traversal(the_graph)
9. l_disjoint(Vertices(the_graph)+Vertices(the_graph);s';s)
10. no_repeats(Vertices(the_graph)+Vertices(the_graph);s')
11. paren(Vertices(the_graph);s')
12. j:Vertices(the_graph). (inr(j) s') x-the_graph- > *j
13. dfs(the_obj;s;x) = (s' @ s)
14. x-the_graph- > *x
15. dfl-traversal(the_graph;L @ [x];s) dfl-traversal(the_graph;L @ [x];s' @ s)
dfl-traversal(the_graph;L @ [x];s) 1 step

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