(18steps total) PrintForm Definitions Lemmas graph 1 3 Sections Graphs Doc

At: dfs-dfl-traversal 2 1
1. the_graph: Graph
2. the_obj: GraphObject(the_graph)
3. L: Vertices(the_graph) List
4. s: traversal(the_graph)
5. x: Vertices(the_graph)
6. dfl-traversal(the_graph;L;s)
7. j:Vertices(the_graph). (inr(j) s) (inl(j) s) j-the_graph- > *x
8. s1: traversal(the_graph)
9. s2: traversal(the_graph)
10. i: Vertices(the_graph)
11. (inr(i) s1)
12. (inl(i) s1)
13. paren(Vertices(the_graph);s2)
14. l_disjoint(Vertices(the_graph)+Vertices(the_graph);s2;s1)
15. no_repeats(Vertices(the_graph)+Vertices(the_graph);s2)
16. j:Vertices(the_graph). (inr(j) s2) i-the_graph- > *j
17. j:Vertices(the_graph). i-the_graph- > j j = i (inl(j) s2) (inl(j) s1) (inr(j) s1)
18. x-the_graph- > *i
19. j:Vertices(the_graph). (inr(j) s1) (inl(j) s1) j-the_graph- > *i
20. dfl-traversal(the_graph;L @ [x];s1)
j:Vertices(the_graph). (inr(j) [inr(i) / s1]) (inl(j) [inr(i) / s1]) j-the_graph- > *i
By:
Auto
THEN
RWO Thm* l:T List, a,x:T. (x [a / l]) x = a (x l) -2
THEN
SplitOrHyps
Generated subgoals:

121. j: Vertices(the_graph)
22. inr(j) = inr(i) Vertices(the_graph)+Vertices(the_graph)
23. (inl(j) [inr(i) / s1])
j-the_graph- > *i		1 step
 
221. j: Vertices(the_graph)
22. (inr(j) s1)
23. (inl(j) [inr(i) / s1])
j-the_graph- > *i		1 step

About:
listconsconsnilunioninl
inruniverseequalimpliesorall

(18steps total) PrintForm Definitions Lemmas graph 1 3 Sections Graphs Doc