(14steps total) PrintForm Definitions Lemmas graph 1 3 Sections Graphs Doc

At: dfs-properties 2 1

1. the_graph: Graph
2. the_obj: GraphObject(the_graph)
3. s: traversal(the_graph)
4. i: Vertices(the_graph)
5. s2: traversal(the_graph)
6. (inl(i) s2) (inl(i) s) (inr(i) s)
7. l_disjoint(Vertices(the_graph)+Vertices(the_graph);s2;s)
8. no_repeats(Vertices(the_graph)+Vertices(the_graph);s2)
9. paren(Vertices(the_graph);s2)
10. dfs(the_obj;s;i) = (s2 @ s)
11. s1: traversal(the_graph)
12. j:Vertices(the_graph). (inr(j) s1) i-the_graph- > *j
13. dfs(the_obj;s;i) = (s1 @ s)
14. s': traversal(the_graph)
15. (inr(i) s) (inl(i) s) s' = nil
16. (inr(i) s) & (inl(i) s) (s2:traversal(the_graph). s' = ([inl(i)] @ s2 @ [inr(i)]) traversal(the_graph))
17. dfs(the_obj;s;i) = (s' @ s)
18. (inr(i) s)
19. (inl(i) s)
s2 = s'

By:
AssertBY ((s' @ s) = (s2 @ s)) Auto
THEN
RWO Thm* x,y,z:T List. (x @ z) = (y @ z) x = y -1


Generated subgoal:

120. s' = s2 (Vertices(the_graph)+Vertices(the_graph)) List
s2 = s'
1 step

About:
listconsnilunioninlinruniverse
equalimpliesandorall
exists

(14steps total) PrintForm Definitions Lemmas graph 1 3 Sections Graphs Doc