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

At: dfs-cases 2 2 1

1. the_graph: Graph
2. the_obj: GraphObject(the_graph)
3. s: traversal(the_graph)
4. i: Vertices(the_graph)
5. x,y:Vertices(the_graph). the_obj.eq(x,y) x = y
6. T:Type, s:T, x:Vertices(the_graph), f:(TVertices(the_graph)T). L:Vertices(the_graph) List. (y:Vertices(the_graph). x-the_graph- > y (y L)) & the_obj.eacc(f,s,x) = list_accum(s',x'.f(s',x');s;L)
7. T:Type, s:T, f:(TVertices(the_graph)T). L:Vertices(the_graph) List. no_repeats(Vertices(the_graph);L) & (y:Vertices(the_graph). (y L)) & the_obj.vacc(f,s) = list_accum(s',x'.f(s',x');s;L)
8. ((inl(i) s) (inr(i) s))
9. L:Vertices(the_graph) List, s:traversal(the_graph). s2:traversal(the_graph). list_accum(s',j.dfs(the_obj;s';j);s;L) = (s2 @ s)
10. L: Vertices(the_graph) List
11. y:Vertices(the_graph). i-the_graph- > y (y L)
12. s2: traversal(the_graph)
13. (inr(i) s) (inl(i) s)
([inl(i)] @ s2 @ [inr(i)]) = nil traversal(the_graph)

By:
Analyze 8
THEN
ObviousFrom [-1]


Generated subgoals:

None

About:
listconsnilassertunioninlinrapply
functionuniverseequalandorall
exists

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