(158steps total) PrintForm Definitions Lemmas graph 1 3 Sections Graphs Doc

At: dfsl-properties 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. dfsl-traversal(the_graph;L1;s)
10. s': traversal(the_graph)
11. (inr(i) s) (inl(i) s) s' = nil
12. (inr(i) s) & (inl(i) s) (s2:traversal(the_graph). s' = ([inl(i)] @ s2 @ [inr(i)]) traversal(the_graph))
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. j:Vertices(the_graph). (inr(j) s') i-the_graph- > *j
17. dfs(the_obj;s;i) = (s' @ s)
18. df-traversal(the_graph;s' @ s)
dfsl-traversal(the_graph;L1 @ [i];s' @ s)
By:
(((Inst Thm* (x,y:T. Dec(x = y)) (s:(T+T) List, i:T. Dec((inl(i) s))) [Vertices(the_graph);s;i]) THENA (Auto THEN (Using [`the_obj',the_obj] (BackThru Thm* For any graph the_obj:GraphObject(the_graph), x,y:V. Dec(x = y))))) THEN (Analyze -1)) THENL [Analyze 11 ;((Analyze 12) THENA (Auto THEN (ParallelOp -1) THEN (BackThru Thm* s':(T+T) List. paren(T;s') (i:T. (inr(i) s') (inl(i) s'))))) THEN ExRepD]
THEN
HypSubst -1 0
Generated subgoals:

111. (inr(i) s) & (inl(i) s) (s2:traversal(the_graph). s' = ([inl(i)] @ s2 @ [inr(i)]) traversal(the_graph))
12. l_disjoint(Vertices(the_graph)+Vertices(the_graph);s';s)
13. no_repeats(Vertices(the_graph)+Vertices(the_graph);s')
14. paren(Vertices(the_graph);s')
15. j:Vertices(the_graph). (inr(j) s') i-the_graph- > *j
16. dfs(the_obj;s;i) = (s' @ s)
17. df-traversal(the_graph;s' @ s)
18. (inl(i) s)
(inr(i) s) (inl(i) s)		1 step
 
211. (inr(i) s) & (inl(i) s) (s2:traversal(the_graph). s' = ([inl(i)] @ s2 @ [inr(i)]) traversal(the_graph))
12. l_disjoint(Vertices(the_graph)+Vertices(the_graph);s';s)
13. no_repeats(Vertices(the_graph)+Vertices(the_graph);s')
14. paren(Vertices(the_graph);s')
15. j:Vertices(the_graph). (inr(j) s') i-the_graph- > *j
16. dfs(the_obj;s;i) = (s' @ s)
17. df-traversal(the_graph;s' @ s)
18. (inl(i) s)
19. s' = nil
dfsl-traversal(the_graph;L1 @ [i];nil @ s)		2 steps
 
312. l_disjoint(Vertices(the_graph)+Vertices(the_graph);s';s)
13. no_repeats(Vertices(the_graph)+Vertices(the_graph);s')
14. paren(Vertices(the_graph);s')
15. j:Vertices(the_graph). (inr(j) s') i-the_graph- > *j
16. dfs(the_obj;s;i) = (s' @ s)
17. df-traversal(the_graph;s' @ s)
18. (inl(i) s)
19. s2: traversal(the_graph)
20. s' = ([inl(i)] @ s2 @ [inr(i)]) traversal(the_graph)
dfsl-traversal(the_graph;L1 @ [i];([inl(i)] @ s2 @ [inr(i)]) @ s)		150 steps

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(158steps total) PrintForm Definitions Lemmas graph 1 3 Sections Graphs Doc