(47steps total) PrintForm Definitions Lemmas graph 1 3 Sections Graphs Doc

At: topsortl-properties
For any graph the_obj:GraphObject(the_graph), L:V List. (i:V. (i L)) (non-trivial-loop-free(the_graph) topsortedl(the_graph;L;topsortl(the_obj;L))) & (i:V. (i topsortl(the_obj;L))) & no_repeats(V;topsortl(the_obj;L))
By:
UnivCD
THEN
Inst Thm* dfsl-properties [the_graph;the_obj;L]
THEN
ExRepD
THEN
Analyze 0
Generated subgoals:

11. the_graph: Graph
2. the_obj: GraphObject(the_graph)
3. L: Vertices(the_graph) List
4. i:Vertices(the_graph). (i L)
5. paren(Vertices(the_graph);dfsl(the_obj;L))
6. no_repeats(Vertices(the_graph)+Vertices(the_graph);dfsl(the_obj;L))
7. dfsl-traversal(the_graph;L;dfsl(the_obj;L))
8. i:Vertices(the_graph). (i L) (inr(i) dfsl(the_obj;L)) & (inl(i) dfsl(the_obj;L))
non-trivial-loop-free(the_graph) topsortedl(the_graph;L;topsortl(the_obj;L))		43 steps
 
21. the_graph: Graph
2. the_obj: GraphObject(the_graph)
3. L: Vertices(the_graph) List
4. i:Vertices(the_graph). (i L)
5. paren(Vertices(the_graph);dfsl(the_obj;L))
6. no_repeats(Vertices(the_graph)+Vertices(the_graph);dfsl(the_obj;L))
7. dfsl-traversal(the_graph;L;dfsl(the_obj;L))
8. i:Vertices(the_graph). (i L) (inr(i) dfsl(the_obj;L)) & (inl(i) dfsl(the_obj;L))
(i:Vertices(the_graph). (i topsortl(the_obj;L))) & no_repeats(Vertices(the_graph);topsortl(the_obj;L))		3 steps

About:
listunioninlinrimpliesandall

(47steps total) PrintForm Definitions Lemmas graph 1 3 Sections Graphs Doc