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

At: dfsl member 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. (iL1.(inr(i) s) & (inl(i) s))
(i@0L1 @ [i].(inr(i@0) dfs(the_obj;s;i)) & (inl(i@0) dfs(the_obj;s;i)))
By:
ParallelOp -1
THEN
Inst Thm* dfs_member [the_graph;the_obj;s;i]
THEN
ExRepDHyps
THEN
HypSubst -1 0
Generated subgoal:

19. 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)
i@0:Vertices(the_graph). (i@0 L1 @ [i]) (inr(i@0) s' @ s) & (inl(i@0) s' @ s)		8 steps

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impliesandorallexists

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