Nuprl - Proof: dfsl member 2 1 1

(11steps 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. i:Vertices(the_graph). (i L1) (inr(i) s)
10. i:Vertices(the_graph). (i L1) (inl(i) s)
11. s': traversal(the_graph)
12. (inl(i) s') (inl(i) s) (inr(i) s)
13. l_disjoint(Vertices(the_graph)+Vertices(the_graph);s';s)
14. no_repeats(Vertices(the_graph)+Vertices(the_graph);s')
15. paren(Vertices(the_graph);s')
16. dfs(the_obj;s;i) = (s' @ s)
17. i@0: Vertices(the_graph)
18. (i@0 L1) i@0 = i

(inr(i@0) s') (inr(i@0) s) & (inl(i@0) s') (inl(i@0) s)

By: Analyze -1

Generated subgoals:

1 18. (i@0 L1)
(inr(i@0) s') (inr(i@0) s) & (inl(i@0) s') (inl(i@0) s) 1 step

2 18. i@0 = i
(inr(i@0) s') (inr(i@0) s) & (inl(i@0) s') (inl(i@0) s) 5 steps

About:

(11steps total) PrintForm Definitions Lemmas graph 1 3 Sections Graphs Doc

1	18. `(i@0 L1)` `(inr(i@0) s') (inr(i@0) s) & (inl(i@0) s') (inl(i@0) s)`	1 step

2	18. `i@0 = i` `(inr(i@0) s') (inr(i@0) s) & (inl(i@0) s') (inl(i@0) s)`	5 steps