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

At: dfsl member 2 1
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)
i@0:Vertices(the_graph). (i@0 L1 @ [i]) (inr(i@0) s' @ s) & (inl(i@0) s' @ s)
By:
RWO Thm* x:T, l1,l2:T List. (x l1 @ l2) (x l1) (x l2) 0
THEN
RWO Thm* a,x:T. (x [a]) x = a 0
THEN
RepeatFor 2 (Analyze 0)
Generated subgoal:

117. 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)		7 steps

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universeequalimpliesandorall

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