Nuprl - Proof: dfsl-properties 2 1 3 2 1 1 1

(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. df-traversal(the_graph;s)
10. i:Vertices(the_graph). (inl(i) s) L1-the_graph- > *i
11. (i:Vertices(the_graph). L1-the_graph- > *i non-trivial-loop(the_graph;i)) (L1@0,L2:Vertices(the_graph) List. L1 = (L1@0 @ L2) (s1,s2:traversal(the_graph). s = (s2 @ s1) traversal(the_graph) & paren(Vertices(the_graph);s1) & paren(Vertices(the_graph);s2) & (j:Vertices(the_graph). ((inl(j) s1) L1@0-the_graph- > *j) & ((inl(j) s2) L2-the_graph- > *j & L1@0-the_graph- > *j))))
12. (inl(i) s)
13. s2: traversal(the_graph)
14. l_disjoint(Vertices(the_graph)+Vertices(the_graph);s2;s)
15. paren(Vertices(the_graph);s2)
16. no_repeats(Vertices(the_graph)+Vertices(the_graph);s2)
17. (inr(i) s2)
18. j:Vertices(the_graph). (inr(j) s2) i-the_graph- > *j
19. df-traversal(the_graph;([inl(i)] @ s2 @ [inr(i)]) @ s)
20. i@0: Vertices(the_graph)
21. inl(i@0) = inl(i) Vertices(the_graph)+Vertices(the_graph)